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 $D < 3$, stays the same when $D = 3$, and is higher when \mbox{$D > 3$}. 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 $D = 3$ 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 $\delta$ 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