748 research outputs found
Toda Soliton Limits on General Backgrounds
AbstractStarting from an arbitrary background solution of the Toda lattice, we study limits ofN-soliton solutions on this given background asNtends to infinity. This yields a new class of solutions of the Toda lattice. Simultaneously, we solve an inverse spectral problem for one dimensional Jacobi operators–we explicitly construct Jacobi operators whose spectrum contains a given (countable, bounded) set of eigenvalues and whose absolutely continuous spectrum coincides with that of a given background operator
MIE Lidar proposed for the German Space Shuttle Mission D2
Firm plans for a second German Spacelab mission (D2-mission), originally scheduled for late 1988 is basically a zero-g mission, but will also include earth observation experiments. On board the D2-facility will allow performance of a number of different measurements with the goal to obtain performance data (cloud top heights, height of the planetary boundary layer, optical thickness, and cloud base height of thin and medium thick clouds, ice/water phase discriminatin for clouds, tropopause height, tropaspheric height, tropospheric aerosols, and stratospheric aerosols
Topologically non-trivial quantum layers
Given a complete non-compact surface embedded in R^3, we consider the
Dirichlet Laplacian in a layer of constant width about the surface. Using an
intrinsic approach to the layer geometry, we generalise the spectral results of
an original paper by Duclos et al. to the situation when the surface does not
possess poles. This enables us to consider topologically more complicated
layers and state new spectral results. In particular, we are interested in
layers built over surfaces with handles or several cylindrically symmetric
ends. We also discuss more general regions obtained by compact deformations of
certain layers.Comment: 15 pages, 6 figure
A Hardy inequality in twisted waveguides
We show that twisting of an infinite straight three-dimensional tube with
non-circular cross-section gives rise to a Hardy-type inequality for the
associated Dirichlet Laplacian. As an application we prove certain stability of
the spectrum of the Dirichlet Laplacian in locally and mildly bent tubes.
Namely, it is known that any local bending, no matter how small, generates
eigenvalues below the essential spectrum of the Laplacian in the tubes with
arbitrary cross-sections rotated along a reference curve in an appropriate way.
In the present paper we show that for any other rotation some critical strength
of the bending is needed in order to induce a non-empty discrete spectrum.Comment: LaTeX, 20 page
Vertical motion of the thermocline, nitracline and chlorophyll maximum layers in relation to currents on the Southern California Shelf
A continuous four-day time series of nitrate concentration, temperature, chlorophyll fluorescence, and currents, sampled at fixed depths, revealed that distributions of temperature and nitrate could be accounted for by vertical motions in the water column associated with the semidiurnal internal tide and internal waves. A probable mixing event was observed: the transport of nitrate into the surface-layer associated with shear instabilities generated by internal waves. On temporal scales of less than a few hours, the variation of chlorophyll fluorescence could also be explained by vertical advection. However, on longer scales, swimming behavior of the phytoplankton assemblage (dominated by Ceratium spp.), along with vertical motions in the water column, appears to account for the vertical distribution of chlorophyll. These results indicate that the nitracline maintains a stable relationship with the density structure of the water column on a scale of days, whereas the subsurface chlorophyll maximum can change significantly over several hours
Polymers in Curved Boxes
We apply results derived in other contexts for the spectrum of the Laplace
operator in curved geometries to the study of an ideal polymer chain confined
to a spherical annulus in arbitrary space dimension D and conclude that the
free energy compared to its value for an uncurved box of the same thickness and
volume, is lower when , stays the same when , and is higher when
\mbox{}. Thus confining an ideal polymer chain to a cylindrical shell,
lowers the effective bending elasticity of the walls, and might induce
spontaneous symmetry breaking, i.e. bending. (Actually, the above mentioned
results show that {\em {any}} shell in induces this effect, except for
a spherical shell). We compute the contribution of this effect to the bending
rigidities in the Helfrich free energy expression.Comment: 20 pages RevTeX, epsf; 4 figures; submitted to Macromoledule
Spectrum of the Schr\"odinger operator in a perturbed periodically twisted tube
We study Dirichlet Laplacian in a screw-shaped region, i.e. a straight
twisted tube of a non-circular cross section. It is shown that a local
perturbation which consists of "slowing down" the twisting in the mean gives
rise to a non-empty discrete spectrum.Comment: LaTeX2e, 10 page
Quantum waveguides with a lateral semitransparent barrier: spectral and scattering properties
We consider a quantum particle in a waveguide which consists of an infinite
straight Dirichlet strip divided by a thin semitransparent barrier on a line
parallel to the walls which is modeled by a potential. We show that if
the coupling strength of the latter is modified locally, i.e. it reaches the
same asymptotic value in both directions along the line, there is always a
bound state below the bottom of the essential spectrum provided the effective
coupling function is attractive in the mean. The eigenvalues and
eigenfunctions, as well as the scattering matrix for energies above the
threshold, are found numerically by the mode-matching technique. In particular,
we discuss the rate at which the ground-state energy emerges from the continuum
and properties of the nodal lines. Finally, we investigate a system with a
modified geometry: an infinite cylindrical surface threaded by a homogeneous
magnetic field parallel to the cylinder axis. The motion on the cylinder is
again constrained by a semitransparent barrier imposed on a ``seam'' parallel
to the axis.Comment: a LaTeX source file with 12 figures (11 of them eps); to appear in J.
Phys. A: Math. Gen. Figures 3, 5, 8, 9, 11 are given at 300 dpi; higher
resolution originals are available from the author
Node counting in wireless ad-hoc networks
We study wireless ad-hoc networks consisting of small microprocessors with limited memory, where the wireless communication between the processors can be highly unreliable. For this setting, we propose a number of algorithms to estimate the number of nodes in the network, and the number of direct neighbors of each node. The algorithms are simulated, allowing comparison of their performance
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