相关论文: Universality of Long-Range Correlations in Expansi…

We investigate finite size scaling aspects of disorder reaction-diffusion processes in one dimension utilizing both numerical and analytical approaches. The former averages the spectrum gap of the associated evolution operators by doubling…

We consider a class of percolation models where the local occupation variables have long-range correlations decaying as a power law $\sim r^{-a}$ at large distances $r$, for some $0< a< d$ where $d$ is the underlying spatial dimension. For…

This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…

Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees relating species. Along branches, sequence evolution is modelled using a continuous-time Markov process characterised by an instantaneous rate…

We investigate the survivor distributions of a spatially extended model of competitive dynamics in different geometries. The model consists of a deterministic dynamical system of individual agents at specified nodes, which might or might…

For cellular biochemical reaction systems where the numbers of molecules is small, significant noise is associated with chemical reaction events. This molecular noise can give rise to behavior that is very different from the predictions of…

Computer modelling for evolutionary systems consists in: 1) to store in the memory the individual features of each member of a large population; and 2) to update the whole system repeatedly, as time goes by, according to some prescribed…

Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates…

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the…

Via molecular dynamics simulations, we study the kinetics in a phase separating active matter model. Quantitative results for the isotropic bicontinuous pattern formation, its growth and aging, studied, respectively, via the two-point…

We study dynamics of quantum entanglement in smooth global quenches with a finite rate, by computing the time evolution of entanglement entropy in 1 + 1 dimensional free scalar theory with time-dependent masses which start from a nonzero…

For percolating systems, we propose a universal exponent relation connecting the leading corrections to scaling of the cluster size distribution with the dynamic corrections to the asymptotic transport behaviour at criticality. Our…

We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…

We elucidate a non-conserved relaxational nonequilibrium dynamics of a O(2) symmetric model. We drive the system out of equilibrium by introducing a non-zero noise cross-correlation of amplitude $D_\times$ in a stochastic Langevin…

A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In the model, the conditional probability that the i-th symbol in the chain equals zero (or unity) is a linear function…

The mean size of exponentially dividing E. coli cells cultured in different nutrient conditions is known to depend on the mean growth rate only. However, the joint fluctuations relating cell size, doubling time and individual growth rate…

Recently described stochastic models of protein evolution have demonstrated that the inclusion of structural information in addition to amino acid sequences leads to a more reliable estimation of evolutionary parameters. We present a…

A generalization of the ABC model, a one-dimensional model of a driven system of three particle species with local dynamics, is introduced, in which the model evolves under either (i) density-conserving or (ii) nonconserving dynamics. For…

We investigate dissipative dynamical systems under the influence of an external driving with two or more frequencies. Our main quantities of interest are long-time averages of expectation values which turn out to exhibit universal features.…

Unveiling universal non-equilibrium scaling laws has been a central theme in modern statistical physics, with recent attention increasingly directed toward non-equilibrium phases that exhibit rich dynamical phenomena. A striking example…