Nonlinear Stochastic Models for Water Level Dynamics in Closed Lakes

This paper presents the results of investigation of nonlinear mathematical models of the behavior of closed lakes using the example of the Caspian Sea. Forecasting the level of the Caspian Sea is crucial both for the economy of the region and for the region's environment. The Caspian Sea is a closed reservoir; it is well known that its level changes considerably due to a variety of factors including global climate change. A series of forecasts exists based on different methods and taking into account some of the following factors: the influence of the sun's activity; the atmospheric circulation; the changing shape of the world's ocean; geological phenomena; the river inflow; and the velocity of evaporation. All of these models were calculated based on the linearization of the relations considered. For the last two decades, the most popular model has been the linear stochastic equation of water balance. This model was used as the base of the well known project of reversing the flow of the northward-flowing rivers. But the real behavior of the Caspian Sea contradicted the forecasting done using this model. One of the reasons of the failure was ignorance of the relations mentioned above. We are inclined to think however that the main reason for failure was that the forecast used a linear equation. The goal of the present paper is to analyze and generalize, from the modern mathematical point of view, the forecasting methodology for the level of the Caspian Sea, including the nonlinear effects crucial influence on the dynamics of sea level. In particular, the mathematical problems concerning the nonlinear stochastic equations are considered

The amplitude of the coherent backscattering intensity peak for discrete random media: effect of packing density

The amplitude of the coherent backscattering intensity peak is computed for a medium composed of densely packed, randomly positioned particles. The cyclical component of the Stokes reflection matrix at exactly the back scatter ing direction is expressed in terms of the ladder component, and the ladder component is rigorously computed by numerically solving the vector radiative transfer equation. The effect of packing density is accounted for by multiplying the single-scattering Mueller matrix by the static structure factor computed in the Percus — Yevick approximation. It is shown that increasing packing density can substantially reduce the amplitude of the copolarized coherent backscattering peak, especially for smaller particles, and can make it significantly lower than 2. The effect of packing density on the amplitude of the cross-polarized peak is significantly weaker.Рассчитывается амплитуда обратного когерентного пика в интенсивности для среды, состоящей из плотно упакованных случайно расположенных частиц. Циклический компонент матрицы отражения в представлении Стокса в направлении точно назад выражен через лестничный компонент. Последний рассчитывается путем численного решения векторного уравнения переноса. Эффект плотной упаковки учитывается путем умножения матрицы Мюллера однократного рассеяния на статисческий структурный фактор, рассчитанный в приближении Перкуса—Йевика. Показано, что увеличение плотности упаковки может значительно ослабить параллельно поляризованный когерентный пик обратного рассеяния и уменьшить его амплитуду до значений, значительно меньших 2. Влияние плотной упаковки на амплитуду поперечно поляризованного пика оказывается намного более слабым.Розраховано амплітуду зворотного когерентного піку інтенсивності для середовища, що складається із щільно упакованих випадково розташованих частинок. Циклічний компонент матриці відбиття у поданні Стокса у напрямку точно назад виражено через драбинний компонент. Останній розраховується шляхом числового розв’язку векторного рівняння переносу. Ефект щільної упаковки враховано шляхом множення матриці Мюллера однократного розсіяння на статичний структурний фактор, розрахований у наближенні Перкуса — Євіка. Показано, що збільшення щільності упаковки може значно послабити паралельно поляризований когерентний пік зворотного розсіяння та зменшити його амплітуду до значень, значно менших від 2. Вплив щільної упаковки на амплітуду поперечно поляризованого піку виявився набагато слабкішим

Some new aspects in analyzing photopolarimetric observations of planets

Some new difficulties appearing in analyzing polarimetric observations of planets with optically thick and optically thin atmospheres are discussed. Using the atmosphere of Jupiter as an example, it is demonstrated that specific choice of particle shape in model computations can affect significantly the values of cloud particle parameters retrieved from photopolarimetric data. Besides, we consider the influence of various factors on the interpretation of ptotopolarimetric observations of Mars performed during periods of high transparency of its atmosphere. The re-analysis of the polarization phase curves obtained in such periods shows the impossibility to derive reliable estimates of the properties of Martian dust particles

