Related papers: Integrability breaking in the Rule 54 cellular aut…
The mathematical modeling and numerical simulation of semiconductor-electrolyte systems play important roles in the design of high-performance semiconductor-liquid junction solar cells. In this work, we propose a macroscopic mathematical…
In this paper, we examine the complex sine-Gordon model in the presence of a boundary, and derive boundary conditions that preserve integrability. We present soliton and breather solutions, investigate the scattering of particles and…
We study numerically how multiple deformable capsules squeeze into a constriction. This situation is largely encountered in microfluidic chips designed to manipulate living cells, which are soft entities. We use fully three-dimensional…
In this paper I describe a cellular automaton model of a multi-species ecosystem, suitable for the study of emergent properties of macroevolution. Unlike majority of ecological models, the number of coexisting species is not fixed. Starting…
The cellular automaton (CA) pulsing model (arXiv:1806.06416) described the surprising phenomenon of spontaneous, sustained and robust rhythmic oscillations, pulsing dynamics, when random wiring is applied to a 2D `glider' rule running in a…
We propose a model of mobile agents to construct social networks, based on a system of moving particles by keeping track of the collisions during their permanence in the system. We reproduce not only the degree distribution, clustering…
The competition between electron localization and de-localization in Mott insulators underpins the physics of strongly-correlated electron systems. Photo-excitation, which re-distributes charge between sites, can control this many-body…
Solvation is a notoriously difficult and nagging problem for the rigorous theoretical description of chemistry in the liquid phase. Successes and failures of various approaches ranging from implicit solvation modeling through dielectric…
By using a variant of the quantum inverse scattering method, commutation relations between all elements of the quantum monodromy matrix of bosonic Massive Thirring (BMT) model are obtained. Using those relations, the quantum integrability…
Symmetry breaking states of matter can transmit symmetry breaking to nearby atoms or molecular complexes, perturbing their spectra. We calculate one such effect, involving the `axion electrodynamics' relevant to topological insulators,…
In this paper, we present a splitting algorithm to solve multicomponent transport models. These models are related to plasma simulations, in which we consider the local thermodynamic equilibrium and weakly ionised plasma-mixture models that…
We present a family of one-dimensional cellular automata modeling the diffusion of an innovation in a population. Starting from simple deterministic rules, we construct models parameterized by the interaction range and exhibiting a…
We examine the performance of various commonly used integration schemes in dissipative particle dynamics simulations. We consider this issue using three different model systems, which characterize a variety of different conditions often…
Particle-like objects are observed to propagate and interact in many spatially extended dynamical systems. For one of the simplest classes of such systems, one-dimensional cellular automata, we establish a rigorous upper bound on the number…
We consider a one-dimensional gas of hard rods, one of the simplest examples of an interacting integrable model. It is well known that the hydrodynamics of such integrable models can be understood by viewing the system as a gas of…
Cell motility is connected to the spontaneous symmetry breaking of a circular shape. In https://doi.org/10.1103/PhysRevLett.110.078102, Blanch-Mercader and Casademunt perfomed a nonlinear analysis of the minimal model proposed by Callan and…
We explore boundary scattering in the sine-Gordon model with a non-integrable family of Robin boundary conditions. The soliton content of the field after collision is analysed using a numerical implementation of the direct scattering…
The dynamics of active matter driven by interacting molecular motors has a non-potential structure at the local scale. However, we show that there exists a quasi-potential effectively describing the collective self-organization of the…
We consider deformations of the $SU(3)$ Affine Toda theory (AT) and investigate the integrability properties of the deformed theories. We find that for some special deformations all conserved quantities change to being conserved only…
We study the model of a molecular switch comprised of a molecule with a soft vibrational degree of freedom coupled to metallic leads. In the presence of strong electron-ion interaction, different charge states of the molecule correspond to…