177,088 research outputs found
Mathematical Models for Dislocations
No full texthe mathematical modelling of defects in cristals (the dislocations) is crucial to understand the microstructure of advanced materials and has a big impact on technological applications (e.g. in microelectronics). The talks of this workshop will describe different approaches to the analysis and simulation of dislocations ranging from variational models to evolutive differential models for their dynamics. Some simulations based on atomistic computations and level set methods will be presented.
The workshop is sponsored by the Galileo Project 2007 "Algorithms for the dynamic of dislocations and applications"
Junction of elastic plates and beams
No full textWe consider the linearized elasticity system in a multidomain of . This multidomain is the union of a horizontal plate with fixed cross section and small thickness ε,
and of a vertical beam with fixed height and small cross section of radius . The lateral boundary of the plate and the top of the beam are assumed to be clamped. When ε and tend to zero simultaneously, with , we identify the limit problem. This limit problem involves six junction conditions
A posteriori error estimates for the effective Hamiltonian of dislocation dynamics
No full textWe study an implicit and discontinuous scheme for a non-local Hamilton-Jacobi equation modelling dislocation dynamics. For the evolution problem, we prove an a posteriori estimate of Crandall-Lions type for the error between continuous and discrete solutions. We deduce an a posteriori error estimate for the effective Hamiltonian associated to a stationary cell problem. In dimension one and under suitable assumptions, we also give improved a posteriori estimates. Numerical simulations are provided. © 2011 Springer-Verlag
Qualitative Methods for Hamilton-Jacobi Equations and Applications
No full text15 interventi sull'analisi, la modellistica e l'approssimazione delle equazioni di Hamilton-Jacobi
programma sul sito:
http://www.mat.uniroma1.it/ricerca/convegni/2006/mathsandapps
Convergence of a generalized fast-marching method for an eikonal equation with a velocity-changing signn
No full textWe present a new fast-marching algorithm for an eikonal equation with a velocity changing sign. This first order equation models a front propagation in the normal direction. The algorithm is an extension of the fast-marching method in two respects. The first is that the new scheme can deal with a time- dependent velocity, and the second is that there is no restriction on its change in sign. We analyze the properties of the algorithm, and we prove its convergence in the class of discontinuous viscosity solutions. Finally, we present some numerical simulations of fronts propagating in R^2
Stability of travelling waves in a model for conical flames in two space dimensions
No full textThis paper deals with the question of the stability of conical-shaped solutions of a class of reaction-diffusion equations in . One first proves the existence of travelling waves solutions with conical-shaped level sets, generalizing earlier results by Bonnet, Hamel and Monneau. One then gives a characterization of the global attractor of these semilinear parabolic equations under some conical asymptotic conditions. Lastly, the global stability of the travelling waves solutions is proved
A convergent scheme for a non local Hamilton-Jacobi equation modelling dislocation dynamic
No full textWe study dislocation dynamics with a level set point of view. The model we present here looks at the zero level set of the solution of a non local Hamilton Jacobi equation, as a dislocation in a plane of a crystal. The front has a normal speed, depending on the solution itself. We prove existence and uniqueness for short time in the set of continuous viscosity solutions. We also present a first order finite difference scheme for the corresponding level set formulation of the model. The scheme is based on monotone numerical Hamiltonian, proposed by Osher and Sethian. The non local character of the problem makesit not monotone. We obtain an explicit convergence rate of the approximate solution to the viscosity solution. We finally provide numerical simulations
Dislocation Dynamics: a Non-local Moving Boundary
No full textIn this article, we present briefly a mathematical study of the dynamics of line defects called dislocations, in crystals. The mathematical model is an eikonal equation describing the motion of the dislocation line with a velocity which is a non-local function of the whole shape of the dislocation. We present some partial existence and uniqueness results. Finally, we also show that the self-dynamics of a dislocation line at large scale is asymptotically described by an anisotropic mean curvature motion.
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