Incorporation of physical optics effects and computation of the Legendre expansion for ray-tracing phase functions involving - function transmission

The standard geometric optics (GO) technique predicts that the phase function for large nonspherical particles with parallel plane facets (e.g., hexagonal ice crystals) should have an infinitesimally narrow δ-function transmission peak caused by rays twice transmitted (refracted) in exactly the forward scattering direction. However, exact T-matrix computations and physical considerations based on the Kirchhoff approximation suggest that this peak is an artifact of GO completely ignoring physical optics effects and must be convolved with the Fraunhofer pattern, thereby producing a phase function component with an angular profile similar to the standard diffraction component. This convolution can be performed with a simple procedure which supplements the standard ray-tracing code and makes the computation of the phase function and its Legendre expansion both more physically realistic and more accurate

Phonon-assisted resonant tunneling of electrons in graphene–boron nitride transistors

We observe a series of sharp resonant features in the differential conductance of graphene-hexagonal boron nitride-graphene tunnel transistors over a wide range of bias voltages between 10 and 200 mV. We attribute them to electron tunneling assisted by the emission of phonons of well-defined energy. The bias voltages at which they occur are insensitive to the applied gate voltage and hence independent of the carrier densities in the graphene electrodes, so plasmonic effects can be ruled out. The phonon energies corresponding to the resonances are compared with the lattice dispersion curves of graphene–boron nitride heterostructures and are close to peaks in the single phonon density of states

Dissipation effects in spin-Hall transport of electrons and holes

We investigate the spin-Hall effect of both electrons and holes in semiconductors using the Kubo formula in the correct zero-frequency limit taking into account the finite momentum relaxation time of carriers in real semiconductors. This approach allows to analyze the range of validity of recent theoretical findings. In particular, the spin-Hall conductivity vanishes for vanishing spin-orbit coupling if the correct zero-frequency limit is performed.Comment: 5 pages, no figures, version to appear in Phys. Rev.

Anisotropic transport in the two-dimensional electron gas in the presence of spin-orbit coupling

In a two-dimensional electron gas as realized by a semiconductor quantum well, the presence of spin-orbit coupling of both the Rashba and Dresselhaus type leads to anisotropic dispersion relations and Fermi contours. We study the effect of this anisotropy on the electrical conductivity in the presence of fixed impurity scatterers. The conductivity also shows in general an anisotropy which can be tuned by varying the Rashba coefficient. This effect provides a method of detecting and investigating spin-orbit coupling by measuring spin-unpolarized electrical currents in the diffusive regime. Our approach is based on an exact solution of the two-dimensional Boltzmann equation and provides also a natural framework for investigating other transport effects including the anomalous Hall effect.Comment: 10 pages, 1 figure included. Discussion of experimental impact enlarged; error in calculation of conductivity contribution corrected (cf. Eq. (A14)), no changes in qualitative results and physical consequence

The AMMA mulid network for aerosol characterization in West Africa

Three ground based portable low power consumption microlidars (MULID) have been built and deployed at three remote sites in Banizoumbou (Niger), Cinzana (Mali) and M'Bour (Senegal) in the framework of the African Monsoon Multidisciplinary Analyses (AMMA) project for the characterization of aerosols optical properties. A description of the instrument and a discussion of the data inversion method, including a careful analysis of measurement uncertainties (systematic and statistical errors) are presented. Some case studies of typical lidar profiles observed over the Banizoumbou site during 2006 are shown and discussed with respect to the AERONET 7-day back-trajectories and the biomass burning emissions from the Combustion Emission database for the AMMA campaign

Optical application and measurement of torque on microparticles of isotropic nonabsorbing material

We show how it is possible to controllably rotate or align microscopic particles of isotropic nonabsorbing material in a TEM00 Gaussian beam trap, with simultaneous measurement of the applied torque using purely optical means. This is a simple and general method of rotation, requiring only that the particle is elongated along one direction. Thus, this method can be used to rotate or align a wide range of naturally occurring particles. The ability to measure the applied torque enables the use of this method as a quantitative tool--the rotational equivalent of optical tweezers based force measurement. As well as being of particular value for the rotation of biological specimens, this method is also suitable for the development of optically-driven micromachines.Comment: 8 pages, 6 figure