A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging

International Nuclear Information System (INIS)

Lu Yujie; Zhu Banghe; Rasmussen, John C; Sevick-Muraca, Eva M; Shen Haiou; Wang Ge

2010-01-01

Fluorescence molecular imaging/tomography may play an important future role in preclinical research and clinical diagnostics. Time- and frequency-domain fluorescence imaging can acquire more measurement information than the continuous wave (CW) counterpart, improving the image quality of fluorescence molecular tomography. Although diffusion approximation (DA) theory has been extensively applied in optical molecular imaging, high-order photon migration models need to be further investigated to match quantitation provided by nuclear imaging. In this paper, a frequency-domain parallel adaptive finite element solver is developed with simplified spherical harmonics (SP N ) approximations. To fully evaluate the performance of the SP N approximations, a fast time-resolved tetrahedron-based Monte Carlo fluorescence simulator suitable for complex heterogeneous geometries is developed using a convolution strategy to realize the simulation of the fluorescence excitation and emission. The validation results show that high-order SP N can effectively correct the modeling errors of the diffusion equation, especially when the tissues have high absorption characteristics or when high modulation frequency measurements are used. Furthermore, the parallel adaptive mesh evolution strategy improves the modeling precision and the simulation speed significantly on a realistic digital mouse phantom. This solver is a promising platform for fluorescence molecular tomography using high-order approximations to the radiative transfer equation.

Symmetry relationships for multiple scattering of polarized light in turbid spherical samples: theory and a Monte Carlo simulation.

Science.gov (United States)

Otsuki, Soichi

2016-02-01

This paper presents a theory describing totally incoherent multiple scattering of turbid spherical samples. It is proved that if reciprocity and mirror symmetry hold for single scattering by a particle, they also hold for multiple scattering in spherical samples. Monte Carlo simulations generate a reduced effective scattering Mueller matrix, which virtually satisfies reciprocity and mirror symmetry. The scattering matrix was factorized by using the symmetric decomposition in a predefined form, as well as the Lu-Chipman polar decomposition, approximately into a product of a pure depolarizer and vertically oriented linear retarding diattenuators. The parameters of these components were calculated as a function of the polar angle. While the turbid spherical sample is a pure depolarizer at low polar angles, it obtains more functions of the retarding diattenuator with increasing polar angle.

Interactions between charged spherical macroions

International Nuclear Information System (INIS)

Stevens, M.J.; Falk, M.L.; Robbins, M.O.

1996-01-01

Monte Carlo (MC) simulations were used to study the screened interactions between charged spherical macroions surrounded by discrete counterions, and to test previous theories of screening. The simulations were performed in the primitive cell of the bcc lattice, and in the spherical Wigner endash Seitz cell that is commonly used in approximate calculations. We found that the Wigner endash Seitz approximation is valid even at high volume fractions φ and large macroion charges Z, because the macroion charge becomes strongly screened. Pressures calculated from Poisson endash Boltzmann theory and local density functional theory deviate from MC values as φ and Z increase, but continue to provide upper and lower bounds for the MC results. While Debye endash Hueckel (DH) theory fails badly when the bare charge is used, MC pressures can be fit with an effective DH charge, Z DH , that is nearly independent of volume fraction. As Z diverges, Z DH saturates at zψ max R m /λ, where z is the counterion charge, R m is the macroion radius, λ is the Bjerrum length, and ψ max is a constant of order 10. copyright 1996 American Institute of Physics

Approximation methods in probability theory

CERN Document Server

Čekanavičius, Vydas

2016-01-01

This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.

A semi-analytical method to estimate the effective slip length of spreading spherical-cap shaped droplets using Cox theory

Science.gov (United States)

Wörner, M.; Cai, X.; Alla, H.; Yue, P.

2018-03-01

The Cox–Voinov law on dynamic spreading relates the difference between the cubic values of the apparent contact angle (θ) and the equilibrium contact angle to the instantaneous contact line speed (U). Comparing spreading results with this hydrodynamic wetting theory requires accurate data of θ and U during the entire process. We consider the case when gravitational forces are negligible, so that the shape of the spreading drop can be closely approximated by a spherical cap. Using geometrical dependencies, we transform the general Cox law in a semi-analytical relation for the temporal evolution of the spreading radius. Evaluating this relation numerically shows that the spreading curve becomes independent from the gas viscosity when the latter is less than about 1% of the drop viscosity. Since inertia may invalidate the made assumptions in the initial stage of spreading, a quantitative criterion for the time when the spherical-cap assumption is reasonable is derived utilizing phase-field simulations on the spreading of partially wetting droplets. The developed theory allows us to compare experimental/computational spreading curves for spherical-cap shaped droplets with Cox theory without the need for instantaneous data of θ and U. Furthermore, the fitting of Cox theory enables us to estimate the effective slip length. This is potentially useful for establishing relationships between slip length and parameters in numerical methods for moving contact lines.

Parallelization of a spherical Sn transport theory algorithm

International Nuclear Information System (INIS)

Haghighat, A.

1989-01-01

The work described in this paper derives a parallel algorithm for an R-dependent spherical S N transport theory algorithm and studies its performance by testing different sample problems. The S N transport method is one of the most accurate techniques used to solve the linear Boltzmann equation. Several studies have been done on the vectorization of the S N algorithms; however, very few studies have been performed on the parallelization of this algorithm. Weinke and Hommoto have looked at the parallel processing of the different energy groups, and Azmy recently studied the parallel processing of the inner iterations of an X-Y S N nodal transport theory method. Both studies have reported very encouraging results, which have prompted us to look at the parallel processing of an R-dependent S N spherical geometry algorithm. This geometry was chosen because, in spite of its simplicity, it contains the complications of the curvilinear geometries (i.e., redistribution of neutrons over the discretized angular bins)

Mathematical analysis, approximation theory and their applications

CERN Document Server

Gupta, Vijay

2016-01-01

Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.

SHADOK-3-6, Transport Equation with Anisotropic Diffusion in P1 Approximation for Spherical and Cylindrical Geometry

International Nuclear Information System (INIS)

Ligou, J.; Thomi, P.A.

1973-01-01

1 - Nature of physical problem solved: Integral transport equation, anisotropy of diffusion in P1 approximation. SHADOK3 - cylindrical geometry; direct solution of the linear system. SHADOK4 - cylindrical geometry; Thermalization iteration; solution of the linear system with inverse matrix calculation. SHADOK5 - like SHADOK3 for spherical geometry. SHADOK6 - like SHADOK4 for spherical geometry. 2 - Method of solution: Analysis in terms of annuli for each of which polynomial approximation is applied. Dynamic allocation (for formulas see report TM(10)). 3 - Restrictions on the complexity of the problem: Relative accuracy of the Bickley functions about 1.0E-13

Operator approximant problems arising from quantum theory

CERN Document Server

Maher, Philip J

2017-01-01

This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory. The research presented is in non-commutative operator approximation theory or, to use Halmos' terminology, in operator approximants. Focusing on the concept of approximants, this self-contained book is suitable for graduate courses.

Methods of Fourier analysis and approximation theory

CERN Document Server

Tikhonov, Sergey

2016-01-01

Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.

Theory of corticothalamic brain activity in a spherical geometry: Spectra, coherence, and correlation

Science.gov (United States)

Mukta, K. N.; MacLaurin, J. N.; Robinson, P. A.

2017-11-01

Corticothalamic neural field theory is applied to a spherical geometry to better model neural activity in the human brain and is also compared with planar approximations. The frequency power spectrum, correlation, and coherence functions are computed analytically and numerically. The effects of cortical boundary conditions and resulting modal aspects of spherical corticothalamic dynamics are explored, showing that the results of spherical and finite planar geometries converge to those for the infinite planar geometry in the limit of large brain size. Estimates are made of the point at which modal series can be truncated and it is found that for physiologically plausible parameters only the lowest few spatial eigenmodes are needed for an accurate representation of macroscopic brain activity. A difference between the geometries is that there is a low-frequency 1 /f spectrum in the infinite planar geometry, whereas in the spherical geometry it is 1 /f2 . Another difference is that the alpha peak in the spherical geometry is sharper and stronger than in the planar geometry. Cortical modal effects can lead to a double alpha peak structure in the power spectrum, although the main determinant of the alpha peak is corticothalamic feedback. In the spherical geometry, the cross spectrum between two points is found to only depend on their relative distance apart. At small spatial separations the low-frequency cross spectrum is stronger than for an infinite planar geometry and the alpha peak is sharper and stronger due to the partitioning of the energy into discrete modes. In the spherical geometry, the coherence function between points decays monotonically as their separation increases at a fixed frequency, but persists further at resonant frequencies. The correlation between two points is found to be positive, regardless of the time lag and spatial separation, but decays monotonically as the separation increases at fixed time lag. At fixed distance the correlation has peaks

Description os surface quadrupole oscillations of heateU spherical nuclei in the Brownian movement approximation

International Nuclear Information System (INIS)

Svin'in, I.R.

1982-01-01

Description of collective phenomena in heated nuclei within the framework of the Brownian approximation may be conditionally divided into two parts: 1) solution of the problem for some realization of a random force, 2) averaging in a set of all the possible realizations. Results of the present work are setted the first part of the problem in the case of surface quadrupole oscillations of spherical heated nuclei. Quadrupole surface oscillations of heated spherical nuclei are considered in the Brownian motion approximation. The integrals of motion are constructed taking into account the energy and angular momentum conservations for the nucleus in the process of relaxation of the collective excitations. Wave functions are obtained for states having definite values of the integrals of motion in the phonon representation. It is noted that the description scheme developed is easily used with respect to other multipolarity oscillations

Development of the α-decay theory of spherical nuclei by means of the shell model

International Nuclear Information System (INIS)

Holan, S.

1978-01-01

The new results achieved within the α-decay theory of spherical nuclei with a (2)-(5) integral formula, unaffected by arbitrary parameters, taking into account the finite shape of the α particle and using a basis of Woods-Saxon uniparticle functions to describe initial and final nuclei, may be summarized as follows: Through α-width calculations performed for many spherical nuclei it has been proved that experimental classifying of α-transition into favoured and unfavoured transitions as well as the hyperfine structure of the transitions can be theoretically explained if considered the nucleon-nucleon correlations in the description of initial and final nuclei; The absolute values of the theoretical α-widths obtained are about 10 2 times smaller compared to the experimental ones. This might be due to an oversimplified approximation of the α-particle-daughter nucleus interaction potential or either to an inaccuracy of the model functions used in describing nucleus decay in the surface area. (author)

Geometric scalar theory of gravity beyond spherical symmetry

Science.gov (United States)

Moschella, U.; Novello, M.

2017-04-01

We construct several exact solutions for a recently proposed geometric scalar theory of gravity. We focus on a class of axisymmetric geometries and a big-bang-like geometry and discuss their Lorentzian character. The axisymmetric solutions are parametrized by an integer angular momentum l . The l =0 (spherical) case gives rise to the Schwarzschild geometry. The other solutions have naked singular surfaces. While not a priori obvious, all the solutions that we present here are globally Lorentzian. The Lorentzian signature appears to be a robust property of the disformal geometries solving the vacuum geometric scalar theory of gravity equations.

Optical properties of non-spherical desert dust particles in the terrestrial infrared – An asymptotic approximation approach

International Nuclear Information System (INIS)

Klüser, Lars; Di Biagio, Claudia; Kleiber, Paul D.; Formenti, Paola; Grassian, Vicki H.

2016-01-01

Optical properties (extinction efficiency, single scattering albedo, asymmetry parameter and scattering phase function) of five different desert dust minerals have been calculated with an asymptotic approximation approach (AAA) for non-spherical particles. The AAA method combines Rayleigh-limit approximations with an asymptotic geometric optics solution in a simple and straightforward formulation. The simulated extinction spectra have been compared with classical Lorenz–Mie calculations as well as with laboratory measurements of dust extinction. This comparison has been done for single minerals and with bulk dust samples collected from desert environments. It is shown that the non-spherical asymptotic approximation improves the spectral extinction pattern, including position of the extinction peaks, compared to the Lorenz–Mie calculations for spherical particles. Squared correlation coefficients from the asymptotic approach range from 0.84 to 0.96 for the mineral components whereas the corresponding numbers for Lorenz–Mie simulations range from 0.54 to 0.85. Moreover the blue shift typically found in Lorenz–Mie results is not present in the AAA simulations. The comparison of spectra simulated with the AAA for different shape assumptions suggests that the differences mainly stem from the assumption of the particle shape and not from the formulation of the method itself. It has been shown that the choice of particle shape strongly impacts the quality of the simulations. Additionally, the comparison of simulated extinction spectra with bulk dust measurements indicates that within airborne dust the composition may be inhomogeneous over the range of dust particle sizes, making the calculation of reliable radiative properties of desert dust even more complex. - Highlights: • A fast and simple method for estimating optical properties of dust. • Can be used with non-spherical particles of arbitrary size distributions. • Comparison with Mie simulations and

Scattering theory and effective medium approximations to heterogeneous materials

International Nuclear Information System (INIS)

Gubernatis, J.E.

1977-01-01

The formal analogy existing between problems studied in the microscopic theory of disordered alloys and problems concerned with the effective (macroscopic) behavior of heterogeneous materials is discussed. Attention is focused on (1) analogous approximations (effective medium approximations) developed for the microscopic problems by scattering theory concepts and techniques, but for the macroscopic problems principally by intuitive means, (2) the link, provided by scattering theory, of the intuitively developed approximations to a well-defined perturbative analysis, (3) the possible presence of conditionally convergent integrals in effective medium approximations

Neutrons moderation theory; Theorie du ralentissement des neutrons

Energy Technology Data Exchange (ETDEWEB)

Vigier, J P

1949-07-01

This report gives a summarized presentation of the theory of fast neutrons diffusion and moderation in a given environment as elaborated by M. Langevin, E. Fermi, R. Marshak and others. This statistical theory is based on three assumptions: there is no inelastic diffusion, the elastic diffusion has a spherical symmetry with respect to the center of gravity of the neutron-nucleus system (s-scattering), and the effects of chemical bonds and thermal agitation of nuclei are neglected. The first chapter analyzes the Boltzmann equation of moderation, its first approximate solution (age-velocity equation) and its domain of validity, the extension of the age-velocity theory (general solution) and the boundary conditions, the upper order approximation (spherical harmonics method and Laplace transformation), the asymptotic solutions, and the theory of spatial momenta. The second chapter analyzes the energy distribution of delayed neutrons (stationary and non-stationary cases). (J.S.)

From Mie to Fresnel through effective medium approximation with multipole contributions

International Nuclear Information System (INIS)

Malasi, Abhinav; Kalyanaraman, Ramki; Garcia, Hernando

2014-01-01

The Mie theory gives the exact solution to scattering from spherical particles while the Fresnel theory provides the solution to optical behavior of multilayer thin film structures. Often, the bridge between the two theories to explain the behavior of materials such as nanoparticles in a host dielectric matrix, is done by effective medium approximation (EMA) models which exclusively rely on the dipolar response of the scattering objects. Here, we present a way to capture multipole effects using EMA. The effective complex dielectric function of the composite is derived using the Clausius–Mossotti relation and the multipole coefficients of the approximate Mie theory. The optical density (OD) of the dielectric slab is then calculated using the Fresnel approach. We have applied the resulting equation to predict the particle size dependent dipole and quadrupole behavior for spherical Ag nanoparticles embedded in glass matrix. This dielectric function contains the relevant properties of EMA and at the same time predicts the multipole contributions present in the single particle Mie model. (papers)

Spherical sampling

CERN Document Server

Freeden, Willi; Schreiner, Michael

2018-01-01

This book presents, in a consistent and unified overview, results and developments in the field of today´s spherical sampling, particularly arising in mathematical geosciences. Although the book often refers to original contributions, the authors made them accessible to (graduate) students and scientists not only from mathematics but also from geosciences and geoengineering. Building a library of topics in spherical sampling theory it shows how advances in this theory lead to new discoveries in mathematical, geodetic, geophysical as well as other scientific branches like neuro-medicine. A must-to-read for everybody working in the area of spherical sampling.

January: IBM 7094 programme for the resolution of cell problems in planar, spherical and cylindrical geometry using the double Pn approximation

International Nuclear Information System (INIS)

Amouyal, A.; Tariel, H.

1966-01-01

Code name: January 1 st SCEA 011S. 2) Computer: IBM 7094; Programme system: Fortran II, 2 nd version. 3) Nature of the problem: resolution of cell problems with one space variable (planar, spherical and cylindrical geometries) and with one energy group, with isotropic sources in the double P n approximation (DP 1 and DP 3 approximation in planar and spherical geometries, DP 1 and DP 2 in cylindrical geometry). 4) Method used: the differential equations with limiting conditions are transformed into differential system with initial conditions which are integrated by a separate-step method. 5) Restrictions: number of physical media [fr

Optical approximation in the theory of geometric impedance

International Nuclear Information System (INIS)

Stupakov, G.; Bane, K.L.F.; Zagorodnov, I.

2007-02-01

In this paper we introduce an optical approximation into the theory of impedance calculation, one valid in the limit of high frequencies. This approximation neglects diffraction effects in the radiation process, and is conceptually equivalent to the approximation of geometric optics in electromagnetic theory. Using this approximation, we derive equations for the longitudinal impedance for arbitrary offsets, with respect to a reference orbit, of source and test particles. With the help of the Panofsky-Wenzel theorem we also obtain expressions for the transverse impedance (also for arbitrary offsets). We further simplify these expressions for the case of the small offsets that are typical for practical applications. Our final expressions for the impedance, in the general case, involve two dimensional integrals over various cross-sections of the transition. We further demonstrate, for several known axisymmetric examples, how our method is applied to the calculation of impedances. Finally, we discuss the accuracy of the optical approximation and its relation to the diffraction regime in the theory of impedance. (orig.)

The sagitta and lens thickness: the exact solution and a matrix approximation for lenses with toric, spherical, and cylindrical surfaces.

Science.gov (United States)

Harris, W F

1989-03-01

The exact equation for sagitta of spherical surfaces is generalized to toric surfaces which include spherical and cylindrical surfaces as special cases. Lens thickness, therefore, can be calculated accurately anywhere on a lens even in cases of extreme spherical and cylindrical powers and large diameters. The sagittae of tire- and barrel-form toric surfaces differ off the principal meridians, as is shown by a numerical example. The same holds for pulley- and capstan-form toric surfaces. A general expression is given for thickness at an arbitrary point on a toric lens. Approximate expressions are derived and re-expressed in terms of matrices. The matrix provides an elegant means of generalizing equations for spherical surfaces and lenses to toric surfaces and lenses.

Shape theory categorical methods of approximation

CERN Document Server

Cordier, J M

2008-01-01

This in-depth treatment uses shape theory as a ""case study"" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximations. It offers students a unified and consolidated presentation of extensive research from category theory, shape theory, and the study of topological algebras.A short introduction to geometric shape explains specifics of the construction of the shape category and relates it to an abstract definition of shape theory. Upon returning to the geometric base, the text considers simplical complexes and

Spherically symmetric solutions in abelian Kaluza-Klein theories

International Nuclear Information System (INIS)

Angus, I.G.

1986-01-01

We present the most general spherically symmetric solution to the field equations of the truncated five-dimensional Kaluza-Klein theory. We also detail some of the special forms of this solution. With the exception of the Gross-Perry-Sorkin monopole and the Schwarzschild solutions we find that most, and we conjecture all, of the solutions have naked curvature singularities. We then proceed to consider higher-dimensional theories with toroidal compactification and we exhibit a class of nonsingular monopole solutions which are the natural generalization of the Gross-Perry-Sorkin monopole to more than five dimensions. We also present some selected solutions including a solution pertaining to a model with a Ricci-flat, but not curvature-flat, internal manifold. All of these other solutions have naked curvature singularities. (orig.)

Towards a unification of the hierarchical reference theory and the self-consistent Ornstein-Zernike approximation.

Science.gov (United States)

Reiner, A; Høye, J S

2005-12-01

The hierarchical reference theory and the self-consistent Ornstein-Zernike approximation are two liquid state theories that both furnish a largely satisfactory description of the critical region as well as phase coexistence and the equation of state in general. Furthermore, there are a number of similarities that suggest the possibility of a unification of both theories. As a first step towards this goal, we consider the problem of combining the lowest order gamma expansion result for the incorporation of a Fourier component of the interaction with the requirement of consistency between internal and free energies, leaving aside the compressibility relation. For simplicity, we restrict ourselves to a simplified lattice gas that is expected to display the same qualitative behavior as more elaborate models. It turns out that the analytically tractable mean spherical approximation is a solution to this problem, as are several of its generalizations. Analysis of the characteristic equations shows the potential for a practical scheme and yields necessary conditions that any closure to the Ornstein-Zernike relation must fulfill for the consistency problem to be well posed and to have a unique differentiable solution. These criteria are expected to remain valid for more general discrete and continuous systems, even if consistency with the compressibility route is also enforced where possible explicit solutions will require numerical evaluations.

The theory of spherically symmetric thin shells in conformal gravity

Science.gov (United States)

Berezin, Victor; Dokuchaev, Vyacheslav; Eroshenko, Yury

The spherically symmetric thin shells are the nearest generalizations of the point-like particles. Moreover, they serve as the simple sources of the gravitational fields both in General Relativity and much more complex quadratic gravity theories. We are interested in the special and physically important case when all the quadratic in curvature tensor (Riemann tensor) and its contractions (Ricci tensor and scalar curvature) terms are present in the form of the square of Weyl tensor. By definition, the energy-momentum tensor of the thin shell is proportional to Diracs delta-function. We constructed the theory of the spherically symmetric thin shells for three types of gravitational theories with the shell: (1) General Relativity; (2) Pure conformal (Weyl) gravity where the gravitational part of the total Lagrangian is just the square of the Weyl tensor; (3) Weyl-Einstein gravity. The results are compared with these in General Relativity (Israel equations). We considered in detail the shells immersed in the vacuum. Some peculiar properties of such shells are found. In particular, for the traceless ( = massless) shell, it is shown that their dynamics cannot be derived from the matching conditions and, thus, is completely arbitrary. On the contrary, in the case of the Weyl-Einstein gravity, the trajectory of the same type of shell is completely restored even without knowledge of the outside solution.

A link between quantum entanglement, secant varieties and sphericity

International Nuclear Information System (INIS)

Sawicki, A; Tsanov, V V

2013-01-01

In this paper, we shed light on the relations between three concepts studied in representation theory, algebraic geometry and quantum information theory. First—spherical actions of reductive groups on projective spaces. Second—secant varieties of homogeneous projective varieties, and the related notions of rank and border rank. Third—quantum entanglement. Our main result concerns the relation between the problem of the state reconstruction from its reduced one-particle density matrices and the minimal number of separable summands in its decomposition. More precisely, we show that sphericity implies that states of a given rank cannot be approximated by states of a lower rank. We call states for which such an approximation is possible exceptional states. For three, important from a quantum entanglement perspective, cases of distinguishable, fermionic and bosonic particles, we also show that non-sphericity implies the existence of exceptional states. Remarkably, the exceptional states belong to non-bipartite entanglement classes. In particular, we show that the W-type states and their appropriate modifications are exceptional states stemming from the second secant variety for three cases above. We point out that the existence of the exceptional states is a physical obstruction for deciding the local unitary equivalence of states by means of the one-particle-reduced density matrices. Finally, for a number of systems of distinguishable particles with a known orbit structure, we list all exceptional states and discuss their possible importance in entanglement theory. (paper)

Semiclassical approximation to time-dependent Hartree--Fock theory

International Nuclear Information System (INIS)

Dworzecka, M.; Poggioli, R.

1976-01-01

Working within a time-dependent Hartree-Fock framework, one develops a semiclassical approximation appropriate for large systems. It is demonstrated that the standard semiclassical approach, the Thomas-Fermi approximation, is inconsistent with Hartree-Fock theory when the basic two-body interaction is short-ranged (as in nuclear systems, for example). However, by introducing a simple extension of the Thomas-Fermi approximation, one overcomes this problem. One also discusses the infinite nuclear matter problem and point out that time-dependent Hartree-Fock theory yields collective modes of the zero sound variety instead of ordinary hydrodynamic (first) sound. One thus emphasizes that one should be extremely circumspect when attempting to cast the equations of motion of time-dependent Hartree-Fock theory into a hydrodynamic-like form

Nekrasov and Argyres–Douglas theories in spherical Hecke algebra representation

Energy Technology Data Exchange (ETDEWEB)

Rim, Chaiho, E-mail: rimpine@sogang.ac.kr; Zhang, Hong, E-mail: kilar@itp.ac.cn

2017-06-15

AGT conjecture connects Nekrasov instanton partition function of 4D quiver gauge theory with 2D Liouville conformal blocks. We re-investigate this connection using the central extension of spherical Hecke algebra in q-coordinate representation, q being the instanton expansion parameter. Based on AFLT basis together with intertwiners we construct gauge conformal state and demonstrate its equivalence to the Liouville conformal state, with careful attention to the proper scaling behavior of the state. Using the colliding limit of regular states, we obtain the formal expression of irregular conformal states corresponding to Argyres–Douglas theory, which involves summation of functions over Young diagrams.

Nekrasov and Argyres-Douglas theories in spherical Hecke algebra representation

Science.gov (United States)

Rim, Chaiho; Zhang, Hong

2017-06-01

AGT conjecture connects Nekrasov instanton partition function of 4D quiver gauge theory with 2D Liouville conformal blocks. We re-investigate this connection using the central extension of spherical Hecke algebra in q-coordinate representation, q being the instanton expansion parameter. Based on AFLT basis together with intertwiners we construct gauge conformal state and demonstrate its equivalence to the Liouville conformal state, with careful attention to the proper scaling behavior of the state. Using the colliding limit of regular states, we obtain the formal expression of irregular conformal states corresponding to Argyres-Douglas theory, which involves summation of functions over Young diagrams.

