An analysis of nonlinear ion transport problem including arbitrary valences of oxidized and reduced species

The nonlocal identification problem related to nonlinear ion transport model including diffusion and migration is studied. Ion transport is assumed to be superposition of diffusion and migration under the influence of an electric field. Mathematical modeling of the experiment leads to an identification problem for a strongly nonlinear parabolic equation with nonlocal additional condition. It is shown that the nonlocal identification problem can be reduced to the initial-boundary value problem for nonlinear parabolic equation. Iteration method for numerical solution of this problem is proposed. Numerical results and their interpretation are presented for wide class of materials, including various values of valences and diffusivities of oxidized and reduced species.     

An analysis of nonlinear ion transport model including diffusion and migration

The nonlocal identification problem related to nonlinear ion transport model including diffusion and migration is studied. Ion transport is assumed to be superposition of diffusion and migration under the influence of an electric field. Mathematical modeling of the experiment leads to an identification problem for a strongly nonlinear parabolic equation with nonlocal additional condition. Uniqueness of the nonlinear direct problem solution, and its continuity with respect to the total charge function is proved. An existence of a quasisolution of the identification problem is proved in the class of derived admissible coefficients. The nonlinear finite difference approximation of this problem, with an appropriate iteration algorithm, is derived. Numerical solutions of the identification problem are presented for various values of valences and diffusivities of oxidized and reduced oxidized species. The obtained results permits one to derive behaviour of the concentration and total charge depending on physical parameters.     

The measurement of average hydrodynamic velocity in capillary zone electrophoresis

Summary Based on the linear relationship between large sample injection time during hydrodynamic injection and migration time in non-stacking runs, a new method is proposed to measure average hydrodynamic velocity in capillary zone electrophoresis (CZE). Only the migration times for large injections need to be measured in this new approach, so the method is simple. Additionally, a modified Poiseuille equation is proposed to eliminate the deviation involved in Poiseuille’s equation. The average hydrodynamic velocity values determined by our method generally compare favorably with those determined by the modified Poiseuille equation.     

Relationship between current response and time in ion transport problem including diffusion and convection. 2. Numerical approach

The mathematical model related to controlled potential experiments in electrochemistry is studied. Ion transport is regarded as the superposition of diffusion and migration under the influence of an electric field. Modeling of the experiment leads to the nonlocal identification problem for nonlinear parabolic equation. It is shown that in some cases the nonlocal identification problem can be transformed to an initial value problem for nonlinear parabolic equation. The finite diference approximation of this problem, with the appropriate iteration algorithm, is derived. Based on these algorithms the solution of the identification problem is presented. The obtained results permits one to derive the behaviour of the current response , depending on time, also the relationship between the current response and Gottrellian is obtained in explicit form. An influence of the valences oxidised and reduced species is also analyzed.      

Wick’s theorem and reconstruction schemes for reduced density matrices

We first obtained a closed form of the Wick’s theorem expressed in Grassman wedge product, which is similar to a binomial expansion. With this new expansion, new reconstruction schemes for reduced density matrices are derived rigorously. The higher order reduced density matrices are systematically decomposed into a sum of the lower order reduced density matrices which could be used to solve the contracted Schr?dinger equation.     

Alternatives to Bazley’s special choice for eigenvalue lower bounds

Bazley’s special choice operator is a lesser operator to a positive perturbation of a self-adjoint semi-bounded operator that possesses an exactly soluble base eigenvalue problem. It allows the construction of an exactly soluble intermediate problem that gives eigenvalues not less than the base problem and not greater than the perturbed problem so that lower bounds to the eigenvalues of the perturbed operator are produced. This paper considers alternate derivations of Bazley’s special choice which lead to two alternate methods to determine eigenvalue lower bounds. One is simpler, but gives poorer bounds; the other is more difficult, but sometimes yields superior bounds. Lower bounds to the particle in a box model with a linear perturbation and lower bounds to the helium atom are calculated using the two methods introduced and are compared to those given with Bazley’s special choice.      

Analytical formulaes and comparative analysis for linear models in chronoamperometry under conditions of diffusion and migration

Mathematical models of ion transport in a potential field are analyzed. Ion transport is regarded as the superposition of diffusion and migration. The explicit analytical formulaes are obtained for the concentration of the reduced species and the current response in the case of pure diffusive as well as diffusion–migration model, for various initial conditions. The comparitive analysis of these formulaes for current responses and deviation from the classical Cottrellian are derived. The proposed approach can predict an influence of ionic diffusivities, valences, initial and boundary concentrations to the behaviour of current response. In addition to these, the analytical formulaes obtained can also be used for numerical and digital simulation methods for Nernst-Planck equations.     

Haar wavelet method for solving some nonlinear Parabolic equations

Wavelet transform or wavelet analysis is a recently developed mathematical tool in applied mathematics. In this paper, we develop an accurate and efficient Haar transform or Haar wavelet method for some of the well-known nonlinear parabolic partial differential equations. The equations include the Nowell-whitehead equation, Cahn-Allen equation, FitzHugh-Nagumo equation, Fisher’s equation, Burger’s equation and the Burgers-Fisher equation. The proposed scheme can be used to a wide class of nonlinear equations. The power of this manageable method is confirmed. Moreover the use of Haar wavelets is found to be accurate, simple, fast, flexible, convenient, small computation costs and computationally attractive.     

Characteristic polynomials of linear polyacenes and their subspectrality

Coefficients of characteristic polynomials (CP) of linear polyacenes (LP) have been shown to be obtainable from Pascal’s triangle by using a graph factorisation and squaring technique. Strong subspectrality existing among the members of the linear polyacene series has been shown from the derivation of the CP’s. Thus it has been shown that the entire eigenspectrum of ann-ring LP is included in that of (2n + 1)-ring LP. Correspondence between the eigenspectra of linear chains and LP’s is brought out by a recently developed vertex-alternation and squaring algorithm.     

