Related papers: Enslaved Phase-Separation Fronts and Liesegang Pat…
We consider a propagation of exotermic transition front in a discrete conservative oscillatory chain. Adequate description of such fronts is a key point in prediction of important transient phenomena, including phase transitions and…
Moving boundary problems allow to model systems with phase transition at an inner boundary. Driven by problems in economics and finance, in particular modeling of limit order books, we consider a stochastic and non-linear extension of the…
Complex interactions leading to phase transitions continue to hold a due interest in the scientific community. We charactersize a phase transition in a coupled oscillators model where interactions are not local in nature. At a first order…
Flow matching has become a leading framework for generative modeling, but quantifying the uncertainty of its samples remains an open problem. Existing approaches retrain the model with auxiliary variance heads, maintain costly ensembles, or…
Employing a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional…
We study the reaction front for the process $A+B\to C$ in which the reagents move subdiffusively. We propose a fractional reaction-subdiffusion equation in which both the motion and the reaction terms are affected by the subdiffusive…
The $S=1/2$ antiferromagnetic Heisenberg model on multi-leg ladders is investigated. Criticality of the ground-state transition is explored by means of finite-size scaling. The ladders with an even number of legs and those with an odd…
A non-isothermal phase field model that captures both displacive and diffusive phase transformations in a unified framework is presented. The model is developed in a formal thermodynamic setting, which provides guidance on admissible…
We consider the mathematical analysis and homogenization of a moving boundary problem posed for a highly heterogeneous, periodically perforated domain. More specifically, we are looking at a one-phase thermo-elasticity system with phase…
We investigate the dynamics of a critical XXZ spin-1/2 chain prepared in an inhomogeneous initial state with different magnetizations on the left and right halves. We simulate the real-time evolution using the time-evolving block decimation…
High-dimensional data must be highly structured to be learnable. Although the compositional and hierarchical nature of data is often put forward to explain learnability, quantitative measurements establishing these properties are scarce.…
The interface separating a liquid from its vapor phase is diffuse: the composition varies continuously from one phase to the other over a finite length. Recent experiments on dynamic jamming fronts in two dimensions [Waitukaitis et al.,…
Using the adaptive time-dependent density matrix renormalization group method, we numerically study the spin dynamics and transport in one-dimensional spin-1/2 systems at zero temperature. Instead of computing transport coefficients from…
We study the phase-ordering kinetics of the one-dimensional Heisenberg model with conserved order parameter, by means of scaling arguments and numerical simulations. We find a rich dynamical pattern with a regime characterized by two…
Many nonlinear partial differential equations (PDEs) display a coarsening dynamics, i.e., an emerging pattern whose typical length scale $L$ increases with time. The so-called coarsening exponent $n$ characterizes the time dependence of the…
We investigate the transport and separation of overdamped particles under the action of a uniform external force in a two-dimensional periodic energy landscape. Exact results are obtained for the deterministic transport in a square lattice…
Critical points and phase transitions are characterized by diverging susceptibilities, reflecting the tendency of the system toward spontaneous symmetry breaking. Equilibrium statistical mechanics bounds these instabilities to occur at zero…
We investigate the application of conformable derivatives to model critical phenomena near continuous phase transitions. By incorporating a deformation parameter into the differential structure, we derive unified expressions for…
The quantum XXZ spin model with alternating bond strengths under magnetic field has a rich equilibrium phase diagram which includes Haldane, Luttinger liquid, singlet, and paramagnetic phases. We show that the nearest neighbor bipartite and…
The non-cooperative eutectoid transformation relies on the presence of pre-existing cementite particles in the parent austenitic phase and yields a product, popularly known as the divorced eutectoid. In isothermal conditions, two of the…