Mixed finite difference and Galerkin methods for solving Burgers equations using interpolating scaling functions

The current paper proposes a technique for the numerical solution of Burgers equations. The method is based on finite difference formula combined with the Galerkin method, which uses the interpolating scaling functions. Several test problems are given, and the numerical results are reported to show the accuracy and efficiency of the new algorithm. Copyright © 2013 John Wiley & Sons, Ltd.     

The use of Chebyshev cardinal functions for the solution of a partial differential equation with an unknown time-dependent coefficient subject to an extra measurement

A numerical technique is presented for the solution of a parabolic partial differential equation with a time-dependent coefficient subject to an extra measurement. The method is derived by expanding the required approximate solution as the elements of Chebyshev cardinal functions. Using the operational matrix of derivative, the problem can be reduced to a set of algebraic equations. From the computational point of view, the solution obtained by this method is in excellent agreement with those obtained by previous works and also it is efficient to use.     

Radio-immunoconjugated,Dox-loaded,surface-modified superparamagnetic iron oxide nanoparticles (SPIONs) as a bioprobe for breast cancer tumor theranostics

In this research, we develop dual modality molecular imaging and also radio-immunotherapy (RIT) bioprobes, in the form of modified superparamagnetic iron oxide nanoparticles (SPIONs) conjugated to radiolabeled antibodies, for PET and MRI of HER2 expressing cancers as well as a PH sensitive drug carrier by embedded an anticancer agent for cancer therapeutic applications. The bioprobes were developed by conjugating ⁶⁴Cu labeled trastuzumab (herceptin) and rituximab (Anti CD-20) antibodies to modified SPIONs. The SPIONs were modified with carboxymethyl chitosan and functionalized with acrylic acid (AA). Also, with the purpose of identifying more effective bifunctional chelator (BFC), we compared the properties of novel BFC, p-NO₂-Bn-PCTA with the commonly used DOTA-NHS for radio-immunoconjugate preparations. Moreover, a chemotherapy drug, doxorubicin, was then loaded onto engineered nanoparticles for targeted intracellular drug delivery and selective cancer cell killing. Resulting radio-immunoconjugated-SPIONs were evaluated for molecular imaging and effective targeting of the HER2+ receptors in SKBR3 cell lines and breast tumor bearing Balb/C mice. Therefore, our biocompatible SPIONs could serve as a promising multifunctional theranostics nanoplatform in dual modality imaging guided RIT of HER2 overexpressing cancer applicable to drug delivery and controlled drug release for trigger both intrinsic and extrinsic pathways of apoptosis.     

The use of cubic B‐spline scaling functions for solving the one‐dimensional hyperbolic equation with a nonlocal conservation condition

Problems for parabolic partial differential equations with nonlocal boundary conditions have been studied in many articles, but boundary value problems for hyperbolic partial differential equations have so far remained nearly uninvestigated. In this article a numerical technique is presented for the solution of a nonclassical problem for the one‐dimensional wave equation. This method uses the cubic B‐spline scaling functions. Some numerical results are reported to support our study. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Random depth access full-field low-coherence interferometry applied to a small punch test

In small punch testing, with approximate preknowledge of the sample deformation, profile measurement need only be made at selected locations in depth. To date, profilometry through full-field low-coherence interferometry has not been applied to small punch testing—conventional methods typically measure the maximum displacement as the sample is deformed, ignoring useful shape and profile information. A modification of full-field low-coherence interferometry is presented, where a digital stepper motor is combined with piezoelectric transducer scanning to achieve random depth access three-dimensional micrometer profile measurement. Offering a rapid, inexpensive, and functional machine vision system, the measurement technique is applied to a small punch test.     

A computational study of surface tension determination of dense fluids as benzene,toluene, methanol,ammonia, ethylene,and carbon monoxide

In this study, the parameters of linear isotherm regularity, which called LIR equation state used to compute the surface tension of some dense fluids as benzene, toluene, methanol, ammonia, ethylene, and carbon monoxide. An expression has derived for radial distribution function (RDF) at constant temperature, g (σ), for a real fluid by the use of LIR. This expression, which is related to intermolecular interaction, can be used to describe the temperature–density dependency of RDF at constant temperature, g (σ, ρ, T). In addition, we derive an expression for surface tension of dense fluids (CO, C₆H₆, C₆H₅CH₃, CH₃OH, NH₃, and C₂H₄) using the LIR and g (σ, ρ, T). Unlike previous models, it has shown that, surface tension can obtain without employing ΔH and ΔS. Only P-V-T experimental data have been used to calculate the surface tension. Comparison of the calculated values of surface tension by LIR with the values obtained experimentally show this method is not precise. This problem has led us to try to obtain the expression for surface tension using the extended parameters A, B (A and B are the temperature-dependent parameters which noticeably are depended on attraction and repulsion). The obtained result shows that the accuracy of this method is very high and quite admissible.     

Numerical solution for the weakly singular Fredholm integro-differential equations using Legendre multiwavelets

An effective method based upon Legendre multiwavelets is proposed for the solution of Fredholm weakly singular integro-differential equations. The properties of Legendre multiwavelets are first given and their operational matrices of integral are constructed. These wavelets are utilized to reduce the solution of the given integro-differential equation to the solution of a sparse linear system of algebraic equations. In order to save memory requirement and computational time, a threshold procedure is applied to obtain the solution to this system of algebraic equations. Through numerical examples, performance of the present method is investigated concerning the convergence and the sparseness of the resulted matrix equation.     

Four techniques based on the B‐spline expansion and the collocation approach for the numerical solution of the Lane–Emden equation

Four numerical techniques based on the linear B‐spline functions are presented for the numerical solution of the Lane–Emden equation. Some properties of the B‐spline functions are presented and are utilized to reduce the solution of the Lane–Emden equation to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the new techniques. Copyright © 2013 John Wiley & Sons, Ltd.     

Numerical solution of Fokker‐Planck equation using the cubic B‐spline scaling functions

In this article a numerical technique is presented for the solution of Fokker‐Planck equation. This method uses the cubic B‐spline scaling functions. The method consists of expanding the required approximate solution as the elements of cubic B‐spline scaling function. Using the operational matrix of derivative, the problem will be reduced to a set of algebraic equations. Some numerical examples are included to demonstrate the validity and applicability of the technique. The method is easy to implement and produces very accurate results. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

The effect of heat treatment in the reducing atmosphere on the physical properties of TiO2 thin films prepared by sol–gel method

Multilayered nanostructured TiO₂ thin films were prepared by sol–gel and dipping deposition on quartz substrate followed by thermal treatment under reducing atmosphere (20 %H₂–80 %Ar). Heat treatment at progressively higher temperatures caused structural, morphological, and optical changes, which were investigated by X-ray diffraction (XRD), atomic force microscopy, scanning electron microscopy, and UV–Vis spectroscopy. The conductivities of the thin films were also measured by 4-point probe method. The XRD results showed that the calcined TiO₂ thin films consist of single anatase phase which was completely transformed into rutile phase after heat treatment at 1,000 °C. The grains of films grew by intra-agglomerate densification after heat treatment at higher temperatures. The root mean square roughness of the samples was found to be in the range of 0.58–3.36 nm. The partially reduced TiO₂ samples have red-shifted transmittance bands due to new energy band formed by oxygen vacancies. The electrical conductivity of the films was also enhanced after heat treatment in reducing atmosphere.