635 research outputs found
Dynamics of Three Agent Games
We study the dynamics and resulting score distribution of three-agent games
where after each competition a single agent wins and scores a point. A single
competition is described by a triplet of numbers , and denoting the
probabilities that the team with the highest, middle or lowest accumulated
score wins. We study the full family of solutions in the regime, where the
number of agents and competitions is large, which can be regarded as a
hydrodynamic limit. Depending on the parameter values , we find six
qualitatively different asymptotic score distributions and we also provide a
qualitative understanding of these results. We checked our analytical results
against numerical simulations of the microscopic model and find these to be in
excellent agreement. The three agent game can be regarded as a social model
where a player can be favored or disfavored for advancement, based on his/her
accumulated score. It is also possible to decide the outcome of a three agent
game through a mini tournament of two-a gent competitions among the
participating players and it turns out that the resulting possible score
distributions are a subset of those obtained for the general three agent-games.
We discuss how one can add a steady and democratic decline rate to the model
and present a simple geometric construction that allows one to write down the
corresponding score evolution equations for -agent games
Dynamics of Multi-Player Games
We analyze the dynamics of competitions with a large number of players. In
our model, n players compete against each other and the winner is decided based
on the standings: in each competition, the mth ranked player wins. We solve for
the long time limit of the distribution of the number of wins for all n and m
and find three different scenarios. When the best player wins, the standings
are most competitive as there is one-tier with a clear differentiation between
strong and weak players. When an intermediate player wins, the standings are
two-tier with equally-strong players in the top tier and clearly-separated
players in the lower tier. When the worst player wins, the standings are least
competitive as there is one tier in which all of the players are equal. This
behavior is understood via scaling analysis of the nonlinear evolution
equations.Comment: 8 pages, 8 figure
The Morphologically Divided Redshift Distribution of Faint Galaxies
We have constructed a morphologically divided redshift distribution of faint
field galaxies using a statistically unbiased sample of 196 galaxies brighter
than I = 21.5 for which detailed morphological information (from the Hubble
Space Telescope) as well as ground-based spectroscopic redshifts are available.
Galaxies are classified into 3 rough morphological types according to their
visual appearance (E/S0s, Spirals, Sdm/dE/Irr/Pec's), and redshift
distributions are constructed for each type. The most striking feature is the
abundance of low to moderate redshift Sdm/dE/Irr/Pec's at I < 19.5. This
confirms that the faint end slope of the luminosity function (LF) is steep
(alpha < -1.4) for these objects. We also find that Sdm/dE/Irr/Pec's are fairly
abundant at moderate redshifts, and this can be explained by strong luminosity
evolution. However, the normalization factor (or the number density) of the LF
of Sdm/dE/Irr/Pec's is not much higher than that of the local LF of
Sdm/dE/Irr/Pec's. Furthermore, as we go to fainter magnitudes, the abundance of
moderate to high redshift Irr/Pec's increases considerably. This cannot be
explained by strong luminosity evolution of the dwarf galaxy populations alone:
these Irr/Pec's are probably the progenitors of present day ellipticals and
spiral galaxies which are undergoing rapid star formation or merging with their
neighbors. On the other hand, the redshift distributions of E/S0s and spirals
are fairly consistent those expected from passive luminosity evolution, and are
only in slight disagreement with the non-evolving model.Comment: 11 pages, 4 figures (published in ApJ
Ballistic Annihilation
Ballistic annihilation with continuous initial velocity distributions is
investigated in the framework of Boltzmann equation. The particle density and
the rms velocity decay as and , with the
exponents depending on the initial velocity distribution and the spatial
dimension. For instance, in one dimension for the uniform initial velocity
distribution we find . We also solve the Boltzmann equation
for Maxwell particles and very hard particles in arbitrary spatial dimension.
