433 research outputs found
Percolation-to-hopping crossover in conductor-insulator composites
Here, we show that the conductivity of conductor-insulator composites in
which electrons can tunnel from each conducting particle to all others may
display both percolation and tunneling (i.e. hopping) regimes depending on few
characteristics of the composite. Specifically, we find that the relevant
parameters that give rise to one regime or the other are (where is
the size of the conducting particles and is the tunneling length) and the
specific composite microstructure. For large values of , percolation
arises when the composite microstructure can be modeled as a regular lattice
that is fractionally occupied by conducting particle, while the tunneling
regime is always obtained for equilibrium distributions of conducting particles
in a continuum insulating matrix. As decreases the percolating behavior
of the conductivity of lattice-like composites gradually crosses over to the
tunneling-like regime characterizing particle dispersions in the continuum. For
values lower than the conductivity has tunneling-like
behavior independent of the specific microstructure of the composite.Comment: 8 pages, 5 figure
Quasi-periodic solutions of completely resonant forced wave equations
We prove existence of quasi-periodic solutions with two frequencies of
completely resonant, periodically forced nonlinear wave equations with periodic
spatial boundary conditions. We consider both the cases the forcing frequency
is: (Case A) a rational number and (Case B) an irrational number.Comment: 25 pages, 1 figur
Positive Least Energy Solutions and Phase Separation for Coupled Schrodinger Equations with Critical Exponent: Higher Dimensional Case
We study the following nonlinear Schr\"{o}dinger system which is related to
Bose-Einstein condensate: {displaymath} {cases}-\Delta u +\la_1 u = \mu_1
u^{2^\ast-1}+\beta u^{\frac{2^\ast}{2}-1}v^{\frac{2^\ast}{2}}, \quad x\in
\Omega, -\Delta v +\la_2 v =\mu_2 v^{2^\ast-1}+\beta v^{\frac{2^\ast}{2}-1}
u^{\frac{2^\ast}{2}}, \quad x\in \om, u\ge 0, v\ge 0 \,\,\hbox{in \om},\quad
u=v=0 \,\,\hbox{on \partial\om}.{cases}{displaymath} Here \om\subset \R^N
is a smooth bounded domain, is the Sobolev critical
exponent, -\la_1(\om)0 and , where
\lambda_1(\om) is the first eigenvalue of with the Dirichlet
boundary condition. When \bb=0, this is just the well-known Brezis-Nirenberg
problem. The special case N=4 was studied by the authors in (Arch. Ration.
Mech. Anal. 205: 515-551, 2012). In this paper we consider {\it the higher
dimensional case }. It is interesting that we can prove the existence
of a positive least energy solution (u_\bb, v_\bb) {\it for any } (which can not hold in the special case N=4). We also study the limit
behavior of (u_\bb, v_\bb) as and phase separation is
expected. In particular, u_\bb-v_\bb will converge to {\it sign-changing
solutions} of the Brezis-Nirenberg problem, provided . In case
\la_1=\la_2, the classification of the least energy solutions is also
studied. It turns out that some quite different phenomena appear comparing to
the special case N=4.Comment: 48 pages. This is a revised version of arXiv:1209.2522v1 [math.AP
The Hypermultiplet with Heisenberg Isometry in N=2 Global and Local Supersymmetry
The string coupling of N=2 supersymmetric compactifications of type II string
theory on a Calabi-Yau manifold belongs to the so-called universal dilaton
hypermultiplet, that has four real scalars living on a quaternion-Kaehler
manifold. Requiring Heisenberg symmetry, which is a maximal subgroup of
perturbative isometries, reduces the possible manifolds to a one-parameter
family that describes the tree-level effective action deformed by the only
possible perturbative correction arising at one-loop level. A similar argument
can be made at the level of global supersymmetry where the scalar manifold is
hyper-Kaehler. In this work, the connection between global and local
supersymmetry is explicitly constructed, providing a non-trivial gravity
decoupled limit of type II strings already in perturbation theory.Comment: 24 page
Diffeomorphism-invariant properties for quasi-linear elliptic operators
For quasi-linear elliptic equations we detect relevant properties which
remain invariant under the action of a suitable class of diffeomorphisms. This
yields a connection between existence theories for equations with degenerate
and non-degenerate coerciveness.Comment: 16 page
Semiclassical stationary states for nonlinear Schroedinger equations with fast decaying potentials
We study the existence of stationnary positive solutions for a class of
nonlinear Schroedinger equations with a nonnegative continuous potential V.
Amongst other results, we prove that if V has a positive local minimum, and if
the exponent of the nonlinearity satisfies N/(N-2)<p<(N+2)/(N-2), then for
small epsilon the problem admits positive solutions which concentrate as
epsilon goes to 0 around the local minimum point of V. The novelty is that no
restriction is imposed on the rate of decay of V. In particular, we cover the
case where V is compactly supported.Comment: 22 page
Noncovalent Interactions by QMC: Speedup by One-Particle Basis-Set Size Reduction
While it is empirically accepted that the fixed-node diffusion Monte-Carlo
(FN-DMC) depends only weakly on the size of the one-particle basis sets used to
expand its guiding functions, limits of this observation are not settled yet.
Our recent work indicates that under the FN error cancellation conditions,
augmented triple zeta basis sets are sufficient to achieve a benchmark level of
0.1 kcal/mol in a number of small noncovalent complexes. Here we report on a
possibility of truncation of the one-particle basis sets used in FN-DMC guiding
functions that has no visible effect on the accuracy of the production FN-DMC
energy differences. The proposed scheme leads to no significant increase in the
local energy variance, indicating that the total CPU cost of large-scale
benchmark noncovalent interaction energy FN-DMC calculations may be reduced.Comment: ACS book chapter, accepte
Acoustic geometry for general relativistic barotropic irrotational fluid flow
"Acoustic spacetimes", in which techniques of differential geometry are used
to investigate sound propagation in moving fluids, have attracted considerable
attention over the last few decades. Most of the models currently considered in
the literature are based on non-relativistic barotropic irrotational fluids,
defined in a flat Newtonian background. The extension, first to special
relativistic barotropic fluid flow, and then to general relativistic barotropic
fluid flow in an arbitrary background, is less straightforward than it might at
first appear. In this article we provide a pedagogical and simple derivation of
the general relativistic "acoustic spacetime" in an arbitrary (d+1) dimensional
curved-space background.Comment: V1: 23 pages, zero figures; V2: now 24 pages, some clarifications, 2
references added. This version accepted for publication in the New Journal of
Physics. (Special issue on "Classical and Quantum Analogues for Gravitational
Phenomena and Related Effects"
Symbiotic Bright Solitary Wave Solutions of Coupled Nonlinear Schrodinger Equations
Conventionally, bright solitary wave solutions can be obtained in
self-focusing nonlinear Schrodinger equations with attractive self-interaction.
However, when self-interaction becomes repulsive, it seems impossible to have
bright solitary wave solution. Here we show that there exists symbiotic bright
solitary wave solution of coupled nonlinear Schrodinger equations with
repulsive self-interaction but strongly attractive interspecies interaction.
For such coupled nonlinear Schrodinger equations in two and three dimensional
domains, we prove the existence of least energy solutions and study the
location and configuration of symbiotic bright solitons. We use Nehari's
manifold to construct least energy solutions and derive their asymptotic
behaviors by some techniques of singular perturbation problems.Comment: to appear in Nonlinearit
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