3,287 research outputs found
An Astonishing Sixty Years: The Legacy of Hiroshima
Nobel Prize Lecture, December 8, 2005Game Theory; Conflict; Cooperation
Schelling segregation in an open city: a kinetically constrained Blume-Emery-Griffiths spin-1 system
In the 70's Schelling introduced a multi-agent model to describe the
segregation dynamics that may occur with individuals having only weak
preferences for 'similar' neighbors. Recently variants of this model have been
discussed, in particular, with emphasis on the links with statistical physics
models. Whereas these models consider a fixed number of agents moving on a
lattice, here we present a version allowing for exchanges with an external
reservoir of agents. The density of agents is controlled by a parameter which
can be viewed as measuring the attractiveness of the city-lattice. This model
is directly related to the zero-temperature dynamics of the
Blume-Emery-Griffiths (BEG) spin-1 model, with kinetic constraints. With a
varying vacancy density, the dynamics with agents making deterministic
decisions leads to a new variety of "phases" whose main features are the
characteristics of the interfaces between clusters of agents of different
types. The domains of existence of each type of interface are obtained
analytically as well as numerically. These interfaces may completely isolate
the agents leading to another type of segregation as compared to what is
observed in the original Schelling model, and we discuss its possible
socio-economic correlates.Comment: 10 pages, 7 figures, final version accepted for publication in PR
Residential segregation and cultural dissemination: An Axelrod-Schelling model
In the Axelrod's model of cultural dissemination, we consider mobility of
cultural agents through the introduction of a density of empty sites and the
possibility that agents in a dissimilar neighborhood can move to them if their
mean cultural similarity with the neighborhood is below some threshold. While
for low values of the density of empty sites the mobility enhances the
convergence to a global culture, for high enough values of it the dynamics can
lead to the coexistence of disconnected domains of different cultures. In this
regime, the increase of initial cultural diversity paradoxically increases the
convergence to a dominant culture. Further increase of diversity leads to
fragmentation of the dominant culture into domains, forever changing in shape
and number, as an effect of the never ending eroding activity of cultural
minorities
A unified framework for Schelling's model of segregation
Schelling's model of segregation is one of the first and most influential
models in the field of social simulation. There are many variations of the
model which have been proposed and simulated over the last forty years, though
the present state of the literature on the subject is somewhat fragmented and
lacking comprehensive analytical treatments. In this article a unified
mathematical framework for Schelling's model and its many variants is
developed. This methodology is useful in two regards: firstly, it provides a
tool with which to understand the differences observed between models;
secondly, phenomena which appear in several model variations may be understood
in more depth through analytic studies of simpler versions.Comment: 21 pages, 3 figure
Local interaction scale controls the existence of a non-trivial optimal critical mass in opinion spreading
We study a model of opinion formation where the collective decision of group
is said to happen if the fraction of agents having the most common opinion
exceeds a threshold value, a \textit{critical mass}. We find that there exists
a unique, non-trivial critical mass giving the most efficient convergence to
consensus. In addition, we observe that for small critical masses, the
characteristic time scale for the relaxation to consensus splits into two. The
shorter time scale corresponds to a direct relaxation and the longer can be
explained by the existence of intermediate, metastable states similar to those
found in [P.\ Chen and S.\ Redner, Phys.\ Rev.\ E \textbf{71}, 036101 (2005)].
This longer time-scale is dependent on the precise condition for
consensus---with a modification of the condition it can go away.Comment: 4 pages, 6 figure
Towards More Accurate Molecular Dynamics Calculation of Thermal Conductivity. Case Study: GaN Bulk Crystals
Significant differences exist among literature for thermal conductivity of
various systems computed using molecular dynamics simulation. In some cases,
unphysical results, for example, negative thermal conductivity, have been
found. Using GaN as an example case and the direct non-equilibrium method,
extensive molecular dynamics simulations and Monte Carlo analysis of the
results have been carried out to quantify the uncertainty level of the
molecular dynamics methods and to identify the conditions that can yield
sufficiently accurate calculations of thermal conductivity. We found that the
errors of the calculations are mainly due to the statistical thermal
fluctuations. Extrapolating results to the limit of an infinite-size system
tend to magnify the errors and occasionally lead to unphysical results. The
error in bulk estimates can be reduced by performing longer time averages using
properly selected systems over a range of sample lengths. If the errors in the
conductivity estimates associated with each of the sample lengths are kept
below a certain threshold, the likelihood of obtaining unphysical bulk values
becomes insignificant. Using a Monte-Carlo approach developed here, we have
determined the probability distributions for the bulk thermal conductivities
obtained using the direct method. We also have observed a nonlinear effect that
can become a source of significant errors. For the extremely accurate results
presented here, we predict a [0001] GaN thermal conductivity of 185 at 300 K, 102 at 500 K, and 74
at 800 K. Using the insights obtained in the work, we have achieved a
corresponding error level (standard deviation) for the bulk (infinite sample
length) GaN thermal conductivity of less than 10 , 5 , and 15 at 300 K, 500 K, and 800 K respectively
Analysis of simulation methodology for calculation of the heat of transport for vacancy thermodiffusion
Computation of the heat of transport Q*(a) in monatomic crystalline solids is investigated using the methodology first developed by Gillan [J. Phys. C: Solid State Phys. 11, 4469 (1978)] and further developed by Grout and coworkers [Philos. Mag. Lett. 74, 217 (1996)], referred to as the Grout-Gillan method. In the case of pair potentials, the hopping of a vacancy results in a heat wave that persists for up to 10 ps, consistent with previous studies. This leads to generally positive values for Q*(a) which can be quite large and are strongly dependent on the specific details of the pair potential. By contrast, when the interactions are described using the embedded atom model, there is no evidence of a heat wave, and Q*(a) is found to be negative. This demonstrates that the dynamics of vacancy hopping depends strongly on the details of the empirical potential. However, the results obtained here are in strong disagreement with experiment. Arguments are presented which demonstrate that there is a fundamental error made in the Grout-Gillan method due to the fact that the ensemble of states only includes successful atom hops and hence does not represent an equilibrium ensemble. This places the interpretation of the quantity computed in the Grout-Gillan method as the heat of transport in doubt. It is demonstrated that trajectories which do not yield hopping events are nevertheless relevant to computation of the heat of transport Q*(a)
Nonequilibrium phase transition in the coevolution of networks and opinions
Models of the convergence of opinion in social systems have been the subject
of a considerable amount of recent attention in the physics literature. These
models divide into two classes, those in which individuals form their beliefs
based on the opinions of their neighbors in a social network of personal
acquaintances, and those in which, conversely, network connections form between
individuals of similar beliefs. While both of these processes can give rise to
realistic levels of agreement between acquaintances, practical experience
suggests that opinion formation in the real world is not a result of one
process or the other, but a combination of the two. Here we present a simple
model of this combination, with a single parameter controlling the balance of
the two processes. We find that the model undergoes a continuous phase
transition as this parameter is varied, from a regime in which opinions are
arbitrarily diverse to one in which most individuals hold the same opinion. We
characterize the static and dynamical properties of this transition
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