Maximal Entropy Random Walk: solvable cases of dynamics

We focus on the study of dynamics of two kinds of random walk: generic random walk (GRW) and maximal entropy random walk (MERW) on two model networks: Cayley trees and ladder graphs. The stationary probability distribution for MERW is given by the squared components of the eigenvector associated with the largest eigenvalue \lambda_0 of the adjacency matrix of a graph, while the dynamics of the probability distribution approaching to the stationary state depends on the second largest eigenvalue \lambda_1. Firstly, we give analytic solutions for Cayley trees with arbitrary branching number, root degree, and number of generations. We determine three regimes of a tree structure that result in different statics and dynamics of MERW, which are due to strongly, critically, and weakly branched roots. We show how the relaxation times, generically shorter for MERW than for GRW, scale with the graph size. Secondly, we give numerical results for ladder graphs with symmetric defects. MERW shows a clear exponential growth of the relaxation time with the size of defective regions, which indicates trapping of a particle within highly entropic intact region and its escaping that resembles quantum tunneling through a potential barrier. GRW shows standard diffusive dependence irrespective of the defects.Comment: 13 pages, 6 figures, 24th Marian Smoluchowski Symposium on Statistical Physics (Zakopane, Poland, September 17-22, 2011

La reacción de la Unión Europea a la crisis migratoria venezolana

The main objective of this article is to analyze the actions undertaken by the European Union (EU) as a reaction to the political and economic crisis which has led to a massive exodus of Venezuelan citizens in recent years (since 2015), and in particular after the last presidential elections. The article will outline current critical situation in Venezuela, first by presenting the political background and then by describing the general picture of the Venezuelan economy and hardships that resulted in this unprecedented migratory movement. Building on the hypothesis that being a global player is in keeping with the aspirations of the EU, the second part of the article analyzes both political and financial measures undertaken by various European institutions to help mitigate this humanitarian crisis.El objetivo principal de este artículo es analizar las acciones emprendidas por la Unión Europea (UE) como una reacción a la crisis política y económica que ha causado un éxodo masivo de ciudadanos venezolanos en los últimos años (desde 2015) y, en particular, tras las últimas elecciones presidenciales. La situación crítica actual en Venezuela se describirá, primero, presentando los antecedentes políticos y luego describiendo el panorama general de la economía venezolana y las dificultades que llevaron a este movimiento migratorio sin precedentes. Partiendo de la hipótesis de que la intervención de la UE está en consonancia con sus aspiraciones de ser un actor global, la segunda parte del artículo analiza las medidas tanto políticas como financieras emprendidas por diversas instituciones europeas para ayudar a mitigar esta crisis humanitaria

A simple non-equilibrium, statistical-physics toy model of thin-film growth

We present a simple non-equilibrium model of mass condensation with Lennard-Jones interactions between particles and the substrate. We show that when some number of particles is deposited onto the surface and the system is left to equilibrate, particles condense into an island if the density of particles becomes higher than some critical density. We illustrate this with numerically obtained phase diagrams for three-dimensional systems. We also solve a two-dimensional counterpart of this model analytically and show that not only the phase diagram but also the shape of the cross-sections of three-dimensional condensates qualitatively matches the two-dimensional predictions. Lastly, we show that when particles are being deposited with a constant rate, the system has two phases: a single condensate for low deposition rates, and multiple condensates for fast deposition. The behaviour of our model is thus similar to that of thin film growth processes, and in particular to Stranski-Krastanov growth.Comment: 26 pages, 16 figure