Characteristic Angles in the Wetting of an Angular Region: Deposit Growth

As was shown in an earlier paper [1], solids dispersed in a drying drop migrate to the (pinned) contact line. This migration is caused by outward flows driven by the loss of the solvent due to evaporation and by geometrical constraint that the drop maintains an equilibrium surface shape with a fixed boundary. Here, in continuation of our earlier paper [2], we theoretically investigate the evaporation rate, the flow field and the rate of growth of the deposit patterns in a drop over an angular sector on a plane substrate. Asymptotic power laws near the vertex (as distance to the vertex goes to zero) are obtained. A hydrodynamic model of fluid flow near the singularity of the vertex is developed and the velocity field is obtained. The rate of the deposit growth near the contact line is found in two time regimes. The deposited mass falls off as a weak power Gamma of distance close to the vertex and as a stronger power Beta of distance further from the vertex. The power Gamma depends only slightly on the opening angle Alpha and stays between roughly -1/3 and 0. The power Beta varies from -1 to 0 as the opening angle increases from 0 to 180 degrees. At a given distance from the vertex, the deposited mass grows faster and faster with time, with the greatest increase in the growth rate occurring at the early stages of the drying process.Comment: v1: 36 pages, 21 figures, LaTeX; submitted to Physical Review E; v2: minor additions to Abstract and Introductio

Monte Carlo simulation of subsurface ordering kinetics in an fcc-alloy model

Within the atom-vacancy exchange mechanism in a nearest-neighbor interaction model we investigate the kinetics of surface-induced ordering processes close to the (001) surface of an fcc A_3B-alloy. After a sudden quench into the ordered phase with a final temperature above the ordering spinodal, T_f > T_sp, the early time kinetics is dominated by a segregation front which propagates into the bulk with nearly constant velocity. Below the spinodal, T_f < T_sp, motion of the segregation wave reflects a coarsening process which appears to be slower than predicted by the Lifschitz-Allen-Cahn law. In addition, in the front-penetrated region lateral growth differs distinctly from perpendicular growth, as a result of the special structure of antiphase boundaries near the surface. Our results are compared with recent experiments on the subsurface ordering kinetics at Cu_3Au (001).Comment: 10 pages, 9 figures, submitted to Phys. Rev. B, in prin

A general T-matrix approach applied to two-body and three-body problems in cold atomic gases

We propose a systematic T-matrix approach to solve few-body problems with s-wave contact interactions in ultracold atomic gases. The problem is generally reduced to a matrix equation expanded by a set of orthogonal molecular states, describing external center-of-mass motions of pairs of interacting particles; while each matrix element is guaranteed to be finite by a proper renormalization for internal relative motions. This approach is able to incorporate various scattering problems and the calculations of related physical quantities in a single framework, and also provides a physically transparent way to understand the mechanism of resonance scattering. For applications, we study two-body effective scattering in 2D-3D mixed dimensions, where the resonance position and width are determined with high precision from only a few number of matrix elements. We also study three fermions in a (rotating) harmonic trap, where exotic scattering properties in terms of mass ratios and angular momenta are uniquely identified in the framework of T-matrix.Comment: 14 pages, 4 figure

Crises and collective socio-economic phenomena: simple models and challenges

Financial and economic history is strewn with bubbles and crashes, booms and busts, crises and upheavals of all sorts. Understanding the origin of these events is arguably one of the most important problems in economic theory. In this paper, we review recent efforts to include heterogeneities and interactions in models of decision. We argue that the Random Field Ising model (RFIM) indeed provides a unifying framework to account for many collective socio-economic phenomena that lead to sudden ruptures and crises. We discuss different models that can capture potentially destabilising self-referential feedback loops, induced either by herding, i.e. reference to peers, or trending, i.e. reference to the past, and account for some of the phenomenology missing in the standard models. We discuss some empirically testable predictions of these models, for example robust signatures of RFIM-like herding effects, or the logarithmic decay of spatial correlations of voting patterns. One of the most striking result, inspired by statistical physics methods, is that Adam Smith's invisible hand can badly fail at solving simple coordination problems. We also insist on the issue of time-scales, that can be extremely long in some cases, and prevent socially optimal equilibria to be reached. As a theoretical challenge, the study of so-called "detailed-balance" violating decision rules is needed to decide whether conclusions based on current models (that all assume detailed-balance) are indeed robust and generic.Comment: Review paper accepted for a special issue of J Stat Phys; several minor improvements along reviewers' comment

Long-range Angular Correlations On The Near And Away Side In P-pb Collisions At √snn=5.02 Tev

7191/Mar294