Polarization locking and nonparaxial spatial solitons in media with electronic Kerr nonlinearity

The polarization structure of nonparaxial spatial solitons in a transparent medium with the electronic mechanism of Kerr nonlinearity is studied theoretically. It is demonstrated analytically in the weak nonparaxiality approximation that the regime of polarization locking, in which all the field components have the same propagation constant, is the only stable regime. Estimates of the rate of transition of the initial metastable regime of rotation of the polarization ellipse to the regime of polarization locking are presented. Based on a numerical solution of the nonlinear Maxwell equations, the presence of the nonparaxial regime of polarization locking is confirmed and the main characteristics of the corresponding spatial solitons are obtained.     

Creating, detecting and locating ultracold molecules in a surface trap

Ultracold molecules have been produced by photoassociation of Cs atoms trapped in a mirror magneto-optical trap. The molecules were detected by resonantly enhanced multi-photon ionization followed by time-of-flight mass spectroscopy. The time-of-flight ofatomic and molecular ions was investigated in the presence of a dc bias voltageapplied to the conducting mirror. This technique provides a new tool for determining the distance between the cold molecules and the mirror surface. This revised version was published online in August 2005 with a corrected cover date.     

Topics in data assimilation: Stochastic processes

Stochastic models with varying degrees of complexity are increasingly widespread in the oceanic and atmospheric sciences. One application is data assimilation, i.e., the combination of model output with observations to form the best picture of the system under study. For any given quantity to be estimated, the relative weights of the model and the data will be adjusted according to estimated model and data error statistics, so implementation of any data assimilation scheme will require some assumption about errors, which are considered to be random. For dynamical models, some assumption about the evolution of errors will be needed. Stochastic models are also applied in studies of predictability.

The formal theory of stochastic processes was well developed in the last half of the twentieth century. One consequence of this theory is that methods of simulation of deterministic processes cannot be applied to random processes without some modification. In some cases the rules of ordinary calculus must be modified.

The formal theory was developed in terms of mathematical formalism that may be unfamiliar to many oceanic and atmospheric scientists. The purpose of this article is to provide an informal introduction to the relevant theory, and to point out those situations in which that theory must be applied in order to model random processes correctly.     

Control of a liquid–liquid heat exchanger

 The analytical solutions of equations describing the dynamics of distributed parameter systems are usually complicated in form and derivations and inconvenient to use for simulation and control system design. The liquid–liquid counter flow heat exchanger is an example of these disturbed parameter systems. An analytical solution of the dynamics of a symmetrically operated counter flow heat exchanger in the form of transfer function matrix is investigated in open-loop and close-loop conditions. The resulting non-linear model was linearized using perturbation approach. A feed-forward path controller to counteract at any disturbances in the boundary temperature and a non-interactive controller to decouple the outputs were implemented. Received on 22 February 2001 / Published online: 29 November 2001     

Unified approach to best unbiased estimation in control problems and linear models

An analog of a sufficient statistic is proposed in the finite-dimensional linear space of statistics. It is shown that the unbiased estimator of the linear function of a parameter closest to a given function, expressed in terms of a minimal linearly sufficient statistic, is potentially unbiased and optimal.Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 51–58, 1986.     

Scientific heritage of Boris Lukich Laptev (4/23/05–1/15/89)

Biographical information on the eminent Soviet geometer Boris Lukich Laptev (4/23/05–1/15-89) is given as well as a survey of his research in the areas of differential geometry and history of mathematics.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 21, pp.27–42, 1989.     

Cathode spot energy transfer simulated by a focused laser beam

Minimum conditions for the formation of surface craters by laser irradiation were studied experimentally and theoretically for various metals. The critical power density for crater formation within 20 ns was about 10¹¹ W/m². It is therefore concluded that crater formation by ion bombardment requires an ion current density on the order of 10¹⁰ A/m²