Group classification of (1+1)-Dimensional Schr\"odinger Equations with Potentials and Power Nonlinearities

We perform the complete group classification in the class of nonlinear Schr\"odinger equations of the form $i\psi_t+\psi_{xx}+|\psi|^\gamma\psi+V(t,x)\psi=0$ where $V$ is an arbitrary complex-valued potential depending on $t$ and $x,$ $\gamma$ is a real non-zero constant. We construct all the possible inequivalent potentials for which these equations have non-trivial Lie symmetries using a combination of algebraic and compatibility methods. The proposed approach can be applied to solving group classification problems for a number of important classes of differential equations arising in mathematical physics.Comment: 10 page

Building Stronger Nonprofits Through Better Financial Management: Early Efforts in 26 Youth-Serving Organizations

Outlines the Financial Management in Out-of-School Time initiative to improve nonprofits' long-term financial management capacity and reform funding practices that weaken it, challenges participating nonprofits faced, progress to date, and early lessons

Exact Soliton-like Solutions of the Radial Gross-Pitaevskii Equation

We construct exact ring soliton-like solutions of the cylindrically symmetric (i.e., radial) Gross- Pitaevskii equation with a potential, using the similarity transformation method. Depending on the choice of the allowed free functions, the solutions can take the form of stationary dark or bright rings whose time dependence is in the phase dynamics only, or oscillating and bouncing solutions, related to the second Painlev\'e transcendent. In each case the potential can be chosen to be time-independent.Comment: 8 pages, 7 figures. Version 2: stability analysis of the dark solutio

Leading Order Calculation of Shear Viscosity in Hot Quantum Electrodynamics from Diagrammatic Methods

We compute the shear viscosity at leading order in hot Quantum Electrodynamics. Starting from the Kubo relation for shear viscosity, we use diagrammatic methods to write down the appropriate integral equations for bosonic and fermionic effective vertices. We also show how Ward identities can be used to put constraints on these integral equations. One of our main results is an equation relating the kernels of the integral equations with functional derivatives of the full self-energy; it is similar to what is obtained with two-particle-irreducible effective action methods. However, since we use Ward identities as our starting point, gauge invariance is preserved. Using these constraints obtained from Ward identities and also power counting arguments, we select the necessary diagrams that must be resummed at leading order. This includes all non-collinear (corresponding to 2 to 2 scatterings) and collinear (corresponding to 1+N to 2+N collinear scatterings) rungs responsible for the Landau-Pomeranchuk-Migdal effect. We also show the equivalence between our integral equations obtained from quantum field theory and the linearized Boltzmann equations of Arnold, Moore and Yaffe obtained using effective kinetic theory.Comment: 45 pages, 22 figures (note that figures 7 and 14 are downgraded in resolution to keep this submission under 1000kb, zoom to see them correctly

Baryon Asymmetry of the Universe without Boltzmann or Kadanoff-Baym

We present a formalism that allows the computation of the baryon asymmetry of the universe from first principles of statistical physics and quantum field theory that is applicable to certain types of beyond the Standard Model physics (such as the neutrino Minimal Standard Model -- $\nu$MSM) and does not require the solution of Boltzmann or Kadanoff-Baym equations. The formalism works if a thermal bath of Standard Model particles is very weakly coupled to a new sector (sterile neutrinos in the $\nu$MSM case) that is out-of-equilibrium. The key point that allows a computation without kinetic equations is that the number of sterile neutrinos produced during the relevant cosmological period remains small. In such a case, it is possible to expand the formal solution of the von Neumann equation perturbatively and obtain a master formula for the lepton asymmetry expressed in terms of non-equilibrium Wightman functions. The master formula neatly separates CP-violating contributions from finite temperature correlation functions and satisfies all three Sakharov conditions. These correlation functions can then be evaluated perturbatively; the validity of the perturbative expansion depends on the parameters of the model considered. Here we choose a toy model (containing only two active and two sterile neutrinos) to illustrate the use of the formalism, but it could be applied to other models.Comment: 26 pages, 10 figure

