On the Membrane Approximation for Thin Elastic Shells in the Hyperbolic Case

Sin resume

Exponential splitting of bound states in a waveguide with a pair of distant windows

We consider Laplacian in a straight planar strip with Dirichlet boundary which has two Neumann ``windows'' of the same length the centers of which are $2l$ apart, and study the asymptotic behaviour of the discrete spectrum as $l\to\infty$. It is shown that there are pairs of eigenvalues around each isolated eigenvalue of a single-window strip and their distances vanish exponentially in the limit $l\to\infty$. We derive an asymptotic expansion also in the case where a single window gives rise to a threshold resonance which the presence of the other window turns into a single isolated eigenvalue

Localized and extended states in a disordered trap

We study Anderson localization in a disordered potential combined with an inhomogeneous trap. We show that the spectrum displays both localized and extended states, which coexist at intermediate energies. In the region of coexistence, we find that the extended states result from confinement by the trap and are weakly affected by the disorder. Conversely, the localized states correspond to eigenstates of the disordered potential, which are only affected by the trap via an inhomogeneous energy shift. These results are relevant to disordered quantum gases and we propose a realistic scheme to observe the coexistence of localized and extended states in these systems.Comment: Published versio

A model of dispersive transport across sharp interfaces between porous materials

Recent laboratory experiments on solute migration in composite porous columns have shown an asymmetry in the solute arrival time upon reversal of the flow direction, which is not explained by current paradigms of transport. In this work, we propose a definition for the solute flux across sharp interfaces and explore the underlying microscopic particle dynamics by applying Monte Carlo simulation. Our results are consistent with previous experimental findings and explain the observed transport asymmetry. An interpretation of the proposed physical mechanism in terms of a flux rectification is also provided. The approach is quite general and can be extended to other situations involving transport across sharp interfaces.Comment: 4 pages, 4 figure

Localization of solitons: linear response of the mean-field ground state to weak external potentials

Two aspects of bright matter-wave solitons in weak external potentials are discussed. First, we briefly review recent results on the Anderson localization of an entire soliton in disordered potentials [Sacha et al. PRL 103, 210402 (2009)], as a paradigmatic showcase of genuine quantum dynamics beyond simple perturbation theory. Second, we calculate the linear response of the mean-field soliton shape to a weak, but otherwise arbitrary external potential, with a detailed application to lattice potentials.Comment: Selected paper presented at the 2010 Spring Meeting of the Quantum Optics and Photonics Section of the German Physical Society. V2: minor changes, published versio

Evaluation of Different Recruitment Methods: Longitudinal, Web-Based, Pan-European Physical Activity Through Sustainable Transport Approaches (PASTA) Project

ABSTRACT Background: Sufficient sample size and minimal sample bias are core requirements for empirical data analyses. Combining opportunistic recruitment with a Web-based survey and data-collection platform yields new benefits over traditional recruitment approaches. Objective: This paper aims to report the success of different recruitment methods and obtain data on participants’ characteristics, participation behavior, recruitment rates, and representativeness of the sample. Methods: A longitudinal, Web-based survey was implemented as part of the European PASTA (Physical Activity through Sustainable Transport Approaches) project, between November 2014 and December 2016. During this period, participants were recruited from 7 European cities on a rolling basis. A standardized guide on recruitment strategy was developed for all cities, to reach a sufficient number of adult participants. To make use of the strengths and minimize weakness, a combination of different opportunistic recruitment methods was applied. In addition, the random sampling approach was applied in the city of Örebro. To reduce the attrition rate and improve real-time monitoring, the Web-based platform featured a participant’s and a researchers’ user interface and dashboard. Results: Overall, 10,691 participants were recruited; most people found out about the survey through their workplace or employer (2300/10691, 21.51%), outreach promotion (2219/10691, 20.76%), and social media (1859/10691, 17.39%). The average number of questionnaires filled in per participant varied significantly between the cities (P<.001), with the highest number in Zurich (11.0, SE 0.33) and the lowest in Örebro (4.8, SE 0.17). Collaboration with local organizations, the use of Facebook and mailing lists, and direct street recruitment were the most effective approaches in reaching a high share of participants (P<.001). Considering the invested working hours, Facebook was one of the most time-efficient methods. Compared with the cities’ census data, the composition of study participants was broadly representative in terms of gender distribution; however, the study included younger and better-educated participants. Conclusions: We observed that offering a mixed recruitment approach was highly effective in achieving a high participation rate. The highest attrition rate and the lowest average number of questionnaires filled in per participant were observed in Örebro, which also recruited participants through random sampling. These findings suggest that people who are more interested in the topic are more willing to participate and stay in a survey than those who are selected randomly and may not have a strong connection to the research topic. Although direct face-to-face contacts were very effective with respect to the number of recruited participants, recruiting people through social media was not only effective but also very time efficient. The collected data are based on one of the largest recruited longitudinal samples with a common recruitment strategy in different European cities

Tailoring Anderson localization by disorder correlations in 1D speckle potentials

We study Anderson localization of single particles in continuous, correlated, one-dimensional disordered potentials. We show that tailored correlations can completely change the energy-dependence of the localization length. By considering two suitable models of disorder, we explicitly show that disorder correlations can lead to a nonmonotonic behavior of the localization length versus energy. Numerical calculations performed within the transfer-matrix approach and analytical calculations performed within the phase formalism up to order three show excellent agreement and demonstrate the effect. We finally show how the nonmonotonic behavior of the localization length with energy can be observed using expanding ultracold-atom gases

New porous medium Poisson-Nernst-Planck equations for strongly oscillating electric potentials

We consider the Poisson-Nernst-Planck system which is well-accepted for describing dilute electrolytes as well as transport of charged species in homogeneous environments. Here, we study these equations in porous media whose electric permittivities show a contrast compared to the electric permittivity of the electrolyte phase. Our main result is the derivation of convenient low-dimensional equations, that is, of effective macroscopic porous media Poisson-Nernst-Planck equations, which reliably describe ionic transport. The contrast in the electric permittivities between liquid and solid phase and the heterogeneity of the porous medium induce strongly oscillating electric potentials (fields). In order to account for this special physical scenario, we introduce a modified asymptotic multiple-scale expansion which takes advantage of the nonlinearly coupled structure of the ionic transport equations. This allows for a systematic upscaling resulting in a new effective porous medium formulation which shows a new transport term on the macroscale. Solvability of all arising equations is rigorously verified. This emergence of a new transport term indicates promising physical insights into the influence of the microscale material properties on the macroscale. Hence, systematic upscaling strategies provide a source and a prospective tool to capitalize intrinsic scale effects for scientific, engineering, and industrial applications

On Random Field Induced Ordering in the Classical XY Model

Consider the classical XY model in a weak random external field pointing along the $Y$ axis with strength $\epsilon$. We study the behavior of this model as the range of the interaction is varied. We prove that in any dimension $d \geq 2$ and for all $\epsilon$ sufficiently small, there is a range $L=L(\epsilon)$ so that whenever the inverse temperature $\beta$ is larger than some $\beta(\epsilon)$, there is strong residual ordering along the $X$ direction.Comment: 30 page

Anderson localization of matter waves in tailored disordered potentials

We show that, in contrast to immediate intuition, Anderson localization of noninteracting particles induced by a disordered potential in free space can increase (i.e., the localization length can decrease) when the particle energy increases, for appropriately tailored disorder correlations. We predict the effect in one, two, and three dimensions, and propose a simple method to observe it using ultracold atoms placed in optical disorder. The increase of localization with the particle energy can serve to discriminate quantum versus classical localization