FEATURE-BASED CRYSTAL CONSTRUCTION IN COMPUTER-AIDED NANO- DESIGN

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1 Poeedings of IDET/IE 008 SME 008 Intentionl Design Engineeing Tehnil onfeenes & omputes nd Infomtion in Engineeing onfeene ugust New Yok ity NY US DET FETURE-SED RYSTL ONSTRUTION IN OMPUTER-IDED NNO- DESIGN heng Qi nd Yn Wng Deptment of Industil Engineeing & Mngement Systems Univesity of entl Floid Olndo FL 386 STRT Poviding nno enginees nd sientists effiient nd esyto-use tools to ete geomety onfomtions tht hve minimum enegies is highly desible in mteil design. Reently we developed peiodi sufe model to ssist the onstution of nno stutues pmetilly fo omputeided nno-design. In this ppe we pesent fetue-bsed ppoh fo ystl onstution. The poposed ppoh stts to ete models of bsi fetues by the ide of peiodi sufes followed by opetions between bsi fetues. The gol is to intodue pid onstution method fo omplex ystl stutues.. INTRODUTION ompute-ided nno-design (ND) is n extension of ompute bsed engineeing design tditionlly t bulk sles to nno sles. The genel tget of modeling nd simultion in nnomteil design is to seh stble nd elizble stutues nd onfomtions with the miniml totl system enegy. Geomety optimiztion is the entl theme in most of the nnosle simultions. Fo the widely used lol seh lgoithms simultion esults e sensitively dependent on the initil onfomtion. Methods tht llow fo the effiient onstution of initil geometies tht e esonbly lose to globl optiml solutions e impotnt to impove both onvegene te nd uy of pedition. Thus enbling effiient stutul desiption nd editing is one of the key eseh issues in ND. t the moleul sle pmeti modeling mehnisms of ptile ggegtes e needed to suppot pid onstution nd modifition of geometies. t the meso sle supe-poous stutues with high sufevolume tios in ntul nd mn-mde mteils lso need effetive geometi desiptions. With the obsevtion tht hypeboli sufes exist in ntue ubiquitously nd peiodi fetues e ommon in ondensed mteils we eently poposed n impliit sufe modeling ppoh peiodi sufe (PS) to epesent geometi stutues in nno sles [ ]. Peiodi sufes e eithe loi o foi. Loi sufes e fitionl ontinuous sufes tht pss though disete ptiles in 3D spe whees foi sufes n be looked s isosufes of potentil o density in whih disete ptiles e enlosed. The model llows fo pmeti onstution fom tomi sle to meso sle. Reonstution of loi sufes fom ystls [3] nd sufe degee opetions to suppot fine-gined modeling [45] wee lso studied. In this ppe we poposed new fetue-bsed ppoh to ete ystl stutues bsed on the PS model. Fetue hs been extensively used in tditionl ompute-ided design (D). It is the bsi opetionl unit tht hs engineeing o funtionl implitions. We extend the peviously developed PS geometi model nd define nnosle fetues whih epesent some ommonly used stutues nd pttens in mteil design. This new fetue-bsed ystl modeling ppoh is to inese the effiieny of ystl model onstution whih is ptiully impotnt to design omplex nno mteil systems in the futue. In the eminde of the ppe Setion gives bief oveview of elted wok in moleul sufe modeling. Setion 3 desibes the bsis of the peiodi sufe model. Setion 4 defines some bsi fetues of PS models fo ystls nd Setion 5 pesents methods of fetue opetions.. MOLEULR SURFE MODELING Fo visuliztion pupose thee hs been some eseh on moleul sufe modeling to visulize moleul stutues [6]. Lee nd Rihds [7] fist intodued solvent-essible sufe the lous of pobe olling ove Vn de Wls sufe to epesent boundy of moleules. onnolly [8] pesented n nlytil method to lulte the sufe. opyight 008 by SME

