2,688 research outputs found
Scaling of impact fragmentation near the critical point
We investigated two-dimensional brittle fragmentation with a flat impact
experimentally, focusing on the low impact energy region near the
fragmentation-critical point. We found that the universality class of
fragmentation transition disagreed with that of percolation. However, the
weighted mean mass of the fragments could be scaled using the pseudo-control
parameter multiplicity. The data for highly fragmented samples included a
cumulative fragment mass distribution that clearly obeyed a power-law. The
exponent of this power-law was 0.5 and it was independent of sample size. The
fragment mass distributions in this regime seemed to collapse into a unified
scaling function using weighted mean fragment mass scaling. We also examined
the behavior of higher order moments of the fragment mass distributions, and
obtained multi-scaling exponents that agreed with those of the simple biased
cascade model.Comment: 6 pages, 6 figure
The Boltzmann Equation in Scalar Field Theory
We derive the classical transport equation, in scalar field theory with a
V(phi) interaction, from the equation of motion for the quantum field. We
obtain a very simple, but iterative, expression for the effective action which
generates all the n-point Green functions in the high-temperature limit. An
explicit closed form is given in the static case.Comment: 10 pages, using RevTeX (corrected TeX misprints
Complete Supersymmetric Quantum Mechanics of Magnetic Monopoles in N=4 SYM Theory
We find the most general low energy dynamics of 1/2 BPS monopoles in the N=4
supersymmetric Yang-Mills theories (SYM) when all six adjoint Higgs expectation
values are turned on. When only one Higgs is turned on, the Lagrangian is
purely kinetic. When all six are turned on, however, this moduli space dynamics
is augmented by five independent potential terms, each in the form of half the
squared norm of a Killing vector field on the moduli space. A generic
stationary configuration of the monopoles can be interpreted as stable non BPS
dyons, previously found as non-planar string webs connecting D3-branes. The
supersymmetric extension is also found explicitly, and gives the complete
quantum mechanics of monopoles in N=4 SYM theory. We explore its supersymmetry
algebra.Comment: Errors in the SUSY algebra corrected. The version to appear in PR
Endogenous Versus Exogenous Shocks in Complex Networks: an Empirical Test Using Book Sale Ranking
Are large biological extinctions such as the Cretaceous/Tertiary KT boundary
due to a meteorite, extreme volcanic activity or self-organized critical
extinction cascades? Are commercial successes due to a progressive reputation
cascade or the result of a well orchestrated advertisement? Determining the
chain of causality for extreme events in complex systems requires disentangling
interwoven exogenous and endogenous contributions with either no clear or too
many signatures. Here, we study the precursory and recovery signatures
accompanying shocks, that we test on a unique database of the Amazon sales
ranking of books. We find clear distinguishing signatures classifying two types
of sales peaks. Exogenous peaks occur abruptly and are followed by a power law
relaxation, while endogenous sale peaks occur after a progressively
accelerating power law growth followed by an approximately symmetrical power
law relaxation which is slower than for exogenous peaks. These results are
rationalized quantitatively by a simple model of epidemic propagation of
interactions with long memory within a network of acquaintances. The slow
relaxation of sales implies that the sales dynamics is dominated by cascades
rather than by the direct effects of news or advertisements, indicating that
the social network is close to critical.Comment: 5 pages including 3 figures final version published in Physical
Review Letter
Fractal and chaotic solutions of the discrete nonlinear Schr\"odinger equation in classical and quantum systems
We discuss stationary solutions of the discrete nonlinear Schr\"odinger
equation (DNSE) with a potential of the type which is generically
applicable to several quantum spin, electron and classical lattice systems. We
show that there may arise chaotic spatial structures in the form of
incommensurate or irregular quantum states. As a first (typical) example we
consider a single electron which is strongly coupled with phonons on a
chain of atoms --- the (Rashba)--Holstein polaron model. In the adiabatic
approximation this system is conventionally described by the DNSE. Another
relevant example is that of superconducting states in layered superconductors
described by the same DNSE. Amongst many other applications the typical example
for a classical lattice is a system of coupled nonlinear oscillators. We
present the exact energy spectrum of this model in the strong coupling limit
and the corresponding wave function. Using this as a starting point we go on to
calculate the wave function for moderate coupling and find that the energy
eigenvalue of these structures of the wave function is in exquisite agreement
with the exact strong coupling result. This procedure allows us to obtain
(numerically) exact solutions of the DNSE directly. When applied to our typical
example we find that the wave function of an electron on a deformable lattice
(and other quantum or classical discrete systems) may exhibit incommensurate
and irregular structures. These states are analogous to the periodic,
quasiperiodic and chaotic structures found in classical chaotic dynamics
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.
Flame propagation in random media
We introduce a phase-field model to describe the dynamics of a
self-sustaining propagating combustion front within a medium of randomly
distributed reactants. Numerical simulations of this model show that a flame
front exists for reactant concentration , while its vanishing at
is consistent with mean-field percolation theory. For , we find
that the interface associated with the diffuse combustion zone exhibits kinetic
roughening characteristic of the Kardar-Parisi-Zhang equation.Comment: 4, LR541
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
Inelastic diffraction and color-singlet gluon-clusters in high-energy hadron-hadron and lepton-hadron collisions
It is proposed, that ``the colorless objects'' which manifest themselves in
large-rapidity-gap events are color-singlet gluon-clusters due to
self-organized criticality (SOC), and that optical-geometrical concepts and
methods are useful in examing the space-time properties of such objects. A
simple analytical expression for the -dependence of the inelastic single
diffractive cross section ( is the four-momentum transfer
squared) is derived. Comparison with the existing data and predictions for
future experiments are presented. The main differences and similarities between
the SOC-approach and the ``Partons in the Pomeron (Pomeron and
Reggeon)''-approach are discussed.Comment: 12 pages, 2 figure
Separation of Spontaneous Chiral Symmetry Breaking and Confinement via AdS/CFT Correspondence
We analyze, in the framework of AdS/CFT correspondence, the gauge theory
phase structure that are supposed to be dual to the recently found
non-supersymmetric dilatonic deformations to AdS_5 X S^5 in type IIB string
theory. Analyzing the probe D7-brane dynamics in the backgrounds of our
interest, which corresponds to the fundamental N=2 hypermultiplet, we show that
the chiral bi-fermion condensation responsible for spontaneous chiral symmetry
breaking is not logically related to the phenomenon of confinement.Comment: LaTex, 21 pages, 3 figures. v2: references adde
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