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Magnetism from Conductors, and Enhanced Non-Linear Phenomena
- Donald Goodwin
- 1 years ago
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1 Mnetism from Conductors, nd Enhnced Non-Liner Phenomen JB Pendry, AJ Holden, DJ Roins, nd WJ Stewrt Astrct - We show tht microstructures uilt from non-mnetic conductin sheets exhiit n effective mnetic permeility, µ eff, which cn e tuned to vlues not ccessile in nturlly occurrin mterils, includin lre iminry components of µ eff. The microstructure is on scle much less thn the wvelenth of rdition, is not resolved y incident microwves, nd uses very low density of metl so tht structures cn e extremely lihtweiht. Most of the structures re resonnt due to internl cpcitnce nd inductnce, nd resonnt enhncement comined with compression of electricl enery into very smll volume retly enhnces the enery density t criticl loctions in the structure, esily y fctors of million nd possily y much more. Wekly non-liner mterils plced t these criticl loctions will show retly enhnced effects risin the possiility of mnufcturin ctive structures whose properties cn e switched t will etween mny sttes. Index Terms - effective permeility, non-linerity, photonic crystls JB Pendry is with The Blckett Lortory, Imperil Collee, London, SW7 BZ, UK. AJ Holden, DJ Roins, nd WJ Stewrt re with GEC-Mrconi Mterils Technoloy Ltd, Cswell, Towcester, Northmptonshire, NN 8EQ, UK. /word/pp/wecs/mwires.doc t 3 Ferury 999 pe
2 I. INTRODUCTION In sense every mteril is composite, even if the individul inredients consist of toms nd molecules. The oriinl ojective in definin permittivity, ε, nd permeility, µ, ws to present n homoeneous view of the electromnetic properties of medium. Therefore it is only smll step to replce the toms of the oriinl concept with structure on lrer scle. We shll consider periodic structures defined y unit cell of chrcteristic dimensions. The contents of the cell will define the effective response of the system s whole. Clerly there must e some restrictions on the dimensions of the cell. If we re concerned out the response of the system to electromnetic rdition of frequency ω the conditions re esy to define: << λ= πc ω () If this condition were not oeyed there would e the possiility tht internl structure of the medium could diffrct s well s refrct rdition ivin the me wy immeditely. Lon wvelenth rdition is too myopic to detect internl structure nd in this limit n effective permittivity nd permeility is vlid concept. In the next section we shll discuss how the microstructure cn e relted to ε, µ. eff eff In n erlier pper [] we showed how structure consistin of very thin infinitely lon metl wires rrned in 3D cuic lttice could model the response of dilute plsm, ivin netive ε eff elow plsm frequency somewhere in the ihertz rne. Theoreticl nlysis of this structure hs een confirmed y experiment []. Sievenpiper et l hve lso investited plsm-like effects in metllic structures [3,4]. Idelly we should like to proceed in the mnetic cse y findin the mnetic nloue of ood electricl conductor: unfortuntely there isn t one! Nevertheless we cn find some lterntives which we elieve do ive rise to interestin mnetic effects. Why should we o to the troule of microstructurin mteril simply to enerte prticulr µ eff? The nswer is tht toms nd molecules prove to e rther restrictive set of elements from which to uild mnetic mteril. This is prticulrly true t frequencies in the ihertz rne where the mnetic response of most mterils is einnin to til off. Those mterils, such s the ferrites, tht remin modertely ctive re often hevy, nd my not hve very desirle mechnicl properties. In contrst, we shll show, microstructured mterils cn e desined with considerle mnetic ctivity, oth dimnetic nd prmnetic, nd cn if desired e mde extremely liht. There is nother quite different motivtion. We shll see tht stron mnetic ctivity implies stronly inhomoeneous fields inside the mteril. In some instnces this my result in locl field strenths mny orders of mnitude lrer thn in free spce. Dopin the composite with non liner mteril t the criticl loctions of field concentrtion ives enhnced non-linerity, reducin power requirements y the field enhncement fctor. This is not n option ville in conventionl mnetic mteril. We show first how to clculte µ eff for system, then we propose some model structures which hve mnetic ctivity nd ive some numers for these systems. Finlly we show how electrosttic enery cn e stronly concentrted in these structures nd hence the demonstrte potentil for enhncin non liner effects. /word/pp/wecs/mwires.doc t 3 Ferury 999 pe
3 II. DEFINING AN EFFECTIVE PERMEABILITY We re seekin to uild structures with effective epsilon nd mu, B D = µ µ H ve eff ve = ε ε E ve eff ve () where we ssume tht the structure is on scle much shorter thn the wvelenth of ny rdition so tht we cn sensily spek of n vere vlue for ll the fields. A key question is how do the veres differ? Clerly if the structure is mde of thin wires or sheets of metl then if the veres were tken over the sme reions of spce, ε, µ would lwys e unity. However we oserve tht Mxwell s equtions, eff eff H = + D / t E = B / t my e pplied in the interl form, zc zc H dl = + E dl = t t zs zs D. ds B. ds (3) (4) where the line interl is tken over loop c which encloses n re s. This form of the equtions immeditely suests prescription for verin the fields. For simplicity we shll ssume tht the periodic structure is descried y unit cell whose xes re orthoonl s shown in fiure elow. Some of the ruments used in this section re similr to those we used in derivin finite difference model of Mxwell s equtions [5]. Fiure. Unit cell of periodic structure. We ssume tht the unit cell dimensions re much smller tht the wvelenth of rdition, nd vere over locl vritions of the fields. In the cse of the B - field we vere over the fces of the cell nd in the cse of the H - field, over one of the edes. We choose to define the components of H ve y verin the H field lon ech of the three xes of the unit cell. If we ssume simple cuic system, /word/pp/wecs/mwires.doc t 3 Ferury 999 pe 3
4 H H H ve x ve y ve z z zz r=,, = H dr r=,, r=,, = H dr r=,, r=,, = H dr r=,, (5) There is only one cvet concernin the definition of the unit cell: its edes must not intersect with ny of the structures contined within the unit cell. This leves us free to cut the structure into whole numer of unit cells when we come to crete surfce nd ensures tht the prllel component of H ve is continuous cross the surfce s required in consistent theory of n effective medium. To define B ve we vere the B field over ech of the three fces of the unit cell defined s follows: S x is the surfce defined y the vectors y, z S y is the surfce defined y the vectors x, z S z is the surfce defined y the vectors x, y Hence we define, B B B ve x ve y ve z = B ds S = B ds z zz S = B ds S x z y The rtio defines the effective epsilon nd mu from (), d i d i d i µ eff = B µ x ve x Hve x µ eff = B µ y ve y Hve y µ eff = B µ z ve z Hve z (6) (7) Thus if we seek lre effect we must try to crete fields tht re s inhomoeneous s possile. We shll explore vrious confiurtions of thin sheets of metl, derive µ eff, nd discuss the results with view to mkin the effect s lre s possile. /word/pp/wecs/mwires.doc t 3 Ferury 999 pe 4
