194,271 research outputs found
Zoology of a non-local cross-diffusion model for two species
We study a non-local two species cross-interaction model with
cross-diffusion. We propose a positivity preserving finite volume scheme based
on the numerical method introduced in Ref. [15] and explore this new model
numerically in terms of its long-time behaviours. Using the so gained insights,
we compute analytical stationary states and travelling pulse solutions for a
particular model in the case of attractive-attractive/attractive-repulsive
cross-interactions. We show that, as the strength of the cross-diffusivity
decreases, there is a transition from adjacent solutions to completely
segregated densities, and we compute the threshold analytically for
attractive-repulsive cross-interactions. Other bifurcating stationary states
with various coexistence components of the support are analysed in the
attractive-attractive case. We find a strong agreement between the numerically
and the analytically computed steady states in these particular cases, whose
main qualitative features are also present for more general potentials
Nonlinear stability of flock solutions in second-order swarming models
In this paper we consider interacting particle systems which are frequently
used to model collective behavior in animal swarms and other applications. We
study the stability of orientationally aligned formations called flock
solutions, one of the typical patterns emerging from such dynamics. We provide
an analysis showing that the nonlinear stability of flocks in second-order
models entirely depends on the linear stability of the first-order aggregation
equation. Flocks are shown to be nonlinearly stable as a family of states under
reasonable assumptions on the interaction potential. Furthermore, we
numerically verify that commonly used potentials satisfy these hypotheses and
investigate the nonlinear stability of flocks by an extensive case-study of
uniform perturbations.Comment: 22 pages, 1 figure, 1 tabl
Two-electron bond-orbital model, 2
The two-electron bond-orbital model of tetrahedrally-coordinated solids is generalized and its application extended. All intrabond matrix elements entering the formalism are explicitly retained, including the direct overlap S between the anion and cation sp3 hybrid wavefunctions. Complete analytic results are obtained for the six two-electron eigenvalues and eigenstates of the anion-cation bond in terms of S, one-electron parameters V2 and V3, and two-electron correlation parameters V4, V5 and V6. Refined formulas for the dielectric constant and the nuclear exchange and pseudodipolar coefficients, as well as new expressions for the valence electron density, polarity of the bond and the cohesive energy, are then derived. The theory gives a good account of the experimentally observed trends in all properties considered and approximate quantitative agreement is achieved for the pseudodipolar coefficient
G\"{o}del-type universes in f(R) gravity
The gravity theories provide an alternative way to explain the current
cosmic acceleration without a dark energy matter component. If gravity is
governed by a theory a number of issues should be reexamined in this
framework, including the violation of causality problem on nonlocal scale. We
examine the question as to whether the gravity theories permit
space-times in which the causality is violated. We show that the field
equations of these gravity theories do not exclude solutions with
breakdown of causality for a physically well-motivated perfect-fluid matter
content. We demonstrate that every perfect-fluid G\"{o}del-type solution of a
generic gravity satisfying the condition is necessarily
isometric to the G\"odel geometry, and therefore presents violation of
causality. This result extends a theorem on G\"{o}del-type models, which has
been established in the context of general relativity. We also derive an
expression for the critical radius (beyond which the causality is
violated) for an arbitrary theory, making apparent that the violation of
causality depends on both the gravity theory and the matter content. As
an illustration, we concretely take a recent gravity theory that is free
from singularities of the Ricci scalar and is cosmologically viable, and show
that this theory accommodates noncausal as well as causal G\"odel-type
solutions.Comment: 7 pages, V3: Version to appear in Phys. Rev. D (2009), typos
corrected, the generality of our main results is emphasized. The illustrative
character of a particular theory is also made explici
Remote preparation of continuous-variable qubits using loss-tolerant hybrid entanglement of light
Transferring quantum information between distant nodes of a network is a key
capability. This transfer can be realized via remote state preparation where
two parties share entanglement and the sender has full knowledge of the state
to be communicated. Here we demonstrate such a process between heterogeneous
nodes functioning with different information encodings, i.e., particle-like
discrete-variable optical qubits and wave-like continuous-variable ones. Using
hybrid entanglement of light as a shared resource, we prepare arbitrary
coherent-state superpositions controlled by measurements on the distant
discrete-encoded node. The remotely prepared states are fully characterized by
quantum state tomography and negative Wigner functions are obtained. This work
demonstrates a novel capability to bridge discrete- and continuous-variable
platforms
Exponential Convergence Towards Stationary States for the 1D Porous Medium Equation with Fractional Pressure
We analyse the asymptotic behaviour of solutions to the one dimensional
fractional version of the porous medium equation introduced by Caffarelli and
V\'azquez, where the pressure is obtained as a Riesz potential associated to
the density. We take advantage of the displacement convexity of the Riesz
potential in one dimension to show a functional inequality involving the
entropy, entropy dissipation, and the Euclidean transport distance. An argument
by approximation shows that this functional inequality is enough to deduce the
exponential convergence of solutions in self-similar variables to the unique
steady states
BCS-BEC Crossover in Symmetric Nuclear Matter at Finite Temperature: Pairing Fluctuation and Pseudogap
By adopting a -matrix based method within approximation for the
pair susceptibility, we studied the effects of pairing fluctuation on the
BCS-BEC crossover in symmetric nuclear matter. The pairing fluctuation induces
a pseudogap in the excitation spectrum of nucleon in both superfluid and normal
phases. The critical temperature of superfluid transition was calculated. It
differs from the BCS result remarkably when density is low. We also computed
the specific heat which shows a nearly ideal BEC type temperature dependence at
low density but a BCS type behavior at high density. This qualitative change of
the temperature dependence of specific heat may serve as a thermodynamic signal
for BCS-BEC crossover.Comment: 11 pages,11 figures,1 table, published version in Phys. Rev. C
Dirac cohomology, elliptic representations and endoscopy
The first part (Sections 1-6) of this paper is a survey of some of the recent
developments in the theory of Dirac cohomology, especially the relationship of
Dirac cohomology with (g,K)-cohomology and nilpotent Lie algebra cohomology;
the second part (Sections 7-12) is devoted to understanding the unitary
elliptic representations and endoscopic transfer by using the techniques in
Dirac cohomology. A few problems and conjectures are proposed for further
investigations.Comment: This paper will appear in `Representations of Reductive Groups, in
Honor of 60th Birthday of David Vogan', edited by M. Nervins and P. Trapa,
published by Springe
Two-electron bond-orbital model, 1
Harrison's one-electron bond-orbital model of tetrahedrally coordinated solids was generalized to a two-electron model, using an extension of the method of Falicov and Harris for treating the hydrogen molecule. The six eigenvalues and eigenstates of the two-electron anion-cation Hamiltonian entering this theory can be found exactly general. The two-electron formalism is shown to provide a useful basis for calculating both non-magnetic and magnetic properties of semiconductors in perturbation theory. As an example of the former, expressions for the electric susceptibility and the dielectric constant were calculated. As an example of the latter, new expressions for the nuclear exchanges and pseudo-dipolar coefficients were calculated. A simple theoretical relationship between the dielectric constant and the exchange coefficient was also found in the limit of no correlation. These expressions were quantitatively evaluated in the limit of no correlation for twenty semiconductors
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