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

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

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

Freshwater Availability for Agriculture in Sundarbans. Variability due to changes in the summer monsoon under current and climate change conditions

The India–UK Water Centre (IUKWC) funded a Pump Priming Project (PPP) titled: “The influence of the monsoon on freshwater availability for agriculture in the Sundarbans region of West Bengal, India, under current and climate change conditions” between June and September 2019. This Knowledge Exchange brief was developed from the outputs of the activities conducted during this study: i) investigating the variability of the Indian Summer Monsoon (ISM) and the ensuing freshwater availability for agriculture in the Sundarbans region through the collection and analysis of climatic data and outputs from Global Climate Models (GCMs); and ii) understanding how changes in water resource availability are affecting livelihoods and discussing issues related to adaptation to those changes through meetings with farmers, NGOs and local government officials engaged in water resource management. The research results were communicated through a workshop with agricultural, water and climate scientists, NGOs and government stakeholders working in the Sundarbans region, where the team gained feedback, and shared knowledge and ideas for future research. This Brief was prepared by Professor Lalu Das, Principal Investigator (PI) and India Project Lead, and Professor Gautam Saha, both from Bidhan Chandra Krishi Viswavidyalaya (BCKV) in India, and Dr Alexandre Gagnon, UK Project Lead, and Dr Indrani Roy from Liverpool John Moores University (LJMU) in the UK

Divergent effects of acute and repeated quetiapine treatment on dopamine neuron activity in normal vs. chronic mild stress induced hypodopaminergic states

Abstract Clinical evidence supports the use of second-generation dopamine D2 receptor antagonists (D2RAs) as adjunctive therapy or in some cases monotherapy in patients with depression. However, the mechanism for the clinical antidepressant effect of D2RAs remains unclear. Specifically, given accumulating evidence for decreased ventral tegmental area (VTA) dopamine system function in depression, an antidepressant effect of a medication that is expected to further reduce dopamine system activity seems paradoxical. In the present paper we used electrophysiological single unit recordings of identified VTA dopamine neurons to characterize the impact of acute and repeated administration of the D2RA quetiapine at antidepressant doses in non-stressed rats and those exposed to the chronic mild stress (CMS) rodent depression model, the latter modeling the hypodopaminergic state observed in patients with depression. We found that acute quetiapine increased dopamine neuron population activity in non-stressed rats, but not in CMS-exposed rats. Conversely, repeated quetiapine increased VTA dopamine neuron population activity to normal levels in CMS-exposed rats, but had no persisting effects in non-stressed rats. These data suggest that D2RAs may exert their antidepressant actions via differential effects on the dopamine system in a normal vs. hypoactive state. This explanation is supported by prior studies showing that D2RAs differentially impact the dopamine system in animal models of schizophrenia and normal rats; the present results extend this phenomenon to an animal model of depression. These data highlight the importance of studying medications in the context of animal models of psychiatric disorders as well as normal conditions

Symmetries of differential-difference dynamical systems in a two-dimensional lattice

Classification of differential-difference equation of the form $\ddot{u}_{nm}=F_{nm}\big(t, \{u_{pq}\}|_{(p,q)\in \Gamma}\big)$ are considered according to their Lie point symmetry groups. The set $\Gamma$ represents the point $(n,m)$ and its six nearest neighbors in a two-dimensional triangular lattice. It is shown that the symmetry group can be at most 12-dimensional for abelian symmetry algebras and 13-dimensional for nonsolvable symmetry algebras.Comment: 24 pages, 1 figur

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

Estimating the Number of Solutions of Cardinality Constraints through range and roots Decompositions

International audienceThis paper introduces a systematic approach for estimating the number of solutions of cardinality constraints. A main difficulty of solutions counting on a specific constraint lies in the fact that it is, in general, at least as hard as developing the constraint and its propaga-tors, as it has been shown on alldifferent and gcc constraints. This paper introduces a probabilistic model to systematically estimate the number of solutions on a large family of cardinality constraints including alldifferent, nvalue, atmost, etc. Our approach is based on their decomposition into range and roots, and exhibits a general pattern to derive such estimates based on the edge density of the associated variable-value graph. Our theoretical result is finally implemented within the maxSD search heuristic, that aims at exploring first the area where there are likely more solutions

Efficacy of Online Training for Improving Camp Staff Competency

Preparing competent staff is a critical issue within the camp community. This quasi-experimental study examined the effectiveness of an online course for improving staff competency in camp healthcare practices among college-aged camp staff and a comparison group (N = 55). We hypothesized that working in camp would increase competency test scores due to opportunities for staff to experientially apply knowledge learned online. Hierarchical linear modeling was used to analyse the cross-level effects of a between-individuals factor (assignment to experimental or comparison group) and within-individual effects of time (pre-test, post-test #1, and post-test #2) on online course test scores. At post-test #2, the difference in average test scores between groups was ~30 points, with the treatment group scoring lower on average than the comparison group. Factors that may have influenced these findings are explored, including fatigue and the limited durability of online learning. Recommendations for research and practice are discussed

Script Concordance Tests: Guidelines for Construction

International audienc