L'accumulation et l'élimination de cadmium par deux mousses aquatiques, Fontinalis dalecarlica et Platyphypnidium ripariodes : Influence de la concentration de Cd, du temps d'exposition, de la dureté de l'eau et de l'espèce de mousses

Cette étude en laboratoire traite de l'accumulation et de l'élimination du Cd réalisées par deux mousses aquatiques indigènes du Québec, Fontinalis dalecarlica et Platyhypnidium riparioides. Les expositions au Cd étaient de 0 (témoin), 0,8, 2 et 10 µg·L-1, concentrations retrouvées en milieu naturel (non contaminé) et contaminé. Les expériences ont été réalisées à trois niveaux de dureté de l'eau (10 à 15, 40 à 50, 80 à 100 mg·L-1 de CaCO3), à alcalinité constante (80 à 100 mg·L-1 de CaCO3) et à pH stable (7,30) durant une période de 28 jours. Les facteurs d'augmentation des concentrations (FAC) ont démontré une diminution de l'accumulation totale de Cd dans les mousses dans 75% des cas lorsque la dureté de l'eau passe de très douce à dure. Les facteurs de contamination résiduelle (FCR) démontrent la lenteur de l'élimination du Cd par les mousses, et ce, indépendamment de la dureté de l'eau ou de la contamination préalablement subie. Deux équations de régression multiple par étape (Stepwise) ont été établies pour expliquer les facteurs influençant l'accumulation et l'élimination de Cd réalisées par les mousses. Les variables indépendantes incluses dans les équations linéaires de prédiction pour l'accumulation et l'élimination étaient la concentration de Cd dans l'eau, le temps d'exposition, la dureté de l'eau, l'espèce de mousses utilisée et/ou les interactions de ces variables. Les équations linéaires de prédiction pour l'accumulation et l'élimination ont permis d'expliquer respectivement 92% et 71% de la variance observée. Cette identification des principaux facteurs influençant l'accumulation et l'élimination du Cd dans les mousses est d'une grande importance pour la compréhension des processus complexes dirigeant l'absortion des métaux lourds par des organismes vivants. Les équations permettent également de mieux expliquer les interactions engendrées par la variation de divers paramètres sur l'accumulation et l'élimination du Cd par les mousses aquatiques.Aquatic mosses have played a large part in the assessment of toxic elements in water. The advantage of mosses over direct water sampling is that the use of the former lessens spatial and temporal variations, enhances the level of contaminant identification by concentrating toxic elements, and provides information relative to the bioavailable portion. However, the concentration of metals that can be measured in mosses is not a reliable indicator of the concentration of toxic elements in the water, which is why we need to model the bioaccumulation phenomenon.The present laboratory study deals with the accumulation and elimination of Cd by two indigenous Quebec aquatic mosses: Fontinalis dalecarlica and Platyhypnidium riparioides. The previously acclimatized mosses were treated with different concentrations of Cd, three different levels of water hardness, a constant alkalinity and constant pH level for a period of 28 days, in order to establish their bioaccumulative capacity. Cd exposure concentrations were 0 (control), 0.8, 2 and 10 mg·L-1, with a replication at 10 mg·L-1. The experiments were carried out at three levels of water hardness (10 to 15, 40 to 50, 80 to 100 mg·L-1 of CaCO3), with a constant degree of alkalinity (80 to 100 mg·L-1 of CaCO3) and stable pH (7.30). The mosses subsequently went through an elimination period (Cd-free water) of 28 days. The triplicate moss samples were mineralized using nitric acid and all Cd measurements were made by atomic absorption spectrophotometry. The results indicate that the water chemistry conditions remained stable and were properly controlled. The aquatic mosses demonstrated a considerable ability to absorb and adsorb Cd: the measured Cd water concentrations were less than the nominal concentrations. Nonetheless, moss uptake of Cd improves with an increase in Cd contamination and the concentration factors (CF) range from 6 to 122. For the same exposure concentration, the CF drops in some 63% of those instances where water hardness rises from very soft, through soft, to hard. In 75% of the cases there is a drop in CF when water hardness increases directly from very soft to hard. With a stable concentration (e.g. 2 mg·L-1), F. dalecarlica has respective CFs of 26.3, 22.2 and 18, which demonstrates the negative gradation of Cd accumulation as water hardness