Self-consistent equation for an interacting Bose gas

We consider interacting Bose gas in thermal equilibrium assuming a positive and bounded pair potential $V(r)$ such that 0<\int d\br V(r) = a<\infty. Expressing the partition function by the Feynman-Kac functional integral yields a classical-like polymer representation of the quantum gas. With Mayer graph summation techniques, we demonstrate the existence of a self-consistent relation $\rho (\mu)=F(\mu-a\rho(\mu))$ between the density $\rho$ and the chemical potential $\mu$, valid in the range of convergence of Mayer series. The function $F$ is equal to the sum of all rooted multiply connected graphs. Using Kac's scaling V_{\gamma}(\br)=\gamma^{3}V(\gamma r) we prove that in the mean-field limit $\gamma\to 0$ only tree diagrams contribute and function $F$ reduces to the free gas density. We also investigate how to extend the validity of the self-consistent relation beyond the convergence radius of Mayer series (vicinity of Bose-Einstein condensation) and study dominant corrections to mean field. At lowest order, the form of function $F$ is shown to depend on single polymer partition function for which we derive lower and upper bounds and on the resummation of ring diagrams which can be analytically performed.Comment: 33 pages, 6 figures, submitted to Phys.Rev.

Metastability in the BCS model

We discuss metastable states in the mean-field version of the strong coupling BCS-model and study the evolution of a superconducting equilibrium state subjected to a dynamical semi-group with Lindblad generator in detailed balance w.r.t. another equilibrium state. The intermediate states are explicitly constructed and their stability properties are derived. The notion of metastability in this genuine quantum system, is expressed by means of energy-entropy balance inequalities and canonical coordinates of observables

Shopping centre siting and modal choice in Belgium: a destination based analysis

Although modal split is only one of the elements considered in decision-making on new shopping malls, it remarkably often arises in arguments of both proponents and opponents. Today, this is also the case in the debate on the planned development of three major shopping malls in Belgium. Inspired by such debates, the present study focuses on the impact of the location of shopping centres on the travel mode choice of the customers. Our hypothesis is that destination-based variables such as embeddedness in the urban fabric, accessibility and mall size influence the travel mode choice of the visitors. Based on modal split data and location characteristics of seventeen existing shopping centres in Belgium, we develop a model for a more sustainable siting policy. The results show a major influence of the location of the shopping centre in relation to the urban form, and of the size of the mall. Shopping centres that are part of a dense urban fabric, measured through population density, are less car dependent. Smaller sites will attract more cyclists and pedestrians. Interestingly, our results deviate significantly from the figures that have been put forward in public debates on the shopping mall issue in Belgium

Cost-benefit analysis of abatement measures for nutrient emission from agriculture

In intensive animal husbandry areas surface water N and P concentrations often remain too high. The Water Framework Directive calls for additional nutrient emission abatement measures. Therefore, costs and benefits for possible agricultural measures in Flanders were first analysed in terms of soil balance surplus. Finally, abatement measures for agriculture, households and industry were set off against each other and ranked according to their cost-efficiency by the Environmental Costing Model. Increased dairy cattle efficiency, winter cover crops and increased pig feed efficiency turn out very cost efficient. Other agricultural measures are less cost efficient than for instance collective treatment for households and industry.nitrogen and phosphorus abatement, surface water, cost efficiency, Environmental Economics and Policy, Livestock Production/Industries,

Miami Classification for Probe-Based Confocal Laser Endomicroscopy

An essential element for any new advanced imaging technology is standardization of indications, terminology, categorization of images, and research priorities. In this review, we propose a state-of-the-art classification system for normal and pathological states in gastrointestinal disease using probe-based confocal laser endomicroscopy (pCLE). The Miami classification system is based on a consensus of pCLE users reached during a meeting held in Miami, Florida, in February 2009

Proof of Bose-Einstein Condensation for Interacting Gases with a One-Particle Spectral Gap

Using a specially tuned mean-field Bose gas as a reference system, we establish a positive lower bound on the condensate density for continuous Bose systems with superstable two-body interactions and a finite gap in the one-particle excitations spectrum, i.e. we prove for the first time standard homogeneous Bose-Einstein condensation for such interacting systems

Systematic Mutational Analysis of the Intracellular Regions of Yeast Gap1 Permease

The yeast general amino acid permease Gap1 is a convenient model for studying the intracellular trafficking of membrane proteins. Present at the plasma membrane when the nitrogen source is poor, it undergoes ubiquitin-dependent endocytosis and degradation upon addition of a good nitrogen source, e.g. ammonium. It comprises 12 transmembrane domains (TM) flanked by cytosol-facing N- and C-terminal tails (NT, CT). The NT of Gap1 contains the acceptor lysines for ubiquitylation and its CT includes a sequence essential to exit from the endoplasmic reticulum (ER).Journal ArticleResearch Support, Non-U.S. Gov'tSCOPUS: ar.jinfo:eu-repo/semantics/publishe

Divergent mathematical treatments in utility theory

In this paper I study how divergent mathematical treatments affect mathematical modelling, with a special focus on utility theory. In particular I examine recent work on the ranking of information states and the discounting of future utilities, in order to show how, by replacing the standard analytical treatment of the models involved with one based on the framework of Nonstandard Analysis, diametrically opposite results are obtained. In both cases, the choice between the standard and nonstandard treatment amounts to a selection of set-theoretical parameters that cannot be made on purely empirical grounds. The analysis of this phenomenon gives rise to a simple logical account of the relativity of impossibility theorems in economic theory, which concludes the paper