2,588 research outputs found
Dynamics of Rumor Spreading in Complex Networks
We derive the mean-field equations characterizing the dynamics of a rumor
process that takes place on top of complex heterogeneous networks. These
equations are solved numerically by means of a stochastic approach. First, we
present analytical and Monte Carlo calculations for homogeneous networks and
compare the results with those obtained by the numerical method. Then, we study
the spreading process in detail for random scale-free networks. The time
profiles for several quantities are numerically computed, which allow us to
distinguish among different variants of rumor spreading algorithms. Our
conclusions are directed to possible applications in replicated database
maintenance, peer to peer communication networks and social spreading
phenomena.Comment: Final version to appear in PR
Superfluidity of fermions with repulsive on-site interaction in an anisotropic optical lattice near a Feshbach resonance
We present a numerical study on ground state properties of a one-dimensional
(1D) general Hubbard model (GHM) with particle-assisted tunnelling rates and
repulsive on-site interaction (positive-U), which describes fermionic atoms in
an anisotropic optical lattice near a wide Feshbach resonance. For our
calculation, we utilize the time evolving block decimation (TEBD) algorithm,
which is an extension of the density matrix renormalization group and provides
a well-controlled method for 1D systems. We show that the positive-U GHM, when
hole-doped from half-filling, exhibits a phase with coexistence of
quasi-long-range superfluid and charge-density-wave orders. This feature is
different from the property of the conventional Hubbard model with positive-U,
indicating the particle-assisted tunnelling mechanism in GHM brings in
qualitatively new physics.Comment: updated with published version
First-principles quantum dynamics for fermions: Application to molecular dissociation
We demonstrate that the quantum dynamics of a many-body Fermi-Bose system can
be simulated using a Gaussian phase-space representation method. In particular,
we consider the application of the mixed fermion-boson model to ultracold
quantum gases and simulate the dynamics of dissociation of a Bose-Einstein
condensate of bosonic dimers into pairs of fermionic atoms. We quantify
deviations of atom-atom pair correlations from Wick's factorization scheme, and
show that atom-molecule and molecule-molecule correlations grow with time, in
clear departures from pairing mean-field theories. As a first-principles
approach, the method provides benchmarking of approximate approaches and can be
used to validate dynamical probes for characterizing strongly correlated phases
of fermionic systems.Comment: Final published versio
Matrix Product Density Operators: Simulation of finite-T and dissipative systems
We show how to simulate numerically both the evolution of 1D quantum systems
under dissipation as well as in thermal equilibrium. The method applies to both
finite and inhomogeneous systems and it is based on two ideas: (a) a
representation for density operators which extends that of matrix product
states to mixed states; (b) an algorithm to approximate the evolution (in real
or imaginary time) of such states which is variational (and thus optimal) in
nature.Comment: See also M. Zwolak et al. cond-mat/040644
Atomic lattice excitons: from condensates to crystals
We discuss atomic lattice excitons (ALEs), bound particle-hole pairs formed
by fermionic atoms in two bands of an optical lattice. Such a system provides a
clean setup to study fundamental properties of excitons, ranging from
condensation to exciton crystals (which appear for a large effective mass ratio
between particles and holes). Using both mean-field treatments and 1D numerical
computation, we discuss the properities of ALEs under varying conditions, and
discuss in particular their preparation and measurement.Comment: 19 pages, 15 figures, changed formatting for journal submission,
corrected minor errors in reference list and tex
RECOMMENDATIONS FOR IMPROVING SOFTWARE COST ESTIMATION IN DOD ACQUISITION
Acquisition initiatives within the Department of Defense (DOD) are becoming increasingly reliant on software. While the DOD has ample experience in estimating costs of hardware acquisition, expertise in estimating software acquisition costs is lacking. The objective of this capstone project is to summarize the current software cost estimating methods, analyze existing software cost estimating models, and suggest areas and methods for improvement. To accomplish this, surveys were conducted to gather program cost data, which was run through existing cost estimating models. From here, the outputs were compared to actual program costs. This established a baseline for the effectiveness of existing methods and guided suggestions for areas of improvement. The Software Resource Data Reports (SRDR) data used seemed to have spurious data reporting from at least one source, and the base cost estimation models were not found to be sufficiently accurate in our study. The capstone finds that calibrating the cost models to the data available improved those models dramatically. In all, the capstone recommends performing data realism checks upon SRDR submissions to ensure data accuracy and calibrating cost models for each contractor with the available data before using them to estimate DOD Acquisition costs.Civilian, Department of the ArmyCivilian, Department of the ArmyCivilian, Department of the ArmyCivilian, Department of the ArmyApproved for public release. Distribution is unlimited
Percolation in invariant Poisson graphs with i.i.d. degrees
Let each point of a homogeneous Poisson process in R^d independently be
equipped with a random number of stubs (half-edges) according to a given
probability distribution mu on the positive integers. We consider
translation-invariant schemes for perfectly matching the stubs to obtain a
simple graph with degree distribution mu. Leaving aside degenerate cases, we
prove that for any mu there exist schemes that give only finite components as
well as schemes that give infinite components. For a particular matching scheme
that is a natural extension of Gale-Shapley stable marriage, we give sufficient
conditions on mu for the absence and presence of infinite components
Slightly generalized Generalized Contagion: Unifying simple models of biological and social spreading
We motivate and explore the basic features of generalized contagion, a model
mechanism that unifies fundamental models of biological and social contagion.
Generalized contagion builds on the elementary observation that spreading and
contagion of all kinds involve some form of system memory. We discuss the three
main classes of systems that generalized contagion affords, resembling: simple
biological contagion; critical mass contagion of social phenomena; and an
intermediate, and explosive, vanishing critical mass contagion. We also present
a simple explanation of the global spreading condition in the context of a
small seed of infected individuals.Comment: 8 pages, 5 figures; chapter to appear in "Spreading Dynamics in
Social Systems"; Eds. Sune Lehmann and Yong-Yeol Ahn, Springer Natur
The Fractal Geometry of Critical Systems
We investigate the geometry of a critical system undergoing a second order
thermal phase transition. Using a local description for the dynamics
characterizing the system at the critical point T=Tc, we reveal the formation
of clusters with fractal geometry, where the term cluster is used to describe
regions with a nonvanishing value of the order parameter. We show that,
treating the cluster as an open subsystem of the entire system, new
instanton-like configurations dominate the statistical mechanics of the
cluster. We study the dependence of the resulting fractal dimension on the
embedding dimension and the scaling properties (isothermal critical exponent)
of the system. Taking into account the finite size effects we are able to
calculate the size of the critical cluster in terms of the total size of the
system, the critical temperature and the effective coupling of the long
wavelength interaction at the critical point. We also show that the size of the
cluster has to be identified with the correlation length at criticality.
Finally, within the framework of the mean field approximation, we extend our
local considerations to obtain a global description of the system.Comment: 1 LaTeX file, 4 figures in ps-files. Accepted for publication in
Physical Review
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