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Dynamical systems on networks with adaptive couplings appear naturally in real-world systems such as power grid networks, social networks as well as neuronal networks. We investigate a paradigmatic system of adaptively coupled phase…
We demonstrate how concepts of statistical mechanics of interacting particles can have important implications in the choice of interaction potentials to model qualitative properties of cell aggregates in theoretical biology. We illustrate…
We study the dynamic scaling properties of an aggregation model in which particles obey both diffusive and driven ballistic dynamics. The diffusion constant and the velocity of a cluster of size $s$ follow $D(s) \sim s^\gamma$ and $v(s)…
We study a stochastic linear discrete metapolulation model to understand the effect of risk spreading by dispersion. We calculate analytically the stable distribution of populations that live in different habitats. The result shows that the…
Allostery, the intriguing phenomenon of long-range communication between distant sites in proteins, plays a central role in biomolecular regulation and signal transduction. While it is commonly attributed to conformational rearrangements,…
We investigate the long time behaviour of the one-dimensional ballistic aggregation model that represents a sticky gas of N particles with random initial positions and velocities, moving deterministically, and forming aggregates when they…
Stochastic dynamic models have been extensively used for the description of processes with uncertainties arising in the operations research, behavioral sciences, and many other application areas. A large class of the problems from these…
Rigidity percolation provides an important basis for understanding the onset of mechanical stability in disordered materials. While most studies on the triangular lattice have focused on static properties at fixed bond~(site) occupation…
We discuss theoretical models for the cooperative binding dynamics of ligands to substrates, such as dimeric motor proteins to microtubules or more extended macromolecules like tropomyosin to actin filaments. We study the effects of steric…
Individual-based models of chemical or biological dynamics usually consider individual entities diffusing in space and performing a birth-death type dynamics. In this work we study the properties of a model in this class where the birth…
Metastable quantum dynamics of an asymmetric triangular cluster that is coupled to a reservoir is investigated. The dynamics is governed by bath-mediated transitions, which in part require a thermal activation process. The decay rate is…
Correlations and other collective phenomena in a schematic model of heterogeneous binary agents (individual spin-glass samples) are considered on the complete graph and also on 2d and 3d regular lattices. The system's stochastic dynamics is…
Two powerful and complementary experimental approaches are commonly used to study the cell cycle and cell biology: One class of experiments characterizes the statistics (or demographics) of an unsynchronized exponentially-growing…
Adaptive dynamical networks appear in various real-word systems. One of the simplest phenomenological models for investigating basic properties of adaptive networks is the system of coupled phase oscillators with adaptive couplings. In this…
This study presents an enhanced method for analyzing cluster dynamics, with a particular focus on tracking clusters' continuity over time using time-series data from molecular dynamics (MD) simulation. The proposed method was applied to…
We introduce and analyse an individual-based evolutionary model, in which a population of genetically diverse organisms compete with each other for limited resources. Through theoretical analysis and stochastic simulations, we show that the…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
A general stochastic approach to the description of coagulating aerosol system is developed. As the object of description one can consider arbitrary mesoscopic values (number of aerosol clusters, their size etc). The birth-and-death…
The dynamics of cellular aggregates is driven by the interplay of mechanochemical processes and cellular activity. Although deterministic models may capture mechanical features, local chemical fluctuations trigger random cell responses,…
The dynamics of particles interacting by key-lock binding of attached biomolecules are studied theoretically. Experimental realizations of such systems include colloids grafted with complementary single-stranded DNA (ssDNA), and particles…