Equilibrium schemes for scalar conservation laws with stiff sources

We consider a simple model case of stiff source terms in hyperbolic conservation laws, namely, the case of scalar conservation laws with a zeroth order source with low regularity. It is well known that a direct treatment of the source term by finite volume schemes gives unsatisfactory results for both the reduced CFL condition and refined meshes required because of the lack of accuracy on equilibrium states. The source term should be taken into account in the upwinding and discretized at the nodes of the grid. In order to solve numerically the problem, we introduce a so-called equilibrium schemes with the properties that (i) the maximum principle holds true; (ii) discrete entropy inequalities are satisfied; (iii) steady state solutions of the problem are maintained. One of the difficulties in studying the convergence is that there are no estimates for this problem. We therefore introduce a kinetic interpretation of upwinding taking into account the source terms. Based on the kinetic formulation we give a new convergence proof that only uses property (ii) in order to ensure desired compactness framework for a family of approximate solutions and that relies on minimal assumptions. The computational efficiency of our equilibrium schemes is demonstrated by numerical tests that show that, in comparison with an usual upwind scheme, the corresponding equilibrium version is far more accurate. Furthermore, numerical computations show that equilibrium schemes enable us to treat efficiently the sources with singularities and oscillating coefficients.

     

Network formed by traces of random walks

We propose a model of time evolving networks in which a kind of transport between vertices generates new edges in the graph. We call the model “Network formed by traces of random walks”, because the transports are represented abstractly by random walks. Our numerical calculations yield several important properties observed commonly in complex networks, although the graph at initial time is only a one-dimensional lattice. For example, the distribution of vertex degree exhibits various behaviors such as exponential, power law like, and bi-modal distribution according to change of probability of extinction of edges. Another property such as strong clustering structure and small mean vertex–vertex distance can also be found. The transports represented by random walks in a framework of strong links between regular lattice is a new mechanisms which yields biased acquisition of links for vertices.     

A kinetic formulation for a model coupling free surface and pressurised flows in closed pipes

The aim of this paper is to present a kinetic formulation of a model for the coupling of transient free surface and pressurised flows. Firstly, we revisit the system of Saint-Venant equations for free surface flow: we state some properties of Saint-Venant equations, we propose a kinetic formulation and we verify that this kinetic formulation leads to a Gibbs equilibrium that minimises (in some general case) an energy and preserves the still water steady state. Secondly, we propose a model for pressurised flows in a Saint-Venant-like conservative formulation. We then propose a kinetic formulation and we verify that this kinetic formulation leads to a Gibbs equilibrium that minimises in any case an energy and preserves the still water steady state. Finally, we propose a dual model that couples these two types of flow.     

BECOOL: Ballooning eigensolver with COOL finite elements

An incompressible variational ideal ballooning mode equation is discretized with the COOL finite element discretization scheme using basis functions composed of variable order Legendre polynomials. This reduces the second order ordinary differential equation to a special block pentadiagonal matrix equation that is solved using an inverse vector iteration method. A benchmark test of BECOOL (Ballooning Eigensolver using COOL finite elements) with second order Legendre polynomials recovers precisely the eigenvalues computed by the VVBAL shooting code. Timing runs reveal the need to determine an optimal lower order case. Eigenvalue convergence runs show that cubic Legendre polynomials construct the optimal ballooning mode equation for intensive computations.     

Elastic line deformed on a pseudo-hypersurface by an external field in pseudo-Euclidean spaces

We derive intrinsic formulation for elastic line deformed on a pseudo-hypersurface by an external field in the pseudo-Euclidean spaces E_v~n.This formulation determines elastic line deformed on a pseudo-hypersurface.     

Adler-Bardeen theorem in path integral formulation

The higher order contributions to Jacobian in Fujikawa’s path integral framework is considered and the form of anomaly equation in higher orders is established. An argument for the Adler-Bardeen theorem in this formulation is given.     

