Coherent memory functions for finite molecular systems. A direct method of calculation

A new direct method for calculation of coherent memory functions (MFs) entering the Nakajima-Zwanzig (or GME) equation is presented for rigid molecular chains with natural boundary conditions. The method is illustrated on the chains with three and five molecules and various kinds of imperfections. Obtained results imply a necessity of a more careful interpretation of experimental data (e.g. diffusivity).     

Eikonal Approximation for Intermediate Coupling

The eikonal approximation for intermediate coupling is studied.It is shown that the accuracy of the eikonal approximation is dependent on the shape of potentials.     

Eikonal equation for partially coherent fields

Coherence is the study of the amplitude correlations of optical fields. Its physical features can be obtained from the cross-spectral density function W(x₁,x₂,γ) which satisfies two coupled Helmholtz equations. In this article, we describe the amplitude of the optical field using the angular spectrum model. With this representation we calculate the propagation of the correlation function emerging from a transmittance plane. We show that the cross-spectral density function, can be described by just one Helmholtz equation. The treatment permits us to associate directional features to the coherence phenomena. This implies the existence of extremal trajectories of correlation, which are characterized by an eikonal equation, and the existence of a function for media fluctuations, which we term the correlation refractive index. Experimental results are shown for the synthesis of partially coherent focusing regions, which are described by an ensemble of extreme correlation trajectories.     

Eikonal approximation for magnetic electron scattering

The eikonal (high-energy) approximation of Yennie et al. for the scattering of electrons from nuclei has been extended to include the transverse interaction, and in particular the case of magnetic scattering. It is applied here to elastic magnetic scattering from ²⁰⁹Bi at 500 MeV as an example.     

The method of generating functions for the calculation of matrix elements in the deformed-harmonic oscillator basis

The method of generating functions which was previously only employed for the spherical basis of harmonic-oscillator single-particle wave functions is here generalized to the deformed (=cylindrical = asymptotic) basis. One-center and two-center matrix elements which are important in fission or heavy-ion scattering theories are obtained for various operators and potentials, i.e., spin-orbit, l-squared, Gaussian, or Gaussian multiplied by a polynomial, etc. If they cannot be calculated explicitely, recurrence formulae are evaluated. The method circumvents integrating the matrix elements by the introduction of generating parameters and looking for the coefficient of some power of the generating parameter in the expansion of the generating function. The method is further simplified by transforming the operators acting on the wave functions into operators which act onto the generating function or into functions to be multiplied by the generating integral.     

Cumulant functions in optical coherence theory

Cumulant functions are introduced to describe the statistical state of a radiation field. These functions are simply related to the optical coherence functions but have some interesting features. It is shown that if the cumulant functions of all orders greater than some numberN ₀ vanish then they also vanish for all orders greater than 2. Thermal field is the only field having this property. This property holds whether the field is described by a classical stochastic process or by a quantum density operator. Further the particular operator ordering used in defining these cumulant functions for the quantized field affects only the second order cumulant function. To describe the statistical state of a vector field such as partially polarized or unpolarized radiation, one would need to introduce cumulant tensors.     

堆外探测器响应函数三维空间分布计算

堆外探测器响应函数代表了堆芯活性区各组件对堆外探测器计数率的贡献,反映了堆芯功率分布与探测器计数率的关系。研究了三维离散纵标法(SN)程序TORT的共轭输运方法,并开发相应的处理程序,实现了柱坐标下的三维共轭中子注量率到压水堆各燃料组件响应函数的转换。并基于CAP1400核电厂反应堆模型,分析了其堆外探测器响应函数空间分布的特性,与采用TORT多次正向输运计算结果进行了对比分析,两者符合较好。通过本文研究,实现了压水堆核电厂堆外探测器响应函数的三维空间分布计算。     

堆外探测器响应函数三维空间分布计算

堆外探测器响应函数代表了堆芯活性区各组件对堆外探测器计数率的贡献,反映了堆芯功率分布与探测器计数率的关系。研究了三维离散纵标法(SN)程序TORT的共轭输运方法,并开发相应的处理程序,实现了柱坐标下的三维共轭中子注量率到压水堆各燃料组件响应函数的转换。并基于CAP1400核电厂反应堆模型,分析了其堆外探测器响应函数空间分布的特性,与采用TORT多次正向输运计算结果进行了对比分析,两者符合较好。通过本文研究,实现了压水堆核电厂堆外探测器响应函数的三维空间分布计算。     

Hydrodynamic calculation of static correlation functions for homogeneous shear

The calculation of static correlation functions for homogeneous shear is reduced to a simple problem in linear algebra. Analytical solutions are given for the static structure factor to second order in the strain rate, including effects arising from short range correlations at equilibrium. Numerical calculations give rise to a critical strain rate, λ_c, beyond which the hydrodynamical model of homogeneous shear is unstable. The value of λ_c is close to the value of the strain rate at which molecular dynamics calculations exhibit a shear-induced phase transition.     

