交通大学理学院个别研究群子计划

1、 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 Physicsn主持人:石至文 (Chih-Wen Shih, NCTU-Applied Math)n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-

2、Pharmacy) 來穎誠 (Ying-Cheng Lai, Arizona State-Physics) ExpertisenJonq Juang, Chih-Wen Shih, Ming-Chia Li: Dynamical system theory and applicationsnCheng-Horng Chang Nonlinear sciences and its applications in Spintronics, Quantum chaos, Biological motors. nJung-Hsin Lin Molecular dynamics, Computation

3、al drug designnYing-Cheng Lai (Fellow, American Physical Society) Nonlinear dynamics, Networks n (1) Develop dynamical system theory that are more applicable to certain biological and physical problemsn (2) Seek for significant and interesting problems in biological physics, e.g. Tumor growth models

4、 Cell motility models Metabolic insulin signaling 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:n Develop dynamical system theory th

5、at are more applicable to certain biological and physical problems.n 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 o

6、n tumor growth, cell motility, biological motors, and protein protein interaction network. nTheory on Nonlinear Dynamics is the main methodology in these investigations, although the considered problems seem diversified. Mathematical Modeling and Scientific ComputationsnThe NCTU-AM department is pla

7、nning 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 Non

8、linear Dynamics.Research ProjectsnMore 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

9、 describing cell crawling. nOther 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 researchnComplete

10、 stability, multistability, in recurrent neural networksnChaotic dynamics application to global searching ability of combinatorial optimization problemsnPattern formations in discrete diffusion systems nRatchet models using driving forces generated by deterministic chaotic mapsnStochastic resonance

11、in a biological motor under complex fluctuation nDynamics on scale free networks Complete stability, Convergence of dynamicsA unique equilibrium to which everything convergesEvery orbit converges to one of the equilibrium points Multi-stability in delayed neural networksShih, et.al. SIAM- Applied Ma

12、th., 2006Patterns formations in discrete diffusion systemsShih, 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 2002Optimal routeCost functionIteration axisCost valueProjec

13、t to 2-dim11y12yOrder axisCity axisSolving TSP via TCNN Some publications by C.-H. ChangnStochastic resonance in a biological motor under complex fluctuation, Phys. Rev. E 69, 021914 (2004). nSpin transmission through quantum dots with strong spin-orbit interaction, Phy. Lett. A 2004. nSpin relaxati

14、on dynamics of quasiclassical electrons in ballistic quantum dots with strong spin-orbit coupling (cond-mat/0405212)nTransfer operator approach on three-dimensional quantum billiards with SO(2) symmetry, Phys. Rev. E 67, 046201 (2003)n Truncation and reset process on the dynamics of Parrondos games,

15、 Phys. Rev. E 67, 025101 (2003). Problems to investigate nSolid tumor growth modelsnMetabolic insulin signaling pathways models (raised by J.S Lin)nCellular motions and thermal fluctuation (the Brownian ratchet) (raised by C.H. Cheng)nComplex network and others (raised by Y.C. Lai) 國家理論科學研究中心數學組國家理論

16、科學研究中心數學組 The NCTS Math division nWorkshop 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 growthn Chaplain, et.al, J. Math. Biol

17、. 42, 387423 (2001) J. Mathematical Biology A tumor growth model (continued)nTumor cells secrete growth-promoting factorsnThe growth inhibitory factor and nutrient distributions compete to control the tumor cell proliferation and therefore ultimately the size of the tumor.nThe predicted spatially he

18、terogeneous steady-states of these two chemicals correspond to observed regions of cellular heterogeneity in actual solid tumors. A tumor growth model (continued)nUse Turings pre-pattern theory to study the growth and invasion of tumorsnExperimental results have demonstrated that tumor cells secrete both growth inhi