Evidence for fast thermalization in the plane-wave matrix model

We report on a numerical simulation of the classical evolution of the plane-wave matrix model with semiclassical initial conditions. Some of these initial conditions thermalize and are dual to a black hole forming from the collision of D-branes in the plane-wave geometry. In particular, we consider a large fuzzy sphere (a D2-brane) plus a single eigenvalue (a D0 particle) going exactly through the center of the fuzzy sphere and aimed to intersect it. Including quantum fluctuations of the off-diagonal modes in the initial conditions, with sufficient kinetic energy the configuration collapses to a small size. We also find evidence for fast thermalization: rapidly decaying autocorrelation functions at late times with respect to the natural time scale of the system.     

Boundary crisis and transient in a dissipative relativistic standard map

Some dynamical properties for a problem concerning the acceleration of particles in a wave packet are studied. The model is described in terms of a two-dimensional nonlinear map obtained from a Hamiltonian which describes the motion of a relativistic standard map. The phase space is mixed in the sense that there are regular and chaotic regions coexisting. When dissipation is introduced, the property of area preservation is broken and attractors emerge. We have shown that a tiny increase of the dissipation causes a change in the phase space. A chaotic attractor as well as its basin of attraction are destroyed thereby leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with the stable manifold of a saddle fixed point. Once the chaotic attractor is destroyed, a chaotic transient described by a power law with exponent −1 is observed.     

Bilinear Sobolev–Poincaré Inequalities and Leibniz-Type Rules

The dual purpose of this article is to establish bilinear Poincaré-type estimates associated with an approximation of the identity and to explore the connections between bilinear pseudo-differential operators and bilinear potential-type operators. The common underlying theme in both topics is their applications to Leibniz-type rules in Sobolev and Campanato–Morrey spaces under Sobolev scaling.     

Fourth order evolution equations which describe pseudospherical surfaces

Differential equations that describe pseudospherical surfaces are considered. These equations are equivalent to the structure equations of a metric with Gaussian curvature K=−1$K=-1$. They can also be described as the compatibility condition of an associated linear problem also referred to as a zero curvature representation. A complete and explicit classification of a class of fourth order evolution equations is given. The classification provides four huge classes (referred to as Types I–IV) of fourth order evolution equations that describe pseudospherical surfaces, together with the associated one (or more) parameter linear problems. The differential equations of each type are determined by choosing certain arbitrary differentiable functions. Fourth-order member of the Burgers hierarchy and a modified Kuramoto–Sivashinsky equation are examples of equations described by Types I and IV, respectively. Many other explicit examples are presented.     

Algebraic functions in quasiprimal algebras

A function is algebraic on an algebra if it can be implicitly defined by a system of equations on . In this note we give a semantic characterization for algebraic functions on quasiprimal algebras. This characterization is applied to obtain necessary and sufficient conditions for a quasiprimal algebra to have every one of its algebraic functions be a term function. We also apply our results to particular algebras such as finite fields and monadic algebras.     

Potassium N‐(6‐oxo­cyclo­hexa‐1,3‐dien‐5‐yl­idene­methyl)­glycinate

We are very interested in characterizing ligands derived from salicyl­aldehyde and α‐amino acids. These ligands form interesting complexes with different transition metals, which are very useful for understanding some biological systems. For Schiff bases derived from salicyl­aldehyde and different alkyl­amines or aryl­amines, the enol–imine form is predominant. The title compound, (I), shows bond distances which are clearly in agreement with the keto–amine form.     

Detecting and imaging dielectric objects from real data: A shape-based approach

In this paper we investigate the performance of a shape-reconstruction technique as tested on the ‘Marseille data’. This approach, which is based on a level set technique, offers several advantages compared to other approaches, as for example well-defined boundaries and the incorporation of an intrinsic regularization in the form of a priori assumptions regarding the general structures in the medium. The level set strategy (which is an implicit representation of the shapes) frees us from topological restrictions during this reconstruction process. Our algorithm is aiming at, not only detecting the objects, but simultaneously determining their approximate locations, sizes and dielectric properties. The numerical experiments show the utility of this method.