IC MR ) ▁since ▁ 2 0 0 5 . ▁ ▁He ▁has ▁made ▁contributions ▁to ▁hom ogen ization ▁theory , ▁theoretical ▁models ▁of ▁tur bul ence , ▁st ochastic ▁partial ▁differential ▁equations , ▁electronic ▁structure ▁analysis , ▁mult isc ale ▁methods , ▁computational ▁fluid ▁dynamics , ▁and ▁weak ▁K AM ▁theory . ▁In ▁the ▁study ▁of ▁rare ▁events , ▁he ▁and ▁collabor ators ▁have ▁developed ▁the ▁string ▁method ▁and ▁transition ▁path ▁theory . ▁ ▁In ▁mult isc ale ▁model ing , ▁he ▁and ▁collabor ators ▁have ▁developed ▁the ▁heter ogeneous ▁mult isc ale ▁methods ▁( H MM ). ▁He ▁has ▁also ▁made ▁significant ▁contributions ▁to ▁the ▁mathematical ▁understanding ▁of ▁the ▁micro scop ic ▁foundation ▁to ▁the ▁macro scop ic ▁theories ▁for ▁sol ids . ▁ ▁Awards ▁He ▁received ▁President ial ▁Early ▁Career ▁Award ▁in ▁Science ▁and ▁Engineering ▁in ▁ 1 9 9 6 , ▁and ▁F eng ▁K ang ▁Prize ▁in ▁Scient ific ▁Comput ing ▁in ▁ 1 9 9 9 . ▁ ▁He ▁was ▁the ▁recip ient ▁of ▁I CI AM ▁Coll atz ▁Prize ▁at ▁the ▁ 5 th ▁International ▁Congress ▁of ▁Indust rial ▁& ▁App lied ▁Math ▁for ▁his ▁work ▁on ▁industrial ▁and ▁applied ▁mathematics , ▁the ▁Ralph ▁E . ▁Klein man ▁Prize ▁in ▁ 2 0 0 9 , ▁and ▁the ▁The odore ▁von ▁K á rm án ▁Prize ▁in ▁ 2 0 1 4 . ▁He ▁was ▁elected ▁as ▁a ▁fellow ▁of ▁Institute ▁of ▁Physics ▁in ▁ 2 0 0 5 , ▁a ▁fellow ▁of ▁SI AM ▁in