Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.

How Does the Unemployment Insurance System Shape the Time Profile of Jobless Duration?

This paper updates a sparse literature on the effects of unemployment benefits (UB) on the time profile of escape rates from unemployment. These effects, as well as those of other regressors, are found to vary profoundly over the course of unemployment.

Synthesis of 3-(4-tert-butylphenyl)-2-propen-1-one, a precursor to Lilial (R), via an aldol condensation in an ionic liquid

An efficient synthesis of a precursor to Lilial(R), based on an aldol condensation in an ionic liquid, is described, utilising piperidine as the base catalyst. The yields obtained with this methodology are significantly increased in comparison with those reported in organic solvents to date. In the ionic liquid, the self-aldol condensation of propanal is suppressed and leads to an increased selectivity with respect to the cross-aldol condensation product without the need to use an excess of 4-tert-butylbenzaldehyde to obtain high selectivities.

The removal of dyes from textile wastewater: a study of the physical characteristics and adsorption mechanisms of diatomaceous earth

The feasibility of using diatomite for the removal of the problematic reactive dyes as well as basic dyes from textile wastewater was investigated. Methylene blue, Cibacron reactive black and reactive yellow dyes were considered. Physical characteristics of diatomite such as pH(solution), pH(ZPC), surface area, Fourier transform infrared, and scanning electron microscopy were investigated. The surface area of diatomite was found to be 27.80 m(2) g(-1) and the pH(ZPC) occurred around pH of 5.4. The results indicated that the surface charge of diatomite decreased as the pH of the solution increased with the maximum methylene blue removal from aqueous solution occurring at basic pH of around (1011). Adsorption isotherms of diatomite with methylene blue, hydrolysed reactive black and yellow dyes were constructed at different pH values, initial dye concentrations and particle sizes. The experimental results were fitted to the Langmuir, Freundlich, and Henry models. The study indicated that electrostatic interactions play an important role in the adsorption of dyes onto diatomite. A model of the adsorption mechanism of methylene blue onto diatomite is proposed. (C) 2003 Elsevier Ltd. All rights reserved.