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World models have recently gained prominence for action-conditioned visual prediction in complex environments. However, relying on only a few recent observations causes them to lose long-term context. Consequently, within a few steps, the…
We study a nonlinear pseudodifferential equation describing the dynamics of dislocations. The long time asymptotics of solutions is described by the self-similar profiles.
We analyze two models of subdiffusion with stochastic resetting. Each of them consists of two parts: subdiffusion based on the continuous-time random walk (CTRW) scheme and independent resetting events generated uniformly in time according…
We study the random walk of a particle in a compartmentalized environment, as realized in biological samples or solid state compounds. Each compartment is characterized by its length $L$ and the boundaries transmittance $T$. We identify two…
Semantic equivalences are used in process algebra to capture the notion of similar behaviour, and this paper proposes a semi-quantitative equivalence for a stochastic process algebra developed for biological modelling. We consider…
Sticky Brownian motion is the simplest example of a diffusion process that can spend finite time both in the interior of a domain and on its boundary. It arises in various applications such as in biology, materials science, and finance.…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
High-fidelity, high-resolution numerical simulations are crucial for studying complex multiscale phenomena in fluid dynamics, such as turbulent flows and ocean waves. However, direct numerical simulations with high-resolution solvers are…
In a common experimental setting, the behaviour of a noisy dynamical system is monitored in response to manipulations of one or more control parameters. Here, we introduce a structured model to describe parametric changes in qualitative…
Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of…
We present sound and complete environmental bisimilarities for a variant of Dybvig et al.'s calculus of multi-prompted delimited-control operators with dynamic prompt generation. The reasoning principles that we obtain generalize and…
The study of first passage times for diffusing particles reaching target states is foundational in various practical applications, including diffusion-controlled reactions. In this work, we present a bi-scaling theory for the probability…
The parametric behavior of regular periodic arrays of rising bubbles is investigated with the aid of 2-dimensional BGK Lattice-Boltzmann (LB) simulators. The Recursive Projection Method is implemented and coupled to the LB simulators,…
The diffusion bridge, which is a diffusion process conditioned on hitting a specific state within a finite period, has found broad applications in various scientific and engineering fields. However, simulating diffusion bridges for modeling…
We consider a reaction-diffusion process with retardation. The particles, immersed in traps initially, remain inactive until another particle is annihilated spontaneously with a rate $\lambda$ at a certain point $\vec x$. In that case the…
The study of interactions between biomimetic membranes and micron-sized particles is crucial for understanding various biological processes. Here, we control microparticle spontaneous engulfment by giant lipid vesicles by tuning particle…
The problem of finding a finite state symbolic model which is bisimilar to a hybrid dynamical system (HDS) and has the minimum number of states is considered. The considered class of HDS allows for discrete-valued inputs that only affect…
We develop a statistical toolbox for a quantitative model evaluation of stochastic reaction-diffusion systems modeling space-time evolution of biophysical quantities on the intracellular level. Starting from space-time data $X_N(t,x)$, as,…
A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…
Analysis of mathematical models in ecology and epidemiology often focuses on asymptotic dynamics, such as stable equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain aspects of the dynamics…