An extension of the Krylov method for calculating the coefficients of the minimal polynomial

The concept of a k-minimal polynomial of an operator is introduced, and a method for approximate calculation of the coefficients of this polynomial is proposed. The method uses the calculated values of certain functionals on iterations of the operator. Special features emerging when the algorithm is used in combination with the Monte Carlo method are discussed, and numerical results are given.     

Characteristics of a photovoltaic X-ray detector based on a GaAs epitaxial structure

The characteristics of a photovoltaic X-ray detector based on the GaAs p ⁺-n-n′-n ⁺ epitaxial structure grown using gas-phase epitaxy are studied. Typical current-voltage and capacitance-voltage characteristics of the epitaxial structures are analyzed together with the built-in electric field profile in the n-GaAs depleted region. The efficiency of charge accumulation in the photovoltaic detector is measured for zero bias and for a bias voltage of 17 V. It is shown that the GaAs-based photovoltaic X-ray detector can operate with zero bias voltage at room temperature. The sensitivity of the detector is measured as a function of the effective energy of X-rays and the angle of incidence of X-ray photons.     

Mechanism of the solvent effect on the rate of the cyclohexene hydroxymethoxycarbonylation catalyzed by bis(triphenylphosphine)palladium

Kinetic data of the cyclohexene hydroxymethoxycarbonylation catalyzed by bis(triphenylphosphine) palladium Pd(PPh₃)₂ were processed and considered on the basis of the quantum-chemical calculations. By the method of density functional DFT PBE/3z we found that among the possible catalyst moleculs based on the tetrakis(triphenylphosphine)palladium the most stable is Pd(PPh₃)₂ with the coordination number of palladium equal 2. The interaction energy of Pd(PPh₃)₂ with acetone, acetonitrile, dichloroethane, 1,4-dioxane, nitromethane, and tetrahydrofuran calculated by PM3 method was found to correlate linearly with the reaction rate logarithm. The mechanism of the solvent effect on the reaction rate consists in a specific complexation with the catalyst depending on the molecule rigidity and the creation of energetic and steric constraints for the substrate to access the catalyst.     

Combined grid-characteristic method for the numerical solution of three-dimensional dynamical elastoplastic problems

A combined method blending the advantages of smoothed particles hydrodynamics (SPH) and the grid-characteristic method (GCM) is proposed for simulating elastoplastic bodies. Various grid methods, including the GCM, have long been used for the numerical simulation of elastoplastic media. This method applies to the simulation of wave processes in elastic media, including elastic impacts, in which case an advantage is the use of moving tetrahedral meshes. Additionally, fracture processes can be simulated by applying various fracture criteria. However, this is a technically complicated task with the accuracy of the results degrading due to the continual updating of the grid. A more suitable approach to the simulation of processes involving substantial fractures and deformations is based on SPH, which is a meshless method. However, this method also has shortcomings: it produces spurious modes, and the simulation of oscillations requires particle refinement. Thus, two families of methods are available that are optimal as applied to two different groups of problems. However, a realworld problem can frequently be a mixed one, which requires a substantial tradeoff in the numerical methods applied. Aimed at solving such problems, a combined GCM-SPH method is developed that blends the advantages of two constituting techniques and partially eliminates their shortcomings.     

Semiconductor ring laser subject to delayed optical feedback: Bifurcations and stability

We study semiconductor ring lasers subject to delayed optical feedback from one or two short external cavities. In case of two cavities we consider the feedback strengths and phases to be either symmetric or asymmetric feedback. When feedback is symmetric, the laser operates in a bi-directional continuous wave or periodic regime for most parameter values. Only for some small parameter regions complex dynamics, such as quasi-periodicity and chaos are obtained. When the feedback is asymmetric complex dynamical regimes, including chaos, are obtained in large parameter regions. We explain complex dynamical regimes obtained in both symmetric and asymmetric feedback cases by linear stability of the stationary solutions calculated using DDE-BIFTOOL.     

Determination of iron(III) ions in aqueous solutions by secondary-emission mass spectrometry

Model aqueous solutions containing micro impurities of iron(III) are studied by secondary-emission mass spectrometry. The possibility of using this method for the analysis of rain deposits and samples of atmospheric aerosols is discussed.     

Application of numerical methods for the calculation of size distribution functions of polymers produced by ionic polymerizations

The application of numerical methods for the calculation of the molecular weight distribution of living ionic polymerization, carried out in the presence of monofunctional and polyfunctional transfer agents, is described. The methods used include the numerical solution of a system of differential equations by the Runge-Kutta-Merson procedure and the statistical Monte-Carlo approach. When a monofunctional transfer agent is used, the Runge-Kutta-Merson procedure is quite useful for the calculation of the molecular weight distribution for various polymerization systems. When a polymerization is carried out in the presence of a polyfunctional transfer agent, the mechanism includes the coupling of polymer chains. Due to the complexity of the system, the Runge-Kutta-Merson procedure is hardly applicable and problems of this type should be solved by a Monte Carlo simulation procedure. Once a computer program has been written, both methods allow the chemist to calculate the molecular weight distribution of a polymer as a function of the different kinetic parameters of the polymerization.