10,385 research outputs found
The "Cameo Principle" and the Origin of Scale-Free Graphs in Social Networks
We formulate a simple edge generation rule based on an inverse like mass
action principle for random graphs over a structured vertex set. We show that
under very weak assumptions on the structure generating distribution we obtain
a scale free distribution for the degree. We furthermore introduce and study a
"my friends are your friends" local search principle which makes the clustering
coefficient large.Comment: 17 pages, Late
Heavy-tailed Distributions In Stochastic Dynamical Models
Heavy-tailed distributions are found throughout many naturally occurring
phenomena. We have reviewed the models of stochastic dynamics that lead to
heavy-tailed distributions (and power law distributions, in particular)
including the multiplicative noise models, the models subjected to the
Degree-Mass-Action principle (the generalized preferential attachment
principle), the intermittent behavior occurring in complex physical systems
near a bifurcation point, queuing systems, and the models of Self-organized
criticality. Heavy-tailed distributions appear in them as the emergent
phenomena sensitive for coupling rules essential for the entire dynamics
What can one learn about Self-Organized Criticality from Dynamical Systems theory ?
We develop a dynamical system approach for the Zhang's model of
Self-Organized Criticality, for which the dynamics can be described either in
terms of Iterated Function Systems, or as a piecewise hyperbolic dynamical
system of skew-product type. In this setting we describe the SOC attractor, and
discuss its fractal structure. We show how the Lyapunov exponents, the
Hausdorff dimensions, and the system size are related to the probability
distribution of the avalanche size, via the Ledrappier-Young formula.Comment: 23 pages, 8 figures. to appear in Jour. of Stat. Phy
Neutron matter at next-to-next-to-next-to-leading order in chiral effective field theory
Neutron matter presents a unique system for chiral effective field theory
(EFT), because all many-body forces among neutrons are predicted to
next-to-next-to-next-to-leading order (N3LO). We present the first complete
N3LO calculation of the neutron matter energy. This includes the subleading
three-nucleon (3N) forces for the first time and all leading four-nucleon (4N)
forces. We find relatively large contributions from N3LO 3N forces. Our results
provide constraints for neutron-rich matter in astrophysics with controlled
theoretical uncertainties.Comment: 5 pages, 4 figures; improved version, 3N ring and 2pi-contact
contributions corrected, conclusions unchanged; v3: minor changes, published
versio
Self-Organized Criticality and Thermodynamic formalism
We introduce a dissipative version of the Zhang's model of Self-Organized
Criticality, where a parameter allows to tune the local energy dissipation. We
analyze the main dynamical features of the model and relate in particular the
Lyapunov spectrum with the transport properties in the stationary regime. We
develop a thermodynamic formalism where we define formal Gibbs measure,
partition function and pressure characterizing the avalanche distributions. We
discuss the infinite size limit in this setting. We show in particular that a
Lee-Yang phenomenon occurs in this model, for the only conservative case. This
suggests new connexions to classical critical phenomena.Comment: 35 pages, 15 Figures, submitte
Small World Graphs by the iterated "My Friends are Your Friends'' Principle
We study graphs obtained by successive creation and destruction of edges into
small neighborhoods of the vertices. Starting with a circle graph of large
diameter we obtain small world graphs with logarithmic diameter, high
clustering coefficients and a fat tail distribution for the degree. Only local
edge formation processes are involved and no preferential attachment was used.
Furthermore we found an interesting phase transition with respect to the
initial conditions.Comment: Latex, 12 pages with 10 figure
A simple quantum gate with atom chips
We present a simple scheme for implementing an atomic phase gate using two
degrees of freedom for each atom and discuss its realization with cold rubidium
atoms on atom chips. We investigate the performance of this collisional phase
gate and show that gate operations with high fidelity can be realized in
magnetic traps that are currently available on atom chips.Comment: 7 pages, 7 figures. One missing reference added in v2. To appear in
European Physical Journal
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