5 III. EXAMPLES OF MAGNETIC MICROSTRUCTURES A. An Arry of Cylinders Fiure. Model A consists of squre rry of metllic cylinders desined to hve mnetic properties in the direction prllel to the xes of the cylinders. We strt with very simple structure for the purposes of illustrtion. Let us pply n externl field, H, which we shll tke to e prllel to the cylinders. We ssume tht the cylinders hve conductin surfce so tht current, j, per unit lenth, flows. The field inside the cylinders is, H = H + j j (8) where the second term on the riht hnd side is the field cused directly y the current, nd the third term is the result of the depolrisin fields with sources t the remote ends of the cylinders. If the cylinders re very lon the depolrisin field will e uniformly spred over the unit cell, ut will hve the sme numer of lines of force in it s the direct field inside the cylinders. We now clculte the totl emf round the circumference of cylinder: L M N M L N O P Q O P Q r emf = π r µ π H + j j t M P = + iωπ r µ H + j j M P σj σj where σ is the resistnce of the cylinder surfce per unit re. The net emf must lnce nd therefore, (9) j = iωπ r µ H = L r i r O r M L π ωπ µ P π σ M N Q N H O r i P + σ ω r µ Q () We re now in position to clculte the relevnt veres. The vere of the B-field over the entire unit cell is, Bve = µ H () /word/pp/wecs/mwires.doc t 3 Ferury 999 pe 5
6 However if we vere the H-field over line lyin entirely outside the cylinders, Hve = H j = H L NM H O r i P + σ ω r µ Q = H L NM σ + i ω rµ O i P + σ ω rµ Q () Hence we define, µ eff σ + i B ve ω rµ = = µ Hve σ + i ω rµ L NM = + σ i ω rµ O QP (3) For n infinitely conductin cylinder, or in the hih frequency limit, µ eff is reduced y the rtio of the cylinder volume to the cell volume. This rtio of volumes will turn out to e the key fctor in determinin the strenth of the effect in ll our models. Evidently in the present model µ eff cn never e less thn zero, or reter thn unity. It should lso e mentioned tht to mximise the effect we could hve replced the metllic cylinders with prisms of squre cross section to mximise the volume enclosed within the prism. If the resistivity of the sheets is hih then the dditionl contriution to µ eff is iminry ut lwys less thn unity, µ eff 3 ω µ + i, σ >> ω rµ (4) σ A further point tht should e noted is tht ll the structures we discuss hve electricl s well s mnetic properties. In this prticulr cse we cn crudely estimte for electric fields perpendiculr to the cylinders, ε eff F HG = F = I KJ where F is the frction of the structure not internl to cylinder. In derivin (5) we ssume tht the cylinder is perfect conductor, nd nelect depolrisin fields risin from interction etween cylinders. Inclusion of ε eff in our clcultions removes one difficulty y ensurin tht, (5) lim ω d i (6) liht eff eff ω c = lim c ε µ = c Evidently without ε eff the velocity of liht in the effective medium would hve exceeded tht in free spce. Most of the structures discussed in this pper hve similr ε eff. /word/pp/wecs/mwires.doc t 3 Ferury 999 pe 6
7 B. A Cpcittive Arry of Sheets Wound on Cylinders The previous structure showed limited mnetic effect. Now we show how to extend the rne of mnetic properties ville to us y introducin cpcittive elements into the structure. We tke the sme structure of cylinders s efore except tht the cylinders re now uilt in split rin confiurtion shown elow in fiure 3. Fiure 3. Model B consists of squre rry of cylinders s for model A ut with the difference tht the cylinders now hve internl structure The sheets re divided into split rin structure nd seprted from ech other y distnce d. In ny one sheet there is p which prevents current from flowin round tht rin. The importnt point is tht there is p which prevents current from flowin round ny one rin. However there is considerle cpcitnce etween the two rins which enles current to flow, Fiure 4. When mnetic field prllel to the cylinder is switched on it induces currents in the split rins s shown in the fiure. The reter the cpcitnce etween the sheets, the reter the current. Detiled clcultions ive, µ eff = F σi 3 + ω rµ 3 π µ ω Cr (7) where F is the frctionl volume of the cell side occupied y the interior of the cylinder, r F = π (8) nd C is the cpcitnce per unit re etween the two sheets, /word/pp/wecs/mwires.doc t 3 Ferury 999 pe 7
8 ε C = = d dc µ (9) Hence, µ eff = σi 3dc + ω rµ 3 π ω r () Becuse we now hve cpcitnce in the system which cn lnce the inductnce present, µ eff hs resonnt form which we sketch elow in fiure 5. µ eff µ eff = ω ω mp ω Fiure 5. The effective mnetic permeility for model B shows resonnt structure dictted y the cpcitnce etween the sheets nd the mnetic inductnce of the cylinder. We sketch the typicl form for hihly conductin smple, σ. Below the resonnt frequency µ eff is enhnced, ut ove resonnce µ eff is less thn unity nd my e netive close to the resonnce. Fiure 5 illustrtes the eneric form of µ eff for ll the structures we present here. We define ω to e the frequency t which µ eff diveres, 3 3dc ω = = 3 3 π µ Cr π r () nd ω mp to e the mnetic plsm frequency ω mp = π µ 3 3 Cr F = π 3 r 3dc F HG I KJ () Note tht the seprtion etween ω ndω mp, which is mesure of the rne of frequencies over which we see stron effect, is determined y /word/pp/wecs/mwires.doc t 3 Ferury 999 pe 8
9 F = (3) the frction of the structure not internl to cylinder. As for the cse A, the simple cylinder, the hih frequency limit is iven y, lim µ eff ω ω = (4) We mention in pssin tht the system sustins lonitudinl mnetic modes t the mnetic plsm frequency, the nloue of the plsm modes of s of free electricl chres [6,7]. Of course, we hve no free mnetic poles, only the ppernce of such s currents round the cylinders mke the cylinder ends pper to support free mnetic poles in the fshion of r mnet. Toether with ε eff iven in eqution (5), which is lso pplicle here, we cn illustrte eneric dispersion reltionship shown elow in fiure 6. Fiure 6. Generic dispersion reltionship for resonnt structures with µ eff. The solid lines represent two-fold deenerte trnsverse modes, the dotted line sinle lonitudinl mnetic plsmon mode. The relevnt points to note re: (i) wherever µ eff is netive there is p in the dispersion reltionship, i.e. for, ω ω ω < < mp (5) (ii) lonitudinl mnetic plsm mode, dispersionless in this pproximtion, is seen t ω = ω mp. (iii) The dispersion reltion converes symptoticlly to the free spce liht cone. s discussed ove. In fct metllic structures in enerl represent fresh pproch to the photonic insultor concept introduced independently y Ylonovitch [8,9] nd John []. If we tke the followin vlues, 3 r =. m 3 = 5. m 4 d =. m (6) /word/pp/wecs/mwires.doc t 3 Ferury 999 pe 9