2 Reently son [9] epesented moleul sufes with - spline wvelet. Edelsbunne [0] desibed moleules with impliit-fom skin sufes. jj et l. [] epesented solvent essible sufes by NURS (non-unifom tionl - spline). u nd Woo [] studied the topologil hnges of momoleules duing folding with the id of ibbons. Ryu et l. [3] onstuted NURS moleul sufes by the id of Euliden Voonoi digms. Zhng et l. [4] onstuted impliit solvtion sufes fom the Gussin kenel. These eseh effots onentte on visuliztion of moleules whees onstution suppot of moleul nd tomi stutues fo design pupose e not onsideed. We eently poposed peiodi sufe model to onstut nno stutues pmetilly. 3. PERIODI SURFE peiodi sufe (PS) is genelly defined s L M T ( πκ ( p ) 0 ( ) μ os () l m T whee κ is the sle pmete p l m [ m bm m θm ] is bsis veto suh s one of e e e e e e e e e e e } { e () 3 whih epesents bsis plne in the 3-spe E T [ x y z w] is the lotion veto with homogeneous oodintes nd is the peiodi moment. We usully μ lm ssume w if not expliitly speified. The degee of () in Eq. () is defined s the numbe of unique peiodi bsis vetos in set { p m } deg( ( )): { p m }. The sle of () is defined s the numbe of unique sle pmetes in set { κ l } s( ( )): { κ l }. We usully ssume the sle pmetes e ntul numbes ( κ N ). Eh bsis veto l 3 n be egded s set of pllel D subspes in E whih plys n impotnt ole in intetive mnipultion of PS models. 3 The lotions of toms o ptiles in the E spe n be detemined by thei simultneous ppenes in thee o moe subspes defined by peiodi sufes. Tiling is the poess of egully subdividing nd disetizing the spe. One of the ppohes fo tiling is by intesetion. Finding the intesetion mong ( 0 ( 0 nd ( 0 is 3 to solve the onstint ( ) ( ) + ( ) + ( ) 0 (3) lm 3 l m P sufes n be used to build ge-like stutues suh s Sodlite minels whih e widely used s moleul sieves nd tlysts in pollution ontol detegent mnuftuing nd othe fields. Figue illusttes tiling by intesetion between P sufe with two Gid sufes to ete Sodlite fmewok. (b) P sufe φ ( ) 0 () Gid sufe ( ) 0 () Sodlite lttie of 4- sided ges. Veties oespond to Si (l) nd edges epesent Si-O-Si (Si-O-l) bonds φ X (d) Gid sufe φ ( ) 0 (e) Sufe intesetion X Figue. Tiling by intesetion of P sufe with Gid sufes to ete Sodlite fmewok 4. SI FETURES The bsi fetues e the fundmentl building bloks fo omplex stutues. In ystllogphy it is well known tht thee e fouteen unique vis ltties in thee dimensions to epesent bsi ystl stutues [5 6]. They e simple ubi body-enteed ubi fe-enteed ubi simple othohombi bse-enteed othohombi body-enteed othohombi fe-enteed othohombi simple tetgonl body-enteed tetgonl simple monolini bse-enteed monolini tilini hombohedl nd hexgonl. ll ystlline mteils eognized until now (not inluding qusiystls) fit in one of these ngements. We onside these fouteen unique spe ltties s bsi fetues. onside the bsi fetues in unit blok domin D [ 05. x y z 05.] (4) y mens of the intesetion opetion mong thee peiodi sufes ll of the fouteen bsi fetues n be effiiently built s shown in Figue. opyight 008 by SME

