Control parameter estimation in a semi-linear parabolic inverse problem using a high accurate method

Parabolic inverse problems have an important role in many branches of science and technology. The aim of this research work is to solve these classes of equations using a high order compact finite difference scheme. We consider the following inverse problem for finding u(x, t) and p(t) governed by u_t = u_xx + p(t)u + φ(x, t) with an over specified condition inside the domain. Spatial derivatives are approximated using central difference scheme. The time advancement of the simulation is performed using a “third order compact Runge-Kutta method”. The convergence orders for the approximation of both u and p are of o(k³ + h²) which improves the results obtained in the literature. An exact test case is used to evaluate the validity of our numerical analysis. We found that the accuracy of the results is better than that of previous works in the literature.     

Heterotrinuclear manganese(II) and vanadium(IV) Schiff base complexes as epoxidation catalysts

The catalytic epoxidation of styrene using urea-hydrogen peroxide and heterotrinuclear Cu(II) complexes with general formula (ML ⁿ )₂Cu(acac)₂, where n = 1–3 and M = VO²⁺ or Mn²⁺ is reported. Schiff base complexes ML ⁿ involving a 3,4-diaminopyridine bridge with free coordination site were used as the ligand, where (Lⁿ)²⁻ is [(5-x-Sal)₂Py]² and x = H, Br or NO₂. The complexes were characterized by physico-chemical and spectroscopic methods. The electrochemical properties of M were modified upon trinuclear complex formation. The trinuclear complexes show high catalytic activity, with up to 86% conversion and 93% selectivity, while no catalytic properties were observed for the monomeric complexes. The catalyst could be reused with some loss of activity.     

On the Loewy Length and the Noetherian Dimension of Artinian Modules

The problem of computing the automorphism groups of an elementary Abelian Hadamard difference set or equivalently of a bent function seems to have attracted not much interest so far. We describe some series of such sets and compute their automorphism group. For some of these sets the construction is based on the nonvanishing of the degree 1-cohomology of certain Chevalley groups in characteristic two. We also classify bent functions f such that Aut(f) together with the translations from the underlying vector space induce a rank 3 group of automorphisms of the associated symmetric design. Finally, we discuss computational aspects associated with such questions.     

Compact finite difference scheme for the solution of time fractional advection-dispersion equation

In this paper, a compact finite difference method is proposed for the solution of time fractional advection-dispersion equation which appears extensively in fluid dynamics. In this approach the time fractional derivative of mentioned equation is approximated by a scheme of order O(τ ^2???α ), 0?<?α?<?1, and spatial derivatives are replaced with a fourth order compact finite difference scheme. We will prove the unconditional stability and solvability of proposed scheme. Also we show that the method is convergence with convergence order O(τ ^2???α ?+?h ⁴). Numerical examples confirm the theoretical results and high accuracy of proposed scheme.     

Adsorption studies of β-naphthol by untreated and treated activated carbon [optimizing of adsorption by central composite design (CCD)]

In the present work the adsorption of aromatic compound, namely ??-naphthol (BN) by two granular activated carbons, one untreated and the other treated with HNO₃ carried out under controlled conditions. The effects of experimental parameters on adsorption process such as pH, contact time and adsorbent dosage have been investigated. Experimental design methodology was applied to optimize the removal of ??-naphthol. The effect of various experimental parameters was investigated using five-level three-factorial central composite design (CCD). The relationship between the parameters and the response for model optimization was found and optimum conditions were obtained by CCD. In the optimum conditions obtained by response surface modeling, 100% BN was adsorbed on the carbons. Treatment with HNO₃ led to a decrease in the point of zero charge and the adsorption capacity (Q _max) of the activated carbon. The adsorption capacity of the carbons was determined using Freundlich and Langmuir homogenous equation. The variation of the model parameters with the solution pH was also studied. The fitted parameters obtained from both models showed the Q _max value decrease with increasing of pH.     

Existence of Time-Periodic Solutions for a Magnetoelastic System in Bounded Domains

We investigate the existence of periodic solutions for a semilinear (nonlinearly coupled) magnetoelastic system in bounded, simply connected, three-dimensional domains with boundaries of class C ². The mathematical model includes a nonlinear mechanical dissipation like ρ(u′)=|u′| ^p u′ and a periodic forcing function of period T. We prove the existence of T-periodic weak solutions when p∈[3,4] (p=0 being a simpler case). In the corresponding two-dimensional case, the existence result holds under the assumption that p≥2.     

Numerical and Experimental Evaluation of Dispersion Coefficient for Resin Transfer Modeling

Resin transfer molding (RTM) is a composite manufacturing process. A preformed fiber is placed in a closed mold and a viscous resin is injected into the mold. In this article, a model is developed to predict the flow pattern, extent of reaction, and temperature change during the filling and curing in a thin rectangular mold. A numerical simulation is presented to predict the free surface and its interactions with heat transfer and cure for flow of a shear-thinning resin through the preformed fiber.To simulate this process, using local thermal equilibrium assumption, it is essential to include the thermal dispersion term in energy equation. The best method to achieve this result is experimental simulation and preparing proportionate system at simple conditions without curing. By comparison of recorded temperature values (using installed instruments at various locations), and the corresponding results from numerical solution for different estimated values of dispersion coefficient, this coefficient has been evaluated based on the best matching estimate. The results show that, to simulate composite manufacturing process by RTM method, the effect of dispersion term in energy equation shall not be neglected.     

Linear frequency-doubling in dual Mid-IR-wavelength quantum cascade laser active region

In this paper we have proposed a novel quantum cascade laser active region design to obtain a dual-mid-IR-wavelength laser which is capable of frequency-doubling (13.77–6.88 μm) without utilizing nonlinear processes in two coupled shallow and deep quantum well structures. Optimized design of the active region leads to higher dipole matrix elements and thus higher laser performances. This method can be used to design laser structures with different frequency ratios.     

High order implicit collocation method for the solution of two‐dimensional linear hyperbolic equation

In this article, we introduce a high‐order accurate method for solving the two dimensional linear hyperbolic equation. We apply a compact finite difference approximation of fourth order for discretizing spatial derivatives of linear hyperbolic equation and collocation method for the time component. The resulted method is unconditionally stable and solves the two‐dimensional linear hyperbolic equation with high accuracy. In this technique, the solution is approximated by a polynomial at each grid point that its coefficients are determined by solving a linear system of equations. Numerical results show that the compact finite difference approximation of fourth order and collocation method give a very efficient approach for solving the two dimensional linear hyperbolic equation. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

A contribution to the linear programming approach to joint cost allocation: Methodology and application

The linear programming (LP) approach has been commonly proposed for joint cost allocation purposes. Within a LP framework, the allocation rules are based on a marginal analysis. Unfortunately, the additivity property which is required to completely allocate joint costs fails in presence of capacity, institutional or environmental constraints.