30,671 research outputs found
Negative Differential Resistivity and Positive Temperature Coefficient of Resistivity effect in the diffusion limited current of ferroelectric thin film capacitors
We present a model for the leakage current in ferroelectric thin- film
capacitors which explains two of the observed phenomena that have escaped
satisfactory explanation, i.e. the occurrence of either a plateau or negative
differential resistivity at low voltages, and the observation of a Positive
Temperature Coefficient of Resistivity (PTCR) effect in certain samples in the
high-voltage regime. The leakage current is modelled by considering a
diffusion-limited current process, which in the high-voltage regime recovers
the diffusion-limited Schottky relationship of Simmons already shown to be
applicable in these systems
Degenerate dispersive equations arising in the study of magma dynamics
An outstanding problem in Earth science is understanding the method of
transport of magma in the Earth's mantle. Models for this process, transport in
a viscously deformable porous media, give rise to scalar degenerate,
dispersive, nonlinear wave equations. We establish a general local
well-posedness for a physical class of data (roughly ) via fixed point
methods. The strategy requires positive lower bounds on the solution. This is
extended to global existence for a subset of possible nonlinearities by making
use of certain conservation laws associated with the equations. Furthermore, we
construct a Lyapunov energy functional, which is locally convex about the
uniform state, and prove (global in time) nonlinear dynamic stability of the
uniform state for any choice of nonlinearity. We compare the dynamics to that
of other problems and discuss open questions concerning a larger range of
nonlinearities, for which we conjecture global existence.Comment: 27 Pages, 7 figures are not present in this version. See
http://www.columbia.edu/~grs2103/ for a PDF with figures. Submitted to
Nonlinearit
Energy bursts in fiber bundle models of composite materials
As a model of composite materials, a bundle of many fibers with
stochastically distributed breaking thresholds for the individual fibers is
considered. The bundle is loaded until complete failure to capture the failure
scenario of composite materials under external load. The fibers are assumed to
share the load equally, and to obey Hookean elasticity right up to the breaking
point. We determine the distribution of bursts in which an amount of energy
is released. The energy distribution follows asymptotically a universal power
law , for any statistical distribution of fiber strengths. A similar
power law dependence is found in some experimental acoustic emission studies of
loaded composite materials.Comment: 5 pages, 4 fig
Ionization history of the cosmic plasma in the light of the recent CBI and future PLANCK data
The paper is devoted to the methods of determination of the cosmological
parameters from recent CMB observations. We show that the more complex models
of kinetics of recombination with a few "missing" parameters describing the
recombination process provide better agreement between measured and expected
characteristics of the CMB anisotropy. In particular, we consider the external
sources of the Ly-{alpha} and Ly-{c} radiation and the model with the strong
clustering of baryonic component. These factors can constrain the estimates of
the cosmological parameters usually discussed. We demonstrate also that the
measurements of polarization can improve these estimates and, for the precision
expected for the PLANCK mission, allow to discriminate a wide class of models.Comment: 25 pages, 7 figures, extended and corrected after the referee report.
Accepted in Ap
Characterization of the Crab Pulsar's Timing Noise
We present a power spectral analysis of the Crab pulsar's timing noise,
mainly using radio measurements from Jodrell Bank taken over the period
1982-1989. The power spectral analysis is complicated by nonuniform data
sampling and the presence of a steep red power spectrum that can distort power
spectra measurement by causing severe power ``leakage''. We develop a simple
windowing method for computing red noise power spectra of uniformly sampled
data sets and test it on Monte Carlo generated sample realizations of red
power-law noise. We generalize time-domain methods of generating power-law red
noise with even integer spectral indices to the case of noninteger spectral
indices. The Jodrell Bank pulse phase residuals are dense and smooth enough
that an interpolation onto a uniform time series is possible. A windowed power
spectrum is computed revealing a periodic or nearly periodic component with a
period of about 568 days and a 1/f^3 power-law noise component with a noise
strength of 1.24 +/- 0.067 10^{-16} cycles^2/sec^2 over the analysis frequency
range 0.003 - 0.1 cycles/day. This result deviates from past analyses which
characterized the pulse phase timing residuals as either 1/f^4 power-law noise
or a quasiperiodic process. The analysis was checked using the Deeter
polynomial method of power spectrum estimation that was developed for the case
of nonuniform sampling, but has lower spectral resolution. The timing noise is
consistent with a torque noise spectrum rising with analysis frequency as f
implying blue torque noise, a result not predicted by current models of pulsar
timing noise. If the periodic or nearly periodic component is due to a binary
companion, we find a companion mass > 3.2 Earth masses.Comment: 53 pages, 9 figures, submitted to MNRAS, abstract condense
Pattern of Reaction Diffusion Front in Laminar Flows
Autocatalytic reaction between reacted and unreacted species may propagate as
solitary waves, namely at a constant front velocity and with a stationary
concentration profile, resulting from a balance between molecular diffusion and
chemical reaction. The effect of advective flow on the autocatalytic reaction
between iodate and arsenous acid in cylindrical tubes and Hele-Shaw cells is
analyzed experimentally and numerically using lattice BGK simulations. We do
observe the existence of solitary waves with concentration profiles exhibiting
a cusp and we delineate the eikonal and mixing regimes recently predicted.Comment: 4 pages, 3 figures. This paper report on experiments and simulations
in different geometries which test the theory of Boyd Edwards on flow
advection of chemical reaction front which just appears in PRL (PRL Vol
89,104501, sept2002
A Co-moving Coordinate System for Relativistic Hydrodynamics
The equations of relativistic hydrodynamics are transformed so that steps
forward in time preserves local simultaneity. In these variables, the
space-time coordinates of neighboring points on the mesh are simultaneous
according to co-moving observers. Aside from the time step varying as a
function of the location on the mesh, the local velocity gradient and the local
density then evolve according to non-relativistic equations of motion. Analytic
solutions are found for two one-dimensional cases with constant speed of sound.
One solution has a Gaussian density profile when mapped into the new
coordinates. That solution is analyzed for the effects of longitudinal
acceleration in relativistic heavy ion collisions at RHIC, especially in
regards to two-particle correlation measurements of the longitudinal size
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