10 we et,. Hz (7) f mp = π ω mp = 47 9 f F HG I 9 = fmp 94 KJ =. Hz (8) Note tht the frequency t which the structure is ctive corresponds to free spce wvelenth of cm, much reter tht the.5cm seprtion etween cylinders. This will e typicl of these cpcittive structures nd implies tht the effective medium pproximtion will e excellent. C Swiss Roll Cpcitor We tke the sme rrnement of cylinders on squre lttice s efore except tht the cylinders re now uild s follows: Fiure 7. In model C metllic sheet is wound round ech cylinder in coil. Ech turn of the coil is spced y distnce d from the previous sheet. The importnt point is in tht no current cn flow round the coil except y virtue of the self cpcitnce, Fiure 8. When mnetic field prllel to the cylinder is switched on it induces currents in the coiled sheets s shown in the fiure. Cpcitnce etween the first nd lst turns of the coil enles current to flow. /word/pp/wecs/mwires.doc t 3 Ferury 999 pe
11 In this instnce we find for the effective permeility, µ eff = F σi + ω rµ N 3 π r µ N ω C (9) = σi dc + ω rµ N 3 π r N ω where F is s efore the frction of the structure not internl to cylinder, nd the cpcitnce per unit re etween the first nd the lst of the coils is, ε C = = d N µ dc N (3) The criticl frequencies re, ω = dc = 3 π r µ C N π r N 3 (3) ω mp = dc = 3 F π r µ C N F I 3 π r N HG KJ (3) If we tke the vlues we used efore in (6), 3 r =. m 3 = 5. m 4 d =. m N = (33) we et, π ω. Hz (34) 9 f = = 38. (35) f mp = π ω mp = i.e. there is much more cpcitnce in this model nd the rne of ctive frequencies is n order of mnitude lower thn it ws in model C which used only two overlppin sheets. Choosin n even smller scle nd reducin the numer of turns in order to drive up the frequencies to our rne of interest, /word/pp/wecs/mwires.doc t 3 Ferury 999 pe
12 4 r =. m 4 = 5. m 5 d =. m N = 3 (36) we et, 9 f = 85. Hz (37) f mp =. 5 9 Hz (38) Note tht the free spce wvelenth t the plsm frequency is round 3cm nd compre this to the very much smller spcin etween cylinders of.5cm. We shll now clculte the dispersion of µ eff for vrious prmeters. First let us tke the prmeters iven in eqution (36). The resultin dispersion of µ eff is shown elow in fiure 9 Fiure 9. Dispersion with frequency of µ eff for Swiss roll structure, clculted for the prmeters shown in eqution (36), ssumin tht the metl hs zero resistivity. Next we enquire wht is the effect of mkin the sheets resistive? Below we present series of clcultions for vrious vlues of the resistivity, σ, iven in Ω. /word/pp/wecs/mwires.doc t 3 Ferury 999 pe
13 Fiure. Dispersion with frequency of µ eff for Swiss roll structure, clculted for the prmeters shown in eqution (36), for vrious vlues of the resistivity of the sheets:.ω,.ω, 5.Ω,.Ω. In fiure we increse the resistivity from. Ω to. Ω. Note the rodenin of the resonnce, the complementry ehviour of µ rel nd µ im, dictted y Krmers Kroni, nd how resistivity limits the mximum effect chieved. Next we explore the dependence on the rdius of the cylinders. In fiure the rdius of the cylinders is decresed, reducin the volume frction occupied y the cylinders, nd risin the resonnt frequency y fctor of two. We lso decrese d, the spcin etween the sheets, incresin the cpcitnce in the system nd rinin the resonnt frequency ck down to its oriinl vlue. /word/pp/wecs/mwires.doc t 3 Ferury 999 pe 3
14 Fiure. Dispersion with frequency of µ eff for Swiss roll structure. Top: clculted for the prmeters shown in eqution (36), except tht the resistivity of the sheets is now.ω, nd the rdius of the cylinders hs een reduced from. 4 m to 6. 4 m, thus risin the resonnt frequency y fctor of two. Bottom: d, the spcin etween the sheets, hs een reduced to. 5 5 m rinin the resonnt frequency ck to the oriinl vlue. Usin cpcittive cylindricl structures such s the Swiss roll structure we cn djust the mnetic permeility typiclly y fctor of two nd, in ddition if we desire, introduce n iminry component of the order of unity. The ltter implies tht n electromnetic wve movin in such mteril would decy to hlf its intensity within sinle wvelenth. This presumes tht we re seekin rod-nd effects tht persist over the reter prt of the -GHz reion. However if we re prepred to settle for n effect over nrrow rne of frequencies spectculr enhncements of the mnetic permeility cn e chieved, limited only e the resistivity of the sheets nd y how nrrow nd we re willin to tolerte. /word/pp/wecs/mwires.doc t 3 Ferury 999 pe 4
15 III. AN ISOTROPIC MAGNETIC MATERIAL The structures shown ove ive mnetic properties when the field is lined lon the xes of the cylinders, ut hve essentilly zero mnetic response in other directions. They suffer from nother potentil prolem: if the lternte polristion is considered where the electric field is not prllel to the cylinders, the system responds like n effective metl ecuse current is free to flow lon the lenth of the cylinders. For some pplictions this hihly nisotropic ehviour my e undesirle. Therefore we redesin the system with view to restorin isotropy, nd minimisin purely electricl effects. To this end we need sic unit tht is more esily pcked into rrys thn is cylinder, nd which voids the continuous electricl pth provided y metl cylinder. We propose n dpttion of the split rin structure in which the cylinder is replced y series of flt disks ech of which retins the split rin confiurtion ut in slihtly modified form: see fiure. First we shll clculte the properties of disks stcked in squre rry s shown if fiure 3. This structure is still nisotropic, prolem we shll ddress in moment, ut y elimintin the continuous conductin pth which the cylinders provided, it elimintes most of the electricl ctivity lon this direction. Fiure. Left: pln view of split rin showin definitions of distnces. Riht sequence of split rins shown in their stckin sequence. Ech split rin comprises two thin sheets of metl. The rin shown is scled up version defined y the prmeters shown elow in fiure 3. /word/pp/wecs/mwires.doc t 3 Ferury 999 pe 5
16 Fiure 3. Pln view of split rin structure in squre rry, lttice spcin. The two dimensionl squre rry shown in fiure 3 cn e mde y printin with metllic inks. If ech printed sheet is then fixed to solid lock of inert mteril, thickness, the locks cn e stcked to ive columns of rins. This would estlish mnetic ctivity lon the direction of stckin, the z xis. The unit cell of this structure is shown in fiure 4 on the left. How do we mke symmetricl structure? Strt from the structure just descried comprisin successive lyers of rins stcked lon the z xis. Next cut up the structure into series of sls thickness, mkin incisions in the y z plne nd ein creful to void slicin throuh ny of the rins. Ech of the new sls contins lyer of rins ut now ech rin is perpendiculr to the plne of the sl nd is emedded within. Print onto the surfce of ech sl nother lyer of rins nd stck the sls ck toether in. The unit cell of this second structure is shown in the middle of fiure 4. In the next step third set of sls is produced y cuttin in the x z plne, printin on the surfce of the sls, nd ressemlin. Finlly we now hve structure with cuic symmetry whose unit cell is shown on the riht of fiure 4. Fiure 4. Buildin 3D symmetry: ech successive re-stckin of the structure dds rin to nother side of the unit cell. /word/pp/wecs/mwires.doc t 3 Ferury 999 pe 6
