title: Missoula, Montana

text: , Missoula ranked 299 nationally in gross metropolitan product with an output of $5billion, the city's total personal income ranked 333 at $4.18billion, an increase of more than 47% since 2003. , per capita personal income ranked 239 at $37,397 a year, 84% of the national average. The Missoula metropolitan area's unemployment rate was 3.7% , dropping nearly 0.8% in the twelve months prior.


title: Missoula, Montana

text: Missoula, often considered the cultural center of Montana, is the location of the state's first university, and an eclectic mix of loggers, hippies, college students, sports fans, and retirees. Community events generally take place downtown either outdoors or in one of the several downtown buildings listed on the National Historic Registry.


title: Missoula, Montana

text: Since 2006, the River City Roots Festival has been an event each August with music, beer, food, and art, and generally attracts crowds of 15,000. The longest-standing event downtown has been the Missoula Farmers Market that was founded in 1972, which provides an outlet for Western Montana produce on Saturday mornings from May to October as well as Tuesday evenings from July to early September. An arts and crafts People's Market and a Clark Fork Market run concurrently. Downtown hosts "First Friday Missoula", a gallery walk on the first Friday of the month to feature local art from museums and galleries, such as that of Monte Dolack. Missoula celebrates "First Night Missoula" on New Year's Eve, which includes food and live entertainment. The "Festival of the Book" to celebrate the literature of the American West was rebranded the "Montana Book Festival" in 2015. Missoula's two historic theatres both hold annual film festivals: the Roxy hosting the International Wildlife Film Festival, established in 1977 as the first juried wildlife film festival in the world; and since 2003, the Wilma accommodating the largest film event in Montana, the Big Sky Documentary Film Festival.


title: Missoula, Montana

text: In performance arts, the Missoula Community Theatre has held performances of musical and nonmusical plays since 1977, with its affiliated Missoula Children's Theatre also acting as an international touring program that visits nearly 1,000 communities per year around the world. Missoula is also home to a number of modern dance companies, including Bare Bait Dance and Headwaters Dance Company. Rocky Mountain Ballet Theatre and Garden City Ballet are also based in Missoula.


title: Missoula, Montana

text: The Montana Museum of Art & Culture, which became a state museum in 2001, is one Montana's oldest cultural reserves, having begun in 1894; its permanent collection houses more than 10,000 original works. The Missoula Museum of Art is housed in a former Carnegie library; it features contemporary art and annually features 20–25 group and solo exhibits. Fort Missoula is home to the Historic Museum, dedicated to preserving the history of Western Montana, and to the Rocky Mountain Museum of Military History and the Northern Rockies Heritage Center. The National Museum of Forest Service History is constructing the National Conservation Legacy and Education Center in Missoula, too.


title: Missoula, Montana

text: Opened in 1987, Missoula's Bayern Brewing is the oldest active brewery in Montana. Big Sky Brewing opened in 1995 and with a production over 38,000 barrels , it is by far Montana's largest brewery, and produces the best-selling beer brewed in Montana, Moose Drool Brown Ale. Missoula has also been home to Kettle House Brewing since 1995 and Draught Works opened in 2011. Big Sky, Bayern, and Kettlehouse represent the first-, second-, and third-largest breweries, respectively, in Montana. Also in 2011, Tamarack Brewing and Flathead Lake Brewing Company from nearby Lake County opened pub houses at downtown Missoula locations. The city also holds annual the Garden City Brewfest and Winterfest, and also periodically hosts the Montana Brewers Festival.


title: Missoula, Montana

text: Missoula plays host to a variety of intercollegiate, youth, and amateur sports organizations in addition to a minor league baseball team. The Montana Grizzlies' football and basketball teams of the University of Montana have the highest attendance. The Montana Grizzlies football team has a successful program within the NCAA D-1 FCS level. Their home games at Washington–Grizzly Stadium have a near 90% winning percentage and average over 25,000 spectators in attendance. All games are televised throughout Montana. The Grizzlies men's and Lady Griz basketball teams have also been successful at the conference level, where they both rank at or near the top in attendance, about 4,000 and 3,000, respectively, and play their home games at Dahlberg Arena.


title: Missoula, Montana

text: Missoula is home to the Missoula PaddleHeads who play in the Rocky Mountain-based Pioneer Baseball League. They play their home games at Ogren Park at Allegiance Field.


title: Missoula, Montana

text: Since 1977, Missoula has also held "Maggotfest", a festival-style rugby tournament hosted by the Missoula Maggots Rugby Club the first weekend in May. The non-elimination tournament focuses on the fun aspect of the game, attracting 36 teams (male and female) from around the United States and Canada. In regular-season play, the Missoula Maggots compete as part of the Montana Rugby Union alongside another local rugby team, the University of Montana Jesters.


title: Missoula, Montana

text: The Thomas Meagher Hurling Club are also based in Missoula and play in the Northwestern division of the USGAA. The club are named after the late Irish nationalist and former acting Territorial Governor of Montana, Thomas Francis Meagher.


title: Missoula, Montana

text: The city has over of parkland, of trails, and nearly of conserved open space. Located at the confluence of three rivers (the Clark Fork, Bitterroot, and Blackfoot), the area is also popular for white water rafting and, thanks largely to the novel and subsequent film "A River Runs Through It" by Missoula native Norman Maclean, is well known for its fly fishing. Additionally, Missoula has two aquatic parks, multiple golf courses, is home to the Adventure Cycling Association, and hosts what "Runner's World" called the "best overall" marathon in the U.S. There are also three ski areas within : Montana Snowbowl, Discovery Ski Area, and Lost Trail Powder Mountain. Slightly farther away are Lookout Pass, Blacktail Mountain, and Big Mountain.


title: Missoula, Montana

text: A system of public parks was developed in Missoula in 1902 with the donation by lumber baron Thomas Greenough and his wife Tessie. They gave a tract of land along Rattlesnake Creek for Greenough Park, on the condition that "the land forever be used as a park and for park purposes to which the people of Missoula may ... find a comfortable, romantic and poetic retreat". In a follow-up nine years later in a letter to the "Missoulian", he stressed his interest in having the park remain in as close to a native state as possible. That request, along with the discovery that non-native Norway maples were inhibiting the growth of native trees and shrubs such as cottonwoods, ponderosa pines, and Rocky Mountain maples, led to the controversial decision to remove Norway maples from the park with the hope of returning it to its natural state.


title: Missoula, Montana

text: In 1924, Bonner Park was created out of John L. Bonner's estate near the university. Today's park has multiple athletic fields and courts, and band shell used by the Missoula City band through the summer. The Kiwanis club set up a Kiwanis Park downtown in 1934, making it the first of a string of parks that line both sides of the Clark Fork River. One of those parks on the southern bank of the river is McCormick Park, which was created with WPA funds out of surplus highway land, a parcel from the American Hide and Fur Company, and land donated from the Kate McCormick estate. The park, named for Washington J. McCormick and his wife, is home to a skate park, aquatics center, a free bike check-out, and a children's fishing pond. Other popular parks include the Jacobs Island Bark Park, a designated area for dogs to play off-leash; the Montana State veterans' memorial rose garden; Waterwise Garden, a "living laboratory" garden utilizing water conservation techniques; and Splash Montana Waterpark at Playfair Park.


title: Missoula, Montana

text: Caras Park is located just south of the historic Wilma Theatre downtown. It is located on land reclaimed when the Higgins Avenue Bridge was widened from two lanes to four in 1962. Before the reclamation, the Clark Fork River divided to create an island with the north channel's bank extending to nearby buildings such as the Wilma Theatre. The south channel was deepened for the increased water flow and the infilled land later became Caras Park. Events in the park were not common until the early 1980s and permanent fixtures such as "Out to Lunch", which began in 1986. The Missoula Downtown Association took over from Parks and Recreation to manage the park and made improvements to make Caras Park more event-friendly. Seating, event circles, brick plazas, restrooms, and storage structures were added. Large temporary tents were used for events until 1997, when a permanent pavilion was constructed. The park is a hub of city festivities including include "Out to Lunch", the International Wildlife Film Festival, First Night Missoula, Garden City BrewFest and offered intimate concert settings for artists such as Jewel, Chris Isaak, Santana, Ziggy Marley, and B.B. King. Located next to Caras Park is A Carousel for Missoula, a wooden, hand-carved and volunteer-built carousel; and Dragon Hollow, a children's recreational area adjacent to the carousel.


title: Missoula, Montana

text: Missoula's system of government has changed four times since 1883, when an aldermanic form of government was approved with the town charter. The city adopted a commission-council form of government in 1911 with the opening of new City Hall and a council–manager government in 1954 before returning to an aldermanic form of government in 1959. Since January 1, 1997, Missoula has been governed in accordance with the Missoula City Charter, which calls for a mayor–council system of government.


title: Missoula, Montana

text: The current system comprises a mayor and city treasurer elected in a citywide vote and 12 city council members who must reside in and are elected from one of six wards, with each ward having two council members. All positions are nominally nonpartisan. Council members and the mayor are elected to four-year terms with council-member elections being staggered to allow only one member from each ward to up for re-election. No term limits exist for either position.


title: Missoula, Montana

text: Missoula's state legislative delegation is the second-largest in the Montana Legislature and is represented by districts 91–100 in the Montana House of Representatives and districts 46–50 in the Montana Senate. Having 13 Democrats and two Republicans in its state legislative delegation, Missoula is known as a more liberal area than the rest of the state.


title: Missoula, Montana

text: Though Missoula's political leanings may not be unique for a college town, its initiative to make marijuana possession the lowest priority of and symbolic resolutions calling on Congress to withdraw from and to amend the U.S. Constitution to declare that "corporations are often put it at odds with the rest of the state. In 2011, the Montana legislature, with a Republican House majority, attempted to overturn Missoula's marijuana law and revoke its ability to have an anti-discrimination ordinance that included the LGBT community. The marijuana repeal was vetoed by then-Governor Brian Schweitzer and the attempt to repeal the anti-discrimination ordinance died in the State Senate.


title: Missoula, Montana

text: In 2020, Missoula County became the first county in Montana to adopt a county sales tax on gasoline (an option afforded to counties in Montana that had gone unused for several decades). The Montana Legislature and Governor Greg Gianforte blocked this decision the following year, repealing the sales tax provision from state law.


