Application of methods of the scattering theory in the statistical theory of liquids

This paper is devoted to the application of the projection methods of the nonrelativistic quantum theory of scattering (the method of Petrov-Bubnov-Galerkin (PBG) and the Bubnov-Galerkin (BG) method) in the statistical theory of liquids. By means of the projection PBG method we have found a new family of equations both for the correlation functions and for the radial distribution function (RDF). In the generalized equation for the RDF we have obtained new terms which are linear and quadratic in the density and the latter are absent in all the previous theories. By means of the projection BG principle the approximate eigenfunctions of the Liouville operator in a liquid were obtained as a linear combination of the Kihara functions. It was shown that the spectrum of the collective excitations is determined by the complex Fourier transformation of the force acting on an arbitrary particle in a liquid.     

Calculation of graviton scattering amplitudes using string-based methods

Techniques based upon the string organisation of amplitudes may be used to simplify field theory calculations. We apply these techniques to perturbative gravity and calculate all one-loop amplitudes for four-graviton scattering with arbitrary internal particle content. Decomposing the amplitudes into contributions arising from supersymmetric multiplets greatly simplifies these calculations. We also discuss how unitarity may be used to constrain the amplitudes.     

Experimental test of the numerical renormalization-group theory for inelastic scattering from magnetic impurities

We present measurements of the phase coherence time taupsi in quasi-one-dimensional Au/Fe Kondo wires and compare the temperature dependence taupsi of with a recent theory of inelastic scattering from magnetic impurities [Phys. Rev. Lett. 93, 107204 (2004)10.1103/PhysRevLett.93.107204]. A very good agreement is obtained for temperatures down to 0.2T(K). Below the Kondo temperature T(K), the inverse of the phase coherence time varies linearly with temperature over almost one decade in temperature.     

Two space scattering theory using the subspace of continuity

We study completeness of the wave operators between pairs of spaces not using the subspace of absolute continuity. Rather we work with the orthogonal complement of the eigenvectors, a subspace which is more natural from the viewpoint of physics. Moreover, we also give sufficient conditions that the singular continuous spectrum be absent. In this case the subspaces mentioned above coincide.     

Analytical and numerical methods in the theory of random wave processes

Summary This paper deals with the evaluation of a two-parameter, two-index, imaginary integral function . The motivation for this analysis arose from the application of stochastic process theory to random ocean wave properties. Physically represents the normalized cross spectrum between any two components of a random state vector whose components are defined by wave amplitude, vector particle velocity, vector particle acceleration and linearized vector hydrodynamic force on a submerged object. The function , however, is developed in a general fashion so as to be applicable to any two-dimensional random wave process. Numerical and analytical methods are employed to develop techniques for the evaluation of and sample graphs are presented.

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Riassunto Si valuta la funzione integrale immaginaria a 2 parametri e 2 indici necessaria per l’applicazione della teoria dei processi stocastici alle proprietà delle onde oceaniche casuali. Fisicamente rappresenta lo spettro normalizzato incrociato preso fra due componenti qualsiasi di un vettore di stato casuale definito dall’ampiezza dell’onda, dal vettore velocità delle particelle, dal vettore accelerazione delle particelle e dal vettore linearizzato forza idrodinamica agente su un oggetto sommerso. La funzione è peraltro sviluppata in modo del tutto generale in modo da risultare applicabile a qualsiasi processo casuale ondoso in 2 dimensioni. Sono presentati metodi sia numerici che analitici, e grafici di esempio.

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Резюме Эта работа посвящена вычислению двух-параметрической, двух-индексной, мнимой целой функции . Указанный анализ связан с применением теории стохастических процессов к изучению свойств случайных океанических волн. Физически представляет нормированный перекрестный спектр между двумя произвольными компонентами случайного вектора состояния, компоненты которого определяются амплитудой волны, вектором скорости частицы, вектором ускорения частицы и линеаризованной векторной гидродинамической силой, действующей на погруженный объект. Однако, функция вычисляется обычным образом для применения к произвольному двумерному случайному волновому процессу. Используются численные и аналитические методы для вычисления и предлагаются графики в качестве примера.

     

Direct reactions and hauser-feshbach theory II numerical methods and statistical tests

Numerical methods and statistical tests are described which form part of a recent paper dealing with Hauser-Feshbach theory in the presence of direct reactions.     

