Stochastic dynamics in spatially extended physical and biological systems

Demographic Noise;Nonequilibrium;Stochastic;Homochirality;Nonnormality;Dislocation Dynamics;Spatial Extension;Turing Patterns;Stochastic Patterns

Jafarpour, Farshid

关键词: Demographic Noise;    Nonequilibrium;    Stochastic;    Homochirality;    Nonnormality;    Dislocation Dynamics;    Spatial Extension;    Turing Patterns;    Stochastic Patterns;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/92701/JAFARPOUR-DISSERTATION-2016.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

In this thesis, I discuss three different problems of stochastic nature in spatially extended systems: (1) a noise induced mechanism for the emergence of biological homochirality in early life self-replicators, (2) the amplification effect of nonnormality on stochastic Turing patterns in reaction diffusion systems, and (3) the velocity statistics of edge dislocations in plastic deformation of crystalline material.In Part I, I present a new model for the origin of homochirality, the observed single-handedness of biological amino acids and sugars, in prebiotic self-replicator. Homochirality has long been attributed to autocatalysis, a frequently assumed precursor for self-replication. However, the stability of homochiral states in deterministic autocatalytic systems relies on cross inhibition of the two chiral states, an unlikely scenario for early life self-replicators. Here, I present a theory for a stochastic individual-level model of autocatalysis due to early life self-replicators. Without chiral inhibition, the racemic state is the global attractor of the deterministic dynamics, but intrinsic multiplicative noise stabilizes the homochiral states, in both well-mixed and spatially-extended systems.I conclude that autocatalysis is a viable mechanism for homochirality, without imposing additional nonlinearities such as chiral inhibition.In Part II, I study the amplification effect of nonnormality on the steady state amplitude of fluctuation-induced Turing patterns. The phenomenon occurs generally in Turing-like pattern forming systems such as reaction-diffusion systems, does not require a large separation of diffusion constant, and yields pattern whose amplitude can be orders of magnitude larger than the fluctuations that cause the patterns. The analytical treatment shows that patterns are amplified due to an interplay between noise, non-orthogonality of eigenvectors of the linear stability matrix, and a separation of time scales, all built-in feature of stochastic pattern forming systems. I conclude that many examples of biological pattern formations are nonnormal stochastic patterns.In Part III, I study the dynamics of edge dislocations with parallel Burgers vectors, moving in the same slip plane, by mapping the problem onto Dyson's model of a two-dimensional Coulomb gas confined in one dimension. I show that the tail distribution of the velocity of dislocations is power-law in form, as a consequence of the pair interaction of nearest neighbors in one dimension. In two dimensions, I show the presence of a pairing phase transition in a system of interacting dislocations with parallel Burgers vectors. The scaling exponent of the velocity distribution at effective temperatures well below this pairing transition temperature can be derived from the nearest-neighbor interaction, while near the transition temperature, the distribution deviates from the form predicted by the nearest-neighbor interaction, suggesting the presence of collective effects.