Efficient molecular density functional theory using generalized spherical harmonics expansions.

Science.gov (United States)

Ding, Lu; Levesque, Maximilien; Borgis, Daniel; Belloni, Luc

2017-09-07

We show that generalized spherical harmonics are well suited for representing the space and orientation molecular density in the resolution of the molecular density functional theory. We consider the common system made of a rigid solute of arbitrary complexity immersed in a molecular solvent, both represented by molecules with interacting atomic sites and classical force fields. The molecular solvent density ρ(r,Ω) around the solute is a function of the position r≡(x,y,z) and of the three Euler angles Ω≡(θ,ϕ,ψ) describing the solvent orientation. The standard density functional, equivalent to the hypernetted-chain closure for the solute-solvent correlations in the liquid theory, is minimized with respect to ρ(r,Ω). The up-to-now very expensive angular convolution products are advantageously replaced by simple products between projections onto generalized spherical harmonics. The dramatic gain in speed of resolution enables to explore in a systematic way molecular solutes of up to nanometric sizes in arbitrary solvents and to calculate their solvation free energy and associated microscopic solvent structure in at most a few minutes. We finally illustrate the formalism by tackling the solvation of molecules of various complexities in water.

Hydrodynamical equations for spherical gravitational collapse in terms of a generalized theory of gravitation with higher derivatives

International Nuclear Information System (INIS)

Nariai, Hidekazu.

1986-06-01

In similar to Misner and Sharp's formalism in general relativity for a spherical gravitational collapse, a formalism for the spherical gravitational collapse is presented on the basis of a generalized theory of gravitation in the sense of Utiyama-DeWitt (which was later extended by Parker's school and Zel'dovich's one). The resulted formalism is somewhat similar to that developed by me in 1972 based on the scalar-tensor theory of gravity. (author)

Methods of Approximation Theory in Complex Analysis and Mathematical Physics

CERN Document Server

Saff, Edward

1993-01-01

The book incorporates research papers and surveys written by participants ofan International Scientific Programme on Approximation Theory jointly supervised by Institute for Constructive Mathematics of University of South Florida at Tampa, USA and the Euler International Mathematical Instituteat St. Petersburg, Russia. The aim of the Programme was to present new developments in Constructive Approximation Theory. The topics of the papers are: asymptotic behaviour of orthogonal polynomials, rational approximation of classical functions, quadrature formulas, theory of n-widths, nonlinear approximation in Hardy algebras,numerical results on best polynomial approximations, wavelet analysis. FROM THE CONTENTS: E.A. Rakhmanov: Strong asymptotics for orthogonal polynomials associated with exponential weights on R.- A.L. Levin, E.B. Saff: Exact Convergence Rates for Best Lp Rational Approximation to the Signum Function and for Optimal Quadrature in Hp.- H. Stahl: Uniform Rational Approximation of x .- M. Rahman, S.K. ...

Spherical Approximation on Unit Sphere

Directory of Open Access Journals (Sweden)

Eman Samir Bhaya

2018-01-01

Full Text Available In this paper we introduce a Jackson type theorem for functions in LP spaces on sphere And study on best approximation of  functions in  spaces defined on unit sphere. our central problem is to describe the approximation behavior of functions in    spaces for  by modulus of smoothness of functions.

Is the classical two-term approximation of electron kinetic theory satisfactory for swarms and plasmas?

International Nuclear Information System (INIS)

White, R D; Robson, R E; Schmidt, B; Morrison, Michael A

2003-01-01

The 'two-term' approximation (representation of the electron distribution by the first two terms of an expansion in spherical harmonics in velocity space) continues to occupy a central role in the low-temperature plasma physics literature, in spite of the mass of evidence illustrating its inadequacy in the swarm (free diffusion) limit for many molecular gases. Part of the problem lies in the failure of many authors to specify quantitatively what they mean when they say that the two-term approximation is 'acceptable'. Thus for example, an error of 10% in transport coefficients may well be acceptable in many plasma applications, but for analysis of highly accurate swarm experiments to compare with ab initio and beam-derived cross-sections, 0.1% or less is required, making 'multi-term' analysis mandatory. While reconciliation of the swarm and plasma literature along the lines of two different accuracy regimes may thus be possible, we dispute claims that the two-term approximation is generally satisfactory for inversion of swarm experiment data to obtain electron impact cross-sections. The unsatisfactory nature of other assumptions implicit in much of the modern plasma kinetic theory literature is also discussed

Adaptive tree multigrids and simplified spherical harmonics approximation in deterministic neutral and charged particle transport

International Nuclear Information System (INIS)

Kotiluoto, P.

2007-05-01

A new deterministic three-dimensional neutral and charged particle transport code, MultiTrans, has been developed. In the novel approach, the adaptive tree multigrid technique is used in conjunction with simplified spherical harmonics approximation of the Boltzmann transport equation. The development of the new radiation transport code started in the framework of the Finnish boron neutron capture therapy (BNCT) project. Since the application of the MultiTrans code to BNCT dose planning problems, the testing and development of the MultiTrans code has continued in conventional radiotherapy and reactor physics applications. In this thesis, an overview of different numerical radiation transport methods is first given. Special features of the simplified spherical harmonics method and the adaptive tree multigrid technique are then reviewed. The usefulness of the new MultiTrans code has been indicated by verifying and validating the code performance for different types of neutral and charged particle transport problems, reported in separate publications. (orig.)

High energy approximations in quantum field theory

International Nuclear Information System (INIS)

Orzalesi, C.A.

1975-01-01

New theoretical methods in hadron physics based on a high-energy perturbation theory are discussed. The approximated solutions to quantum field theory obtained by this method appear to be sufficiently simple and rich in structure to encourage hadron dynamics studies. Operator eikonal form for field - theoretic Green's functions is derived and discussion is held on how the eikonal perturbation theory is to be renormalized. This method is extended to massive quantum electrodynamics of scalar charged bosons. Possible developments and applications of this theory are given [pt

Gauge/gravity duality for interactions of spherical membranes in 11-dimensional pp-wave

International Nuclear Information System (INIS)

Lee, Hok Kong; McLoughlin, Tristan; Wu Xinkai

2005-01-01

We investigate the gauge/gravity duality in the interaction between two spherical membranes in the 11-dimensional pp-wave background. On the supergravity side, we find the solution to the field equations at locations close to a spherical source membrane, and use it to obtain the light-cone Lagrangian of a spherical probe membrane very close to the source, i.e., with their separation much smaller than their radii. On the gauge theory side, using the BMN matrix model, we compute the one-loop effective potential between two membrane fuzzy spheres. Perfect agreement is found between the two sides. Moreover, the one-loop effective potential we obtain on the gauge theory side is valid beyond the small-separation approximation, giving the full interpolation between interactions of membrane-like objects and that of graviton-like objects

Aft-body loading function for penetrators based on the spherical cavity-expansion approximation.

Energy Technology Data Exchange (ETDEWEB)

Longcope, Donald B., Jr.; Warren, Thomas Lynn; Duong, Henry

2009-12-01

In this paper we develop an aft-body loading function for penetration simulations that is based on the spherical cavity-expansion approximation. This loading function assumes that there is a preexisting cavity of radius a{sub o} before the expansion occurs. This causes the radial stress on the cavity surface to be less than what is obtained if the cavity is opened from a zero initial radius. This in turn causes less resistance on the aft body as it penetrates the target which allows for greater rotation of the penetrator. Results from simulations are compared with experimental results for oblique penetration into a concrete target with an unconfined compressive strength of 23 MPa.

Continuum orbital approximations in weak-coupling theories for inelastic electron scattering

International Nuclear Information System (INIS)

Peek, J.M.; Mann, J.B.

1977-01-01

Two approximations, motivated by heavy-particle scattering theory, are tested for weak-coupling electron-atom (ion) inelastic scattering theory. They consist of replacing the one-electron scattering orbitals by their Langer uniform approximations and the use of an average trajectory approximation which entirely avoids the necessity for generating continuum orbitals. Numerical tests for a dipole-allowed and a dipole-forbidden event, based on Coulomb-Born theory with exchange neglected, reveal the error trends. It is concluded that the uniform approximation gives a satisfactory prediction for traditional weak-coupling theories while the average approximation should be limited to collision energies exceeding at least twice the threshold energy. The accuracy for both approximations is higher for positive ions than for neutral targets. Partial-wave collision-strength data indicate that greater care should be exercised in using these approximations to predict quantities differential in the scattering angle. An application to the 2s 2 S-2p 2 P transition in Ne VIII is presented

Kinematics of the 3(RPSP-S Fully Spherical Parallel Manipulator by Means of Screw Theory

Directory of Open Access Journals (Sweden)

Jaime Gallardo-Alvarado

2018-06-01

Full Text Available In this work, the kinematics of a spherical parallel manipulator composed of three peripheral limbs equipped with linear actuators and a passive center shaft is approached by means of the theory of screws. The displacement analysis is carried out solving closure equations, which are obtained upon simple linear combinations of the components of two unit vectors describing the orientation of the moving platform. After, the input-output equations of velocity and acceleration of the spherical parallel manipulator are systematically obtained by resorting to reciprocal-screw theory. This strategy avoids the computation of the passive joint velocity and acceleration rates of the robot manipulator. Numerical examples illustrate the efficiency of the proposed method.

Generalized theory of resonance scattering (GTRS) using the translational addition theorem for spherical wave functions.

Science.gov (United States)

Mitri, Farid

2014-11-01

The generalized theory of resonance scattering (GTRS) by an elastic spherical target in acoustics is extended to describe the arbitrary scattering of a finite beam using the addition theorem for the spherical wave functions of the first kind under a translation of the coordinate origin. The advantage of the proposed method over the standard discrete spherical harmonics transform previously used in the GTRS formalism is the computation of the off-axial beam-shape coefficients (BSCs) stemming from a closed-form partial-wave series expansion representing the axial BSCs in spherical coordinates. With this general method, the arbitrary acoustical scattering can be evaluated for any particle shape and size, whether the particle is partially or completely illuminated by the incident beam. Numerical examples for the axial and off-axial resonance scattering from an elastic sphere placed arbitrarily in the field of a finite circular piston transducer with uniform vibration are provided. Moreover, the 3-D resonance directivity patterns illustrate the theory and reveal some properties of the scattering. Numerous applications involving the scattering phenomenon in imaging, particle manipulation, and the characterization of multiphase flows can benefit from the present analysis because all physically realizable beams radiate acoustical waves from finite transducers as opposed to waves of infinite extent.

Nonstandard approximation schemes for lower dimensional quantum field theories

International Nuclear Information System (INIS)

Fitzpatrick, D.A.

1981-01-01

The purpose of this thesis has been to apply two different nonstandard approximation schemes to a variety of lower-dimensional schemes. In doing this, we show their applicability where (e.g., Feynman or Rayleigh-Schroedinger) approximation schemes are inapplicable. We have applied the well-known mean-field approximation scheme by Guralnik et al. to general lower dimensional theories - the phi 4 field theory in one dimension, and the massive and massless Thirring models in two dimensions. In each case, we derive a bound-state propagator and then expand the theory in terms of the original and bound-state propagators. The results obtained can be compared with previously known results thereby show, in general, reasonably good convergence. In the second half of the thesis, we develop a self-consistent quantum mechanical approximation scheme. This can be applied to any monotonic polynomial potential. It has been applied in detail to the anharmonic oscillator, and the results in several analytical domains are very good, including extensive tables of numerical results

Fundamentals of spherical array processing

CERN Document Server

Rafaely, Boaz

2015-01-01

This book provides a comprehensive introduction to the theory and practice of spherical microphone arrays. It is written for graduate students, researchers and engineers who work with spherical microphone arrays in a wide range of applications.   The first two chapters provide the reader with the necessary mathematical and physical background, including an introduction to the spherical Fourier transform and the formulation of plane-wave sound fields in the spherical harmonic domain. The third chapter covers the theory of spatial sampling, employed when selecting the positions of microphones to sample sound pressure functions in space. Subsequent chapters present various spherical array configurations, including the popular rigid-sphere-based configuration. Beamforming (spatial filtering) in the spherical harmonics domain, including axis-symmetric beamforming, and the performance measures of directivity index and white noise gain are introduced, and a range of optimal beamformers for spherical arrays, includi...

Quantal density functional theory II. Approximation methods and applications

International Nuclear Information System (INIS)

Sahni, Viraht

2010-01-01

This book is on approximation methods and applications of Quantal Density Functional Theory (QDFT), a new local effective-potential-energy theory of electronic structure. What distinguishes the theory from traditional density functional theory is that the electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and the correlation contribution to the kinetic energy -- the Correlation-Kinetic effects -- are separately and explicitly defined. As such it is possible to study each property of interest as a function of the different electron correlations. Approximations methods based on the incorporation of different electron correlations, as well as a many-body perturbation theory within the context of QDFT, are developed. The applications are to the few-electron inhomogeneous electron gas systems in atoms and molecules, as well as to the many-electron inhomogeneity at metallic surfaces. (orig.)

Pairing renormalization and regularization within the local density approximation

International Nuclear Information System (INIS)

Borycki, P.J.; Dobaczewski, J.; Nazarewicz, W.; Stoitsov, M.V.

2006-01-01

We discuss methods used in mean-field theories to treat pairing correlations within the local density approximation. Pairing renormalization and regularization procedures are compared in spherical and deformed nuclei. Both prescriptions give fairly similar results, although the theoretical motivation, simplicity, and stability of the regularization procedure make it a method of choice for future applications

Transverse signal decay under the weak field approximation: Theory and validation.

Science.gov (United States)

Berman, Avery J L; Pike, G Bruce

2018-07-01

To derive an expression for the transverse signal time course from systems in the motional narrowing regime, such as water diffusing in blood. This was validated in silico and experimentally with ex vivo blood samples. A closed-form solution (CFS) for transverse signal decay under any train of refocusing pulses was derived using the weak field approximation. The CFS was validated via simulations of water molecules diffusing in the presence of spherical perturbers, with a range of sizes and under various pulse sequences. The CFS was compared with more conventional fits assuming monoexponential decay, including chemical exchange, using ex vivo blood Carr-Purcell-Meiboom-Gill data. From simulations, the CFS was shown to be valid in the motional narrowing regime and partially into the intermediate dephasing regime, with increased accuracy with increasing Carr-Purcell-Meiboom-Gill refocusing rate. In theoretical calculations of the CFS, fitting for the transverse relaxation rate (R 2 ) gave excellent agreement with the weak field approximation expression for R 2 for Carr-Purcell-Meiboom-Gill sequences, but diverged for free induction decay. These same results were confirmed in the ex vivo analysis. Transverse signal decay in the motional narrowing regime can be accurately described analytically. This theory has applications in areas such as tissue iron imaging, relaxometry of blood, and contrast agent imaging. Magn Reson Med 80:341-350, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Spherically Symmetric Solutions of the Einstein-Bach Equations and a Consistent Spin-2 Field Theory

International Nuclear Information System (INIS)

Janda, A.

2006-01-01

We briefly present a relationship between General Relativity coupled to certain spin-0 and spin-2 field theories and higher derivatives metric theories of gravity. In a special case, described by the Einstein-Bach equations, the spin-0 field drops out from the theory and we obtain a consistent spin-two field theory interacting gravitationally, which overcomes a well known inconsistency of the theory for a linear spin-two field coupled to the Einstein's gravity. Then we discuss basic properties of static spherically symmetric solutions of the Einstein-Bach equations. (author)

Exact solution of the neutron transport equation in spherical geometry

Energy Technology Data Exchange (ETDEWEB)

Anli, Fikret; Akkurt, Abdullah; Yildirim, Hueseyin; Ates, Kemal [Kahramanmaras Suetcue Imam Univ. (Turkey). Faculty of Sciences and Letters

2017-03-15

Solution of the neutron transport equation in one dimensional slab geometry construct a basis for the solution of neutron transport equation in a curvilinear geometry. Therefore, in this work, we attempt to derive an exact analytical benchmark solution for both neutron transport equations in slab and spherical medium by using P{sub N} approximation which is widely used in neutron transport theory.

Two-fluid static spherical configurations with linear mass function in the Einstein-Cartan theory

International Nuclear Information System (INIS)

Gallakhmetov, A.M.

2002-01-01

In the framework of the Einstein-Cartan theory, two-fluid static spherical configurations with linear mass function are considered. One of these modelling anisotropic matter distributions within star and the other fluid is a perfect fluid representing a source of torsion. It is shown that the solutions of the Einstein equations for anisotropic relativistic spheres in General Relativity may generate the solutions in the Einstein-Cartan theory. Some exact solutions are obtained

The general class of the vacuum spherically symmetric equations of the general relativity theory

International Nuclear Information System (INIS)

Karbanovski, V. V.; Sorokin, O. M.; Nesterova, M. I.; Bolotnyaya, V. A.; Markov, V. N.; Kairov, T. V.; Lyash, A. A.; Tarasyuk, O. R.

2012-01-01

The system of the spherical-symmetric vacuum equations of the General Relativity Theory is considered. The general solution to a problem representing two classes of line elements with arbitrary functions g 00 and g 22 is obtained. The properties of the found solutions are analyzed.

Dynamical Mean Field Approximation Applied to Quantum Field Theory

CERN Document Server

Akerlund, Oscar; Georges, Antoine; Werner, Philipp

2013-12-04

We apply the Dynamical Mean Field (DMFT) approximation to the real, scalar phi^4 quantum field theory. By comparing to lattice Monte Carlo calculations, perturbation theory and standard mean field theory, we test the quality of the approximation in two, three, four and five dimensions. The quantities considered in these tests are the critical coupling for the transition to the ordered phase and the associated critical exponents nu and beta. We also map out the phase diagram in four dimensions. In two and three dimensions, DMFT incorrectly predicts a first order phase transition for all bare quartic couplings, which is problematic, because the second order nature of the phase transition of lattice phi^4-theory is crucial for taking the continuum limit. Nevertheless, by extrapolating the behaviour away from the phase transition, one can obtain critical couplings and critical exponents. They differ from those of mean field theory and are much closer to the correct values. In four dimensions the transition is sec...

Transition operators in electromagnetic-wave diffraction theory. II - Applications to optics

Science.gov (United States)

Hahne, G. E.

1993-01-01

The theory developed by Hahne (1992) for the diffraction of time-harmonic electromagnetic waves from fixed obstacles is briefly summarized and extended. Applications of the theory are considered which comprise, first, a spherical harmonic expansion of the so-called radiation impedance operator in the theory, for a spherical surface, and second, a reconsideration of familiar short-wavelength approximation from the new standpoint, including a derivation of the so-called physical optics method on the basis of quasi-planar approximation to the radiation impedance operator, augmented by the method of stationary phase. The latter includes a rederivation of the geometrical optics approximation for the complete Green's function for the electromagnetic field in the presence of a smooth- and a convex-surfaced perfectly electrically conductive obstacle.

Post-Newtonian approximation of the maximum four-dimensional Yang-Mills gauge theory

International Nuclear Information System (INIS)

Smalley, L.L.

1982-01-01

We have calculated the post-Newtonian approximation of the maximum four-dimensional Yang-Mills theory proposed by Hsu. The theory contains torsion; however, torsion is not active at the level of the post-Newtonian approximation of the metric. Depending on the nature of the approximation, we obtain the general-relativistic values for the classical Robertson parameters (γ = β = 1), but deviations for the Nordtvedt effect and violations of post-Newtonian conservation laws. We conclude that in its present form the theory is not a viable theory of gravitation

Relativistic continuum random phase approximation in spherical nuclei

International Nuclear Information System (INIS)

Daoutidis, Ioannis

2009-01-01

Covariant density functional theory is used to analyze the nuclear response in the external multipole fields. The investigations are based on modern functionals with zero range and density dependent coupling constants. After a self-consistent solution of the Relativistic Mean Field (RMF) equations for the nuclear ground states multipole giant resonances are studied within the Relativistic Random Phase Approximation (RRPA), the small amplitude limit of the time-dependent RMF. The coupling to the continuum is treated precisely by calculating the single particle Greens-function of the corresponding Dirac equation. In conventional methods based on a discretization of the continuum this was not possible. The residual interaction is derived from the same RMF Lagrangian. This guarantees current conservation and a precise decoupling of the Goldstone modes. For nuclei with open shells pairing correlations are taken into account in the framework of BCS theory and relativistic quasiparticle RPA. Continuum RPA (CRPA) presents a robust method connected with an astonishing reduction of the numerical effort as compared to conventional methods. Modes of various multipolarities and isospin are investigated, in particular also the newly discovered Pygmy modes in the vicinity of the neutron evaporation threshold. The results are compared with conventional discrete RPA calculations as well as with experimental data. We find that the full treatment of the continuum is essential for light nuclei and the study of resonances in the neighborhood of the threshold. (orig.)

Relativistic continuum random phase approximation in spherical nuclei

Energy Technology Data Exchange (ETDEWEB)

Daoutidis, Ioannis

2009-10-01

Covariant density functional theory is used to analyze the nuclear response in the external multipole fields. The investigations are based on modern functionals with zero range and density dependent coupling constants. After a self-consistent solution of the Relativistic Mean Field (RMF) equations for the nuclear ground states multipole giant resonances are studied within the Relativistic Random Phase Approximation (RRPA), the small amplitude limit of the time-dependent RMF. The coupling to the continuum is treated precisely by calculating the single particle Greens-function of the corresponding Dirac equation. In conventional methods based on a discretization of the continuum this was not possible. The residual interaction is derived from the same RMF Lagrangian. This guarantees current conservation and a precise decoupling of the Goldstone modes. For nuclei with open shells pairing correlations are taken into account in the framework of BCS theory and relativistic quasiparticle RPA. Continuum RPA (CRPA) presents a robust method connected with an astonishing reduction of the numerical effort as compared to conventional methods. Modes of various multipolarities and isospin are investigated, in particular also the newly discovered Pygmy modes in the vicinity of the neutron evaporation threshold. The results are compared with conventional discrete RPA calculations as well as with experimental data. We find that the full treatment of the continuum is essential for light nuclei and the study of resonances in the neighborhood of the threshold. (orig.)

Canonical theory of spherically symmetric spacetimes with cross-streaming null dusts

Science.gov (United States)

Bičák, Jiří; Hájíček, Petr

2003-11-01

The Hamiltonian dynamics of two-component spherically symmetric null dust is studied with regard to the quantum theory of gravitational collapse. The components—the ingoing and outgoing dusts—are assumed to interact only through gravitation. Different kinds of singularities, naked or “clothed,” which can form during collapse processes are described. The general canonical formulation of the one-component null-dust dynamics by Bičák and Kuchař is restricted to the spherically symmetric case and used to construct an action for the two components. The transformation from a metric variable to the quasilocal mass is shown to simplify the mathematics. The action is reduced by a choice of gauge and the corresponding true Hamiltonian is written down. Asymptotic coordinates and energy densities of dust shells are shown to form a complete set of Dirac observables. The action of the asymptotic time translation on the observables is defined but it has been calculated explicitly only in the case of one-component dust (Vaidya metric).

New Trends in Approximation Theory : in Memory of André Boivin

CERN Document Server

Manolaki, Myrto; Gauthier, Paul

2018-01-01

The international conference entitled "New Trends in Approximation Theory" was held at the Fields Institute, in Toronto, from July 25 until July 29, 2016. The conference was fondly dedicated to the memory of our unique friend and colleague, André Boivin, who gave tireless service in Canada until his very last moment of his life in October 2014. The impact of his warm personality and his fine work on Complex Approximation Theory was reflected by the mathematical excellence and the wide research range of the 37 participants. In total there were 27 talks, delivered by well-established mathematicians and young researchers. In particular, 19 invited lectures were delivered by leading experts of the field, from 8 different countries. The wide variety of presentations composed a mosaic of aspects of approximation theory, highlighting interesting connections with important contemporary areas of Analysis. Primary topics discussed include application of approximation theory (isoperimetric inequalities, construction of...

Modification of linear response theory for mean-field approximations

NARCIS (Netherlands)

Hütter, M.; Öttinger, H.C.

1996-01-01

In the framework of statistical descriptions of many particle systems, the influence of mean-field approximations on the linear response theory is studied. A procedure, analogous to one where no mean-field approximation is involved, is used in order to determine the first order response of the

Numerical Test of Different Approximations Used in the Transport Theory of Energetic Particles

Science.gov (United States)

Qin, G.; Shalchi, A.

2016-05-01

Recently developed theories for perpendicular diffusion work remarkably well. The diffusion coefficients they provide agree with test-particle simulations performed for different turbulence setups ranging from slab and slab-like models to two-dimensional and noisy reduced MHD turbulence. However, such theories are still based on different analytical approximations. In the current paper we use a test-particle code to explore the different approximations used in diffusion theory. We benchmark different guiding center approximations, simplifications of higher-order correlations, and the Taylor-Green-Kubo formula. We demonstrate that guiding center approximations work very well as long as the particle's unperturbed Larmor radius is smaller than the perpendicular correlation length of the turbulence. Furthermore, the Taylor-Green-Kubo formula and the definition of perpendicular diffusion coefficients via mean square displacements provide the same results. The only approximation that was used in the past in nonlinear diffusion theory that fails is to replace fourth-order correlations by a product of two second-order correlation functions. In more advanced nonlinear theories, however, this type of approximation is no longer used. Therefore, we confirm the validity of modern diffusion theories as a result of the work presented in the current paper.

Some approximate calculations in SU2 lattice mean field theory

International Nuclear Information System (INIS)

Hari Dass, N.D.; Lauwers, P.G.

1981-12-01

Approximate calculations are performed for small Wilson loops of SU 2 lattice gauge theory in mean field approximation. Reasonable agreement is found with Monte Carlo data. Ways of improving these calculations are discussed. (Auth.)