title: Missoula, Montana

text: Missoula's first school was opened in late 1869 with 16 students from around the region and their teacher Emma C. Slack, who had come to Missoula by a two-month trip by horseback, railroad, and boat from Baltimore at the invitation of her brother. She resigned two years later upon marrying (the first couple married in Missoula) and was replaced by Elizabeth Countryman, who later married Missoula's first mayor, The first public high school was opened in 1904, but was converted back to a grade school after the Missoula County High School (now Hellgate High School) was opened in 1908. After several expansions, Stanford University was commissioned in 1951 to create a master building plan to manage future growth. It suggested purchasing land and building an additional campus at the Garden City Airport's Hale Field, which was gradually being replaced by the Missoula County Airport, which was then southwest of town. The new school (now Sentinel High School) was opened in 1957. Initially, the two campuses were separated between upper and lower classmen with upper classmen in the new school, but in 1965, the two campuses became separate high schools. In 1974, the private Loyola Sacred Heart Catholic High School was created from a merger of the all-girls Sacred Heart Academy (.1873) and the all-boys Loyola High School (.1912). In 1980, Missoula's third public high school, Big Sky, was established.


title: Missoula, Montana

text: Missoula's public schools are part of the Missoula County Public School In Missoula, there are nine public elementary schools (kindergarten to 5th grade), three public middle schools (6th to 8th grades), four public high schools (9th to 12th grades), and three public schools serving kindergarten to 8th grade. Missoula also has several private schools including an international school, religious-affiliated schools, as well as Next Step Prep, a theater academy high school operated by the Missoula Children's Theatre.


title: Missoula, Montana

text: The University of Montana dominates higher education in Missoula. The university, established in 1893, was Montana's first, and has the state's second-largest enrollment, with 12,922 students . The campus houses six colleges and three schools including Montana's first and only law school, the Alexander Blewett III School of Law at the University of Montana. The university is also the location of the state's Regional Federal Depository Library, and houses the state Arboretum. The University of Montana College of Technology, established in 1956 and formerly known as the Missoula Vocational Technical Center, offers fast-track learning programs. Multiple vocational programs not affiliated with the university ranging from photography and massage to truck driving also have a presence in Missoula.


title: Missoula, Montana

text: Missoula's single–broadcast over–air television media market is the largest in Montana and ranked 165 nationally . Though Missoula itself is second in population to Billings, Montana, Missoula's single-broadcast over-air television media market includes all of Missoula, Ravalli, Granite, Mineral, Lake, Flathead, and Sanders Counties in the more densely populated western region of Montana and serves over 112,600 television homes . Missoula is home to three local affiliate channels: KPAX-TV (CBS/MTN, ; founded 1970; ), KECI-TV (NBC; founded 1954 as KGVO-TV; ), and KTMF-TV (ABC, FOX; founded 1991; ). Also based in Missoula at the University of Montana is (founded 1984; ).


title: Missoula, Montana

text: Missoula has three main sources of print and digital media: the "Missoulian" (daily), The "Missoula Current" (daily), and "Montana Kaimin" (college). The "Missoulian" was founded as a weekly publication in 1870 as "The Missoula and Cedar Creek Pioneer" and remains the city's oldest news product. The "Missoula Current" was founded in 2015 and provides local and regional coverage and is the state's largest digital-only news product. The "MontanaKaimin" (founded 1891) is distributed for free throughout parts of Missoula with heavy student traffic from the University of Montana where the newspaper is printed Monday through Friday during the school year.


title: Missoula, Montana

text: Missoula has two primary health care facilities: St. Patrick Hospital and Health Sciences Center and Community Medical Center. St. Patrick's was founded in 1873 under the sponsorship of the Sisters of Providence. It is the only Level II trauma center in western Montana and has undergone three major expansions since the 1980s. The hospital has 195 acute-care beds and admitted over 9,700 patients in 2003. The name was changed from "St. Patrick Hospital" to "St. Patrick Hospital and Health Sciences Center" in 2000 to reflect an increasing involvement with national medical research and education. The Community Medical Center and its adjacent medical facilities are located near Fort Missoula and is part of a modern complex that includes a nursing home, the Missoula Crippled Children's Center, and private offices. It was founded in 1922 as Thornton Hospital by doctors Will Thornton and Charles Thornton and has been at its current location since 1972. Although originally a locally owned, nonprofit hospital, it is now owned by a large corporation headquartered in Nashville, Tennessee, and is a for-profit entity. It is the only hospital in Western Montana with a separate Pediatric Intensive Care Unit. The center is partnered with Seattle Children's Hospital. The nearest Level I trauma center to Missoula is Harborview Medical Center in Seattle, Washington.


title: Missoula, Montana

text: The earliest Missoulians drew their water directly from the Clark Fork River or nearby Rattlesnake Creek. The first water system consisted of a Native American known as One-Eyed Riley and his friend filling buckets of water from the Rattlesnake Creek and hauling them door to door on a donkey cart. In 1871 city co-founder Frank Worden began construction of a long pipe and wooden main system that flowed from the Rattlesnake Creek north of the city. With the addition of two small covered reservoirs, the first municipal water system was begun in 1880. With an intake dam built-in 1901 with a settling basin capacity of , the Rattlesnake Creek continued to meet the demands of the city until 1935 when five wells were added to respond to increased summer and fall demand. This system is still maintained as an emergency backup but was discontinued as a primary source after Giardia outbreak in 1983. Since then, Missoula has relied on the Missoula Valley Aquifer as the sole source of water. In 1889, the first electrical plant was built by to power his major downtown properties such as the Missoula Mercantile and the Florence Hotel. In 1905, the Missoula Mercantile (by then owned by Copper King William A. Clark purchased the water system and consolidated it with its vast electrical holdings to create the Missoula Light and Water Company (ML&W) a year later. Electricity and water remained bundled after ML&W's sale to the Montana Power Company (MPC) in 1929. In 1979, MPC sold its water utility holdings as Mountain Water Company to Park Water Company in Downey, California, which since 2011 has been a subsidiary of The Carlyle Group. In 2015, the City of Missoula was legally granted its right to acquire the water system by exercising its power of eminent domain", but the decision was upheld by a district court.


title: Missoula, Montana

text: Following the deregulation of Montana's electricity market in 1997, Montana Power Company began to divest its energy business. MPC sold substantially all its electrical generating assets to the PPL Corporation in December 1997 and its energy transmission and distribution business to NorthWestern Corporation in February 2002. Despite filing for bankruptcy in 2002, NorthWestern Corporation's subsidiary NorthWestern Energy is the primary provider of electric and natural gas service to Missoula in addition to the Rural Utilities Service's Missoula Electric Cooperative.


title: Missoula, Montana

text: Local telephone service in the area is provided by CenturyLink and Blackfoot Telecommunications. Major cell phone providers include AT&T, Sprint, Verizon, and T-Mobile. Allied Waste handles recycling through a program where customers can purchase special blue bags to designate recyclables. Recycling has also been offered by Missoula Valley Recycling since 1992, by Garden City Recycling since 2010 which offers curbside pickup, and by Pacific Steel & Recycling which offers drop-off recycling. Sewer service is handled by the City of Missoula Wastewater Division.


title: Missoula, Montana

text: In the mid-1860s, and Frank Worden began plotting what would become the town of Missoula along the Mullan Military Road, which ran parallel to the Clark Fork River. Through downtown Missoula, the route of the road is now Front Street. It is intersected by Higgins Avenue, to which a bridge across the Clark Fork was added in 1873. The intersection of these two streets became the default center of the city, and remains the numerical center regarding city street addresses. The arrival of the Northern Pacific Railway in 1883 led to a housing boom along the tracks, particularly on the northern side where many of the railway workers would reside. When the Higgins Avenue Bridge was replaced in 1893, they debated whether the bridge should continue southwest toward the Bitterroot Valley as it had earlier or due south. Attorneys and had already laid out plots of land five years earlier for what they hoped would be a new town of "South Missoula". The streets there were perpendicular to the Bitterroot Wagon Road. In contrast, Judge Hiram Knowles who owned the land just south of the river preferred the north–south plan and did not want to become part of South Missoula. The result was a along the west side of Higgins Avenue commonly referred to as the "Slant Streets" centered along what is now Stephens Avenue. Stephens Avenue and Brooks Street are the only arterials to traverse the city diagonally along with the Bitterroot Branch of Montana Rail Link. With the exception of Downtown, the rest of the city, where streets follow the angle of the river, and newer expansions into the hills, strictly follow the grid plan. With the establishment of the University of Montana in 1893 and the announcement that the tracks of the Milwaukee Road would be located south of the river, houses began to spread quickly throughout the university and south side districts. The area near the university was promoted as high-end and luxurious homes appeared on Hammond Avenue (then nicknamed "Millionaires Row" and known today as Gerald Avenue).


title: Missoula, Montana

text: The arrival of Interstate90 in the mid-1960s forced the removal of 60 homes, including the Greenough Mansion. The north side of Missoula became isolated between the Interstate and the tracks while the Greenough Mansion was moved to a South Hills golf course and converted to a restaurant. This dichotomy has prevailed with the North Side feeling neglected by the city while the South Hills became an upscale neighborhood. The Missoula Downtown Master Plan of 2009 emphasized redevelopment of the North Side's former rail yard and the area just south of the tracks.


title: Missoula, Montana

text: The city is divided into 18 neighborhood councils, of which all Missoula residents are members. The city further contains 10 historical districts: Downtown Missoula, East Pine Street, Fort Missoula, Lower Rattlesnake, McCormick, Northside, Southside, University Area and, the campus of the University of Montana.


title: Missoula, Montana

text: Missoula has an extensive trail system for both commuting and recreation that extends over . The city is actively trying to connect its various sections within the city to each other and to recreational trails extending beyond the city. The heart of the Missoula Commuter Bike Network is the trails along either side of the Clark Fork River that link Downtown with surrounding neighborhoods, the university, city parks, and outlying open space with smooth surfaces and three bicycle/pedestrian bridges. The most southern of these is Milwaukee Trail, which follows the former Milwaukee Railroad and continues east out of town as the Kim Williams Nature Trail beside Mount Sentinel. The Bitterroot Branch Trail connects to the Riverfront trails west of Downtown and, when completed, will provide a trail from Downtown to Southgate Mall. Near the Bitterroot Branch Trail, but not connected, is the South Avenue Trail on the west side of Reserve Street that connects the Community Medical Center with Fort Missoula, nearby athletic fields, and the Bitterroot River. The South Hills neighborhood has its own system of trails that is also approaching, but not quite meeting, the larger network.


