Positron Emission Tomography and Random Coefficients Regression

We further explore the relation between random coefficients regression (RCR) and computerized tomography. Recently, Beran et al. (1996, Ann. Statist., 24, 2569–2592) explored this connection to derive an estimation method for the non-parametric RCR problem which is closely related to image reconstruction methods in X-ray computerized tomography. In this paper we emphasize the close connection of the RCR problem with positron emission tomography (PET). Specifically, we show that the RCR problem can be viewed as an idealized (continuous) version of a PET experiment, by demonstrating that the nonparametric likelihood of the RCR problem is equivalent to that of a specific PET experiment. Consequently, methods independently developed for either of the two problems can be adapted from one problem to the other. To demonstrate the close relation between the two problems we use the estimation method of Beran, Feuerverger and Hall for image reconstruction in PET.     

On the efficiency of water soluble antioxidants

The wide use of high intensity ultrasound (HIU) in modern medicine raises the question of bio-safety. It has been shown that the effect of HIU in biological media may have similarity to the effects of ionizing radiation. Exposure of biological media to HIU field may lead to cavitation phenomenon followed by formation of free radicals such as hydroxyl radical (OH) and the super-oxide ion (O₂-). These are highly reactive species that may cause harmful effects and induce oxidative stress. In the present study we employed electron spin resonance (ESR) spectroscopy together with spin traps to quantify the dynamics of hydroxyl radical formation during exposure to HIU field in the presence of different amounts of six antioxidants. Thus, the efficiency of water-soluble antioxidants, namely Allicin, Melatonin, Deoxyribose, Trolox, Nuphlutine and Hermidin, to suppress accumulation of OH radicals was examined. The results show that among the six, Trolox and Allicin reduce hydroxyl concentration with the highest efficiency.     

Film condensation of multicomponent mixtures

The classic Nusselt model is generalized for the condensation process of a multicomponent vapor mixture. The condensed vapors may be miscible in their liquid state or contain noncondensable gases.The reduction in the condensation rate owing to the accumulation of a noncondensable gas or the more volatile components near the condensate interface is demonstrated for three component systems of methanol—water—air and acetone—methanol—water. Also the effects of interfacial suction and forced convection are included.The analytical solution incorporates Diffusion Law for a multicomponent system and both exact and approximate integral method solutions are applied. The accuracy of the integral method turns out to be remarkably good.     

Wave scattering from a rough surface: Solution by an iterative method

Two iterative solutions of the Helmholtz equation for a scalar field in above a rough surface that admits the Dirichlet boundary condition are derived. The bases for the two iterative methods are two different boundary integral equations that represent the solution. The first integral equation is classified as a Fredholm integral equation of the first kind. The second is classified as a Fredholm integral equation of the second kind. This classification suggests that it is easier to find stable solution methods to the second equation. In both methods, the boundary integral was separated into a major part which is easy to calculate and a local residual part. The major part is a convolution and thus can be calculated using FFT in complexity O(N log N), where N is the number of surface points in which the surface height and its first derivatives together with the incoming wave and its normal derivative are all known. The residual element of the equations can be approximated efficiently only for surfaces where their amplitude is less than the wavelength of the incoming wave. The iterative schemes were tested numerically against a reference solution in order to examine the applicability range, the error estimation and the stability of the schemes. All tests supported the superiority of the second method. In particular the error estimation and stability tests indicated good performance for surfaces with slope up to 1. Yet, being an equation in the scattered field alone, makes the first method useful as a benchmark solution in its domain of applicability.     

Low-energy resonances in photodissociation of CH+

Close coupling calculations for the photodissociation cross sections of CH⁺+hv → C⁺(²P) + H(²S) exhibit near threshold peaks not ascribable only to quasi-bound levels in the A ¹Π potential. Our calculations demonstrate the importance of non-adiabatic transitions and thereby suggest the necessity to revise earlier predictions of the rate of radiative association of C⁺ with H.     

Disintegration of Cnoidal Waves over Smooth Topography

The transformation of cnoidal waves in a basin with smooth topography is studied in the frame of the variable-coefficient Korteweg–de Vries equation and the generalized Zakharov's system. It is shown that the cnoidal structure of the propagating nonlinear wave is destroyed if the topography contains a periodic component with a characteristic scale close to the nonlinearity length. Focusing on waves in intermediate depth, a simple analytical model based on a two-harmonic representation of the cnoidal wave demonstrates the main features of the process of disintegration of the cnoidal structure of the nonlinear wave. Numerical simulations of the interaction of several harmonics confirm the analytical conclusions.     

On uniformly accurate high‐order Boussinesq difference equations for water waves

A new accurate finite‐difference (AFD) numerical method is developed specifically for solving high‐order Boussinesq (HOB) equations. The method solves the water‐wave flow with much higher accuracy compared to the standard finite‐difference (SFD) method for the same computer resources. It is first developed for linear water waves and then for the nonlinear problem. It is presented for a horizontal bottom, but can be used for variable depth as well. The method can be developed for other equations as long as they use Padé approximation, for example extensions of the parabolic equation for acoustic wave problems. Finally, the results of the new method and the SFD method are compared with the accurate solution for nonlinear progressive waves over a horizontal bottom that is found using the stream function theory. The agreement of the AFD to the accurate solution is found to be excellent compared to the SFD solution. Copyright © 2005 John Wiley & Sons, Ltd.     

Application of the VOF method to the sloshing of a fluid in a partially filled cylindrical container

In a previous work we solved numerically the steady-state motion of an ideal fluid that fills a moving cylindrical container with partitions, and were able to compute the equivalent moments of inertia. Here we extend this work in two steps. First we introduce time dependence and then free surfaces, and are able to compute the transient motion of the fluid not filling the container. The main body of the work has to do with the treatment of free surfaces. Our approach is an extention to three dimensions of the volume of fluid method of Hirt and Nichols. The solution algorithm is outlined, and two examples that demonstrate its capability are presented.