3 ubi ody-enteed Fe-enteed Othohombi se-enteed ody-enteed Fe-enteed b b b b b b b b Tetgonl Monolini ody-enteed se-enteed γ γ β β α α α 90 β γ 90 α 90 β γ 90 Tilini Rhombohedl Hexgonl γ γ α β α β α β γ 90 α β γ 90 Figue. Fouteen bsi ystl fetues 3 opyight 008 by SME

4 ystl Stutue Impliit Peiodi Sufe Model ubi os ( π x) + os ( πy) + os ( πz) 0 ody-enteed ubi Fe-enteed ubi Othohombi se-enteed Othohombi ody-enteed Othohombi Fe-enteed Othohombi Tetgonl ody-enteed Tetgonl Monolini se-enteed Monolini Tilini Rhombohedl os ( π( x y+ 0.5)) + os ( π( x+ y+ 0.5) + os ( π( y+ z+ 0.5) 0 os ( π( x+ y+ z)) + os ( π( x+ y+ z)) + os ( π( x y+ z) 0 os ( πx/ ) os ( πy/ b) os ( πz/ ) b os ( π( / / 0.5)) os ( π( / / 0.5) os ( π / ) 0 x y b+ + x + y b+ + z b os ( π( / / 0.5)) os ( π( / / 0.5) os ( π( / / 0.5)) 0 x y b+ + x + y b+ + y b+ z + b os ( π( / / / )) os ( π( / / / )) os ( π( / / / )) 0 x + y b+ z + x + y b+ z + x y b+ z b + + os ( πx/ ) os ( πy/ ) os ( πz/ ) 0 os ( π( / / 0.5)) os ( π( / / 0.5) os ( π( / / 0.5)) 0 x y + + x + y + + y + z + os ( π( x/( tg α) + z/(tgα ))) + os ( π y) + os ( πz 0 α 90 os ( π( x/(tgα ) + z/(tgα ) )) + os ( π( x/( tg α) + y z/(tgα ) + 0.5)) + os ( πz 0 α 90 π π os [ ( xsin γ + yos γ zk )] + os [ ( y+ zk )] + os ( πz 0 α β γ 90 sin γ os γ k k osα + os β os γ os β + osα os γ k k [os β + os( α γ)][os β + os( α + γ)] [os β + os( α γ)][os β + os( α + γ)] π πzk sin γ sin ( os β + os α os γ) os [ π( x / y / tn γ zk / sin λ)] os [ ( y zk )] os [ ] 0 α β γ 90 osα + os β os γ os β + osα os γ k k [os β + os( α γ)][os β + os( α + γ)] [os β + os( α γ)][os β + os( α + γ)] γ Hexgonl os ( π( x/ 3 0.5)) os ( πy/ ) os ( π( x/ 3 z/ 0.5)) Tble lists the oesponding PS models of the fouteen bsi fetues. Fetue is lled n extended fetue of Fetue if the lttie points in is subset of the ones in. ody-enteed fe-enteed nd bse-enteed fetues e extended fetues fom simple bsi fetue nd they e in Tble. Peiodi sufe models of the fouteen bsi ystl fetues the sme tegoy s tht of the simple bsi fetue. simple bsi fetue n be simple ubi simple othohombi simple tetgonl o simple monolini. The fouteen bsi fetues e then gouped into seven tegoies whih e ubi othohombi tetgonl monolini tilini hombohedl 4 opyight 008 by SME

5 nd hexgonl. s it n be seen the degee of eh peiodi sufe is one so tht ll of these bsi fetues ould be epesented by intesetions mong thee peiodi plnes in 3 E spe. Tnsfomtion opetions [3] on single peiodi sufe suh s ottion tnsltion nd sling n be pplied to djust positions. Simultneous tnsfomtion opetions of the thee peiodi plnes e equivlent to pplying opetions to the oesponding bsi fetue. 5. FETURE OPERTIONS In pevious wok [] ppohes of ptiles tiling suh s loi sufes intesetion wee disussed. In this setion we extend the tiling to fetue-bsed opetions to pidly lote ptiles in ystl stutues. The new fetue-bsed ppoh povides moe effiient wy to ete ystl stutues thn diet loi sufe intesetion espeilly when stutues beome omplex nd the numbe of loi sufes ineses odingly. The fetue opetions tht e desibed hee inlude: ente symmety tnsltion sling msking demsking imposing union nd insetion. 