27,056 research outputs found
Why charges go to the surface: a generalized Thomson problem
We study a generalization of a Thomson problem of n particles confined to a
sphere and interacting by a 1/r^g potential. It is found that for g \le 1 the
electrostatic repulsion expels all the charges to the surface of the sphere.
However for g>1 and n>n_c(g) occupation of the bulk becomes energetically
favorable. It is curious to note that the Coulomb law lies exactly on the
interface between these two regimes
Inverse spectral results for Schr\"odinger operators on the unit interval with potentials in L^P spaces
We consider the Schr\"odinger operator on with potential in . We
prove that two potentials already known on () and having
their difference in are equal if the number of their common eigenvalues
is sufficiently large. The result here is to write down explicitly this number
in terms of (and ) showing the role of
Coulomb Glasses: A Comparison Between Mean Field and Monte Carlo Results
Recently a local mean field theory for both eqilibrium and transport
properties of the Coulomb glass was proposed [A. Amir et al., Phys. Rev. B 77,
165207 (2008); 80, 245214 (2009)]. We compare the predictions of this theory to
the results of dynamic Monte Carlo simulations. In a thermal equilibrium state
we compare the density of states and the occupation probabilities. We also
study the transition rates between different states and find that the mean
field rates underestimate a certain class of important transitions. We propose
modified rates to be used in the mean field approach which take into account
correlations at the minimal level in the sense that transitions are only to
take place from an occupied to an empty site. We show that this modification
accounts for most of the difference between the mean field and Monte Carlo
rates. The linear response conductance is shown to exhibit the Efros-Shklovskii
behaviour in both the mean field and Monte Carlo approaches, but the mean field
method strongly underestimates the current at low temperatures. When using the
modified rates better agreement is achieved
Blind Normalization of Speech From Different Channels
We show how to construct a channel-independent representation of speech that
has propagated through a noisy reverberant channel. This is done by blindly
rescaling the cepstral time series by a non-linear function, with the form of
this scale function being determined by previously encountered cepstra from
that channel. The rescaled form of the time series is an invariant property of
it in the following sense: it is unaffected if the time series is transformed
by any time-independent invertible distortion. Because a linear channel with
stationary noise and impulse response transforms cepstra in this way, the new
technique can be used to remove the channel dependence of a cepstral time
series. In experiments, the method achieved greater channel-independence than
cepstral mean normalization, and it was comparable to the combination of
cepstral mean normalization and spectral subtraction, despite the fact that no
measurements of channel noise or reverberations were required (unlike spectral
subtraction).Comment: 25 pages, 7 figure
Superconducting pipes and levitating magnets
Motivated by a beautiful demonstration of the Faraday's and Lenz's law in
which a small neodymium magnet falls slowly through a conducting
non-ferromagnetic tube, we consider the dynamics of a magnet falling through a
superconducting pipe. Unlike the case of normal conducting pipes, in which the
magnet quickly reaches the terminal velocity, inside a superconducting tube the
magnet falls freely. On the other hand, to enter the pipe the magnet must
overcome a large electromagnetic energy barrier. For sufficiently strong
magnets, the barrier is so large that the magnet will not be able to penetrate
it and will be suspended over the front edge. We calculate the work that must
done to force the magnet to enter a superconducting tube. The calculations show
that superconducting pipes are very efficient at screening magnetic fields. For
example, the magnetic field of a dipole at the center of a short pipe of radius
and length decays, in the axial direction, with a
characteristic length . The efficient screening of the
magnetic field might be useful for shielding highly sensitive superconducting
quantum interference devices, SQUIDs. Finally, the motion of the magnet through
a superconducting pipe is compared and contrasted to the flow of ions through a
trans-membrane channel
Predictions for Impurity-Induced Tc Suppression in the High-Temperature Superconductors
We address the question of whether anisotropic superconductivity is
compatible with the evidently weak sensitivity of the critical temperature Tc
to sample quality in the high-Tc copper oxides. We examine this issue
quantitatively by solving the strong-coupling Eliashberg equations numerically
as well as analytically for s-wave impurity scattering within the second Born
approximation. For pairing interactions with a characteristically low energy
scale, we find an approximately universal dependence of the d-wave
superconducting transition temperature on the planar residual resistivity which
is independent of the details of the microscopic pairing. These results, in
conjunction with future systematic experiments, should help elucidate the
symmetry of the order parameter in the cuprates.Comment: 13 pages, 4 figures upon request, revtex version
Use of 2G coated conductors for efficient shielding of DC magnetic fields
This paper reports the results of an experimental investigation of the
performance of two types of magnetic screens assembled from YBa2Cu3O7-d (YBCO)
coated conductors. Since effective screening of the axial DC magnetic field
requires the unimpeded flow of an azimuthal persistent current, we demonstrate
a configuration of a screening shell made out of standard YBCO coated conductor
capable to accomplish that. The screen allows the persistent current to flow in
the predominantly azimuthal direction at a temperature of 77 K. The persistent
screen, incorporating a single layer of superconducting film, can attenuate an
external magnetic field of up to 5 mT by more than an order of magnitude. For
comparison purposes, another type of screen which incorporates low critical
temperature quasi-persistent joints was also built. The shielding technique we
describe here appears to be especially promising for the realization of large
scale high-Tc superconducting screens.Comment: 8 pages, 3 figure
Application of Monte Carlo Algorithms to the Bayesian Analysis of the Cosmic Microwave Background
Power spectrum estimation and evaluation of associated errors in the presence
of incomplete sky coverage; non-homogeneous, correlated instrumental noise; and
foreground emission is a problem of central importance for the extraction of
cosmological information from the cosmic microwave background. We develop a
Monte Carlo approach for the maximum likelihood estimation of the power
spectrum. The method is based on an identity for the Bayesian posterior as a
marginalization over unknowns. Maximization of the posterior involves the
computation of expectation values as a sample average from maps of the cosmic
microwave background and foregrounds given some current estimate of the power
spectrum or cosmological model, and some assumed statistical characterization
of the foregrounds. Maps of the CMB are sampled by a linear transform of a
Gaussian white noise process, implemented numerically with conjugate gradient
descent. For time series data with N_{t} samples, and N pixels on the sphere,
the method has a computational expense $KO[N^{2} +- N_{t} +AFw-log N_{t}],
where K is a prefactor determined by the convergence rate of conjugate gradient
descent. Preconditioners for conjugate gradient descent are given for scans
close to great circle paths, and the method allows partial sky coverage for
these cases by numerically marginalizing over the unobserved, or removed,
region.Comment: submitted to Ap
Charge renormalization and phase separation in colloidal suspensions
We explore the effects of counterion condensation on fluid-fluid phase
separation in charged colloidal suspensions. It is found that formation of
double layers around the colloidal particles stabilizes suspensions against
phase separation. Addition of salt, however, produces an instability which, in
principle, can lead to a fluid-fluid separation. The instability, however, is
so weak that it should be impossible to observe a fully equilibrated
coexistence experimentally.Comment: 7 pages, Europhysics Letters (in press
- …