23,262 research outputs found
On a nonlocal degenerate parabolic problem
Conditions for the existence and uniqueness of weak solutions for a class of
nonlinear nonlocal degenerate parabolic equations are established. The
asymptotic behaviour of the solutions as time tends to infinity are also
studied. In particular, the finite time extinction and polynomial decay
properties are proved
Bifurcations in the theory of current transfer to cathodes of dc discharges and observations of transitions between different modes
General scenarios of transitions between different spot patterns on
electrodes of dc gas discharges and their relation to bifurcations of
steady-state solutions are analyzed. In the case of cathodes of arc discharges,
it is shown that any transition between different modes of current transfer is
related to a bifurcation of steady-state solutions. In particular, transitions
between diffuse and spot modes on axially symmetric cathodes, frequently
observed in the experiment, represent an indication of the presence of
pitchfork or fold bifurcations of steady-state solutions. Experimental
observations of transitions on cathodes of dc glow microdischarges are analyzed
and those potentially related to bifurcations of steady-state solutions are
identified. The relevant bifurcations are investigated numerically and the
computed patterns are found to conform to those observed in the course of the
corresponding transitions in the experiment
Convergence of the Crank-Nicolson-Galerkin finite element method for a class of nonlocal parabolic systems with moving boundaries
The aim of this paper is to establish the convergence and error bounds to the
fully discrete solution for a class of nonlinear systems of reaction-diffusion
nonlocal type with moving boundaries, using a linearized
Crank-Nicolson-Galerkin finite element method with polynomial approximations of
any degree. A coordinate transformation which fixes the boundaries is used.
Some numerical tests to compare our Matlab code with some existing moving
finite elements methods are investigated
Uniform approximation for the overlap caustic of a quantum state with its translations
The semiclassical Wigner function for a Bohr-quantized energy eigenstate is
known to have a caustic along the corresponding classical closed phase space
curve in the case of a single degree of freedom. Its Fourier transform, the
semiclassical chord function, also has a caustic along the conjugate curve
defined as the locus of diameters, i.e. the maximal chords of the original
curve. If the latter is convex, so is its conjugate, resulting in a simple fold
caustic. The uniform approximation through this caustic, that is here derived,
describes the transition undergone by the overlap of the state with its
translation, from an oscillatory regime for small chords, to evanescent
overlaps, rising to a maximum near the caustic. The diameter-caustic for the
Wigner function is also treated.Comment: 14 pages, 9 figure
Experimental investigation of quantum key distribution with position and momentum of photon pairs
We investigate the utility of Einstein-Podolsky-Rosen correlations of the
position and momentum of photon pairs from parametric down-conversion in the
implementation of a secure quantum key distribution protocol. We show that
security is guaranteed by the entanglement between downconverted pairs, and can
be checked by either direct comparison of Alice and Bob's measurement results
or evaluation of an inequality of the sort proposed by Mancini et al. (Phys.
Rev. Lett. 88, 120401 (2002)).Comment: 6 pages, 6 figures, subimitted for publicatio
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