title: Missoula, Montana

text: runs east–west along the northern edge of Missoula at the base of the North Hills, with all but a small portion of the city located south of the highway. Completed in 1965 at the expense of 60 homes, the Garden City Brewery, and the Greenough Mansion, I‑90 has four city exits and makes connections with , and Montana Highway 200. The original , approved by the AASHO in 1939 to extend west into Montana, did not include Missoula until the highway was rerouted along State Route6 in October 1959 and was not extended west from Missoula until 1962. The road now crosses Missoula southwest–northeast. serves as a major economic corridor for western Montana connecting Missoula with the Bitterroot Valley communities to the south and Flathead Lake, Kalispell, and Glacier National Park to the north. , the longest state highway in the United States enters Missoula from the east and provides access along the Blackfoot River and a direct route to Great Falls.


title: Missoula, Montana

text: Public transportation in Missoula began as early as 1890 with a horse-drawn streetcar system (electrified in 1910) operated by the Missoula Street Railway Company that connected Downtown Missoula with the University, Bonner, the fairgrounds, and Fort Missoula. These streetcars were then replaced by buses in 1932 due to cost. Bus service today is provided by Mountain Line, a public transit agency created by public vote in 1976 as part of the Missoula Urban Transportation District (MUTD) that began operation in December 1977. Mountain Line operates twelve bus routes within a area, serving Missoula, East Missoula, Bonner, Target Range, Rattlesnake, and the airport. Additionally the line has offered paratransit services since 1991 to assist the disabled, senior van since 2008, and has four park‑and‑ride lots throughout Missoula. Special bus service is offered to the University of Montana through three of the city's park‑and‑ride lots in addition to a late-night UDASH shuttle that offers service between the University and Downtown. a three-year pilot program of zero-fare transportation on all Mountain Line buses began, with the goal of increasing ridership by 45 percent.


title: Missoula, Montana

text: Intercity rail travel was available from 1883, when the Northern Pacific Railway began service through Missoula, until 1979 when Amtrak discontinued its "North Coast Hiawatha" route across southern Montana. In 1901, Northern Pacific built their station at the terminus of Higgins Avenue; since 1985, it has been on the National Register of Historic Places. The Chicago, Milwaukee, St. Paul and Pacific Railroad also built their "Pacific Extension" through Missoula, and that station was also listed on the National Register of Historic Places in 1982.


title: Missoula, Montana

text: A feasibility study was commissioned by Congress in 2008 to examine the merits of reopening the "North Coast Hiawatha", but , the nearest rail station to Missoula is the Whitefish station of Amtrak's "Empire Builder", to the north.


title: Missoula, Montana

text: In 2009, the Missoula metropolitan statistical area (MSA) ranked as the fifth highest in the United States for percentage of commuters who biked to work (5 percent). In 2013, the Missoula MSA ranked as the tenth lowest in the United States for percentage of workers who commuted by private automobile (77.2 percent). In the same year, 8.5 percent of Missoula area commuters walked to work.


title: Missoula, Montana

text: In 1927, air travel to Missoula began; today the city is served by Missoula Montana Airport, a public airport run by the Missoula County Airport Authority. It is the largest airport in western Montana, serving 848,444 passengers in 2018. The current building contains three jet bridges and three ground‑level boarding gates. There are direct flights year‑round to Billings, Dallas, Denver, Las Vegas, Minneapolis, Phoenix, Portland, Salt Lake City, Seattle, and seasonally to Atlanta, Chicago, Los Angeles, Oakland, and San Francisco.


title: Missoula, Montana

text: Missoula has produced and been home to a number of notable individuals in varying fields. Its natives and residents are referred to as "Missoulians". In politics, Jeannette Rankin, the first woman in Congress, was born and raised in Missoula while Senators Mike Mansfield, the U.S.'s longest serving Senate Majority Leader, and Max Baucus, Montana's longest serving U.S. Senator both established careers and joined politics while living in the city.


title: Missoula, Montana

text: Noted athletes who were born or resided in Missoula include five Olympic medalists, Pro Football Hall of Fame Quarterback John Elway, and former Milwaukee Bucks coach Larry Krystkowiak.


title: Missoula, Montana

text: Actor Dana Carvey, filmmaker David Lynch, and award‑winning biologist Leroy Hood were born in Missoula, while Carroll O'Connor and J. K. Simmons attended the University of Montana. Composer David Maslanka (1943-2017) lived in Missoula, and musician Jeff Ament, and musician, vlogger, and author Hank Green reside in Missoula. Academically, Missoula has been home to Nobel Prize winners Harold C. Urey and Steve Running as well as 20th century Montana historian K. Ross Toole.


title: Missoula, Montana

text: Noted names in literature include Native American poet James Welch, crime novelist James Crumley, former head of the University of Montana's Creative Writing Program Richard Hugo, William Kittredge, a western writer and professor of creative writing at the University of Montana at Missoula, and Norman Maclean, whose "A River Runs Through It" chronicles his life in early 20th-century Missoula. Joanna Klink, poet and professor at the University of Montana. Michael Punke, the author of the best-selling novel "The Revenant", also lives in Missoula.


title: Missoula, Montana

text: Missoula's Sister City relationship with Palmerston North, New Zealand, began after Missoula resident and later University of Montana professor Harold Bockemuehl returned from obtaining his PhD from Massey University. The relationship was made official in 1983 after a meeting between then UM President Neil Bucklew and officials from Massey University. Each May, Missoula celebrates "New Zealand Day" in honor of the relationship with rugby, food, and entertainment. Missoula's second Sister City relationship began in 1991 after a Neckargemünd delegation, led by Mayor Oskar Schuster, visited Missoula following a Fulbright-sponsored faculty exchange between Heidelberg University and the University of Montana. Every September the Missoula Cultural Council holds an annual "Germanfest" to celebrate German culture and this relationship.


title: Missoula, Montana

text: Author Norman Maclean grew up in Missoula and wrote about it in his 1976 autobiographical novella "A River Runs Through It". The work was adapted into a 1992 motion picture of the same name, directed by Robert Redford and starring Brad Pitt and Craig Sheffer.


title: Missoula, Montana

text: "Missoula: Rape and the Justice System in a College Town", a prominent 2015 book by Jon Krakauer, focused on a series of sexual assault cases between 2010 and 2012 and the way that the Missoula Police Department, Missoula County Attorney's Office, and University of Montana handled those cases. Missoula's handling of rape cases sparked a Justice Department's investigation that found a "pattern of disrespect and indifference toward alleged victims" by Missoula law enforcement, prosecutors, and the University, with scathing blame directed at the Attorney's Office. While being interviewed on NPR about the book, Krakauer stated, "I don't mean to single out Missoula: Its rape rate is a little less than the national average; I think its problems with dealing with rape are pretty depressingly typical." Nevertheless, reporting by Krakauer and local and national journalists showed what they characterized as a troubling pattern of authorities mishandling investigations, treating victims with hostility and suspicion, reflexively protecting alleged perpetrators at the expense of victims, declining to prosecute large numbers of credible rape allegations, and creating an atmosphere where victims were unlikely to come forward after an attack. Krakauer placed the greatest blame for mishandling rape prosecutions on a single Deputy County Attorney, Kirsten Pabst, who now serves as the Missoula County Attorney. The book also charted deep divisions within the town about the allegations, particularly those involving football players from the Montana Grizzlies.


title: Missoula, Montana

text: There is a lengthy study of Missoula in the title essay of British writer Jonathan Raban's "Driving Home: An American Journey": despite writing that on his arrival, "I had the powerful impression that I had driven deep into the Rocky Mountains and somehow arrived in Rotherham or Barnsley," and that "the overall effect was oddly unsettling; the streets too open for comfort, the town too closed in, inducing mild claustrophobia and agoraphobia at the same time", he notes the literary heritage of the city and its reputation as a "kindly town" (evidenced by its being a place where "odds and ends naturally collected and cohered").


title: Missoula, Montana

text: Missoula is mentioned as being the closest city to the fictional Hope County in "Far Cry 5". The game's first mission involves the player trying to escape the county to reach Missoula.


title: Shaun Wright-Phillips

text: Shaun Cameron Wright-Phillips (born 25 October 1981) is an English former professional footballer who played as a winger. He played in the Premier League and Football League for Manchester City, Chelsea and Queens Park Rangers, in Major League Soccer for the New York Red Bulls, in the United Soccer League for the New York Red Bulls II and Phoenix Rising FC, and at senior international level for the England national team.


title: Shaun Wright-Phillips

text: A Nottingham Forest youth product, he spent 13 seasons playing in the Premier League during spells with Manchester City, Chelsea and Queens Park Rangers. In 2015, he joined Major League Soccer club New York Red Bulls alongside his brother, Bradley. Wright-Phillips joined Phoenix Rising FC in 2017.


title: Shaun Wright-Phillips

text: The England international scored six goals in 36 appearances for the national team, which included selection for the 2010 FIFA World Cup.


title: Shaun Wright-Phillips

text: Shaun Cameron Wright-Phillips was born on 25 October 1981 in Greenwich, Greater London. He is the son of former England international Ian Wright, who adopted him at the age of three. His younger brother, Bradley Wright-Phillips, is also a professional footballer and the all-time top scorer for the New York Red Bulls. Wright-Phillips grew up in Brockley and attended Haberdashers' Aske's Hatcham College in New Cross Gate. Wright-Phillips is of Trinidadian and Grenadian descent.


title: Shaun Wright-Phillips

text: Wright-Phillips was released by Nottingham Forest aged 17 and Manchester City took him to Maine Road. He made his first-team debut as a substitute in the second leg of a League Cup match against Burnley, replacing Terry Cooke. His league debut came two months later at Port Vale. Brought on as substitute striker, he helped his team turn a 1–0 deficit into a 2–1 win. His shot resulted in the first Manchester City goal, which Wright-Phillips attempted to claim, though the strike was later credited as an own goal instead. He then started the next two matches in place of Paul Dickov, who was absent through injury. Once Dickov recovered, Wright-Phillips returned to the reserves, making only one further first team appearance that season. City finished second in the First Division, resulting in promotion to the Premier League for the 2000–01 season.