Simplified method for polarization-sensitive optical coherence tomography

We report a method for extracting the birefringence properties of biological samples with micrometer-scale resolution in three dimensions, using a new form of polarization-sensitive optical coherence tomography. The method measures net retardance, net fast axis, and total reflectivity as a function of depth into the sample. Polarization sensing is accomplished by illumination of the sample with at least three separate polarization states during consecutive acquisitions of the same pixel, A scan, or B scan. The method can be implemented by use of non-polarization-maintaining fiber and a single detector. In a calibration test of the system, net retardance was measured with an average error of 7.5 degrees (standard deviation 2.2 degrees ) over the retardance range 0 degrees to 180 degrees , and a fast axis with average error of 4.8 degrees over the range 0 degrees to 180 degrees .     

An extended parabolic equation and its application to the calculation of transverse and longitudinal mutual coherence functions in atmospheric turbulence

An extended, wide forward angle scattering version of the parabolic equation is considered and an operator expression for the solution of the generalized nmth moment of the electromagnetic wave field is obtained. Here, 'generalized' connotes the consideration of both the transverse as well as the longitudinal spatial moments of the wave field. A unified solution for the generalized second-order moment, i.e. the mutual coherence function (MCF), is found. The solution is applied to the case of Kolmogorov turbulent fluctuations within the atmosphere. In addition to demonstrating an interesting decaying oscillatory behaviour of the longitudinal MCF in atmospheric turbulence, it is found that the use of the extended parabolic equation yields negligible corrections to the transverse MCF, as calculated from the parabolic equation in the paraxial approximation.     

Thermodynamic calculation of spin scaling functions

Critical phenomena theory centers on the scaled thermodynamic potential per spin $?(\beta ,h)=|t{|}^{p}Y(h|t{|}^{?q})$, with inverse temperature $\beta =1/T$, $h=?\beta H$, ordering field H, reduced temperature $t=t(\beta )$, critical exponents p and q, and function $Y(z)$ of $z=h|t{|}^{?q}$. I discuss calculating $Y(z)$ with the information geometry of thermodynamics. Scaled solutions are found to obtain with three admissible functions $t(\beta )$: 1) $t=e^{?J\beta }$, 2) $t={\beta }^{?1}$, and 3) $t={\beta }_C?\beta$, where J and ${\beta }_C$ are constants. For $p=q$, information geometry yields $Y(z)=\sqrt{1+z^2}$, consistent with the one-dimensional (1D) ferromagnetic Ising model.     

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.     

An alternative method for CARS-spectra calculation

We propose an alternative method for CARS-spectra calculation. This kind of spectrum-calculation allows the decomposition of the CARS-intensity into physically interpretable components. The method is based on Yuratich's analysis of effects of laser linewidth on CARS-spectroscopy. With the help of an equivalent representation of the plasma-dispersion function the CARS-intensity can be expressed via a Fourier-transform in a very easy manageable form for numerical investigations. As an example we applied our method to the Q-branch-spectrum of N₂.     

Eikonal description of nucleon-nucleon polarizations

Nucleon-nucleon elastic polarization data are analyzed within an eikonal framework in the range 6?plab?45 GeV/c and |t| 2.5 GeV/V². The isovector component is found to be dominated by a nearly exchange degenerate ρ-A₂ contribution while the isoscalar part requires both a lower lying Regge-pole exchange and an asymptotic pomeron contribution.     

Eikonal description of quantal scattering

Elastic and inelastic quantal scattering is described by a theory in which the contribution of a range of impact parameters to the scattering amplitude is determined by a phase integral (“eikonal”) which is integrated along a real curved “quantal” trajectory. This amplitude reduces to the Glauber expression in the high-energy, forward-angle limit, and to the usual semiclassical amplitude in the classical limit. The formulation can be applied to the study of heavy-ion scattering. The quantal trajectories are investigated analytically for the case of Coulomb scattering. A numerical analysis of elastic ¹⁶O¹⁶O scattering is carried out. The results show appreciable improvement as compared with the Glauber approximation.     

Fully vectorial eigenmode calculation of dielectric waveguides using a Rayleigh--Ritz method with rational basis functions

A fully vectorial Rayleigh--Ritz method for the eigenmode calculation of dielectric waveguides is presented. It uses the four transversal field components and takes rational functions as an orthonormal basis. This formalism is especially useful near the cutoff frequency and has been applied for the investigation of the polarization properties of the output waveguides in integrated spot-size transformers. This revised version was published online in November 2006 with corrections to the Cover Date.