Related papers: Rare mutations in the spatial Lambda-Fleming-Viot …
We investigate the existence and uniqueness of strong solutions up to an explosion time for regime-switching diffusion processes in an infinite state space. Instead of concrete conditions on coefficients, our existence and uniqueness result…
We demonstrate slow dynamics and constrained motion of domain walls in one-dimensional (1D) interacting bosons with double-well dispersion. In the symmetry-broken regime, the domain-wall motion is ``fractonlike'' -- a single domain wall…
We investigate single-particle diffusion in a two-state Langevin model where the friction coefficient randomly switches between low-friction (liquid-like) and high-friction (glassy-like) states. The dynamics are governed by the ratio…
Deriving evolution equations accounting for both anomalous diffusion and reactions is notoriously difficult, even in the simplest cases. In contrast to normal diffusion, reaction kinetics cannot be incorporated into evolution equations…
We report a molecular dynamics simulation of a supercooled simple monatomic glass-forming liquid. It is found that the onset of the supercooled regime results in formation of distinct domains of slow diffusion which are confined to the…
We present a novel approach allowing the study of rare events like fixation under fluctuating environments, modeled as extrinsic noise, in evolutionary processes characterized by the dominance of one species. Our treatment consists of…
Environmental heterogeneity can drive genetic heterogeneity in expanding populations; mutant strains may emerge that trade overall growth rate for an improved ability to survive in patches that are hostile to the wild type. This…
We present results of the numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy tailed probability distribution functions. Assuming that the distribution function of the random fluctuations…
Anomalous dynamics in which local perturbations spread faster than diffusion are ubiquitously observed in the long-time behavior of a wide variety of systems. Here, the manner by which such systems evolve towards their asymptotic…
Moving-habitat models track the density of a population whose suitable habitat shifts as a consequence of climate change. Whereas most previous studies in this area consider 1-dimensional space, we derive and study a spatially 2-dimensional…
Anomalous diffusion phenomenon is an intriguing process that tracer diffusion presents in numerous complex systems. Current experimental and theoretical investigations have reported the emergence of random diffusivity scenarios accompanied…
We study the evolution of a collection of individuals subject to Brownian diffusion, reproduction and disappearance. In particular, we focus on the case where the individuals are initially prepared at equilibrium within a confined geometry.…
We consider a single genetic locus with two alleles $A_1$ and $A_2$ in a large haploid population. The locus is subject to selection and two-way, or recurrent, mutation. Assuming the allele frequencies follow a Wright-Fisher diffusion and…
We systematically investigate the embedding of U(1)_X Froggatt-Nielsen models in (four-dimensional) local supersymmetry. We restrict ourselves to models with a single flavon field. We do not impose a discrete symmetry by hand, e.g.…
We investigate the $\Lambda$-Seed-Bank-Wright-Fisher process, a model describing allele frequency dynamics in populations exhibiting both skewed offspring distributions and dormancy. By performing a change of measure, we condition this…
The Fleming-Viot measure-valued diffusion is a Markov process describing the evolution of (allelic) types under mutation, selection and random reproduction. We enrich this process by genealogical relations of individuals so that the random…
Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is $\langle x^2(t)\rangle\simeq\mathscr{K}(t)t$ with…
We provide (upper and lower) scaling bounds for a singular perturbation model for the cubic-to-tetragonal phase transformation with (partial) displacement boundary data. We illustrate that the order of lamination of the affine displacement…
Natural populations often show enhanced genetic drift consistent with a strong skew in their offspring number distribution. The skew arises because the variability of family sizes is either inherently strong or amplified by population…
The scaled Brownian motion (SBM) is regarded as one of the paradigmatic random processes, featuring the anomalous diffusion property characterized by the diffusion exponent. It is a Gaussian, self-similar process with independent…