Controlling soliton explosions

We investigate the dynamics of solitons in generalized Klein–Gordon equations in the presence of nonlinear damping and spatiotemporal perturbations. We will present different mechanisms for soliton explosions. We show (both analytically and numerically) that some space-dependent perturbations or nonlinear damping can make the soliton internal mode unstable leading to soliton explosion. We will show that, in some cases, while some conditions are satisfied, the soliton explodes becoming a permanent, extremely complex, spatiotemporal dynamics. We believe these mechanisms can explain some of the phenomena that recently have been reported to occur in excitable media. We present a method for controlling soliton explosions.     

Transgression and twisted anomaly cancellation formulas on odd dimensional manifolds

We compute the transgressed forms of some modularly invariant characteristic forms, which are related to the twisted elliptic genera. We study the modularity properties of these secondary characteristic forms and relations among them. We also get some twisted anomaly cancellation formulas on some odd dimensional manifolds.     

High energy nuclear collisions: Theory overview

We review some basic concepts of relativistic heavy-ion physics and discuss our understanding of some key results from the experimental program at the relativistic heavy-ion collider (RHIC). We focus in particular on the early time dynamics of nuclear collisions, some result from lattice QCD, hard probes and photons.     

No-Signaling in Quantum Mechanics

We review some concepts and reasonings regarding the notion of no-signaling and its relation to quantum mechanics in bipartite Bell-type scenarios. We recapitulate the no-signaling property of joint conditional probability distributions in geometrical and information theoretic terms. We summarize the reasons why quantum mechanics does not enable instantaneous communication. We make some comments on quantum field theoretic aspects.     

Transitivity and ergodicity of quantum systems

We generalize the notion of a topological transitive or a topologically mixing system for quantum mechanical systems in a consistent way. We compare these ergodic properties with the classical results. We deal with some aspects of nearly Abelian systems and investigate some relations between these notions.     

On the quantum mechanical superposition of macroscopically distinguishable states

We consider the superposition of macroscopically distinguishable states for a measuring process whose time evolution is described by the Schrödinger equation. We ask whether it is possible to observe interference effects due to the above mentioned superposition and how to observe them, taking into consideration an experiment performed by other authors. We find a necessary condition in order to be able to observe these effects. We also point out some very serious difficulties in observing them and analyse the connection between some of these difficulties and the Wigner-Araki-Yanase theory. We try to explain why the whole problem seems to us to be far from having a solution and we suggest some paths we think worthy of further investigation.     

高温超导的压力效应研究

从修正的依赖时间的金兹堡-朗道方程出发研究高温超导体的压力效应，考虑序参量为一个复数. 在外界压力作用下，理论上获得了压强与高温超导温度的一些表达式.在一些特殊情况下，得到高温超导的临界温度T随外压强的增加而降低；在另外某些条件下高温超导的临界温度T_C随外压强的增加而增加.外部施加的压强，只有一部分反映在高温超导态. 关键词： 高温超导 压强 临界温度     

Reiterated Ergodic Algebras and Applications

We redefine the homogenization algebras without requiring the separability assumption. We show that this enables one to treat more complicated homogenization problems than those solved by the previous theory. In particular we exhibit an example of algebra which, contrary to the algebra of almost periodic functions, induces no homogenization algebra. We prove some general compactness results which are then applied to the resolution of some homogenization problems related to the generalized Reynolds type equations and to some nonlinear hyperbolic equations.     

Absence of screening in certain lattice gauge and plasma models

We discuss some Abelian lattice gauge models of the noncompact variety, including models of relativistic and nonrelativistic plasmas. For all these models we show absence of exponential clustering for some observables in some domains in parameter space. We comment on the physical meaning of these results, in particular with respect to Debye screening of static electric charges.     

Hodge Integrals and Integrable Hierarchies

We show that the generating series of some Hodge integrals involving one or two partitions are τ-functions of the KP hierarchy or the 2-Toda hierarchy, respectively. We also reformulate the results as a relationship between the relative invariants of some local Calabi-Yau geometries and integrable hierarchies and present some more examples using the topological vertex.     

