56 research outputs found
Spatial Organization in the Reaction A + B --> inert for Particles with a Drift
We describe the spatial structure of particles in the (one dimensional)
two-species annihilation reaction A + B --> 0, where both species have a
uniform drift in the same direction and like species have a hard core
exclusion. For the case of equal initial concentration, at long times, there
are three relevant length scales: the typical distance between similar
(neighboring) particles, the typical distance between dissimilar (neighboring)
particles, and the typical size of a cluster of one type of particles. These
length scales are found to be generically different than that found for
particles without a drift.Comment: 10 pp of gzipped uuencoded postscrip
Annihilation of Charged Particles
The kinetics of irreversible annihilation of charged particles performing
overdamped motion induced by long-range interaction force, , is investigated. The system exhibits rich kinetic behaviors
depending on the force exponent . In one dimension we find that the
densities decay as and when
and , respectively, with logarithmic correction at
. For , the asymptotic behavior is shown to be
dependent on system size.Comment: 17 pages, plain TeX, 3 figures available upon request from
[email protected]
Symmetries of microcanonical entropy surfaces
Symmetry properties of the microcanonical entropy surface as a function of
the energy and the order parameter are deduced from the invariance group of the
Hamiltonian of the physical system. The consequences of these symmetries for
the microcanonical order parameter in the high energy and in the low energy
phases are investigated. In particular the breaking of the symmetry of the
microcanonical entropy in the low energy regime is considered. The general
statements are corroborated by investigations of various examples of classical
spin systems.Comment: 15 pages, 5 figures include
Exact Solution of Two-Species Ballistic Annihilation with General Pair-Reaction Probability
The reaction process is modelled for ballistic reactants on an
infinite line with particle velocities and and initially
segregated conditions, i.e. all A particles to the left and all B particles to
the right of the origin. Previous, models of ballistic annihilation have
particles that always react on contact, i.e. pair-reaction probability .
The evolution of such systems are wholly determined by the initial distribution
of particles and therefore do not have a stochastic dynamics. However, in this
paper the generalisation is made to , allowing particles to pass through
each other without necessarily reacting. In this way, the A and B particle
domains overlap to form a fluctuating, finite-sized reaction zone where the
product C is created. Fluctuations are also included in the currents of A and B
particles entering the overlap region, thereby inducing a stochastic motion of
the reaction zone as a whole. These two types of fluctuations, in the reactions
and particle currents, are characterised by the `intrinsic reaction rate', seen
in a single system, and the `extrinsic reaction rate', seen in an average over
many systems. The intrinsic and extrinsic behaviours are examined and compared
to the case of isotropically diffusing reactants.Comment: 22 pages, 2 figures, typos correcte
Inelastically scattering particles and wealth distribution in an open economy
Using the analogy with inelastic granular gasses we introduce a model for
wealth exchange in society. The dynamics is governed by a kinetic equation,
which allows for self-similar solutions. The scaling function has a power-law
tail, the exponent being given by a transcendental equation. In the limit of
continuous trading, closed form of the wealth distribution is calculated
analytically.Comment: 8 pages 5 figure
Large deviation techniques applied to systems with long-range interactions
We discuss a method to solve models with long-range interactions in the
microcanonical and canonical ensemble. The method closely follows the one
introduced by Ellis, Physica D 133, 106 (1999), which uses large deviation
techniques. We show how it can be adapted to obtain the solution of a large
class of simple models, which can show ensemble inequivalence. The model
Hamiltonian can have both discrete (Ising, Potts) and continuous (HMF, Free
Electron Laser) state variables. This latter extension gives access to the
comparison with dynamics and to the study of non-equilibri um effects. We treat
both infinite range and slowly decreasing interactions and, in particular, we
present the solution of the alpha-Ising model in one-dimension with
Spatial organization in cyclic Lotka-Volterra systems
We study the evolution of a system of interacting species which mimics
the dynamics of a cyclic food chain. On a one-dimensional lattice with N<5
species, spatial inhomogeneities develop spontaneously in initially homogeneous
systems. The arising spatial patterns form a mosaic of single-species domains
with algebraically growing size, , where
(1/2) and 1/3 for N=3 with sequential (parallel) dynamics and N=4,
respectively. The domain distribution also exhibits a self-similar spatial
structure which is characterized by an additional length scale, , with and 2/3 for N=3 and 4, respectively. For
, the system quickly reaches a frozen state with non interacting
neighboring species. We investigate the time distribution of the number of
mutations of a site using scaling arguments as well as an exact solution for
N=3. Some possible extensions of the system are analyzed.Comment: 18 pages, 10 figures, revtex, also available from
http://arnold.uchicago.edu/~ebn
Molecular weight effects on chain pull-out fracture of reinforced polymeric interfaces
Using Brownian dynamics, we simulate the fracture of polymer interfaces
reinforced by diblock connector chains. We find that for short chains the
interface fracture toughness depends linearly on the degree of polymerization
of the connector chains, while for longer chains the dependence becomes
. Based on the geometry of initial chain configuration, we propose a
scaling argument that accounts for both short and long chain limits and
crossover between them.Comment: 5 pages, 3 figure
Aging and its Distribution in Coarsening Processes
We investigate the age distribution function P(tau,t) in prototypical
one-dimensional coarsening processes. Here P(tau,t) is the probability density
that in a time interval (0,t) a given site was last crossed by an interface in
the coarsening process at time tau. We determine P(tau,t) analytically for two
cases, the (deterministic) two-velocity ballistic annihilation process, and the
(stochastic) infinite-state Potts model with zero temperature Glauber dynamics.
Surprisingly, we find that in the scaling limit, P(tau,t) is identical for
these two models. We also show that the average age, i. e., the average time
since a site was last visited by an interface, grows linearly with the
observation time t. This latter property is also found in the one-dimensional
Ising model with zero temperature Glauber dynamics. We also discuss briefly the
age distribution in dimension d greater than or equal to 2.Comment: 7 pages, RevTeX, 4 ps files included, to be submitted to Phys. Rev.
Basic kinetic wealth-exchange models: common features and open problems
We review the basic kinetic wealth-exchange models of Angle [J. Angle, Social
Forces 65 (1986) 293; J. Math. Sociol. 26 (2002) 217], Bennati [E. Bennati,
Rivista Internazionale di Scienze Economiche e Commerciali 35 (1988) 735],
Chakraborti and Chakrabarti [A. Chakraborti, B. K. Chakrabarti, Eur. Phys. J. B
17 (2000) 167], and of Dragulescu and Yakovenko [A. Dragulescu, V. M.
Yakovenko, Eur. Phys. J. B 17 (2000) 723]. Analytical fitting forms for the
equilibrium wealth distributions are proposed. The influence of heterogeneity
is investigated, the appearance of the fat tail in the wealth distribution and
the relaxation to equilibrium are discussed. A unified reformulation of the
models considered is suggested.Comment: Updated version; 9 pages, 5 figures, 2 table
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