18,189 research outputs found
Modeling relaxation and jamming in granular media
We introduce a stochastic microscopic model to investigate the jamming and
reorganization of grains induced by an object moving through a granular medium.
The model reproduces the experimentally observed periodic sawtooth fluctuations
in the jamming force and predicts the period and the power spectrum in terms of
the controllable physical parameters. It also predicts that the avalanche
sizes, defined as the number of displaced grains during a single advance of the
object, follow a power-law, , where the exponent is
independent of the physical parameters
Mutual Coherence of Polarized Light in Disordered Media: Two-Frequency Method Extended
The paper addresses the two-point correlations of electromagnetic waves in
general random, bi-anisotropic media whose constitutive tensors are complex
Hermitian, positive- or negative-definite matrices. A simplified version of the
two-frequency Wigner distribution (2f-WD) for polarized waves is introduced and
the closed form Wigner-Moyal equation is derived from the Maxwell equations. In
the weak-disorder regime with an arbitrarily varying background the
two-frequency radiative transfer (2f-RT) equations for the associated coherence matrices are derived from the Wigner-Moyal equation by using the
multiple scale expansion. In birefringent media, the coherence matrix becomes a
scalar and the 2f-RT equations take the scalar form due to the absence of
depolarization. A paraxial approximation is developed for spatialy anisotropic
media. Examples of isotropic, chiral, uniaxial and gyrotropic media are
discussed
Resonant Hawking radiation in Bose-Einstein condensates
We study double-barrier interfaces separating regions of asymptotically
subsonic and supersonic flow of Bose condensed atoms. These setups contain at
least one black hole sonic horizon from which the analog of Hawking radiation
should be generated and emitted against the flow in the subsonic region.
Multiple coherent scattering by the double-barrier structure strongly modulates
the transmission probability of phonons, rendering it very sensitive to their
frequency. As a result, resonant tunneling occurs with high probability within
a few narrow frequency intervals. This gives rise to highly non-thermal spectra
with sharp peaks. We find that these peaks are mostly associated to decaying
resonances and only occasionally to dynamical instabilities. Even at achievable
nonzero temperatures, the radiation peaks can be dominated by the spontaneous
emission, i.e. enhanced zero-point fluctuations, and not, as often in analog
models, by stimulated emission.Comment: 20 pages, 9 figures, revised versio
Drinfeld Twists and Symmetric Bethe Vectors of Supersymmetric Fermion Models
We construct the Drinfeld twists (factorizing -matrices) of the
-invariant fermion model. Completely symmetric representation of the
pseudo-particle creation operators of the model are obtained in the basis
provided by the -matrix (the -basis). We resolve the hierarchy of the
nested Bethe vectors in the -basis for the supersymmetric model.Comment: Latex File, 24 pages, no figure, some misprints are correcte
Multi-Magnon Scattering in the Ferromagnetic XXX-Model with Inhomogeneities
We determine the transition amplitude for multi-magnon scattering induced
through an inhomogeneous distribution of the coupling constant in the
ferromagnetic XXX-model. The two and three particle amplitudes are explicitely
calculated at small momenta. This suggests a rather plausible conjecture also
for a formula of the general n-particle amplitude.Comment: 21 pages, latex, no figure
Dislocation Free Island Formation in Heteroepitaxial Growth: An Equilibrium Study
We investigate the equilibrium properties of strained heteroepitaxial
systems, incorporating the formation and the growth of a wetting film,
dislocation free island formation, and ripening. The derived phase diagram
provides a detailed characterization of the possible growth modes in terms of
the island density, equilibrium island size, and wetting layer thickness.
Comparing our predictions with experimental results we discuss the growth
conditions that can lead to stable islands as well as ripening.Comment: 4 pages, LaTeX, 3 ps figure
Jamming and Fluctuations in Granular Drag
We investigate the dynamic evolution of jamming in granular media through
fluctuations in the granular drag force. The successive collapse and formation
of jammed states give a stick-slip nature to the fluctuations which is
independent of the contact surface between the grains and the dragged object --
thus implying that the stress-induced collapse is nucleated in the bulk of the
granular sample. We also find that while the fluctuations are periodic at small
depths, they become "stepped" at large depths, a transition which we interpret
as a consequence of the long-range nature of the force chains.Comment: 7 pages, 4 figures, RevTe
Dynamical and spectral properties of complex networks
Dynamical properties of complex networks are related to the spectral
properties of the Laplacian matrix that describes the pattern of connectivity
of the network. In particular we compute the synchronization time for different
types of networks and different dynamics. We show that the main dependence of
the synchronization time is on the smallest nonzero eigenvalue of the Laplacian
matrix, in contrast to other proposals in terms of the spectrum of the
adjacency matrix. Then, this topological property becomes the most relevant for
the dynamics.Comment: 14 pages, 5 figures, to be published in New Journal of Physic
Bound, virtual and resonance -matrix poles from the Schr\"odinger equation
A general method, which we call the potential -matrix pole method, is
developed for obtaining the -matrix pole parameters for bound, virtual and
resonant states based on numerical solutions of the Schr\"odinger equation.
This method is well-known for bound states. In this work we generalize it for
resonant and virtual states, although the corresponding solutions increase
exponentially when . Concrete calculations are performed for the
ground and the first excited states of , the resonance
states (, ), low-lying states of and
, and the subthreshold resonances in the proton-proton system. We
also demonstrate that in the case the broad resonances their energy and width
can be found from the fitting of the experimental phase shifts using the
analytical expression for the elastic scattering -matrix. We compare the
-matrix pole and the -matrix for broad resonance in
Comment: 14 pages, 5 figures (figures 3 and 4 consist of two figures each) and
4 table
Activity driven modeling of time varying networks
Network modeling plays a critical role in identifying statistical
regularities and structural principles common to many systems. The large
majority of recent modeling approaches are connectivity driven. The structural
patterns of the network are at the basis of the mechanisms ruling the network
formation. Connectivity driven models necessarily provide a time-aggregated
representation that may fail to describe the instantaneous and fluctuating
dynamics of many networks. We address this challenge by defining the activity
potential, a time invariant function characterizing the agents' interactions
and constructing an activity driven model capable of encoding the instantaneous
time description of the network dynamics. The model provides an explanation of
structural features such as the presence of hubs, which simply originate from
the heterogeneous activity of agents. Within this framework, highly dynamical
networks can be described analytically, allowing a quantitative discussion of
the biases induced by the time-aggregated representations in the analysis of
dynamical processes.Comment: 10 pages, 4 figure
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