Related papers: Existence of solutions for a mathematical model re…
In this paper, the finite volume method is developed to analyze coupled dynamic problems of nonlinear thermoelasticity. The major focus is given to the description of martensitic phase transformations essential in the modelling of shape…
In this paper, we consider a coupled PDE system describing phase separation and damage phenomena in elastically stressed alloys in the presence of inertial effects. The material is considered on a bounded Lipschitz domain with mixed…
In this paper we analyze a new temperature-dependent model for adhesive contact that encompasses nonlocal adhesive forces and damage effects, as well as nonlocal heat flux contributions on the contact surface. The related PDE system…
In this paper we consider a nonlinear partial differential equation describing heat flow with ice-water phase transition in permafrost soils. Such models and their numerical approximations have been well explored in the applications…
The decomposition kinetics of a solid-solution into separate phases are analyzed with an equation of motion initially developed to account for dissipative processes in quantum systems. This equation and the steepest-entropy-ascent quantum…
This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial…
The mechanical response of solids depends on temperature because the way atoms and molecules respond collectively to deformation is affected at various levels by thermal motion. This is a fundamental problem of solid state science and plays…
We overview the concept of dynamical phase transitions in isolated quantum systems quenched out of equilibrium. We focus on non-equilibrium transitions characterized by an order parameter, which features qualitatively distinct temporal…
In many applications, the governing PDE to be solved numerically contains a stiff component. When this component is linear, an implicit time stepping method that is unencumbered by stability restrictions is often preferred. On the other…
We consider problems of dynamic viscoelasticity taking into account the coupling of elastic and thermal fields. Efficient approximate models are developed and computational results on thermomechanical behaviour of shape-memory-alloy…
Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.…
Metastability appears when a thermodynamic system, such as supercooled water (which is liquid below freezing temperature), lands on the "wrong" side of a phase transition, and remains for a very long time in a state different from its…
We introduce and analyse a continuum model for an interacting particle system of Vicsek type. The model is given by a non-linear kinetic partial differential equation (PDE) describing the time-evolution of the density $f_t$, in the single…
The computation of correspondences between shapes is a principal task in shape analysis. To this end, methods based on partial differential equations (PDEs) have been established, encompassing e.g. the classic heat kernel signature as well…
We study phase transitions and the nature of order in a class of classical generalized $O(N)$ nonlinear $\sigma$-models (NLS) constructed by minimally coupling pure NLS with additional degrees of freedom in the form of (i) Ising…
We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…
Recent biological evidence suggests the presence of a two-phase ageing process in several species. We introduce a system of two age-structured partial differential equations (PDE) representing two phases of ageing of a wild population. The…
This paper develops a control and estimation design for the one-phase Stefan problem. The Stefan problem represents a liquid-solid phase transition as time evolution of a temperature profile in a liquid-solid material and its moving…
In this paper, we establish the existence of a positive, bounded solution for a class of parabolic partial differential equations with nonlinear boundary conditions, where the boundary conditions depend on the solution on the boundary at a…
Shape-memory alloys exhibit a solid-to-solid phase transition that involves a temperature-driven rearrangement of their crystal structure and is responsible for their remarkable properties and numerous technological applications. Here, we…