A one-dimensional spot welding model.
A simple and efficient scheme for phase field crystal simulation
We propose an unconditionally stable semi-implicit time discretization of the phase field crystal evolution. It is based on splitting the underlying energy into convex and concave parts and then performing H-1 gradient descent steps implicitly for the former and explicitly for the latter. The splitting is effected in such a way that the resulting equations are linear in each time step and allow an extremely simple implementation and efficient solution. We provide the associated stability and error...
Asymptotic behaviour for a phase-field model with hysteresis in one-dimensional thermo-visco-plasticity
The asymptotic behaviour for of the solutions to a one-dimensional model for thermo-visco-plastic behaviour is investigated in this paper. The model consists of a coupled system of nonlinear partial differential equations, representing the equation of motion, the balance of the internal energy, and a phase evolution equation, determining the evolution of a phase variable. The phase evolution equation can be used to deal with relaxation processes. Rate-independent hysteresis effects in the strain-stress...
Compact attractors for a Stefan problem with kinetics.
Comparative Study of a Solid Film Dewetting in an Attractive Substrate Potentials with the Exponential and the Algebraic Decay
We compare dewetting characteristics of a thin nonwetting solid film in the absence of stress, for two models of a wetting potential: the exponential and the algebraic. The exponential model is a one-parameter (r) model, and the algebraic model is a two-parameter (r, m) model, where r is the ratio of the characteristic wetting length to the height of the unperturbed film, and m is the exponent of h (film height) in a smooth function that interpolates the system's surface energy above and below...
Exponential attractors for a Cahn-Hilliard model in bounded domains with permeable walls.
Hybrid level set phase field method for topology optimization of contact problems
The paper deals with the analysis and the numerical solution of the topology optimization of system governed by variational inequalities using the combined level set and phase field rather than the standard level set approach. The standard level set method allows to evolve a given sharp interface but is not able to generate holes unless the topological derivative is used. The phase field method indicates the position of the interface in a blurry way but is flexible in the holes generation. In the...
Multi-component Allen-Cahn equation for elastically stressed solids.
Self-similarly expanding networks to curve shortening flow
We consider a network in the Euclidean plane that consists of three distinct half-lines with common start points. From that network as initial condition, there exists a network that consists of three curves that all start at one point, where they form degree angles, and expands homothetically under curve shortening flow. We also prove uniqueness of these networks.