Spherically Symmetric Geometries in f(T) and f(R) Gravitational Theories

International Nuclear Information System (INIS)

Nashed, Gamal G. L.

2015-01-01

Using the well know relation between Ricci scalar, R, and torsion scalar, T, that is, R=-T-2∇_αT"α, we show that, for any spherically symmetric spacetime whose (i) scalar torsion vanishing, that is, T=T_μ_ν"αS_α"μ"ν=0 or (ii) total derivative term, that is, ∇_αT"α with T"α is the contraction of the torsion, vanishing, or (iii) the combination of scalar torsion and total derivative term vanishing, could be solution for f(T) and f(R) gravitational theories.

Towards an analytical theory for charged hard spheres

Directory of Open Access Journals (Sweden)

L.Blum

2007-09-01

Full Text Available Ion mixtures require an exclusion core to avoid collapse. The Debye Hueckel (DH theory, where ions are point charges, is accurate only in the limit of infinite dilution. The mean spherical approximation (MSA is the embedding of hard cores into DH, and is valid for higher densities. The properties of any ionic mixture can be represented by the single screening parameter Γ which for the equal ionic size restricted model is obtained from the Debye parameter κ. This Γ representation, the binding mean spherical approximation (BIMSA, is also valid for complex/associating systems, such as the general n-polyelectrolytes. The BIMSA is the only theory that satisfies the infinite dilution limit of the DH theory for any chain length. Furthermore, the contact pair distribution function calculated from our theory agrees with the Monte Carlo of Bresmeea. (Phys. Rev. E, 1995, 51, 289.

ɛ-connectedness, finite approximations, shape theory and coarse graining in hyperspaces

Science.gov (United States)

Alonso-Morón, Manuel; Cuchillo-Ibanez, Eduardo; Luzón, Ana

2008-12-01

We use upper semifinite hyperspaces of compacta to describe ε-connectedness and to compute homology from finite approximations. We find a new connection between ε-connectedness and the so-called Shape Theory. We construct a geodesically complete R-tree, by means of ε-components at different resolutions, whose behavior at infinite captures the topological structure of the space of components of a given compact metric space. We also construct inverse sequences of finite spaces using internal finite approximations of compact metric spaces. These sequences can be converted into inverse sequences of polyhedra and simplicial maps by means of what we call the Alexandroff-McCord correspondence. This correspondence allows us to relate upper semifinite hyperspaces of finite approximation with the Vietoris-Rips complexes of such approximations at different resolutions. Two motivating examples are included in the introduction. We propose this procedure as a different mathematical foundation for problems on data analysis. This process is intrinsically related to the methodology of shape theory. This paper reinforces Robins’s idea of using methods from shape theory to compute homology from finite approximations.

Parallel/vector algorithms for the spherical SN transport theory method

International Nuclear Information System (INIS)

Haghighat, A.; Mattis, R.E.

1990-01-01

This paper discusses vector and parallel processing of a 1-D curvilinear (i.e. spherical) S N transport theory algorithm on the Cornell National SuperComputer Facility (CNSF) IBM 3090/600E. Two different vector algorithms were developed and parallelized based on angular decomposition. It is shown that significant speedups are attainable. For example, for problems with large granularity, using 4 processors, the parallel/vector algorithm achieves speedups (for wall-clock time) of more than 4.5 relative to the old serial/scalar algorithm. Furthermore, this work has demonstrated the existing potential for the development of faster processing vector and parallel algorithms for multidimensional curvilinear geometries. (author)

Communication: Random phase approximation renormalized many-body perturbation theory

International Nuclear Information System (INIS)

Bates, Jefferson E.; Furche, Filipp

2013-01-01

We derive a renormalized many-body perturbation theory (MBPT) starting from the random phase approximation (RPA). This RPA-renormalized perturbation theory extends the scope of single-reference MBPT methods to small-gap systems without significantly increasing the computational cost. The leading correction to RPA, termed the approximate exchange kernel (AXK), substantially improves upon RPA atomization energies and ionization potentials without affecting other properties such as barrier heights where RPA is already accurate. Thus, AXK is more balanced than second-order screened exchange [A. Grüneis et al., J. Chem. Phys. 131, 154115 (2009)], which tends to overcorrect RPA for systems with stronger static correlation. Similarly, AXK avoids the divergence of second-order Møller-Plesset (MP2) theory for small gap systems and delivers a much more consistent performance than MP2 across the periodic table at comparable cost. RPA+AXK thus is an accurate, non-empirical, and robust tool to assess and improve semi-local density functional theory for a wide range of systems previously inaccessible to first-principles electronic structure calculations

Polarized Radiative Transfer of a Cirrus Cloud Consisting of Randomly Oriented Hexagonal Ice Crystals: The 3 x 3 Approximation for Non-Spherical Particles

Science.gov (United States)

Stamnes, S.; Ou, S. C.; Lin, Z.; Takano, Y.; Tsay, S. C.; Liou, K.N.; Stamnes, K.

2016-01-01

The reflection and transmission of polarized light for a cirrus cloud consisting of randomly oriented hexagonal columns were calculated by two very different vector radiative transfer models. The forward peak of the phase function for the ensemble-averaged ice crystals has a value of order 6 x 10(exp 3) so a truncation procedure was used to help produce numerically efficient yet accurate results. One of these models, the Vectorized Line-by-Line Equivalent model (VLBLE), is based on the doubling- adding principle, while the other is based on a vector discrete ordinates method (VDISORT). A comparison shows that the two models provide very close although not entirely identical results, which can be explained by differences in treatment of single scattering and the representation of the scattering phase matrix. The relative differences in the reflected I and Q Stokes parameters are within 0.5 for I and within 1.5 for Q for all viewing angles. In 1971 Hansen showed that for scattering by spherical particles the 3 x 3 approximation is sufficient to produce accurate results for the reflected radiance I and the degree of polarization (DOP), and he conjectured that these results would hold also for non-spherical particles. Simulations were conducted to test Hansen's conjecture for the cirrus cloud particles considered in this study. It was found that the 3 x 3 approximation also gives accurate results for the transmitted light, and for Q and U in addition to I and DOP. For these non-spherical ice particles the 3 x 3 approximation leads to an absolute error 2 x 10(exp -6) for the reflected and transmitted I, Q and U Stokes parameters. Hence, it appears to be an excellent approximation, which significantly reduces the computational complexity and burden required for multiple scattering calculations.

Hard Thermal Loop approximation in the Light Front Quantum Field Theory

International Nuclear Information System (INIS)

Silva, Charles da Rocha; Perez, Silvana

2011-01-01

Full text: In this paper we generalize the Hard Thermal Loop approximation (HTL) for the Thermal Light Front Quantum Field Theory. This technique was developed by Braaten e Pisarski [PRL. 63 (1989) 1129, Nucl. Phys. B337 (1990) 569], for the Thermal Quantum Field Theory at equal time and is particularly useful to solve problems of convergence of the amplitudes within Quantum Chromodynamics, caused by the inherently nonperturbative behavior. The HTL approximation satisfies simple Ward identities, is ultraviolet finite and gauge independent. Here we use the light front generalized coordinates (GLFC) proposed by one of us (V. S. Alves, Ashok Das, e Silvana Perez [PRD. 66, (2002) 125008]) and analyze the one loop amplitudes for the λφ3 theory and the Quantum Electrodynamics in (3+1) dimensions at finite temperature in the HTL approximation. For the scalar theory, we evaluate the two-point function, recovering the usual dispersion relations. We also analyze the rotational invariance of the model. We then consider the Quantum Electrodynamics in (3+1) dimensions and calculate the polarization tensor and the vertex function at finite temperature in the HTL approximation. In future, our interest will be to apply the Generalized Light Front formalism to understand the confinement mechanism which occurs in the Quantum Chromodynamics. There is an expectation that the Light Front Quantum Field Theory formalism is more appropriate to study this problems. (author)

Hard Thermal Loop approximation in the Light Front Quantum Field Theory

Energy Technology Data Exchange (ETDEWEB)

Silva, Charles da Rocha [Instituto Federal de Educacao, Ciencia e Tecnologia do Para (IFPA), Belem, PA (Brazil); Universidade Federal do Para (UFPA), Belem, PA (Brazil); Perez, Silvana [Universidade Federal do Para (UFPA), Belem, PA (Brazil)

2011-07-01

Full text: In this paper we generalize the Hard Thermal Loop approximation (HTL) for the Thermal Light Front Quantum Field Theory. This technique was developed by Braaten e Pisarski [PRL. 63 (1989) 1129, Nucl. Phys. B337 (1990) 569], for the Thermal Quantum Field Theory at equal time and is particularly useful to solve problems of convergence of the amplitudes within Quantum Chromodynamics, caused by the inherently nonperturbative behavior. The HTL approximation satisfies simple Ward identities, is ultraviolet finite and gauge independent. Here we use the light front generalized coordinates (GLFC) proposed by one of us (V. S. Alves, Ashok Das, e Silvana Perez [PRD. 66, (2002) 125008]) and analyze the one loop amplitudes for the {lambda}{phi}3 theory and the Quantum Electrodynamics in (3+1) dimensions at finite temperature in the HTL approximation. For the scalar theory, we evaluate the two-point function, recovering the usual dispersion relations. We also analyze the rotational invariance of the model. We then consider the Quantum Electrodynamics in (3+1) dimensions and calculate the polarization tensor and the vertex function at finite temperature in the HTL approximation. In future, our interest will be to apply the Generalized Light Front formalism to understand the confinement mechanism which occurs in the Quantum Chromodynamics. There is an expectation that the Light Front Quantum Field Theory formalism is more appropriate to study this problems. (author)

Orbitally invariant internally contracted multireference unitary coupled cluster theory and its perturbative approximation: theory and test calculations of second order approximation.

Science.gov (United States)

Chen, Zhenhua; Hoffmann, Mark R

2012-07-07

A unitary wave operator, exp (G), G(+) = -G, is considered to transform a multiconfigurational reference wave function Φ to the potentially exact, within basis set limit, wave function Ψ = exp (G)Φ. To obtain a useful approximation, the Hausdorff expansion of the similarity transformed effective Hamiltonian, exp (-G)Hexp (G), is truncated at second order and the excitation manifold is limited; an additional separate perturbation approximation can also be made. In the perturbation approximation, which we refer to as multireference unitary second-order perturbation theory (MRUPT2), the Hamiltonian operator in the highest order commutator is approximated by a Mo̸ller-Plesset-type one-body zero-order Hamiltonian. If a complete active space self-consistent field wave function is used as reference, then the energy is invariant under orbital rotations within the inactive, active, and virtual orbital subspaces for both the second-order unitary coupled cluster method and its perturbative approximation. Furthermore, the redundancies of the excitation operators are addressed in a novel way, which is potentially more efficient compared to the usual full diagonalization of the metric of the excited configurations. Despite the loss of rigorous size-extensivity possibly due to the use of a variational approach rather than a projective one in the solution of the amplitudes, test calculations show that the size-extensivity errors are very small. Compared to other internally contracted multireference perturbation theories, MRUPT2 only needs reduced density matrices up to three-body even with a non-complete active space reference wave function when two-body excitations within the active orbital subspace are involved in the wave operator, exp (G). Both the coupled cluster and perturbation theory variants are amenable to large, incomplete model spaces. Applications to some widely studied model systems that can be problematic because of geometry dependent quasidegeneracy, H4, P4

Progress in approximation theory and applicable complex analysis in memory of Q.I. Rahman

CERN Document Server

Mohapatra, Ram; Qazi, Mohammed; Schmeisser, Gerhard

2017-01-01

Current and historical research methods in approximation theory are presented in this book beginning with the 1800s and following the evolution of approximation theory via the refinement and extension of classical methods and ending with recent techniques and methodologies. Graduate students, postdocs, and researchers in mathematics, specifically those working in the theory of functions, approximation theory, geometric function theory, and optimization will find new insights as well as a guide to advanced topics. The chapters in this book are grouped into four themes; the first, polynomials (Chapters 1 –8), includes inequalities for polynomials and rational functions, orthogonal polynomials, and location of zeros. The second, inequalities and extremal problems are discussed in Chapters 9 –13. The third, approximation of functions, involves the approximants being polynomials, rational functions, and other types of functions and are covered in Chapters 14 –19. The last theme, quadrature, cubature and appl...

A CLOSED-FORM EXPRESSION APPROXIMATING THE MIE SOLUTION FOR THE REAL-IN-LINE TRANSMISSION OF CERAMICS WITH SPHERICAL INCLUSIONS OR PORES

Directory of Open Access Journals (Sweden)

Pabst W.

2013-06-01

Full Text Available A new closed-form expression is presented for estimating the real-in-line transmission of ceramics consisting of non-absorbing phases in dependence of the inclusion or pore size. The classic approximations to the exact Mie solution of the scattering problem for spheres are recalled (Rayleigh, Fraunhofer, Rayleigh-Gans-Debye/RGD, van de Hulst, and it is recalled that the large-size variant of the RGD approximation is the basis of the Apetz-van-Bruggen approach. All approximations and our closed-form expression are compared mutually and vis-a-vis the exact Mie solution. A parametric study is performed for monochromatic light in the visible range (600 nm for two model systems corresponding to composites of yttrium aluminum garnet (YAG, refractive index 1.832 with spherical alumina inclusions (refractive index 1.767, and to porous YAG ceramics with spherical pores (refractive index 1. It is shown that for the YAG-alumina composites to achieve maximum transmission with inclusion volume fractions of 1 % (and slab thickness 1 mm, inclusion sizes of up to 100 nm can be tolerated, while pore sizes of 100 nm will be completely detrimental for porosities as low as 0.1 %. While the van-de-Hulst approximation is excellent for small phase contrast and low concentration of inclusions, it fails for principal reasons for small inclusion or pore sizes. Our closed-form expression, while less precise in the aforementioned special case, is always the safer choice and performs better in most cases of practical interest, including high phase contrasts and high concentrations of inclusions or pores.

Variational formulation of two scalar-tetradic theories of gravitation

International Nuclear Information System (INIS)

Saez, D.

1983-01-01

In this paper we obtain two scalar-tetradic theories of gravitation (theories A and B) from a variational principle. In these theories the gravitational energy is localized and the principle of equivalence holds. They combine some aspects of Moller theory and the Brans-Dicke theory. The first-order approximations and an introduction to the study of both theories in the static spherically symmetric case are presented

Vacancy-rearrangement theory in the first Magnus approximation

International Nuclear Information System (INIS)

Becker, R.L.

1984-01-01

In the present paper we employ the first Magnus approximation (M1A), a unitarized Born approximation, in semiclassical collision theory. We have found previously that the M1A gives a substantial improvement over the first Born approximation (B1A) and can give a good approximation to a full coupled channels calculation of the mean L-shell vacancy probability per electron, p/sub L/, when the L-vacancies are accompanied by a K-shell vacancy (p/sub L/ is obtained experimentally from measurements of K/sub α/-satellite intensities). For sufficiently strong projectile-electron interactions (sufficiently large Z/sub p/ or small v) the M1A ceases to reproduce the coupled channels results, but it is accurate over a much wider range of Z/sub p/ and v than the B1A. 27 references

A modular spherical harmonics approach to the neutron transport equation

International Nuclear Information System (INIS)

Inanc, F.; Rohach, A.F.

1989-01-01

A modular nodal method was developed for solving the neutron transport equation in 2-D xy coordinates. The spherical harmonic expansion was used for approximating the second-order even-parity form of the neutron transport equation. The boundary conditions of the spherical harmonics approximation were derived in a form to have forms analogous to the partial currents in the neutron diffusion equation. Relations were developed for generating both the second-order spherical harmonic equations and the boundary conditions in an automated computational algorithm. Nodes using different orders of the spherical harmonics approximation to the transport equation were interfaced through mixed-type boundary conditions. The determination of spherical harmonic orders implemented in the nodes were determined by the scheme in an automated manner. Results of the method compared favorably to benchmark problems. (author)

Space-angle approximations in the variational nodal method

International Nuclear Information System (INIS)

Lewis, E. E.; Palmiotti, G.; Taiwo, T.

1999-01-01

The variational nodal method is formulated such that the angular and spatial approximations maybe examined separately. Spherical harmonic, simplified spherical harmonic, and discrete ordinate approximations are coupled to the primal hybrid finite element treatment of the spatial variables. Within this framework, two classes of spatial trial functions are presented: (1) orthogonal polynomials for the treatment of homogeneous nodes and (2) bilinear finite subelement trial functions for the treatment of fuel assembly sized nodes in which fuel-pin cell cross sections are represented explicitly. Polynomial and subelement trial functions are applied to benchmark water-reactor problems containing MOX fuel using spherical harmonic and simplified spherical harmonic approximations. The resulting accuracy and computing costs are compared

Nucleation theory - Is replacement free energy needed?. [error analysis of capillary approximation

Science.gov (United States)

Doremus, R. H.

1982-01-01

It has been suggested that the classical theory of nucleation of liquid from its vapor as developed by Volmer and Weber (1926) needs modification with a factor referred to as the replacement free energy and that the capillary approximation underlying the classical theory is in error. Here, the classical nucleation equation is derived from fluctuation theory, Gibb's result for the reversible work to form a critical nucleus, and the rate of collision of gas molecules with a surface. The capillary approximation is not used in the derivation. The chemical potential of small drops is then considered, and it is shown that the capillary approximation can be derived from thermodynamic equations. The results show that no corrections to Volmer's equation are needed.

Description of spherical heavy nuclei in a model of interacting quasi particles. Application to tin isotopes

International Nuclear Information System (INIS)

Arvieu, Robert

1963-01-01

This research thesis deals with nuclear physics theory, and more particularly with the issues of collective states and matching properties. In a first part, the author presents the formalism and approximations used to obtain individual states and collective states of spherical nuclei, notably by studying the Bogoliubov-Valatin transformation and how it is possible to report matching phenomena, and then by introducing collective modes by means of an approximate diagonalization and of the 'quasi bosons' method. The phenomenon mechanism is described on a simple example, and, in a second part, the theory is applied to the detailed description of tin isotopes by means of finite range interaction

Relativistic time-dependent local-density approximation theory and applications to atomic physics

International Nuclear Information System (INIS)

Parpia, F.Z.

1984-01-01

A time-dependent linear-response theory appropriate to the relativistic local-density approximation (RLDA) to quantum electrodynamics (QED) is developed. The resulting theory, the relativistic time-dependent local-density approximation (RTDLDA) is specialized to the treatment of electric excitations in closed-shell atoms. This formalism is applied to the calculation of atomic photoionization parameters in the dipole approximation. The static-field limit of the RTDLDA is applied to the calculation of dipole polarizabilities. Extensive numerical calculations of the photoionization parameters for the rare gases neon, argon, krypton, and xenon, and for mercury from the RTDLDA are presented and compared in detail with the results of other theories, in particular the relativistic random-phase approximation (RRPA), and with experimental measurements. The predictions of the RTDLDA are comparable with the RRPA calculations made to date. This is remarkable in that the RTDLDA entails appreciably less computational effort. Finally, the dipole polarizabilities predicted by the static-field RTDLDA are compared with other determinations of these quantities. In view of its simplicity, the static-field RTDLDA demonstrates itself to be one of the most powerful theories available for the calculation of dipole polarizabilities

Fundamentals and approximations of multilevel resonance theory for reactor physics applications

International Nuclear Information System (INIS)

Moore, M.S.

1980-01-01

The formal theory of nuclear reactions leads to any of a number of alternative representations for describing resonance behavior. None of these is satisfactory for applications, and, depending on the problem to be addressed, approximate expressions are used. The specializations and approximations found to be most useful by evaluators are derived from R-matrix theory and are discussed from the viewpoint of convenience in numerical calculations. Finally, we illustrate the application of the theory by reviewing a particular example: the spin-separated neutron-induced cross sections of 235 U in the resolved and unresolved resonance regions and the use of these results in the U.S. evaluated nuclear data file ENDF/B. (author)

Variational, projection methods and Pade approximants in scattering theory

International Nuclear Information System (INIS)

Turchetti, G.

1980-12-01

Several aspects on the scattering theory are discussed in a perturbative scheme. The Pade approximant method plays an important role in such a scheme. Solitons solutions are also discussed in this same scheme. (L.C.) [pt

Gravitational effects in field gravitation theory

International Nuclear Information System (INIS)

Denisov, V.I.; Logunov, A.A.; Mestvirishvili, M.A.; Vlasov, A.A.

1979-01-01

The possibilities to describe various gravitation effects of field gravitation theory (FGT) are considered. Past-Newtonian approximation of the FGT has been constructed and on the basis of this approximation it has been shown that the field theory allows one to describe the whole set of experimental facts. The comparison of post-Newtonian parameters in FGT with those in the Einstein's theory makes it clear that these two; theories are undistinguishable from the viewpoint of any experiments, realized with post-Newtonian accuracy. Gravitational field of an island type source with spherically symmetrical distribution of matter and unstationary homogeneous model of Universe, which allows to describe the effect of cosmological red shift, are considered

Thermodynamic properties and static structure factor for a Yukawa fluid in the mean spherical approximation.

Science.gov (United States)

Montes-Perez, J; Cruz-Vera, A; Herrera, J N

2011-12-01

This work presents the full analytic expressions for the thermodynamic properties and the static structure factor for a hard sphere plus 1-Yukawa fluid within the mean spherical approximation. To obtain these properties of the fluid type Yukawa analytically it was necessary to solve an equation of fourth order for the scaling parameter on a large scale. The physical root of this equation was determined by imposing physical conditions. The results of this work are obtained from seminal papers of Blum and Høye. We show that is not necessary the use the series expansion to solve the equation for the scaling parameter. We applied our theoretical result to find the thermodynamic and the static structure factor for krypton. Our results are in good agreement with those obtained in an experimental form or by simulation using the Monte Carlo method.

Effect of the spherical Earth on a simple pendulum

OpenAIRE

Burko, Lior M.

2003-01-01

We consider the period of a simple pendulum in the gravitational field of the spherical Earth. Effectively, gravity is enhanced compared with the often used flat Earth approximation, such that the period of the pendulum is shortened. We discuss the flat Earth approximation, and show when the corrections due to the spherical Earth may be of interest.

Nonlinear analysis approximation theory, optimization and applications

CERN Document Server

2014-01-01

Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.

Semiclassical approximations in a mean-field theory with collision terms

International Nuclear Information System (INIS)

Galetti, D.

1986-01-01

Semiclassical approximations in a mean-field theory with collision terms are discussed taking the time dependent Hartree-Fock method as framework in the obtainment of the relevant parameters.(L.C.) [pt

Generalized theory of resonance excitation by sound scattering from an elastic spherical shell in a nonviscous fluid.

Science.gov (United States)

Mitri, Farid G

2012-08-01

This work presents the general theory of resonance scattering (GTRS) by an elastic spherical shell immersed in a nonviscous fluid and placed arbitrarily in an acoustic beam. The GTRS formulation is valid for a spherical shell of any size and material regardless of its location relative to the incident beam. It is shown here that the scattering coefficients derived for a spherical shell immersed in water and placed in an arbitrary beam equal those obtained for plane wave incidence. Numerical examples for an elastic shell placed in the field of acoustical Bessel beams of different types, namely, a zero-order Bessel beam and first-order Bessel vortex and trigonometric (nonvortex) beams are provided. The scattered pressure is expressed using a generalized partial-wave series expansion involving the beam-shape coefficients (BSCs), the scattering coefficients of the spherical shell, and the half-cone angle of the beam. The BSCs are evaluated using the numerical discrete spherical harmonics transform (DSHT). The far-field acoustic resonance scattering directivity diagrams are calculated for an albuminoidal shell immersed in water and filled with perfluoropropane gas, by subtracting an appropriate background from the total far-field form function. The properties related to the arbitrary scattering are analyzed and discussed. The results are of particular importance in acoustical scattering applications involving imaging and beam-forming for transducer design. Moreover, the GTRS method can be applied to investigate the scattering of any beam of arbitrary shape that satisfies the source-free Helmholtz equation, and the method can be readily adapted to viscoelastic spherical shells or spheres.

The perturbation theory model of a spherical oscillator in electric field and the vibrational stark effect in polyatomic molecular species

Science.gov (United States)

Petreska, Irina; Ivanovski, Gjorgji; Pejov, Ljupčo

2007-04-01

The effect of external electrostatic fields on the spherical oscillator energy states was studied using stationary perturbation theory. Besides the spherical oscillator with ideal symmetry, also a variety of the deformed systems were considered in which the deformations may be induced by the external fields, but also by the short-range crystal lattice forces. The perturbation theory analysis was carried out using the field-dependent basis functions. Predicted spectral appearances and band splittings due to the deformations and external field influences were shown to be helpful in interpreting the experimental spectra of molecular oscillator possessing subsets of mutually orthogonal triply degenerate normal modes (such as, e.g. tetrahedral species). To verify the results of the perturbation theory treatments, as well as to provide a further illustration of the usefulness of the employed technique, a numerical HF/aug-cc-pVTZ study of the vibrational states of methane molecule in external electrostatic field was performed.

Thermodynamic Analysis of the Static Spherically Symmetric Field Equations in Rastall Theory

International Nuclear Information System (INIS)

Moradpour, Hooman; Salako, Ines G.

2016-01-01

The restrictions on the Rastall theory due to application of the Newtonian limit to the theory are derived. In addition, we use the zero-zero component of the Rastall field equations as well as the unified first law of thermodynamics to find the Misner-Sharp mass content confined to the event horizon of the spherically symmetric static spacetimes in the Rastall framework. The obtained relation is calculated for the Schwarzschild and de-Sitter back holes as two examples. Bearing the obtained relation for the Misner-Sharp mass in mind together with recasting the one-one component of the Rastall field equations into the form of the first law of thermodynamics, we obtain expressions for the horizon entropy and the work term. Finally, we also compare the thermodynamic quantities of system, including energy, entropy, and work, with their counterparts in the Einstein framework to have a better view about the role of the Rastall hypothesis on the thermodynamics of system.

