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The jamming transition between flow and amorphous-solid states exhibits paradoxical properties characterized by hyperuniformity (suppressed spatial fluctuations) and criticality (hyperfluctuations), whose origin remains unclear. Here we…
A theoretical model of vapor-liquid phase transition in a system of charged hard cores of different diameters is suggested (with the parameters of the transition obtained in a number of studies using the Monte Carlo method). The model is…
The qualitative behavior of a thermodynamically consistent two-phase Stefan problem with surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state…
A multi-phase-field model for the description of the discontinuous precipitation reaction is formulated which takes into account surface diffusion along grain boundaries and interfaces as well as volume diffusion. Simulations reveal that…
Thermodynamical properties of nuclear matter undergoing multifragmentation are studied within a simplified version of the statistical model. An exact analytical solution has been found for the grand canonical ensemble. Excluded volume…
We investigate nonlinear aggregation dynamics of phase elements distributed on the unit circle under parametrically modulated external fields. Our model, inspired by flaky particle rotation in fluids, employs the equation ${d\alpha/dt} =…
The behavior of a class of solutions of the shallow water Airy system originating from initial data with discontinuous derivatives is considered. Initial data are obtained by splicing together self-similar parabolae with a constant…
The advantages of evolutionary algorithms with respect to traditional methods have been greatly discussed in the literature. While particle swarm optimizers share such advantages, they outperform evolutionary algorithms in that they require…
Clarifying the factors that control the contact angle of a liquid on a solid substrate is a long-standing scientific problem pertinent across physics, chemistry and materials science. Progress has been hampered by the lack of a…
Surfactant self-assembly at solid-liquid interfaces governs interfacial stability, transport, and reactivity across many technologies, yet resolving interfacial surfactant phases and their transition kinetics in situ remains challenging.…
The nonlocal-to-local asymptotics investigation for evolutionary problems is a central topic both in the theory of PDEs and in functional analysis. More recently, it became the main core of the mathematical analysis of phase-separation…
Hydrodynamic systems arising in swarming modelling include nonlocal forces in the form of attractive-repulsive potentials as well as pressure terms modelling strong local repulsion. We focus on the case where there is a balance between…
We establish regularity and, under suitable assumptions, convergence to stationary states for weak solutions of a parabolic equation with a non-linear non-local drift term; this equation was derived from a model of active Brownian particles…
Let $(\phi_t)$ be an area-preserving smooth flow on a compact, connected, orientable surface $\mathcal M$ with at least one but finitely many fixed points. Assume that $(\phi_t)$ is analytic (up to a canonical change of coordinates) in the…
The conserved Swift-Hohenberg equation with cubic nonlinearity provides the simplest microscopic description of the thermodynamic transition from a fluid state to a crystalline state. The resulting phase field crystal model describes a…
The study of liquid-liquid phase transition has attracted considerable attention. One interesting example of such phenomenon is phosphorus for which the existence a first-order phase transition between a low density insulating molecular…
Heating a long-range ordered adsorbate phase beyond its stability temperature does not necessarily result in a disordered phase, it can also break up into heavily fluctuating ordered domains. Temporal and/or spatial averaging over these…
The stability analysis of self-similar solutions is an important approach to confirm whether they act as an attractor in general non-self-similar gravitational collapse. Assuming that the collapsing matter is a perfect fluid with the…
In this paper, we revisit the classical problem of solving over-determined systems of nonsmooth equations numerically. We suggest a nonsmooth Levenberg--Marquardt method for its solution which, in contrast to the existing literature, does…
We address the issues of decoherence, frustrated hops and internal consistency in surface hopping. We demonstrate that moving away from an independent-trajectory picture is the strategy which allows us to propose a robust surface hopping…