5. ente Symmety Let S sym be the ente efletion tnsfomtion mtix whih is symmeti othonoml nd self-invese i.e. T S S S. The ente symmety opetion of fetue sym sym sym is defined s ( ( ) + ( ) + ( 0 3 [ ] T (): ( S ) (5) sym Lemm. The fouteen bsi fetues in Tble e self ente symmeti. Poof. pply the ente symmeti tnsfomtion to the sufe models in Tble we eeive Tsym [ ( ) ] ( Ssym ) + ( Ssym ) + 3( Ssym ) T T T T os ( πκl( pm Ssym )) + os ( πκ l( pm Ssym )) T T + os ( πκl3( pm3 Ssym )) T T os ( πκl( pm )) + os ( πκl( pm )) T + os ( πκl3( pm3 )) T T os (πκl( pm )) + os ( πκl( pm )) T + os ( πκl3( pm3 )) () Theefoe the fouteen bsi fetues e self ente symmeti. sym 5. Tnsltion Given bsi fetue ( ( ) + ( ) + ( 0 3 the tnsltion opetion is defined s Ttn [ ( ) ] ( ( T ) (6) whih is equivlent to tnslting peiodi sufe ( ) ( ) nd ( ) simultneously whee t x t x 0 0 t ( ) T t y y T T 0 0 t t z z t t t x y z 5.3 Sling Given bsi fetue ( ( ) + ( ) + ( 0 3 the sling opetion is defined s T [ ( ) s s s ] ( S ) whih is equivlent to sle sl x y z the peiodi sufes ( ) ( ) nd ( ) 3 simultneously whee sx / sx s 0 0 T y 0 / s 0 0 S S nd y S 0 0 sz / sz Msking It is known in ystllogphy tht eh lttie point of vis lttie epesents the sme goup of toms whih fit in one of fouteen vis ltties in smlle sle. Tht is eh lttie point of vis ltties n be futhe expnded nd beomes unit of lttie itself. Theefoe we popose msking opetion to suppot suh stutue expnsion. Given bsi fetues ( ' ( ') + ( ') + ( ' 0 3 nd ( ' ( ') + ( ') + ( ' 0 in the domin D 3 the msking opetion is defined s Tmsk[ ( ') ( ') m]( ): (7) ( ') + Tsym[ Ttn[ Tsl[ ( ') m m m] ]] whee ( ') is the min fetue ( ') is the msk fetue nd m is the msk index. The opetion of msking expnds eh lttie point of bsi fetue ( ') eh of whih beomes the bsi fetue ( '). Figue 3 nd Figue 4 illustte the fetue expnsion effet of the msking opetion. 5 opyight 008 by SME

6 T msk ( the stutue ( ') into single lttie point. The demsking opetion n be looked s the invese opetion of the msking opetion. Figue 6 nd Figue 7 illustte the fetue ollpse effet of the demsking opetion. Figue 3. tetgonl msked by simple ubi (m5) T dem ( T msk ( Figue 6. Demsking opetion by simple ubi (m0) Figue 4. hexgonl msked by body-enteed ubi (m0) The msking opetion n lso be pplied when the min fetue is ny stutue othe thn bsi fetue. Figue 5 illusttes the effet of the msking opetion between Sodlite fmewok nd body-enteed ubi. T dem ( Figue 7. Demsking opetion by body-enteed ubi (m0) T msk ( Figue 5. Sodlite fmewok msked by body-enteed ubi (m0) Lemm. The sling opetion of msked stutue is equivlent to the msking opetion pplied to both of the sled min fetue nd the sled msk fetue by the sme sling opetion. Poof. T [ T [ ( ') ( ') mmm ]( ) s s s] sl msk x y z Tsl[ ( ') + T [ T [ T [ ( ') m m m] ]] s s s ] sym tn sl x y z T [ ( ') s s s ] + T [ T [ T [ T [ ( ') m m m] ]] s s s ] sl x y z sl sym tn sl x y z ( S ') T [ T [ T [ ( S ') mmm ] ] sym tn sl + T [ T [ ( ') s s s ] T [ ( ') s s s ] m m m]( ) msk sl x y z sl x y z 5.5 Demsking Given n oiginl stutue ( ') nd msk fetue ( ' ( ') + ( ') + ( ' 0 demsking opetion 3 is defined s T [ ( ') ( ') m]( ): dem (8) { ' T [ T [ ( ') m m m] ] 0 ( ' 0 tn sl } whee m is the demsking index. The opetion of demsking ollpses ny of the msk fetue ( ') whih is vilble in Lemm 3. The demsking opetion ollpses not only the msk fetue but lso its extended fetues whih e vilble in the oiginl fetue. Poof. ssuming ( ') is n oiginl stutue nd ( ') is n extended fetue of msk fetue ( '). Sine ( ') is subset of ( ') ( ' 0 ( ' 0. Theefoe T [ ( ') ( ') m]( ) dem { ' T [ T [ ( ') m m m] ] 0 ( ') 0} tn sl { ' T [ T [ ( ') m m m] ] 0 ( ') 0} T dem [ ( ') ( ') m]( ) tn sl Figue 8 illusttes the subset effet of demsking. n expnded stutue is eted by msking hexgonl with body-enteed ubi. When the expnded stutue is demsked by simple ubi the hexgonl n be eoveed. 