Performance study of the multiwavelet discontinuous Galerkin approach for solving the Green-Naghdi equations

This paper presents a multiresolution discontinuous Galerkin (DG) scheme for the adaptive solution of Boussinesq-type equations. The model combines multiwavelet (MW)–based grid adaptation with a DG solver based on the system of fully nonlinear and weakly dispersive Green-Naghdi (GN) equations. The key feature of the adaptation procedure is to conduct a multiresolution analysis using MWs on a hierarchy of nested grids to improve the efficiency of the reference DG scheme on a uniform grid by computing on a locally refined adapted grid. This way, the local resolution level will be determined by manipulating MW coefficients controlled by a single user-defined threshold value. The proposed adaptive multiwavelet DG solver for GN equations is assessed using several benchmark problems related to wave propagation and transformation in nearshore areas. The numerical results demonstrate that the proposed scheme retains the accuracy of the reference scheme, while significantly reducing the computational cost.     

One-Dimensional Matrix-Fracture Transfer in Dual Porosity Systems with Variable Block Size Distribution

Most of the developed models for fractured reservoirs assume ideal matrix block size distribution. This assumption may not be valid in reality for naturally fractured reservoirs and possibly lead to errors in prediction of production from the naturally fractured reservoirs especially during a transient period or early time production from the matrix blocks. In this study, we investigate the effect of variable block size distribution on one- dimensional flow of compressible fluids in fractured reservoirs. The effect of different matrix block size distributions on the single phase matrix-fracture transfer is studied using a recently developed semi-analytical approach. The proposed model is able to simulate fluid exchange between matrix and fracture for continuous or discrete block size distributions using probability density functions or structural information of a fractured formation. The presented semi-analytical model demonstrates a good accuracy compared to the numerical results. There have been recent attempts to consider the effect of variable block size distribution in naturally fractured reservoir modeling for slightly compressible fluids with a constant viscosity and compressibility. The main objective of this study is to consider the effect of variable block size distribution on a one-dimensional matrix-fracture transfer function for single-phase flow of a compressible fluid in fractured porous media. In the proposed semi-analytical model, the pressure variability of viscosity and isothermal compressibility is considered by solving the nonlinear partial differential equation of compressible fluid flow in the fractured media. The closed form solution provided can be applied to flow of compressible fluids with variable matrix block size distribution in naturally fractured gas reservoirs.     

On a Class of Neumann Boundary Value Equations Driven by a (p1, , Pn)-Laplacian Operator

In this paper we prove the existence of an open interval (λ' ,λ") for each λ in the interval a class of Neumann boundary value equations involving the (p_1,..., p_n)- Laplacian and depending on λ admits at least three solutions. Our main tool is a recent three critical points theorem of Averna and Bonanno [Topol. Methods Nonlinear Anal. [1] (2003) 93-103].     

Synthesis and Reactivity of Functionalized Binary and Ternary Thiometallate Complexes [(RT)4S6], [(RSn)3S4]2−, [(RT)2(CuPPh3)6S6], and [(RSn)6(OMe)6Cu2S6]4− (R=C2H4COOH,CMe2CH2COMe; T=Ge,Sn)

Caged chalcogens : A series of novel, functionalized T_nS_m cages (T=Ge, Sn; n/m=4:6, 3:4) with terminal COO(H) or COMe groups were synthesized and show further reactivity toward Cu^I complexes (an example of which is shown here) and to hydrazines. This led to the generation of functionalized Cu/T/S clusters or the formation of Schiff bases at the C?O groups, respectively, with or without further fragmentation of the T/S core.

     

Multiplicity results for a two-point boundary value double eigenvalue problem

The purpose of this note is to prove the existence of three solutions for a two-point boundary value double eigenvalue problem. The approach is fully based on a recent three critical points theorem of B. Ricceri [A three critical points theorem revisited, Nonlinear Anal., 70/9 (2009) 3084–3089].     

The effects induced by proton irradiation on structural characteristics of nuclear graphite

A grade TSX graphite was irradiated by a 2.5 MeV proton and a dose of 1.47 × 10¹⁸ ion cm⁻² at 330 K. The displacement per atom under this irradiation condition was about 0.02. The lattice parameter, crystallite size and the vacancies density in the graphite was measured before and after irradiation. It was found that the proton irradiation led to an increase in the volume of the sample. The volume change in the irradiated sample was confirmed by atomic force and scanning electron microscopes observations as increased roughness and pore size. Also, FTIR results showed that graphite is slightly oxidized by irradiation.

     

On principal eigenvalues for boundary value problems with indefinite weight and Robin boundary conditions

We investigate the existence of principal eigenvalues (i.e., eigenvalues corresponding to positive eigenfunctions) for the boundary value problem on ; on , where is a bounded region in , is an indefinite weight function and may be positive, negative or zero.

     

Application of variational iteration method and homotopy–perturbation method for nonlinear heat diffusion and heat transfer equations

Perturbation methods depend on a small parameter which is difficult to be found for real-life nonlinear problems. To overcome this shortcoming, two new but powerful analytical methods are introduced to solve nonlinear heat transfer problems in this Letter; one is He's variational iteration method (VIM) and the other is the homotopy–perturbation method (HPM). Nonlinear convective–radiative cooling equations are used as examples to illustrate the simple solution procedures. These methods are useful and practical for solving the nonlinear heat diffusion equation, which is associated with variable thermal conductivity condition. Comparison of the results obtained by both methods with exact solutions reveals that both methods are tremendously effective.     

Surfactant to dye binding degree method for the determination of fluvoxamine maleate and citalopram hydrobromide in pharmaceuticals

The surfactant to dye binding degree (SBDB) methodology was used to determine fluvoxamine maleate and citalopram hydrobromide. Neutral red and sodium dodecyl sulfate (SDS) were used as the dye and surfactant, respectively, to form dye-surfactant aggregates. When a cationic drug is added to dye-surfactant mixture, it interacts with the surfactant and decreases the dye-surfactant binding degree. This decrease is proportional to the drug concentration. This was measured by monitoring the absorbance changes of the dye at 532 nm. Under the optimum conditions, the calibration graphs were linear over the range of 1.2–15 μg mL⁻¹ and 1.1–15 μg mL⁻¹ for fluvoxamine maleate and citalopram hydrobromide, respectively. The detection limits (signal to noise ratio = 3) were found to be 0.37 and 0.35 μg mL⁻¹, for fluvoxamine maleate and citalopram hydrobromide, respectively.