title: Shaun Wright-Phillips

text: Wright-Phillips featured more regularly than the previous season but was still not fully established in the first team, making 12 starts and seven substitute appearances playing in a variety of attacking positions. Manchester City's stay in the Premier League was brief; at the end of the season they were relegated.


title: Shaun Wright-Phillips

text: Under Keegan, Wright-Phillips firmly established himself in the first team, not as a forward, but as a wing-back. Keegan was known for playing attacking football, and decided to use the attacking Wright-Phillips in a traditionally defensive position due to his mobility and dribbling ability. From 2000 to 2003, Wright-Phillips won Manchester City's Young Player of the Year award four times in succession, surpassing Steve Kinsey's record of three times.


title: Shaun Wright-Phillips

text: On 17 November 2004, he became one of the main targets of racist chants from sections of the Spanish crowd at an international friendly between England and Spain in Madrid. However, he brushed that aside with his performance in his next Manchester City appearance at Portsmouth, saying to reporters after the match, "I just let the football do the talking". He also has a similar response regarding his father, saying in an interview with manchesteronline.co.uk: "The press brought up my adopted father's name. They relate to his name and that is fine by me – it comes with the name, but I will be my own man. I have made my own path and started to take my own steps.". His son is also going through City's youth ranks at the moment.


title: Shaun Wright-Phillips

text: On 18 July 2005, Wright-Phillips completed a £21 million move to Premier League champions Chelsea, returning to his native London. He joined the club on a five-year contract after agreeing to personal terms and passing a medical. He had previously said he would not leave Manchester City. His appearances were initially limited, starting only 15 times for Chelsea in 2005–06 and struggling to find scoring form. An inconsistent first season with Chelsea culminated in him missing out on the opportunity to travel to Germany with the England squad for the 2006 FIFA World Cup.


title: Shaun Wright-Phillips

text: Despite making few first-team appearances, Wright-Phillips maintained that he was happy at Chelsea and wanted to stay and fight for a first-team place. He received a boost from his manager José Mourinho, when the latter declined to make an approach for Real Betis winger Joaquín, stating that he had enough options in terms of wingers. His first goal for the club came in a 2–0 Champions League win over Levski Sofia on 5 December 2006, in his 52nd match and almost 17 months after his transfer.


title: Shaun Wright-Phillips

text: As 2006–07 progressed, Wright-Phillips picked up form and scored his first league goal against West Ham United on 18 April, following it up with his second in the same match. Subsequently, he started in several matches towards the end of the season including the 2007 FA Cup Final which Chelsea won.


title: Shaun Wright-Phillips

text: At the beginning of 2007–08, Wright-Phillips maintained his starting place on the right wing. He also maintained his place after José Mourinho left Chelsea and under new coach Avram Grant. He was selected to play in the 2008 League Cup Final, which Chelsea lost to Tottenham Hotspur. He only made another six appearances that season and failed to make the match day squad for the 2008 UEFA Champions League Final. Having made 65 starting appearances for the club, with a further 60 as a substitute, Wright-Phillips had been unable to secure a regular place in the team under Grant and Mourinho. After falling out of favour with new manager Luiz Felipe Scolari, he was allowed to leave the club.


title: Shaun Wright-Phillips

text: On 28 August 2008, he re-joined former club Manchester City on a four-year contract for an undisclosed fee, believed to be in the region of £8.5 million. On his second debut, Wright-Phillips scored two goals against Sunderland in the 3–0 away win in the Premier League. His third goal for City came in a 6–0 victory over Portsmouth on 21 September 2008. Wright-Phillips equalled his entire goalscoring record at Chelsea just over a month after returning to City. His right footed drive in the second half against Omonia Nicosia on 2 October helped steer City through to the group stages of the UEFA Cup for the first time. On 29 October, Wright-Phillips swore at former Middlesbrough manager Gareth Southgate during Manchester City's 2–0 defeat to his club, after Southgate complained about Wright-Phillips appearing to go down too easily after a challenge. The Football Association warned Wright-Phillips about his future conduct.


title: Shaun Wright-Phillips

text: The 2009–10 season started very well for Wright-Phillips, setting up Emmanuel Adebayor's first goal for Man City in the third minute of a 2–0 win against Blackburn Rovers. He followed that up with a goal in a League Cup tie with Crystal Palace. Three weeks later against Arsenal, he set up a goal for Adebayor before scoring one for himself. He went on to score in successive home matches against Burnley and Hull City where he delivered an assist for Carlos Tevez's debut Man City goal. During his next game against Arsenal he scored in a 3–0 League Cup win which saw City progress to the tournament's semi finals. He found himself in-and-out of the team under manager Roberto Mancini, with new signing Adam Johnson's form forcing Wright-Phillips to be a substitute in most matches, including City's match at his former club Chelsea at Stamford Bridge. He came off the bench to replace Johnson in the 60th minute and then set up Craig Bellamy's second goal in the 4–2 win. Despite his impact in the match, Wright-Phillips had not secured a place in the team. He started for City on the final match of the 2009–10 Premier League against West Ham at Upton Park, where he scored the equaliser in a 1–1 draw.


title: Shaun Wright-Phillips

text: The 2010–11 season saw Wright-Phillips only make seven league appearances, with the increased competition for places following the signings of David Silva and Yaya Touré resulting in him rarely being included in the club's matchday squad. City won the 2010–11 FA Cup, and despite being left out of the squad for the final, he did contribute some appearances earlier in the cup run, including coming on as a substitute against Manchester United in the semi-final.


title: Shaun Wright-Phillips

text: On 31 August 2011, the final day of the transfer window, Wright-Phillips signed for Queens Park Rangers (QPR) on a three-year contract for an undisclosed fee. He made his full debut for QPR against Newcastle United on 12 September 2011, making the starting line-up and winning man of the match by supporters. He failed to score a goal for almost a year before scoring his first the following season for QPR against Walsall in the League Cup on 28 August 2012. His only goal for QPR in the Premier League came during the derby against former club Chelsea on 2 January 2013, which ended 1–0. Despite this, QPR would find themselves relegated to the Championship at the end of the season. QPR would return to the Premiership at the first time of asking, defeating Derby County in the play-off finals, though Wright-Phillips would increasingly find his role throughout the season diminished to the occasional cameo from the subs bench and reserve outings. After featuring even more sporadically during 2014–15, QPR announced that Wright-Phillips would be released from his contract in a batch of players that included fellow former England internationals Rio Ferdinand and Joey Barton.


title: Shaun Wright-Phillips

text: In June 2015, Wright-Phillips began training with Major League Soccer club the New York Red Bulls to regain fitness following his departure from QPR. Impressing head coach Jesse Marsch, he suggested he would sign for the club when his contract officially expired on 30 June.


title: Shaun Wright-Phillips

text: On 27 July, he completed a move to join his brother, Bradley Wright-Phillips, at the New York Red Bulls. He made his debut on 1 August, coming off the bench to win a penalty and assist his brother in a 3–1 victory at the Philadelphia Union. Wright-Phillips was named in the MLS Team of the Week following the performance.


title: Shaun Wright-Phillips

text: Wright-Phillips was released by the Red Bulls at the end of the 2015 Major League Soccer season, but was later re-signed on 25 January 2016.


title: Shaun Wright-Phillips

text: On 23 February 2017, Wright-Phillips signed for United Soccer League club Phoenix Rising FC. He made his debut on 26 March 2017, in a 1–0 defeat to Toronto FC II.


title: Shaun Wright-Phillips

text: Wright-Phillips made his England debut as a substitute for Nicky Butt against Ukraine on 18 August 2004. He scored the last of England's goals in a 3–0 win, described by BBC Sport as "crowning a solo run with a stunning finish." He was a regular member of England's squad during qualification for the 2006 FIFA World Cup and made his first competitive start in a 1–0 away win over Wales. After a decline in form, however, especially a poor performance away to Northern Ireland, and a lack of matches following his move to Chelsea, he missed out on a place in the squad for the World Cup finals.


title: Shaun Wright-Phillips

text: After a good start to the 2007–08 season, Wright-Phillips received an England recall to play against Germany in a friendly match at the new Wembley Stadium. Wright-Phillips was brought on as a substitute in the second half during the match in which England lost 2–1 to Germany and he was named the England sponsor's man of the match after an impressive performance.


title: Shaun Wright-Phillips

text: On 8 September 2007, Wright-Phillips was selected to start against Israel in a UEFA Euro 2008 qualifier he scored the first goal in the 3–0 victory and won the England sponsor's man of the match award with his performance. He was then selected to start for England against Estonia and scored his third goal for England and the opener in a third consecutive 3–0 win at Wembley. He was selected in England's critical Euro 2008 qualifying match against Croatia, substituted at half time in favour of David Beckham with England trailing 2–0, with England eventually losing 3–2 and therefore missing out on Euro 2008.


title: Shaun Wright-Phillips

text: On 14 October 2009, with England having already qualified for the 2010 World Cup, Wright-Phillips was selected in the starting XI against Belarus at Wembley Stadium." Unusually, he was joined in the team (which was missing Wayne Rooney through injury) by Tottenham Hotspur's Aaron Lennon, meaning England played with two recognised wingers. Mid-way through the second half, Wright-Phillips drove in a shot from the edge of the penalty area which beat the dive of the Belarus goalkeeper. He appeared as a second-half substitute against Egypt on 3 March 2010, scoring England's second goal and assisting Peter Crouch for the third as they came from behind to win 3–1.


title: Shaun Wright-Phillips

text: On 1 June 2010, Wright-Phillips was selected for England's final 23-man squad that was to play in the 2010 FIFA World Cup in South Africa. He appeared as a substitute in England's opening two group matches against United States and Algeria.


title: Shaun Wright-Phillips

text: Wright-Phillips has a son, D'Margio Wright-Phillips, who plays for Stoke City. He is also capped for England U16s.


title: Wave equation

text: The (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields — as they occur in classical physics — such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves). It arises in fields like acoustics, electromagnetism, and fluid dynamics. Single mechanical or electromagnetic waves propagating in a pre-defined direction can also be described with the first-order one-way wave equation which is much easier to solve and also valid for inhomogenious media.


