Phonon Transmission Rate, Fluctuations, and Localization in Random Semiconductor Superlattices: Green's Function Approach

We analytically study phonon transmission and localization in random superlattices by using a Green's function approach. We derive expressions for the average transmission rate and localization length, or Lyapunov exponent, in terms of the superlattice structure factor. This is done by considering the backscattering of phonons, due to the complex mass density fluctuations, which incorporates all of the forward scattering processes. These analytical results are applied to two types of random superlattices and compared with numerical simulations based on the transfer matrix method. Our analytical results show excellent agreement with the numerical data. A universal relation for the transmission fluctuations versus the average transmission is derived explicitly, and independently confirmed by numerical simulations. The transient of the distribution of transmission to the log-normal distribution for the localized phonons is also studied.Comment: 36 pages, Late

Statistical Signatures of Photon Localization

The realization that electron localization in disordered systems (Anderson localization) is ultimately a wave phenomenon has led to the suggestion that photons could be similarly localized by disorder. This conjecture attracted wide interest because the differences between photons and electrons - in their interactions, spin statistics, and methods of injection and detection - may open a new realm of optical and microwave phenomena, and allow a detailed study of the Anderson localization transition undisturbed by the Coulomb interaction. To date, claims of three-dimensional photon localization have been based on observations of the exponential decay of the electromagnetic wave as it propagates through the disordered medium. But these reports have come under close scrutiny because of the possibility that the decay observed may be due to residual absorption, and because absorption itself may suppress localization. Here we show that the extent of photon localization can be determined by a different approach - measurement of the relative size of fluctuations of certain transmission quantities. The variance of relative fluctuations accurately reflects the extent of localization, even in the presence of absorption. Using this approach, we demonstrate photon localization in both weakly and strongly scattering quasi-one-dimensional dielectric samples and in periodic metallic wire meshes containing metallic scatterers, while ruling it out in three-dimensional mixtures of aluminum spheres.Comment: 5 pages, including 4 figure

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

Magnetic structures and reorientation transitions in noncentrosymmetric uniaxial antiferromagnets

A phenomenological theory of magnetic states in noncentrosymmetric tetragonal antiferromagnets is developed, which has to include homogeneous and inhomogeneous terms (Lifshitz-invariants) derived from Dzyaloshinskii-Moriya couplings. Magnetic properties of this class of antiferromagnets with low crystal symmetry are discussed in relation to its first known members, the recently detected compounds Ba2CuGe2O7 and K2V3O8. Crystallographic symmetry and magnetic ordering in these systems allow the simultaneous occurrence of chiral inhomogeneous magnetic structures and weak ferromagnetism. New types of incommensurate magnetic structures are possible, namely, chiral helices with rotation of staggered magnetization and oscillations of the total magnetization. Field-induced reorientation transitions into modulated states have been studied and corresponding phase diagrams are constructed. Structures of magnetic defects (domain-walls and vortices) are discussed. In particular, vortices, i.e. localized non-singular line defects, are stabilized by the inhomogeneous Dzyaloshinskii-Moriya interactions in uniaxial noncentrosymmetric antiferromagnets.Comment: 18 pages RevTeX4, 13 figure

Black hole thermodynamical entropy

As early as 1902, Gibbs pointed out that systems whose partition function diverges, e.g. gravitation, lie outside the validity of the Boltzmann-Gibbs (BG) theory. Consistently, since the pioneering Bekenstein-Hawking results, physically meaningful evidence (e.g., the holographic principle) has accumulated that the BG entropy $S_{BG}$ of a $(3+1)$ black hole is proportional to its area $L^2$ ($L$ being a characteristic linear length), and not to its volume $L^3$. Similarly it exists the \emph{area law}, so named because, for a wide class of strongly quantum-entangled $d$-dimensional systems, $S_{BG}$ is proportional to $\ln L$ if $d=1$, and to $L^{d-1}$ if $d>1$, instead of being proportional to $L^d$ ($d \ge 1$). These results violate the extensivity of the thermodynamical entropy of a $d$-dimensional system. This thermodynamical inconsistency disappears if we realize that the thermodynamical entropy of such nonstandard systems is \emph{not} to be identified with the BG {\it additive} entropy but with appropriately generalized {\it nonadditive} entropies. Indeed, the celebrated usefulness of the BG entropy is founded on hypothesis such as relatively weak probabilistic correlations (and their connections to ergodicity, which by no means can be assumed as a general rule of nature). Here we introduce a generalized entropy which, for the Schwarzschild black hole and the area law, can solve the thermodynamic puzzle.Comment: 7 pages, 2 figures. Accepted for publication in EPJ

Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem

Portal vein thrombosis; risk factors, clinical presentation and treatment

<p>Abstract</p> <p>Background</p> <p>Portal vein thrombosis (PVT) is increasingly frequently being diagnosed, but systematic descriptions of the natural history and clinical handling of the condition are sparse. The aim of this retrospective study was to describe risk factors, clinical presentation, complications and treatment of portal vein thrombosis in a single-centre.</p> <p>Methods</p> <p>Sixty-seven patients were identified in the electronic records from 1992 to 2005. All data were obtained from the patient records.</p> <p>Results</p> <p>One or more risk factors (e.g. prothrombotic disorder or abdominal inflammation) were present in 87%. Symptoms were abdominalia, splenomegaly, fever, ascites, haematemesis, and weight loss. Abdominalia and fever occurred more frequently in patients with acute PVT. Frequent complications were splenomegaly, oesophageal- and gastric varices with or without bleeding, portal hypertensive gastropathy and ascites. Varices and bleeding were more frequent in patients with chronic PVT. Patients who received anticoagulant therapy more frequently achieved partial/complete recanalization. Patients with varices who were treated endoscopically in combination with β-blockade had regression of the varices. The overall mortality was 13% in one year, and was dependent on underlying causes.</p> <p>Conclusion</p> <p>Most patients had a combination of local and systemic risk factors for PVT. We observed that partial/complete recanalization was more frequent in patients treated with anticoagulation therapy, and that regression of varices was more pronounced in patients who where treated with active endoscopy combined with pharmacological treatment.</p

Pentoxifylline Does Not Decrease Short-term Mortality but Does Reduce Complications in Patients With Advanced Cirrhosis

Background &amp; AimsPentoxifylline, an inhibitor of tumor necrosis factor-α, is given to patients with liver diseases, but its effects in patients with advanced cirrhosis are unknown. We performed a randomized, placebo-controlled, double-blind trial of its effects in patients with cirrhosis. Methods A total of 335 patients with cirrhosis (Child–Pugh class C) were assigned to groups given either pentoxifylline (400 mg, orally, 3 times daily; n = 164) or placebo (n = 171) for 6 months. The primary end point was mortality at 2 months. Secondary end points were mortality at 6 months and development of liver-related complications. Results By 2 months, 28 patients in the pentoxifylline group (16.5%) and 31 in the placebo group (18.2%) had died (P = .84). At 6 months, 50 patients in the pentoxifylline group (30.0%) and 54 in the placebo group (31.5%) had died (P = .75). The proportions of patients without complications (eg, bacterial infection, renal insufficiency, hepatic encephalopathy, or gastrointestinal hemorrhage) were higher in the pentoxifylline group than in the placebo group at 2 months (78.6% vs 63.4%; P = .006) and 6 months (66.8% vs 49.7%; P = .002). The probability of survival without complications was higher in the pentoxifylline group than in the placebo group at 2 and 6 months (P = .04). In multivariate analysis, the factors associated with death were age, the Model for End-Stage Liver Disease score, and presence of early-stage carcinoma. Treatment with pentoxifylline was the only factor associated with liver-related complications. Conclusions Although pentoxifylline does not decrease short-term mortality in patients with advanced cirrhosis, it does reduce the risk of complications