Consistent relations in the method of reducibility in the cluster variation method

A redundancy is noted in the set of Lagrange multipliers—effective fields and effective interactions—used in the expressions of the reduced density matrices given by Morita⁽⁴⁾ in some problems with less symmetry⁽⁶⁾. The expressions of the reduced density matrices without this redundancy are given. An argument showing that a certain expression of the free energy in terms of the Lagrange multipliers is stationary with respect to the variations of these is presented.     

Autonomous models solvable through the full interval method

The most general exclusion single species one dimensional reaction-diffusion models with nearest-neighbor interactions which are both autonomous and can be solved exactly through full interval method are introduced. Using a generating function method, the general solution for F _n , the probability that n consecutive sites be full, is obtained. Some other correlation functions of number operators at nonadjacent sites are also explicitly obtained. It is shown that for a special choice of initial conditions some correlation functions of number operators called full intervals remain uncorrelated.     

Determining the antenna guidance accuracy by the radio-astronomical method

We study the possibilities of determining the antenna guidance accuracy based on radio-astronomical observation data and using two main assumptions, namely, that the variance of the measured signal increases with respect to the variance of a signal from the reference region when a discrete source of radiation is observed and that the distribution of measured points is nonsymmetric with respect to the mean value. We develop a model and numerically simulate the nonuniform motion of the antenna during the source tracking and study the influence of such a motion on characteristics of the received signals. Results of experimental verification of the proposed method are presented. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 1, pp. 1–8, January 2006.     

Canonical transformation method in classical electrodynamics

The solutions of Maxwell's equations in the parabolic equation approximation is obtained on the basis of the canonical transformation method. The Hamiltonian form of the equations for the field in an anisotropic stratified medium is also examined. The perturbation theory for the calculation of the wave reflection and transmission coefficients is developed.     

Extended discrete-ordinate method considering full polarization state

This paper presents an extension to the standard discrete-ordinate method (DOM) to consider generalized sources including: beam sources which can be placed at any (vertical) position and illuminate in any direction, thermal emission from the atmosphere and angularly distributed sources which illuminate from a surface as continuous functions of zenith and azimuth angles. As special cases, the thermal emission from the surface and deep space can be implemented as angularly distributed sources. Analytical-particular solutions for all source types are derived using the infinite medium Green's function. Radiation field zenith angle interpolation using source function integration is developed for all source types. The development considers the full state of polarization, including the sources (as applicable) and the (BRDF) surface, but the development can be reduced easily to scalar problems and is ready to be implemented in a single set of code for both scalar and vector radiative transfer computation.     

Invariant relations for kirchhoff equations and the Kowalewski method

The Kowalewski exponents in the problem on the motion of a solid under the Chaplygin condition are calculated (when there is a velocity-linear invariant relation). The method of calculation uses the generalizing Ioshida theorems on the Kowalewski exponents found by V.V. Kozlov. It is shown that the general solution of the equations of motion branches out in the complex time plane under the Chaplygin conditions.     

Determining H0 using a model-independent method

By using type Ia supernovae (SNIa) to provide the luminosity distance (LD) directly, which depends on the value of the Hubble constant H₀ = 100h km ? s^-1 ? Mpc^-1, and the angular diameter distance from galaxy clusters or baryon acoustic oscillations (BAOs) to give the derived LD according to the distance duality relation, we propose a model-independent method to determine h from the fact that different observations should give the same LD at a given redshift. Combining the Sloan Digital Sky Survey II (SDSS-II) SNIa from the MLCS2k2 light curve fit and galaxy cluster data, we find that at the 1σ confidence level (CL), h = 0:5867 ± 0:0303 for the sample of the elliptical β model for galaxy clusters, and h = 0:6199 ± 0:0293 for that of the spherical β model. The former is smaller than the values from other observations, whereas the latter is consistent with the Planck result at the 2σ CL and agrees very well with the value reconstructed directly from the H(z) data. With the SDSS-II SNIa and BAO measurements, a tighter constraint, h = 0:6683 ± 0:0221, is obtained. For comparison, we also consider the Union 2.1 SNIa from the SALT2 light curve fitting. The results from the Union 2.1 SNIa are slightly larger than those from the SDSS-II SNIa, and the Union 2.1 SNIa + BAOs give the tightest value. We find that the values from SNIa + BAOs are quite consistent with those from the Planck and the BAOs, as well as the local measurement from Cepheids and very-low-redshift SNIa.     

Four-nucleon force using the method of unitary transformation

We discuss in detail the derivation of the leading four-nucleon force in chiral effective field theory using the method of unitary transformation. The resulting four-nucleon force is given in both momentum and configuration space. It does not contain any unknown parameters and can be used in few- and many-nucleon studies.     

Random Baxter-Wu model: Duality relations and the replica method

Replica partition function for quenched bond disorder in a Baxter-Wu system is investigated. Its duality relations are obtained which yield exact values for the percolation concentration p_c. Arguments used by Domany and others for the bond-random Ising model are extended and refined and T_c(p) near p_c is calculated. Exact results for the equiconcentration case with arbitrary (positive) bonds J_A and J_B are also obtained. Finally, the possibility of a Baxter-Wu spin-glass is mooted and a qualitative estimate for its location is given.     

量子变换的李代数方法

利用李代数生成元构成幺正算符,对耦合玻色体系给出了一种简单的对角化方法.     

Determining the sum of flexoelectric coefficients in nematic liquid crystals by the capacitance method

A detailed theoretical analysis of determining the sum of flexoelectric coefficients in nematic liquid crystals using the capacitance method is given. In the strong anchoring parallel aligned nematic （PAN） and hybrid aligned nematic （HAN） cells, the dependences of the capacitance on the sum of flexoelectric coefficients and the applied voltage are obtained by numerical simulations, and the distributions of the director and the electric potential for different applied voltages and flexoelectric coefficients are also given. Based on this theoretical analysis, we propose an experimental design for measuring the capacitance of a liquid crystal cell using the improved precision LCR meter E4980A （Agilent）. Through comparing the experimental data with the simulated results, the sum of flexoeletric coefficients can be determined.     

Resonating group method and frequency transformation

A new technique for calculating the resonating-group-method (RGM) kernels is proposed by use of frequency transformations in order to treat cluster systems involving unequal oscillator frequencies. The present technique is useful for both analytical and numerical deviations of matrix elements of the RGM kernels. The eigenvalue problem of the norm kernel of the RGM is solved for a wide range of systems consisting of an α-particle and a closed-shell nucleus (¹⁶O, ⁴⁰Ca, ⁴⁸Ca, ⁵⁶Ni, ⁸⁰Zr, ⁹⁰Zr, ¹²⁰Sn, ¹⁴⁰Yb or ²⁰⁸Pb) with realistic oscillator frequencies. These eigenvalues and eigenfunctions are shown to have characteristic features. With these eigenvalues, α-particle reducedwidth amplitudes and spectroscopic factors of the ground states of ²⁰Ne, ⁴⁴Ti, ⁹⁴Mo, ¹²⁴Te and ²¹²Po are calculated by employing simple configurations of the harmonic-oscillator shell model. In heavy nuclei the results with realistic oscillator frequencies are shown to be very different from those with a common oscillator frequency. The effect of the spurious c.m. motion in the generator coordinate method is discussed.