An alternative to the Allen-Cahn phase field model for interfaces in solids - numerical efficiency

The derivation of the Allen-Cahn and Cahn-Hilliard equations is based on the Clausius-Duhem inequality. This is not a derivation in the strict sense of the word, since other phase field equations can be fomulated satisfying this inequality. Motivated by the form of sharp interface problems, we formulate such an alternative equation and compare the properties of the models for the evolution of phase interfaces in solids, which consist of the elasticity equations and the Allen-Cahn equation or the alternative equation. We find that numerical simulations of phase interfaces with small interface energy based on the alternative model are more effective then simulations based on the Allen-Cahn model.Comment: arXiv admin note: text overlap with arXiv:1505.0544

Resonant Geometric Phases for Soliton Equations

The goal of the present paper is to introduce a multidimensional generalization of asymptotic reduction given in a paper by Alber and Marsden [1992], to use this to obtain a new class of solutions that we call resonant solitons, and to study the corresponding geometric phases. The term "resonant solitons" is used because those solutions correspond to a spectrum with multiple points, and they also represent a dividing solution between two different types of solitons. In this sense, these new solutions are degenerate and, as such, will be considered as singular points in the moduli space of solitons

On Soliton-type Solutions of Equations Associated with N-component Systems

The algebraic geometric approach to $N$-component systems of nonlinear integrable PDE's is used to obtain and analyze explicit solutions of the coupled KdV and Dym equations. Detailed analysis of soliton fission, kink to anti-kink transitions and multi-peaked soliton solutions is carried out. Transformations are used to connect these solutions to several other equations that model physical phenomena in fluid dynamics and nonlinear optics.Comment: 43 pages, 16 figure

Complex geometric asymptotics for nonlinear systems on complex varieties

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Biomedical modeling: the role of transport and mechanics

This issue contains a series of papers that were invited following a workshop held in July 2011 at the University of Notre Dame London Center. The goal of the workshop was to present the latest advances in theory, experimentation, and modeling methodologies related to the role of mechanics in biological systems. Growth, morphogenesis, and many diseases are characterized by time dependent changes in the material properties of tissues—affected by resident cells—that, in turn, affect the function of the tissue and contribute to, or mitigate, the disease. Mathematical modeling and simulation are essential for testing and developing scientific hypotheses related to the physical behavior of biological tissues, because of the complex geometries, inhomogeneous properties, rate dependences, and nonlinear feedback interactions that it entails

Wave Solutions of Evolution Equations and Hamiltonian Flows on Nonlinear Subvarieties of Generalized Jacobians

The algebraic-geometric approach is extended to study solutions of N-component systems associated with the energy dependent Schrodinger operators having potentials with poles in the spectral parameter, in connection with Hamiltonian flows on nonlinear subvariaties of Jacobi varieties. The systems under study include the shallow water equation and Dym type equation. The classes of solutions are described in terms of theta-functions and their singular limits by using new parameterizations. A qualitative description of real valued solutions is provided

Robustness of the BB84 quantum key distribution protocol against general coherent attacks

It is demonstrated that for the entanglement-based version of the Bennett-Brassard (BB84) quantum key distribution protocol, Alice and Bob share provable entanglement if and only if the estimated qubit error rate is below 25% or above 75%. In view of the intimate relation between entanglement and security, this result sheds also new light on the unconditional security of the BB84 protocol in its original prepare-and-measure form. In particular, it indicates that for small qubit error rates 25% is the ultimate upper security bound for any prepare-and-measure BB84-type QKD protocol. On the contrary, for qubit error rates between 25% and 75% we demonstrate that the correlations shared between Alice and Bob can always be explained by separable states and thus, no secret key can be distilled in this regime.Comment: New improved version. A minor mistake has been eliminate

Completely positive covariant two-qubit quantum processes and optimal quantum NOT operations for entangled qubit pairs

The structure of all completely positive quantum operations is investigated which transform pure two-qubit input states of a given degree of entanglement in a covariant way. Special cases thereof are quantum NOT operations which transform entangled pure two-qubit input states of a given degree of entanglement into orthogonal states in an optimal way. Based on our general analysis all covariant optimal two-qubit quantum NOT operations are determined. In particular, it is demonstrated that only in the case of maximally entangled input states these quantum NOT operations can be performed perfectly.Comment: 14 pages, 2 figure

Hydrodynamical analysis of single inclusive spectra and Bose-Einstein correlations for Pb+PbPb+Pb at 160 AGeV

We present the first analysis of preliminary data for $Pb+Pb$ at 160 $AGeV$ using 3+1-dimensional relativistic hydrodynamics. We find excellent agreement with the rapidity spectra of negative hadrons and the correlation measurements. The data indicates a large amount of stopping; $65\%$ of the invariant energy of the collision is thermalized and $73\%$ of the baryons are contained in the central fireball. Within our model this implies that a quark-gluon-plasma of lifetime 3.4 $fm/c$ was formed.Comment: 13 pages, 5 Postscript figures (attached to this file as compressed and uuencoded Postscript file