These solvable cases provide bounds for the decay exponents of the hard sphere
gas.Comment: 4 RevTeX pages and 1 Eps figure; submitted to Phys. Rev. Let
Kinetics of Clustering in Traffic Flows
We study a simple aggregation model that mimics the clustering of traffic on
a one-lane roadway. In this model, each ``car'' moves ballistically at its
initial velocity until it overtakes the preceding car or cluster. After this
encounter, the incident car assumes the velocity of the cluster which it has
just joined. The properties of the initial distribution of velocities in the
small velocity limit control the long-time properties of the aggregation
process. For an initial velocity distribution with a power-law tail at small
velocities, \pvim as , a simple scaling argument shows that the
average cluster size grows as n \sim t^{\va} and that the average velocity
decays as v \sim t^{-\vb} as . We derive an analytical solution
for the survival probability of a single car and an asymptotically exact
expression for the joint mass-velocity distribution function. We also consider
the properties of spatially heterogeneous traffic and the kinetics of traffic
clustering in the presence of an input of cars.Comment: 18 pages, Plain TeX, 2 postscript figure
The Relationship Between Stellar Light Distributions of Galaxies and their Formation Histories
A major problem in extragalactic astronomy is the inability to distinguish in
a robust, physical, and model independent way how galaxy populations are
related to each other and to their formation histories. A similar, but
distinct, and also long standing question is whether the structural appearances
of galaxies, as seen through their stellar light distributions, contain enough
physical information to offer this classification. We argue through the use of
240 images of nearby galaxies that three model independent parameters measured
on a single galaxy image reveal its major ongoing and past formation modes, and
can be used as a robust classification system. These parameters quantitatively
measure: the concentration (C), asymmetry (A) and clumpiness (S) of a galaxy's
stellar light distribution. When combined into a three dimensional `CAS' volume
all major classes of galaxies in various phases of evolution are cleanly
distinguished. We argue that these three parameters correlate with important
modes of galaxy evolution: star formation and major merging activity. This is
argued through the strong correlation of Halpha equivalent width and broad band
colors with the clumpiness parameter, the uniquely large asymmetries of 66
galaxies undergoing mergers, and the correlation of bulge to total light
ratios, and stellar masses, with the concentration index. As an obvious goal is
to use this system at high redshifts to trace evolution, we demonstrate that
these parameters can be measured, within a reasonable and quantifiable
uncertainty, with available data out to z ~ 3 using the Hubble Space Telescope
GOODS ACS and Hubble Deep Field images.Comment: ApJS, in press, 30 pages, Figures 15 and 16 are in color. For a full
resolution version, please go to http://www.astro.caltech.edu/~cc/cas.p
Persistence with Partial Survival
We introduce a parameter , called partial survival, in the persistence of
stochastic processes and show that for smooth processes the persistence
exponent changes continuously with , being the usual
persistence exponent. We compute exactly for a one-dimensional
deterministic coarsening model, and approximately for the diffusion equation.
Finally we develop an exact, systematic series expansion for , in
powers of , for a general Gaussian process with finite density of
zero crossings.Comment: 5 pages, 2 figures, references added, to appear in Phys.Rev.Let
Persistence in Cluster--Cluster Aggregation
Persistence is considered in diffusion--limited cluster--cluster aggregation,
in one dimension and when the diffusion coefficient of a cluster depends on its
size as . The empty and filled site persistences are
defined as the probabilities, that a site has been either empty or covered by a
cluster all the time whereas the cluster persistence gives the probability of a
cluster to remain intact. The filled site one is nonuniversal. The empty site
and cluster persistences are found to be universal, as supported by analytical
arguments and simulations. The empty site case decays algebraically with the
exponent . The cluster persistence is related to the
small behavior of the cluster size distribution and behaves also
algebraically for while for the behavior is
stretched exponential. In the scaling limit and with fixed the distribution of intervals of size between
persistent regions scales as , where is the average interval size and . For finite the
scaling is poor for , due to the insufficient separation of the two
length scales: the distances between clusters, , and that between
persistent regions, . For the size distribution of persistent regions
the time and size dependences separate, the latter being independent of the
diffusion exponent but depending on the initial cluster size
distribution.Comment: 14 pages, 12 figures, RevTeX, submitted to Phys. Rev.
Competitive random sequential adsorption of point and fixed-sized particles: analytical results
We study the kinetics of competitive random sequential adsorption (RSA) of
particles of binary mixture of points and fixed-sized particles within the
mean-field approach. The present work is a generalization of the random car
parking problem in the sense that it considers the case when either a car of
fixed size is parked with probability q or the parking space is partitioned
into two smaller spaces with probability (1-q) at each time event. This allows
an interesting interplay between the classical RSA problem at one extreme
(q=1), and the kinetics of fragmentation processes at the other extreme (q=0).
We present exact analytical results for coverage for a whole range of q values,
and physical explanations are given for different aspects of the problem. In
addition, a comprehensive account of the scaling theory, emphasizing on
dimensional analysis, is presented, and the exact expression for the scaling
function and exponents are obtained.Comment: 7 pages, latex, 3 figure
Jamming transition in a homogeneous one-dimensional system: the Bus Route Model
We present a driven diffusive model which we call the Bus Route Model. The
model is defined on a one-dimensional lattice, with each lattice site having
two binary variables, one of which is conserved (``buses'') and one of which is
non-conserved (``passengers''). The buses are driven in a preferred direction
and are slowed down by the presence of passengers who arrive with rate lambda.
We study the model by simulation, heuristic argument and a mean-field theory.
All these approaches provide strong evidence of a transition between an
inhomogeneous ``jammed'' phase (where the buses bunch together) and a
homogeneous phase as the bus density is increased. However, we argue that a
strict phase transition is present only in the limit lambda -> 0. For small
lambda, we argue that the transition is replaced by an abrupt crossover which
is exponentially sharp in 1/lambda. We also study the coarsening of gaps
between buses in the jammed regime. An alternative interpretation of the model
is given in which the spaces between ``buses'' and the buses themselves are
interchanged. This describes a system of particles whose mobility decreases the
longer they have been stationary and could provide a model for, say, the flow
of a gelling or sticky material along a pipe.Comment: 17 pages Revtex, 20 figures, submitted to Phys. Rev.
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