Related papers: Robust exponential attractors for the modified pha…

We propose a phase-field theory for enriched continua. To generalize classical phase-field models, we derive the phase-field gradient theory based on balances of microforces, microtorques, and mass. We focus on materials where second…

In this paper we establish the existence and uniqueness of global solutions (in time), as well as the existence, regularity and stability (upper semicontinuity) of the attractor for the semigroup generated by the solutions of a…

The main objective of this paper is to investigate exponential attractors for a nonlocal delayed reaction-diffusion equation on an unbounded domain. We first obtain the existence of a globally attractive absorbing set for the dynamical…

The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arising in molecular dynamics. This is because the phase-field…

In this work we consider the non local evolution equation with time-dependent terms which arises in models of phase separation in $\mathbb{R}^N$ \[ \partial_t u=- u + g \left(\beta(J*u) +\beta h(t,u)\right) \] under some restrictions on…

Computing stationary states is an important topic for phase field crystal (PFC) models. Great efforts have been made for energy dissipation of the numerical schemes when using gradient flows. However, it is always time-consuming due to the…

We study a coupled nonlinear evolution system arising from the Ginzburg-Landau theory for atomic Fermi gases near the BCS-BEC crossover. First, we prove that the initial boundary value problem generates a strongly continuous semigroup on a…

Inflationary $\alpha$-attractor models can be naturally implemented in supergravity with hyperbolic geometry. They have stable predictions for observables, such as $n_s=1-{2/ N_e} $, assuming that the potential in terms of the original…

P. Galenko et al. proposed a modified Cahn-Hilliard equation to model rapid spinodal decomposition in non-equilibrium phase separation processes. This equation contains an inertial term which causes the loss of any regularizing effect on…

Let $M$ be a locally compact metric space endowed with a continuous flow $\phi : M \times \mathbb{R} \longrightarrow M$. Frequently an attractor $K$ for $\phi$ exists which is of interest, not only in itself but also the dynamics in its…

It is shown, under weak conditions, that the dynamical evolution of an important class of large systems of globally coupled, heterogeneous frequency, phase oscillators is, in an appropriate physical sense, time-asymptotically attracted…

We analyze a phase-field system where the energy balance equation is linearly coupled with a nonlinear and nonlocal ODE for the order parameter $\chi$. The latter equation is characterized by a space convolution term which models particle…

In a previous work a model was proposed for the phase transitions of crystals with localized magnetic moments which at low temperature have a "conical" arrangement that at higher T transforms into a more symmetrical structure (depending on…

We derive a phase field crystal model that couples the diffusive evolution of a microscopic structure with the fast dynamics of a macroscopic velocity field, explicitly accounting for the relaxation of elastic excitations. This model…

Models of cosmological scalar fields often feature "attractor solutions" to which the system evolves for a wide range of initial conditions. There is some tension between this well-known fact and another well-known fact: Liouville's theorem…

We establish the well-posedness of a strongly damped semilinear wave equation equipped with nonlinear hyperbolic dynamic boundary conditions. Results are carried out with the presence of a parameter distinguishing whether the underlying…

One of the major difficulties in employing phase field crystal (PFC) modeling and the associated amplitude (APFC) formulation is the ability to tune model parameters to match experimental quantities. In this work we address the problem of…

A superconductor with 4-fermion attraction, considered by Ma\'{c}kowiak and Tarasewicz is modified by adding to the Hamiltonian a long-range magnetic interaction $V$ between conduction fermions and localized distinguishable spin 1/2…

Under consideration is the damped semilinear wave equation \[ u_{tt}+u_t-\Delta u+u+f(u)=0 \] in a bounded domain $\Omega$ in $\mathbb{R}^3$ subject to an acoustic boundary condition with a singular perturbation, which we term "massless…

The structural phase transformations of 0.7Pb(Mg1/3Nb2/3)O3-0.3PbTiO3 (PMN-30%PT) have been studied using x-ray diffraction (XRD) and neutron scattering as a function of temperature and electric field. We observe the phase transformational…