New perspectives on approximation and sampling theory Festschrift in honor of Paul Butzer's 85th birthday

CERN Document Server

Schmeisser, Gerhard

2014-01-01

Paul Butzer, who is considered the academic father and grandfather of many prominent mathematicians, has established one of the best schools in approximation and sampling theory in the world. He is one of the leading figures in approximation, sampling theory, and harmonic analysis. Although on April 15, 2013, Paul Butzer turned 85 years old, remarkably, he is still an active research mathematician. In celebration of Paul Butzer’s 85th birthday, New Perspectives on Approximation and Sampling Theory is a collection of invited chapters on approximation, sampling, and harmonic analysis written by students, friends, colleagues, and prominent active mathematicians. Topics covered include approximation methods using wavelets, multi-scale analysis, frames, and special functions. New Perspectives on Approximation and Sampling Theory requires basic knowledge of mathematical analysis, but efforts were made to keep the exposition clear and the chapters self-contained. This volume will appeal to researchers and graduate...

No surprise in the first Born approximation for electron scattering

International Nuclear Information System (INIS)

Lentzen, M.

2014-01-01

In a recent article it is argued that the far-field expansion of electron scattering, a pillar of electron diffraction theory, is wrong (Treacy and Van Dyck, 2012 [1]). It is further argued that in the first Born approximation of electron scattering the intensity of the electron wave is not conserved to first order in the scattering potential. Thus a “mystery of the missing phase” is investigated, and the supposed flaw in scattering theory is seeked to be resolved by postulating a standing spherical electron wave (Treacy and Van Dyck, 2012 [1]). In this work we show, however, that these theses are wrong. A review of the essential parts of scattering theory with careful checks of the underlying assumptions and limitations for high-energy electron scattering yields: (1) the traditional form of the far-field expansion, comprising a propagating spherical wave, is correct; (2) there is no room for a missing phase; (3) in the first Born approximation the intensity of the scattered wave is conserved to first order in the scattering potential. The various features of high-energy electron scattering are illustrated by wave-mechanical calculations for an explicit target model, a Gaussian phase object, and for a Si atom, considering the geometric conditions in high-resolution transmission electron microscopy. - Highlights: Treacy and Van Dyck (2012) argue that the far-field expansion of electron scattering is wrong. The chief theses of that former work are wrong. There is no room for the missing phase proposed by Treacy and Van Dyck. There is no violation of the intensity conservation to first order in the scattering potential. Calculations for a phase object and an atomic target confirm traditional scattering theory

Approximate analytic theory of the multijunction grill

International Nuclear Information System (INIS)

Hurtak, O.; Preinhaelter, J.

1991-03-01

An approximate analytic theory of the general multijunction grill is developed. Omitting the evanescent modes in the subsidiary waveguides both at the junction and at the grill mouth and neglecting multiple wave reflection, simple formulae are derived for the reflection coefficient, the amplitudes of the incident and reflected waves and the spectral power density. These quantities are expressed through the basic grill parameters (the electric length of the structure and phase shift between adjacent waveguides) and two sets of reflection coefficients describing wave reflections in the subsidiary waveguides at the junction and at the plasma. Approximate expressions for these coefficients are also given. The results are compared with a numerical solution of two specific examples; they were shown to be useful for the optimization and design of multijunction grills.For the JET structure it is shown that, in the case of a dense plasma,many results can be obtained from the simple formulae for a two-waveguide multijunction grill. (author) 12 figs., 12 refs

Non-linear perturbations of a spherically collapsing star

International Nuclear Information System (INIS)

Brizuela, David

2009-01-01

Linear perturbation theory has been a successful tool in General Relativity, and can be considered as complementary to full nonlinear simulations. Going to second and higher perturbative orders improves the approximation and offers a controlled way to analyze the nonlinearities of the theory, though the problem becomes much harder computationally. We present a systematic approach to the treatment of high order metric perturbations, focusing on the scenario of nonspherical perturbations of a dynamical spherical background. It is based on the combination of adapted geometrical variables and the use of efficient computer algebra techniques. After dealing with a number of theoretical issues, like the construction of gauge invariants, we apply the formalism to the particular case of a perfect fluid star surrounded by a vacuum exterior. We describe the regularization of the divergences of the perturbations at null infinity and the matching conditions through the surface of the star.

Renormalization and scaling behaviour of eikonal perturbation theories. [Eikonal approximation

Energy Technology Data Exchange (ETDEWEB)

Din, A M [Chalmers Tekniska Hoegskola, Goeteborg (Sweden). Institutionen foer Teoretisk Fysik; Nielsen, N K [Aarhus Univ. (Denmark)

1975-01-04

Some observations on the renormalization and scaling behaviour of the charged-particle propagator in scalar quantum electrodynamics, in the ordinary eikonal approximation as well as in the eikonal perturbation theory, are reported. The conclusions indicate that scaling behaviour is not realized in the simple sense.

Minimum Q Electrically Small Spherical Magnetic Dipole Antenna - Theory

DEFF Research Database (Denmark)

Breinbjerg, Olav; Kim, Oleksiy S.

2009-01-01

The stored energies, radiated power, and quality factor of a magnetic-dipole antenna, consisting of a spherical electrical surface current density enclosing a magnetic core, is obtained through direct spatial integration of the internally and externally radiated field expressed in terms...... of spherical vector waves. The obtained quality factor agrees with that of Wheeler and Thal for vanishing free-space electric radius but holds also for larger radii and facilitates the optimal choice of permeability in the presence of the resonances....

Approximating the Shifted Hartree-Exchange-Correlation Potential in Direct Energy Kohn-Sham Theory.

Science.gov (United States)

Sharpe, Daniel J; Levy, Mel; Tozer, David J

2018-02-13

Levy and Zahariev [Phys. Rev. Lett. 113 113002 (2014)] have proposed a new approach for performing density functional theory calculations, termed direct energy Kohn-Sham (DEKS) theory. In this approach, the electronic energy equals the sum of orbital energies, obtained from Kohn-Sham-like orbital equations involving a shifted Hartree-exchange-correlation potential, which must be approximated. In the present study, density scaling homogeneity considerations are used to facilitate DEKS calculations on a series of atoms and molecules, leading to three nonlocal approximations to the shifted potential. The first two rely on preliminary Kohn-Sham calculations using a standard generalized gradient approximation (GGA) exchange-correlation functional and the results illustrate the benefit of describing the dominant Hartree component of the shift exactly. A uniform electron gas analysis is used to eliminate the need for these preliminary Kohn-Sham calculations, leading to a potential with an unconventional form that yields encouraging results, providing strong motivation for further research in DEKS theory.

Stability of the spherical form of nuclei

International Nuclear Information System (INIS)

Sabry, A.A.

1976-08-01

An extension of the mass formula for a spherical nucleus in the drop model to include a largely deformed nucleus of different forms is investigated. It is found that although the spherical form is stable under small deformations from equilibrium, there exists for heavier nuclei another more favourable stable form, which can be approximated by two, or three touching prolate ellipsoids of revolution

Integrals of products of spherical functions

International Nuclear Information System (INIS)

Veverka, O.

1975-01-01

Various branches of mathematical physics use integral formulas of the products of spherical functions. In quantum mechanics and in transport theory the integrals ∫sub((4π))dΩ vectorYsub(s)sup(t)(Ω vector)Ysub(l)sup(k)(Ω vector)Ysub(n)sup(m)(Ω vector), ∫sub(-1)sup(1)dμPsub(s)sup(t)(μ)Psub(l)sup(k)(μ)Psub(n)sup(m)(μ), ∫sub(-1)sup(1)dμPsub(s)(μ)Psub(l)(μ)Psub(n)(μ) are generally applied, where Ysub(α)sup(β)(Ω vector) are spherical harmonics, Psub(α)sup(β)(μ) are associated Legendre functions, and Psub(α)(μ) are Legendre polynomials. In the paper, the general procedure of calculating the integrals of the products of any combination of spherical functions is given. The procedure is referred to in a report on the boundary conditions for the cylindrical geometry in neutron transport theory for both the outer and inner cylindrical boundaries. (author)

An efficient approach for electric load forecasting using distributed ART (adaptive resonance theory) and HS-ARTMAP (Hyper-spherical ARTMAP network) neural network

International Nuclear Information System (INIS)

Cai, Yuan; Wang, Jian-zhou; Tang, Yun; Yang, Yu-chen

2011-01-01

This paper presents a neural network based on adaptive resonance theory, named distributed ART (adaptive resonance theory) and HS-ARTMAP (Hyper-spherical ARTMAP network), applied to the electric load forecasting problem. The distributed ART combines the stable fast learning capabilities of winner-take-all ART systems with the noise tolerance and code compression capabilities of multi-layer perceptions. The HS-ARTMAP, a hybrid of an RBF (Radial Basis Function)-network-like module which uses hyper-sphere basis function substitute the Gaussian basis function and an ART-like module, performs incremental learning capabilities in function approximation problem. The HS-ARTMAP only receives the compressed distributed coding processed by distributed ART to deal with the proliferation problem which ARTMAP (adaptive resonance theory map) architecture often encounters and still performs well in electric load forecasting. To demonstrate the performance of the methodology, data from New South Wales and Victoria in Australia are illustrated. Results show that the developed method is much better than the traditional BP and single HS-ARTMAP neural network. -- Research highlights: → The processing of the presented network is based on compressed distributed data. It's an innovation among the adaptive resonance theory architecture. → The presented network decreases the proliferation the Fuzzy ARTMAP architectures usually encounter. → The network on-line forecasts electrical load accurately, stably. → Both one-period and multi-period load forecasting are executed using data of different cities.

On the independent particle approximation of Gauge theories: a simple example

International Nuclear Information System (INIS)

Palladino, B.E.

1992-08-01

In this work, the independent particle model formulation is studied as a mean-field approximation of gauge theories using the path integral approach in the framework of quantum electrodynamics in 1+1 dimensions. It is shown how a mean-field approximation scheme can be applied to fit an effective potential to an independent particle model, building a straightforward relation between the model and the associated gauge field theory. An example is made considering the problem of massive Dirac fermions on a line, the so called massive Schwinger model. An interesting result is found, indicating a behaviour of screening of the charges in the relativistic limit of strong coupling. A forthcoming application of the method developed to confining potentials in independent quark models for QCD is in view and is briefly discussed. (author)

Approximate self-consistent potentials for density-functional-theory exchange-correlation functionals

International Nuclear Information System (INIS)

Cafiero, Mauricio; Gonzalez, Carlos

2005-01-01

We show that potentials for exchange-correlation functionals within the Kohn-Sham density-functional-theory framework may be written as potentials for simpler functionals multiplied by a factor close to unity, and in a self-consistent field calculation, these effective potentials find the correct self-consistent solutions. This simple theory is demonstrated with self-consistent exchange-only calculations of the atomization energies of some small molecules using the Perdew-Kurth-Zupan-Blaha (PKZB) meta-generalized-gradient-approximation (meta-GGA) exchange functional. The atomization energies obtained with our method agree with or surpass previous meta-GGA calculations performed in a non-self-consistent manner. The results of this work suggest the utility of this simple theory to approximate exchange-correlation potentials corresponding to energy functionals too complicated to generate closed forms for their potentials. We hope that this method will encourage the development of complex functionals which have correct boundary conditions and are free of self-interaction errors without the worry that the functionals are too complex to differentiate to obtain potentials

Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes

DEFF Research Database (Denmark)

Zhang, H.W.; Schäffer, Hemming Andreas

2007-01-01

An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....

Spherical Demons: Fast Surface Registration

Science.gov (United States)

Yeo, B.T. Thomas; Sabuncu, Mert; Vercauteren, Tom; Ayache, Nicholas; Fischl, Bruce; Golland, Polina

2009-01-01

We present the fast Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizers for the modified demons objective function can be efficiently implemented on the sphere using convolution. Based on the one parameter subgroups of diffeomorphisms, the resulting registration is diffeomorphic and fast – registration of two cortical mesh models with more than 100k nodes takes less than 5 minutes, comparable to the fastest surface registration algorithms. Moreover, the accuracy of our method compares favorably to the popular FreeSurfer registration algorithm. We validate the technique in two different settings: (1) parcellation in a set of in-vivo cortical surfaces and (2) Brodmann area localization in ex-vivo cortical surfaces. PMID:18979813

Local density approximation for exchange in excited-state density functional theory

OpenAIRE

Harbola, Manoj K.; Samal, Prasanjit

2004-01-01

Local density approximation for the exchange energy is made for treatment of excited-states in density-functional theory. It is shown that taking care of the state-dependence of the LDA exchange energy functional leads to accurate excitation energies.

Motion of spinning particles. Post-Newtonian approximation in the Einstein-Cartan theory

Energy Technology Data Exchange (ETDEWEB)

Boccaletti, D; Agostini, W; Festa, P [Rome Univ. (Italy). Ist. di Matematica

1979-01-11

The equations of motion of spinning particles are obtained in the post-Newtonian approximation of the Einstein-Cartan theory. The starting point of the calculation is the Hehl combined equation and a semi-classical model is assumed for the system of spinning particles. Comparison is made with an analogous quantum result obtained in the context of Gupta quantization of the linearized Einstein theory.

Many-body perturbation theory using the density-functional concept: beyond the GW approximation.

Science.gov (United States)

Bruneval, Fabien; Sottile, Francesco; Olevano, Valerio; Del Sole, Rodolfo; Reining, Lucia

2005-05-13

We propose an alternative formulation of many-body perturbation theory that uses the density-functional concept. Instead of the usual four-point integral equation for the polarizability, we obtain a two-point one, which leads to excellent optical absorption and energy-loss spectra. The corresponding three-point vertex function and self-energy are then simply calculated via an integration, for any level of approximation. Moreover, we show the direct impact of this formulation on the time-dependent density-functional theory. Numerical results for the band gap of bulk silicon and solid argon illustrate corrections beyond the GW approximation for the self-energy.

Dynamics of Shape Fluctuations of Quasi-spherical Vesicles Revisited

DEFF Research Database (Denmark)

Miao, L.; Lomholt, Michael Andersen; Kleis, J.

2002-01-01

In this paper, the dynamics of spontaneous shape fluctuations of a single, giant quasi-spherical vesicle formed from a single lipid species is revisited theoretically. A coherent physical theory for the dynamics is developed based on a number of fundamental principles and considerations, and a sy......In this paper, the dynamics of spontaneous shape fluctuations of a single, giant quasi-spherical vesicle formed from a single lipid species is revisited theoretically. A coherent physical theory for the dynamics is developed based on a number of fundamental principles and considerations...... of the phenomenological constants in a canonical continuum description of fluid lipid-bilayer membranes and shown the consequences of this new interpretation in terms of the characteristics of the dynamics of vesicle shape fluctuations. Moreover, we have used the systematic formulation of our theory as a framework...... against which we have discussed the previously existing theories and their discrepancies. Finally, we have made a systematic prediction about the system-dependent characteristics of the relaxation dynamics of shape fluctuations of quasi-spherical vesicles with a view of experimental studies...

Diophantine approximation and badly approximable sets

DEFF Research Database (Denmark)

Kristensen, S.; Thorn, R.; Velani, S.

2006-01-01

. The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...

Position space Green's function and its application to a non-muffin tin band theory

International Nuclear Information System (INIS)

Brown, R.G.

1982-01-01

A new way of applying the non-spherically symmetric phase functional method of Williams and Van Morgan to the band structure problem is derived that results in a generalized (non-muffin tin) multiple scattering band theory that is variationally stationary and exact in the single-electron, local potential Schroedinger theory. The phase functional basis derived arises from considering integral equation solutions to differential equations of the Schroedinger or inhomogeneous Helmholtz type. It is shown to be conditionally complete on any spherical domain. It is applied to the ordinary scattering problem and the general multiple scattering problem, where it is shown that any multiple scattering theory that is muffin tin approximated can probably have the approximation removed. The so-called near field correction that is believed to destroy the separability of KKR-like band theories or multiple scattering problems where the bounding spheres of nearest neighbor domains overlap is shown to be generally absorbed in a convergent fashion into the usual sum over structure constants in the theory. The extension of this theory to a full self-consistent-field calculation is briefly discussed, but the actual derivations are deferred until various numerical tests in progress are completed

Modeling mantle convection in the spherical annulus

Science.gov (United States)

Hernlund, John W.; Tackley, Paul J.

2008-12-01

Most methods for modeling mantle convection in a two-dimensional (2D) circular annular domain suffer from innate shortcomings in their ability to capture several characteristics of the spherical shell geometry of planetary mantles. While methods such as rescaling the inner and outer radius to reduce anomalous effects in a 2D polar cylindrical coordinate system have been introduced and widely implemented, such fixes may have other drawbacks that adversely affect the outcome of some kinds of mantle convection studies. Here we propose a new approach that we term the "spherical annulus," which is a 2D slice that bisects the spherical shell and is quantitatively formulated at the equator of a spherical polar coordinate system after neglecting terms in the governing equations related to variations in latitude. Spherical scaling is retained in this approximation since the Jacobian function remains proportional to the square of the radius. We present example calculations to show that the behavior of convection in the spherical annulus compares favorably against calculations performed in other 2D annular domains when measured relative to those in a fully three-dimensional (3D) spherical shell.

The Pade approximate method for solving problems in plasma kinetic theory

International Nuclear Information System (INIS)

Jasperse, J.R.; Basu, B.

1992-01-01

The method of Pade Approximates has been a powerful tool in solving for the time dependent propagator (Green function) in model quantum field theories. We have developed a modified Pade method which we feel has promise for solving linearized collisional and weakly nonlinear problems in plasma kinetic theory. In order to illustrate the general applicability of the method, in this paper we discuss Pade solutions for the linearized collisional propagator and the collisional dielectric function for a model collisional problem. (author) 3 refs., 2 tabs

Theory of the interface between a classical plasma and a hard wall

International Nuclear Information System (INIS)

Ballone, P.; Pastore, G.; Tosi, M.P.; Trieste Univ.

1983-09-01

The interfacial density profile of a classical one-component plasma confined by a hard wall is studied in planar and spherical geometries. The approach adapts to interfacial problems a modified hypernetted-chain approximation developed by Lado and by Rosenfeld and Ashcroft for the bulk structure of simple liquids. The specific new aim is to embody self-consistently into the theory a 'contact theorem', fixing the plasma density at the wall through an equilibrium condition which involves the electrical potential drop across the interface and the bulk pressure. The theory is brought into fully quantitative contact with computer simulation data for a plasma confined in a spherical cavity of large but finite radius. It is also shown that the interfacial potential at the point of zero charge is accurately reproduced by suitably combining the contact theorem with relevant bulk properties in a simple, approximate representation of the interfacial charge density profile. (author)

Extended Finite Element Method with Simplified Spherical Harmonics Approximation for the Forward Model of Optical Molecular Imaging

Directory of Open Access Journals (Sweden)

Wei Li

2012-01-01

Full Text Available An extended finite element method (XFEM for the forward model of 3D optical molecular imaging is developed with simplified spherical harmonics approximation (SPN. In XFEM scheme of SPN equations, the signed distance function is employed to accurately represent the internal tissue boundary, and then it is used to construct the enriched basis function of the finite element scheme. Therefore, the finite element calculation can be carried out without the time-consuming internal boundary mesh generation. Moreover, the required overly fine mesh conforming to the complex tissue boundary which leads to excess time cost can be avoided. XFEM conveniences its application to tissues with complex internal structure and improves the computational efficiency. Phantom and digital mouse experiments were carried out to validate the efficiency of the proposed method. Compared with standard finite element method and classical Monte Carlo (MC method, the validation results show the merits and potential of the XFEM for optical imaging.

An approximation theory for nonlinear partial differential equations with applications to identification and control

Science.gov (United States)

Banks, H. T.; Kunisch, K.

1982-01-01

Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

Matrix model approximations of fuzzy scalar field theories and their phase diagrams

Energy Technology Data Exchange (ETDEWEB)

Tekel, Juraj [Department of Theoretical Physics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynska Dolina, Bratislava, 842 48 (Slovakia)

2015-12-29

We present an analysis of two different approximations to the scalar field theory on the fuzzy sphere, a nonperturbative and a perturbative one, which are both multitrace matrix models. We show that the former reproduces a phase diagram with correct features in a qualitative agreement with the previous numerical studies and that the latter gives a phase diagram with features not expected in the phase diagram of the field theory.

All the Four-Dimensional Static, Spherically Symmetric Solutions of Abelian Kaluza-Klein Theory

International Nuclear Information System (INIS)

Cvetic, M.; Youm, D.

1995-01-01

We present the explicit form for all the four-dimensional, static, spherically symmetric solutions in (4+n)-d Abelian Kaluza-Klein theory by performing a subset of SO(2,n) transformations corresponding to four SO(1,1) boosts on the Schwarzschild solution, supplemented by SO(n)/SO(n-2) transformations. The solutions are parametrized by the mass M, Taub-NUT charge a, and n electric rvec Q and n magnetic rvec P charges. Nonextreme black holes (with zero Taub-NUT charge) have either the Reissner-Nordstroem or Schwarzschild global space-time. Supersymmetric extreme black holes have a null or naked singularity, while nonsupersymmetric extreme ones have a global space-time of extreme Reissner-Nordstroem black holes. copyright 1995 The American Physical Society

Resonance energy transfer: The unified theory via vector spherical harmonics

Energy Technology Data Exchange (ETDEWEB)

Grinter, Roger, E-mail: r.grinter@uea.ac.uk; Jones, Garth A., E-mail: garth.jones@uea.ac.uk [School of Chemistry, University of East Anglia, Norwich NR4 7TJ (United Kingdom)

2016-08-21

In this work, we derive the well-established expression for the quantum amplitude associated with the resonance energy transfer (RET) process between a pair of molecules that are beyond wavefunction overlap. The novelty of this work is that the field of the mediating photon is described in terms of a spherical wave rather than a plane wave. The angular components of the field are constructed in terms of vector spherical harmonics while Hankel functions are used to define the radial component. This approach alleviates the problem of having to select physically correct solution from non-physical solutions, which seems to be inherent in plane wave derivations. The spherical coordinate system allows one to easily decompose the photon’s fields into longitudinal and transverse components and offers a natural way to analyse near-, intermediate-, and far-zone RET within the context of the relative orientation of the transition dipole moments for the two molecules.

Worldwide complete spherical Bouguer and isostatic anomaly maps

Science.gov (United States)

Bonvalot, S.; Balmino, G.; Briais, A.; Peyrefitte, A.; Vales, N.; Biancale, R.; Gabalda, G.; Reinquin, F.

2011-12-01

We present here a set of digital maps of the Earth's gravity anomalies (surface "free air", Bouguer and isostatic), computed at Bureau Gravimetric International (BGI) as a contribution to the Global Geodetic Observing Systems (GGOS) and to the global geophysical maps published by the Commission for the Geological Map of the World (CGMW). The free air and Bouguer anomaly concept is extensively used in geophysical interpretation to investigate the density distributions in the Earth's interior. Complete Bouguer anomalies (including terrain effects) are usually computed at regional scales by integrating the gravity attraction of topography elements over and beyond a given area (under planar or spherical approximations). Here, we developed and applied a worldwide spherical approach aimed to provide a set of homogeneous and high resolution gravity anomaly maps and grids computed at the Earth's surface, taking into account a realistic Earth model and reconciling geophysical and geodetic definitions of gravity anomalies. This first version (1.0) has been computed by spherical harmonics analysis / synthesis of the Earth's topography-bathymetry up to degree 10800. The detailed theory of the spherical harmonics approach is given in Balmino et al., (Journal of Geodesy, submitted). The Bouguer and terrain corrections have thus been computed in spherical geometry at 1'x1' resolution using the ETOPO1 topography/bathymetry, ice surface and bedrock models from the NOAA (National Oceanic and Atmospheric Administration) and taking into account precise characteristics (boundaries and densities) of major lakes, inner seas, polar caps and of land areas below sea level. Isostatic corrections have been computed according to the Airy Heiskanen model in spherical geometry for a constant depth of compensation of 30km. The gravity information given here is provided by the Earth Geopotential Model (EGM2008), developed at degree 2160 by the National Geospatial Intelligence Agency (NGA) (Pavlis

Spherical model for superfluidity in a restricted geometry

International Nuclear Information System (INIS)

Fishman, S.; Ziman, T.A.L.