Strings, tachyons and deconfinement

We argue that the tachyons which exist in some string models are a signal of deconfinement. We compare the deconfinement temperature obtained from Monte Carlo calculations with some strings models.     

Sequential Product of Quantum Effects: An Overview

This article presents an overview for the theory of sequential products of quantum effects. We first summarize some of the highlights of this relatively recent field of investigation and then provide some new results. We begin by discussing sequential effect algebras which are effect algebras endowed with a sequential product satisfying certain basic conditions. We then consider sequential products of (discrete) quantum measurements. We next treat transition effect matrices (TEMs) and their associated sequential product. A TEM is a matrix whose entries are effects and whose rows form quantum measurements. We show that TEMs can be employed for the study of quantum Markov chains. Finally, we prove some new results concerning TEMs and vector densities.     

Black-hole thermodynamics: Entropy, information and beyond

We review some recent advances in black-hole thermodynamics including statistical mechanical origins of black-hole entropy and its leading order corrections from the view points of various quantum gravity theories. We then examine the problem of information loss and some possible approaches to its resolution. Finally, we study some proposed experiments which may be able to provide experimental signatures of black holes.     

The power of the small

We review some of the ways clusters offer special kinds of insights both into properties of bulk matter and properties unique to small systems. We then survey some of the tantalizing open questions that lie ahead in cluster science.     

Algebraic classification of higher dimensional spacetimes

We algebraically classify some higher dimensional spacetimes, including a number of vacuum solutions of the Einstein field equations which can represent higher dimensional black holes.We discuss some consequences of this work.     

Some Global and Local Aspects of Bigravity

We review some global and local aspects of bigravity theories concerning the causal structure of two interacting metrics. We provide some general settings where global hyperbolicity is lost even if both metrics are independently globally hyperbolic. Finally we say some words about the spectrum of these theories and their relation to the cosmological constant problem. To appear in the Proceedings of Peyresq Cosmology Meeting 2005.     

Self-avoiding Walks and Polymer Adsorption: Low Temperature Behaviour

We give a brief review of the self-avoiding walk model of polymer adsorption highlighting some open problems in the area. We then discuss the low temperature behaviour and derive some results about the behaviour of the free energy at low temperatures.     

Elastography

We present a concise summary of some of the fundamentals and of our work in the field of elastography over the past 12 years. This summary is not exhaustive, since several recent reviews of this area are available. We begin by presenting some relevant background material from the field of biomechanics, which forms the foundation of this work. We then proceed to discuss the basic principles and limitations that are involved in the production of strain images (elastograms) of biological tissues. Early results as well as current results from biological tissues in vitro and in vivo are shown. We conclude with some thoughts regarding the potential of elastography for medical diagnosis.     

A simple 2D SOC model for one of the main sources of geomagnetic disturbances: Flares

We introduce a simple model for solar flares, one of the main sources of geomagnetic disturbances. We have obtained power-laws for the probability distribution functions of some relevant physical characteristics of flares which could serve as the fingerprint of a critical state at the base of such phenomena and, given that we have not introduced a fine tune mechanism, of self-organized criticality. We compare our results with some recent experimental work on the statistics of flares and analyze the possible connection of these power laws with others already found by our group in geomagnetic disturbances distributions. We also present some limitations of our model as well as possible extensions and corrections to be taken into account in future works.     

Type II quantum algorithms

We review and analyze the hybrid quantum-classical NMR computing methodology referred to as Type II quantum computing. We show that all such algorithms considered so far within this paradigm are equivalent to some classical lattice Boltzmann scheme. We derive a sufficient and necessary constraint on the unitary operator representing the quantum mechanical part of the computation which ensures that the model reproduces the Boltzmann approximation of a lattice-gas model satisfying semi-detailed balance. Models which do not satisfy this constraint represent new lattice Boltzmann schemes which cannot be formulated as the average over some underlying lattice-gas. We conclude the paper with some discussion of the strengths, weaknesses and possible future direction of Type II quantum computing.