Solving a parabolic PDE with nonlocal boundary conditions using the Sinc method

In this paper, the problem of solving the parabolic partial differential equations subject to given initial and nonlocal boundary conditions is considered. We change the problem to a system of Volterra integral equations of convolution type. By using Sinc-collocation method, the resulting integral equations are replaced by a system of linear algebraic equations. The convergence analysis is included, and it is shown that the error in the approximate solution is bounded in the infinity norm by the condition number of the coefficient matrix multiplied by a factor that decays exponentially with the size of the system. Some examples are considered to illustrate the ability of this method.     

Thermal conductivity of anisotropic spin-1/2 two leg ladder: Green’s function approach

We study the thermal transport of a spin-1/2 two leg antiferromagnetic ladder in the direction of legs. The possible effect of spin-orbit coupling and crystalline electric field are investigated in terms of anisotropies in the Heisenberg interactions on both leg and rung couplings. The original spin ladder is mapped to a bosonic model via a bond-operator transformation, where an infinite hard-core repulsion is imposed to constrain one boson occupation per site. The Green’s function approach is applied to obtain the energy spectrum of quasi-particle excitations responsible for thermal transport. The thermal conductivity is found to be monotonically decreasing with temperature due to increased scattering among triplet excitations at higher temperatures. A tiny dependence of thermal transport on the anisotropy in the leg direction at low temperatures is observed in contrast to the strong one on the anisotropy along the rung direction, due to the direct effect of the triplet densities. Our results reach asymptotically the ballistic regime of the spin-1/2 Heisenberg chain and present a complement regime for the exact diagonalization data.     

Doubling and Tripling Constructions for Defining Sets in Steiner Triple Systems

 A minimal defining set of a Steiner triple system on v points (STS(v)) is a partial Steiner triple system contained in only this STS(v), and such that any of its proper subsets is contained in at least two distinct STS(v)s. We consider the standard doubling and tripling constructions for STS(2v+1) and STS(3v) from STS(v) and show how minimal defining sets of an STS(v) gives rise to minimal defining sets in the larger systems. We use this to construct some new families of defining sets. For example, for Steiner triple systems on 3 ⁿ points, we construct minimal defining sets of volumes varying by as much as 7 ⁿ⁻² . Received: September 16, 2000 Final version received: September 13, 2001 RID="*" ID="*" Research supported by the Australian Research Council A49937047, A49802044     

Potentiometric membrane sensors based on zirconyl(IV) phthalocyanine for detection of sulfosalicylic acid

A metallophthalocyanine complex with zirconium(IV) ion in the center (as an oxo-zirconium, Zr=O, group) was used in poly vinyl chloride (PVC) membranes for the selective detection of 5-sulfosalicylic acid (SSA). The resulting electrodes demonstrate Nernstian responses over a wide range of sulfosalicylic acid concentration (10⁻⁶ to 10⁻¹ mol dm⁻³) with a slope of about −29 mV per decade. The influence of lipophilic ion-exchanger sites on the response properties of the electrodes was investigated. The optimal potentiometric response was observed for the electrode in the presence of about 150 mol% of cationic additive (relative to ionophore) in the phase membrane. The electrodes have a fast response time, micromolar detection limit and good long-term stability (more than 2 months). The feasibility of the application of these sensors for the potentiometric titration of iron in solutions that were prepared from magnetite samples was investigated.     

Amperometric Detection of Dopamine in the Presence of Ascorbic Acid Using a Nafion Coated Glassy Carbon Electrode Modified with Catechin Hydrate as a Natural Antioxidant

Catechin hydrate (trans-3,3,4,5,7-penta-hydroxyflavone) is a derivative of catechol, and it is one of the natural antioxidant and anticarcinogenic compounds found in many fruits and agricultural foods. A new electrode was prepared by electrodeposition of a catechin-hydrate film on the surface of an activated glassy carbon electrode, followed by coating with nafion layer. Cyclic voltammetry was used for the deposition process, and the resulting modified electrode was found to retain the activity of the quinone/hydroquinone group anticipated for a surface-immobilized redox couple. The cyclic voltammograms of the modified electrode indicated that the surface-confined catechin-hydrate was strongly dependent on the solution pH. The electrochemical behaviour and stability of the modified electrode were studied by cyclic voltammetry. The apparent charge transfer rate constant (k _s ) and electron transfer coefficient () between the electrode surface and adsorbed catechin hydrate were calculated as 0.41 and 0.31s^z–1 0.31, respectively. The modified electrode exhibits an electrocatalytic effect on dopamine oxidation in the pH range of 2 to 7. The modified electrode was used for the electrocatalytic oxidation of dopamine in the presence of ascorbic acid and the elimination of the interference by ascorbic acid (AA) when present in a 200-fold concentration excess. A very large decrease (400mV) in the overpotential for the oxidation of dopamine and current increase were observed on the surface of the modified electrode. Dopamine was determined amperometrically at the modified electrode in the concentration range of 100nM to 0.1mM. The detection limit (signal to noise is 3) and sensitivity are 11nM and 16nA/µM, respectively. The modified electrode was employed to determine DA in biological mediums.     