1982-01-01

The spherical model is solved on a hypercubic lattice in d dimensions, each bond of which is decorated with l spins. The thermodynamic functions and the helicity modulus, analogous to a superfluid density, are calculated. We find that at least two spherical fields are required for the model to exhibit low-temperature properties that can approximate reasonably those of O(n) models. The heuristic prediction that the critical temperature behaves as T/sub c/(l)approx.(l+1) -1 is checked for the model and found to hold quite accurately even for small l(> or approx. =2). The helicity modulus and magnetization of the two-constraint spherical model are found to scale approximately with the critical temperature, but the relation between them is more complex than in the undecorated model. This relation is used to check heuristic arguments concerning the helicity modulus at low temperatures. We comment on the relevance to physical systems, in particular, the problem of boson condensation in a restricted geometry

Approximate models for broken clouds in stochastic radiative transfer theory

International Nuclear Information System (INIS)

Doicu, Adrian; Efremenko, Dmitry S.; Loyola, Diego; Trautmann, Thomas

2014-01-01

This paper presents approximate models in stochastic radiative transfer theory. The independent column approximation and its modified version with a solar source computed in a full three-dimensional atmosphere are formulated in a stochastic framework and for arbitrary cloud statistics. The nth-order stochastic models describing the independent column approximations are equivalent to the nth-order stochastic models for the original radiance fields in which the gradient vectors are neglected. Fast approximate models are further derived on the basis of zeroth-order stochastic models and the independent column approximation. The so-called “internal mixing” models assume a combination of the optical properties of the cloud and the clear sky, while the “external mixing” models assume a combination of the radiances corresponding to completely overcast and clear skies. A consistent treatment of internal and external mixing models is provided, and a new parameterization of the closure coefficient in the effective thickness approximation is given. An efficient computation of the closure coefficient for internal mixing models, using a previously derived vector stochastic model as a reference, is also presented. Equipped with appropriate look-up tables for the closure coefficient, these models can easily be integrated into operational trace gas retrieval systems that exploit absorption features in the near-IR solar spectrum. - Highlights: • Independent column approximation in a stochastic setting. • Fast internal and external mixing models for total and diffuse radiances. • Efficient optimization of internal mixing models to match reference models

Cooperative effects in spherical spasers

DEFF Research Database (Denmark)

Bordo, Vladimir

2017-01-01

A fully analytical semiclassical theory of cooperative optical processes which occur in an ensemble of molecules embedded in a spherical core-shell nanoparticle is developed from first principles. Both the plasmonic Dicke effect and spaser generation are investigated for the designs in which...... a shell/core contains an arbitrarily large number of active molecules in the vicinity of a metallic core/shell. An essential aspect of the theory is an ab initio account of the feedback from the core/shell boundaries which significantly modifies the molecular dynamics. The theory provides rigorous, albeit...

Simplified discrete ordinates method in spherical geometry

International Nuclear Information System (INIS)

Elsawi, M.A.; Abdurrahman, N.M.; Yavuz, M.

1999-01-01

The authors extend the method of simplified discrete ordinates (SS N ) to spherical geometry. The motivation for such an extension is that the appearance of the angular derivative (redistribution) term in the spherical geometry transport equation makes it difficult to decide which differencing scheme best approximates this term. In the present method, the angular derivative term is treated implicitly and thus avoids the need for the approximation of such term. This method can be considered to be analytic in nature with the advantage of being free from spatial truncation errors from which most of the existing transport codes suffer. In addition, it treats the angular redistribution term implicitly with the advantage of avoiding approximations to that term. The method also can handle scattering in a very general manner with the advantage of spending almost the same computational effort for all scattering modes. Moreover, the methods can easily be applied to higher-order S N calculations

January: IBM 7094 programme for the resolution of cell problems in planar, spherical and cylindrical geometry using the double P{sub n} approximation; Janvier: programme de resolution sur IBM 7094 des problemes de cellules en geometrie plane, spherique et cylindrique dans l'approximation double P{sub n}

Energy Technology Data Exchange (ETDEWEB)

Amouyal, A; Tariel, H [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1966-07-01

Code name: January 1{sup st} SCEA 011S. 2) Computer: IBM 7094; Programme system: Fortran II, 2{sup nd} version. 3) Nature of the problem: resolution of cell problems with one space variable (planar, spherical and cylindrical geometries) and with one energy group, with isotropic sources in the double P{sub n} approximation (DP 1 and DP 3 approximation in planar and spherical geometries, DP 1 and DP 2 in cylindrical geometry). 4) Method used: the differential equations with limiting conditions are transformed into differential system with initial conditions which are integrated by a separate-step method. 5) Restrictions: number of physical media < 100, number of geometrical regions < 100, number of points < 1000. 6) Physical approximations: limiting conditions for reflection, black body or grey body (restrictions for spherical and cylindrical geometries). The diffusion can include an isotropy term in cylindrical geometry, 2 terms in the other geometries. Taking into account of macroscopic data. 7) Duration: calculation time for a network of 100 points: planar and spherical geometry: double P 1 1 second, D P 3 = 4 seconds; cylindrical geometry: double P 1 2 seconds, D P 2 = 4 seconds. To these times should be added the 3 seconds required for the output. 8) State of the programme under production. (authors) [French] 1) Nom du Code: Janvier 1 SCEA 011S. 2) Calculateur: IBM 7094; Systeme de programmation: Fortran II version-2. 3) Nature du probleme: resolution des problemes de cellule a une variable d'espace (geometries plane, spherique et cylindrique) et un groupe d'energie, avec sources isotropes, dans l'approxirnation double P{sub n} (Approximations DP 1 et DP 3 en geometrie plane et spherique, approximations DP 1 et DP 2 en geometrie cylindrique). Methode employee: les equations differentielles avec conditions aux limites sont transformees en systemes differentiels avec conditions initiales que l'on integre par une methode a pas separes. 5) Restrictions: nombre de

Approximation scheme for strongly coupled plasmas: Dynamical theory

International Nuclear Information System (INIS)

Golden, K.I.; Kalman, G.

1979-01-01

The authors present a self-consistent approximation scheme for the calculation of the dynamical polarizability α (k, ω) at long wavelengths in strongly coupled one-component plasmas. Development of the scheme is carried out in two stages. The first stage follows the earlier Golden-Kalman-Silevitch (GKS) velocity-average approximation approach, but goes much further in its application of the nonlinear fluctuation-dissipation theorem to dynamical calculations. The result is the simple expression for α (k, ω), αatsub GKSat(k, ω) 4 moment sum rule. In the second stage, the above dynamical expression is made self-consistent at long wavelengths by postulating that a decomposition of the quadratic polarizabilities in terms of linear ones, which prevails in the k → 0 limit for weak coupling, can be relied upon as a paradigm for arbitrary coupling. The result is a relatively simple quadratic integral equation for α. Its evaluation in the weak-coupling limit and its comparison with known exact results in that limit reveal that almost all important correlational and long-time effects are reproduced by our theory with very good numerical accuracy over the entire frequency range; the only significant defect of the approximation seems to be the absence of the ''dominant'' γ ln γ -1 (γ is the plasma parameter) contribution to Im α

Approximate design theory for a simple block design with random block effects

OpenAIRE

Christof, Karin

1985-01-01

Approximate design theory for a simple block design with random block effects / K. Christof ; F. Pukelsheim. - In: Linear statistical inference / ed. by T. Calinski ... - Berlin u. a. : Springer, 1985. - S. 20-28. - (Lecture notes in statistics ; 35)

On the validity of the use of a localized approximation for helical beams. I. Formal aspects

Science.gov (United States)

Gouesbet, Gérard; André Ambrosio, Leonardo

2018-03-01

The description of an electromagnetic beam for use in light scattering theories may be carried out by using an expansion over vector spherical wave functions with expansion coefficients expressed in terms of Beam Shape Coefficients (BSCs). A celebrated method to evaluate these BSCs has been the use of localized approximations (with several existing variants). We recently established that the use of any existing localized approximation is of limited validity in the case of Bessel and Mathieu beams. In the present paper, we address a warning against the use of any existing localized approximation in the case of helical beams. More specifically, we demonstrate that a procedure used to validate any existing localized approximation fails in the case of helical beams. Numerical computations in a companion paper will confirm that existing localized approximations are of limited validity in the case of helical beams.

Theory of a spherical electrostatic probe in a continuum plasma: Analytical models

International Nuclear Information System (INIS)

Brailsford, A.D.

1977-01-01

A simple physical model of the charge distribution surrounding a biased spherical probe in a quiescent plasma, suggested by the theory of Su and Lam, is used to rederive the probe current-voltage characteristic. The result is compared with that of a slightly different version due to Kiel and with the exact numerical results of Baum and Chapkis. It is shown that if the ratio of the probe radius to the Debye length of the plasma is greater than or of the order of unity, the model calculation is in excellent agreement with the exact results when the dimensionless probe voltage phi/sup asterisk//sub p/,=vertical-barephi/sub p//kTvertical-bar in standard notation, is greater than 10, for both thick and thin sheaths. The comparison also provides an assessment of the importance of various additional validity criteria encountered in analytical treatments of the problem

Spherical proton emitters

International Nuclear Information System (INIS)

Berg, S.; Semmes, P.B.; Nazarewicz, W.

1997-01-01

Various theoretical approaches to proton emission from spherical nuclei are investigated, and it is found that all the methods employed give very similar results. The calculated decay widths are found to be qualitatively insensitive to the parameters of the proton-nucleus potential, i.e., changing the potential parameters over a fairly large range typically changes the decay width by no more than a factor of ∼3. Proton half-lives of observed heavy proton emitters are, in general, well reproduced by spherical calculations with the spectroscopic factors calculated in the independent quasiparticle approximation. The quantitative agreement with experimental data obtained in our study requires that the parameters of the proton-nucleus potential be chosen carefully. It also suggests that deformed proton emitters will provide invaluable spectroscopic information on the angular momentum decomposition of single-proton orbitals in deformed nuclei. copyright 1997 The American Physical Society

Analytic theory of the spherical electron to ion convertor

International Nuclear Information System (INIS)

Verdeyen, J.T.; Miller, P.A.

1980-01-01

Calculations will be presented which indicate that one could, with high efficiency, convert the electron beam energy transported from many pinched diode to ions at a reasonably sized evacuated spherical shell - or a light bulb

Spherical Tensor Calculus for Local Adaptive Filtering

Science.gov (United States)

Reisert, Marco; Burkhardt, Hans

In 3D image processing tensors play an important role. While rank-1 and rank-2 tensors are well understood and commonly used, higher rank tensors are rare. This is probably due to their cumbersome rotation behavior which prevents a computationally efficient use. In this chapter we want to introduce the notion of a spherical tensor which is based on the irreducible representations of the 3D rotation group. In fact, any ordinary cartesian tensor can be decomposed into a sum of spherical tensors, while each spherical tensor has a quite simple rotation behavior. We introduce so called tensorial harmonics that provide an orthogonal basis for spherical tensor fields of any rank. It is just a generalization of the well known spherical harmonics. Additionally we propose a spherical derivative which connects spherical tensor fields of different degree by differentiation. Based on the proposed theory we present two applications. We propose an efficient algorithm for dense tensor voting in 3D, which makes use of tensorial harmonics decomposition of the tensor-valued voting field. In this way it is possible to perform tensor voting by linear-combinations of convolutions in an efficient way. Secondly, we propose an anisotropic smoothing filter that uses a local shape and orientation adaptive filter kernel which can be computed efficiently by the use spherical derivatives.

Hartree-type approximation applied to a phi4 field theory

International Nuclear Information System (INIS)

Chang, S.-J.

1976-01-01

Recently, there has been considerable interest in studying the relativistic field theories by means of nonperturbative method. These studies are partially motivated by the now fashionable physical picture that the hadrons are created from an 'abnormal vacuum state'. This abnormal vacuum state is the ground state associated with a spontaneously broken symmetry and is usually characterized by the non-vanishing expectation value of one or more scale fields. Presently, nearly all understandings of hadrons in the above description are based on semi-classical calculations. It is important to know how significant are the effects of the quantum corrections. Some results on the quantum fluctuations in a phi 4 field theory based in a self-consistent Hartree-type approximation are described. (Auth.)

Complete hierarchies of efficient approximations to problems in entanglement theory

International Nuclear Information System (INIS)

Eisert, Jens; Hyllus, Philipp; Guehne, Otfried; Curty, Marcos

2004-01-01

We investigate several problems in entanglement theory from the perspective of convex optimization. This list of problems comprises (A) the decision whether a state is multiparty entangled, (B) the minimization of expectation values of entanglement witnesses with respect to pure product states, (C) the closely related evaluation of the geometric measure of entanglement to quantify pure multiparty entanglement, (D) the test whether states are multiparty entangled on the basis of witnesses based on second moments and on the basis of linear entropic criteria, and (E) the evaluation of instances of maximal output purities of quantum channels. We show that these problems can be formulated as certain optimization problems: as polynomially constrained problems employing polynomials of degree 3 or less. We then apply very recently established known methods from the theory of semidefinite relaxations to the formulated optimization problems. By this construction we arrive at a hierarchy of efficiently solvable approximations to the solution, approximating the exact solution as closely as desired, in a way that is asymptotically complete. For example, this results in a hierarchy of efficiently decidable sufficient criteria for multiparticle entanglement, such that every entangled state will necessarily be detected in some step of the hierarchy. Finally, we present numerical examples to demonstrate the practical accessibility of this approach

Finite-measuring approximation of operators of scattering theory in representation of wave packets

International Nuclear Information System (INIS)

Kukulin, V.I.; Rubtsova, O.A.

2004-01-01

Several types of the packet quantization of the continuos spectrum in the scattering theory quantum problems are considered. Such a quantization leads to the convenient finite-measuring (i.e. matrix) approximation of the integral operators in the scattering theory and it makes it possible to reduce the solution of the singular integral equations, complying with the scattering theory, to the convenient purely algebraic equations on the analytical basis, whereby all the singularities are separated in the obvious form. The main attention is paid to the problems of the method practical realization [ru

Analytic number theory, approximation theory, and special functions in honor of Hari M. Srivastava

CERN Document Server

Rassias, Michael

2014-01-01

This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality, and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics, and other computational and applied sciences.

Cellular neural network to the spherical harmonics approximation of neutron transport equation in x-y geometry. Part I: Modeling and verification for time-independent solution

International Nuclear Information System (INIS)

Pirouzmand, Ahmad; Hadad, Kamal

2011-01-01

Highlights: → This paper describes the solution of time-independent neutron transport equation. → Using a novel method based on cellular neural networks (CNNs) coupled with P N method. → Utilize the CNN model to simulate spatial scalar flux distribution in steady state. → The accuracy, stability, and capabilities of CNN model are examined in x-y geometry. - Abstract: This paper describes a novel method based on using cellular neural networks (CNN) coupled with spherical harmonics method (P N ) to solve the time-independent neutron transport equation in x-y geometry. To achieve this, an equivalent electrical circuit based on second-order form of neutron transport equation and relevant boundary conditions is obtained using CNN method. We use the CNN model to simulate spatial response of scalar flux distribution in the steady state condition for different order of spherical harmonics approximations. The accuracy, stability, and capabilities of CNN model are examined in 2D Cartesian geometry for fixed source and criticality problems.

Emulating Spherical Wave Channel Models in Multi-probe Anechoic Chamber Setups

DEFF Research Database (Denmark)

Fan, Wei; Carreño, Xavier; Nielsen, Jesper Ødum

2015-01-01

to emulate spherical wave channel models in multi-probe anechoic chamber setups. In this paper, a technique based on the field synthesis principle is proposed to approximate spherical waves emitted from arbitrarily located point sources with arbitrary polarizations. Simulation results show that static......Spherical wave channel modeling has attracted huge research attention for massive multiple-input multiple-output (MIMO) and short-distance MIMO systems. Current research work in multi-probe anechoic chamber systems is limited to reproduce radio channels assuming planar wavefronts. There is a need...... spherical waves can be reproduced with a limited number of probes, and the field synthesis accuracy of spherical wave depends on the location of the source point....

PADÉ APPROXIMANTS FOR THE EQUATION OF STATE FOR RELATIVISTIC HYDRODYNAMICS BY KINETIC THEORY

Energy Technology Data Exchange (ETDEWEB)

Tsai, Shang-Hsi; Yang, Jaw-Yen, E-mail: shanghsi@gmail.com [Institute of Applied Mechanics, National Taiwan University, Taipei 10764, Taiwan (China)

2015-07-20

A two-point Padé approximant (TPPA) algorithm is developed for the equation of state (EOS) for relativistic hydrodynamic systems, which are described by the classical Maxwell–Boltzmann statistics and the semiclassical Fermi–Dirac statistics with complete degeneracy. The underlying rational function is determined by the ratios of the macroscopic state variables with various orders of accuracy taken at the extreme relativistic limits. The nonunique TPPAs are validated by Taub's inequality for the consistency of the kinetic theory and the special theory of relativity. The proposed TPPA is utilized in deriving the EOS of the dilute gas and in calculating the specific heat capacity, the adiabatic index function, and the isentropic sound speed of the ideal gas. Some general guidelines are provided for the application of an arbitrary accuracy requirement. The superiority of the proposed TPPA is manifested in manipulating the constituent polynomials of the approximants, which avoids the arithmetic complexity of struggling with the modified Bessel functions and the hyperbolic trigonometric functions arising from the relativistic kinetic theory.

Computation of antenna pattern correlation and MIMO performance by means of surface current distribution and spherical wave theory

Directory of Open Access Journals (Sweden)

O. Klemp

2006-01-01

Full Text Available In order to satisfy the stringent demand for an accurate prediction of MIMO channel capacity and diversity performance in wireless communications, more effective and suitable models that account for real antenna radiation behavior have to be taken into account. One of the main challenges is the accurate modeling of antenna correlation that is directly related to the amount of channel capacity or diversity gain which might be achieved in multi element antenna configurations. Therefore spherical wave theory in electromagnetics is a well known technique to express antenna far fields by means of a compact field expansion with a reduced number of unknowns that was recently applied to derive an analytical approach in the computation of antenna pattern correlation. In this paper we present a novel and efficient computational technique to determine antenna pattern correlation based on the evaluation of the surface current distribution by means of a spherical mode expansion.

Measurements of plasma density fluctuations and electric wave fields using spherical electrostatic probes

International Nuclear Information System (INIS)

Eriksson, A.I.; Bostroem, R.

1995-04-01

Spherical electrostatic probes are in wide use for the measurements of electric fields and plasma density. This report concentrates on the measurements of fluctuations of these quantities rather than background values. Potential problems with the technique include the influence of density fluctuations on electric field measurements and vice versa, effects of varying satellite potential, and non-linear rectification in the probe and satellite sheaths. To study the actual importance of these and other possible effects, we simulate the response of the probe-satellite system to various wave phenomena in the plasma by applying approximate analytical as well as numerical methods. We use a set of non-linear probe equations, based on probe characteristics experimentally obtained in space, and therefore essentially independent of any specific probe theory. This approach is very useful since the probe theory for magnetized plasmas is incomplete. 47 refs

A theory of frequency domain invariants: spherical harmonic identities for BRDF/lighting transfer and image consistency.

Science.gov (United States)

Mahajan, Dhruv; Ramamoorthi, Ravi; Curless, Brian

2008-02-01

This paper develops a theory of frequency domain invariants in computer vision. We derive novel identities using spherical harmonics, which are the angular frequency domain analog to common spatial domain invariants such as reflectance ratios. These invariants are derived from the spherical harmonic convolution framework for reflection from a curved surface. Our identities apply in a number of canonical cases, including single and multiple images of objects under the same and different lighting conditions. One important case we consider is two different glossy objects in two different lighting environments. For this case, we derive a novel identity, independent of the specific lighting configurations or BRDFs, that allows us to directly estimate the fourth image if the other three are available. The identity can also be used as an invariant to detecttampering in the images. While this paper is primarily theoretical, it has the potential to lay the mathematical foundations for two important practical applications. First, we can develop more general algorithms for inverse rendering problems, which can directly relight and change material properties by transferring the BRDF or lighting from another object or illumination. Second, we can check the consistency of an image, to detect tampering or image splicing.

Effect of hydrostatic pressure in the ground state on the perturbed elastic deformable bodies in first post-Newtonian approximation

International Nuclear Information System (INIS)

Song Guoxuan

2009-01-01

Based on the dynamical equations for a nonrotating elastic deformable astronomical body in the first post-Newtonian approximation of Einstein's theory of gravity, we re-examined the boundary(junction) conditions and have proven that a term, which is missing in the customary boundary(junction) conditions, is found. This term is induced by the existence of initial equilibrium hydrostatic pressure. A physical explanation of this term is given in the Newtonian approximation as well. By using the correcting boundary conditions the relation of the free spherically symmetrical radial oscillation frequency of a nonrotating homogeneously and isotropically elastic sphere with constant density is derived.

Elastic properties of spherically anisotropic piezoelectric composites

International Nuclear Information System (INIS)

En-Bo, Wei; Guo-Qing, Gu; Ying-Ming, Poon

2010-01-01

Effective elastic properties of spherically anisotropic piezoelectric composites, whose spherically anisotropic piezoelectric inclusions are embedded in an infinite non-piezoelectric matrix, are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials under a uniform external strain are derived exactly. Taking into account of the coupling effects of elasticity, permittivity and piezoelectricity, the formula is derived for estimating the effective elastic properties based on the average field theory in the dilute limit. An elastic response mechanism is revealed, in which the effective elastic properties increase as inclusion piezoelectric properties increase and inclusion dielectric properties decrease. Moreover, a piezoelectric response mechanism, of which the effective piezoelectric response vanishes due to the symmetry of spherically anisotropic composite, is also disclosed. (condensed matter: structure, thermal and mechanical properties)

Lattice approximation of gauge theories with Dirac Kaehler fermions

International Nuclear Information System (INIS)

Joos, H.

1988-01-01

A program which tries to overcome the systematic difficulties caused by the lattice fermion problem by the consideration of models which describe Dirac fields by differential forms is reported. In the first lecture the formalism is developped and applied to the formulation of geometric QCD and of a Geometric Standard Model. The second lecture treats the characteristic symmetry problems which appear in the lattice approximation of geometric field theories. In the last lecture strong coupling dynamics of geometric QCD are considered with the final aim of a derivation of the quark model for the hadron spectrum. (author) [pt

Scattering by non-spherical particles of size comparable to a wavelength - A new semi-empirical theory. [atmospheric radiative transfer

Science.gov (United States)

Pollack, J. B.; Cuzzi, J. N.

1978-01-01

Mie theory, which is generally used to describe the scattering behavior of particles at a certain wavelength, is only rigorously correct for spherical particles. Particles found as atmospheric constituents, with the exception of cloud droplets, are, however, decidedly nonspherical. An investigation is, therefore, conducted regarding the significant ways in which the scattering behavior of irregularly shaped particles differs from that of spheres. A systematic method is formulated for treating the real scalar scattering behavior. A description is presented of a new semiempirical theory based on simple physical principles and data obtained in laboratory measurements, which successfully reproduces the single scattering phase function for a wide range of particle shapes, sizes, and refractive indices.

Ergodic model for the expansion of spherical nanoplasmas.

Science.gov (United States)

Peano, F; Coppa, G; Peinetti, F; Mulas, R; Silva, L O

2007-06-01

Recently, the collisionless expansion of spherical nanoplasmas has been analyzed with a new ergodic model, clarifying the transition from hydrodynamiclike to Coulomb-explosion regimes, and providing accurate laws for the relevant features of the phenomenon. A complete derivation of the model is presented here. The important issue of the self-consistent initial conditions is addressed by analyzing the initial charging transient due to the electron expansion, in the approximation of immobile ions. A comparison among different kinetic models for the expansion is presented, showing that the ergodic model provides a simplified description, which retains the essential information on the electron distribution, in particular, the energy spectrum. Results are presented for a wide range of initial conditions (determined from a single dimensionless parameter), in excellent agreement with calculations from the exact Vlasov-Poisson theory, thus providing a complete and detailed characterization of all the stages of the expansion.

A variational approach to operator and matrix Pade approximation. Applications to potential scattering and field theory

International Nuclear Information System (INIS)

Mery, P.

1977-01-01

The operator and matrix Pade approximation are defined. The fact that these approximants can be derived from the Schwinger variational principle is emphasized. In potential theory, using this variational aspect it is shown that the matrix Pade approximation allow to reproduce the exact solution of the Lippman-Schwinger equation with any required accuracy taking only into account the knowledge of the first two coefficients in the Born expansion. The deep analytic structure of this variational matrix Pade approximation (hyper Pade approximation) is discussed

Subsystem density functional theory with meta-generalized gradient approximation exchange-correlation functionals.

Science.gov (United States)

Śmiga, Szymon; Fabiano, Eduardo; Laricchia, Savio; Constantin, Lucian A; Della Sala, Fabio

2015-04-21

We analyze the methodology and the performance of subsystem density functional theory (DFT) with meta-generalized gradient approximation (meta-GGA) exchange-correlation functionals for non-bonded molecular systems. Meta-GGA functionals depend on the Kohn-Sham kinetic energy density (KED), which is not known as an explicit functional of the density. Therefore, they cannot be directly applied in subsystem DFT calculations. We propose a Laplacian-level approximation to the KED which overcomes this limitation and provides a simple and accurate way to apply meta-GGA exchange-correlation functionals in subsystem DFT calculations. The so obtained density and energy errors, with respect to the corresponding supermolecular calculations, are comparable with conventional approaches, depending almost exclusively on the approximations in the non-additive kinetic embedding term. An embedding energy error decomposition explains the accuracy of our method.

Simulation and scaling analysis of a spherical particle-laden blast wave

Science.gov (United States)

Ling, Y.; Balachandar, S.

2018-05-01

A spherical particle-laden blast wave, generated by a sudden release of a sphere of compressed gas-particle mixture, is investigated by numerical simulation. The present problem is a multiphase extension of the classic finite-source spherical blast-wave problem. The gas-particle flow can be fully determined by the initial radius of the spherical mixture and the properties of gas and particles. In many applications, the key dimensionless parameters, such as the initial pressure and density ratios between the compressed gas and the ambient air, can vary over a wide range. Parametric studies are thus performed to investigate the effects of these parameters on the characteristic time and spatial scales of the particle-laden blast wave, such as the maximum radius the contact discontinuity can reach and the time when the particle front crosses the contact discontinuity. A scaling analysis is conducted to establish a scaling relation between the characteristic scales and the controlling parameters. A length scale that incorporates the initial pressure ratio is proposed, which is able to approximately collapse the simulation results for the gas flow for a wide range of initial pressure ratios. This indicates that an approximate similarity solution for a spherical blast wave exists, which is independent of the initial pressure ratio. The approximate scaling is also valid for the particle front if the particles are small and closely follow the surrounding gas.

Simulation and scaling analysis of a spherical particle-laden blast wave

Science.gov (United States)

Ling, Y.; Balachandar, S.