CVD全离散化的混合有限元解的数值模拟

在已有的对CVD化学方程半离散化和全离散化混合有限元解的存在性及其误差分析的基础上,对其全离散化混合有限元解进行了数值模拟,结果进一步表明了混合有限元解的高精度、易于计算的良好性质.     

Application of the fractional factorial design in multiple W/O/W emulsions

In presented research, multiple W/O/W emulsions were developed by using experimental design method. A 24-1 fractional factorial design was performed by varying the following input parameters: primary polymeric emulsifier (PEG 30-dipolyhydroxystearate) concentration (0.8% and 2.4%), secondary polymeric emulsifier (Poloxamer 407) concentration (0.8% and 1.2%), electrolyte magnesium sulfate heptahydrate (0.08% and 0.4%) and electrolyte sodium chloride (0.08% and 0.4%). Multiple emulsions were prepared by a two-step emulsification process. Obtained emulsions were characterized with rheological measurements, conductivity and centrifugation tests. Factorial analysis revealed that the concentration of the primary emulsifier was the predominant factor influencing the phase separation, conductivity and maximal apparent viscosity. Additionally, electrolyte magnesium sulfate heptahydrate was more efficient in stabilizing these systems, compared to sodium chloride. The applied fractional factorial design method enabled determination of the optimal concentrations of the primary and secondary emulsifier, as well as the concentration of electrolytes, in order to obtain W/O/W emulsions with desired maximal apparent viscosities, low values of conductivity and without phase separation after centrifugation.     

Geometrically non-linear transverse vibrations of C-S-S-S and C-S-C-S rectangular plates

This paper is concerned with a new improved formulation of the theoretical model previously developed by Benamar et al. based on Hamilton's principle and spectral analysis, for the geometrically non-linear vibrations of thin structures. The problem is reduced to a non-linear algebraic system, the solution of which leads to determination of the amplitude-dependent fundamental non-linear mode shapes, the frequency parameters, and the non-linear stress distributions. The cases of C-S-C-S and C-S-S-S rectangular plates are examined, and the results obtained are in a good qualitative and quantitative agreement with the previous available works, based on various methods. In order to obtain explicit analytical solutions for the first non-linear mode shapes of C-S-C-S RP² and C-S-S-S RP, which are expected to be very useful in engineering applications and in further analytical developments, the improved version of the semi-analytical model developed by El Kadiri et al. For beams and fully clamped rectangular plates, has been slightly modified, and adapted to the above cases, leading to explicit expressions for the higher basic function contributions, which are shown to be in a good agreement with the iterative solutions, for maximum non-dimensional vibration amplitude values up to 0.75 and 0.6 for the first non-linear mode shapes of C-S-C-S RP and C-S-S-S RP, respectively.     

A novel application of immobilization on membranes for the separation and spectrofluorimetric quantification of amiloride and furosemide in pharmaceutical samples

A new, simple and highly sensitive method for spectrofluorimetric determination of amiloride (AMI) and furosemide (FUR) in pharmaceuticals is presented. The proposed method is based on the separation of AMI from FUR by solid-phase extraction using a nylon membrane, followed by spectrofluorimetric determination of both drugs, on the solid surface and the filtered aqueous solution, respectively. AMI shows low native fluorescence, but its separation-preconcentration by immobilization (solid-phase extraction) on nylon membrane surface provides a considerable enhancement in fluorescence intensity. The fluorescence determination is carried out at λ_ex = 237, λ_em = 415 nm for FUR; and λ_ex = 365, λ_em = 406 nm for AMI. The calibration graphs are linear in the range 3.20 × 10⁻⁴ to 0.8 μg mL⁻¹and 1.33 × 10⁻³ to 4.0 μg mL⁻¹, for AMI and FUR, respectively, with a detection limit of 9.62 × 10⁻⁵ and 4.01 × 10⁻⁴ μg mL⁻¹ (S/N = 3). The commonly found excipients in commercial pharmaceutical formulations do not interfere. The developed method is successfully applied to the determination of both drugs in pharmaceutical formulations.