17 Of course n lternte method of mnufcturin this structure would e to strt from set of cues of the inert mteril nd loriously stick rins to their sides efore ssemlin the cues into lttice. The cut nd pste method we suest ove is much more efficient. Now let us clculte the effective permeility. First we need to clculte the cpcitnce etween the two elements of the split rin. We shll ssume: r >> c, r >> d (39) l < r (4) ln c d >> π (4) Under these conditions we cn clculte the cpcitnce etween unit lenth of two prllel sections of the metllic strips: ε c C c = ln = π d πµ c d ln (4) The effective mnetic permeility we clculte on the ssumption tht the rins re sufficiently close toether tht the mnetic lines of force due to currents in the stcked rins, re essentilly the sme s those in continuous cylinder. This cn only e true if the rdius of the rins is of the sme order s the unit cell side. We rrive t: µ eff = = σ + i 3 l l σ c ω rµ + l i 3 l 3 π µ ω C r ω rµ c πω d r 3 ln where σ is the resistnce of unit lenth of the sheets mesured round the circumference. (43) To ive some exmples let us choose convenient set of prmeters: - =. m -3 c =. m -4 d =. m -3 l =. m -3 r =. m (44) Fiures, 3 show the rins drwn to scle. These prmeters do not quite stisfy ll the inequlities, which is difficult to do with resonle numers, ut note tht the inequlities re only importnt to the ccurcy of our formule, not to the functionin of the structure. The resonnt frequency t which µ eff diveres is iven y, 3lc ω = = 7. c 3 π ln d r (45) /word/pp/wecs/mwires.doc t 3 Ferury 999 pe 7
18 or, ω = π 35. GHz (46) If we choose to mnufcture the split rins from lyer of copper, it is esily possile to chieve σ.. Evidently from fiure 5, this produces hihly resonnt structure. Fiure 5. Plot of µ eff for the cuic split rin structure clculted usin the chosen prmeters. Left: for copper rins, σ =. ; riht: for more resistive rins, σ =.. In order to see sustntil effect we hve to increse the resistnce either y incresin the resistivity of the mteril of which the rins re mde, or y mkin them thinner. The sclin of frequency with size cn e deduced from (45) we see tht the resonnt frequency scles uniformly with size: if we doule the size of ll elements in iven structure, the resonnt frequency hlves. Nerly ll the criticl properties re determined y this frequency. IV. ENHANCED NON-LINEAR EFFECTS We hve seen how the ddition of cpcitnce to the structure ives fr richer vriety of mnetic ehviour. Typiclly this hppens throuh resonnt interction etween the nturl inductnce of the structure nd the cpcittive elements, nd t the resonnt frequency electromnetic enery is shred etween the mnetic fields nd the electrosttic fields within the cpcittive structure. To put this more explicitly: tke the split rin structure descried in fiures, 3: most of the electrosttic enery of the cpcitor is locted in the tiny p etween the rins. Concentrtin most of the electromnetic enery in this very smll volume will results in n enormously enhnced enery density. If we wish to enhnce the non-liner ehviour of iven compound, we locte smll mount of the sustnce in the p where the stron electrosttic fields re locted. Since the response scles s the cue of the field mplitude, we cn expect enhncements of the order of the enery density enhncement squred. Furthermore not only does the structure enhnce the non-linerity, it does so in mnner tht is very economicl with the mteril: less tht % of the structure need e filled with the non-liner sustnce. /word/pp/wecs/mwires.doc t 3 Ferury 999 pe 8
19 Note tht there is symmetry etween, on the one hnd the present structures desined to enerte mnetic permeility nd within which we find enhnced electrosttic fields, nd on the other hnd the erlier thin wire structures [,] desined to enerte netive electricl permittivity, nd within which we find enhnced mnetic fields. We shll now clculte the enery density in the cpcitnce etween the two split rins in fiures,3. First we clculte the volte etween the two rins s function of the incident mnetic field, H. V in V out s= s= s= V out V in Fiure 6. The emf ctin round one of the sheets of the split rin in fiure s function of the distnce, s, round the rin. V in denotes the emf on the inner rin, nd V out tht on the outer rin. Note tht this rin is cut t s = so tht the emf is discontinuous. The electric field etween the two hlves of the rin is then of the order, E rin V d (47) We clculte tht, 3li H V = ωcπ r L i 3 O r 3 M P + lσ l ω µ π µ ω C r N Q (48) Hence on sustitutin from (4) nd (47) into (48): E rin 3lµ c i H c dr L ω ln i c d O r c NM QP + lσ 3l ω µ 3 πω r ln d (49) Now we rue tht the electrosttic enery density in the incident electromnetic field is equl to the mnetic enery density, which in turn cn e relted to the electrosttic enery density in the rin. Hence, 3l ε E rin ε π r d ωcπ r = µ µ H lσ i 3 l ve + ω rµ 3 π µ ω C r If we evlute this formul on resonnce we et much simplified formul, (5) /word/pp/wecs/mwires.doc t 3 Ferury 999 pe 9
20 ε Erin ω resonnt enhncement= Q = = µ H ω 3 πω r µ 4lσ dc (5) Let us tke s n exmple the prmeters used to clculte fiure 5, Hence, d =. m σ ω l =. m r =. m Q = R = =. ct = 7. L NM πω r µ 4lσdc O QP (5) = (53) A more detil picture of enhncement s function of frequency is shown in fiure 7. Fiure 7. Enhncement of the enery density of the electric field within the p etween the split rins (see fiures nd 3) for two different vlues of the resistivity of the metl sheet. The correspondin vlues of µ eff re shown in fiure 5. For exmple: em of microwves t 3.4GHz with power flux of 4 wm hs n electric field strenth of the order of 3 Vm in vcuo. If this em were incident on, nd entirely trnsmitted into, our mnetic structure it would enerte field strenth of the order of /word/pp/wecs/mwires.doc t 3 Ferury 999 pe
