2,683 research outputs found
A Cellular Automaton Model for Diffusive and Dissipative Systems
We study a cellular automaton model, which allows diffusion of energy (or
equivalently any other physical quantities such as mass of a particular
compound) at every lattice site after each timestep. Unit amount of energy is
randomly added onto a site. Whenever the local energy content of a site reaches
a fixed threshold , energy will be dissipated. Dissipation of energy
propagates to the neighboring sites provided that the energy contents of those
sites are greater than or equal to another fixed threshold . Under such dynamics, the system evolves into three different types of
states depending on the values of and as reflected in their
dissipation size distributions, namely: localized peaks, power laws, or
exponential laws. This model is able to describe the behaviors of various
physical systems including the statistics of burst sizes and burst rates in
type-I X-ray bursters. Comparisons between our model and the famous forest-fire
model (FFM) are made.Comment: in REVTEX 3.0. Figures available on request. Extensively revised.
Accepted by Phys.Rev.
d_c=4 is the upper critical dimension for the Bak-Sneppen model
Numerical results are presented indicating d_c=4 as the upper critical
dimension for the Bak-Sneppen evolution model. This finding agrees with
previous theoretical arguments, but contradicts a recent Letter [Phys. Rev.
Lett. 80, 5746-5749 (1998)] that placed d_c as high as d=8. In particular, we
find that avalanches are compact for all dimensions d<=4, and are fractal for
d>4. Under those conditions, scaling arguments predict a d_c=4, where
hyperscaling relations hold for d<=4. Other properties of avalanches, studied
for 1<=d<=6, corroborate this result. To this end, an improved numerical
algorithm is presented that is based on the equivalent branching process.Comment: 4 pages, RevTex4, as to appear in Phys. Rev. Lett., related papers
available at http://userwww.service.emory.edu/~sboettc
Condensation of Tubular D2-branes in Magnetic Field Background
It is known that in the Minkowski vacuum a bunch of IIA superstrings with
D0-branes can be blown-up to a supersymmetric tubular D2-brane, which is
supported against collapse by the angular momentum generated by crossed
electric and magnetic Born-Infeld (BI) fields. In this paper we show how the
multiple, smaller tubes with relative angular momentum could condense to a
single, larger tube to stabilize the system. Such a phenomena could also be
shown in the systems under the Melvin magnetic tube or uniform magnetic field
background. However, depending on the magnitude of field strength, a tube in
the uniform magnetic field background may split into multiple, smaller tubes
with relative angular momentum to stabilize the system.Comment: Latex 10 pages, mention the dynamical joining of the tubes, modify
figure
Dynamics of the DBI Spike Soliton
We compare oscillations of a fundamental string ending on a D3-brane in two
different settings: (1) a test-string radially threading the horizon of an
extremal black D3-brane and (2) the spike soliton of the DBI effective action
for a D3-brane. Previous work has shown that overall transverse modes of the
test-string appear as l=0 modes of the transverse scalar fields of the DBI
system. We identify DBI world-volume degrees of freedom that have dynamics
matching those of the test-string relative transverse modes. We show that there
is a map, resembling T-duality, between relative and overall transverse modes
for the test-string that interchanges Neumann and Dirichlet boundary conditions
and implies equality of the absorption coefficients for both modes. We give
general solutions to the overall and relative transverse parts of the DBI
coupled gauge and scalar system and calculate absorption coefficients for the
higher angular momentum modes in the low frequency limit. We find that there is
a nonzero amplitude for l>0 modes to travel out to infinity along the spike,
demonstrating that the spike remains effectively 3+1-dimensional.Comment: 15 pages, 1 figur
Noise induced state transitions, intermittency and universality in the noisy Kuramoto-Sivashinsky equation
We analyze the effect of pure additive noise on the long-time dynamics of the
noisy Kuramoto-Sivashinsky (KS) equation in a regime close to the instability
onset. We show that when the noise is highly degenerate, in the sense that it
acts only on the first stable mode, the solution of the KS equation undergoes
several transitions between different states, including a critical on-off
intermittent state that is eventually stabilized as the noise strength is
increased. Such noise-induced transitions can be completely characterized
through critical exponents, obtaining that both the KS and the noisy Burgers
equation belong to the same universality class. The results of our numerical
investigations are explained rigorously using multiscale techniques.Comment: 4 pages, 4 figure
Radiation Damping of a BPS Monopole; an Implication to S-duality
The radiation reaction of a BPS monopole in the presence of incident
electromagnetic waves as well as massless Higgs waves is analyzed classically.
The reactive forces are compared to those of boson that is interpreted as a
dual partner of the BPS monopole. It is shown that the damping of acceleration
is dual to each other, while in the case of finite size effects the duality is
broken explicitly. Their implications on the duality are discussed.Comment: 20 pages, uses revtex, changes in reference
Perturbative Analysis of Nonabelian Aharonov-Bohm Scattering
We perform a perturbative analysis of the nonabelian Aharonov-Bohm problem to
one loop in a field theoretic framework, and show the necessity of contact
interactions for renormalizability of perturbation theory. Moreover at critical
values of the contact interaction strength the theory is finite and preserves
classical conformal invariance.Comment: 12 pages in LaTeX, uses epsf.sty, 5 uuencoded Postscript figures sent
separately. MIT-CTP-228
Dynamics of BPS States in the Dirac-Born-Infeld Theory
The Dirac-Born-Infeld action with transverse scalar fields is considered to
study the dynamics of various BPS states. We first describe the characteristic
properties of the so-called 1/2 and 1/4 BPS states on the D3 brane, which can
be interpreted as F/D-strings ending on a D3-brane in Type IIB string theory
picture. We then study the response of the BPS states to low energy excitations
of massless fields on the brane, the scalar fields representing the shape
fluctuation of the brane and U(1) gauge fields describing the open string
excitations on the D-brane. This leads to an identification of interactions
between BPS states including the static potentials and the kinetic
interactions.Comment: 19 pages, 4 figures References added, Typographical errors are
correcte
Sierpinski signal generates spectra
We investigate the row sum of the binary pattern generated by the Sierpinski
automaton: Interpreted as a time series we calculate the power spectrum of this
Sierpinski signal analytically and obtain a unique rugged fine structure with
underlying power law decay with an exponent of approximately 1.15. Despite the
simplicity of the model, it can serve as a model for spectra in a
certain class of experimental and natural systems like catalytic reactions and
mollusc patterns.Comment: 4 pages (4 figs included). Accepted for publication in Physical
Review
Self-organized critical neural networks
A mechanism for self-organization of the degree of connectivity in model
neural networks is studied. Network connectivity is regulated locally on the
basis of an order parameter of the global dynamics which is estimated from an
observable at the single synapse level. This principle is studied in a
two-dimensional neural network with randomly wired asymmetric weights. In this
class of networks, network connectivity is closely related to a phase
transition between ordered and disordered dynamics. A slow topology change is
imposed on the network through a local rewiring rule motivated by
activity-dependent synaptic development: Neighbor neurons whose activity is
correlated, on average develop a new connection while uncorrelated neighbors
tend to disconnect. As a result, robust self-organization of the network
towards the order disorder transition occurs. Convergence is independent of
initial conditions, robust against thermal noise, and does not require fine
tuning of parameters.Comment: 5 pages RevTeX, 7 figures PostScrip
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