交通大学理学院个别研究群子计划

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)ExpertiseJonqJuang,Chih-WenShih,Ming-ChiaLi:DynamicalsystemtheoryandapplicationsCheng-HorngChangNonlinearsciencesanditsapplicationsinSpintronics,Quantumchaos,Biologicalmotors.Jung-HsinLinMoleculardynamics,ComputationaldrugdesignYing-ChengLai(Fellow,AmericanPhysicalSociety)Nonlineardynamics,Networks(1)Developdynamicalsystemtheorythataremoreapplicabletocertainbiologicalandphysicalproblems(2)Seekforsignificantandinterestingproblemsinbiologicalphysics,e.g.TumorgrowthmodelsCellmotilitymodelsMetabolicinsulinsignalingmodelsMoleculardynamicssothatinvestigationswithmathematicalanalysisanddynamicalsystemtheorycancontributetowardresolutionofthecorrespondingproblemsinthemodelequations.Missionandobjectives:Developdynamicalsystemtheorythataremoreapplicabletocertainbiologicalandphysicalproblems.Toconductacross-disciplinaryresearchonMathematicalBiologyandBiologicalPhysics,withexpertiseinmathematicalanalysis,nonlineardynamicsandscientificcomputations.Weareespeciallyinterestedinmathematicalmodelsontumorgrowth,cellmotility,biologicalmotors,andprotein‐proteininteractionnetwork.TheoryonNonlinearDynamicsisthemainmethodologyintheseinvestigations,althoughtheconsideredproblemsseemdiversified.MathematicalModelingandScientificComputationsTheNCTU-AMdepartmentisplanningtoestablishTheGraduateInstituteofMathematicalModelingandScientificComputations(Pre-approvedbytheCollegeofScience)Thepresentprojectaimstoignitetheresearchcollaborationsalongthelineofmodelingandcomputationsamongvariousdisciplines,startingfromthepointofNonlinearDynamics.ResearchProjectsMoreprecisely,ourfirstprojectistoapplyourtechniquesindiscrete-diffusionequations[PhysicaD2005]tothefollowingmodelsgovernedbyreaction-diffusionequations.(i)Spatio-temporalpatternformationonsolidtumorgrowthmodels(ii)Cellmotilitymodelsdescribingcellcrawling.OtherprojectsincludeRatchetmodelsusingdrivingforcesgeneratedbydeterministicchaoticmaps,spatialandtemporalsymmetrybreakingwhichinducesdirectedtransport,ratchetmechanismonbiologicalmotors,dynamicsonscalefreenetworks,etc.OurresearchCompletestability,multistability,inrecurrentneuralnetworksChaoticdynamics–applicationtoglobalsearchingabilityofcombinatorialoptimizationproblemsPatternformationsindiscretediffusionsystemsRatchetmodelsusingdrivingforcesgeneratedbydeterministicchaoticmapsStochasticresonanceinabiologicalmotorundercomplexfluctuationDynamicsonscalefreenetworksCompletestability,ConvergenceofdynamicsAuniqueequilibriumtowhicheverythingconvergesEveryorbitconvergestooneoftheequilibriumpointsMulti-stabilityindelayedneuralnetworks[Shih,et.al.SIAM-AppliedMath.,2006]Patternsformationsindiscretediffusionsystems[Shih,et.al.PhysicaD,2005]ReactiondiffusionsystemsApplicationofchaosinsolvingTSP[Shihet.al.,Transversalhomoclinicorbitsinatransientlychaoticneuralnetwork,Chaos2002]OptimalrouteCostfunctionIterationaxisCostvalueProjectto2-dim11y12yOrderaxisCityaxisSolvingTSPviaTCNNSomepublicationsbyC.-H.ChangStochasticresonanceinabiologicalmotorundercomplexfluctuation,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).ProblemstoinvestigateSolidtumorgrowthmodelsMetabolicinsulinsignalingpathwaysmodels(raisedbyJ.SLin)Cellularmotionsandthermalfluctuation(theBrownianratchet)(raisedbyC.H.Cheng)Complexnetworkandothers(raisedbyY.C.Lai)國家理論科學研究中心數學組TheNCTS–MathdivisionWorkshopofMathematicalModelsandProblemsinCellMotilityandTumorGrowthJan11-19,2006AtumorgrowthmodelSpatio-temporalpatternformationonsphericalsurfaces:numericalsimulationandapplicationtosolidtumorgrowth[Chaplain,et.al,J.Math.Biol.42,387–423(2001)J.MathematicalBiology]Atumorgrowthmodel(continued)Tumorcellssecretegrowth-promotingfactorsThegrowthinhibitoryfactorandnutrientdistributionscompetetocontrolthetumorcellproliferationandthereforeultimatelythesizeofthetumor.Thepredictedspatiallyheterogeneoussteady-statesofthesetwochemicalscorrespondtoobservedregionsofcellularheterogeneityinactualsolidtumors.Atumorgrowthmodel(continued)UseTuring’spre-patterntheorytostudythegrowthandinvasionoftumorsExperimentalresultshavedemonstratedthattumorcellssecretebothgrowthinhibitingandgrowth-activatingchemicalsinanautocrinemannerandthatthebalanceandinteractionbetweenthesefactorsplayanimportantroleinthedevelopmentandprogressionoftumors.Atumorgrowthmodel(continued)Systemofreaction-diffusionequationsonthesurfaceofasphereu:concentrationof