5.6 Impose Given two bsi fetues () () + () + () 0 3 nd () () + () + () 0 in the domin D 3 the impose opetion is defined s T [ () ()]: () () (9) imp The impose opetion ovelps one fetue onto nothe one. Figue 9 illusttes the fetue ovelp effet of the impose opetion. 6 opyight 008 by SME

7 T msk ( T dem ( 5.7 Union The union opetion joins two bsi fetues in the sme tegoy. y union of two bsi fetues the two e joined togethe by shing lttie positions on thei edge ut sufes. Figue illusttes the union opetion between two fetues whee the ed blok nd the blue blok epesent the two bsi fetues. Joined by the union opetion the two fetues e mixed nd ppe peiodilly in 3D spe. It is obvious tht the union of bsi fetue with itself keeps the fetue unhnged. T imp ( Figue 8. n exmple of the subset effet in Lemm 3 (m0) Figue 9. ody-enteed ubi imposed by Fe-enteed ubi dimond stutue n be eted by n impose opetion between two fe-enteed ubi one of whih is tnslted long x y nd z dietions. Moe speifilly if () is fe-enteed ubi stutue dimond stutue n be onstuted by T [ ( ) T [ ( ) ]] imp tn whee ( ) T. Figue 0 illusttes the onstution of the dimond lttie. T tn ( Lye 3 Lye Lye Figue. n illusttion of union opetion Notie tht if the stutue in Figue is demsked by the ed blok the esult of this demsking opetion is feenteed bsi fetue if the ed blok is not subset of the blue blok. sed on this obsevtion we genelize the definition of the union opetion s follows. If () is the feenteed bsi fetue in the sme tegoy s the bsi fetues () nd () ( () () ) the union opetion is defined s T [ ( ) ( )] : T [ ( ) [ ( ) ( )] ] un msk T imp (0) Figue gives top view of the thee diffeent lyes in Figue. Eh ell with ente point epesents ed blok. The union opetion is equivlent to epling eh of the blue ente points with the imposed stutue between () nd () whih is lso edued the sle by hlf. Lye Lye Lye 3 T imp ( Figue 0. n illusttion of onstution of dimond stutue It is esy to veify tht bsi fetue keeps itself unhnged fte n impose opetion with itself. n extended bsi fetue keeps itself unhnged fte n impose opetion with simple bsi fetue in the sme tegoy. Sling n imposed stutue is equivlent to imposing two sled fetues. Figue. thee-lye view of the union stutue in Figue The union opetion n be looked s speil se of the msking opetion whee the msk index m lwys equls to. pply the union opetion defined in Eq.(0) we eeive:.if () is simple bsi fetue nd () is bse-enteed bsi fetue T [ () ()] T [ ()] un sl. 7 opyight 008 by SME

