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JNS
2010
55views more  JNS 2010»
13 years 5 months ago
Initiation of Cracks in Griffith's Theory: An Argument of Continuity in Favor of Global Minimization
The initiation of a crack in a sound body is a real issue in the setting of Griffith's theory of brittle fracture. If one uses the concept of critical energy release rate (Gri...
Jean-Jacques Marigo
JNS
2010
89views more  JNS 2010»
13 years 5 months ago
The Pattern of Multiple Rings from Morphogenesis in Development
Under certain conditions the problem of morphogenesis in development and the problem of morphology in block copolymers may be reduced to one geometric problem. In two dimensions t...
Xiaosong Kang, Xiaofeng Ren
JNS
2010
107views more  JNS 2010»
13 years 5 months ago
Ground States and Critical Points for Aubry-Mather Theory in Statistical Mechanics
We consider statistical mechanics systems defined on a set with some symmetry properties (namely, the set admits an action by a group, which is finitely generated and residually fi...
Rafael de La Llave, Enrico Valdinoci
JNS
2010
98views more  JNS 2010»
13 years 9 months ago
Analysis of a General Family of Regularized Navier-Stokes and MHD Models
ABSTRACT. We consider a general family of regularized Navier-Stokes and Magnetohydrodynamics (MHD) models on n-dimensional smooth compact Riemannian manifolds with or without bound...
Michael Holst, Evelyn Lunasin, Gantumur Tsogtgerel
JNS
2010
82views more  JNS 2010»
13 years 9 months ago
On a Diffusive Version of the Lifschitz-Slyozov-Wagner Equation
This paper is concerned with the Becker-D¨oring (BD) system of equations and their relationship to the Lifschitz-Slyozov-Wagner (LSW) equations. A diffusive version of the LSW eq...
Joseph G. Conlon
JNS
2010
50views more  JNS 2010»
13 years 9 months ago
Revisiting Energy Release Rates in Brittle Fracture
Antonin Chambolle, Gilles A. Francfort, Jean-Jacqu...
JNS
2010
67views more  JNS 2010»
13 years 9 months ago
A System of ODEs for a Perturbation of a Minimal Mass Soliton
We study soliton solutions to the nonlinear Schr¨odinger equation (NLS) with a saturated nonlinearity. NLS with such a nonlinearity is known to possess a minimal mass soliton. We ...
Jeremy L. Marzuola, Sarah Raynor, Gideon Simpson
JNS
2010
61views more  JNS 2010»
13 years 9 months ago
Validity and Failure of the Boltzmann Approximation of Kinetic Annihilation
This paper introduces a new method to show the validity of a continuum description for the deterministic dynamics of many interacting particles. Here the many particle evolution is...
Karsten Matthies, Florian Theil
JNS
2010
62views more  JNS 2010»
13 years 9 months ago
On the Existence of Quasipattern Solutions of the Swift-Hohenberg Equation
Quasipatterns (two-dimensional patterns that are quasiperiodic in any spatial direction) remain one of the outstanding problems of pattern formation. As with problems involving qu...
G. Iooss, A. M. Rucklidge