Aspects of the stochastic Burgers equation and their connection with turbulence

We present results for the 1 dimensional stochastically forced Burgers equation when the spatial range of the forcing varies. As the range of forcing moves from small scales to large scales, the system goes from a chaotic, structureless state to a structured state dominated by shocks. This transition takes place through an intermediate region where the system exhibits rich multifractal behavior. This is mainly the region of interest to us. We only mention in passing the hydrodynamic limit of forcing confined to large scales, where much work has taken place since that of Polyakov. In order to make the general framework clear, we give an introduction to aspects of isotropic, homogeneous turbulence, a description of Kolmogorov scaling, and, with the help of a simple model, an introduction to the language of multifractality which is used to discuss intermittency corrections to scaling. We continue with a general discussion of the Burgers equation and forcing, and some aspects of three dimensional turbulence where - because of the mathematical analogy between equations derived from the Navier-Stokes and Burgers equations - one can gain insight from the study of the simpler stochastic Burgers equation. These aspects concern the connection of dissipation rate intermittency exponents with those characterizing the structure functions of the velocity field, and the dynamical behavior, characterized by different time constants, of velocity structure functions. We also show how the exponents characterizing the multifractal behavior of velocity structure functions in the above mentioned transition region can effectively be calculated in the case of the stochastic Burgers equation.Comment: 25 pages, 4 figure

Drifting diffusion on a circle as continuous limit of a multiurn Ehrenfest model

We study the continuous limit of a multibox Erhenfest urn model proposed before by the authors. The evolution of the resulting continuous system is governed by a differential equation, which describes a diffusion process on a circle with a nonzero drifting velocity. The short time behavior of this diffusion process is obtained directly by solving the equation, while the long time behavior is derived using the Poisson summation formula. They reproduce the previous results in the large $M$ (number of boxes) limit. We also discuss the connection between this diffusion equation and the Schr$\ddot{\rm o}$dinger equation of some quantum mechanical problems.Comment: 4 pages prevtex4 file, 1 eps figur

Extension of the Representative Elementary Watershed approach for cold regions: constitutive relationships and an application

International audienceThe Representative Elementary Watershed (REW) approach proposed by Reggiani et al. (1998, 1999) represents an attempt to develop a scale adaptable modeling framework for the hydrological research community. Tian et al. (2006) extended the original REW theory for cold regions through explicit treatment of energy balance equations to incorporate associated cold regions processes, such as snow and glacier melting/accumulation, and soil freezing/thawing. However, constitutive relationships for the cold regions processes needed to complete these new balance equations have been left unspecified in this derivation. In this paper we propose a set of closure schemes for cold regions processes within the extended framework. An energy balance method is proposed to close the balance equations of melting/accumulation processes as well as the widely-used and conceptual degree-day method, whereas the closure schemes for soil freezing and thawing are based on the maximum unfrozen-water content model. The proposed closure schemes are coupled to the previously derived balance equations and implemented within the Thermodynamic Watershed Hydrological Model (THModel, Tian, 2006) and then applied to the headwaters of the Urumqi River in Western China. The results of the 5-year calibration and 3-year validation analyses show that THModel can indeed simulate runoff processes in this glacier and snow-dominated catchment reasonably well, which shows the prospects of the REW approach and the developed closure schemes for cold regions processes

Parameterization invariance and shape equations of elastic axisymmetric vesicles

The issue of different parameterizations of the axisymmetric vesicle shape addressed by Hu Jian-Guo and Ou-Yang Zhong-Can [ Phys.Rev. E {\bf 47} (1993) 461 ] is reassesed, especially as it transpires through the corresponding Euler - Lagrange equations of the associated elastic energy functional. It is argued that for regular, smooth contours of vesicles with spherical topology, different parameterizations of the surface are equivalent and that the corresponding Euler - Lagrange equations are in essence the same. If, however, one allows for discontinuous (higher) derivatives of the contour line at the pole, the differently parameterized Euler - Lagrange equations cease to be equivalent and describe different physical problems. It nevertheless appears to be true that the elastic energy corresponding to smooth contours remains a global minimum.Comment: 10 pages, latex, one figure include

Simulations of “tunnelling of the 3rd kind”

We consider the phenomenon of ``tunnelling of the 3rd kind" \cite{third}, whereby a magnetic field may traverse a classically impenetrable barrier by pair creation of unimpeded quantum fermions. These propagate through the barrier and generate a magnetic field on the other side. We study this numerically using quantum fermions coupled to a classical Higgs-gauge system, where we set up a magnetic field outside a box shielded by two superconducting barriers. We examine the magnitude of the internal magnetic field, and find agreement with existing perturbative results within a factor of two

Macroscopic phase segregation in superconducting K0.73Fe1.67Se2 as seen by muon spin rotation and infrared spectroscopy

Using muon spin rotation (\muSR) and infrared spectroscopy we investigated the recently discovered superconductor K0.73Fe1.67Se2 with Tc = 32 K. We show that the combined data can be consistently described in terms of a macroscopically phase segregated state with a matrix of ~88% volume fraction that is insulating and strongly magnetic and inclusions with a ~12% volume fraction which are metallic, superconducting and non-magnetic. The electronic properties of the latter, in terms of the normal state plasma frequency and the superconducting condensate density, appear to be similar as in other iron selenide or arsenide superconductors.Comment: 22 pages, 8 figures. (citation list correction.

Treating Chronic Wounds Using Photoactive Metabolites: Data Mining the Chinese Pharmacopoeia for Potential Lead Species (#)

Efficient wound treatment that addresses associated infections and inflammation remains one of the big unmet needs, especially in low- and middle-income countries. One strategy for securing better healthcare can be using medicinal plants if sufficient evidence on their safety and therapeutic benefits can be ascertained. A unique novel opportunity could be photo-enhanced wound treatment with a combination of light-sensitive plant preparations and local exposure to daylight. Data mining strategies using existing resources offer an excellent basis for developing such an approach with many potential plant candidates. In the present analysis, we researched the 535 botanical drugs included in the Chinese pharmacopeia and identified 183 medicinal plant species, 82 for treating open wounds caused by trauma and 101 for inflammatory skin conditions. After further screening for reports on the presence of known photoactive compounds, we determined a core group of 10 scientifically lesser-known botanical species that may potentially be developed into more widely used topical preparations for photodynamic treatment of infected wounds. Our predictive approach may contribute to developing a more evidence-based use of herbal medicines

Poincar\'{e} cycle of a multibox Ehrenfest urn model with directed transport

We propose a generalized Ehrenfest urn model of many urns arranged periodically along a circle. The evolution of the urn model system is governed by a directed stochastic operation. Method for solving an $N$-ball, $M$-urn problem of this model is presented. The evolution of the system is studied in detail. We find that the average number of balls in a certain urn oscillates several times before it reaches a stationary value. This behavior seems to be a peculiar feature of this directed urn model. We also calculate the Poincar\'{e} cycle, i.e., the average time interval required for the system to return to its initial configuration. The result can be easily understood by counting the total number of all possible microstates of the system.Comment: 10 pages revtex file with 7 eps figure