8 . If () is simple bsi fetue nd () is fe-enteed bsi fetue T [ () ()] T [ ()] un sl. 3. If () is bse-enteed bsi fetue nd () is fe-enteed bsi fetue T [ () ()] T [ ()] un sl. 4. If () is simple bsi fetue nd () is body-enteed fetue T [ ( ) ( )] T [ ( ) ( )] un msk whee () is fe-enteed bsi fetue in the sme tegoy s () nd (). Figue 3 illusttes the effet of the union opetion between the simple ubi nd the bodyenteed bsi fetues. T un ( Figue 3. simple ubi union with body-enteed ubi 5. If () is body-enteed bsi fetue nd () is fe-enteed bsi fetue the union opetion between these two is T [ ( ) ( )] T [ ( ) [ ( ) ( )] ] un msk T imp Figue 4 illusttes the effet of the union opetion between these two bsi fetues. T un ( Figue 5. bse-enteed othohombi union with body-enteed othohombi Lemm 4. Sling unioned stutue is equivlent to the union of two fetues fte sling them fist. Poof. Tsl [ T [ ( ) ( )] s ] un x sy sz Tsl[ Tmsk [ ( ) T [ ( ) ( )] ] ] imp s x sy sz Tmsk [ Tsl[ ( ) s ] [ [ ( ) ( )] ] ] x sy sz Tsl Timp s x sy sz Tmsk [ ( S ) T [ [ ( ) ] [ imp Tsl s x sy sz Tsl ( ) sx sy sz]] ] Tmsk[ ( S ) T [ ( ) ( )] imp S S T [ ( S ) ( S )] un whee () (). 5.8 Insetion The insetion opetion lso dels with the two bsi fetues in the sme tegoy. y insetion the two bsi fetues e septed lye by lye in x- y- o z-xis dietion. Figue 6 shows the effet of the insetion opetion in z xis. The ed blok lyes e septed by the blue lye fte the insetion opetion between the ed blok nd the blue blok. T un ( Figue 4. body-enteed ubi union with fe-enteed ubi 6. If () is bse-enteed bsi fetue nd () is body-enteed bsi fetue the union opetion between these two is T [ ( ) ( )] : T [ ( ) [ ( ) ( )] ] un msk T imp whee () is fe-enteed bsi fetue in the sme tegoy s () nd (). Figue 5 illusttes the effet of the union opetion between these two bsi fetues. Lye 3 Lye Lye Figue 6. n illusttion of insetion opetion long z xis Notie tht if the stutue in Figue 6 is demsked by the ed blok the esult of this demsking opetion is tetgonl bsi fetue whee if the ed blok is not subset of the blue blok. The tetgonl bsi fetue n lso be looked s sled simple ubi fetue in z-xis dietion. Theefoe we genelize the definition of the insetion opetion in z-xis dietion s follows. If () is the simple bsi fetue () is the body-enteed bsi fetue () is the bseenteed bsi fetue nd F D E () is the fe-enteed bsi fetue in the sme tegoy s the bsi fetues () nd () ( () () ) the insetion opetion in z dietion is 8 opyight 008 by SME

9 defined s T [ ( ) ( )]: un Tmsk[ Tsl[ ( )0.5] ( )] if ( ( ) Timp[ Tmsk [ Tsl [ ( ) 0.5] ( )] if () D() T [ T [ ( )0.5]00 ]] nd () () tn sl () if () E() nd ( ) F () Figue 7 illusttes the effet of insetion opetion between simple ubi nd body-enteed ubi in z-xis dietion. Figue 8 illusttes the effet of the insetion opetion between simple ubi nd fe-enteed ubi. Figue 9 illusttes the effet of insetion opetion between body-enteed ubi nd fe-enteed ubi. T ins ( Figue 7. Insetion between simple ubi nd body-enteed ubi in z xis dietion T ins ( Figue 8. Insetion between simple ubi nd fe-enteed ubi in z xis dietion T ins ( Figue 9. Insetion between body-enteed ubi nd feenteed ubi in z xis dietion Insetion opetion long x o y xis is simil to its definition in z xis exept when one of () nd () is bse-enteed bsi fetue nd the othe is fe-enteed bsi fetue. Figue 0 shows the effet of the insetion opetion in x o y xis. Figue 0. n illusttion of insetion opetion long x o y xis If () is the simple bsi fetue () is the bodyenteed bsi fetue E D () is the bse-enteed bsi fetue nd F () is the fe-enteed bsi fetue in the sme tegoy s the bsi