2018-02-01

A spherical particle-laden blast wave, generated by a sudden release of a sphere of compressed gas-particle mixture, is investigated by numerical simulation. The present problem is a multiphase extension of the classic finite-source spherical blast-wave problem. The gas-particle flow can be fully determined by the initial radius of the spherical mixture and the properties of gas and particles. In many applications, the key dimensionless parameters, such as the initial pressure and density ratios between the compressed gas and the ambient air, can vary over a wide range. Parametric studies are thus performed to investigate the effects of these parameters on the characteristic time and spatial scales of the particle-laden blast wave, such as the maximum radius the contact discontinuity can reach and the time when the particle front crosses the contact discontinuity. A scaling analysis is conducted to establish a scaling relation between the characteristic scales and the controlling parameters. A length scale that incorporates the initial pressure ratio is proposed, which is able to approximately collapse the simulation results for the gas flow for a wide range of initial pressure ratios. This indicates that an approximate similarity solution for a spherical blast wave exists, which is independent of the initial pressure ratio. The approximate scaling is also valid for the particle front if the particles are small and closely follow the surrounding gas.

Analytical Solutions of Electromagnetic Fields from Current Dipole Moment on Spherical Conductor in a Low-Frequency Approximation

International Nuclear Information System (INIS)

Okita, Taishi; Takagi, Toshiyuki

2010-01-01

We analytically derive the solutions for electromagnetic fields of electric current dipole moment, which is placed in the exterior of the spherical homogeneous conductor, and is pointed along the radial direction. The dipole moment is driven in the low frequency f = 1 kHz and high frequency f = 1 GHz regimes. The electrical properties of the conductor are appropriately chosen in each frequency. Electromagnetic fields are rigorously formulated at an arbitrary point in a spherical geometry, in which the magnetic vector potential is straightforwardly given by the Biot-Savart formula, and the scalar potential is expanded with the Legendre polynomials, taking into account the appropriate boundary conditions at the spherical surface of the conductor. The induced electric fields are numerically calculated along the several paths in the low and high frequency excitation. The self-consistent solutions obtained in this work will be of much importance in a wide region of electromagnetic induction problems. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Approximating the imbibition and absorption behavior of a distribution of matrix blocks by an equivalent spherical block

International Nuclear Information System (INIS)

Zimmerman, R.W.; Bodvarsson, G.S.

1994-03-01

A theoretical study is presented of the effect of matrix block shape and matrix block size distribution on liquid imbibition and solute absorption in a fractured rock mass. It is shown that the behavior of an individual irregularly-shaped matrix block can be modeled with reasonable accuracy by using the results for a spherical matrix block, if one uses an effective radius a = 3V/A, where V is the volume of the block and A is its surface area. In the early-time regime of matrix imbibition, it is shown that a collection of blocks of different sizes can be modeled by a single equivalent block, with an equivalent radius of -1 > -1 , where the average is taken on a volumetrically-weighted basis. In an intermediate time regime, it is shown for the case where the radii are normally distributed that the equivalent radius is reasonably well approximated by the mean radius . In the long-time limit, where no equivalent radius can be rigorously defined, an asymptotic expression is derived for the cumulative diffusion as a function of the mean and the standard deviation of the radius distribution function

A simple formula for emittance growth due to spherical aberration in a solenoid lens

International Nuclear Information System (INIS)

Kumar, V.; Phadte, D.; Patidar, C.B.

2011-01-01

We analyse the beam dynamics in a solenoid without the paraxial approximation, including up to the fifth order term in the radial displacement. We use this analysis to derive expressions for the coefficients of spherical aberration in terms of the on-axis field profile of the solenoid. Under the thin lens approximation, a simple formula is derived for the growth of rms emittance resulting due to spherical aberration in a solenoid. (author)

Description of surface quadrupole oscillations of heated spherical nuclei in the Brownian-motion approximation

International Nuclear Information System (INIS)

Svin'in, I.R.

1982-01-01

The Brownian motion of a quadrupole quantum oscillator is considered as a model of surface quadrupole oscillations of heated spherical nuclei. The integrals of the motion related to energy and angular momentum conservation are constructed and the wave functions are obtained for states with definite values of these integrals of the motion in the phonon representation

Local Instruction Theory (LIT) on spherical geometry for enhancement students’ strategic competence

Science.gov (United States)

Nuraida, I.; Kusumah, Y. S.; Kartasasmita, B. G.

2018-03-01

This research focused on the analysis of the materials spherical geometry of the wake in an attempt to enhancemet the strategic competence of students and to produce learning trajectory. That is because the materials that are used less catchy concept gives students. Learning materials with Local Instructional Theory (LIT) can enhancemet the strategic competence of the students. This research aims to study the difference of achievement and improving the strategic competence of the students who got the Realistics Mathematics Education (RME) and (LIT) with conventional learning. This research is the Design Research with two cycles. This research has three phases i.e. 1) preparing for the experiment/preliminary; 2) teaching eksperiment; 3) retrospective analysis. The population of the research was the whole IX group junior high school 1 Rajapolah with samples of IXg and IXj group. Results of the analysis of the data shows that students based on Mathematical Prior Knowledge (MPK) acquire learning achievement have RME and LIT and enhancement strategic competence of the mathematical that are higher than those of students who obtain the conventional learning.

Spherical cows in dark matter indirect detection

Energy Technology Data Exchange (ETDEWEB)

Bernal, Nicolás [Centro de Investigaciones, Universidad Antonio Nariño, Cra 3 Este # 47A-15, Bogotá (Colombia); Necib, Lina; Slatyer, Tracy R., E-mail: nicolas.bernal@uan.edu.co, E-mail: lnecib@mit.edu, E-mail: tslatyer@mit.edu [Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States)

2016-12-01

Dark matter (DM) halos have long been known to be triaxial, but in studies of possible annihilation and decay signals they are often treated as approximately spherical. In this work, we examine the asymmetry of potential indirect detection signals of DM annihilation and decay, exploiting the large statistics of the hydrodynamic simulation Illustris. We carefully investigate the effects of the baryons on the sphericity of annihilation and decay signals for both the case where the observer is at 8.5 kpc from the center of the halo (exemplified in the case of Milky Way-like halos), and for an observer situated well outside the halo. In the case of Galactic signals, we find that both annihilation and decay signals are expected to be quite symmetric, with axis ratios very different from 1 occurring rarely. In the case of extragalactic signals, while decay signals are still preferentially spherical, the axis ratio for annihilation signals has a much flatter distribution, with elongated profiles appearing frequently. Many of these elongated profiles are due to large subhalos and/or recent mergers. Comparing to gamma-ray emission from the Milky Way and X-ray maps of clusters, we find that the gamma-ray background appears less spherical/more elongated than the expected DM signal from the large majority of halos, and the Galactic gamma ray excess appears very spherical, while the X-ray data would be difficult to distinguish from a DM signal by elongation/sphericity measurements alone.

Deep-inelastic structure functions in an approximation to the bag theory

International Nuclear Information System (INIS)

Jaffe, R.L.

1975-01-01

A cavity approximation to the bag theory developed earlier is extended to the treatment of forward virtual Compton scattering. In the Bjorken limit and for small values of ω (ω = vertical-bar2p center-dot q/q 2 vertical-bar) it is argued that the operator nature of the bag boundaries might be ignored. Structure functions are calculated in one and three dimensions. Bjorken scaling is obtained. The model provides a realization of light-cone current algebra and possesses a parton interpretation. The structure functions show a quasielastic peak. The spreading of the structure functions about the peak is associated with confinement. As expected, Regge behavior is not obtained for large ω. The ''momentum sum rule'' is saturated, indicating that the hadron's charged constituents carry all the momentum in this model. νW/subL/ is found to scale and is calculable. Application of the model to the calculation of spin-dependent and chiral-symmetry--violating structure functions is proposed. The nature of the intermediate states in this approximation is discussed. Problems associated with the cavity approximation are also discussed

Spherical subsystem of galactic radiosources

Energy Technology Data Exchange (ETDEWEB)

Gorshkov, A G; Popov, M V [Moskovskij Gosudarstvennyj Univ. (USSR). Gosudarstvennyj Astronomicheskij Inst. ' ' GAISh' '

1975-05-01

The concentration of statistically complete sampling radiosources of the Ohiof scanning with plane spectra towards the Galaxy centre has been discovered. Quantitative calculations have showed that the sources form a spheric subsystem, which is close in parameters to such old formations in the Galaxy as globular clusters and the RRLsub(YR) type stars. The luminosity of the galaxy spheric subsystem object equals 10/sup 33/ erg/sec, the total number of objects being 7000. The existence of such a subsystem explains s the anomalously by low incline of statistics lgN-lgS in HF scanning PKS (..gamma..-2700Mgz) and the Michigan University scanning (..gamma..=8000Mgz) because the sources of galaxy spheric subsystem make up a considerable share in the total number of sources, especially at high frequencies (50% of sources with a flux greater than a unit of flux per 8000Mgz). It is very probable that the given subsystem consists of the representatives of one of the following class of objects: a) heat sources - the H2H regions with T=10/sup 40/K, Nsub(e)=10/sup 3/, l=1 ps b) supermass black holes with mass M/Mo approximately 10/sup 5/.

Implementation of the CCGM approximation for surface diffraction using Wigner R-matrix theory

International Nuclear Information System (INIS)

Lauderdale, J.G.; McCurdy, C.W.

1983-01-01

The CCGM approximation for surface scattering proposed by Cabrera, Celli, Goodman, and Manson [Surf. Sci. 19, 67 (1970)] is implemented for realistic surface interaction potentials using Wigner R-matrix theory. The resulting procedure is highly efficient computationally and is in no way limited to hard wall or purely repulsive potentials. Comparison is made with the results of close-coupling calculations of other workers which include the same diffraction channels in order to fairly evaluate the CCGM approximation which is an approximation to the coupled channels Lippman--Schwinger equation for the T matrix. The shapes of selective adsorption features, whether maxima or minima, in the scattered intensity are well represented in this approach for cases in which the surface corrugation is not too strong

Determination of stamp deformation during imprinting on semi-spherical surfaces

DEFF Research Database (Denmark)

Kafka, Jan; Matschuk, Maria; Pranov, Henrik

of sol-gel was applied onto spherical injection mold inserts and subsequently imprinted using a flexible stamp. A hard curing step transformed the sol-gel into a quartz-like and durable material. As an example, we present theory and results regarding the imprint of pillar nanostructures on semi......-spherical mold surfaces. Imprints were realized on three different radii of circumferenceof the spherical mold: R = 0.5 mm, R = 1.0 mm, and R = 2 mm. After hard-curing of theimprinted sol-gel, the inserts were used for cold-mold as well as vario-therm injection molding.The polymer replicas and the inserts were...

A variational solution of transport equation based on spherical geometry

International Nuclear Information System (INIS)

Liu Hui; Zhang Ben'ai

2002-01-01

A variational method with differential forms gives better precision for numerical solution of transport critical problem based on spherical geometry, and its computation seems simple than other approximate methods

Spherical grating based x-ray Talbot interferometry

Energy Technology Data Exchange (ETDEWEB)

Cong, Wenxiang, E-mail: congw@rpi.edu, E-mail: xiy2@rpi.edu, E-mail: wangg6@rpi.edu; Xi, Yan, E-mail: congw@rpi.edu, E-mail: xiy2@rpi.edu, E-mail: wangg6@rpi.edu; Wang, Ge, E-mail: congw@rpi.edu, E-mail: xiy2@rpi.edu, E-mail: wangg6@rpi.edu [Biomedical Imaging Center, Rensselaer Polytechnic Institute, Troy, New York 12180 (United States)

2015-11-15

Purpose: Grating interferometry is a state-of-the-art x-ray imaging approach, which can acquire information on x-ray attenuation, phase shift, and small-angle scattering simultaneously. Phase-contrast imaging and dark-field imaging are very sensitive to microstructural variation and offers superior contrast resolution for biological soft tissues. However, a common x-ray tube is a point-like source. As a result, the popular planar grating imaging configuration seriously restricts the flux of photons and decreases the visibility of signals, yielding a limited field of view. The purpose of this study is to extend the planar x-ray grating imaging theory and methods to a spherical grating scheme for a wider range of preclinical and clinical applications. Methods: A spherical grating matches the wave front of a point x-ray source very well, allowing the perpendicular incidence of x-rays on the grating to achieve a higher visibility over a larger field of view than the planer grating counterpart. A theoretical analysis of the Talbot effect for spherical grating imaging is proposed to establish a basic foundation for x-ray spherical gratings interferometry. An efficient method of spherical grating imaging is also presented to extract attenuation, differential phase, and dark-field images in the x-ray spherical grating interferometer. Results: Talbot self-imaging with spherical gratings is analyzed based on the Rayleigh–Sommerfeld diffraction formula, featuring a periodic angular distribution in a polar coordinate system. The Talbot distance is derived to reveal the Talbot self-imaging pattern. Numerical simulation results show the self-imaging phenomenon of a spherical grating interferometer, which is in agreement with the theoretical prediction. Conclusions: X-ray Talbot interferometry with spherical gratings has a significant practical promise. Relative to planar grating imaging, spherical grating based x-ray Talbot interferometry has a larger field of view and

Spherical grating based x-ray Talbot interferometry

International Nuclear Information System (INIS)

Cong, Wenxiang; Xi, Yan; Wang, Ge

2015-01-01

Purpose: Grating interferometry is a state-of-the-art x-ray imaging approach, which can acquire information on x-ray attenuation, phase shift, and small-angle scattering simultaneously. Phase-contrast imaging and dark-field imaging are very sensitive to microstructural variation and offers superior contrast resolution for biological soft tissues. However, a common x-ray tube is a point-like source. As a result, the popular planar grating imaging configuration seriously restricts the flux of photons and decreases the visibility of signals, yielding a limited field of view. The purpose of this study is to extend the planar x-ray grating imaging theory and methods to a spherical grating scheme for a wider range of preclinical and clinical applications. Methods: A spherical grating matches the wave front of a point x-ray source very well, allowing the perpendicular incidence of x-rays on the grating to achieve a higher visibility over a larger field of view than the planer grating counterpart. A theoretical analysis of the Talbot effect for spherical grating imaging is proposed to establish a basic foundation for x-ray spherical gratings interferometry. An efficient method of spherical grating imaging is also presented to extract attenuation, differential phase, and dark-field images in the x-ray spherical grating interferometer. Results: Talbot self-imaging with spherical gratings is analyzed based on the Rayleigh–Sommerfeld diffraction formula, featuring a periodic angular distribution in a polar coordinate system. The Talbot distance is derived to reveal the Talbot self-imaging pattern. Numerical simulation results show the self-imaging phenomenon of a spherical grating interferometer, which is in agreement with the theoretical prediction. Conclusions: X-ray Talbot interferometry with spherical gratings has a significant practical promise. Relative to planar grating imaging, spherical grating based x-ray Talbot interferometry has a larger field of view and

Hyper-spherical harmonics and anharmonics in m-dimensional space

International Nuclear Information System (INIS)

Shojaei, M.R.; Rajabi, A.A.; Hasanabadi, H.

2008-01-01

In quantum mechanics the hyper-spherical method is one of the most well-established and successful computational tools. The general theory of harmonic polynomials and hyper-spherical harmonics is of central importance in this paper. The interaction potential V is assumed to depend on the hyper-radius ρ only where ρ is the function of the Jacobi relative coordinate x 1 , x 2 ,…, x n which are functions of the particles' relative positions. (author)

Rotating field current drive in spherical plasmas

International Nuclear Information System (INIS)

Brotherton-Ratcliffe, D.; Storer, R.G.

1988-01-01

The technique of driving a steady Hall current in plasmas using a rotating magnetic field is studied both numerically and analytically in the approximation of negligible ion flow. A spherical plasma bounded by an insulating wall and immersed in a uniform magnetic field which has both a rotating component (for current drive) and a constant ''vertical'' component (for MHD equilibrium) is considered. The problem is formulated in terms of an expansion of field quantities in vector spherical harmonics. The numerical code SPHERE solves the resulting pseudo-harmonic equations by a multiple shooting technique. The results presented, in addition to being relevant to non-inductive current drive generally, have a direct relevance to the rotamak experiments. For the case of no applied vertical field the steady state toroidal current driven by the rotating field per unit volume of plasma is several times less than in the long cylinder limit for a plasma of the same density, resistivity and radius. The application of a vertical field, which for certain parameter regimes gives rise to a compact torus configuration, improves the current drive dramatically and in many cases gives ''better'' current drive than the long cylinder limit. This result is also predicted by a second order perturbation analysis of the pseudo-harmonic equations. A steady state toroidal field is observed which appears consistent with experimental observations in rotamaks regarding magnitude and spatial dependence. This is an advance over previous analytical theory which predicted an oppositely directed toroidal field of undefined magnitude. (author)

ns-ms excitation of alkali atoms in the Glauber approximation

International Nuclear Information System (INIS)

Barros, H.G. de P.L. de

1980-05-01

An expression for the scattering amplitude in the Glauber approximation for ns-ms electronic excitation of alkali atoms is obtained. The interaction potential between the incident electron, the core electrons and N-1 protons is approximated by an appropriate spherical potential. (Author) [pt

Operator approach to effective medium theory to overcome a breakdown of Maxwell Garnett approximation

DEFF Research Database (Denmark)

Popov, Vladislav; Lavrinenko, Andrei; Novitsky, Andrey

2016-01-01

that the zeroth-, first-, and second-order approximations of the operator effective medium theory correspond to electric dipoles, chirality, and magnetic dipoles plus electric quadrupoles, respectively. We discover that the spatially dispersive bianisotropic effective medium obtained in the second...

Reggeon field theory at D = 2 in two-loop approximation

International Nuclear Information System (INIS)

Eremyan, Sh.S.; Nazaryan, A.E.

1982-01-01

A general method of constructing an explicit representation is developed for the pomeron propagator in the presence of additional parameters, such as the pomeron production threshold xi 0 , momentum transfer K vector or the intercept shift delta 0 . The method is shown to be applicable in both one-loop and two-loop approximations. The obtained general formulae allow to consider the pomeron propagator in both asymptotic region and the region of the perturbation theory applicability. Besides, they provide the smooth matching of both these regions. The observed values are calculated, and the results connected with asymptotically high energies are discussed

Intelligent control-II: review of fuzzy systems and theory of approximate reasoning

International Nuclear Information System (INIS)

Nagrial, M.H.

2004-01-01

Fuzzy systems are knowledge-based or rule-based systems. The heart of a fuzzy systems knowledge base consisting of the so-called fuzzy IF -THEN rules. This paper reviews various aspects of fuzzy IF-THEN rules. The theory of approximate reasoning, which provides a powerful framework for reasoning the imprecise and uncertain information, , is also reviewed. Additional properties of fuzzy systems are also discussed. (author)

Spherically symmetric solutions of general second-order gravity

International Nuclear Information System (INIS)

Whitt, B.

1988-01-01

The general second-order gravity theory, whose Lagrangian includes higher powers of the curvature, is considered in arbitrary dimensions. It is shown that spherically symmetric solutions are static, except in certain, special, unphysical cases. Spherically symmetric solutions are found and classified. Each theory's solutions fall into a number of distinct branches, which may represent finite space with two singular boundaries, or an asymptotically either flat or (anti--)de Sitter space with one singular boundary. A theory may contain at most one branch of solutions in which all singularities are hidden by event horizons. Such horizons generally emit Hawking radiation, though in certain cases the horizon may have zero temperature. Black holes do not necessarily radiate away all their mass: they may terminate in a zero-temperature black hole, a naked singularity, or a hot black hole in equilibrium with a ''cosmological'' event horizon. The thermodynamics of black-hole solutions is discussed; entropy is found to be an increasing function of horizon area, and the first law is shown to hold

Kinematic approximation in the theory of stimulated nuclear polarization in radical recombination

International Nuclear Information System (INIS)

Mikhailov, S.A.; Purtov, P.A.

1989-01-01

Within the kinematic approximation, we have developed the theory of stimulated nuclear polarization (SNP) in reactions of geminal recombination of radicals in a strong d.c. magnetic field. We have obtained analytical formulas which are applicable for analysis of SNP effects occurring when the reactions are carried out in nonviscous solutions. The result is represented in the form of integrals with respect to the Green's function determining the kinematics of reagent approach. As an illustration of the proposed theory, we have calculated the polarization of nuclei formed in the reaction products of p-benzoquinone in CD 3 OD and in C 6 D 6 with addition of phenol, and we compare with experiment

Ultra-long magnetization needle induced by focusing azimuthally polarized beams with a spherical mirror.

Science.gov (United States)

Hang, Li; Luo, Kai; Fu, Jian; Chang, Yizhe; Wang, Ying; Chen, Peifeng

2018-03-20

Based on extended Richards-Wolf theory for axisymmetric surfaces and the inverse Faraday effect, we propose the generation of a purely longitudinal magnetization needle by focusing Gaussian annular azimuthally polarized beams with a spherical mirror. The needle obtained has a longitudinal length varying hundreds to thousands of wavelengths while keeping the lateral size under 0.4λ, and the corresponding aspect ratio can easily reach more than 2000. It may be the first time that a magnetization needle whose aspect ratio is over 500 has been achieved. The approximate analytical expressions of the magnetization needle are given, and the longitudinal length is tunable by changing the value of the angular thickness and the position of the annular beams.

Recent Progress on Spherical Torus Research

Energy Technology Data Exchange (ETDEWEB)

Ono, Masayuki [PPPL; Kaita, Robert [PPPL

2014-01-01

The spherical torus or spherical tokamak (ST) is a member of the tokamak family with its aspect ratio (A = R0/a) reduced to A ~ 1.5, well below the normal tokamak operating range of A ≥ 2.5. As the aspect ratio is reduced, the ideal tokamak beta β (radio of plasma to magnetic pressure) stability limit increases rapidly, approximately as β ~ 1/A. The plasma current it can sustain for a given edge safety factor q-95 also increases rapidly. Because of the above, as well as the natural elongation κ, which makes its plasma shape appear spherical, the ST configuration can yield exceptionally high tokamak performance in a compact geometry. Due to its compactness and high performance, the ST configuration has various near term applications, including a compact fusion neutron source with low tritium consumption, in addition to its longer term goal of attractive fusion energy power source. Since the start of the two megaampere class ST facilities in 2000, National Spherical Torus Experiment (NSTX) in the US and Mega Ampere Spherical Tokamak (MAST) in UK, active ST research has been conducted worldwide. More than sixteen ST research facilities operating during this period have achieved remarkable advances in all of fusion science areas, involving fundamental fusion energy science as well as innovation. These results suggest exciting future prospects for ST research both near term and longer term. The present paper reviews the scientific progress made by the worldwide ST research community during this new mega-ampere-ST era.

Renormalization in self-consistent approximation schemes at finite temperature I: theory

International Nuclear Information System (INIS)

Hees, H. van; Knoll, J.

2001-07-01

Within finite temperature field theory, we show that truncated non-perturbative self-consistent Dyson resummation schemes can be renormalized with local counter-terms defined at the vacuum level. The requirements are that the underlying theory is renormalizable and that the self-consistent scheme follows Baym's Φ-derivable concept. The scheme generates both, the renormalized self-consistent equations of motion and the closed equations for the infinite set of counter terms. At the same time the corresponding 2PI-generating functional and the thermodynamic potential can be renormalized, in consistency with the equations of motion. This guarantees the standard Φ-derivable properties like thermodynamic consistency and exact conservation laws also for the renormalized approximation scheme to hold. The proof uses the techniques of BPHZ-renormalization to cope with the explicit and the hidden overlapping vacuum divergences. (orig.)

Contractions of affine spherical varieties

International Nuclear Information System (INIS)

Arzhantsev, I V

1999-01-01

The language of filtrations and contractions is used to describe the class of G-varieties obtainable as the total spaces of the construction of contraction applied to affine spherical varieties, which is well-known in invariant theory. These varieties are local models for arbitrary affine G-varieties of complexity 1 with a one-dimensional categorical quotient. As examples, reductive algebraic semigroups and three-dimensional SL 2 -varieties are considered

Improvement of the Derjaguin-Broekhoff-de Boer theory for the capillary condensation/evaporation of nitrogen in spherical cavities and its application for the pore size analysis of silicas with ordered cagelike mesopores.

Science.gov (United States)

Kowalczyk, Piotr; Jaroniec, Mietek; Kaneko, Katsumi; Terzyk, Artur P; Gauden, Piotr A

2005-11-08

In a previous work, we proposed an improvement of the Derjaguin-Broekhoff-de Boer (DBdB) theory for capillary condensation/evaporation in open-ended cylindrical mesopores. In this paper, we report a further extension of this approach to the capillary condensation/evaporation of nitrogen in siliceous spherical cavities. The main idea of this improvement is to employ the Gibbs-Tolman-Koenig-Buff equation to predict the variation of the surface tension in spherical mesopores. In addition, the statistical film thickness (the so-called t-curve), which is evaluated accurately on the basis of adsorption isotherms measured for MCM-41 materials, is used instead of the originally proposed t-curve to take into account the excess chemical potential due to the surface forces. It is shown that the aforementioned modifications of the original DBdB theory that was refined by Ravikovitch and Neimark have significant implications for the pore size analysis of cagelike mesoporous silicas. To verify the proposed improvement of the DBdB pore size analysis (IDBdB), two series of FDU-1 samples, which are well-defined cagelike mesoporous materials (composed of siliceous spherical cavities interconnected by short necks), were used for the evaluation of the pore size distributions (PSDs). The correlation between the spinodal condensation point in the spherical pores predicted by the nonlocal density functional theory (NDFT) developed by Ravikovitch and Neimark and that predicted by the IDBdB theory is very good in the whole range of mesopores. This feature is mirrored to the realistic PSD characterized by the bimodal structure of pores computed from the IDBdB theory. As in the case of open-ended cylindrical pores, the improvement of the classical DBdB theory preserves its simplicity and simultaneously ensures a significant improvement of the pore size analysis, which is confirmed by the independent estimation of the average pore size by the NDFT and the powder X-ray diffraction method.

