814 research outputs found
Random walker in a temporally deforming higher-order potential forces observed in financial crisis
Basic peculiarities of market price fluctuations are known to be well
described by a recently developed random walk model in a temporally deforming
quadric potential force whose center is given by a moving average of past price
traces [Physica A 370, pp91-97, 2006]. By analyzing high-frequency financial
time series of exceptional events such as bubbles and crashes, we confirm the
appearance of nonlinear potential force in the markets. We show statistical
significance of its existence by applying the information criterion. This new
time series analysis is expected to be applied widely for detecting a
non-stationary symptom in random phenomena.Comment: 5 pages, 13 figure
Nonequilibrium Phase Transitions in Models of Aggregation, Adsorption, and Dissociation
We study nonequilibrium phase transitions in a mass-aggregation model which
allows for diffusion, aggregation on contact, dissociation, adsorption and
desorption of unit masses. We analyse two limits explicitly. In the first case
mass is locally conserved whereas in the second case local conservation is
violated. In both cases the system undergoes a dynamical phase transition in
all dimensions. In the first case, the steady state mass distribution decays
exponentially for large mass in one phase, and develops an infinite aggregate
in addition to a power-law mass decay in the other phase. In the second case,
the transition is similar except that the infinite aggregate is missing.Comment: Major revision of tex
Effect of spatial bias on the nonequilibrium phase transition in a system of coagulating and fragmenting particles
We examine the effect of spatial bias on a nonequilibrium system in which
masses on a lattice evolve through the elementary moves of diffusion,
coagulation and fragmentation. When there is no preferred directionality in the
motion of the masses, the model is known to exhibit a nonequilibrium phase
transition between two different types of steady states, in all dimensions. We
show analytically that introducing a preferred direction in the motion of the
masses inhibits the occurrence of the phase transition in one dimension, in the
thermodynamic limit. A finite size system, however, continues to show a
signature of the original transition, and we characterize the finite size
scaling implications of this. Our analysis is supported by numerical
simulations. In two dimensions, bias is shown to be irrelevant.Comment: 7 pages, 7 figures, revte
Exact Phase Diagram of a model with Aggregation and Chipping
We revisit a simple lattice model of aggregation in which masses diffuse and
coalesce upon contact with rate 1 and every nonzero mass chips off a single
unit of mass to a randomly chosen neighbour with rate . The dynamics
conserves the average mass density and in the stationary state the
system undergoes a nonequilibrium phase transition in the plane
across a critical line . In this paper, we show analytically that in
arbitrary spatial dimensions, exactly and hence,
remarkably, independent of dimension. We also provide direct and indirect
numerical evidence that strongly suggest that the mean field asymptotic answer
for the single site mass distribution function and the associated critical
exponents are super-universal, i.e., independent of dimension.Comment: 11 pages, RevTex, 3 figure
Exact Calculation of the Spatio-temporal Correlations in the Takayasu model and in the q-model of Force Fluctuations in Bead Packs
We calculate exactly the two point mass-mass correlations in arbitrary
spatial dimensions in the aggregation model of Takayasu. In this model, masses
diffuse on a lattice, coalesce upon contact and adsorb unit mass from outside
at a constant rate. Our exact calculation of the variance of mass at a given
site proves explicitly, without making any assumption of scaling, that the
upper critical dimension of the model is 2. We also extend our method to
calculate the spatio-temporal correlations in a generalized class of models
with aggregation, fragmentation and injection which include, in particular, the
-model of force fluctuations in bead packs. We present explicit expressions
for the spatio-temporal force-force correlation function in the -model.
These can be used to test the applicability of the -model in experiments.Comment: 15 pages, RevTex, 2 figure
Propagation and Extinction in Branching Annihilating Random Walks
We investigate the temporal evolution and spatial propagation of branching
annihilating random walks in one dimension. Depending on the branching and
annihilation rates, a few-particle initial state can evolve to a propagating
finite density wave, or extinction may occur, in which the number of particles
vanishes in the long-time limit. The number parity conserving case where
2-offspring are produced in each branching event can be solved exactly for unit
reaction probability, from which qualitative features of the transition between
propagation and extinction, as well as intriguing parity-specific effects are
elucidated. An approximate analysis is developed to treat this transition for
general BAW processes. A scaling description suggests that the critical
exponents which describe the vanishing of the particle density at the
transition are unrelated to those of conventional models, such as Reggeon Field
Theory. P. A. C. S. Numbers: 02.50.+s, 05.40.+j, 82.20.-wComment: 12 pages, plain Te
Phase Transition in the Takayasu Model with Desorption
We study a lattice model where particles carrying different masses diffuse,
coalesce upon contact, and also unit masses adsorb to a site with rate or
desorb from a site with nonzero mass with rate . In the limit (without
desorption), our model reduces to the well studied Takayasu model where the
steady-state single site mass distribution has a power law tail for large mass. We show that varying the desorption rate induces
a nonequilibrium phase transition in all dimensions. For fixed , there is a
critical such that if , the steady state mass distribution,
for large as in the Takayasu case. For , we
find where is a new exponent, while for
, for large . The model is studied
analytically within a mean field theory and numerically in one dimension.Comment: RevTex, 11 pages including 5 figures, submitted to Phys. Rev.
The Dynamics of Internet Traffic: Self-Similarity, Self-Organization, and Complex Phenomena
The Internet is the most complex system ever created in human history.
Therefore, its dynamics and traffic unsurprisingly take on a rich variety of
complex dynamics, self-organization, and other phenomena that have been
researched for years. This paper is a review of the complex dynamics of
Internet traffic. Departing from normal treatises, we will take a view from
both the network engineering and physics perspectives showing the strengths and
weaknesses as well as insights of both. In addition, many less covered
phenomena such as traffic oscillations, large-scale effects of worm traffic,
and comparisons of the Internet and biological models will be covered.Comment: 63 pages, 7 figures, 7 tables, submitted to Advances in Complex
System
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