23,576 research outputs found
Constrained Orthogonal Polynomials
We define sets of orthogonal polynomials satisfying the additional constraint
of a vanishing average. These are of interest, for example, for the study of
the Hohenberg-Kohn functional for electronic or nucleonic densities and for the
study of density fluctuations in centrifuges. We give explicit properties of
such polynomial sets, generalizing Laguerre and Legendre polynomials. The
nature of the dimension 1 subspace completing such sets is described. A
numerical example illustrates the use of such polynomials.Comment: 11 pages, 10 figure
On the energy momentum dispersion in the lattice regularization
For a free scalar boson field and for U(1) gauge theory finite volume
(infrared) and other corrections to the energy-momentum dispersion in the
lattice regularization are investigated calculating energy eigenstates from the
fall off behavior of two-point correlation functions. For small lattices the
squared dispersion energy defined by is in both cases
negative ( is the Euclidean space-time dimension and the
energy of momentum eigenstates). Observation of has
been an accepted method to demonstrate the existence of a massless photon
() in 4D lattice gauge theory, which we supplement here by a study of
its finite size corrections. A surprise from the lattice regularization of the
free field is that infrared corrections do {\it not} eliminate a difference
between the groundstate energy and the mass parameter of the free
scalar lattice action. Instead, the relation is
derived independently of the spatial lattice size.Comment: 9 pages, 2 figures. Parts of the paper have been rewritten and
expanded to clarify the result
Monte Carlo simulation and global optimization without parameters
We propose a new ensemble for Monte Carlo simulations, in which each state is
assigned a statistical weight , where is the number of states with
smaller or equal energy. This ensemble has robust ergodicity properties and
gives significant weight to the ground state, making it effective for hard
optimization problems. It can be used to find free energies at all temperatures
and picks up aspects of critical behaviour (if present) without any parameter
tuning. We test it on the travelling salesperson problem, the Edwards-Anderson
spin glass and the triangular antiferromagnet.Comment: 10 pages with 3 Postscript figures, to appear in Phys. Rev. Lett
Thermodynamics of two lattice ice models in three dimensions
In a recent paper we introduced two Potts-like models in three dimensions,
which share the following properties: (A) One of the ice rules is always
fulfilled (in particular also at infinite temperature). (B) Both ice rules hold
for groundstate configurations. This allowed for an efficient calculation of
the residual entropy of ice I (ordinary ice) by means of multicanonical
simulations. Here we present the thermodynamics of these models. Despite their
similarities with Potts models, no sign of a disorder-order phase transition is
found.Comment: 5 pages, 7 figure
Drops with non-circular footprints
In this paper we study the morphology of drops formed on partially wetting
substrates, whose footprint is not circular. This type of drops is a
consequence of the breakup processes occurring in thin films when anisotropic
contact line motions take place. The anisotropy is basically due to hysteresis
effects of the contact angle since some parts of the contact line are wetting,
while others are dewetting. Here, we obtain a peculiar drop shape from the
rupture of a long liquid filament sitting on a solid substrate, and analyze its
shape and contact angles by means of goniometric and refractive techniques. We
also find a non--trivial steady state solution for the drop shape within the
long wave approximation (lubrication theory), and compare most of its features
with experimental data. This solution is presented both in Cartesian and polar
coordinates, whose constants must be determined by a certain group of measured
parameters. Besides, we obtain the dynamics of the drop generation from
numerical simulations of the full Navier--Stokes equation, where we emulate the
hysteretic effects with an appropriate spatial distribution of the static
contact angle over the substrate
Dispersion and polarization conversion of whispering gallery modes in arbitrary cross-section nanowires
We investigate theoretically the optical properties of Nano-Wires (NWs) with
cross sections having either discrete or cylindrical symmetry. The material
forming the wire is birefringent, showing a different dielectric response in
the plane and along the axis of the wire, which is typically the case for wires
made of wurtzite materials, such as ZnO or GaN. We look for solutions of
Maxwell`s equations having the proper symmetry. The dispersions and the
linewidths versus angle of incident light for the modes having high momentum in
the cross-section plane, so called whispering gallery modes, are calculated. We
put a special emphasis on the case of hexagonal cross sections. The energy
positions of the modes for a set of azimuthal quantum numbers are shown. We
demonstrate the dependence of the energy splitting between TE and TM modes
versus birefringence. The polarization conversion from TE to TM with increase
of the axial wave vectoris discussed for both cylindrical and discrete
symmetry.Comment: 9 pages, 10 figure
Grundstate Properties of the 3D Ising Spin Glass
We study zero--temperature properties of the 3d Edwards--Anderson Ising spin
glass on finite lattices up to size . Using multicanonical sampling we
generate large numbers of groundstate configurations in thermal equilibrium.
Finite size scaling with a zero--temperature scaling exponent describes the data well. Alternatively, a descriptions in terms of Parisi
mean field behaviour is still possible. The two scenarios give significantly
different predictions on lattices of size .Comment: LATEX 9pages,figures upon request ,SCRI-9
Multicanonical Recursions
The problem of calculating multicanonical parameters recursively is
discussed. I describe in detail a computational implementation which has worked
reasonably well in practice.Comment: 23 pages, latex, 4 postscript figures included (uuencoded
Z-compressed .tar file created by uufiles), figure file corrected
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