Algorithms for calculation of the transport tensor components in the generalized first collision probability method

The first collision probability (FCP) method allows generalization by introducing several angular modes in each zone. Algorithms are proposed for calculating the components of the corresponding first collision tensor. These algorithms do not increase the computational complexity beyond that of the matrix calculation algorithm in the traditional FCP method and allow calculating a system described in terms of combinatorial geometry. Fourfold integrals are numerically taken in calculation of a three-dimensional system and twofold integrals are taken for two-dimensional geometry. The geometrical capabilities are ensured by using the standard geometrical module of the Monte Carlo method.     

水下目标回波特性计算的图形声学方法

根据Kirchhoff近似公式建立了一种水下目标回波特性实时工程预报的新方法-可视化图形声学计算方法GRACO (Graphical Acoustics Computing)。该方法利用三维图形处理系统,采用建模软件对水下复杂目标进行几何建模,并基于OpenGL技术把几何模型转化为屏幕上目标的可视化像素图形,获取像素中包含的目标表面法向量和空间距离信息,最后通过把回波特性预报中的面积分转化为屏幕上可视化图形的像素求和计算,完成水下目标回波特性预报。计算结果表明图形声学方法有较高的精度,计算速度比板块元方法快9~10倍。     

Preliminary study on CAD-based method of characteristics for neutron transport calculation

Our new method makes use of a CAD-based automatic modeling tool, MCAM, for geometry modeling and ray tracing of particle transport in method of characteristics （MOC）. It was found that it could considerably enhance the capability of MOC to deal with more complicated models for neutron transport calculation. In our study, the diamond-difference scheme was applied to MOC to reduce the spatial discretization errors of the fiat flux approximation. Based on MCAM and MOC, a new 2D MOC code was developed and integrated into the SuperMC system, which is a Super Multi-function Computational system for neutronics and radiation simulation. The numerical results demonstrated the feasibility and effectiveness of the new method for neutron transport calculation in MOC.     

Preliminary study on CAD-based method of characteristics for neutron transport calculation

Our new method makes use of a CAD-based automatic modeling tool, MCAM, for geometry modeling and ray tracing of particle transport in method of characteristics (MOC). It was found that it could considerably enhance the capability of MOC to deal with more complicated models for neutron transport calculation. In our study, the diamond-difference scheme was applied to MOC to reduce the spatial discretization errors of the flat flux approximation. Based on MCAM and MOC, a new 2D MOC code was developed and integrated into the SuperMC system, which is a Super Multi-function Computational system for neutronics and radiation simulation. The numerical results demonstrated the feasibility and effectiveness of the new method for neutron transport calculation in MOC.     

Numerical calculation of soft-X ray transition probability for the muffin-tin potential

The matrix elements of the coordinate, the momentum and the gradient of the potential were used to calculate the optical transition probability between the valence and core states, obtained for the muffin-tin model of the crystal potential. It has been found that gradV is the most suitable form for the numerical calculation while the other forms can yield substantial errors for both transition and simple metals when the core energy amounts few Rydbergs and the amplitude of the core function reaches at the muffin-tin radius 10^–3-10^–2 of its maximum value.     

The probability of multiphoton processes

Russian Physics Journal -     

On the calculation of memory functions for nonlinear irreversible processes

A linear inhomogeneous Volterra integral equation for the memory functions of the nonlinear theory of irreversible processes is derived. No projection operator is involved. Recursion relations for the solution of the integral equation are given. If the kernels are expanded about equilibrium, the exact linear and nonlinear Onsager coefficients are obtained.     

Orthogonal polynomial expansion of Pearson's probability densities for non-Markov processes

Expansions of Pearson's conditional and two-dimensional probability densities are obtained for non-Markov processes in orthogonal Hermite, Laguerre, and Jacobi polynomials.Ryazan State Radio-Engineering Academy. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 12, pp. 1559–1566, December, 1994.     

On the Taylor expansion of the expression for the transition probability for normal absorption processes

Molecular reorientation of 2-chloropyrimidine dissolved in CS₂ (0·1 M) has been investigated by means of ¹³C and proton relaxation. Although weakly coupled, the proton system subjected to non-selective 180-τ-90 pulse sequences allows the determination of one autocorrelation and one cross-correlation dipolar spectral density. The proton and carbon-13 relaxation data allow the complete determination of the rotational diffusional tensor:

and

It is shown that scalar relaxation due to nitrogen-14, has no effect on proton longitudinal relaxation time, because of a cross term due to the symmetry of the molecule, although this mechanism could, a priori, have been thought to be important. Finally, the nitrogen relaxation time recalculated with D_xx , D_yy , D_zz and the quadrupolar coupling tensor is in agreement with the observed linewidth.     

倒易点阵与晶面指数的关系

倒易点阵的概念和性质可以在没有任何假定的情况下很自然地从晶面指数的定义导出.这和流行教科书中分开定义的办法相比,简单而不易引起混乱.     

Direct calculation of the probability of pionium ionization in the target

The goal of the DIRAC experiment at CERN is the lifetime measurement of pionium (π ⁺ π ⁻ atom). Its lifetime is mainly defined by the charge-exchange process π ⁺ π ⁻ → π ⁰ π ⁰. The value of the lifetime in the ground state is predicted in the framework of chiral perturbation theory with high precision: τ _1S = (2.9 ± 0.1) × 10⁻¹⁵ s. The method used by DIRAC is based on analysis of π ⁺ π ⁻-pair spectra with small relative momenta in their center-of-mass system in order to find out the signal from pionium ionization (breakup) in the target. Pioniums are produced in proton-nucleus collisions and have relativistic velocities (γ > 10). For fixed values of the pionium momentum and the target thickness, the probability of pionium ionization in the target depends on its lifetime in a unique way; thus, the pionium lifetime can be deduced from the experimentally defined probability of pionium ionization. On the basis of ionization cross sections of pionium with target atoms, we perform the first direct calculation of the pionium ionization probability in the target. The text was submitted by the author in English     

On the calculation of functionals from Wiener processes

The procedure of calculating some functionals of Wiener processes is suggested.