21 4 Vm in the spce etween the split rins, or of the order of 6 V etween the edes of the two rins: more thn enouh to cuse electricl rekdown in ir! It is evident tht these structures hve considerle potentil for enhncin non-liner phenomen. Furthermore the nonliner medium need only e present in the smll volume within which the enery is concentrted, openin the possiility of usin smll quntities of expensive mteril, nd reducin ny requirements of mechnicl interity tht lrer structure would impose. In pssin we drw n nloy with surfce enhnced Rmn sctterin (SERS), oserved on rouh metllic surfces, typiclly silver surfces. The Rmn sinl from molecules dsored on these surfces my e enhnced y fctors of the order of 6 over tht seen on insultin surfces. The Rmn effect is proportionl to the second power of the electromnetic mode density t the surfce, 3 4 nd it is known tht rouhness cn enhnce the locl mode density y fctors of up to, hence the spectculr Rmn enhncement (see [] for further detils nd references). A very similr locl enhncement tkes plce in our system nd, we expect, cn e exploited in n nloous fshion. In conclusion: we hve shown how to desin structures mde from non-mnetic thin sheets of metl, which respond to microwve rdition s if they hd n effective mnetic permeility. A wide rne of permeilties cn e chieved y vryin the prmeters of the structures. Since the ctive inredient in the structure, the this metl film, comprises very smll frction of the volume, typiclly : 4, the structures my e very liht, nd reinforced with stron insultin mteril to ensure mechnicl strenth, without dversely ffectin their mnetic properties. It is likely tht the structures will e exploited for their ility to concentrte the electromnetic enery in very smll volume, incresin its density y hue fctor, nd retly enhncin ny non-liner effects present. REFERENCES [] J.B. Pendry, A.J. Holden, W.J. Stewrt, I. Youns, Extremely Low Frequency Plsmons in Metllic Meso Structures, Phys. Rev. Lett. vol. 76, pp , 996. [] J.B. Pendry, A.J. Holden, D.J. Roins, nd W.J. Stewrt, Low Frequency Plsmons in Thin Wire Structures, J. Phys. [Condensed Mtter], vol., pp , 998. [3] D.F. Sievenpiper, M.E. Sickmiller nd E. Ylonovitch, 3D Wire mesh photonic crystls Phys. Rev. Lett., vol. 76 pp , 996. [4] D.F. Sievenpiper, E. Ylonovitch, J.N. Winn, S. Fn, P.R. Villeneuve, nd J.D. Jonnopoulos, 3D Metllo-Dielectric Photonic Crystls with Stron Cpcitive Couplin etween Metllic Islnds, Phys. Rev. Lett., vol. 8, pp 89-83, 998. [5] J.B. Pendry Clcultin Photonic Bnd Structure J. Phys. [Condensed Mtter], vol. 8 pp 85-8, 996. [6] D. Pines nd D. Bohm, A Collective Description of Electron Interctions: II Collective vs Individul Prticle Aspects of the Interctions, Phys. Rev. vol. 85 pp , 95. [7] D. Bohm nd D. Pines, A Collective Description of Electron Interctions: III Coulom Interctions in Deenerte Electron Gs, Phys. Rev. vol. 9. pp 69-65, 953. [8] E. Ylonovitch, Inhiited Spontneous Emission in Solid Stte Physics nd Electronics, Phys. Rev. Lett., vol. 58, pp 59-6, 987. [9] E. Ylonovitch, Photonic Bnd Gp Crystls, J. Phys.: [Condensed Mtter], vol. 5, pp , 993. [] S. John, Stron Loclistion of Photons in Certin Disordered Lttices, Phys. Rev. Lett., vol. 58, pp , 987. [] F.J. Grci Vidl nd J.B. Pendry, Collective Theory for Surfce Enhnced Rmn Sctterin, Phys. Rev. Lett., vol. 77, pp 63-66, 996. /word/pp/wecs/mwires.doc t 3 Ferury 999 pe
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Searching for AMD's Triple-Core Phenom
title=Manufacturing Tricks} When it first introduced the tri-core Phenom last year, AMD planned to market the processor as a compromise between the full-blown performance of its quad-core chip and an upgrade from its older line of dual-core Athlon processors. This meant the tri-core could appeal to both PC enthusiasts who want more processing power for their desktops but not at the price of a quad-core, and for enterprise users who need a more robust desktop for tasks involving content creation applications.In the build up to the tri-core Phenom, AMD has not offered a full explanation about how it created such a chip. Whitman explained in an e-mail that this Phenom takes advantage of AMD's Direct Connect Architecture, which directly connects the cores together and allows for better communication between the integrated memory controller and the I/O. "AMD's Direct Connect Architecture and true native multicore design allow for direct communication between cores, integrated memory controller, and I/O?ö?ç?Âreducing unnecessary bottlenecks," Whitman wrote. "And thus, this approach enables us to deliver varying core configurations?ö?ç?Âincluding dual, triple and quad." Some industry analysts believe that AMD is merely shutting off one core with its quad-core Phenom desktop and repackaging it as a new chip. If that's the case, it should help the company get better yields from its manufacturing process where flawed chips with defects?ö?ç?Âin this case at least one inoperable processing core within a quad-core chip?ö?ç?Âare common. Dean McCarron, an analyst with Mercury Research, believes that the triple-core Phenom is more than just interesting marketing from AMD and that the company could create a tactical position for itself through aggressive pricing of the processor. "This buys them a lot of flexibility," said McCarron. "AMD as a company has a history of coming up with these sort of tactical devices and they use them as an advantage against Intel." McCarron said he would not be surprised if Intel countered AMD with offering a high-performing dual-core processor or aggressively dropping the price of one of its desktop quad-core processors at some point.
Manufacturing Tricks
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Private In-Home and Online HSPT Tutoring in Salem, MA
Receive personally tailored HSPT lessons from exceptional tutors in a one-on-one setting. We help you connect with in-home and online tutoring that offers flexible scheduling and your choice of locations.
Recent Tutoring Session Reviews
"The student and I worked through the Writing section of the lesson. He demonstrates good understanding of the English both spoken and written language knowing many of the rules he needs to use."
"Introductory session: We went over practice tests 1-3 for Literature on a website. We went over Pre-Columbian practice test for US History on a website."
"The student and I began this session by discussing his updated list of examples for the essay. After making another revision, we decided that it was a very strong and well-rounded list. Next, we reviewed the essay that she wrote for homework. Then, we began working on the math section. We discussed the content areas covered in chapters 15 and 16, talked about general approaches to the math section, and practiced two important problem-solving strategies. After that we began completing some practice problems together, where the student did great! Overall it was a solid session."
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"Lights of Roma from a Tiber Dinner Cruise" Top 5 Page for this destination Tevere - Tiber River - Bridges Tip by icunme
Tevere - Tiber River - Bridges, Rome: 41 reviews and 75 photos
You can enjoy a different night dining at the River Cafe aboard the Agrippina Maggiore, the Queen of Battelli di Roma's fleet. The traditional Italian cuisine, the elegant and cordial atmosphere and the background music are all the ingredients for a lovely evening as you view the lights of Roma floating by.
The tour lasts 2 hours and 15 minutes. Service operates on Thurs, Fri, Sat except for weather conditions that prevent a cruise and departs between 9 p.m. from Castel Sant Angelo. The boat is available on request for exclusive events even during other days of the week.
53 Euro per person excluding beverages - many options available on different tours.
Disabled people can access the service.
