3,473 research outputs found
Quantum hydrodynamics for supersolid crystals and quasicrystals
Supersolids are theoretically predicted quantum states that break the
continuous rotational and translational symmetries of liquids while preserving
superfluid transport properties. Over the last decade, much progress has been
made in understanding and characterizing supersolid phases through numerical
simulations for specific interaction potentials. The formulation of an
analytically tractable framework for generic interactions still poses
theoretical challenges. By going beyond the usually considered quadratic
truncations, we derive a systematic higher-order generalization of the
Gross-Pitaevskii mean field model in conceptual similarity with the
Swift-Hohenberg theory of pattern formation. We demonstrate the tractability of
this broadly applicable approach by determining the ground state phase diagram
and the dispersion relations for the supersolid lattice vibrations in terms of
the potential parameters. Our analytical predictions agree well with numerical
results from direct hydrodynamic simulations and earlier quantum Monte-Carlo
studies. The underlying framework is universal and can be extended to
anisotropic pair potentials with complex Fourier-space structure.Comment: 18 pages, 10 figures; supplementary information available on reques
On Wireless Scheduling Using the Mean Power Assignment
In this paper the problem of scheduling with power control in wireless
networks is studied: given a set of communication requests, one needs to assign
the powers of the network nodes, and schedule the transmissions so that they
can be done in a minimum time, taking into account the signal interference of
concurrently transmitting nodes. The signal interference is modeled by SINR
constraints. Approximation algorithms are given for this problem, which use the
mean power assignment. The problem of schduling with fixed mean power
assignment is also considered, and approximation guarantees are proven
Instability and wavelength selection during step flow growth of metal surfaces vicinal to fcc(001)
We study the onset and development of ledge instabilities during growth of
vicinal metal surfaces using kinetic Monte Carlo simulations. We observe the
formation of periodic patterns at [110] close packed step edges on surfaces
vicinal to fcc(001) under realistic molecular beam epitaxy conditions. The
corresponding wavelength and its temperature dependence are studied by
monitoring the autocorrelation function for step edge position. Simulations
suggest that the ledge instability on fcc(1,1,m) vicinal surfaces is controlled
by the strong kink Ehrlich-Schwoebel barrier, with the wavelength determined by
dimer nucleation at the step edge. Our results are in agreement with recent
continuum theoretical predictions, and experiments on Cu(1,1,17) vicinal
surfaces.Comment: 4 pages, 4 figures, RevTe
Asymptotic Values of Subharmonic Functions
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135520/1/plms0404.pd
Exact and efficient discrete random walk method for time-dependent two-dimensional environments
We present an exact method for speeding up random walk in two-dimensional complicated lattice environments. To this end, we derive the discrete two-dimensional probability distribution function for a diffusing particle starting at the center of a square of linear size s. This is used to propagate random walkers from the center of the square to sites which are nearest neighbors to its perimeter sites, thus saving O(s2) steps in numerical simulations. We discuss in detail how this method can be implemented efficiently. We examine its performance in the diffusion limited aggregation model which produces fractal structures, and in a one-sided step-growth model producing compact, fingerlike structures. We show that in both cases, the square propagator method reduces the computational effort by a factor proportional to the linear system size as compared to standard random walk.Peer reviewe
Reverse Khas'minskii condition
The aim of this paper is to present and discuss some equivalent
characterizations of p-parabolicity in terms of existence of special exhaustion
functions. In particular, Khas'minskii in [K] proved that if there exists a
2-superharmonic function k defined outside a compact set such that , then R is 2-parabolic, and Sario and Nakai in [SN] were
able to improve this result by showing that R is 2-parabolic if and only if
there exists an Evans potential, i.e. a 2-harmonic function with \lim_{x\to \infty} \E(x)=\infty. In this paper, we will prove a
reverse Khas'minskii condition valid for any p>1 and discuss the existence of
Evans potentials in the nonlinear case.Comment: final version of the article available at http://www.springer.co
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