Related papers: Existence of solutions for a mathematical model re…
In the present paper we consider a partial differential system describing a phase-field model with temperature dependent constraint for the order parameter. The system consists of an energy balance equation with a fairly general nonlinear…
The identification and use of reversible Martensitic transformations, typically described as shape memory transformations, as a new class of solid-solid phase change material is experimentally demonstrated here for the first time. To prove…
We propose a class of temporally high-order parametric finite element methods for simulating solid-state dewetting of thin films in two dimensions using a sharp-interface model. The process is governed by surface diffusion and contact point…
We prove the global in time existence of spherically symmetric solutions to an initial-boundary value problem for a system of partial differential equations, which consists of the equations of linear elasticity and a nonlinear,…
Phase field simulations play a key role in the understanding of microstructure evolution in additive manufacturing. However, they have been found extremely computationally expensive. One of the reasons is the small time step requirement to…
We develop a new generalized coupling approach to the study of stochastic delay equations with H\"older continuous coefficients, for which analytical PDE-based methods are not available. We prove that such equations possess unique weak…
A three-dimensional model is presented for the prediction of solidification behavior using a nonlinear transformation of the enthalpy equation in a Smoothed Particle Hydrodynamics (SPH) discretization. The effect of phase change in the form…
The quasistatic problem of shape memory alloys is reviewed within the phenomenological mechanics of solids without microphysics analysis. The assumption is that the temperature variation rate is small. Reissner's type of generalized…
In this paper, we propose a new unified first order hyperbolic model of Newtonian continuum mechanics coupled with electro-dynamics. The model is able to describe the behavior of moving elasto-plastic dielectric solids as well as viscous…
These lectures present the analysis of stability and control of long time behavior of PDE models described by nonlinear evolutions of hyperbolic type. Specific examples of the models under consideration include: (i) nonlinear systems of…
Alternative approach for description of the non-equilibrium phenomena arising in solids at a severe external loading is analyzed. The approach is based on the new form of kinetic equations in terms of the internal and modified free energy.…
In this paper, a macroscopic three dimensional non-isothermal model is proposed to describe hysteresis phenomena and phase transformations in shape memory alloys (SMAs). The model is of phase-field type and is based on the Ginzburg-Landau…
The present work proposes a well-balanced finite volume-type numerical method for the solution of non-conservative hyperbolic partial differential equations (PDEs) with source terms. The method is characterized, first, by the use of a…
One of the most widely used active materials for phase-change memories (PCM), the ternary stoichiometric compound Ge$_2$Sb$_2$Te$_5$ (GST), has a low crystallization temperature of around 150$^\circ$C. One solution to achieve higher…
This work studies a variational formulation and numerical solution of a regularized morphoelasticity problem of shape evolution. The foundation of our analysis is based on the governing equations of linear elasticity, extended to account…
Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…
We present a new strategy for solving stiff ODEs with explicit methods. By adaptively taking a small number of stabilizing small explicit time steps when necessary, a stiff ODE system can be stabilized enough to allow for time steps much…
Driven systems offer the potential to realize a wide range of non-equilibrium phenomena that are inaccessible in static systems, such as the discrete time crystals. Time rondeau crystals with a partial temporal order have been proposed as a…
A class of abstract nonlinear time-periodic evolution problems is considered which arise in electrical engineering and other scientific disciplines. An efficient solver is proposed for the systems arising after discretization in time based…
A model of phase transitions with coupling between the order parameter and its gradient is proposed. It is shown, that this nonlinear model is suitable for the description of phase transitions accompanied by the formation of spatially…