Stochastic theory of direct simulation Monte Carlo method

A treatment of direct simulation Monte Carlo method as a Markov process with a master equation is given and the corresponding master equation is derived. A hierarchy of equations for the reduced probability distributions is derived from the master equation. An equation similar to the Boltzmann equation for single particle probability distribution is derived using assumption of molecular chaos. It is shown that starting from an uncorrelated state, the system remains uncorrelated always in the limit N→∞, where N is the number of particles. Simple applications of the formalism to direct simulation money games are given as examples to the formalism. The formalism is applied to the direct simulation of homogenous gases. It is shown that appropriately normalized single particle probability distribution satisfies the Boltzmann equation for simple gases and Wang Chang–Uhlenbeck equation for a mixture of molecular gases. As a consequence of this development we derive Birds no time counter algorithm. We extend the analysis to the inhomogeneous gases and define a new direct simulation algorithm for this case. We show that single particle probability distribution satisfies the Boltzmann equation in our algorithm in the limit N→∞, V _k →0, Δt→0 where V _k is the volume of kth cell. We also show that our algorithm and Bird’s algorithm approach each other in the limit N _k →∞ where N _k is the number of particles in the volume V _k .     

Theoretical investigation of the optical and EPR parameters for VOion in some complexes

The molecular orbital coefficients and the EPR parameters of trisodium citrate dihydrate, sodium hydrogen oxalate monohydrate, potassium d-gluconate monohydrate and L-Alanine vanadyl complexes are calculated theoretically. Two d-d transition spectra and EPR parameters for the VO²⁺ complex are calculated theoretically by using crystal-field theory. The calculated g and A paramaters have indicated that paramagnetic center is axially symmetric. Having the relations of g_∥〈g_⊥〈g_e and A_∥〉A_⊥ for VO²⁺ ions, it can be concluded that VO²⁺ ions are located in distorted octahedral sites (C_4v) elongated along the z-axis and the ground state of the paramagnetic electron is d_xy.     

Two photon absorption characteristics of bulk GaTe crystal

We have investigated the structural and optical properties of bulk GaTe crystal grown by vertical Bridgman method. Two photon absorption (TPA) properties of GaTe crystal have been investigated by the open aperture Z-scan technique under 1064 nm wavelength with 4 ns or 65 ps pulse durations. The TPA coefficients are greater in ns regime than that of ps regime. Upon increasing intensity of incident light from 5.02×10⁷ W/cm² to 1.07×10⁸ W/cm², the TPA coefficients increased from 3.47×10^?6 cm/W to 8.53×10^?6 cm/W for nanosecond excitation. Similarly, when intensity of incident light was increased from 6.81×10⁸ W/cm² to 9.94×10⁸ W/cm² the TPA coefficients increased from 3.53×10^?7 cm/W to 6.83×10^?7 cm/W for picosecond excitation. Measured TPA coefficient of GaTe crystal is larger than that of GaSe and GaS layered crystals.     

Influence of ion implantation on structural and photoconductive properties of Bridgman grown GaSe single crystals

The structure and temperature dependent spectral photoconductivity of as‐grown and N‐and Si‐implanted GaSe single crystals have been studied. It was observed that post‐annealing results in a complete recovery of the crystalline nature that was moderately reduced upon implantation. The band edge is shifted in the implanted sample which is attributed to the structural modifications and continuous shallow levels introduced upon implantation and annealing. Our calculations showed that the trap density is increased upon implantation and annealing which confirms a possibility of explanation the phenomenon within a framework of continuous trap levels. Photocurrent measurements as a function of photo‐excitation intensity also support continuous distribution of localized states in the band gap. © 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Reactions of some pyrrole‐2,3‐diones with hydrazine hydrate and o‐phenylenediamine

2,3‐Dihydro‐1H‐pyrrole‐2,3‐diones 1a‐d react with hydrazine hydrate 2 and o‐phenylenediamine 4 under different conditions to yield the pyrazole‐3‐carboxamide derivatives 3a‐d , the pyrrol‐2‐ones 5a‐d and the quinoxaline‐2‐one derivatives 6a‐d , respectively. Hydrolysis of the quinoxaline‐2‐one derivatives 6a‐d gave a substituted furo[2,3‐b]quinoxaline 7 . The structures of the synthesized compounds were assigned on the basis of analytical results as well as spectroscopic data.     

Synthesis of 4-hydroxy-4,5-dihydro-1,2,4-triazol-5-ones

Summary A series of hydroxamic acid ethoxycarbonylhydrazides was obtained by reactions of ester ethoxycarbonylhydrazones with hydroxylamine. The corresponding 3-substituted 4-hydroxy-4,5-dihydro-1,2,4-triazol-5-ones were synthesized by cyclization of these hydroxamic acid derivatives in basic medium.

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Synthesen von 4-Hydroxy-4,5-dihydro-1,2,4-triazol-5-onen

Zusammenfassung Durch Reaktion von Esterethoxycarbonylhydrazonen und Hydroxylamin wurde eine Reihe von Hydroxamsäureethoxycarbonylhydraziden gewonnen; Cyclisierung dieser Verbindungen durch Base gab die entsprechenden 3-substituierten 4-Hydroxy-4,5-dihydro-1,2,4-triazol-5-one.

     

Electrical and optical properties of Co doped TlGaS2 crystals

In this study, Co doped TlGaS₂ single crystals which belongs to the class of A^IIIB^IIIX₂^VI have been investigated by means of XRD, temperature dependent dark and illuminated conductivity, Space Charge Limited Currents and absorption measurements. The room temperature conductivity and trap concentration values were about 10^‐8 (Ω‐cm)^‐1 and 7.5 × 10¹³ cm^‐3, respectively. From the temperature dependent conductivity measurements, two activation energies namely 271 and 12 meV have been determined in the high and low temperature regions, respectively. The trap level at 271 meV that was determined by the dark temperature dependent conductivity measurement has also been verified by Space Charge Limited Currents analysis. The absorption measurements have showed that the layered compound had indirect and direct band gaps and the values were determined to be 2.49 and 2.56 eV, respectively. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Computation of the Macroscopic Tangent for Multiscale Volumetric Homogenization Problems

For the computation of the macroscopic tangent that is required in multiscale volumetric homogenization techniques, two methods are summarized. First, a condensation approach is followed where the linearity of variational terms associated with the penalty enforcement of boundary conditions is explored in order to extract a macroscopic tangent at any stage of the Newton–Raphson iterations of a microstructural testing procedure. As an alternative approach, a second method is explored that requires only the knowledge of infinitesimally close macroscopic deformation states. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)