title: Wave equation

text: The (two-way) wave equation is a second-order partial differential equation describing waves, including traveling and standing waves; the latter can be considered as linear superpositions of waves traveling in opposite directions. This article mostly focuses on the scalar wave equation describing waves in scalars by scalar functions of a time variable (a variable representing time) and one or more spatial variables (variables representing a position in a space under discussion) while there are vector wave equations describing waves in vectors such as waves for electrical field, magnetic field, and magnetic vector potential and elastic waves. By comparison with vector wave equations, the scalar wave equation can be seen as a special case of the vector wave equations; in the Cartesian coordinate system, the scalar wave equation is the equation to be satisfied by each component (for each coordinate axis, such as the x-component for the x-axis) of a vector wave without sources of waves in the considered domain (i.e., a space and time). For example, in the Cartesian coordinate system, for formula_1 as the representation of an electric vector field wave formula_2 in the absence of wave sources, each coordinate axis component formula_3 ("i" = "x", "y", or "z") must satisfy the scalar wave equation. Other scalar wave equation solutions are for physical quantities in scalars such as pressure in a liquid or gas, or the displacement, along some specific direction, of particles of a vibrating solid away from their resting (equilibrium) positions.


title: Wave equation

text: The equation states that at any given instance, at any given point, the way the displacement accelerates is proportional to the way the displacement's changes are squashed up in the surrounding area.


title: Wave equation

text: Or in even simpler terms, the way displacements get pushed around is proportional to how pointy the displacement is, and vice versa.


title: Wave equation

text: Using the notations of Newtonian mechanics and vector calculus, the wave equation can be written more compactly as


title: Wave equation

text: where the double dot on formula_7 denotes double time derivative of , is the nabla operator, and is the (spatial) Laplacian operator (not vector Laplacian):


title: Wave equation

text: A solution of this (two-way) wave equation can be quite complicated, but it can be analyzed as a linear combination of simple solutions that are sinusoidal plane waves with various directions of propagation and wavelengths but all with the same propagation speed . This analysis is possible because the wave equation is linear and homogeneous; so that any multiple of a solution is also a solution, and the sum of any two solutions is again a solution. This property is called the superposition principle in physics.


title: Wave equation

text: The wave equation alone does not specify a physical solution; a unique solution is usually obtained by setting a problem with further conditions, such as initial conditions, which prescribe the amplitude and phase of the wave. Another important class of problems occurs in enclosed spaces specified by boundary conditions, for which the solutions represent standing waves, or harmonics, analogous to the harmonics of musical instruments.


title: Wave equation

text: The two-way wave equation – describing a standing wave field – is the simplest example of a second-order hyperbolic differential equation. It, and its modifications, play fundamental roles in continuum mechanics, quantum mechanics, plasma physics, general relativity, geophysics, and many other scientific and technical disciplines. In the case that only the propagation of a single wave in a predefined direction is of interest, a first-order partial differential equation – one-way wave equation – can be considered.


title: Wave equation

text: This equation is typically described as having only one space dimension , because the only other independent variable is the time . Nevertheless, the dependent variable may represent a second space dimension, if, for example, the displacement takes place in -direction, as in the case of a string that is located in the .


title: Wave equation

text: The wave equation in one space dimension can be derived in a variety of different physical settings. Most famously, it can be derived for the case of a string that is vibrating in a two-dimensional plane, with each of its elements being pulled in opposite directions by the force of tension.


title: Wave equation

text: Another physical setting for derivation of the wave equation in one space dimension utilizes Hooke's Law. In the theory of elasticity, Hooke's Law is an approximation for certain materials, stating that the amount by which a material body is deformed (the strain) is linearly related to the force causing the deformation (the stress).


title: Wave equation

text: The wave equation in the one-dimensional case can be derived from Hooke's Law in the following way: imagine an array of little weights of mass interconnected with massless springs of length . The springs have a spring constant of :


title: Wave equation

text: Here the dependent variable measures the distance from the equilibrium of the mass situated at , so that essentially measures the magnitude of a disturbance (i.e. strain) that is traveling in an elastic material. The forces exerted on the mass at the location are:


title: Wave equation

text: If the array of weights consists of weights spaced evenly over the length of total mass , and the total spring constant of the array we can write the above equation as:


title: Wave equation

text: which is from the definition of a second derivative. is the square of the propagation speed in this particular case.


title: Wave equation

text: In the case of a stress pulse propagating longitudinally through a bar, the bar acts much like an infinite number of springs in series and can be taken as an extension of the equation derived for Hooke's law. A uniform bar, i.e. of constant cross-section, made from a linear elastic material has a stiffness given by


title: Wave equation

text: where is the cross-sectional area and is the Young's modulus of the material. The wave equation becomes


title: Wave equation

text: The one-dimensional wave equation is unusual for a partial differential equation in that a relatively simple general solution may be found. Defining new variables:


title: Wave equation

text: In other words, solutions of the 1D wave equation are sums of a right traveling function and a left traveling function . "Traveling" means that the shape of these individual arbitrary functions with respect to stays constant, however the functions are translated left and right with time at the speed . This was derived by Jean le Rond d'Alembert.


title: Wave equation

text: From this, must have the form , and from this the correct form of the full solution can be deduced. The usual second order wave equation is sometimes called the "two-way wave equation" (superposition of two waves) to distinguish it from the first-order one-way wave equation describing the wave propagation of a single wave in a pre-defined direction.


title: Wave equation

text: For an initial value problem, the arbitrary functions and can be determined to satisfy initial conditions:


title: Wave equation

text: In the classical sense if and then . However, the waveforms and may also be generalized functions, such as the delta-function. In that case, the solution may be interpreted as an impulse that travels to the right or the left.


title: Wave equation

text: The basic wave equation is a linear differential equation and so it will adhere to the superposition principle. This means that the net displacement caused by two or more waves is the sum of the displacements which would have been caused by each wave individually. In addition, the behavior of a wave can be analyzed by breaking up the wave into components, e.g. the Fourier transform breaks up a wave into sinusoidal components.


title: Wave equation

text: Another way to solve the one-dimensional wave equation is to first analyze its frequency eigenmodes. A so-called eigenmode is a solution that oscillates in time with a well-defined "constant" angular frequency , so that the temporal part of the wave function takes the form , and the amplitude is a function of the spatial variable , giving a separation of variables for the wave function:


title: Wave equation

text: which is precisely an eigenvalue equation for , hence the name eigenmode. It has the well-known plane wave solutions


title: Wave equation

text: Eigenmodes are useful in constructing a full solution to the wave equation, because each of them evolves in time trivially with the phase factor formula_36. so that a full solution can be decomposed into an eigenmode expansion


title: Wave equation

text: which is exactly in the same form as in the algebraic approach. Functions are known as the Fourier component and are determined by initial and boundary conditions. This is a so-called frequency-domain method, alternative to direct time-domain propagations, such as FDTD method, of the wave packet , which is complete for representing waves in absence of time dilations. Completeness of the Fourier expansion for representing waves in the presence of time dilations has been challenged by chirp wave solutions allowing for time variation of . The chirp wave solutions seem particularly implied by very large but previously inexplicable radar residuals in the flyby anomaly, and differ from the sinusoidal solutions in being receivable at any distance only at proportionally shifted frequencies and time dilations, corresponding to past chirp states of the source.


title: Wave equation

text: The vectorial wave equation (from which the scalar wave equation can be directly derived) can be obtained by applying a force equilibrium to an infinitesimal volume element. In a homogeneous continuum (cartesian coordinate formula_39) with a constant modulus of elasticity formula_40 [Pa] a vectorial, elastic deflection formula_41 [m] causes the stress tensor formula_42 [Pa]. The local equilibrium of a) the tension force formula_43 [N/mformula_44] due to deflection formula_45 [m] and b) the inertial force formula_46 formula_47 [N/mformula_44] caused by the local acceleration formula_49 [m/sformula_50] can be written as


title: Wave equation

text: By merging density formula_46 [kg/m3] and elasticity module formula_40 the sound velocity formula_54 [m/s] results (material law). After insertion follows the well-known governing wave equation for a homogeneous medium:


title: Wave equation

text: The above vectorial partial differential equation of the 2nd order delivers two mutually independent solutions. From the quadratic velocity term formula_56 can be seen that there are two waves travelling in opposite directions formula_57 and formula_58 are possible, hence results the designation “Two-way wave equation”.


title: Wave equation

text: It can be shown for plane longitudinal wave propagation that the synthesis of two one-way wave equations leads to a general two-way wave equation. For special two-wave equation with the d'Alembert operator results:


title: Wave equation

text: Therefore, the vectorial 1st order One-way wave equation with waves travelling in a pre-defined propagation direction formula_61 results as:


title: Wave equation

text: A solution of the initial-value problem for the wave equation in three space dimensions can be obtained from the corresponding solution for a spherical wave. The result can then be also used to obtain the same solution in two space dimensions.


title: Wave equation

text: The wave equation can be solved using the technique of separation of variables. To obtain a solution with constant frequencies, let us first Fourier-transform the wave equation in time as


title: Wave equation

text: This is the Helmholtz equation and can be solved using separation of variables. If spherical coordinates are used to describe a problem, then the solution to the angular part of the Helmholtz equation is given by spherical harmonics and the radial equation now becomes


title: Wave equation

text: To gain a better understanding of the nature of these spherical waves, let us go back and look at the case when . In this case, there is no angular dependence and the amplitude depends only on the radial distance i.e. . In this case, the wave equation reduces to


title: Wave equation

text: where the quantity satisfies the one-dimensional wave equation. Therefore, there are solutions in the form


title: Wave equation

text: where and are general solutions to the one-dimensional wave equation, and can be interpreted as respectively an outgoing or incoming spherical wave. The outgoing wave can be generated by a point source, and they make possible sharp signals whose form is altered only by a decrease in amplitude as increases (see an illustration of a spherical wave on the top right). Such waves exist only in cases of space with odd dimensions.


title: Wave equation

text: For physical examples of non-spherical wave solutions to the 3D wave equation that do possess angular dependence, see dipole radiation.


