资源描述
Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,*,按一下以編輯母片標題樣式,按一下以編輯母片,第二層,第三層,第四層,第五層,*,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,(Nonlinear Dynamics and Biological Physics),邁向頂尖大學,Nonlinear Dynamics and Biological Physics,主持人:石至文,(,Chih-Wen Shih,NCTU-Applied Math,),參加人員:莊重,(,Jonq Juang,NCTU-Applied Math,),李明佳,(,Ming-Chia Li,NCTU-Applied Math,),張正宏,(,Cheng-Horng Chang,NCTU-Physics,),林榮信(,Jung-Hsin Lin,NTU-Pharmacy,),來穎誠,(,Ying-Cheng Lai,Arizona State-Physics),Expertise,Jonq Juang,Chih-Wen Shih,Ming-Chia Li,:,Dynamical system theory and applications,Cheng-Horng Chang,Nonlinear sciences and its applications in,Spintronics,Quantum chaos,Biological motors.,Jung-Hsin Lin,Molecular dynamics,Computational drug design,Ying-Cheng Lai(Fellow,American Physical Society),Nonlinear dynamics,Networks,(1)Develop dynamical system theory that are more,applicable to certain biological and physical problems,(2)Seek for significant and interesting problems in biological,physics,e.g.,Tumor growth,models,Cell motility,models,Metabolicinsulinsignaling,models,Molecular dynamics,so that investigations with mathematical analysis and,dynamical system theory can contribute toward resolution of,the corresponding problems in the model equations.,Mission and objectives:,Develop dynamical system theory that are more applicable to certain biological and physical problems.,To conduct a cross-disciplinary research on Mathematical Biology and Biological Physics,with expertise in mathematical analysis,nonlinear dynamics and scientific computations.We are especially interested in mathematical models on tumor growth,cell motility,biological motors,and proteinproteininteraction network.,Theory on Nonlinear Dynamics is the main methodology in these investigations,although the considered problems seem diversified.,Mathematical Modeling and Scientific Computations,The NCTU-AM department is planning to establish,The,Graduate Institute of,Mathematical Modeling and Scientific Computations,(Pre-approved by the College of Science),The present project aims to ignite the research collaborations along the line of modeling and computations among various disciplines,starting from the point of Nonlinear Dynamics.,Research Projects,More precisely,our first project is to apply our techniques in discrete-diffusion equations Physica D 2005 to the following models governed by reaction-diffusion equations.,(i)Spatio-temporal pattern formation on solid tumor growth,models,(ii)Cell motility models describing cell crawling.,Other projects include Ratchet models using driving forces generated by deterministic chaotic maps,spatial and temporal symmetry breaking which induces directed transport,ratchet mechanism on biological motors,dynamics on scale free networks,etc.,Our research,Complete stability,multistability,in recurrent neural networks,Chaotic dynamics application to global searching ability of combinatorial optimization problems,Pattern formations in discrete diffusion systems,Ratchet models using driving forces generated by deterministic chaotic maps,Stochastic resonance in a biological motor under complex fluctuation,Dynamics on scale free networks,Complete stability,Convergence of dynamics,A unique equilibrium to which,everything converges,Every orbit converges to,one of the equilibrium points,Multi-stability in delayed neural networks,Shih,et.al.SIAM-Applied Math.,2006,Patterns formations in discrete diffusion systems,Shih,et.al.Physica D,2005,Reaction diffusion systems,Application of chaos in solving TSP,Shih et.al.,Transversal homoclinic orbits in a transiently chaotic neural network,Chaos,2002,Optimal route,Cost function,Iteration axis,Cost value,Project to 2-dim,Order axis,City axis,Solving TSP,via TCNN,Some publications by C.-H.Chang,Stochastic resonance in a biological motor under complex fluctuation,Phys.Rev.E 69,021914(2004).,Spin transmission through quantum dots with strong spin-orbit interaction,Phy.Lett.A 2004.,Spin relaxation dynamics of quasiclassical electrons in ballistic quantum dots with strong spin-orbit coupling(cond-mat/0405212),Transfer operator approach on three-dimensional quantum billiards with SO(2)symmetry,Phys.Rev.E 67,046201(2003),Truncation and reset process on the dynamics of Parrondos games,Phys.Rev.E 67,025101(2003).,Problems to investigate,Solid tumor growth models,Metabolicinsulinsignalingpathways models,(raised by J.S Lin),Cellular motions and thermal fluctuation(the Brownian ratchet),(raised by C.H.Cheng),Complex network and others,(raised by Y.C.Lai),國家理論科學研究中心數學組 The NCTS Math division,Workshop of Mathematical Models and Problems in Cell Motility and Tumor Growth,Jan 11-19,2006,A tumor growth model,Spatio-temporal pattern formation on spherical surfaces:numerical simulation and application to solid tumor growth,Chaplain,et.al,J.Math.Biol.42,387423(2001),J.Mathematical Biology,A tumor growth model,(continued),Tumor cells secrete growth-promoting factors,The growth i
展开阅读全文