1,283 research outputs found
The three-dimensional random field Ising magnet: interfaces, scaling, and the nature of states
The nature of the zero temperature ordering transition in the 3D Gaussian
random field Ising magnet is studied numerically, aided by scaling analyses. In
the ferromagnetic phase the scaling of the roughness of the domain walls,
, is consistent with the theoretical prediction .
As the randomness is increased through the transition, the probability
distribution of the interfacial tension of domain walls scales as for a single
second order transition. At the critical point, the fractal dimensions of
domain walls and the fractal dimension of the outer surface of spin clusters
are investigated: there are at least two distinct physically important fractal
dimensions. These dimensions are argued to be related to combinations of the
energy scaling exponent, , which determines the violation of
hyperscaling, the correlation length exponent , and the magnetization
exponent . The value is derived from the
magnetization: this estimate is supported by the study of the spin cluster size
distribution at criticality. The variation of configurations in the interior of
a sample with boundary conditions is consistent with the hypothesis that there
is a single transition separating the disordered phase with one ground state
from the ordered phase with two ground states. The array of results are shown
to be consistent with a scaling picture and a geometric description of the
influence of boundary conditions on the spins. The details of the algorithm
used and its implementation are also described.Comment: 32 pp., 2 columns, 32 figure
A Simple Model of Epidemics with Pathogen Mutation
We study how the interplay between the memory immune response and pathogen
mutation affects epidemic dynamics in two related models. The first explicitly
models pathogen mutation and individual memory immune responses, with contacted
individuals becoming infected only if they are exposed to strains that are
significantly different from other strains in their memory repertoire. The
second model is a reduction of the first to a system of difference equations.
In this case, individuals spend a fixed amount of time in a generalized immune
class. In both models, we observe four fundamentally different types of
behavior, depending on parameters: (1) pathogen extinction due to lack of
contact between individuals, (2) endemic infection (3) periodic epidemic
outbreaks, and (4) one or more outbreaks followed by extinction of the epidemic
due to extremely low minima in the oscillations. We analyze both models to
determine the location of each transition. Our main result is that pathogens in
highly connected populations must mutate rapidly in order to remain viable.Comment: 9 pages, 11 figure
Evolving networks with disadvantaged long-range connections
We consider a growing network, whose growth algorithm is based on the
preferential attachment typical for scale-free constructions, but where the
long-range bonds are disadvantaged. Thus, the probability to get connected to a
site at distance is proportional to , where is a
tunable parameter of the model. We show that the properties of the networks
grown with are close to those of the genuine scale-free
construction, while for the structure of the network is vastly
different. Thus, in this regime, the node degree distribution is no more a
power law, and it is well-represented by a stretched exponential. On the other
hand, the small-world property of the growing networks is preserved at all
values of .Comment: REVTeX, 6 pages, 5 figure
Edge overload breakdown in evolving networks
We investigate growing networks based on Barabasi and Albert's algorithm for
generating scale-free networks, but with edges sensitive to overload breakdown.
the load is defined through edge betweenness centrality. We focus on the
situation where the average number of connections per vertex is, as the number
of vertices, linearly increasing in time. After an initial stage of growth, the
network undergoes avalanching breakdowns to a fragmented state from which it
never recovers. This breakdown is much less violent if the growth is by random
rather than preferential attachment (as defines the Barabasi and Albert model).
We briefly discuss the case where the average number of connections per vertex
is constant. In this case no breakdown avalanches occur. Implications to the
growth of real-world communication networks are discussed.Comment: To appear in Phys. Rev.