title: Wave equation

text: Although the word "monochromatic" is not exactly accurate since it refers to light or electromagnetic radiation with well-defined frequency, the spirit is to discover the eigenmode of the wave equation in three dimensions. Following the derivation in the previous section on Plane wave eigenmodes, if we again restrict our solutions to spherical waves that oscillate in time with well-defined "constant" angular frequency , then the transformed function has simply plane wave solutions,


title: Wave equation

text: From this we can observe that the peak intensity of the spherical wave oscillation, characterized as the squared wave amplitude


title: Wave equation

text: For an incident wave traveling from one medium (where the wave speed is ) to another medium (where the wave speed is ), one part of the wave will transmit into the second medium, while another part reflects back into the other direction and stays in the first medium. The amplitude of the transmitted wave and the reflected wave can be calculated by using the continuity condition at the boundary.


title: Wave equation

text: Consider the component of the incident wave with an angular frequency of , which has the waveformformula_75At t=0, the incident reaches the boundary between the two media at x=0. Therefore, the corresponding reflected wave and the transmitted wave will have the waveformsformula_76The continuity condition at the boundary isformula_77This gives the equationsformula_78And we have the reflectivity and transmissivityformula_79When , the reflected wave has a reflection phase change of 180°, since . The energy conservation can be verified by formula_80The above discussion holds true for any component, regardless of its angular frequency of .


title: Wave equation

text: The limiting case of corresponds to a "fixed end" that doesn't move, whereas the limiting case of corresponds to a "free end".


title: Wave equation

text: A flexible string that is stretched between two points and satisfies the wave equation for and . On the boundary points, may satisfy a variety of boundary conditions. A general form that is appropriate for applications is


title: Wave equation

text: where and are non-negative. The case where u is required to vanish at an endpoint (i.e. "fixed end") is the limit of this condition when the respective or approaches infinity. The method of separation of variables consists in looking for solutions of this problem in the special form


title: Wave equation

text: The eigenvalue must be determined so that there is a non-trivial solution of the boundary-value problem


title: Wave equation

text: This is a special case of the general problem of Sturm–Liouville theory. If and are positive, the eigenvalues are all positive, and the solutions are trigonometric functions. A solution that satisfies square-integrable initial conditions for and can be obtained from expansion of these functions in the appropriate trigonometric series.


title: Wave equation

text: Approximating the continuous string with a finite number of equidistant mass points one gets the following physical model:


title: Wave equation

text: If each mass point has the mass , the tension of the string is , the separation between the mass points is and are the offset of these points from their equilibrium points (i.e. their position on a straight line between the two attachment points of the string) the vertical component of the force towards point is


title: Wave equation

text: The wave equation is obtained by letting in which case takes the form where is continuous function of two variables, takes the form and


title: Wave equation

text: with formula_92</ref> with all formula_93. The blue curve is the state at time formula_94 i.e. after a time that corresponds to the time a wave that is moving with the nominal wave velocity would need for one fourth of the length of the string.


title: Wave equation

text: Figure 3 displays the shape of the string at the times formula_95. The wave travels in direction right with the speed without being actively constraint by the boundary conditions at the two extremes of the string. The shape of the wave is constant, i.e. the curve is indeed of the form .


title: Wave equation

text: Figure 4 displays the shape of the string at the times formula_96. The constraint on the right extreme starts to interfere with the motion preventing the wave to raise the end of the string.


title: Wave equation

text: Figure 5 displays the shape of the string at the times formula_97 when the direction of motion is reversed. The red, green and blue curves are the states at the times formula_98 while the 3 black curves correspond to the states at times formula_99 with the wave starting to move back towards left.


title: Wave equation

text: Figure 6 and figure 7 finally display the shape of the string at the times formula_100 and formula_101. The wave now travels towards left and the constraints at the end points are not active any more. When finally the other extreme of the string the direction will again be reversed in a way similar to what is displayed in figure 6.


title: Wave equation

text: The one-dimensional initial-boundary value theory may be extended to an arbitrary number of space dimensions. Consider a domain in -dimensional space, with boundary . Then the wave equation is to be satisfied if is in and . On the boundary of , the solution shall satisfy


title: Wave equation

text: where is the unit outward normal to , and is a non-negative function defined on . The case where vanishes on is a limiting case for approaching infinity. The initial conditions are


title: Wave equation

text: where and are defined in . This problem may be solved by expanding and in the eigenfunctions of the Laplacian in , which satisfy the boundary conditions. Thus the eigenfunction satisfies


title: Wave equation

text: In the case of two space dimensions, the eigenfunctions may be interpreted as the modes of vibration of a drumhead stretched over the boundary . If is a circle, then these eigenfunctions have an angular component that is a trigonometric function of the polar angle , multiplied by a Bessel function (of integer order) of the radial component. Further details are in Helmholtz equation.


title: Wave equation

text: If the boundary is a sphere in three space dimensions, the angular components of the eigenfunctions are spherical harmonics, and the radial components are Bessel functions of half-integer order.


title: Wave equation

text: The function is often called the source function because in practice it describes the effects of the sources of waves on the medium carrying them. Physical examples of source functions include the force driving a wave on a string, or the charge or current density in the Lorenz gauge of electromagnetism.


title: Wave equation

text: One method to solve the initial value problem (with the initial values as posed above) is to take advantage of a special property of the wave equation in an odd number of space dimensions, namely that its solutions respect causality. That is, for any point , the value of depends only on the values of and and the values of the function between and . This can be seen in d'Alembert's formula, stated above, where these quantities are the only ones that show up in it. Physically, if the maximum propagation speed is , then no part of the wave that can't propagate to a given point by a given time can affect the amplitude at the same point and time.


title: Wave equation

text: In terms of finding a solution, this causality property means that for any given point on the line being considered, the only area that needs to be considered is the area encompassing all the points that could causally affect the point being considered. Denote the area that causally affects point as . Suppose we integrate the inhomogeneous wave equation over this region.


title: Wave equation

text: The left side is now the sum of three line integrals along the bounds of the causality region. These turn out to be fairly easy to compute


title: Wave equation

text: In the above, the term to be integrated with respect to time disappears because the time interval involved is zero, thus .


title: Wave equation

text: For the other two sides of the region, it is worth noting that is a constant, namely , where the sign is chosen appropriately. Using this, we can get the relation , again choosing the right sign:


title: Wave equation

text: In the last equation of the sequence, the bounds of the integral over the source function have been made explicit. Looking at this solution, which is valid for all choices compatible with the wave equation, it is clear that the first two terms are simply d'Alembert's formula, as stated above as the solution of the homogeneous wave equation in one dimension. The difference is in the third term, the integral over the source.


title: Wave equation

text: For one-way wave propagation, i.e. wave are travelling in a pre-defined wave direction (formula_57 or formula_58) in inhomogeneous media, wave propagation can also be calculated with a tensorial one-way wave equation (resulting from factorization of the vectorial two way wave equation) and an analytical solution can be derived.


title: Wave equation

text: In three dimensions, the wave equation, when written in elliptic cylindrical coordinates, may be solved by separation of variables, leading to the Mathieu differential equation.


title: Wave equation

text: The elastic wave equation (also known as the Navier–Cauchy equation) in three dimensions describes the propagation of waves in an isotropic homogeneous elastic medium. Most solid materials are elastic, so this equation describes such phenomena as seismic waves in the Earth and ultrasonic waves used to detect flaws in materials. While linear, this equation has a more complex form than the equations given above, as it must account for both longitudinal and transverse motion:


title: Wave equation

text: By using the elastic wave equation can be rewritten into the more common form of the Navier–Cauchy equation.


title: Wave equation

text: Note that in the elastic wave equation, both force and displacement are vector quantities. Thus, this equation is sometimes known as the vector wave equation.


title: Wave equation

text: As an aid to understanding, the reader will observe that if and are set to zero, this becomes (effectively) Maxwell's equation for the propagation of the electric field , which has only transverse waves.


title: Wave equation

text: In dispersive wave phenomena, the speed of wave propagation varies with the wavelength of the wave, which is reflected by a dispersion relation


title: Wave equation

text: where is the angular frequency and is the wavevector describing plane wave solutions. For light waves, the dispersion relation is , but in general, the constant speed gets replaced by a variable phase velocity:


title: Sharknado

text: Sharknado is a 2013 American made-for-television science fiction comedy disaster film directed by Anthony C. Ferrante. It tells about a waterspout that lifts sharks out of the ocean and deposits them in Los Angeles. It is the first installment in the "Sharknado" film series. It first aired on the Syfy channel on July 11, 2013, and stars Tara Reid, Ian Ziering, and John Heard. It was also given a one-night-only special midnight theatrical screening via Regal Cinemas and Fathom Events, where it earned $200,000 from 200 screenings. The over-the-top premise and theatrics of the film quickly earned it a cult following. The idea was first introduced and may have been inspired by the comic Cow and Boy, in an October 2, 2006 comic referencing this ridiculous idea for a movie.


title: Sharknado

text: Five sequels were produced: "", "", "" and "". "", the sixth and final film in the franchise, was released on August 19, 2018. Though the original film was not explicitly a comedy, maintaining at least a façade of seriousness despite the implausible plot, the sequels were more openly comedic in nature.


title: Sharknado

text: Off the coast of Mexico, the ship of shark fin smuggler Carlos Santiago is caught in a cyclone, interrupting his meeting with a potential buyer. A tornado throws swarms of sharks onto the boat, killing all aboard.


title: Sharknado

text: The cyclone soon hits Los Angeles, flooding the city with shark-infested seawater. Bar owner and surfer Fin sets out with his friends, Baz, Nova, and George, to rescue his estranged wife, April, and their teenage daughter, Claudia, after the bar and boardwalk are destroyed by the flooding. While heading to April's home, the group stops on a freeway to save people as flooding causes sharks to attack. George is killed and the group learns of a tornado warning. They arrive at April's house just before the first floor is flooded and shark-infested. Collin, April's boyfriend, is eaten by sharks, but the rest of the group escapes unharmed from the house, which gets hit by a huge wave causing it to collapse.


title: Sharknado

text: As they travel, the group comes across a school bus trapped in the floodwaters and surrounded by sharks. Fin stops to save the children and bus driver by rappelling down to the bus from a bridge. Afterward, the bus driver is killed by a letter in the Hollywood Sign. While Nova is driving the car, a shark lands on top of the car and rips the roof off. Fin's hand is cut and the group abandons the car before it explodes. They steal another car and meet up with Fin and April's son Matt, who is found taking shelter at his flight school. Three tornadoes develop and absorb the floodwater, turning into shark-filled "sharknados". The group borrow equipment from nearby storage and Matt and Nova become attracted to each other. Matt and Nova decide to stop the threat of the incoming sharknados by tossing bombs into them from a helicopter. Two are destroyed, but they are unable to stop the third one.


