2,064 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
"Universal" Distribution of Inter-Earthquake Times Explained
We propose a simple theory for the ``universal'' scaling law previously
reported for the distributions of waiting times between earthquakes. It is
based on a largely used benchmark model of seismicity, which just assumes no
difference in the physics of foreshocks, mainshocks and aftershocks. Our
theoretical calculations provide good fits to the data and show that
universality is only approximate. We conclude that the distributions of
inter-event times do not reveal more information than what is already known
from the Gutenberg-Richter and the Omori power laws. Our results reinforces the
view that triggering of earthquakes by other earthquakes is a key physical
mechanism to understand seismicity.Comment: 4 pages with two figure
Exact 4-point Scattering Amplitude of the Superconformal Schrodinger Chern-Simons Theory
We consider the non-relativistic superconformal U(N) X U(N) Chern-Simons
theory with level (k,-k) possessing fourteen supersymmetries. We obtain an
exact four-point scattering amplitude of the theory to all orders in 1/N and
1/k and prove that the scattering amplitude becomes trivial when k=1 and 2. We
confirm this amplitude to one-loop order by using an explicit field theoretic
computation and show that the beta function for the contact interaction
vanishes to the one-loop order, which is consistent with the quantum conformal
invariance of the underlying theory.Comment: 16 page
Long-Term Clustering, Scaling, and Universality in the Temporal Occurrence of Earthquakes
Scaling analysis reveals striking regularities in earthquake occurrence. The
time between any one earthquake and that following it is random, but it is
described by the same universal-probability distribution for any spatial region
and magnitude range considered. When time is expressed in rescaled units, set
by the averaged seismic activity, the self-similar nature of the process
becomes apparent. The form of the probability distribution reveals that
earthquakes tend to cluster in time, beyond the duration of aftershock
sequences. Furthermore, if aftershock sequences are analysed in an analogous
way, yet taking into account the fact that seismic activity is not constant but
decays in time, the same universal distribution is found for the rescaled time
between events.Comment: short paper, only 2 figure
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
Fuzzy BIon
We construct a solution of the BFSS matrix theory, which is a counterpart of
the BIon solution representing a fundamental string ending on a bound state of
a D2-brane and D0-branes. We call this solution the `fuzzy BIon' and show that
this configuration preserves 1/4 supersymmetry of type IIA superstring theory.
We also construct an effective action for the fuzzy BIon by analyzing the
nonabelian Born-Infeld action for D0-branes. When we take the continuous limit,
with some conditions, this action coincides with the effective action for the
BIon configuration.Comment: 11 pages, 1 figure, reference and note adde
A Universal Lifetime Distribution for Multi-Species Systems
Lifetime distributions of social entities, such as enterprises, products, and
media contents, are one of the fundamental statistics characterizing the social
dynamics. To investigate the lifetime distribution of mutually interacting
systems, simple models having a rule for additions and deletions of entities
are investigated. We found a quite universal lifetime distribution for various
kinds of inter-entity interactions, and it is well fitted by a
stretched-exponential function with an exponent close to 1/2. We propose a
"modified Red-Queen" hypothesis to explain this distribution. We also review
empirical studies on the lifetime distribution of social entities, and
discussed the applicability of the model.Comment: 10 pages, 6 figures, Proceedings of Social Modeling and Simulations +
Econophysics Colloquium 201
Scale free networks of earthquakes and aftershocks
We propose a new metric to quantify the correlation between any two
earthquakes. The metric consists of a product involving the time interval and
spatial distance between two events, as well as the magnitude of the first one.
According to this metric, events typically are strongly correlated to only one
or a few preceding ones. Thus a classification of events as foreshocks, main
shocks or aftershocks emerges automatically without imposing predefined
space-time windows. To construct a network, each earthquake receives an
incoming link from its most correlated predecessor. The number of aftershocks
for any event, identified by its outgoing links, is found to be scale free with
exponent . The original Omori law with emerges as a
robust feature of seismicity, holding up to years even for aftershock sequences
initiated by intermediate magnitude events. The measured fat-tailed
distribution of distances between earthquakes and their aftershocks suggests
that aftershock collection with fixed space windows is not appropriate.Comment: 7 pages and 7 figures. Submitte
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
The quantum phase transition of itinerant helimagnets
We investigate the quantum phase transition of itinerant electrons from a
paramagnet to a state which displays long-period helical structures due to a
Dzyaloshinskii instability of the ferromagnetic state. In particular, we study
how the self-generated effective long-range interaction recently identified in
itinerant quantum ferromagnets is cut-off by the helical ordering. We find that
for a sufficiently strong Dzyaloshinskii instability the helimagnetic quantum
phase transition is of second order with mean-field exponents. In contrast, for
a weak Dzyaloshinskii instability the transition is analogous to that in
itinerant quantum ferromagnets, i.e. it is of first order, as has been observed
in MnSi.Comment: 5 pages RevTe
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