1,473 research outputs found

### Charging Spectrum of a Small Wigner Crystal Island

Charging of a clean two-dimensional island is studied in the regime of small
concentration of electrons when they form the Wigner crystal. The number of
electrons in the island is assumed to be not too big (N < 100). It is shown
that the total energy of the island as a function of N has a quasi-periodic
component of a universal shape, that is independent of the form of
electron-electron interactions. These oscillations are caused by the
combination of the geometric effects associated with packing of the triangular
lattice into the circular island. These effects are: the shell effect,
associated with starting a new crystalline row, and the so-called confinement
polaronic effect. In the presence of close metallic gates, which eliminate the
long-range part of the electron-electron interactions, the oscillations of the
energy bring about simultaneous entering of the dot by a few electrons.Comment: 8 pages, Latex, 8 Postscript pages are include

### Electron correlations in two-dimensional small quantum dots

We consider circular and elliptic quantum dots with parabolic external
confinement, containing 0 - 22 electrons and with values of r_s in the range 0
< r_s < 3. We perform restricted and unrestricted Hartree-Fock calculations,
and further take into account electron correlations using second-order
perturbation theory. We demonstrate that in many cases correlations
qualitatively change the spin structure of the ground state from that obtained
under Hartree-Fock and spin-density-functional calculations. In some cases the
correlation effects destroy Hund's rule. We also demonstrate that the
correlations destroy static spin-density waves observed in Hartree-Fock and
spin-density-functional calculations.Comment: 11 pages, 9 figures. This replacement contains new content. Results
have been recalculated for dots with zero effective thickness (true 2D). For
6 electrons, results have been compared with configuration interaction
results from the literatur

### A note on the effective slip properties for microchannel flows with ultra-hydrophobic surfaces

A type of super-hydrophobic surface consists of a solid plane boundary with
an array of grooves which, due to the effect of surface tension, prevent a
complete wetting of the wall. The effect is greatest when the grooves are
aligned with the flow. The pressure difference between the liquid and the gas
in the grooves causes a curvature of the liquid surface resisted by surface
tension. The effects of this surface deformation are studied in this paper. The
corrections to the effective slip length produced by the curvature are analyzed
theoretically and a comparison with available data and related mathematical
models is presented.Comment: 19 pages, 5 figure

### Screening of a hypercritical charge in graphene

Screening of a large external charge in graphene is studied. The charge is
assumed to be displaced away or smeared over a finite region of the graphene
plane. The initial decay of the screened potential with distance is shown to
follow the 3/2 power. It gradually changes to the Coulomb law outside of a
hypercritical core whose radius is proportional to the external charge.Comment: (v1) 4 pages, 1 figure (v2) Much improved introduction; extended
range of numeric

### DERMATITIS ARTEFACTA AND SEXUAL ABUSE

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65276/1/j.1365-4362.1993.tb02776.x.pd

### Solution of the Percus-Yevick equation for hard discs

We solve the Percus-Yevick equation in two dimensions by reducing it to a set
of simple integral equations. We numerically obtain both the pair correlation
function and the equation of state for a hard disc fluid and find good
agreement with available Monte-Carlo calculations. The present method of
resolution may be generalized to any even dimension.Comment: 9 pages, 3 figure

### Self-similar impulsive capillary waves on a ligament

We study the short-time dynamics of a liquid ligament, held between two solid
cylinders, when one is impulsively accelerated along its axis. A set of
one-dimensional equations in the slender-slope approximation is used to
describe the dynamics, including surface tension and viscous effects. An exact
self-similar solution to the linearized equations is successfully compared to
experiments made with millimetric ligaments. Another non-linear self-similar
solution of the full set of equations is found numerically. Both the linear and
non-linear solutions show that the axial depth at which the liquid is affected
by the motion of the cylinder scales like $\sqrt{t}$. The non-linear solution
presents the peculiar feature that there exists a maximum driving velocity
$U^\star$ above which the solution disappears, a phenomenon probably related to
the de-pinning of the contact line observed in experiments for large pulling
velocities

### Structure of hard-hypersphere fluids in odd dimensions

The structural properties of single component fluids of hard hyperspheres in
odd space dimensionalities $d$ are studied with an analytical approximation
method that generalizes the Rational Function Approximation earlier introduced
in the study of hard-sphere fluids [S. B. Yuste and A. Santos, Phys. Rev. A
{\bf 43}, 5418 (1991)]. The theory makes use of the exact form of the radial
distribution function to first order in density and extends it to finite
density by assuming a rational form for a function defined in Laplace space,
the coefficients being determined by simple physical requirements. Fourier
transform in terms of reverse Bessel polynomials constitute the mathematical
framework of this approximation, from which an analytical expression for the
static structure factor is obtained. In its most elementary form, the method
recovers the solution of the Percus-Yevick closure to the Ornstein-Zernike
equation for hyperspheres at odd dimension. The present formalism allows one to
go beyond by yielding solutions with thermodynamic consistency between the
virial and compressibility routes to any desired equation of state. Excellent
agreement with available computer simulation data at $d=5$ and $d=7$ is
obtained. As a byproduct of this study, an exact and explicit polynomial
expression for the intersection volume of two identical hyperspheres in
arbitrary odd dimensions is given.Comment: 18 pages, 7 figures; v2: new references added plus minor changes; to
be published in PR

### Hard collinear gluon radiation and multiple scattering in a medium

The energy loss of hard jets produced in the Deep-Inelastic scattering (DIS)
off a large nucleus is considered in the collinear limit. In particular, the
single gluon emission cross section due to multiple scattering in the medium is
calculated. Calculations are carried out in the higher-twist scheme, which is
extended to include contributions from multiple transverse scatterings on both
the produced quark and the radiated gluon. The leading length enhanced parts of
these power suppressed contributions are resummed. Various interferences
between such diagrams lead to the Landau-Pomeranchuk-Migdal (LPM) effect. We
resum the corrections from an arbitrary number of scatterings and isolate the
leading contributions which are suppressed by one extra power of the hard scale
$Q^{2}$. All powers of the emitted gluon forward momentum fraction $y$ are
retained. We compare our results with the previous calculation of single
scattering per emission in the higher-twist scheme as well as with multiple
scattering resummations in other schemes. It is found that the leading
($1/Q^2$) contribution to the double differential gluon production cross
section, in this approach, is equivalent to that obtained from the single
scattering calculation once the transverse momentum of the final quark is
integrated out. We comment on the generalization of this formalism to
Monte-Carlo routines.Comment: 30 pages, 7 figures, revtex4, typos correcte

### Differential constraints compatible with linearized equations

Differential constraints compatible with the linearized equations of partial
differential equations are examined. Recursion operators are obtained by
integrating the differential constraints

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