title: Sharknado

text: As Nova fights off a shark that had latched onto the helicopter, she falls out of the helicopter and directly into another shark's mouth. Matt is heartbroken. Baz is also lost in the storm along with Matt's friends Bobby and Luellyn. Ultimately, Fin destroys the last sharknado with a bomb attached to his car and the sharks begin to plummet toward the ground. One falling shark flies directly toward the remaining members of the group. Fin jumps into its mouth with a chainsaw and cuts his way out. He emerges carrying an unconscious but otherwise unharmed Nova. Matt is reunited with Nova, and Fin gets back together with April.


title: Sharknado

text: "Sharknado" was directed for film studio The Asylum by Anthony C. Ferrante, whose previous directing credits include the horror film "Boo", and written by Thunder Levin, whose previous writing credits include the film "Mutant Vampire Zombies from the 'Hood!". The film's tagline is "Enough said!" "Sharknado" is one of many B-movies commissioned by Syfy. Robbie Rist said in an interview that he came upon the film's poster at the American Film Market and became enthusiastic about the concept. When his friend Ferrante said that he had been approached to direct the film, Rist insisted that Ferrante take the job. Rist was given a small role in the film and composed the theme.


title: Sharknado

text: Actress Tara Reid said of the film, "It is silly, and there's only a certain amount of barriers you could go into. You can't take it so seriously when it's absolutely the sharks flying in the sky. It's so out there that it's actually really funny." The cast had to imagine the presence of sharks due to a green screen being frequently in use. Ian Ziering stated that he had serious reservations about the script but was motivated, in part, by the need to earn enough to qualify for Screen Actors Guild health insurance for his family.


title: Sharknado

text: In an interview with Uproxx's Danger Guerrero, Ferrante summarized the film's plot: "There's a flood. And a storm. Don't worry about it."


title: Sharknado

text: The premiere of the film was watched by 1.37 million viewers, which is slightly below the average audience of 1.5 million viewers for a typical Syfy original film. However, the film was a trend on Twitter, including discussion by celebrities such as Damon Lindelof, Wil Wheaton, and Olivia Wilde and also by Cory Monteith, whose last tweet before his death was about the film. Due to an increase in publicity (mostly through Twitter), Syfy repeated "Sharknado" on Thursday, July 18, 2013, one week after its premiere. That airing was watched by 1.89 million viewers, an increase of 38% over its initial airing. On July 27, a third airing of "Sharknado" got 2.1 million viewers, continuing the increase in popularity of the film and setting a record for most watched original film encore in Syfy history. "Sharknado" was projected to increase revenue for The Asylum from $5 million in 2009 to $19 million in 2013.


title: Sharknado

text: A representative of the National Weather Service jokingly recommended what to do in case of a sharknado, saying: "As with any waterspout or tornado, the best advice is to be in an interior part of the lowest floor of a sturdy building – and not outside, whether sharks are raining down or not." Organizations such as the Red Cross of Oklahoma City also used the film as an opportunity to pass on storm safety information while others incorporated it into their own advertising.


title: Sharknado

text: Regal Cinemas announced that at midnight on August 2, 2013, it would play the film in roughly 200 theaters nationally. Tickets sold out quickly in New York, Boston, and Seattle, where more showings were added to appease customer demand. Box office numbers were weak for the midnight showings; estimates were at under $200,000.


title: Sharknado

text: Syfy and The Asylum announced in August 2013 that "Sharknado" merchandise would be made available, including T-shirts and potentially other products, such as costumes, bags and posters.


title: Sharknado

text: Rotten Tomatoes gives the film an approval rating of 74% based on 19 reviews; the average rating is 6.12/10. The site's consensus states: "Proudly, shamelessly, and gloriously brainless, "Sharknado" redefines 'so bad it's good' for a new generation."


title: Sharknado

text: Reviewer Mary McNamara, writing for the "Los Angeles Times", mentioned that the plot holes are "the whole point of movies like this: fabulous in-home commentary. Often accompanied by the consumption of many alcoholic beverages." David Hinckley of the New York "Daily News" said ""Sharknado" is an hour and a half of your life that you'll never get back. And you won't want to."


title: Sharknado

text: Kim Newman of "Empire" called the film "cynical rubbish, with an attention-getting title and just enough footage of terrible CG sharks in a terrible CG tornado chomping on people to fill out a trailer suitable for attracting YouTube hits."


title: Sharknado

text: "Sharknado" has become a cult film. The film was used for a RiffTrax Live event in July 2014, where former "Mystery Science Theater 3000" cast members mocked the film for a live audience and broadcast to other theaters through NCM Fathom; the idea for using the film for this was prompted by the "Sharknado" producers discussing the film with Fathom at the same time. After the event, Ferrante said that "Being skewered by the MST3K guys was an honor." In 2016, Homes.com added a page to their disaster prep guides on How to Prepare Your Home For a Sharknado.


title: Sharknado

text: The success of "Sharknado" spawned a series of sequels, with the sixth and final entry in the series being released on August 19, 2018.


title: Ashnikko

text: Ashton Nicole Casey (born February 19, 1996), known professionally as Ashnikko ( ), is an American singer and rapper. She rose to prominence with her 2019 single "Stupid" with Baby Tate, which gained viral popularity on the video-sharing platform TikTok and was certified gold in the United States and Canada. Ashnikko's debut mixtape, "Demidevil", was released in January 2021, and spawned the singles "Daisy" and "Slumber Party" featuring Princess Nokia.


title: Ashnikko

text: Ashton Nicole Casey was born on February 19, 1996, in Oak Ridge, North Carolina, and raised in the city of Greensboro. Her parents exposed her to country music and Slipknot. She recalls becoming interested in music, specifically rap music, when she listened to "Arular" by M.I.A. at the age of 10, and says she did not listen to male musicians until she was 16 years old. As a teenager, her family moved to Estonia for her father's studies, spending a year there before relocating again to Riga, Latvia. At one point, she was the only American in Latvia to attend a Latvian public high school. At the age of 18, Ashnikko moved to London by herself.


title: Ashnikko

text: Ashnikko's first song, "Krokodil", was produced by Raf Riley and published to SoundCloud in July 2016. She released her first EP, "Sass Pancakes", under Digital Picnic Records in 2017. The EP was produced by Raf Riley and features appearances from Avelino. Ashnikko's second EP, "Unlikeable", was released in November 2018. The EP spawned the singles "Blow", "Nice Girl", "Invitation" featuring Kodie Shane, and "No Brainer".


title: Ashnikko

text: Ashnikko released her third EP, "Hi It's Me", in July 2019. The EP was preceded by the promotional single "Special" and was launched alongside the EP's title track and lead single, "Hi It's Me". The second official single, "Stupid", featuring Yung Baby Tate, gained viral popularity on the video-sharing platform TikTok. The song reached number one on the "Billboard" Bubbling Under Hot 100 chart, the "Billboard" Bubbling Under R&B/Hip-Hop chart, and the Spotify Viral 50 chart. "Stupid" was also certified gold in the United States in August 2020, as well as in Canada. Another song from the EP, "Working Bitch", also found popularity on TikTok. Ashnikko embarked on a North American tour supporting American rapper Danny Brown in October 2019. She released the promotional single "Halloweenie II: Pumpkin Spice" in October 2019. She co-wrote eight songs, two of which she is featured on, on Brooke Candy's debut album, "Sexorcism", which was released in October 2019.


title: Ashnikko

text: Ashnikko co-wrote the song "Boss Bitch" with American rapper Doja Cat, which was included on the "Birds of Prey" soundtrack, "Birds of Prey: The Album". Prior to the COVID-19 pandemic, Ashnikko was scheduled to accompany Doja Cat on her Hot Pink Tour throughout the United States in March 2020 before it was canceled. In March 2020, she released the standalone single "Tantrum". Later that month, she performed "Tantrum" live as part of "The Fader"s Digital Fader Fort event. "Cry", featuring Canadian musician Grimes, was then released in June 2020, alongside an animated music video. The song's music video was nominated for "Best Pop Video - UK" at the 2020 UK Music Video Awards. Following this, "Daisy" was released in July 2020, and a music video for the song was released in collaboration with Beats by Dre and TikTok a month later. "Daisy" became Ashnikko's breakthrough hit, charting internationally in countries including Australia, Belgium and the United Kingdom. It reached a peak of number 24 on the UK Singles Chart, becoming her first charting and first top 40 hit in the UK. Ashnikko's third Halloween song, "Halloweenie III: Seven Days", was released in October 2020. She was nominated for Best Push Act at the 2020 MTV Europe Music Awards.


title: Ashnikko

text: "Cry" and "Daisy" both appear on Ashnikko's debut mixtape, "Demidevil", which was released on January 15, 2021. "Deal with It" featuring Kelis and "Slumber Party" featuring Princess Nokia served as the third and fourth singles from the mixtape, respectively. In support of the mixtape, Ashnikko announced The Demidevil Tour, which is set to take place in October 2021, with shows in North America, the UK, and Ireland.


title: Ashnikko

text: More recently, Ashnikko co-wrote the song "Frost" released on May 31, 2021, which figures in Korean boy band Tomorrow X Together – TXT's album "" and its repackage album "" released on August 17, 2021. She sent the hyper-pop, trap-based song over to TXT in English. The song was then translated to Korean.


title: Ashnikko

text: Ashnikko's musical style has been described by critics as a fusion of several genres, including pop, indie pop, rock, alt-pop, hip hop, bubblegum pop, indie rock, punk, and electropop. She described her style of music as "angry, punk, hip hop, sad-girl-feminist, bubblegum, poo-poo music", and has clarified that her music is not intended to be comedic or parody-based.


title: Ashnikko

text: Ashnikko is known for her Tokyo-inspired street fashion. She is also known for her unique blue hair, which is originally brown. In the video for "Nice Girl" and some of her early vlogs, her hair is pastel green. Her hair in the "Daisy" music video is yellow, pink, and red.


