Finite-Element Discretization of Static Hamilton-Jacobi Equations Based on a Local Variational Principle

We propose a linear finite-element discretization of Dirichlet problems for static Hamilton-Jacobi equations on unstructured triangulations. The discretization is based on simplified localized Dirichlet problems that are solved by a local variational principle. It generalizes several approaches known in the literature and allows for a simple and transparent convergence theory. In this paper the resulting system of nonlinear equations is solved by an adaptive Gauss-Seidel iteration that is easily implemented and quite effective as a couple of numerical experiments show.Comment: 19 page

Dynamical two electron states in a Hubbard-Davydov model

We study a model in which a Hubbard Hamiltonian is coupled to the dispersive phonons in a classical nonlinear lattice. Our calculations are restricted to the case where we have only two quasi-particles of opposite spins, and we investigate the dynamics when the second quasi-particle is added to a state corresponding to a minimal energy single quasi-particle state. Depending on the parameter values, we find a number of interesting regimes. In many of these, discrete breathers (DBs) play a prominent role with a localized lattice mode coupled to the quasiparticles. Simulations with a purely harmonic lattice show much weaker localization effects. Our results support the possibility that DBs are important in HTSC.Comment: 14 pages, 12 fig

Age and structure of the Shyok Suture in the Ladakh region of Northwestern India: Implications for slip on the Karakoram Fault System

A precise age for the collision of the Kohistan-Ladakh block with Eurasia along the Shyok suture zone (SSZ) is one key to understanding the accretionary history of Tibet and the tectonics of Eurasia during the India-Eurasia collision. Knowing the age of the SSZ also allows the suture to be used as a piercing line for calculating total offset along the Karakoram Fault, which effectively represents the SE border of the Tibetan Plateau and has played a major role in plateau evolution. We present a combined structural, geochemical, and geochronologic study of the SSZ as it is exposed in the Nubra region of India to test two competing hypotheses: that the SSZ is of Late Cretaceous or, alternatively, of Eocene age. Coarse-continental strata of the Saltoro Molasse, mapped in this area, contain detrital zircon populations suggestive of derivation from Eurasia despite the fact that the molasse itself is deposited unconformably onto Kohistan-Ladakh rocks, indicating that the molasse is postcollisional. The youngest population of detrital zircons in these rocks (approximately 92 Ma) and a U/Pb zircon date for a dike that cuts basal molasse outcrops (approximately 85 Ma) imply that deposition of the succession began in the Late Cretaceous. This establishes a minimum age for the SSZ and rules out the possibility of an Eocene collision between Kohistan-Ladakh and Eurasia. Our results support correlation of the SSZ with the Bangong suture zone in Tibet, which implies a total offset across the Karakoram Fault of approximately 130–190 km

Violence in sleep

Although generally considered as mutually exclusive, violence and sleep can coexist. Violence related to the sleep period is probably more frequent than generally assumed and can be observed in various conditions including parasomnias (such as arousal disorders and rapid eye movement sleep behaviour disorder), epilepsy (in particular nocturnal frontal lobe epilepsy) and psychiatric diseases (including delirium and dissociative states). Important advances in the fields of genetics, neuroimaging and behavioural neurology have expanded the understanding of the mechanisms underlying violence and its particular relation to sleep. The present review outlines the different sleep disorders associated with violence and aims at providing information on diagnosis, therapy and forensic issues. It also discusses current pathophysiological models, establishing a link between sleep-related violence and violence observed in other setting

Born-Oppenheimer Approximation near Level Crossing

We consider the Born-Oppenheimer problem near conical intersection in two dimensions. For energies close to the crossing energy we describe the wave function near an isotropic crossing and show that it is related to generalized hypergeometric functions 0F3. This function is to a conical intersection what the Airy function is to a classical turning point. As an application we calculate the anomalous Zeeman shift of vibrational levels near a crossing.Comment: 8 pages, 1 figure, Lette

Eliashberg-type equations for correlated superconductors

The derivation of the Eliashberg -- type equations for a superconductor with strong correlations and electron--phonon interaction has been presented. The proper account of short range Coulomb interactions results in a strongly anisotropic equations. Possible symmetries of the order parameter include s, p and d wave. We found the carrier concentration dependence of the coupling constants corresponding to these symmetries. At low hole doping the d-wave component is the largest one.Comment: RevTeX, 18 pages, 5 ps figures added at the end of source file, to be published in Phys.Rev. B, contact: [email protected]

Airy processes and variational problems

We review the Airy processes; their formulation and how they are conjectured to govern the large time, large distance spatial fluctuations of one dimensional random growth models. We also describe formulas which express the probabilities that they lie below a given curve as Fredholm determinants of certain boundary value operators, and the several applications of these formulas to variational problems involving Airy processes that arise in physical problems, as well as to their local behaviour.Comment: Minor corrections. 41 pages, 4 figures. To appear as chapter in "PASI Proceedings: Topics in percolative and disordered systems

On the partial connection between random matrices and interacting particle systems

In the last decade there has been increasing interest in the fields of random matrices, interacting particle systems, stochastic growth models, and the connections between these areas. For instance, several objects appearing in the limit of large matrices arise also in the long time limit for interacting particles and growth models. Examples of these are the famous Tracy-Widom distribution functions and the Airy_2 process. The link is however sometimes fragile. For example, the connection between the eigenvalues in the Gaussian Orthogonal Ensembles (GOE) and growth on a flat substrate is restricted to one-point distribution, and the connection breaks down if we consider the joint distributions. In this paper we first discuss known relations between random matrices and the asymmetric exclusion process (and a 2+1 dimensional extension). Then, we show that the correlation functions of the eigenvalues of the matrix minors for beta=2 Dyson's Brownian motion have, when restricted to increasing times and decreasing matrix dimensions, the same correlation kernel as in the 2+1 dimensional interacting particle system under diffusion scaling limit. Finally, we analyze the analogous question for a diffusion on (complex) sample covariance matrices.Comment: 31 pages, LaTeX; Added a section concerning the Markov property on space-like path

The 1+1-dimensional Kardar-Parisi-Zhang equation and its universality class

We explain the exact solution of the 1+1 dimensional Kardar-Parisi-Zhang equation with sharp wedge initial conditions. Thereby it is confirmed that the continuum model belongs to the KPZ universality class, not only as regards to scaling exponents but also as regards to the full probability distribution of the height in the long time limit.Comment: Proceedings StatPhys 2