Lattice Boltzmann method for polymer kinetic theory

The purpose of this work is to extend the applicability of the lattice Boltzmann method (LBM) to the field of polymer kinetic theory or more generally suspensions that could be described in the Fokker–Planck formalism. This method has been, in a first time, used for gas kinetic theory, where the resolution space corresponds to the physical space coordinate. In a second time is has been generalized to be applied to fluid flow involving different behaviours: turbulence, porous media, multiphase flow, etc. However this powerful, parallel, and efficient algorithm has not been applied for solving Fokker–Planck equations widely used to describe suspension kinetic theory. In this scale, molecular models involve a high computational costs because of the multidimensionality of the fully coupled micro–macro complex flow. The originality of this work consists to apply the lattice Boltzmann technique for solving Fokker–Planck equation based on a discretization of the configuration space where the resolution coordinates correspond to the microscopic configuration space (and not the physical coordinates). The result of this work emphasizes the optimality of the used technique that, in addition to its parallel ability, gathers the simplicity of the stochastic simulation and the robustness of the traditional fixed mesh support (such as the finite element method). Accuracy and convergence of the LBM will be compared to the stochastic and the finite element techniques for homogeneous shear flow.     

Large deviations for Brownian motion in a random scenery

We prove large deviations principles in large time, for the Brownian occupation time in random scenery . The random field is constant on the elements of a partition of ^d into unit cubes. These random constants, say consist of i.i.d. bounded variables, independent of the Brownian motion {B_s,s0}. This model is a time-continuous version of Kesten and Spitzer's random walk in random scenery. We prove large deviations principles in ``quenched' and ``annealed' settings.Mathematics Subject Classification (2000):60F10, 60J55, 60K37     

Determination of mercury(II), methylmercury and ethylmercury in the ng/ml range with an electrochemical enzyme glucose probe

Hg(II), methylmercury and ethylmercury have been determined with an electrochemical glucose probe. Mercury and its compounds inhibit the enzyme invertase which, in presence of its substrate, sucrose, produces glucose. When invertase is in presence of mercury its activity decreases; this causes a decrease of glucose production, which is monitored by the glucose sensor and correlated to the concentration of mercury in solution. Parameters such as pH, enzyme concentration, substrate concentration, and reaction and incubation time were optimized. Results showed that mercury, methylmercury and ethylmercury can be detected directly in aqueous solution in the range 2–10 ng/ml.     

Rapid and Selective Electrochemical Determination of Nitrite in Cured Meat in the Presence of Ascorbic Acid

A simple, fast and selective amperometric procedure for nitrite determination in cured meat based on the use of a carbon paste electrode is presented. Direct interference of ascorbic acid, which interferes with electrochemical detection, was eliminated by applying a cellulose acetate membrane of 100Da molecular weight cut-off on the electrode. Indirect interference of ascorbic acid due to its auto-oxidation reaction and its reaction with nitrite is discussed. In order to stabilise the ascorbic acid, metaphosphoric acid and EDTA were added.In contrast to the standard spectrophotometric method, which requires careful control of pH and the use of carcinogenic reagents, amperometric determination of nitrite is simple, rapid, and works without reagents. Also, sample preparation is simpler because it requires neither heating to 80°C nor the centrifugation steps of the official spectrophotometric method. The detection limit achieved was 14ppb (0.2µM) nitrite in the solution, which corresponds to a detection of 2.8ppm in meat samples. The method was compared with the standard spectrophotometric procedure and applied to the detection of nitrites in cured meat samples with satisfactory results.     

Determination of mercury(II) by invertase enzyme inhibition coupled with batch injection analysis

The determination of mercury(II) ions at the trace level by inhibition of the invertase enzyme-catalysed hydrolysis of sucrose into glucose and fructose coupled to electrochemical batch injection analysis was investigated using two approaches. In the first, the glucose produced was detected by injection of 100 microliters samples into the batch injection cell containing a platinum electrode modified by immobilised glucose oxidase. In the second, the glucose and fructose present in injected samples were oxidised directly at a copper-modified glassy carbon electrode. The experimental parameters were optimised and the degree of enzyme inhibition by mercury(II) ions under both conditions was measured. Mercury concentrations in the ng ml-1 range were determined by these two techniques with low sample and reagent consumption. Comparison is made between the two methods and perspectives as a screening test for field application are indicated.     

Convective heat transfer over two blocks arbitrary located in a 2D plane channel using a hybrid lattice Boltzmann-finite difference method

The present paper deals with the numerical investigation of a 2D laminar fluid flow and heat transfer in a plane channel with two square blocks located at arbitrary positions. The numerical model is based on a coupling between the multiple relaxation time-lattice Boltzmann equation and the finite difference method for incompressible flow. Both the horizontal and the vertical separation distances between the two blocks are varied. Particular attention was paid to the distribution patterns of the time averaged local Nusselt number on the top and bottom walls. Results obtained from the present study show a complex flow patterns developed in the channel due to the change of the square blocks positions.     

On the Cauchy problem for a class of iterated Fuchsian partial differential equations

In this paper, we consider the Cauchy problem with ramified data for a class of iterated Fuchsian partial differential equations. We give an explicit representation of the solution in terms of Gauss hypergeometric functions. Our results are illustrated through some examples.