Address: Flowing through the center of Rome
Directions: Dock at Castel Sant Angelo
Phone: 066789361
Website: http://italiannotes.com/bridges-in-rome/
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Jun 05, 2007 · What happened to tracy thurman? ... How is her son and is Buck out ... This was the only action taken by the judge despite the fact that Charles "Buck ... - read more
Charles 'Buck' Thurman. Motuzick, ... OLD€TINCH€GRIST€MILL€RESTORED€BY€KENNETH€KING. ... Is Charles Buck Thurman Out Of Ja? ASKIVER. Contact Us; - read more


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Tamil Nadu Public Service Commission Recruitment @Deputy Collector / Deputy Superintendent of Police on 09 Aug 2015 @ Tamil Nadu
|Company Name
|Tamil Nadu Public Service Commission Recruitment
|Company Website
|Deputy Collector / Deputy Superintendent of Police
|Any degree
|No of Vacancy
|Rs.15600-39100/-+G.P Rs.5400/-p.m.
|Job Location
|Tamil Nadu
|Last date to apply
|09 Aug 2015
Details of Tamil Nadu Public Service Commission TNPSC 2015 Deputy Collector / Deputy Superintendent of Police / Assistant Commissioner / District Registrar Recruitment
Applications are invited only through online mode upto 9.8.2015 for direct recruitment to the vacancies in the following posts included in CCS-I Examination (Group-I Services):- Sl. No Name of the Post and Post Code Name of the Service and Code No.(001) No. of vacancies Scale of pay 1 Deputy Collector (Post Code: 1001) Tamil Nadu Civil Service 19 Rs.15600-39100/- +G.P Rs.5400/- (PB-3) 2 Deputy Superintendent of Police (Category – I) (Post Code: 1002) Tamil Nadu Police Service 26 3 Assistant Commissioner (C.T.) (Post Code:1003) Tamil Nadu Commercial Taxes Service 21 4 District Registrar (Post code: 1005) Tamil Nadu Registration Service 8
(A) AGE (as on 01.07.2015) :
(i) "Others" (i.e.,) candidates not belonging to SC's, SC(A')s, ST's, MBC's/DC's, BC's and BCM's who have put in 5 years and more of service in the State / Central Government are not eligible to apply even if they are within the age limit. (ii) The Technical and Non-Technical Staff of TANSI who have faced retrenchment and have not been absorbed in the Government Corporations/ Undertakings (evidence should be produced) may also apply, if they are otherwise qualified except age and the relevant age rule will be relaxed by the Government in their favour if they come up for selection. (iii) Instructions given with regard to maximum age limit under para. 5 of the 'Instructions to the candidates' will not apply to this recruitment.
Candidates should possess the following or its equivalent qualification:- Candidates should possess a degree of any of the Universities incorporated by an Act of the Central or State Legislature in India or any other Educational Institutions established by an Act of Parliament or declared to be deemed as a University under Section 3 of the University Grants Commission Act, 1956.
(i) "The qualification prescribed for these posts should have been obtained by passing the required qualification in the order of studies 10th + HSC+U.G. degree.
(ii) Certificate of Physical Fitness :
Candidates selected for appointment to the post included in Group-I Services will be required to produce a certificate of physical fitness in the form prescribed below:- Name of the Post Minimum Age (should have completed) Maximum Age (should not have completed) SC's, SC(A)'s, ST's, MBC's/DC's, BC's, BCM's and DW's of all castes "Others" i.e candidates not belonging to SC's, SC(A)'s, ST's, MBC's/DC's, BC's and BCM's 1.For all the posts except the post of Assistant Commissioner (C.T) 21Years 35 Years 30 Years
(iii) The candidates, who have written the final year degree examination, may also apply for the Preliminary Examination for direct recruitment to the posts included in Group-I Services, subject to the condition that they should produce proof of having passed the degree examination when admitted to the Main Written Examination, failing which they will not be admitted to the Main Written Examination.
The candidates, who have passed the final professional M.B.B.S or any other Medical Examination, but have not completed the internship, may also apply to the Preliminary Examination for direct recruitment to the posts included in Group-I Services provided they should submit when admitted to the main written examination a copy of certificate from the concerned authority of the University/Institution that they had passed the requisite final professional medical examination. In such cases, the candidates will be required to produce at the time of their certificate verification / oral test, original degree or a certificate from the concerned competent authority of the University/ Institution that they had completed all requirements (including completion of internship) for the award of the degree.
Candidates claiming equivalence of qualification to the prescribed qualification should upload evidence for equivalence of qualification in the form of G.O. issued prior to the date of this notification when called for. Failing which their application will be summarily rejected. The G.O's issued regarding equivalence of prescribed qualification after the date of this notification will not be accepted. (Refer para. 10 of the 'Instruction to the candidates') Provided that, other things being equal, preference will be given to the candidates, who possess the qualification mentioned against each of the following posts:- Sl. No Name of the Post Qualification
- Deputy Superintendent of Police (Category – I) A degree or diploma in criminology and forensic science and also to those who possess national Awards for physical efficiency. 2. Assistant Commissioner (C.T.) First Preference _ A degree both in commerce and law together with a diploma in taxation laws. Second Preference _ A degree both in commerce and law. Third Preference _ A degree either in commerce or law together with a diploma in taxation laws. Fourth Preference _ A degree either in commerce or law. Sl. No. Name of the Post Standard of Vision Prescribed Form of Certificate of Physical Fitness 1. Deputy Collector Standard III or better Form prescribed for 2. Executive Posts. Assistant Commissioner (C.T.) 3. District Registrar Form prescribed for the posts other than Executive and Ministerial.
- Assistant Commissioner (C.T.) (i) For candidates possessing any degree 21 Years 35 Years 30 Years (ii) For candidates possessing B.L. degree of any University or Institution recognized by the University Grants Commission. 21 Years 36 Years 31 Years
Dates to remember
Last Date to Apply for this job : 09/08/2015
Last date for payment of Fee through Bank or Post Office : 11-8-2015
Date of Preliminary examination : 08-11-2015 10.00 A.M. to 1.00 P .M.
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BC Coastal Recreation Kayaking and Small Boat Atlas
Volume Two: British Columbia's West Vancouver Island: A Companion to the Wild Coast Kayaking and Recreation Guides
By (author) John Kimantas
Format: Paperback / softback
Normal Price: $76.12
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BC Coastal Recreation Kayaking and Small Boat Atlas by John Kimantas
Book Description"An essential tool for kayaking British Columbia's coast." BC Coastal Recreation, Kayaking and Small Boat Atlas, in two volumes, provides splashproof and manageably sized collections of detailed maps of British Columbia's shorelines. Numerous land-based features are identified, among them campsites and launch locations. These colorful books are ideal for kayakers who want a detailed overview in a format much easier to use than bulky charts. Recreational boaters will also appreciate the convenience of these maps. Together these two volumes cover every mile of British Columbia's south coast in a format, and with a degree of detail, not currently available. They augment the "Wild Coast" series of guidebooks (also by John Kimantas), with links that provide information not supplied by the maps. Volume 1, South BC Coast and East Vancouver Island This volume provides an overview of British Columbia's south coast from Victoria to Port McNeill, and from Howe Sound to the Broughton Islands. Volume 2, West Vancouver Island This volume provides an overview of West Vancouver Island from Sooke to Port Hardy.
Buy BC Coastal Recreation Kayaking and Small Boat Atlas book by John Kimantas from Australia's Online Bookstore, Boomerang Books.
Book DetailsISBN: 9781552858653
(359mm x 284mm x 13mm)
Imprint: Whitecap Books
Publisher: Whitecap Books
Publish Date: 1-Jan-2010
Country of Publication: United States
Books By Author John Kimantas
Wild Coast, Volume 2, Paperback / softback (January 2010)» View all books by John Kimantas
A well-illustrated guide to coastal BC north of Vancouver Island, including history and geography. Distinct areas are identified with attractions, ecoloogy, amenities, place names, landing and camp sites.
» Have you read this book? We'd like to know what you think about it - write a review about BC Coastal Recreation Kayaking and Small Boat Atlas book by John Kimantas and you'll earn 50c in Boomerang Bucks loyalty dollars (you must be a member - it's free to sign up!)
