The existence of smooth densities for the prediction filtering and smoothing problems

The qualitative behavior of buckled states of two different models of elastic beams is studied. It is assumed that random imperfections affect the governing nonlinear equations. It is shown that near the first critical value of the buckling load the stochastic bifurcation is described asymptotically by an algebraic equation whose coeffficients are Gaussian random variables. The corresponding asymptotic expansion for the displacement is to lowest order a Gaussian stochastic process.Work supported by NSF Grant No. DCR81-14726.Work supported by NSF Grant No. DMS87-01895.     

Well-posed absorbing layer for hyperbolic problems

Summary. The perfectly matched layer (PML) is an efficient tool to simulate propagation phenomena in free space on unbounded domain. In this paper we consider a new type of absorbing layer for Maxwell's equations and the linearized Euler equations which is also valid for several classes of first order hyperbolic systems. The definition of this layer appears as a slight modification of the PML technique. We show that the associated Cauchy problem is well-posed in suitable spaces. This theory is finally illustrated by some numerical results. It must be underlined that the discretization of this layer leads to a new discretization of the classical PML formulation. Received May 5, 2000 / Published online November 15, 2001     

On the Point-Particle (Newtonian) Limit¶of the Non-Linear Hartree Equation

We consider the nonlinear Hartree equation describing the dynamics of weakly interacting non-relativistic Bosons. We show that a nonlinear M?ller wave operator describing the scattering of a soliton and a wave can be defined. We also consider the dynamics of a soliton in a slowly varying background potential W(ɛx). We prove that the soliton decomposes into a soliton plus a scattering wave (radiation) up to times of order ɛ⁻¹. To leading order, the center of the soliton follows the trajectory of a classical particle in the potential W(ɛx). Received: 30 June 2000 / Accepted: 25 June 2001     

Approximate and Exact Small Signal Analysis for Single-Mode Fiber Near Zero Dispersion Wavelength with Higher Order Dispersion

This article presents the comparison of approximate and exact small-signal theories for analyzing the influence of the higher-order dispersion terms on dispersive optical communication systems operating near zero dispersion wavelength for linear single-mode fiber. For the approximate theory, the generalized conversion matrix has been reported and gives the transfer function of intensity and phase from the fiber input to fiber output for a laser source including the influence of any higher-order dispersion term. In addition, expressions for the small-signal frequency response and the relative intensity noise (RIN) response of an ultrafast laser diode including noises are derived. However, it is observed that the approximation assumed for the second-order dispersion term for the approximate analysis is not valid. From the approximate theory, the exact generalized conversion matrix and exact expressions for small-signal frequency response and relative intensity noise (RIN) are obtained. We show that for the exact theory, the second-order dispersion term has no effect on intensity and frequency response even at large modulating frequencies and large propagation distances contrary to the approximate theory as reported by other authors. But we show that third-order dispersion term certainly has some minute impact on the frequency and RIN response for long distance links at high modulating frequencies.     

Improved bounds for sampling contingency tables

We study the problem of sampling contingency tables (nonnegative integer matrices with specified row and column sums) uniformly at random. We give an algorithm which runs in polynomial time provided that the row sums r_i and the column sums c_j satisfy r_i = Ω(n^3/2m log m), and c_j = Ω(m^3/2n log n). This algorithm is based on a reduction to continuous sampling from a convex set. The same approach was taken by Dyer, Kannan, and Mount in previous work. However, the algorithm we present is simpler and has weaker requirements on the row and column sums. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 21: 135–146, 2002     

Holographic interferometry as electrochemical emission spectroscopy of a carbon steel in 5–20 ppm TROS C-70 inhibited seawater