title: Ashnikko

text: Ashnikko has cited her musical influences as M.I.A., Gwen Stefani, Lil' Kim, Björk, Paramore, Avril Lavigne, Nicki Minaj, Missy Elliott, Dolly Parton, Janis Joplin, and Joan Jett, and has stated that her favorite song is "Bossy" by Kelis. She has also listed Doja Cat, Grimes, Tierra Whack, Rico Nasty, Princess Nokia, Kim Petras, and Charli XCX as her "peers" and artists she "really respects".


title: Ashnikko

text: Ashnikko stated on Twitter in June 2019 that she is bisexual and later clarified in a 2020 interview that she is pansexual. In May 2021, Ashnikko came out as genderfluid on Twitter, saying that "i just didn't feel ready to tell the internet yet but i guess now's a good time since everyone's doing a dissection into my sexuality and gender identity". She uses she/her and they/them pronouns.


title: Ashnikko

text: In July 2020, while discussing the meaning behind the lyrics of her single "Daisy", she said that while her family practices Christianity, she does not.


title: Ashnikko

text: Ashnikko has described herself as a feminist and has attributed discovering intersectional feminism through microblogging website Tumblr as a teenager as a turning point for her. She has been vocal about a range of social justice issues, having spoken out about the commercialization of feminism in November 2019, while advocating for victims of police brutality through social media.


title: Phosgene

text: Phosgene is the organic chemical compound with the formula COCl. It is a toxic, colorless gas; in low concentrations, its musty odor resembles that of freshly cut hay or grass. Phosgene is a valued and important industrial building block, especially for the production of precursors of polyurethanes and polycarbonate plastics.


title: Phosgene

text: Phosgene is extremely poisonous and was used as a chemical weapon during World War I, where it was responsible for 85,000 deaths. It was a highly potent pulmonary irritant and quickly filled enemy trenches due to it being a heavy gas.


title: Phosgene

text: It is classified as a Schedule 3 substance under the Chemical Weapons Convention. In addition to its industrial production, small amounts occur from the breakdown and the combustion of organochlorine compounds, such as chloroform.


title: Phosgene

text: Phosgene is a planar molecule as predicted by VSEPR theory. The C=O distance is 1.18 Å, the C−Cl distance is 1.74 Å and the Cl−C−Cl angle is 111.8°. Phosgene is a carbon oxohalide and it can be considered one of the simplest acyl chlorides, being formally derived from carbonic acid.


title: Phosgene

text: Industrially, phosgene is produced by passing purified carbon monoxide and chlorine gas through a bed of porous activated carbon, which serves as a catalyst:


title: Phosgene

text: This reaction is exothermic and is typically performed between 50 and 150 °C. Above 200 °C, phosgene reverts to carbon monoxide and chlorine, "K"(300 K) = 0.05. World production of this compound was estimated to be 2.74 million tonnes in 1989.


title: Phosgene

text: Phosgene is fairly simple to produce, but is listed as a Schedule 3 substance under the Chemical Weapons Convention. As such, it is usually considered too dangerous to transport in bulk quantities. Instead, phosgene is usually produced and consumed within the same plant, as part of an "on demand" process. This involves maintaining equivalent rates of production and consumption, which keeps the amount of phosgene in the system at any one time fairly low, reducing the risks in the event of an accident. Some batch production does still take place, but efforts are made to reduce the amount of phosgene stored.


title: Phosgene

text: Upon ultraviolet (UV) irradiation in the presence of oxygen, simple organochlorides such as chloroform (CHCl) slowly convert into phosgene. Phosgene is also formed as a metabolite of chloroform, likely via the action of cytochrome P-450.


title: Phosgene

text: Carbon tetrachloride (CCl) can turn into phosgene when exposed to heat in air. This was a problem as carbon tetrachloride is an effective fire suppressant and was formerly in widespread use in fire extinguishers. There are reports of fatalities caused by its use to fight fires in confined spaces. Carbon tetrachloride's generation of phosgene and its own toxicity mean it is no longer used for this purpose.


title: Phosgene

text: Phosgene was synthesized by the Cornish chemist John Davy (1790–1868) in 1812 by exposing a mixture of carbon monoxide and chlorine to sunlight. He named it "phosgene" from Greek "φῶς" ("phos", light) and "γεννάω (gennaō", to give birth) in reference of the use of light to promote the reaction. It gradually became important in the chemical industry as the 19th century progressed, particularly in dye manufacturing.


title: Phosgene

text: The synthesis of isocyanates from amines illustrates the electrophilic character of this reagent and its use in introducing the equivalent synthon "CO":


title: Phosgene

text: Such reactions are conducted on laboratory scale in the presence of a base such as pyridine that neutralizes the hydrogen chloride side-product.


title: Phosgene

text: On an industrial scale, phosgene is used in excess to increase yield and avoid side reactions. The phosgene excess is separated during the work-up of resulting end products and recycled into the process, with any remaining phosgene decomposed in water using activated carbon as the catalyst.


title: Phosgene

text: Phosgene is used in industry for the production of aromatic di-isocyanates like toluene diisocyanate (TDI) and methylene diphenyl diisocyanate (MDI), which are precursors for production of polyurethanes. It is also used to form polycarbonates, via a reaction with bisphenol A. More than 90% of the worldwide produced phosgene is used in these processes, with the biggest production units located in the United States (Texas and Louisiana), Germany, Shanghai, Japan, and South Korea. The most important producers are Dow Chemical, Covestro, and BASF. Phosgene is used in the production of aliphatic diisocyanates such as hexamethylene diisocyanate (HDI) and isophorone diisocyanate (IPDI), which are precursors for the production of advanced coatings. Phosgene is also used to produce monoisocyanates, used as pesticide precursors ("e.g." methyl isocyanate (MIC).


title: Phosgene

text: In the research laboratory, due to safety concerns phosgene nowadays finds limited use in organic synthesis. A variety of substitutes have been developed, notably trichloromethyl chloroformate ("diphosgene"), a liquid at room temperature, and bis(trichloromethyl) carbonate ("triphosgene"), a crystalline substance.


title: Phosgene

text: Aside from the widely used reactions described above, phosgene is also used to produce acyl chlorides from carboxylic acids:


title: Phosgene

text: In these syntheses, phosgene is used in excess to prevent formation of the corresponding carbonate ester.


title: Phosgene

text: With amino acids, phosgene (or its trimer) reacts to give amino acid N-carboxyanhydrides. More generally, phosgene acts to link two nucleophiles by a carbonyl group. For this purpose, alternatives to phosgene such as carbonyldiimidazole (CDI) are safer. CDI itself is prepared by reacting phosgene with imidazole.


title: Phosgene

text: Phosgene is stored in metal cylinders. In the US, the cylinder valve outlet is a tapered thread known as "CGA 160" that is used only for phosgene.


title: Phosgene

text: It is listed on Schedule 3 of the Chemical Weapons Convention: All production sites manufacturing more than 30 tonnes per year must be declared to the OPCW. Although less toxic than many other chemical weapons such as sarin, phosgene is still regarded as a viable chemical warfare agent because of its simpler manufacturing requirements when compared to that of more technically advanced chemical weapons such as tabun, a first-generation nerve agent.


title: Phosgene

text: Phosgene was first deployed as a chemical weapon by the French in 1915 in World War I. It was also used in a mixture with an equal volume of chlorine, with the chlorine helping to spread the denser phosgene. Phosgene was more potent than chlorine, though some symptoms took 24 hours or more to manifest.


title: Phosgene

text: Phosgene was then only infrequently used by the Imperial Japanese Army against the Chinese during the Second Sino-Japanese War. Gas weapons, such as phosgene, were produced by Unit 731.


title: Phosgene

text: The odor detection threshold for phosgene is 0.4 ppm, four times the threshold limit value. Its high toxicity arises from the action of the phosgene on the –OH, –NH and –SH groups of the proteins in pulmonary alveoli (the site of gas exchange), respectively forming ester, amide and thioester functional groups in accord with the reactions discussed above. This results in disruption of the blood–air barrier, eventually causing pulmonary edema. The extent of damage in the alveoli does not primarily depend on phosgene concentration in the inhaled air, with the dose (amount of inhaled phosgene) being the critical factor. Dose can be approximately calculated as "concentration" × "duration of exposure". Therefore, persons in workplaces where there exists risk of accidental phosgene release usually wear indicator badges close to the nose and mouth. Such badges indicate the approximate inhaled dose, which allows for immediate treatment if the monitored dose rises above safe limits.


title: Phosgene

text: In case of low or moderate quantities of inhaled phosgene, the exposed person is to be monitored and subjected to precautionary therapy, then released after several hours. For higher doses of inhaled phosgene (above 150 ppm × min) a pulmonary edema often develops which can be detected by X-ray imaging and regressive blood oxygen concentration. Inhalation of such high doses can eventually result in fatality within hours up to 2–3 days of the exposure.


title: Phosgene

text: The risk connected to a phosgene inhalation is based not so much on its toxicity (which is much lower in comparison to modern chemical weapons like sarin or tabun) but rather on its typical effects: the affected person may not develop any symptoms for hours until an edema appears, at which point it could be too late for medical treatment to assist. Nearly all fatalities as a result of accidental releases from the industrial handling of phosgene occurred in this fashion. On the other hand, pulmonary edemas treated in a timely manner usually heal in the mid- and longterm, without major consequences once some days or weeks after exposure have passed. Nonetheless, the detrimental health effects on pulmonary function from untreated, chronic low-level exposure to phosgene should not be ignored; although not exposed to concentrations high enough to immediately cause an edema, many synthetic chemists ("e.g." Leonidas Zervas) working with the compound were reported to experience chronic respiratory health issues and eventual respiratory failure from continuous low-level exposure.


title: Phosgene

text: If accidental release of phosgene occurs in an industrial or laboratory setting, it can be mitigated with ammonia gas; in the case of liquid spills ("e.g." of diphosgene or phosgene solutions) an absorbent and sodium carbonate can be applied.


title: Primorsky Krai

text: Primorsky Krai (), informally known as Primorye (, ), is a federal subject (a krai) of Russia, located in the Far East region of the country and is a part of the Far Eastern Federal District. The city of Vladivostok is the administrative center of the krai, and the second largest city in the Russian Far East, after Khabarovsk. The krai has the largest economy among the federal subjects in the Russian Far East, and a population of 1,956,497 as of the 2010 Census.