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Australian policy makers were publicly frustrated by the currency's stubborn strength when commodities tumbled earlier this decade. Now they're conspicuously quiet as it fails to keep pace with resurgent resource prices.
Since the end of June, JPMorgan Chase & Co.'s real effective exchange rate for the Aussie has risen 4 percent, while Westpac Banking Corp.'s Australian export commodity index has soared by 43 percent. The mismatch is another reason why central bank Governor Philip Lowe is comfortable sitting on his hands: he's getting an easing of financial conditions without having to touch the monetary policy lever.
Indeed, money markets now see little chance the Reserve Bank of Australia will cut interest rates from the current record-low 1.5 percent next year; in fact they're pricing in some possibility of a hike in November and December.
``Normally, it's a drop in the currency that gives a bit more stimulus to the economy; but in this case it has gone up -- just by not as much as commodity prices -- and that's delivering the boost,'' said Sally Auld, head of fixed-income and currency strategy for Australia at JPMorgan.``Given how important the whole terms of trade dynamic has been for the economy and the currency, it makes sense for the RBA just to watch and wait.''
Australia's economy is enjoying an unexpected windfall from this year's almost 300 percent surge in coking coal prices after output from China, the world's biggest miner, tumbled amid government pressure to cut overcapacity. Meanwhile the price of iron ore, Australia's biggest export, has jumped 70 percent over the period. That's sparked a rebound in the terms of trade, or the ratio of export prices to import prices, a key determinant of national income that had been declining for 2 1/2 years.
Skeptics say that coal is unlikely to sustain its rally, citing concerns about bad weather shutting production in the key state of Queensland this quarter and next as factors shoring up the price. They also point to the RBA failing to upgrade its economic growth and inflation forecasts at this month's quarterly review, suggesting it has little faith in the longevity of the spikes.
But in the meantime, Australia is enjoying strong services exports from its southeast together with a windfall from commodity prices in its north and west, which is helping to rapidly improve the country's trade picture. That's likely to keep the RBA on the sidelines for some time yet.


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For Calgary skate shop The Source, the almost 20 year old store has looked to Daniel Curtis to create their Fine Dining series of decks. Shot with all real food which has passed through the gullet of Daniel Curtis, the series is a fun play on the theme of fine dining as it encompasses designs including hot dogs, donuts, fries and burgers. Look for the decks to hit sourceboards.com
Source: Kitsune Noir


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Listen to David Guetta Radio on iHeartRadio
David Guetta has new music on the way. The French electronic music star dropped the news that a single will be arriving next Monday October 6th, and his new album is set to drop on November 24th.
Last month, he told Billboard that the album will be "completely different from anything [he's] ever done before." He hinted that there will be featured artists to provide vocals for his electronic tunes, but "none that you'd expect" to sing with him. Guetta says the album has now been in the works for three years.
Photo: Getty Images


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Coolest Bumble Bee Halloween Costume 2
by Saatchi B
This Halloween I really wanted to be a Bumble Bee. Because I'm 14, and most bumble bee Halloween costumes are for little kids, I tried finding a costume that was right for me. The only ones that were not super scandalous were way too overpriced.
Because I couldn't find a costume, I decided to make it. I finally chose to make a tutu, and then use different black and yellow pieces of clothing.
Materials I used:
2.5 yards of Yellow Tulle (fabric)
2 yards of Black Tulle (fabric)
28 inch waistband
Yellow Ribbon
Rest of Costume:
Pair of Black Tights
Long Yellow Softball Socks
Yellow Duct Tape
Black Tee/Thermal
First, I made the tutu. I found the directions on youtube, and it turned out amazing. (For the tutu (if anyone's making it) I used the pattern of 2 yellow then 2 black then 2 yellow...After the tutu was complete, I made the wings, I just shaped little pieces of wire and then on Halloween morning taped them on (with the yellow duct tape).
The tape striped on the shirt was the most complicated part of the costume. First I tried to put the tape on the shirt, but then when I put the shirt on, it was too tight. So, I waited till the morning of Halloween to tape my shirt. I wore the black tights with the yellow socks and the black shirt with my tutu. I striped the tape horizontally on the shirt, and all down the back. I tried it on the tights too, but it looked a little bit weird, so I didn't. Voila!
Comments for Coolest Bumble Bee Halloween Costume 2
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Coolest Bumble Bee Baby Costume 3
by Kristina
(Colorado, USA)
I made this Bumble Bee Baby Costume for my 18mo son. I took a white onesie and dyed it yellow by adding turmeric spice to a bowl of water and soaking for several hours. Then I hung it to dry thoroughly to set the color, rinsed it well, and dried it again. I used electrical tape for the black bee stripes, three strips of tape for each wide stripe.
However, the onesie didn't stretch with tape on it and was hard to get on and off, so black fabric paint might have worked better. I ended up having to reposition the tape with my son wearing the costume. I used the black tape for the stinger too.
The wings were cut out of a scrap of window screen fabric and stuck in under the electrical tape. I made them kind of small so my son wouldn't grab and pull on them. He wore black pants with this.
Comments for Coolest Bumble Bee Baby Costume 3
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Coolest Bumble Bee Girl's Halloween Costume 7
by Kristie
(Pittsburgh, PA)
Homemade Bumble Bee Girl's Costume
I took black and yellow felt and sewed strips of it together and then eyeballed the general shape of the shirt and cut those out, along with black lining. One of the shoulders was left open and velcros together. I sewed that all together and stuffed the costume with batting. I took hard felt and cut out the wing shapes and sewed that on.
For the antenae I sewed a tube of yellow felt that was left over, pinched it together around a pipe cleaner that I attached a ball on the end, tying the pinch with a fabric strip. This Homemade Bumble Bee Girl's Costume was very easy to make.
Return to Other Homemade Costumes 2.


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This post may contain affiliate links. View the full disclosure statement for more details. Sign up for the Schooling a Monkey newsletter to gain access to more hands-on activity ideas!
Hands-On Activities to Make Homeschooling Fun
This week's edition of the Homeschool Showcase is all about hands-on activities to make homeschooling fun. I tend to get bogged down in the day-to-day lessons and often forget to add hands-on activities to make homeschooling fun, so I am excited to read the posts in this week's showcase!
My girls are both obsessed with dinosaurs right now, so they would love this project Hatch Dinosaur Eggs With Science from Steam Powered Family.
In Texas, the weather is great right now, so we will definitely be using this Free Nature Explorer Guide from PK1HomeschoolFUN.
Multiplication is our life right now with Monkey. We came up with this hands-on math game to help her memorize her multiplication facts.
For a bit more practical activities, Dianna from the Kennedy Adventures is sharing How they make time for music lessons in their homeschool.
Perfect for this time of year, here are some hands-on activities to make homeschooling fun by Teaching Kids Gratitude.
One of our favorite fall-themed crafts was when we made these Rice Crispy treat owls a few years ago. These would look so cute on a Thanksgiving table or at a fall party.
It's almost time for winter-themed science experiments. The experiments on this list are perfect hands-on activities to make homeschooling fun for preschoolers.