Catalytic oxidation of thiols at preheated glassy carbon electrode modified with abrasive immobilization of multiwall carbon nanotubes: applications to amperometric detection of thiocytosine, l-cysteine and glutathione

The performance of preheated glassy carbon electrode modified with carbon nanotubes is described. First glassy carbon electrode is heated for 5 min at 50 °C, then abrasive immobilization of multiwall carbon nanotubes on a preheated glassy carbon electrode was achieved by gentle rubbing of electrode surface on a filter paper supporting carbon nanotubes. Carbon nanotubes (CNTs)-modified glassy carbon electrodes exhibit strong and stable electrocatalytic response toward thiols oxidation in wide pH range. These properties permit an important decrease in over voltage for the oxidation of thiocytosine, glutathione and l-cysteine, as well as a dramatic increase in the peak currents in comparison with bare glassy carbon electrode. Furthermore, the thiols amperometric response of the coated electrodes is extremely stable, with more than 95% of the initial activity after 30 min stirring of 0.1 mM thiols. The electrocatalytic behavior is further exploited as a sensitive detection scheme for thiols detection by hydrodynamic amperometry. The substantial decrease in the overvoltage of the thiols oxidation associated with a stable amperometric response and antifouling properties of nanotubes films allow the development of highly sensitive thiols sensor without using any redox mediator. Such ability of carbon nanotubes to promote the thiols electron transfer reaction, short response time (5 s) and long-term stability, low detection limit, extended linear concentration range, high sensitivity suggest great promise for thiols amperometric sensors and detector for chromatographic analysis of thiol derivatives.     

Enhancement of the analytical properties and catalytic activity of a nickel hexacyanoferrate modified carbon ceramic electrode prepared by two-step sol-gel technique: application to amperometric detection of hydrazine and hydroxyl amine

The electroless sol-gel technique was used for the construction of nickel hexacyanoferrat (NiHCF) modified carbon composite electrodes (CCEs).This involves two steps: formation of a carbon ceramic electrode fabricated by nickel powder and then immersing the electrode into a sodium- hexacyanoferate solution for the immobilization of NiHCF films. The cyclic voltammety of the resulting modified CCEs prepared under optimum conditions, shows a well defined surface redox couple due to the [Ni^IIFe^III/II(CN)₆]^−2/−1 system. The effect of different alkali metal cations in supporting electrolyte on the behavior of the modified electrode were studied. The charge transfer coefficient (α) and charge transfer rate constant (k_s) for modified films were calculated. Hydrazine and hydroxylamine have been chosen as a model to elucidate the electocatalytic ability and analytical parameters of NiHCF modified CCE prepared by one and two-step sol-gel techniques and these compounds determined amperometically at the surface of modified electrodes. The latter shows a good electocatalytic activity towards the oxidation of hydrazine and hydroxylamine in the pH range 3-8 in comparison with CCEs modified by homogeneous mixture of graphite powder, Ni(NO₃)₂ and Na₂[Fe(CN)₆], (one-step sol-gel technique). Furthermore, the catalytic rate constant, linear dynamic range, limit of detection, and sensitivity for hydrazine and hydroxylamine detections were evaluated and compared with CCEs prepared with one-step sol-gel method. The modified CCEs containing NiHCF shows good repeatability, short response time, t 90%<3 s, long term stability (3 months) and excellent catalytic activity. Furthermore, the method of preparation is rapid and simple and the modified electrodes are renewed by simple mechanical polishing and immersing in [Na₃Fe(CN]₆] solution.     

Manganese Oxide Nanoparticles/Reduced Graphene Oxide as Novel Electrochemical Platform for Immobilization of FAD and its Application as Highly Sensitive Persulfate Sensor

In this study, manganese oxide nanoparticles/reduced graphene oxide(MnOxNPs/rGO) was used as support for strong immobilization of flavin adenine dinucleotide(FAD). A thin film of rGO cast on the electrode surface, followed by performing electrodeposition of MnOxNPs at applied constant potential of +1.4 V vs. Ag/AgCl for 200 s. Finally, FAD was electrodeposited onto the rGO/MnOxNPs film by potential cycling between 1.0 to ?1.0 V in solution containing 1 mg ml^?1 FAD. Electrochemical properties and catalytic activity of GCE/rGO‐MnOxNPs/FAD toward persulfate (S₂O₈^2?) reduction was investigated. Under optimized condition, the concentration calibration range, detection limit, and sensitivity were 0.1 μM–2 mM, 90 nM and 125.8 nA/μM, respectively, using hydrodynamic amperometry technique.     

Biological synthesis and characterization of gold nanoparticles using Verbascum speciosum Schrad. and cytotoxicity properties toward HepG2 cancer cell line

Research on Chemical Intermediates - Gold nanoparticles (AuNPs) are considered as one of the best modes of drug releasing plans for the treatment of various diseases. AuNPs have different...     

Phase-Transition Thermal Charging of a Channel-Shape Thermal Energy Storage Unit: Taguchi Optimization Approach and Copper Foam Inserts

Thermal energy storage is a technique that has the potential to contribute to future energy grids to reduce fluctuations in supply from renewable energy sources. The principle of energy storage is to drive an endothermic phase change when excess energy is available and to allow the phase change to reverse and release heat when energy demand exceeds supply. Unwanted charge leakage and low heat transfer rates can limit the effectiveness of the units, but both of these problems can be mitigated by incorporating a metal foam into the design of the storage unit. This study demonstrates the benefits of adding copper foam into a thermal energy storage unit based on capric acid enhanced by copper nanoparticles. The volume fraction of nanoparticles and the location and porosity of the foam were optimized using the Taguchi approach to minimize the charge leakage expected from simulations. Placing the foam layer at the bottom of the unit with the maximum possible height and minimum porosity led to the lowest charge time. The optimum concentration of nanoparticles was found to be 4 vol.%, while the maximu possible concentration was 6 vol.%. The use of an optimized design of the enclosure and the optimum fraction of nanoparticles led to a predicted charging time for the unit that was approximately 58% shorter than that of the worst design. A sensitivity analysis shows that the height of the foam layer and its porosity are the dominant variables, and the location of the porous layer and volume fraction of nanoparticles are of secondary importance. Therefore, a well-designed location and size of a metal foam layer could be used to improve the charging speed of thermal energy storage units significantly. In such designs, the porosity and the placement-location of the foam should be considered more strongly than other factors.