A numerical evaluation of Rayleigh's theory applied to scattering by randomly rough dielectric surfaces

Abstract

We present a numerical simulation of scattering by one-dimensional randomly rough surfaces. It is based on the use of plane-wave expansions to describe the Melds on the surface (i.e. Rayleigh hypothesis). Accuracy and convergence properties of two different numerical implementations are studied. Some examples of results for a dielectric and a metallic Gaussian rough surface are shown to be in good agreement with calculations by a rigorous numerical method. The Rayleigh method appears to be a fast computation tool for dielectric surfaces with slopes of less than 0.2.     

Comparison of the light scattering methods using the spherical basis

A comparative analysis of the widely known methods for solving the problem of light scattering by nonspherical particles—of the method of separation of variables (MSV), of the extended boundary condition method (EBCM), and the point-matching method (PMM), which use the spherical wave functions as a basis for the expansions of the fields—is carried out. In the scientific literature, these methods have been analyzed independently of one another in spite of their evident similarity: The same expansion coefficients are determined from similar set of equations and all optical characteristics are calculated with the same formulas. The ranges of applicability of the methods for dielectric spheroids and Chebyshev particles are studied in the same manner. It was found that, when considering the far-field zone, theoretical conditions of mathematical correctness of the EBCM and the MSV, apparently, differ fundamentally, although, as was shown, the methods themselves are extremely closely related. The performed numerical calculations suggest that the EBCM is preferable for spheroids, the MSV is preferable for Chebyshev particles, and the PMM, which is the most time-consuming method, gives satisfactory results in many cases when two other methods are inapplicable. Since the methods supplement one another well and their programs differ only in several tens of operators, we propose combining these methods within the framework of one universal program.     

Abstract scattering theory

The asymptotic condition is formulated for a system whose theory is more general than quantum mechanics. Its logic forms an orthocomplemented weakly modular -lattice. The set of states , consisting of all the probability measures on , is endowed with the most suitable metric physically, called here the natural one. In this space it is proved that the asymptotic condition implies the existence of two convex automorphisms _+- of which we call the wave-automorphisms. From these theS-automorphism _– ^–1 ₊ is defined and corresponds to the scattering operator in conventional quantum theory.     

Analysis of diffuse scattering of single crystals using monte carlo methods

While conventional crystal structure analysis using Bragg intensities reveals only information about the average structure of the crystal, diffuse scattering contains additional information about the disorder, i.e. departure from the average structure, of the studied material. Two different approaches to the analysis of diffuse scattering based on Monte Carlo methods are described in this paper: the direct Monte Carlo (MC) simulation technique and the Reverse Monte Carlo (RMC) method. The MC method requires the construction of a model for the disorder based on physical and chemical considerations and the selection of a set of near-neighbour interactions. The given model is realized by minimizing the total energy of the crystal via MC simulations. Next, the corresponding diffraction pattern is calculated and compared with the experimental data. By adjusting the near-neighbour interaction and repeating the process, a qualitative “match” between observed and calculated diffuse scattering is obtained. In contrast, the RMC method minimizes the difference between observed and calculated diffuse scattering intensities directly. This method leads to one real space structure consistent with the observed diffuse scattering but does not automatically result in a chemically sensible structure or further insight into the particular disorder problem.

The first example given in this paper demonstrates the viability of the RMC method by refining diffuse scattering data calculated from simulated structures with known disorder parameters. These structures were generated using the MC technique. As a second example MC and RMC simulations of the diffuse scattering of stabilized zirconias (CSZ) are shown, modelling occupational disorder as well as displacements.     

