3,286 research outputs found
P2_5 Jovian Gravitational Perturbations on Earth's Orbit
In a hypothetical situations in which the solar system contains varied masses of Jupiter, the orbit of the Earth may fall subject to considerable gravitational perturbations. With the aid of the Newtonian gravity simulator, Universe SandboxTM, the effects of these perturbations can be observed .The orbit is found alter by an approximate 30x106 km before being ejected from the solar system, at Jovian mass of 0.7 Mʘ
Genetic Correlations in Mutation Processes
We study the role of phylogenetic trees on correlations in mutation
processes. Generally, correlations decay exponentially with the generation
number. We find that two distinct regimes of behavior exist. For mutation rates
smaller than a critical rate, the underlying tree morphology is almost
irrelevant, while mutation rates higher than this critical rate lead to strong
tree-dependent correlations. We show analytically that identical critical
behavior underlies all multiple point correlations. This behavior generally
characterizes branching processes undergoing mutation.Comment: revtex, 8 pages, 2 fig
First Passage Properties of the Erdos-Renyi Random Graph
We study the mean time for a random walk to traverse between two arbitrary
sites of the Erdos-Renyi random graph. We develop an effective medium
approximation that predicts that the mean first-passage time between pairs of
nodes, as well as all moments of this first-passage time, are insensitive to
the fraction p of occupied links. This prediction qualitatively agrees with
numerical simulations away from the percolation threshold. Near the percolation
threshold, the statistically meaningful quantity is the mean transit rate,
namely, the inverse of the first-passage time. This rate varies
non-monotonically with p near the percolation transition. Much of this behavior
can be understood by simple heuristic arguments.Comment: 10 pages, 9 figures, 2-column revtex4 forma
Rank Statistics in Biological Evolution
We present a statistical analysis of biological evolution processes.
Specifically, we study the stochastic replication-mutation-death model where
the population of a species may grow or shrink by birth or death, respectively,
and additionally, mutations lead to the creation of new species. We rank the
various species by the chronological order by which they originate. The average
population N_k of the kth species decays algebraically with rank, N_k ~ M^{mu}
k^{-mu}, where M is the average total population. The characteristic exponent
mu=(alpha-gamma)/(alpha+beta-gamma)$ depends on alpha, beta, and gamma, the
replication, mutation, and death rates. Furthermore, the average population P_k
of all descendants of the kth species has a universal algebraic behavior, P_k ~
M/k.Comment: 4 pages, 3 figure
Stable Distributions in Stochastic Fragmentation
We investigate a class of stochastic fragmentation processes involving stable
and unstable fragments. We solve analytically for the fragment length density
and find that a generic algebraic divergence characterizes its small-size tail.
Furthermore, the entire range of acceptable values of decay exponent consistent
with the length conservation can be realized. We show that the stochastic
fragmentation process is non-self-averaging as moments exhibit significant
sample-to-sample fluctuations. Additionally, we find that the distributions of
the moments and of extremal characteristics possess an infinite set of
progressively weaker singularities.Comment: 11 pages, 5 figure
Continuously-variable survival exponent for random walks with movable partial reflectors
We study a one-dimensional lattice random walk with an absorbing boundary at
the origin and a movable partial reflector. On encountering the reflector, at
site x, the walker is reflected (with probability r) to x-1 and the reflector
is simultaneously pushed to x+1. Iteration of the transition matrix, and
asymptotic analysis of the probability generating function show that the
critical exponent delta governing the survival probability varies continuously
between 1/2 and 1 as r varies between 0 and 1. Our study suggests a mechanism
for nonuniversal kinetic critical behavior, observed in models with an infinite
number of absorbing configurations.Comment: 5 pages, 3 figure
Anomalous self-diffusion in the ferromagnetic Ising chain with Kawasaki dynamics
We investigate the motion of a tagged spin in a ferromagnetic Ising chain
evolving under Kawasaki dynamics. At equilibrium, the displacement is Gaussian,
with a variance growing as . The temperature dependence of the
prefactor is derived exactly. At low temperature, where the static
correlation length is large, the mean square displacement grows as
in the coarsening regime, i.e., as a finite fraction of the
mean square domain length. The case of totally asymmetric dynamics, where
(resp. ) spins move only to the right (resp. to the left), is also
considered. In the steady state, the displacement variance grows as . The temperature dependence of the prefactor is derived exactly,
using the Kardar-Parisi-Zhang theory. At low temperature, the displacement
variance grows as in the coarsening regime, again proportionally to
the mean square domain length.Comment: 22 pages, 8 figures. A few minor changes and update
Crossover from directed percolation to compact directed percolation
We study critical spreading in a surface-modified directed percolation model
in which the left- and right-most sites have different occupation probabilities
than in the bulk. As we vary the probability for growth at an edge, the
critical exponents switch from the compact directed percolation class to
ordinary directed percolation. We conclude that the nonuniversality observed in
models with multiple absorbing configurations cannot be explained as a simple
surface effect.Comment: 4 pages, Revtex, 5 figures postscrip
Sharp interface limits of phase-field models
The use of continuum phase-field models to describe the motion of
well-defined interfaces is discussed for a class of phenomena, that includes
order/disorder transitions, spinodal decomposition and Ostwald ripening,
dendritic growth, and the solidification of eutectic alloys. The projection
operator method is used to extract the ``sharp interface limit'' from phase
field models which have interfaces that are diffuse on a length scale . In
particular,phase-field equations are mapped onto sharp interface equations in
the limits and , where and are
respectively the interface curvature and velocity and is the diffusion
constant in the bulk. The calculations provide one general set of sharp
interface equations that incorporate the Gibbs-Thomson condition, the
Allen-Cahn equation and the Kardar-Parisi-Zhang equation.Comment: 17 pages, 9 figure
How self-organized criticality works: A unified mean-field picture
We present a unified mean-field theory, based on the single site
approximation to the master-equation, for stochastic self-organized critical
models. In particular, we analyze in detail the properties of sandpile and
forest-fire (FF) models. In analogy with other non-equilibrium critical
phenomena, we identify the order parameter with the density of ``active'' sites
and the control parameters with the driving rates. Depending on the values of
the control parameters, the system is shown to reach a subcritical (absorbing)
or super-critical (active) stationary state. Criticality is analyzed in terms
of the singularities of the zero-field susceptibility. In the limit of
vanishing control parameters, the stationary state displays scaling
characteristic of self-organized criticality (SOC). We show that this limit
corresponds to the breakdown of space-time locality in the dynamical rules of
the models. We define a complete set of critical exponents, describing the
scaling of order parameter, response functions, susceptibility and correlation
length in the subcritical and supercritical states. In the subcritical state,
the response of the system to small perturbations takes place in avalanches. We
analyze their scaling behavior in relation with branching processes. In
sandpile models because of conservation laws, a critical exponents subset
displays mean-field values ( and ) in any dimensions. We
treat bulk and boundary dissipation and introduce a new critical exponent
relating dissipation and finite size effects. We present numerical simulations
that confirm our results. In the case of the forest-fire model, our approach
can distinguish between different regimes (SOC-FF and deterministic FF) studied
in the literature and determine the full spectrum of critical exponents.Comment: 21 RevTex pages, 3 figures, submitted to Phys. Rev.
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