交通大学理学院个别群子计划

交通大學理學院個別研究群子計劃非線性動態學與生物物理(NonlinearDynamicsandBiologicalPhysics)『邁向頂尖大學』

NonlinearDynamicsandBiologicalPhysics主持人:石至文(Chih-WenShih,NCTU-AppliedMath)參加人員:莊重(JonqJuang,NCTU-AppliedMath)李明佳(Ming-ChiaLi,NCTU-AppliedMath)張正宏(Cheng-HorngChang,NCTU-Physics)林榮信(Jung-HsinLin,NTU-Pharmacy)來穎誠(Ying-ChengLai,ArizonaState-Physics)

ExpertiseJonqJuang,Chih-WenShih,Ming-ChiaLi:

DynamicalsystemtheoryandapplicationsCheng-HorngChang

NonlinearsciencesanditsapplicationsinSpintronics,Quantumchaos,Biologicalmotors.Jung-HsinLin

Moleculardynamics,ComputationaldrugdesignYing-ChengLai(Fellow,AmericanPhysicalSociety)

Nonlineardynamics,Networks

(1)Developdynamicalsystemtheorythataremoreapplicabletocertainbiologicalandphysicalproblems(2)Seekforsignificantandinterestingproblemsinbiologicalphysics,e.g.

TumorgrowthmodelsCellmotilitymodelsMetabolic

insulin

signalingmodelsMoleculardynamicssothatinvestigationswithmathematicalanalysisanddynamicalsystemtheorycancontributetowardresolutionofthecorrespondingproblemsinthemodelequations.Missionandobjectives:

Developdynamicalsystemtheorythataremoreapplicabletocertainbiologicalandphysicalproblems.Toconductacross-disciplinaryresearchonMathematicalBiologyandBiologicalPhysics,withexpertiseinmathematicalanalysis,nonlineardynamicsandscientificcomputations.Weareespeciallyinterestedinmathematicalmodelsontumorgrowth,cellmotility,biologicalmotors,andprotein‐protein

interactionnetwork.TheoryonNonlinearDynamicsisthemainmethodologyintheseinvestigations,althoughtheconsideredproblemsseemdiversified.

MathematicalModelingandScientificComputationsTheNCTU-AMdepartmentisplanningtoestablishTheGraduateInstituteof

MathematicalModelingandScientificComputations

(Pre-approvedbytheCollegeofScience)Thepresentprojectaimstoignitetheresearchcollaborationsalongthelineofmodelingandcomputationsamongvariousdisciplines,startingfromthepointofNonlinearDynamics.ResearchProjectsMoreprecisely,ourfirstprojectistoapplyourtechniquesindiscrete-diffusionequations[PhysicaD2005]tothefollowingmodelsgovernedbyreaction-diffusionequations.(i)Spatio-temporalpatternformationonsolidtumorgrowthmodels(ii)Cellmotilitymodelsdescribingcellcrawling.OtherprojectsincludeRatchetmodelsusingdrivingforcesgeneratedbydeterministicchaoticmaps,spatialandtemporalsymmetrybreakingwhichinducesdirectedtransport,ratchetmechanismonbiologicalmotors,dynamicsonscalefreenetworks,etc.OurresearchCompletestability,multistability,inrecurrentneuralnetworksChaoticdynamics–applicationtoglobalsearchingabilityofcombinatorialoptimizationproblemsPatternformationsindiscretediffusionsystemsRatchetmodelsusingdrivingforcesgeneratedbydeterministicchaoticmapsStochasticresonanceinabiologicalmotorundercomplexfluctuation

DynamicsonscalefreenetworksCompletestability,ConvergenceofdynamicsAuniqueequilibriumtowhicheverythingconvergesEveryorbitconvergestooneoftheequilibriumpointsMulti-stabilityindelayedneuralnetworks

[Shih,et.al.SIAM-AppliedMath.,2006]Patternsformationsindiscretediffusionsystems[Shih,et.al.PhysicaD,2005]ReactiondiffusionsystemsApplicationofchaosinsolvingTSP[Shihet.al.,Transversalhomoclinicorbitsinatransientlychaoticneuralnetwork,Chaos2002]OptimalrouteCostfunctionIterationaxisCostvalueProjectto2-dimOrderaxisCityaxisSolvingTSPviaTCNNSomepublicationsbyC.-H.ChangStochasticresonanceinabiologicalmotorundercomplexfluctuation,Phys.Rev.E69,021914(2004).Spintransmissionthroughquantumdotswithstrongspin-orbitinteraction,Phy.Lett.A2004.Spinrelaxationdynamicsofquasiclassicalelectronsinballisticquantumdotswithstrongspin-orbitcoupling(cond-mat/0405212)Transferoperatorapproachonthree-dimensionalquantumbilliardswithSO(2)symmetry,Phys.Rev.E67,046201(2003)TruncationandresetprocessonthedynamicsofParrondo'sgames,Phys.Rev.E67,025101(2003).ProblemstoinvestigateSolidtumorgrowthmodelsMetabolic

insulin

signalingpathwaysmodels(raisedbyJ.SLin)Cellularmotionsandthermalfluctuation(theBrownianratchet)(raisedbyC.H.Cheng)Complexnetworkandothers(raisedbyY.C.Lai)國家理論科科學研究中中心數學組組TheNCTS––MathdivisionWorkshopofMathematicalModelsandProblemsinCellMotilityandTumorGrowthJan11-19,2006AtumorgrowthmodelSpatio-temporalpatternformationonsphericalsurfaces:numericalsimulationandapplicationtosolidtumorgrowth[Chaplain,et.al,J.Math.Biol.42,387––423(2001)J.MathematicalBiology]Atumorgrowthmodel(continued)Tumorcellssecretegrowth-promotingfactorsThegrowthinhibitoryfactorandnutrientdistributionscompetetocontrolthetumorcellproliferationandthereforeultimatelythesizeofthetumor.Thepredictedspatiallyheterogeneoussteady-statesofthesetwochemicalscorrespondtoobservedregionsofcellularheterogeneityinactualsolidtumors.Atumorgrowthmodel(continued)UseTuring’’spre-patterntheorytostudythegrowthandinvasionoftumorsExperimentalresultshavedemonstratedthattumorcellssecretebothgrowthinhibitingandgrowth-activatingchemicalsinanautocrinemannerandthatt