increases. The residual contamination factors (RCF) bear witness to the slow rate of Cd elimination by the mosses, irrespective of the level of water hardness or of any previous contamination. The elimination factor for RCF is never greater than 2. Mosses take up metals faster than they can eliminate them and have a memory of past contaminations, which is an advantage when it comes to studying ad hoc and/or sporadic contamination phenomena.Two stepwise multiple regression equations have been set up to explain the factors that impact on accumulation and elimination of Cd by mosses. The variables included in the equations were: level of Cd concentration in the water; exposure time; water hardness; the moss species involved, and/or the interactions between these variables. The predictive linear equations for the accumulation and elimination provided explanations for 92% and 71% respectively of the observed variances. The predictive linear equation for accumulation establishes that the length of exposure is the principal parameter responsible for the uptake of Cd by the aquatic mosses. It shows that the accumulation of Cd by the mosses is initially influenced by the level of Cd concentration in the water, but also depends on the length of time over which the bryophytes are exposed to this concentration. Thus, the higher the Cd concentration, the shorter the exposure time for the moss contamination, and vice versa. The second variable is the effect of water hardness taken together with the exposure time. This is a negative variable: the greater the increase in water hardness, the greater the exposure time required to obtain the same degree of moss contamination. This is indicative of the impact of Ca++ and Mg++ on moss uptake. The impact of water hardness is probably the consequence of the availability of or preference of plant-binding sites for Ca++ and Mg++ ions, thus reducing the number of available locations for Cd accumulation. Water hardness and Cd concentration levels are the third variable in this equation and are probably linked to the effect of water hardness on the bioavailability of Cd for the mosses. This variable may also explain why the increase in Cd concentration levels in the water lessens the impact of water hardness on the total accumulation of Cd in the mosses. Finally, the equation identifies a greater level of accumulation in the P. riparoides.Release linear regression shows that the absence of Cd in the water is the major parameter in the elimination of Cd by aquatic mosses. We should remember that the bryophytes are seeking to achieve a steady state condition with their environment, since the Cd is an element that is neither regulated or essential. Its elimination has little to do with water hardness, but is caused by the inversion of a diffusion gradient when the environment is no longer Cd contaminated. During the elimination process, the Ca++ and Mg++ ions have no real impact on the release of Cd by the mosses. The length of prior exposure does affect elimination: the greater it is, the longer the release period required for moss decontamination. Exposure time is less important during elimination than during accumulation. Elimination is a very slow process, and a longer study would probably have shown that this is a major factor in the elimination of moss-accumulated Cd.The present identification of the major factors impacting on the accumulation and elimination of Cd in mosses is extremely important if we are to understand the complex processes that determine the absorption of heavy metals by living organisms. The equations also allow us to better explain the interactions caused by variations in the different parameters with respect to the accumulation and elimination of Cd by aquatic mosses

Dynamics of Large-Scale Plastic Deformation and the Necking Instability in Amorphous Solids

We use the shear transformation zone (STZ) theory of dynamic plasticity to study the necking instability in a two-dimensional strip of amorphous solid. Our Eulerian description of large-scale deformation allows us to follow the instability far into the nonlinear regime. We find a strong rate dependence; the higher the applied strain rate, the further the strip extends before the onset of instability. The material hardens outside the necking region, but the description of plastic flow within the neck is distinctly different from that of conventional time-independent theories of plasticity.Comment: 4 pages, 3 figures (eps), revtex4, added references, changed and added content, resubmitted to PR