fetues () nd () ( () () ) the insetion opetion long x xis is defined s T [ ( ) ( )]: un Tmsk[ Tsl[ ( )0.5] ( )] if ( ( ) Timp[ Tmsk[ Tsl [ ( )0.5] ( )] if () D() T [ [ nd () () tn Tsl ( )0.5] 00]] Timp[ Tmsk[ Tsl [ ( )0.5 ] ( )] if ( E( ) T [ [ nd () () tn Tsl ( )0.5] 00.5 ]] F The insetion opetion long y xis is defined s T [ ( ) ( )]: un Tmsk[ Tsl[ ()0.5] ()] if () () Timp[ Tmsk [ Tsl[ ( )0.5] ( )] if () D() T [ [ nd () () tn Tsl ( )0.5]0 0]] Timp[ Tmsk [ Tsl[ ( )0.5 ] ( )] if ( E( ) T [ [ nd () () tn Tsl ( )0.5]0 0.5 ]] F 6. SUMMRY In this ppe pid onstution of ystl stutues bsed on bsi fetues is studied. The bsi fetues known s fouteen vis ltties e eted by the id of impliit peiodi sufe models. Sevel fetue opetions e defined s n effiient ppoh to onstut omplex stutues fom the bsi fetues. This new fetue-bsed ppoh helps us to genete ystl stutues effiiently in n intetive ND 9 opyight 008 by SME

10 envionment. omped to the existing ystl onstution ppohes tht lote the toms one by one the fetue-bsed ppoh enbles us to ete ystl stutues with building bloks insted of fom sth. This fetue-bsed ppoh is itil if we need to build omplex stutues. With the fouteen bsi fetues nd fetue opetions omplex ltties n be built effiiently by opetions between bsi fetues. Use-defined fetues n be eted bsed on these opetions. Theefoe simil to the fetue-bsed pmeti modeling in uent D systems fo mo sle engineeing design the most impotnt dvntge of the poposed ppoh ove the existing ppohes in nnosle simultion tools is to povide nno enginees nd sientists n esy-to-use tool to build nd modify omplex ystl stutues effiiently. KNOWLEDGEMENT This wok is suppoted in pt by the NSF gnt MMI [] u.k. nd Woo T.. (004) Ribbons: thei geomety nd topology. ompute-ided Design & pplitions (- 4): -6 [3] Ryu J. Kim D. ho Y. Pk R. nd Kim D.-S. (005) omputtion of moleul sufe using Euliden Voonoi Digm. ompute-ided Design & pplitions (-4): [4] Zhng Y. Xu G. nd jj. ( 006) Qulity meshing of impliit solvtion models of biomoleul stutues. ompute-ided Geometi Design 3(6): [5] Mky.L. nd Pwley G.S. (963) vis Ltties in Fou-dimensionl Spe. t ystllogphi 6: -9 [6] Pittei M. nd Znzotto G. (996) On the definition nd lssifition of vis Ltties. t ystllogphi 5: REFERENES [] Wng Y. (006) Geometi modeling of nno stutues with peiodi sufes. Letue Notes in ompute Siene Vol.4077 pp [] Wng Y. (007) Peiodi sufe modeling fo ompute ided Nno Design. ompute-ided Design 39(3): [3] Wng Y. (007) Loi peiodi sufe eonstution fom ystls. ompute-ided Design & pplitions 4(-4): [4] Wng Y. (007) Degee opetions on peiodi sufes. Po. 007 IDET/IE onfeene Sept Ls Vegs NV Ppe No. DET [ 5 ] Wng Y. (008) Degee elevtion nd edution of peiodi sufes. ompute-ided Design & pplitions in pess [6] onnolly M.L. (996) Moleul Sufes: Review. Netwok Siene vilble t [7] Lee. nd Rihds F.M. (97) The intepettion of potein stutues: Estimtion of stti essibility. J. Mol. iol. 55: [ 8 ] onnolly M.L. (983) Solvent-essible sufes of poteins nd nulei ids. Siene (46): [9] son M (996) Wvelets nd moleul stutue. J. omp. ided Mol. Des. 0: [ 0 ] Edelsbunne H. (999) Defomble smooth sufe design. Disete & omputtionl Geomety : 87-5 [ ] jj. Psui V. Shmi. Holt R. nd Netvli. (003) Dynmi Mintenne nd Visuliztion of Moleul Sufes. Disete pplied Mthemtis 7: opyight 008 by SME