Effect of disorder on condensation in the lattice gas model on a random graph

The lattice gas model of condensation in a heterogeneous pore system, represented by a random graph of cells, is studied using an exact analytical solution. A binary mixture of pore cells with different coordination numbers is shown to exhibit two phase transitions as a function of chemical potential in a certain temperature range. Heterogeneity in interaction strengths is demonstrated to reduce the critical temperature and, for large enough degree of disorder, divides the cells into ones which are either on average occupied or unoccupied. Despite treating the pore space loops in a simplified manner, the random-graph model provides a good description of condensation in porous structures containing loops. This is illustrated by considering capillary condensation in a structural model of mesoporous silica SBA-15.Comment: 22 pages, 16 figure

Capillary condensation in one-dimensional irregular confinement

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Prominent effect of soil network heterogeneity on microbial invasion

Using a network representation for real soil samples and mathematical models for microbial spread, we show that the structural heterogeneity of the soil habitat may have a very significant influence on the size of microbial invasions of the soil pore space. In particular, neglecting the soil structural heterogeneity may lead to a substantial underestimation of microbial invasion. Such effects are explained in terms of a crucial interplay between heterogeneity in microbial spread and heterogeneity in the topology of soil networks. The main influence of network topology on invasion is linked to the existence of long channels in soil networks that may act as bridges for transmission of microorganisms between distant parts of soil

Socialization of the elderly in outdoor health circuits

En los parques biosaludables, originalmente concebidos para la población madura y anciana, se encuentran usuarios de diferentes edades y con distintas formas de entender la actividad física. El presente trabajo intenta examinar las relaciones de las personas mayores con el resto de usuarios para determinar en qué medida dichos parques pueden cumplir alguna función social más allá del fomento de hábitos saludables. Para ello se ha llevado a cabo una serie de observaciones, participantes y no participantes, en tres parques de la ciudad de Granada, donde se ha visto que, si bien existe una proporción minoritaria pero importante de usuarios jóvenes (aproximadamente un tercio del total), estos tienden a evitar una interacción que parte de los usuarios de mayor edad buscan expresamente

Training-induced criticality in martensites

We propose an explanation for the self-organization towards criticality observed in martensites during the cyclic process known as `training'. The scale-free behavior originates from the interplay between the reversible phase transformation and the concurrent activity of lattice defects. The basis of the model is a continuous dynamical system on a rugged energy landscape, which in the quasi-static limit reduces to a sandpile automaton. We reproduce all the principal observations in thermally driven martensites, including power-law statistics, hysteresis shakedown, asymmetric signal shapes, and correlated disorder.Comment: 5 pages, 4 figure

Modelling avalanches in martensites

Solids subject to continuous changes of temperature or mechanical load often exhibit discontinuous avalanche-like responses. For instance, avalanche dynamics have been observed during plastic deformation, fracture, domain switching in ferroic materials or martensitic transformations. The statistical analysis of avalanches reveals a very complex scenario with a distinctive lack of characteristic scales. Much effort has been devoted in the last decades to understand the origin and ubiquity of scale-free behaviour in solids and many other systems. This chapter reviews some efforts to understand the characteristics of avalanches in martensites through mathematical modelling.Comment: Chapter in the book "Avalanches in Functional Materials and Geophysics", edited by E. K. H. Salje, A. Saxena, and A. Planes. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-45612-6_

Stable, metastable and unstable states in the mean-field RFIM at T=0

We compute the probability of finding metastable states at a given field in the mean-field random field Ising model at T=0. Remarkably, this probability is finite in the thermodynamic limit, even on the so-called ``unstable'' branch of the magnetization curve. This implies that the branch is reachable when the magnetization is controlled instead of the magnetic field, in contrast with the situation in the pure system.Comment: 10 pages, 3 figure

Reinforcement-Driven Spread of Innovations and Fads

We propose kinetic models for the spread of permanent innovations and transient fads by the mechanism of social reinforcement. Each individual can be in one of M+1 states of awareness 0,1,2,...,M, with state M corresponding to adopting an innovation. An individual with awareness k<M increases to k+1 by interacting with an adopter. Starting with a single adopter, the time for an initially unaware population of size N to adopt a permanent innovation grows as ln(N) for M=1, and as N^{1-1/M} for M>1. The fraction of the population that remains clueless about a transient fad after it has come and gone changes discontinuously as a function of the fad abandonment rate lambda for M>1. The fad dies out completely in a time that varies non-monotonically with lambda.Comment: 4 pages, 2 columns, 5 figures, revtex 4-1 format; revised version has been expanded and put into iop format, with one figure adde

Zero-temperature random-field Ising model on a bilayered Bethe lattice

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