Spherical harmonics and integration in superspace

International Nuclear Information System (INIS)

Bie, H de; Sommen, F

2007-01-01

In this paper, the classical theory of spherical harmonics in R m is extended to superspace using techniques from Clifford analysis. After defining a super-Laplace operator and studying some basic properties of polynomial null-solutions of this operator, a new type of integration over the supersphere is introduced by exploiting the formal equivalence with an old result of Pizzetti. This integral is then used to prove orthogonality of spherical harmonics of different degree, Green-like theorems and also an extension of the important Funk-Hecke theorem to superspace. Finally, this integration over the supersphere is used to define an integral over the whole superspace, and it is proven that this is equivalent with the Berezin integral, thus providing a more sound definition of the Berezin integral

Scattering by non-spherical particles of size comparable to a wavelength - A new semi-empirical theory

Science.gov (United States)

Pollack, J. B.; Cuzzi, J. N.

1980-01-01

An approximate method is proposed for evaluating the interaction of randomly oriented, nonspherical particles with the total intensity component of electromagnetic radiation. When the particle size parameter, x, the ratio of particle circumference to wavelength, is less than some upper bound x(o) (about 5), Mie theory is used. For x greater than x(o), the interaction is divided into three components: diffraction, external reflection, and transmission. Physical optics theory is used to obtain the first of these components; geometrical optics theory is applied to the second; and a simple parameterization is employed for the third. The predictions of this theory are found to be in very good agreement with laboratory measurements for a wide variety of particle shapes, sizes, and refractive indexes. Limitations of the theory are also noted.

Towards linearization of atmospheric radiative transfer in spherical geometry

International Nuclear Information System (INIS)

Walter, Holger H.; Landgraf, Jochen

2005-01-01

We present a general approach for the linearization of radiative transfer in a spherical planetary atmosphere. The approach is based on the forward-adjoint perturbation theory. In the first part we develop the theoretical background for a linearization of radiative transfer in spherical geometry. Using an operator formulation of radiative transfer allows one to derive the linearization principles in a universally valid notation. The application of the derived principles is demonstrated for a radiative transfer problem in simplified spherical geometry in the second part of this paper. Here, we calculate the derivatives of the radiance at the top of the atmosphere with respect to the absorption properties of a trace gas species in the case of a nadir-viewing satellite instrument

Theory of magnetohydrodynamic waves: The WKB approximation revisited

International Nuclear Information System (INIS)

Barnes, A.

1992-01-01

Past treatments of the eikonal or WKB theory of the propagation of magnetohydrodynamics waves have assumed a strictly isentropic background. IF in fact there is a gradient in the background entropy, then in second order in the WKB ordering, adiabatic fluctuations (in the Lagrangian sense) are not strictly isentropic in the Eulerian sense. This means that in the second order of the WKB expansion, which determines the variation of wave amplitude along rays, the violation of isentropy must be accounted for. The present paper revisits the derivation of the WKB approximation for small-amplitude magnetohydrodynamic waves, allowing for possible spatial variation of the background entropy. The equation of variation of wave amplitude is rederived; it is a bilinear equation which, it turns out, can be recast in the action conservation form. It is shown that this action conservation equation is in fact equivalent to the action conservation law obtained from Lagrangian treatments

Relativistic Random-Phase Approximation with Density-dependent Meson-nucleon Couplings at Finite Temperature

International Nuclear Information System (INIS)

Niu, Y.; Paar, N.; Vretenar, D.; Meng, J.

2009-01-01

The fully self-consistent relativistic random-phase approximation (RRPA) framework based on effective interactions with a phenomenological density dependence is extended to finite temperatures. The RRPA configuration space is built from the spectrum of single-nucleon states at finite temperature obtained by the temperature dependent relativistic mean field (RMF-T) theory based on effective Lagrangian with density dependent meson-nucleon vertex functions. As an illustration, the dependence of binding energy, radius, entropy and single particle levels on temperature for spherical nucleus 2 08P b is investigated in RMF-T theory. The finite temperature RRPA has been employed in studies of giant monopole and dipole resonances, and the evolution of resonance properties has been studied as a function of temperature. In addition, exotic modes of excitation have been systematically explored at finite temperatures, with an emphasis on the case of pygmy dipole resonances.(author)

Comparison of Poloidal Velocity Meassurements to Neoclassical Theory on the National Spherical Torus Experiment

International Nuclear Information System (INIS)

Bell, R.E.; Andre, R.; Kaye, S.M.; Kolesnikov, R.A.; LeBlance, B.P.; Rewolldt, G.; Wang, W.X.; Sabbagh, S.A.

2010-01-01

Knowledge of poloidal velocity is necessary for the determination of the radial electric field, Er, which along with its gradient is linked to turbulence suppression and transport barrier formation. Recent measurements of poloidal flow on conventional tokamaks have been reported to be an order of magnitude larger than expected from neoclassical theory. In contrast, recent poloidal velocity measurements on the NSTX spherical torus (S. M. Kaye et al., Phys. Plasmas 8, 1977 (2001)) are near or below neoclassical estimates. A novel charge exchange recombination spectroscopy diagnostic is used, which features active and passive sets of up/down symmetric views to produce line-integrated poloidal velocity measurements that do not need atomic physics corrections. Local profiles are obtained with an inversion. Poloidal velocity measurements are compared with neoclassical values computed with the codes NCLASS (W. A. Houlberg et al., Phys. Plasmas 4, 3230 (1997)) and GTC-Neo (W. X. Wang, et al., Phys. Plasmas 13, 082501 (2006)), which has been updated to handle impurities.

Numerical determination of the effective moments of non-spherical particles

International Nuclear Information System (INIS)

Green, Nicolas G; Jones, Thomas B

2007-01-01

Dielectric characterisation of polarisable particles, and prediction of the forces and torques exerted upon them, relies on the knowledge of the effective, induced dipole moment. In turn, through the mechanism of depolarisation, the induced dipole moment of a particle is strongly dependent upon its shape. Since realistic shapes create modelling difficulties, the 'spherical particle' approximation is often invoked. However, in many cases, including biological dielectric spectroscopy and dielectrophoresis, this assumption is a poor one. For example, human erythrocytes are essentially oblate spheroids with indented sides, while viruses and bacteria often have elongated cigar shapes. Since shape-dependent polarisation both strongly influences the accuracy of conventional dielectric characterisation methods using Maxwell's mixture formula and confounds accurate prediction of dielectrophoretic forces and torques, it is important to develop means to treat non-spherical particles. In this paper, we demonstrate a means to extract the dipole moment directly from numerical solutions of the induced electrostatic potential when a particle is placed in a uniform electric field. The accuracy of the method is demonstrated for a range of particle shapes: spherical, ellipsoidal, truncated cylinders and an approximation of an erythrocyte, the red blood cell

Scattering of Gaussian beam by a spherical particle with a spheroidal inclusion

International Nuclear Information System (INIS)

Zhang Huayong; Liao Tongqing

2011-01-01

A generalized Lorenz-Mie theory framework (GLMT) is applied to the study of Gaussian beam scattering by a spherical particle with an embedded spheroid at the center. By virtue of a transformation between the spherical and spheroidal vector wave functions, a theoretical procedure is developed to deal with the boundary conditions. Numerical results of the normalized differential scattering cross section are presented.

Thermodynamic properties of sticky electrolytes in the HNC/MS approximation

International Nuclear Information System (INIS)

Herrera, J.N.; Blum, L.

1991-01-01

We study an approximation for a model which combines the sticky potential of Baxter and charged spheres. In the hypernetted chain (HNC)/mean spherical approximation (MSA), simple expressions for the thermodynamic functions are obtained. There equations should be useful in representing the properties of real electrolytes. Approximate expressions that are similar to those of the primitive model are obtained, for low densities (concentrations) of the electrolyte (Author)

Derivation of fluid dynamics from kinetic theory with the 14-moment approximation

International Nuclear Information System (INIS)

Denicol, G.S.; Molnar, E.; Niemi, H.; Rischke, D.H.

2012-01-01

We review the traditional derivation of the fluid-dynamical equations from kinetic theory according to Israel and Stewart. We show that their procedure to close the fluid-dynamical equations of motion is not unique. Their approach contains two approximations, the first being the so-called 14-moment approximation to truncate the single-particle distribution function. The second consists in the choice of equations of motion for the dissipative currents. Israel and Stewart used the second moment of the Boltzmann equation, but this is not the only possible choice. In fact, there are infinitely many moments of the Boltzmann equation which can serve as equations of motion for the dissipative currents. All resulting equations of motion have the same form, but the transport coefficients are different in each case. (orig.)

Holographic Spherically Symmetric Metrics

Science.gov (United States)

Petri, Michael

The holographic principle (HP) conjectures, that the maximum number of degrees of freedom of any realistic physical system is proportional to the system's boundary area. The HP has its roots in the study of black holes. It has recently been applied to cosmological solutions. In this article we apply the HP to spherically symmetric static space-times. We find that any regular spherically symmetric object saturating the HP is subject to tight constraints on the (interior) metric, energy-density, temperature and entropy-density. Whenever gravity can be described by a metric theory, gravity is macroscopically scale invariant and the laws of thermodynamics hold locally and globally, the (interior) metric of a regular holographic object is uniquely determined up to a constant factor and the interior matter-state must follow well defined scaling relations. When the metric theory of gravity is general relativity, the interior matter has an overall string equation of state (EOS) and a unique total energy-density. Thus the holographic metric derived in this article can serve as simple interior 4D realization of Mathur's string fuzzball proposal. Some properties of the holographic metric and its possible experimental verification are discussed. The geodesics of the holographic metric describe an isotropically expanding (or contracting) universe with a nearly homogeneous matter-distribution within the local Hubble volume. Due to the overall string EOS the active gravitational mass-density is zero, resulting in a coasting expansion with Ht = 1, which is compatible with the recent GRB-data.

On the relation between reduced quantisation and quantum reduction for spherical symmetry in loop quantum gravity

International Nuclear Information System (INIS)

Bodendorfer, N; Zipfel, A

2016-01-01

Building on a recent proposal for a quantum reduction to spherical symmetry from full loop quantum gravity, we investigate the relation between a quantisation of spherically symmetric general relativity and a reduction at the quantum level. To this end, we generalise the previously proposed quantum reduction by dropping the gauge fixing condition on the radial diffeomorphisms, thus allowing us to make direct contact with previous work on reduced quantisation. A dictionary between spherically symmetric variables and observables with respect to the reduction constraints in the full theory is discussed, as well as an embedding of reduced quantum states to a subsector of the quantum symmetry reduced full theory states. On this full theory subsector, the quantum algebra of the mentioned observables is computed and shown to qualitatively reproduce the quantum algebra of the reduced variables in the large quantum number limit for a specific choice of regularisation. Insufficiencies in recovering the reduced algebra quantitatively from the full theory are attributed to the oversimplified full theory quantum states we use. (paper)

Cellular neural network to the spherical harmonics approximation of neutron transport equation in x–y geometry

International Nuclear Information System (INIS)

Pirouzmand, Ahmad; Hadad, Kamal

2012-01-01

Highlights: ► This paper describes the solution of time-dependent neutron transport equation. ► We use a novel method based on cellular neural networks (CNNs) coupled with the spherical harmonics method. ► We apply the CNN model to simulate step and ramp perturbation transients in a core. ► The accuracy and capabilities of the CNN model are examined for x–y geometry. - Abstract: In an earlier paper we utilized a novel method using cellular neural networks (CNNs) coupled with spherical harmonics method to solve the steady state neutron transport equation in x–y geometry. Here, the previous work is extended to the study of time-dependent neutron transport equation. To achieve this goal, an equivalent electrical circuit based on a second-order form of time-dependent neutron transport equation and one equivalent group of neutron precursor density is obtained by the CNN method. The CNN model is used to simulate step and ramp perturbation transients in a typical 2D core.

Spin-Density Functionals from Current-Density Functional Theory and Vice Versa: A Road towards New Approximations

International Nuclear Information System (INIS)

Capelle, K.; Gross, E.

1997-01-01

It is shown that the exchange-correlation functional of spin-density functional theory is identical, on a certain set of densities, with the exchange-correlation functional of current-density functional theory. This rigorous connection is used to construct new approximations of the exchange-correlation functionals. These include a conceptually new generalized-gradient spin-density functional and a nonlocal current-density functional. copyright 1997 The American Physical Society

Temperature dynamics of liquid outside a spherical bubble

International Nuclear Information System (INIS)

Sharipov, Vasily

2011-01-01

Radial Fourier equation describing temperature distribution outside a spherical bubble is considered. This equation appears from the energy conservation law written for a single bubble. Analytical approximation to the solution of this equation was built for radius and temperature of the surface of the bubble as arbitrary functions of time. In zero-order approximation it is assumed that variation amplitude of bubble radius is much smaller than its value. Together with first-order correction the so obtained solution is in good agreement with numerical results. Reported analytical approximation reduces computation efforts more than 10 times with comparison to the conventional numerical scheme. Finally presented semi-analytical approximation provides a possibility to describe acoustic effects and cavitations being incorporated into the multiphase flow code. (author)

Some comments on the hydrogen atom in a spherical enclosure

International Nuclear Information System (INIS)

Aguilera-Navarro, V.C.; Koo, E.L.; Zimerman, A.H.

1980-01-01

Some properties of the ground state energy solutions for the hydrogen atom in a spherical enclosure are discussed. The application of the many-point Pade approximants to this kind of systems inside a box is consider also. (Author) [pt

The time-dependent relativistic mean-field theory and the random phase approximation

International Nuclear Information System (INIS)

Ring, P.; Ma, Zhong-yu; Van Giai, Nguyen; Vretenar, D.; Wandelt, A.; Cao, Li-gang

2001-01-01

The Relativistic Random Phase Approximation (RRPA) is derived from the Time-Dependent Relativistic Mean-Field (TD RMF) theory in the limit of small amplitude oscillations. In the no-sea approximation of the RMF theory, the RRPA configuration space includes not only the usual particle-hole ph-states, but also αh-configurations, i.e. pairs formed from occupied states in the Fermi sea and empty negative-energy states in the Dirac sea. The contribution of the negative-energy states to the RRPA matrices is examined in a schematic model, and the large effect of Dirac-sea states on isoscalar strength distributions is illustrated for the giant monopole resonance in 116 Sn. It is shown that, because the matrix elements of the time-like component of the vector-meson fields which couple the αh-configurations with the ph-configurations are strongly reduced with respect to the corresponding matrix elements of the isoscalar scalar meson field, the inclusion of states with unperturbed energies more than 1.2 GeV below the Fermi energy has a pronounced effect on giant resonances with excitation energies in the MeV region. The influence of nuclear magnetism, i.e. the effect of the spatial components of the vector fields is examined, and the difference between the nonrelativistic and relativistic RPA predictions for the nuclear matter compression modulus is explained

Random distance distribution for spherical objects: general theory and applications to physics

International Nuclear Information System (INIS)

Tu Shuju; Fischbach, Ephraim

2002-01-01

A formalism is presented for analytically obtaining the probability density function, P n (s), for the random distance s between two random points in an n-dimensional spherical object of radius R. Our formalism allows P n (s) to be calculated for a spherical n-ball having an arbitrary volume density, and reproduces the well-known results for the case of uniform density. The results find applications in geometric probability, computational science, molecular biological systems, statistical physics, astrophysics, condensed matter physics, nuclear physics and elementary particle physics. As one application of these results, we propose a new statistical method derived from our formalism to study random number generators used in Monte Carlo simulations. (author)

A new expression for determination of fluences from a spherical moderator neutron source for the calibration of spherical neutron measuring devices

International Nuclear Information System (INIS)

Khoshnoodi, M.; Sohrabi, M.

1997-01-01

A new expression modifying the inverse square law for determination of neutron fluences from spherical moderator neutron sources is reported. The formalism is based on the neutron fluence at a point outside the moderator as the summation of fluxes of two groups of neutrons: direct neutrons from the central region of the moderator, and moderated neutrons which, to a first approximation, are scattered from the outermost layers of the spherical moderator. The expression has been further developed for spherical neutron measuring devices with an appropriate geometry factor which corrects the reading of the device for non-uniform irradiation of the detector. The combination of the new fluence function and those of the air and room scattered components introduce a calibration model. The fluence relationship obtained for moderated sources may conveniently be used for calculating the more rapid change of neutron dose at close distances than that which is based on the inverse square dependence. (author)

Regular reduction of relativistic theories of gravitation with a quadratic Lagrangian

International Nuclear Information System (INIS)

Bel, L.; Zia, H.S.

1985-01-01

We consider those relativistic theories of gravitation which generalize Einstein's theory in the sense that their field equations derive from a scalar Lagrangian which, besides the matter term, contains a linear combination of the Ricci scalar, its square, and the square of the Ricci tensor. Using a generalization of a technique which has been used to deal with some dynamical systems, we regularly and covariantly reduce the corresponding fourth-order differential equations to second-order ones. We examine, in particular, at a low order of approximation, these reduced equations in cosmology, and for static and spherically symmetric interior solutions with constant density

TIMEX, 1-D Time-Dependent Multigroup Transport Theory with Delayed Neutron, Planar Cylindrical and Spherical Geometry

International Nuclear Information System (INIS)

Hill, T. R.; Reed, W. H.

1980-01-01

1 - Description of problem or function: TIMEX solves the time- dependent, one-dimensional multigroup transport equation with delayed neutrons in plane, cylindrical, spherical, and two-angle plane geometries. Both regular and adjoint, inhomogeneous and homogeneous problems subject to vacuum, reflective, periodic, white, albedo or inhomogeneous boundary flux conditions are solved. General anisotropic scattering is allowed and anisotropic inhomogeneous sources are permitted. 2 - Method of solution: The discrete ordinates approximation for the angular variable is used with the diamond (central) difference approximation for the angular extrapolation in curved geometries. A linear discontinuous finite element representation for the angular flux in each spatial mesh cell is used. Negative fluxes are eliminated by a local set-to-zero and correct algorithm. The time variable is differenced by an explicit technique that is unconditionally stable so that arbitrarily large time-steps can be taken. Two acceleration methods, exponential extrapolation and re-balance, are utilized to improve the accuracy of the time differencing scheme. 3 - Restrictions on the complexity of the problem: Variable dimensioning is used so that any combination of problem parameters leading to a container array less than MAXCOR can be accommodated. In addition, the CDC version permits the use of extended core storage less than MAXECS

The efficiency of Flory approximation

International Nuclear Information System (INIS)

Obukhov, S.P.

1984-01-01

The Flory approximation for the self-avoiding chain problem is compared with a conventional perturbation theory expansion. While in perturbation theory each term is averaged over the unperturbed set of configurations, the Flory approximation is equivalent to the perturbation theory with the averaging over the stretched set of configurations. This imposes restrictions on the integration domain in higher order terms and they can be treated self-consistently. The accuracy δν/ν of Flory approximation for self-avoiding chain problems is estimated to be 2-5% for 1 < d < 4. (orig.)

Site-occupation embedding theory using Bethe ansatz local density approximations

Science.gov (United States)

Senjean, Bruno; Nakatani, Naoki; Tsuchiizu, Masahisa; Fromager, Emmanuel

2018-06-01

Site-occupation embedding theory (SOET) is an alternative formulation of density functional theory (DFT) for model Hamiltonians where the fully interacting Hubbard problem is mapped, in principle exactly, onto an impurity-interacting (rather than a noninteracting) one. It provides a rigorous framework for combining wave-function (or Green function)-based methods with DFT. In this work, exact expressions for the per-site energy and double occupation of the uniform Hubbard model are derived in the context of SOET. As readily seen from these derivations, the so-called bath contribution to the per-site correlation energy is, in addition to the latter, the key density functional quantity to model in SOET. Various approximations based on Bethe ansatz and perturbative solutions to the Hubbard and single-impurity Anderson models are constructed and tested on a one-dimensional ring. The self-consistent calculation of the embedded impurity wave function has been performed with the density-matrix renormalization group method. It has been shown that promising results are obtained in specific regimes of correlation and density. Possible further developments have been proposed in order to provide reliable embedding functionals and potentials.

Using satellite technology (global positioning system) to teach the spherical polar coordinate system

International Nuclear Information System (INIS)

O'Brien, William P Jr

2003-01-01

Students discover the equivalence between plausible geographic variables (co-latitude and longitude) of the Earth and less-familiar geometric variables (polar and azimuthal angles) of spherical polar coordinates by collecting and analysing positional data recorded during field exercises with a handheld global positioning system (GPS) receiver. This pedagogical approach to teaching spherical geometry, based on field experience rather than classroom theory, uses GPS technology to capture the curiosity of contemporary students, technical or otherwise, who might not normally find the topic of the spherical polar coordinate system comprehensible, relevant or interesting

Semi-classical approximation and the problem of boundary conditions in the theory of relativistic particle radiation

International Nuclear Information System (INIS)

Akhiezer, A.I.; Shul'ga, N.F.

1991-01-01

The process of relativistic particle radiation in an external field has been studied in the semi-classical approximation rather extensively. The main problem arising in the studies is in expressing the formula of the quantum theory of radiation in terms of classical quantities, for example of the classical trajectories. However, it still remains unclear how the particle trajectory is assigned, that is which particular initial or boundary conditions determine the trajectory in semi-classical approximation quantum theory of radiation. We shall try to solve this problem. Its importance comes from the fact that in some cases one and the same boundary conditions may give rise to two or more trajectories. We demonstrate that this fact must necessarily be taken into account on deriving the classical limit for the formulae of the quantum theory of radiation, since it leads to a specific interference effect in radiation. The method we used to deal with the problem is similar to the method employed by Fock to analyze the problem of a canonical transformation in classical and quantum mechanics. (author)

The Fatigue Life Prediction of Train Wheel Rims Containing Spherical Inclusions

Science.gov (United States)

Li, Yajie; Chen, Huanguo; Cai, Li; Chen, Pei; Qian, Jiacheng; Wu, Jianwei

2018-03-01

It is a common phenomenon that fatigue crack initiation occurs frequently in the inclusions of wheel rims. Research on the fatigue life of wheel rims with spherical inclusions is of great significance on the reliability of wheels. To find the danger point and working condition of a wheel, the stress state of the wheel rim with spherical inclusions was analyzed using the finite element method. Results revealed that curve conditions are dangerous. The critical plane method, based on the cumulative fatigue damage theory, was used to predict the fatigue life of the wheel rim and whether it contained spherical inclusions or not under curve conditions. It was found that the fatigue life of the wheel rim is significantly shorter when the wheel rim contains spherical inclusions. Analysis of the results can provide a theoretical basis and technical support for train operations and maintenance.

Sparse approximation with bases

CERN Document Server

2015-01-01

This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications.  The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...

Approximation and Computation

CERN Document Server

Gautschi, Walter; Rassias, Themistocles M

2011-01-01

Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovia, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational alg

The ''Dolphin'' power laser installation for spherical thermonuclear target heating

International Nuclear Information System (INIS)

Basov, N.G.; Bykovskij, N.E.; Danilov, A.E.

1978-01-01

12-channel laser installation the ''Dolphin'' for thermonuclear target heating in the radiation spheric geometry has been developed to carry out series of physical investigations of laser-thermonuclear plasma system, optimization of target heating conditions and obtaining a comparatively large value of thermonuclear output in ratio to the energy of absorbed light radiation in the target. The description of installation main elements, consisting of the following components, is given: 1)neodymium laser with the maximum permissible radiation energy of 10kJ, with light pulse duration of 10 -10 /10 -9 c and radiation divergence of approximately 5x10 -4 rad; 2)vacuum chamber, where laser radiation interaction with plasma takes place; 3)diagnostic means of laser and plasma parameters and 4)focus system. The focus system provides a high degree of target spherical radiation symmetry at current maximum density on its surface of approximately 10 15 W/cm 2

Plane-wave decomposition by spherical-convolution microphone array

Science.gov (United States)

Rafaely, Boaz; Park, Munhum

2004-05-01

Reverberant sound fields are widely studied, as they have a significant influence on the acoustic performance of enclosures in a variety of applications. For example, the intelligibility of speech in lecture rooms, the quality of music in auditoria, the noise level in offices, and the production of 3D sound in living rooms are all affected by the enclosed sound field. These sound fields are typically studied through frequency response measurements or statistical measures such as reverberation time, which do not provide detailed spatial information. The aim of the work presented in this seminar is the detailed analysis of reverberant sound fields. A measurement and analysis system based on acoustic theory and signal processing, designed around a spherical microphone array, is presented. Detailed analysis is achieved by decomposition of the sound field into waves, using spherical Fourier transform and spherical convolution. The presentation will include theoretical review, simulation studies, and initial experimental results.

Eigenvalues and eigenvectors of the translation matrices of spherical waves of multiple-scattering theory

International Nuclear Information System (INIS)

Torrini, M.

1983-01-01

The exponential nature of the translation matrix G of spherical free waves has been set forth in a previous paper.The explicit expression of the exponential form of the translation matrix is given here, once the eigenvectros and the eigenvalues of G have been found. In addition, the eigenproblem relative to the matrix which transforms outgoing waves scattered by a centre in a set of spherical free waves centered at a different point is solved

Particles in spherical electromagnetic radiation fields

International Nuclear Information System (INIS)

Mitter, H.; Thaller, B.

