We introduce a new method for studying the Cauchy problem for systems of conservation laws in one space dimension. This method is based on the equivalence of the Cauchy problems in Eulerian and Lagrangian coordinates, as regards the existence and uniqueness of entropy solutions. The main idea is to solve the problem in Lagrangian coordinates and determine the transformation linking the two coor...

We present a surface Cauchy-Born approach to modeling FCC metals with nanometer scale dimensions for which surface stresses contribute significantly to the overall mechanical response. The model is based on an extension of the traditional Cauchy-Born theory in which a surface energy term that is obtained from the underlying crystal structure and governing interatomic potential is used to augmen...

It is generally considered as self evident that the lifetime of our vacuum in the landscape of string theory cannot be much shorter than the current age of the universe. Here I show why this lower limit is invalid. A certain type of " parallel universes " is a necessary consequence of the string-landscape dynamics and might well allow us to " survive " vacuum decay. As a consequence our stringy...

We consider an atomistic interaction potential in one dimension given through a minimization problem, which gives rise to a field. The forces on atoms are in this case given by local expressions involving this field. A convenient feature of this model is the existence of a weak formulation for the forces, which provides a natural connection point for the coupling with a continuum model. We sugg...

A concurrent multiscale method has been developed based on the combination of the advanced meshfree method and molecular dynamics (MD). An advanced transition algorithm using regular transition particles was employed to ensure the compatibility of both displacements and their gradients. An effective local quasi-continuum approach is also applied to obtain the equivalent continuum strain energy ...

First-principles calculations are presented for parent B2 phase and martensitic B19 and B190 phases in NiTi. The results indicate that both B19 and B190 are energetically more stable than the parent B2 phase. By means of ab initio density functional theory, the complete distortion–shuffle energy landscape associated with B2? B19 transformation in NiTi is then determined. In addition to accounti...

We derive the equivalent energy of a square lattice that either deforms into the threedimensional Euclidean space or remains planar. Interactions are not restricted to pairs of points and take into account changes of angles. Under some relationships between the local energies associated with the four vertices of an elementary square, we show that the limit energy can be obtained by mere quasico...

During the last ten years or so, derivations of the Born rule based on decision theory have been proposed and developed, and it is claimed that these are valid in the context of the Everett interpretation. This claim is critically assessed and it is shown that one of its key assumptions is a natural consequence of the principles underlying the Copenhagen interpretation, but constitutes a major ...