Related papers: Cahn-Hilliard Equations on Lattices: Dynamic Trans…
This work builds on an existing model of discrete canonical evolution and applies it to the general case of a linear dynamical system, i.e., a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q} $ and linear…
This article presents a phenomenological dynamic phase transition theory -- modeling and analysis -- for superfluids. As we know, although the time-dependent Ginzburg-Landau model has been successfully used in superconductivity, and the…
We introduce a gravitational lattice theory defined in an AdS$_3$ black hole background that provides a holographic dual description of the linear-to-zigzag structural phase transition, characterized by the spontaneous breaking of parity…
Linear dynamics restricted to invariant submanifolds generally gives rise to nonlinear dynamics. Submanifolds in the quantum framework may emerge for several reasons: one could be interested in specific properties possessed by a given…
We propose a new class of phase field models coupled to viscoelasticity with large deformations, obtained from a diffuse interface mixture model composed by a phase with elastic properties and a liquid phase. The model is formulated in the…
This work addresses the problem of solving the Cahn-Hilliard equation numerically. For that we introduce an abstract formulation for Cahn-Hilliard type equations with dynamic boundary conditions, we conduct the spatial semidiscretization…
Spatio-temporal pattern formation over the square and rectangular domain has received significant attention from researchers. A wide range of stationary and non-stationary patterns produced by two interacting populations is abundant in the…
Dynamical systems with complex delayed interactions arise commonly when propagation times are significant, yielding complicated oscillatory instabilities. In this Letter, we introduce a class of systems with multiple, hierarchically long…
Cahn-Hilliard models are central for describing the evolution of interfaces in phase separation processes and free boundary problems. In general, they have non-constant and often degenerate mobilities. However, in the latter case, the…
We study semiclassical dynamics of anisotropic Heisenberg models in two and three dimensions. Such models describe lattice spin systems and hard core bosons in optical lattices. We solve numerically Landau-Lifshitz type equations on a…
We study structural transitions in a system of interacting particles arranged as a crystalline bilayer, as a function of the density $\rho$ and the distance $d$ between the layers. As $d$ is decreased a sequence of transitions involving…
We discuss the microscopic origin of dynamical instabilities and segregation patterns discovered in granular mixtures under oscillating horizontal shear, by investigating, via molecular dynamics simulations, the effective interaction…
Polarity fields are known to exhibit long distance patterns, in both physical and biological systems. The mechanisms behind such patterns are poorly understood. Here, we describe the dynamics of polarity fields using an original physical…
Nonlinear systems are often subject to random influences. Sometimes the noise enters the system through physical boundaries and this leads to stochastic dynamic boundary conditions. A dynamic, as opposed to static, boundary condition…
We study the problem of folding of the regular triangular lattice in the presence of bending rigidity K and magnetic field h (conjugate to the local normal vectors to the triangles). A numerical study of the transfer matrix of the problem…
It is shown how the combination of atomic deposition and nonlinear diffusion may lead, below a critical temperature, to the growth of nonuniform layers on a substrate. The dynamics of such a system is of the Cahn-Hilliard type, supplemented…
The formation and dynamics of a wide variety of binary two-dimensional ordered structures and superlattices are investigated through a phase field crystal model with sublattice ordering. Various types of binary ordered phases, the phase…
The world of two-dimensional crystals is of great significance for the design and study of structural and functional materials with novel properties. The world of two-dimensional crystals is of great significance for the design and study of…
Real-time dynamics of charge density and lattice displacements is studied during photoinduced ionic-to-neutral phase transitions by using a one-dimensional extended Peierls-Hubbard model with alternating potentials for the one-dimensional…
We present a phase-field model based on the Cahn-Hilliard equation to investigate the properties of phase separation in DNA nanostar systems. Leveraging a realistic free-energy functional derived from Wertheim theory, our model captures the…