An 8-month longitudinal exploration of body image and disordered eating in the UK during the COVID-19 pandemic
Research suggests that the COVID-19 pandemic is negatively impacting mental health, with rates of eating disorder referrals in particular rising steeply during the pandemic. This study aimed to examine 8-month changes in body image and disordered eating during the COVID-19 pandemic, and explore whether any changes were moderated by gender, age, or eating disorder history. This study used a longitudinal survey design in which 587 adults living in the UK (85 % women; mean age = 32.87 years) completed assessments every two months over five timepoints from May/June 2020 to January/February 2021. Measures included body esteem, disordered eating, and psychological distress. Mixed effect models showed small but significant improvements in body esteem and disordered eating symptoms from May/June 2020 to January/February 2021. These improvements were independent of changes in psychological distress, and did not vary by gender, age or eating disorder history. Whilst poor body image and disordered eating may have been elevated in the early period of the pandemic, this study suggests improvements, rather than worsening, of these outcomes over time. This may reflect adaptation to this changing context
Low Energy Excitations in Spin Glasses from Exact Ground States
We investigate the nature of the low-energy, large-scale excitations in the
three-dimensional Edwards-Anderson Ising spin glass with Gaussian couplings and
free boundary conditions, by studying the response of the ground state to a
coupling-dependent perturbation introduced previously. The ground states are
determined exactly for system sizes up to 12^3 spins using a branch and cut
algorithm. The data are consistent with a picture where the surface of the
excitations is not space-filling, such as the droplet or the ``TNT'' picture,
with only minimal corrections to scaling. When allowing for very large
corrections to scaling, the data are also consistent with a picture with
space-filling surfaces, such as replica symmetry breaking. The energy of the
excitations scales with their size with a small exponent \theta', which is
compatible with zero if we allow moderate corrections to scaling. We compare
the results with data for periodic boundary conditions obtained with a genetic
algorithm, and discuss the effects of different boundary conditions on
corrections to scaling. Finally, we analyze the performance of our branch and
cut algorithm, finding that it is correlated with the existence of
large-scale,low-energy excitations.Comment: 18 Revtex pages, 16 eps figures. Text significantly expanded with
more discussion of the numerical data. Fig.11 adde
Large-Deviation Functions for Nonlinear Functionals of a Gaussian Stationary Markov Process
We introduce a general method, based on a mapping onto quantum mechanics, for
investigating the large-T limit of the distribution P(r,T) of the nonlinear
functional r[V] = (1/T)\int_0^T dT' V[X(T')], where V(X) is an arbitrary
function of the stationary Gaussian Markov process X(T). For T tending to
infinity at fixed r we find that P(r,T) behaves as exp[-theta(r) T], where
theta(r) is a large deviation function. We present explicit results for a
number of special cases, including the case V(X) = X \theta(X) which is related
to the cooling and the heating degree days relevant to weather derivatives.Comment: 8 page
Signatures of small-world and scale-free properties in large computer programs
A large computer program is typically divided into many hundreds or even
thousands of smaller units, whose logical connections define a network in a
natural way. This network reflects the internal structure of the program, and
defines the ``information flow'' within the program. We show that, (1) due to
its growth in time this network displays a scale-free feature in that the
probability of the number of links at a node obeys a power-law distribution,
and (2) as a result of performance optimization of the program the network has
a small-world structure. We believe that these features are generic for large
computer programs. Our work extends the previous studies on growing networks,
which have mostly been for physical networks, to the domain of computer
software.Comment: 4 pages, 1 figure, to appear in Phys. Rev.
The spread of epidemic disease on networks
The study of social networks, and in particular the spread of disease on
networks, has attracted considerable recent attention in the physics community.
In this paper, we show that a large class of standard epidemiological models,
the so-called susceptible/infective/removed (SIR) models can be solved exactly
on a wide variety of networks. In addition to the standard but unrealistic case
of fixed infectiveness time and fixed and uncorrelated probability of
transmission between all pairs of individuals, we solve cases in which times
and probabilities are non-uniform and correlated. We also consider one simple
case of an epidemic in a structured population, that of a sexually transmitted
disease in a population divided into men and women. We confirm the correctness
of our exact solutions with numerical simulations of SIR epidemics on networks.Comment: 12 pages, 3 figure
Correlations in Scale-Free Networks: Tomography and Percolation
We discuss three related models of scale-free networks with the same degree
distribution but different correlation properties. Starting from the
Barabasi-Albert construction based on growth and preferential attachment we
discuss two other networks emerging when randomizing it with respect to links
or nodes. We point out that the Barabasi-Albert model displays dissortative
behavior with respect to the nodes' degrees, while the node-randomized network
shows assortative mixing. These kinds of correlations are visualized by
discussig the shell structure of the networks around their arbitrary node. In
spite of different correlation behavior, all three constructions exhibit
similar percolation properties.Comment: 6 pages, 2 figures; added reference
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