45 research outputs found
Flow Path Resistance in Heterogeneous Porous Media Recast into a Graph-Theory Problem
Acknowledgment is made to the U.S. NSF (EAR-1847689) and the Donors of the American Chemical Society Petroleum Research Fund (59864-DNI9) for partial support of this research. The authors also thank Drs Matthias Willmann, Jefrey Hyman and Markus Holzner for assistance with numerical simulations and insightful discussionsPeer reviewedPublisher PD
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
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_
Spanning avalanches in the three-dimensional Gaussian Random Field Ising Model with metastable dynamics: field dependence and geometrical properties
Spanning avalanches in the 3D Gaussian Random Field Ising Model (3D-GRFIM)
with metastable dynamics at T=0 have been studied. Statistical analysis of the
field values for which avalanches occur has enabled a Finite-Size Scaling (FSS)
study of the avalanche density to be performed. Furthermore, direct measurement
of the geometrical properties of the avalanches has confirmed an earlier
hypothesis that several kinds of spanning avalanches with two different fractal
dimensions coexist at the critical point. We finally compare the phase diagram
of the 3D-GRFIM with metastable dynamics with the same model in equilibrium at
T=0.Comment: 16 pages, 17 figure
Complexity and anisotropy in host morphology make populations safer against epidemic outbreaks
One of the challenges in epidemiology is to account for the complex
morphological structure of hosts such as plant roots, crop fields, farms,
cells, animal habitats and social networks, when the transmission of infection
occurs between contiguous hosts. Morphological complexity brings an inherent
heterogeneity in populations and affects the dynamics of pathogen spread in
such systems. We have analysed the influence of realistically complex host
morphology on the threshold for invasion and epidemic outbreak in an SIR
(susceptible-infected-recovered) epidemiological model. We show that disorder
expressed in the host morphology and anisotropy reduces the probability of
epidemic outbreak and thus makes the system more resistant to epidemic
outbreaks. We obtain general analytical estimates for minimally safe bounds for
an invasion threshold and then illustrate their validity by considering an
example of host data for branching hosts (salamander retinal ganglion cells).
Several spatial arrangements of hosts with different degrees of heterogeneity
have been considered in order to analyse separately the role of shape
complexity and anisotropy in the host population. The estimates for invasion
threshold are linked to morphological characteristics of the hosts that can be
used for determining the threshold for invasion in practical applications.Comment: 21 pages, 8 figure
Epidemics in Networks of Spatially Correlated Three-dimensional Root Branching Structures
Using digitized images of the three-dimensional, branching structures for
root systems of bean seedlings, together with analytical and numerical methods
that map a common 'SIR' epidemiological model onto the bond percolation
problem, we show how the spatially-correlated branching structures of plant
roots affect transmission efficiencies, and hence the invasion criterion, for a
soil-borne pathogen as it spreads through ensembles of morphologically complex
hosts. We conclude that the inherent heterogeneities in transmissibilities
arising from correlations in the degrees of overlap between neighbouring
plants, render a population of root systems less susceptible to epidemic
invasion than a corresponding homogeneous system. Several components of
morphological complexity are analysed that contribute to disorder and
heterogeneities in transmissibility of infection. Anisotropy in root shape is
shown to increase resilience to epidemic invasion, while increasing the degree
of branching enhances the spread of epidemics in the population of roots. Some
extension of the methods for other epidemiological systems are discussed.Comment: 21 pages, 8 figure
The T=0 random-field Ising model on a Bethe lattice with large coordination number: hysteresis and metastable states
In order to elucidate the relationship between rate-independent hysteresis
and metastability in disordered systems driven by an external field, we study
the Gaussian RFIM at T=0 on regular random graphs (Bethe lattice) of finite
connectivity z and compute to O(1/z) (i.e. beyond mean-field) the quenched
complexity associated with the one-spin-flip stable states with magnetization m
as a function of the magnetic field H. When the saturation hysteresis loop is
smooth in the thermodynamic limit, we find that it coincides with the envelope
of the typical metastable states (the quenched complexity vanishes exactly
along the loop and is positive everywhere inside). On the other hand, the
occurence of a jump discontinuity in the loop (associated with an infinite
avalanche) can be traced back to the existence of a gap in the magnetization of
the metastable states for a range of applied field, and the envelope of the
typical metastable states is then reentrant. These findings confirm and
complete earlier analytical and numerical studies.Comment: 29 pages, 9 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
Fine Structure of Avalanches in the Abelian Sandpile Model
We study the two-dimensional Abelian Sandpile Model on a square lattice of
linear size L. We introduce the notion of avalanche's fine structure and
compare the behavior of avalanches and waves of toppling. We show that
according to the degree of complexity in the fine structure of avalanches,
which is a direct consequence of the intricate superposition of the boundaries
of successive waves, avalanches fall into two different categories. We propose
scaling ans\"{a}tz for these avalanche types and verify them numerically. We
find that while the first type of avalanches has a simple scaling behavior, the
second (complex) type is characterized by an avalanche-size dependent scaling
exponent. This provides a framework within which one can understand the failure
of a consistent scaling behavior in this model.Comment: 10 page