In the present investigation, holographic interferometry was utilized for the first time to determine the rate change of the number of the fringe evolutions during the corrosion test of a carbon steel in blank seawater and seawater with different concentrations of a corrosion inhibitor. In other words, the anodic dissolution behaviors (corrosion) of the carbon steel were determined simultaneously by holographic interferometry, as an electromagnetic method, and by the electrochemical impedance (EI) spectroscopy, as an electronic method. So, the abrupt rate change of the number of the fringe evolutions during corrosion tests, EI spectroscopy, of the carbon steel is called electrochemical emission spectroscopy. The corrosion process of the steel samples was carried out in blank seawater and seawater with different concentrations, 5–20 ppm, of TROS C-70 corrosion inhibitor using the EI spectroscopy method, at room temperature. The electrochemical-emission spectra of the carbon steel in different solutions represent a detailed picture of the rate change of the anodic dissolution of the steel throughout the corrosion processes. Furthermore, the optical interferometry data of the carbon steel were compared to the data, which was obtained from the EI. spectroscopy. Consequently, holographic interferometry is found very useful for monitoring the anodic dissolution behaviors of metals, in which the number of the fringe evolutions of the steel samples can be determined in situ.     

EFFECT OF SEATING ON EXPOSURES TO WHOLE-BODY VIBRATION IN VEHICLES

The vibration isolation efficiency of seating has been evaluated in 100 work vehicles in 14 categories (cars, vans, lift trucks, lorries, tractors, buses, dumpers, excavators, helicopters, armoured vehicles, mobile cranes, grass rollers, mowers and milk floats). Seat isolation efficiency, expressed by the SEAT value, was determined for all seats (67 conventional seats and 33 suspension seats) from the vertical acceleration measured on the floors and on the seats of the vehicles.For most categories of vehicle, the average SEAT value was less than 100%, indicating that the average seat provided some attenuation of vibration. However, there were large variations in SEAT values between vehicles within categories. Two alternative vibration frequency weightings (W_b from BS 6841, 1987; W_k from ISO 2631, 1997) yielded SEAT values that differed by less than 6%. Overall, the SEAT values determined by two alternative methods (the ratio of r.m.s. values and the ratio of vibration dose values) differed by less than 4·5% when using weighting W_b, although larger differences may be expected in some situations. The median SEAT value for the suspension seats was 84·6%; the median SEAT value for the conventional seats was 86·9% (based on weighting W_b and the ratio of r.m.s. values).Predicted SEAT values were obtained assuming that each seat could be interchanged between vehicles without altering its transmissibility. The calculations suggest that 94% of the vehicles investigated might benefit from changing the current seat to a seat from one of the other vehicles investigated. Although the predictions are based on assumptions that will not always apply, it is concluded that the severity of whole-body vibration exposures in many work environments can be lessened by improvements to seating dynamics.     

Modelling for the planning and management of bed capacities in hospitals

The internal dynamics of a hospital represent a complex non-linear structure. Planning and management of bed capacities must be evaluated within an environment of uncertainty, variability and limited resources. A common approach is to plan and manage capacities based on simple deterministic spreadsheet calculations. This paper demonstrates that these calculations typically do not provide the appropriate information and result in underestimating true bed requirements. More sophisticated, flexible and necessarily detailed capacity models are needed. The development and use of such a simulation model is presented in this paper. The modelling work, in conjunction with a major UK NHS Trust, considers various types of patient flows, at the individual patient level, and resulting bed needs over time. The consequence of changes in capacity planning policies and management of existing capacities can be readily examined. The work has highlighted the need for evaluating hospital bed capacities in light of both bed occupancies and refused admission rates. The relationship between occupancy and refusals is complex and often overlooked by hospital managers.     

A linearized vector radiative transfer model for atmospheric trace gas retrieval

We present a plane parallel radiative transfer model for polarized light, that provides the intensity vector as well as the derivatives of the four Stokes parameters with respect to atmospheric trace gas profiles. These derivatives are essential for retrieval of height resolved trace gas information from satellite measurements of backscattered sunlight. The model uses the Gauss-Seidel iteration technique for solving the radiative transfer equation. For the first time, the forward-adjoint radiative perturbation theory is applied for the linearization of a radiative transfer model including polarization. The accuracy of the model is better than 0.025% for all four Stokes parameters and better than 0.03% for the derivatives.