Evaluation of assumed-PDF methods in two-phase flows using direct numerical simulation

The hypothesis of uncorrelated temperature (T) and vapor-fuel mass fraction (Y_v), frequently made when modeling reaction rates using assumed-PDF models, is examined utilizing transitional databases from direct numerical simulation (DNS) of three-dimensional mixing-layers two-phase (TP) flows with evaporation. Because the databases do not contain chemical reaction, which would further correlate variables, finding here a correlation between T and Y_v is sufficient for invalidating reaction rate modeling of the joint (T, Y_v) probability distribution function (PDF) as a product of the marginal PDFs. The databases comprise four multicomponent fuels, two mass loadings and two free-stream gas temperatures. For comparison, databases for single-phase (SP) flows are also analyzed at two initial Reynolds numbers. The examination is conducted in the mixing layer excluding the free streams and in a more restricted part of the mixing layer constituting its core. The analysis is performed at the DNS and large eddy simulation (LES) scales, and subgrid scale (SGS). To obtain the LES database, the DNS database is filtered, and an evaluation of the examined correlation at the LES and SGS scales is made at two filter sizes. At the DNS scale, T and Y_v are practically uncorrelated for SP flows, showing the weak influence of the perfect-gas equation of state, whereas for TP flows the correlation is strong and increases with mass loading indicating the powerful effect of the phase change. At the LES scale, the findings emulate those at the DNS scale. The fluctuations of the SGS scale are uncorrelated for SP flows, but the product of the marginal PDFs is different from the joint PDF. For TP flows, the fluctuations are correlated and the correlation increases with temperature, casting doubt on current assumed PDFs used to model chemistry in reacting sprays. These results are independent of filter size. The joint PDFs for TP and SP fluctuations are successfully modeled.     

Correlation between mechano-electronic features and scattering rates using deformation potential theory

This research paper provides valuable insight into the electronic,mechanical and transport properties of the Sr₂RuO₂F₂ compound.The study shows that the Sr₂RuO₄ compound exhibits a metallic ground state and that the energy gap widens with oxygen substitution with fluorine.The concept of absolute deformation potential and its correlation with band energies and strains is explained using deformation potential theory.The paper also examines the...     

Identification of cavity fillers in elastic solids using the resonance scattering theory

Elastic waves incident on and scattered by fluid-filled (spherical) cavities in solids are usually described by summed scattering amplitudes. These summed amplitudes, when analysed one partial wave at a time, are seen to consist of two interfering contributions. One is a smooth background corresponding to scattering from an empty cavity, and the other is a superimposed set of resonance ‘spikes’ (lines with narrow width) of the filler fluid. We show in this paper how these modal resonances and their widths can be used to identify the material composition of the filler fluid in a way that resembles the spectroscopic methods used to identify chemical elements by means of their optical spectra.     

General three-particle scattering theory

A unified treatment of three-particle scattering theory with a three-body force in addition to the usual pair interactions is developed. The relationship of the generalized AGS and Faddeev formalisms to each other as well as distinct versions of each corresponding to the two most natural techniques for handling the three-body potential are established. It is found, just as in the case without the three-particle force, that the AGS formalism appears to be more practical for considering elastic and rearrangement scattering in two-body channels. On the other hand, for scattering amplitudes with at least one three-body channel (breakup and the 3-to-3) the Faddeev version of the theory is preferable. Other advantages of each formalism depending upon the treatment of the three-body interaction are noted.     

基于衍射理论的Z扫描技术分析与数值模拟

以菲涅耳-基尔霍夫衍射理论为基础,对通过非线性介质的高斯光束传输行为进行理论分析,分别给出了强吸收、无吸收情况下开孔、闭孔Z扫描曲线公式;对不同条件下非线性介质的归一化透过率进行数值模拟计算,发现Z扫描曲线透射峰和透射谷表现出3种新的特性:随着入射激光峰值光强的增加,Z扫描曲线透射峰的高度受到抑制,而透射谷则加强变得更深;非线性相移的增加对Z扫描曲线透射峰和透射谷均有增高和加深的作用;激光束束腰半径越大,Z扫描曲线的峰谷特征越明显。     

基于衍射理论的Z扫描技术分析与数值模拟

以菲涅耳-基尔霍夫衍射理论为基础,对通过非线性介质的高斯光束传输行为进行理论分析,分别给出了强吸收、无吸收情况下开孔、闭孔Z扫描曲线公式;对不同条件下非线性介质的归一化透过率进行数值模拟计算,发现Z扫描曲线透射峰和透射谷表现出3种新的特性：随着入射激光峰值光强的增加,Z扫描曲线透射峰的高度受到抑制,而透射谷则加强变得更深;非线性相移的增加对Z扫描曲线透射峰和透射谷均有增高和加深的作用;激光束束腰半径越大,Z扫描曲线的峰谷特征越明显。