Want a fun and delicious hands-on activity? These Easy Turkey Cupcakes are perfect!
Do you spend time learning about character in your homeschool? These Free Character Association Flash Cards are perfect for creating your own hands-on activities to make homeschooling fun.
Have you ever made a play store? We use ours to help fortify Monkey and Bo's math skills.
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Family in Rapid City
Our daycare provider is moving the end of May. Our son will be 14 months old at that time. He's a very sweet guy. We live on the West side and would like to find care for him near us. We pay through automatic payments so there's never any hassle.
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Lightweight and durable drywall is used for many kinds of finishing: they can coat the walls of it, you can create partitions, build ceilings.
For any work with this material, you must create a framework of special profiles, which are attached lists.
Profiles for gypsum boards arefixing and guide elements which serve for the frame structure. Typically, the profiles are manufactured from metal, most frequently made of galvanized steel - durable and lightweight material. To manage the work with plasterboard without profiles can, if need be lined wall - simply glue the sheets to the surface, but in this case the quality of work is poor, because the guides allow to achieve a perfectly flat surface, attach the design rigidity.
Types of profiles for plasterboard
There are several different types of profilesdrywall, their diversity, and various applications can confuse beginners. For major works with this material is enough to have an idea of a few main types of profiles. This guides the standard frame depth of 40 millimeters and a width varying from 50 to 100 millimeters. They can be used for different types of work, including finishing of walls or ceiling.
There are special ceiling railsDevice intended for the construction of suspended ceilings. These enclosed ceiling profiles, they can be secured by anchors or direct hangers to the ceiling and create a finished frame for attaching drywall. For walls and create partitions using plasterboard wall or rack-mount profiles, which are fixed to the guide rails. The price of these elements depends on the width and the material from which they are made.
Corner profiles serve for alignment angles, the flashing - alignment walls.
Fasteners Drywall
The metal frame is attached to a wall or othersurface by means of special fastening elements. The most frequently used plugs of plastics or metal. You can use direct hangers, they are installed on marked lines with a pitch of about 60 cm. It also can be Connectors "crab", anchor clips, duplex connectors, self-tapping screws, wood screws. Selection of an appropriate fixture will depend on operation - for example, when the device is used to flatten the ceiling connectors such as "crab", they allow setting sheets of the same level.
If the ceiling has a length of more than four meters, it is necessary to use an extension cord.
Sometimes, instead of fastening elementsProfile segments are used the same guide, their bent-shaped "T" and fixed to wall anchors, and by means of screws which are screwed on the frame. Skilled craftsmen say it is the most rigid structure.


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Outrageous Acts and Everyday Rebellions
Outrageous acts and everyday rebellions by Gloria Steinem A bestselling first collection of humorous and insightful essays by a luminary of the women's liberation movement These essays from Gloria Steinem's first three decades of work offer a portrait of.... Published date on: 2012-05-15 with total page: 426 pages. Publisher of Outrageous Acts and Everyday Rebellions is Open Road Media.
A bestselling first collection of humorous and insightful essays by a luminary of the women's liberation movement These essays from Gloria Steinem's first three decades of work offer a portrait of a woman who was not only one of the savviest leaders of the women's liberation movement, but also a profoundly humane thinker with a wide-ranging intellect and irresistible wit. In "If Men Could Menstruate," Steinem engages readers in a flight of imagination as incisive as it is hilarious. She offers first-person journalism in her underground exposé "I Was a Playboy Bunny," provides heartbreaking memoir in the story of her mother's struggles in "Ruth's Song," and stakes important positions in feminist theory in "Erotica vs. Pornography." This is Steinem at her most provocative—and most compassionate.
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Latest Updates
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Maps The historical war map.
About this Item
- Title
- The historical war map.
- Contributor Names
- Asher & Co.
- Created / Published
- Buffalo, N.Y., E. R. Jewett & Co., engravers, c1862
- Subject Headings
- - United States--History--Civil War, 1861-1865--Maps
- - United States
- Notes
- - Scale ca. 1:3,250,000.
- - LC Civil War Maps (2nd ed.), 20
- - Map of southeastern United States showing forts and battlefields, railroads, state boundaries, rivers, and town.
- - Includes brief descriptions of the principal engagements. The last battle described is the capitulation of Norfolk, May 10, 1862.
- - Description derived from published bibliography.
- - Available also through the Library of Congress web site as raster image.
- Medium
- 1 map, col., 62 x 87 cm.
- Call Number/Physical Location
- Repository
- Library of Congress Geography and Map Division Washington, D.C. 20540-4650 dcu
- Digital Id
- http://hdl.loc.gov/loc.gmd/g3701s.cw0020000
- Library of Congress Control Number
- 99447066
- Online Format
- image
- LCCN Permalink
- https://lccn.loc.gov/99447066
- Additional Metadata Formats
- MARCXML Record
- MODS Record
- Dublin Core Record
Part of...
ContributorsAsher & Co.
LocationUnited States
SubjectsCivil War
United States
Rights & Access
Rights assessment is your responsibility.
The maps in the Map Collections materials were either published prior to 1922, produced by the United States government, or both (see catalogue records that accompany each map for information regarding date of publication and source). The Library of Congress is providing access to these materials for educational and research purposes and is not aware of any U.S. copyright protection (see Title 17 of the United States Code) or any other restrictions in the Map Collection materials.
Note that the written permission of the copyright owners and/or other rights holders (such as publicity and/or privacy rights) is required for distribution, reproduction, or other use of protected items beyond that allowed by fair use or other statutory exemptions. Responsibility for making an independent legal assessment of an item and securing any necessary permissions ultimately rests with persons desiring to use the item.
Credit Line: Library of Congress, Geography and Map Division.
More about Copyright and other Restrictions
For guidance about compiling full citations consult Citing Primary Sources.
Cite This Item
Citations are generated automatically from bibliographic data as a convenience, and may not be complete or accurate.
Chicago citation style:
Asher & Co. The Historical War Map. Buffalo, N.Y., E. R. Jewett & Co., engravers, 1862. Map. Retrieved from the Library of Congress, https://www.loc.gov/item/99447066/. (Accessed February 24, 2017.)
APA citation style:
Asher & Co. (1862) The Historical War Map. Buffalo, N.Y., E. R. Jewett & Co., engravers. [Map] Retrieved from the Library of Congress, https://www.loc.gov/item/99447066/.
MLA citation style:
Asher & Co. The Historical War Map. Buffalo, N.Y., E. R. Jewett & Co., engravers, 1862. Map. Retrieved from the Library of Congress, <https://www.loc.gov/item/99447066/>.


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Adams Employee Payroll Record Book
2-Part, 4-3/16" x 7-3/16", 50 Sets Per Book, 12 Books Per Carton
Item #: ABFD4740
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Description: Tracks hours worked, gross earnings, deductions and net pay. 2-part carbonless (white, canary paper sequence). 50 sets per book. Consecutively numbered.
- Tracks hours worked, gross earnings, deductions, and net pay
- 2-part carbonless (white, canary paper sequence)
- 50 sets per book
- Consecutively numbered
- Made in the USA
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