Boltzmann-Type Equation in Anelastic Case: A Convergence Result

In this Letter, a convergence result for the BBGKY hierarchy to a Boltzmann-like equation, in the case of an Anelastic collision, is shown. Boltzmann-like equations are often used to model dissipative dynamical systems such as granular media. This convergence result aims to make a contribution towards a mathematical foundation to these applications.     

Passive control of the flow around a square cylinder using porous media

The passive control of bluff body flows using porous media is investigated by means of the penalization method. This method is used to create intermediate porous media between solid obstacles and the fluid in order to modify the boundary layer behaviour. The study covers a wide range of two‐dimensional flows from low transitional flow to fully established turbulence by direct numerical simulation of incompressible Navier–Stokes equations. A parametric study is performed to illustrate the effect of the porous layer permeability and thickness on the passive control. The numerical results reveal the ability of porous media to both regularize the flow and to reduce the drag forces up to 30%. Copyright © 2004 John Wiley & Sons, Ltd.     

Radiation heat transfer in axisymmetric quartz glass tubes

A mathematical model is proposed to describe the heat transfer in quartz glass axisymmetric tubes. Heat is transferred inside the glass by radiation and conduction. Scattering of thermal radiation inside the glass is ignored. At the boundaries of the tube the radiative intensity is specularly reflected. The spectral dependent radiative intensity and the temperature distribution inside the tube are determined. The model is applied to simulate the cooling process of a quartz glass tube. The calculated temperature is in agreement with that obtained from an experiment. Furthermore, steady-state temperature distributions in quartz glass tubes of different lengths have been determined.     

The modified characteristic finite difference fractional steps method for the coupled system of fluid dynamics in porous media and its analysis

For the coupled system of multilayer fluid dynamics in porous media, the modified characteristic finite difference fractional steps method applicable to parallel arithmetic is put forward and two‐dimensional and three‐dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, energy method, piecewise biquadratic interpolation, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L² norm are derived to determine the error in the approximate solution. This method has already been applied to the numerical simulation of multilayer fluid dynamics in porous media. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 665–681, 2003.     

Pulsed-Field-Gradient Measurements of Time-Dependent Gas Diffusion

Pulsed-field-gradient NMR techniques are demonstrated for measurements of time-dependent gas diffusion. The standard PGSE technique and variants, applied to a free gas mixture of thermally polarized xenon and O₂, are found to provide a reproducible measure of the xenon diffusion coefficient (5.71 × 10⁻⁶m²s⁻¹for 1 atm of pure xenon), in excellent agreement with previous, non-NMR measurements. The utility of pulsed-field-gradient NMR techniques is demonstrated by the first measurement of time-dependent (i.e., restricted) gas diffusion inside a porous medium (a random pack of glass beads), with results that agree well with theory. Two modified NMR pulse sequences derived from the PGSE technique (named the Pulsed Gradient Echo, or PGE, and the Pulsed Gradient Multiple Spin Echo, or PGMSE) are also applied to measurements of time dependent diffusion of laser polarized xenon gas, with results in good agreement with previous measurements on thermally polarized gas. The PGMSE technique is found to be superior to the PGE method, and to standard PGSE techniques and variants, for efficiently measuring laser polarized noble gas diffusion over a wide range of diffusion times.     

4-Aminophthalimide Derivatives as Environment-Sensitive Probes

The potential of 4-aminophthalimide (AP) and its derivatives as fluorescence probes for organized media is highlighted. The fluorescence response of AP, as measured from the position of the fluorescence maximum, fluorescence intensity and lifetime, is highly sensitive to the polarity of the medium. The sensitivity of the fluorescence parameters is further enhanced due to the involvement of the emitting intramolecular charge transfer state in hydrogen bonding interaction with the solvent molecules containing hydroxyl groups. It is shown that the microheterogeneous environments of organized media such as cyclodextrins and micelles can be very conveniently monitored using this probe. The results of the investigations carried out employing AP and its derivatives as fluorescence probe molecules in these media clearly suggest that a combination of the hydrophobic interaction with the host media and hydrogen bonding interaction with the solvent molecules determine the location of the fluorophore, which in all cases is found to be the interfacial region separating the nonpolar core of the micelle or the cyclodextrin cavity and the polar aqueous environment. Guidelines for the design of probes of this class of systems for the nonpolar core region of the micelles are provided and possible ways to increase the sensitivity of the fluorescence response of the systems are suggested.     

Fluctuation kinetics of diffusion-controlled processes: Strong effects due to correlations and fluctuations

We summarize some recent results related to fluctuation-induced kinetics of diffusion-controlled processes. We show that kinetic behavior can be drastically changed due to fluctuation effects, spatial correlations between particles, and anomalous transport properties. In addition, we show that correlation-induced kinetics in some systems can govern the temporal evolution over the entire time domain.