Dynamics of electron hopping in redox polymer electrodes using kinetic Ising model

The analysis of diffusion-migration equations pertaining to electron hopping and physical displacement in redox polymer electrodes is carried out using kinetic Ising model formalism. It is shown that, by the appropriate choice of transition probabilities obeying detailed balancing conditions, a hierarchy of transport equations can be derived. Earlier transport equations due to Nernst-Planck and Savéant are derived as special cases. The dependence of apparent diffusion coefficient on number density of redox centres, polymer morphology etc. are pointed out. Several new insights concerning the microscopic basis underlying the hitherto known phenomenological equations are demonstrated. Received: 27 May 1997 / Accepted: 24 July 1997     

Consequences of Holba-Šesták equation

It was proved on the basis of Holba-Šesták equation (1972) that the one is very interesting point of view to define the relative rate of reaction/process. Thereby, the assumption about interconnection between three-parametric equation and thermodynamic condition determined by equilibrium conversion degree in given temperature, is strengthened. Further considerations, still based on analysis of the inequality, made possible proposition of thesis about maximal rate of reaction/process in dynamic conditions in relation to modified van’t Hoff’s isobar (equation).     

Spectral shift function and trace formula

The complete proofs of Krein’s theorem on the spectral shift function and the trace formula are given for a pair of self-adjoint operators such that either (i) their difference is trace-class or (ii) the difference of their resolvents is trace-class. The proofs, essentially due to Krein, is based on Herglotz’s theorem on the boundary value of the analytic functions whose imaginary part is non-negative on the upper half plane, and an almost optimal class of functions are obtained for which the trace formula is valid. Also an alternative method based on Weyl-von Neumann’s theorem for self-adjoint operators, avoiding the complex function theory and inspired by Voiculescu’s work, is given for the first case. Furthermore, some applications of the spectral shift function have been discussed.     

Thermoanalytical study of fluoxetine hydrochloride

The thermal decomposition of two inclusion compounds Mn(HCOO)₂·1/3C₄H₈O₂ and Mn(HCOO)₂·1/3C₄H₈O was studied in the inert atmosphere. The process of both dioxane, and tetrahydrofurane removal has two steps; the intermediate phase is unstable and kinetically hindered. Manganese formate is stable up to 330°C. Thermogravimetric data (obtained at different rates of linear heating) were processed with computer program (with ‘Model free’ approach). Kinetic parameters were calculated for the first decomposition step, and the process is described by equation of n-order reaction with autocatalysis.     

Detection of ligand binding hot spots on protein surfaces via fragment-based methods: application to DJ-1 and glucocerebrosidase

The identification of hot spots, i.e., binding regions that contribute substantially to the free energy of ligand binding, is a critical step for structure-based drug design. Here we present the application of two fragment-based methods to the detection of hot spots for DJ-1 and glucocerebrosidase (GCase), targets for the development of therapeutics for Parkinson’s and Gaucher’s diseases, respectively. While the structures of these two proteins are known, binding information is lacking. In this study we employ the experimental multiple solvent crystal structures (MSCS) method and computational fragment mapping (FTMap) to identify regions suitable for the development of pharmacological chaperones for DJ-1 and GCase. Comparison of data derived via MSCS and FTMap also shows that FTMap, a computational method for the identification of fragment binding hot spots, is an accurate and robust alternative to the performance of expensive and difficult crystallographic experiments.     

Surface treatment of zinc by Schiff’s bases and its corrosion study

The zinc metal surface is chemically modified by newly synthesized Schiff’s bases and its corrosion protection is investigated. The influence of concentration of Schiff’s bases on modification of zinc surface and immersion time in treatment bath are investigated and optimized for maximum corrosion protection efficiency. The electrochemical studies of treated zinc specimens are performed in aqueous acid solution using galvanostatic polarization technique. The treated zinc samples show good corrosion resistance. The recorded electrochemical data of chemically treated samples indicate a basic modification of the zinc surface. The protection efficiency of organic layer formed on zinc surface is tested by varying the acid concentration and temperature of the corrosive medium. The corrosion protection efficiency increases with the concentration of Schiff’s bases and immersion time. This is due to a strong interaction between zinc and the organic molecules, which results in the formation of a protective layer. This layer prevents the contact of aggressive medium with the zinc surface. The surface modification is confirmed by the scanning electron microscopy images. The interaction between metal atoms and Schiff’s bases is also established by IR studies. Published in Russian in Elektrokhimiya, 2007, Vol. 43, No. 7, pp. 886–892. The text was submitted by the authors in English.     

Adaptive approach for nonlinear sensitivity analysis of reaction kinetics

We present a unified approach for linear and nonlinear sensitivity analysis for models of reaction kinetics that are stated in terms of systems of ordinary differential equations (ODEs). The approach is based on the reformulation of the ODE problem as a density transport problem described by a Fokker-Planck equation. The resulting multidimensional partial differential equation is herein solved by extending the TRAIL algorithm originally introduced by Horenko and Weiser in the context of molecular dynamics (J. Comp. Chem. 2003, 24, 1921) and discussed it in comparison with Monte Carlo techniques. The extended TRAIL approach is fully adaptive and easily allows to study the influence of nonlinear dynamical effects. We illustrate the scheme in application to an enzyme-substrate model problem for sensitivity analysis w.r.t. to initial concentrations and parameter values.     

Comparison of the boundary theory with the contact rule of phase regions and Gupta’s method

The phase boundary theory and the contact rule of phase regions are compared, and some weaknesses of the latter are manifested. The comparison between the Gupta’s method and the boundary theory method for constructing multicomponent isobaric sections is also presented.