1984-03-01

If the time-dependence of a Hamiltonian can be compensated by an appropriate symmetry transformation, the corresponding quantum mechanical problem can be reduced to an effectively stationary one. With this result we investigate the behavior of nonrelativistic particles in a spherical radiation field produced by a rotating source. Then the symmetry transformation corresponds to a rotation. We calculate the transition probabilities in Born approximation. The extension to problems involving an additional Coulomb potential is briefly discussed. (Author)

Charge transfer excitations from exact and approximate ensemble Kohn-Sham theory

Science.gov (United States)

Gould, Tim; Kronik, Leeor; Pittalis, Stefano

2018-05-01

By studying the lowest excitations of an exactly solvable one-dimensional soft-Coulomb molecular model, we show that components of Kohn-Sham ensembles can be used to describe charge transfer processes. Furthermore, we compute the approximate excitation energies obtained by using the exact ensemble densities in the recently formulated ensemble Hartree-exchange theory [T. Gould and S. Pittalis, Phys. Rev. Lett. 119, 243001 (2017)]. Remarkably, our results show that triplet excitations are accurately reproduced across a dissociation curve in all cases tested, even in systems where ground state energies are poor due to strong static correlations. Singlet excitations exhibit larger deviations from exact results but are still reproduced semi-quantitatively.

Boundary causality versus hyperbolicity for spherical black holes in Gauss–Bonnet gravity

International Nuclear Information System (INIS)

Andrade, Tomás; Cáceres, Elena; Keeler, Cynthia

2017-01-01

We explore the constraints boundary causality places on the allowable Gauss–Bonnet gravitational couplings in asymptotically AdS spaces, specifically considering spherical black hole solutions. We additionally consider the hyperbolicity properties of these solutions, positing that hyperbolicity-violating solutions are sick solutions whose causality properties provide no information about the theory they reside in. For both signs of the Gauss–Bonnet coupling, spherical black holes violate boundary causality at smaller absolute values of the coupling than planar black holes do. For negative coupling, as we tune the Gauss–Bonnet coupling away from zero, both spherical and planar black holes violate hyperbolicity before they violate boundary causality. For positive coupling, the only hyperbolicity-respecting spherical black holes which violate boundary causality do not do so appreciably far from the planar bound. Consequently, eliminating hyperbolicity-violating solutions means the bound on Gauss–Bonnet couplings from the boundary causality of spherical black holes is no tighter than that from planar black holes. (paper)

The point ground electrode in vicinity of the semi-spherical inhomogenity

Directory of Open Access Journals (Sweden)

Cvetković Nenad N.

2005-01-01

Full Text Available Characterization of the point ground electrode placed in the surroundings or inside of the semi-spherical earth inhomogenity and fed by low frequency (LF current using isolated earthling conductor, is presented in this paper. The ground impedance (resistance and reactance and potential distribution on the ground surface are determined. Image theory for two-layer semi conducting media, as well as for the one point electrode placed nearby or inside of the spherical body is used during the analysis.

Numerical relativity in spherical coordinates with the Einstein Toolkit

Science.gov (United States)

Mewes, Vassilios; Zlochower, Yosef; Campanelli, Manuela; Ruchlin, Ian; Etienne, Zachariah B.; Baumgarte, Thomas W.

2018-04-01

Numerical relativity codes that do not make assumptions on spatial symmetries most commonly adopt Cartesian coordinates. While these coordinates have many attractive features, spherical coordinates are much better suited to take advantage of approximate symmetries in a number of astrophysical objects, including single stars, black holes, and accretion disks. While the appearance of coordinate singularities often spoils numerical relativity simulations in spherical coordinates, especially in the absence of any symmetry assumptions, it has recently been demonstrated that these problems can be avoided if the coordinate singularities are handled analytically. This is possible with the help of a reference-metric version of the Baumgarte-Shapiro-Shibata-Nakamura formulation together with a proper rescaling of tensorial quantities. In this paper we report on an implementation of this formalism in the Einstein Toolkit. We adapt the Einstein Toolkit infrastructure, originally designed for Cartesian coordinates, to handle spherical coordinates, by providing appropriate boundary conditions at both inner and outer boundaries. We perform numerical simulations for a disturbed Kerr black hole, extract the gravitational wave signal, and demonstrate that the noise in these signals is orders of magnitude smaller when computed on spherical grids rather than Cartesian grids. With the public release of our new Einstein Toolkit thorns, our methods for numerical relativity in spherical coordinates will become available to the entire numerical relativity community.

One-Body Potential Theory of Molecules and Solids Modified Semiempirically for Electron Correlation

International Nuclear Information System (INIS)

March, N.H.

2010-08-01

The study of Cordero, March and Alonso (CMA) for four spherical atoms, Be,Ne,Mg and Ar, semiempirically fine-tunes the Hartree-Fock (HF) ground-state electron density by inserting the experimentally determined ionization potentials. The present Letter, first of all, relates this approach to the very recent work of Bartlett 'towards an exact correlated orbital theory for electrons'. Both methods relax the requirement of standard DFT that a one-body potential shall generate the exact ground-state density, though both work with high quality approximations. Unlike DFT, the CMA theory uses a modified HF non-local potential. It is finally stressed that this potential generates also an idempotent Dirac density matrix. The CMA approach is thereby demonstrated to relate, albeit approximately, to the DFT exchange-correlation potential. (author)

Equivalent-spherical-shield neutron dose calculations

International Nuclear Information System (INIS)

Russell, G.J.; Robinson, H.

1988-01-01

Neutron doses through 162-cm-thick spherical shields were calculated to be 1090 and 448 mrem/h for regular and magnetite concrete, respectively. These results bracket the measured data, for reinforced regular concrete, of /approximately/600 mrem/h. The calculated fraction of the high-energy (>20 MeV) dose component also bracketed the experimental data. The measured and calculated doses were for a graphite beam stop bombarded with 100 nA of 800-MeV protons. 6 refs., 2 figs., 1 tab

The quasi-diffusive approximation in transport theory: Local solutions

International Nuclear Information System (INIS)

Celaschi, M.; Montagnini, B.

1995-01-01

The one velocity, plane geometry integral neutron transport equation is transformed into a system of two equations, one of them being the equation of continuity and the other a generalized Fick's law, in which the usual diffusion coefficient is replaced by a self-adjoint integral operator. As the kernel of this operator is very close to the Green function of a diffusion equation, an approximate inversion by means of a second order differential operator allows to transform these equations into a purely differential system which is shown to be equivalent, in the simplest case, to a diffusion-like equation. The method, the principles of which have been exposed in a previous paper, is here extended and applied to a variety of problems. If the inversion is properly performed, the quasi-diffusive solutions turn out to be quite accurate, even in the vicinity of the interface between different material regions, where elementary diffusion theory usually fails. 16 refs., 3 tabs

Many-body perturbation theory using the density-functional concept: beyond the GW approximation

OpenAIRE

Bruneval, Fabien; Sottile, Francesco; Olevano, Valerio; Del Sole, Rodolfo; Reining, Lucia

2005-01-01

We propose an alternative formulation of Many-Body Perturbation Theory that uses the density-functional concept. Instead of the usual four-point integral equation for the polarizability, we obtain a two-point one, that leads to excellent optical absorption and energy loss spectra. The corresponding three-point vertex function and self-energy are then simply calculated via an integration, for any level of approximation. Moreover, we show the direct impact of this formulation on the time-depend...

General theory for calculating disorder-averaged Green's function correlators within the coherent potential approximation

Science.gov (United States)

Zhou, Chenyi; Guo, Hong

2017-01-01

We report a diagrammatic method to solve the general problem of calculating configurationally averaged Green's function correlators that appear in quantum transport theory for nanostructures containing disorder. The theory treats both equilibrium and nonequilibrium quantum statistics on an equal footing. Since random impurity scattering is a problem that cannot be solved exactly in a perturbative approach, we combine our diagrammatic method with the coherent potential approximation (CPA) so that a reliable closed-form solution can be obtained. Our theory not only ensures the internal consistency of the diagrams derived at different levels of the correlators but also satisfies a set of Ward-like identities that corroborate the conserving consistency of transport calculations within the formalism. The theory is applied to calculate the quantum transport properties such as average ac conductance and transmission moments of a disordered tight-binding model, and results are numerically verified to high precision by comparing to the exact solutions obtained from enumerating all possible disorder configurations. Our formalism can be employed to predict transport properties of a wide variety of physical systems where disorder scattering is important.

Spherical neutron generator

Science.gov (United States)

Leung, Ka-Ngo

2006-11-21

A spherical neutron generator is formed with a small spherical target and a spherical shell RF-driven plasma ion source surrounding the target. A deuterium (or deuterium and tritium) ion plasma is produced by RF excitation in the plasma ion source using an RF antenna. The plasma generation region is a spherical shell between an outer chamber and an inner extraction electrode. A spherical neutron generating target is at the center of the chamber and is biased negatively with respect to the extraction electrode which contains many holes. Ions passing through the holes in the extraction electrode are focused onto the target which produces neutrons by D-D or D-T reactions.

Phase behavior of charged hydrophobic colloids on flat and spherical surfaces

Science.gov (United States)

Kelleher, Colm P.

For a broad class of two-dimensional (2D) materials, the transition from isotropic fluid to crystalline solid is described by the theory of melting due to Kosterlitz, Thouless, Halperin, Nelson and Young (KTHNY). According to this theory, long-range order is achieved via elimination of the topological defects which proliferate in the fluid phase. However, many natural and man-made 2D systems posses spatial curvature and/or non-trivial topology, which require the presence of topological defects, even at T=0. In principle, the presence of these defects could profoundly affect the phase behavior of such a system. In this thesis, we develop and characterize an experimental system of charged colloidal particles that bind electrostatically to the interface between an oil and an aqueous phase. Depending on how we prepare the sample, this fluid interface may be flat, spherical, or have a more complicated geometry. Focusing on the cases where the interface is flat or spherical, we measure the interactions between the particles, and probe various aspects of their phase behavior. On flat interfaces, this phase behavior is well-described by KTHNY theory. In spherical geometries, however, we observe spatial structures and inhomogeneous dynamics that cannot be captured by the measures traditionally used to describe flat-space phase behavior. We show that, in the spherical system, ordering is achieved by a novel mechanism: sequestration of topological defects into freely-terminating grain boundaries ("scars"), and simultaneous spatial organization of the scars themselves on the vertices of an icosahedron. The emergence of icosahedral order coincides with the localization of mobility into isolated "lakes" of fluid or glassy particles, situated at the icosahedron vertices. These lakes are embedded in a rigid, connected "continent" of locally crystalline particles.

Spherical harmonic expansion of short-range screened Coulomb interactions

Energy Technology Data Exchange (ETDEWEB)

Angyan, Janos G [Laboratoire de Cristallographie et de Modelisation des Materiaux Mineraux et Biologiques, UMR 7036, CNRS-Universite Henri Poincare, BP 239, F-54506 Vandoeuvre-les-Nancy (France); Gerber, Iann [Laboratoire de Cristallographie et de Modelisation des Materiaux Mineraux et Biologiques, UMR 7036, CNRS-Universite Henri Poincare, BP 239, F-54506 Vandoeuvre-les-Nancy (France); Marsman, Martijn [Institut fuer Materialphysik and Center for Computational Materials Science, Universitaet Wien, Sensengasse 8, A-1090, Vienna (Austria)

2006-07-07

Spherical harmonic expansions of the screened Coulomb interaction kernel involving the complementary error function are required in various problems in atomic, molecular and solid state physics, like for the evaluation of Ewald-type lattice sums or for range-separated hybrid density functionals. A general analytical expression is derived for the kernel, which is non-separable in the radial variables. With the help of series expansions a separable approximate form is proposed, which is in close analogy with the conventional multipole expansion of the Coulomb kernel in spherical harmonics. The convergence behaviour of these expansions is studied and illustrated by the electrostatic potential of an elementary charge distribution formed by products of Slater-type atomic orbitals.

On transparent potentials: a Born approximation study

International Nuclear Information System (INIS)

Coudray, C.

1980-01-01

In the frame of the scattering inverse problem at fixed energy, a class of potentials transparent in Born approximation is obtained. All these potentials are spherically symmetric and are oscillating functions of the reduced radial variable. Amongst them, the Born approximation of the transparent potential of the Newton-Sabatier method is found. In the same class, quasi-transparent potentials are exhibited. Very general features of potentials transparent in Born approximation are then stated. And bounds are given for the exact scattering amplitudes corresponding to most of the potentials previously exhibited. These bounds, obtained at fixed energy, and for large values of the angular momentum, are found to be independent on the energy

The Gaussian formula and spherical aberrations of static and relativistic curved mirrors from Fermat's principle

International Nuclear Information System (INIS)

Sutanto, Sylvia H; Tjiang, Paulus C

2011-01-01

The Gaussian formula and spherical aberrations of static and relativistic curved mirrors are analyzed using the optical path length (OPL) and Fermat's principle. The geometrical figures generated by the rotation of conic sections about their symmetry axes are considered for the shapes of the mirrors. By comparing the results in static and relativistic cases, it is shown that the focal lengths and the spherical aberration relations of the relativistic mirrors obey the Lorentz contraction. Further analysis of the spherical aberrations for both static and relativistic cases have resulted in information about the limits for the paraxial approximation, as well as for the minimum speed of the systems to reduce the spherical aberrations

Determining spherical lens correction for astronaut training underwater.

Science.gov (United States)

Porter, Jason; Gibson, C Robert; Strauss, Samuel

2011-09-01

To develop a model that will accurately predict the distance spherical lens correction needed to be worn by National Aeronautics and Space Administration astronauts while training underwater. The replica space suit's helmet contains curved visors that induce refractive power when submersed in water. Anterior surface powers and thicknesses were measured for the helmet's protective and inside visors. The impact of each visor on the helmet's refractive power in water was analyzed using thick lens calculations and Zemax optical design software. Using geometrical optics approximations, a model was developed to determine the optimal distance spherical power needed to be worn underwater based on the helmet's total induced spherical power underwater and the astronaut's manifest spectacle plane correction in air. The validity of the model was tested using data from both eyes of 10 astronauts who trained underwater. The helmet's visors induced a total power of -2.737 D when placed underwater. The required underwater spherical correction (FW) was linearly related to the spectacle plane spherical correction in air (FAir): FW = FAir + 2.356 D. The mean magnitude of the difference between the actual correction worn underwater and the calculated underwater correction was 0.20 ± 0.11 D. The actual and calculated values were highly correlated (r = 0.971) with 70% of eyes having a difference in magnitude of astronauts. The model accurately predicts the actual values worn underwater and can be applied (more generally) to determine a suitable spectacle lens correction to be worn behind other types of masks when submerged underwater.

Spherical null geodesics of rotating Kerr black holes

International Nuclear Information System (INIS)

Hod, Shahar

2013-01-01

The non-equatorial spherical null geodesics of rotating Kerr black holes are studied analytically. Unlike the extensively studied equatorial circular orbits whose radii are known analytically, no closed-form formula exists in the literature for the radii of generic (non-equatorial) spherical geodesics. We provide here an approximate formula for the radii r ph (a/M;cosi) of these spherical null geodesics, where a/M is the dimensionless angular momentum of the black hole and cos i is an effective inclination angle (with respect to the black-hole equatorial plane) of the orbit. It is well-known that the equatorial circular geodesics of the Kerr spacetime (the prograde and the retrograde orbits with cosi=±1) are characterized by a monotonic dependence of their radii r ph (a/M;cosi=±1) on the dimensionless spin-parameter a/M of the black hole. We use here our novel analytical formula to reveal that this well-known property of the equatorial circular geodesics is actually not a generic property of the Kerr spacetime. In particular, we find that counter-rotating spherical null orbits in the range (3√(3)−√(59))/4≲cosi ph (a/M;cosi=const) on the dimensionless rotation-parameter a/M of the black hole. Furthermore, it is shown that spherical photon orbits of rapidly-rotating black holes are characterized by a critical inclination angle, cosi=√(4/7), above which the coordinate radii of the orbits approach the black-hole radius in the extremal limit. We prove that this critical inclination angle signals a transition in the physical properties of the spherical null geodesics: in particular, it separates orbits which are characterized by finite proper distances to the black-hole horizon from orbits which are characterized by infinite proper distances to the horizon.

A vectorial description of electromagnetic scattering by large bodies of spherical shape

International Nuclear Information System (INIS)

Bourrely, C.; Lemaire, T.; Chiappetta, P.; Centre National de la Recherche Scientifique, 13 - Marseille

1989-10-01

We present a new method to obtain a vectorial solution of Helmholtz equation for large homogeneous scatterers having a cylindrical symmetry and a shape approximately spherical. Limitations of the method for arbitrarily shaped particles are discussed

Transformation-based spherical cloaks designed by an implicit transformation-independent method: theory and optimization

International Nuclear Information System (INIS)

Novitsky, Andrey; Qiu, C-W; Zouhdi, Said

2009-01-01

Based on the concept of the cloak generating function, we propose an implicit transformation-independent method for the required parameters of spherical cloaks without knowing the needed coordinate transformation beforehand. A non-ideal discrete model is used to calculate and optimize the total scattering cross-sections of different profiles of the generating function. A bell-shaped quadratic spherical cloak is found to be the best candidate, which is further optimized by controlling the design parameters involved. Such improved invisibility is steady even when the model is highly discretized.

Comparisons of perturbation and integral equation theories for the angular pair correlation function in molecular fluids

International Nuclear Information System (INIS)

Murad, S.; Gubbins, K.E.; Gray, C.G.

1983-01-01

We compare several recently proposed theories for the angular pair correlation function g(rω 1 ω 2 ), including first- and second-order perturbation theory (the u-expansion), a Pade approximant to this series, first-order f-expansion, the single superchain, generalized mean field, linearized hypernetted chain, and quadratic hypernetted chain approximations. Numerical results from these theories are compared with available computer simulation data for four model fluids whose intermolecular pair potential is of the form u 0 +usub(a), where u 0 is a hard-sphere of Lennard-Jones model, while usub(a) is a dipole-dipole or quadrupole-quadrupole interaction; we refer to these model fluids as HS+μμ, HS+QQ, LJ+μμ, and LJ+QQ. Properties studied include the angular pair correlation function and its spherical harmonic components, the thermodynamic properties, and the angular correlation parameters G 1 and G 2 that are related to the dielectric and Kerr constants. The second-order perturbation theory is superior to the integral equation theories for the thermodynamic harmonics of g(rω 1 ω 2 ) and for the thermodynamic properties themselves at moderate multipole strengths. For other harmonics and properties, the integral equation theories are better, with the quadratic hypernetted chain approximation being the best overall. (orig.)

Quasi-spherical compression of a spark-channel plasma

International Nuclear Information System (INIS)

Panarella, E.

1980-01-01

An axial spark channel in deuterium has been used as a target for implosive shock waves created with a conventional cylindrical theta-pinch device. The compression of the channel by the implosive waves raised the plasma electron temperature to approximately 120 eV for approximately 6 kJ of condenser bank energy and 1 Torr initial gas pressure. In order to improve the efficiency of compression of the channel plasma and to reduce the end losses inherent in the cylindrical configuration, the theta-pinch geometry was then converted from cylindrical into spherical. Under identical conditions of gas pressure and condenser bank energy, the electron temperature now peaked at approximately 400 eV. When the bank energy was increased to approximately 10 kJ, neutron production was observed. The total neutron output per shot ranged from 10 5 to 10 6 and increased inversely with the pinch discharge volume

On Perturbation Solutions for Axisymmetric Bending Boundary Values of a Deep Thin Spherical Shell

Directory of Open Access Journals (Sweden)

Rong Xiao

2014-01-01

Full Text Available On the basis of the general theory of elastic thin shells and the Kirchhoff-Love hypothesis, a fundamental equation for a thin shell under the moment theory is established. In this study, the author derives Reissner’s equation with a transverse shear force Q1 and the displacement component w. These basic unknown quantities are derived considering the axisymmetry of the deep, thin spherical shell and manage to constitute a boundary value question of axisymmetric bending of the deep thin spherical shell under boundary conditions. The asymptotic solution is obtained by the composite expansion method. At the end of this paper, to prove the correctness and accuracy of the derivation, an example is given to compare the numerical solution by ANSYS and the perturbation solution. Meanwhile, the effects of material and geometric parameters on the nonlinear response of axisymmetric deep thin spherical shell under uniform external pressure are also analyzed in this paper.

Cooperative effects in spherical spasers: Ab initio analytical model

Science.gov (United States)

Bordo, V. G.

2017-06-01

A fully analytical semiclassical theory of cooperative optical processes which occur in an ensemble of molecules embedded in a spherical core-shell nanoparticle is developed from first principles. Both the plasmonic Dicke effect and spaser generation are investigated for the designs in which a shell/core contains an arbitrarily large number of active molecules in the vicinity of a metallic core/shell. An essential aspect of the theory is an ab initio account of the feedback from the core/shell boundaries which significantly modifies the molecular dynamics. The theory provides rigorous, albeit simple and physically transparent, criteria for both plasmonic superradiance and surface plasmon generation.

Self-consistent Random Phase Approximation applied to a schematic model of the field theory; Approximation des phases aleatoires self-consistante appliquee a un modele schematique de la theorie des champs

Energy Technology Data Exchange (ETDEWEB)

Bertrand, Thierry [Inst. de Physique Nucleaire, Lyon-1 Univ., 69 - Villeurbanne (France)

1998-12-11

The self-consistent Random Phase Approximation (SCRPA) is a method allowing in the mean-field theory inclusion of the correlations in the ground and excited states. It has the advantage of not violating the Pauli principle in contrast to RPA, that is based on the quasi-bosonic approximation; in addition, numerous applications in different domains of physics, show a possible variational character. However, the latter should be formally demonstrated. The first model studied with SCRPA is the anharmonic oscillator in the region where one of its symmetries is spontaneously broken. The ground state energy is reproduced by SCRPA more accurately than RPA, with no violation of the Ritz variational principle, what is not the case for the latter approximation. The success of SCRPA is the the same in case of ground state energy for a model mixing bosons and fermions. At the transition point the SCRPA is correcting RPA drastically, but far from this region the correction becomes negligible, both methods being of similar precision. In the deformed region in the case of RPA a spurious mode occurred due to the microscopical character of the model.. The SCRPA may also reproduce this mode very accurately and actually it coincides with an excitation in the exact spectrum 40 refs., 33 figs., 14 tabs.

Direct Simulation of Extinction in a Slab of Spherical Particles

Science.gov (United States)

Mackowski, D.W.; Mishchenko, Michael I.

2013-01-01

The exact multiple sphere superposition method is used to calculate the coherent and incoherent contributions to the ensemble-averaged electric field amplitude and Poynting vector in systems of randomly positioned nonabsorbing spherical particles. The target systems consist of cylindrical volumes, with radius several times larger than length, containing spheres with positional configurations generated by a Monte Carlo sampling method. Spatially dependent values for coherent electric field amplitude, coherent energy flux, and diffuse energy flux, are calculated by averaging of exact local field and flux values over multiple configurations and over spatially independent directions for fixed target geometry, sphere properties, and sphere volume fraction. Our results reveal exponential attenuation of the coherent field and the coherent energy flux inside the particulate layer and thereby further corroborate the general methodology of the microphysical radiative transfer theory. An effective medium model based on plane wave transmission and reflection by a plane layer is used to model the dependence of the coherent electric field on particle packing density. The effective attenuation coefficient of the random medium, computed from the direct simulations, is found to agree closely with effective medium theories and with measurements. In addition, the simulation results reveal the presence of a counter-propagating component to the coherent field, which arises due to the internal reflection of the main coherent field component by the target boundary. The characteristics of the diffuse flux are compared to, and found to be consistent with, a model based on the diffusion approximation of the radiative transfer theory.

Photons in a spherical cavity

International Nuclear Information System (INIS)

Ionescu-Pallas, N.; Vlad, V.I.

1999-01-01

The spectrum of black body radiation at the absolute temperature T, in an ideal spherical cavity of radius R, is studied. The departures from the classical predictions of Planck's theory, due to the discrete energies of the radiation quanta confined inside the cavity, depend on the adiabatic invariant RT and are significant for RT≤ 1 cm K. Special attention was paid to evidence sudden changes in the spectrum intensities, forbidden bands of frequency, as well as major modifications of the total energy for RT≤ 1 cm K. Similar effects were present in case of a cubic cavity too. (authors)

Quantum theory of anharmonic oscillators - a variational and systematic general approximation method

International Nuclear Information System (INIS)

Yamazaki, K.; Kyoto Univ.

1984-01-01

The paper investigates the energy levels and wavefunctions of an anharmonic oscillator characterised by the potential 1/2ω 2 q 2 +lambdaq 4 . As a lowest-order approximation an extremely simple formula for energy levels, Esub(i)sup(0) = (i+1/2)1/4(3/αsub(i)+αsub(i)), is derived (i being the quantum number of the energy level). This formula reproduces the exact energy levels within an error of about 1%. Systematically higher orders of the present perturbation theory are developed. The present second-order perturbation theory reduces the errors of the lowest-order results by a factor of about 1/5 in general. Various ranges (large, intermediate, small) of (i, lambda) are investigated and compared with the exact values obtained by other workers. For i = 0, 1, even the fourth-order perturbation calculation can be elaborated explicitly, which reduces the error to about 0.01% for any lambda. For small lambda it gives correct numerical coefficients up to lambda 4 terms, as it should. (author)

Low Rank Approximation Algorithms, Implementation, Applications

CERN Document Server

Markovsky, Ivan

2012-01-01

Matrix low-rank approximation is intimately related to data modelling; a problem that arises frequently in many different fields. Low Rank Approximation: Algorithms, Implementation, Applications is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory. Applications described include: system and control theory: approximate realization, model reduction, output error, and errors-in-variables identification; signal processing: harmonic retrieval, sum-of-damped exponentials, finite impulse response modeling, and array processing; machine learning: multidimensional scaling and recommender system; computer vision: algebraic curve fitting and fundamental matrix estimation; bioinformatics for microarray data analysis; chemometrics for multivariate calibration; ...

Hawking radiation from a spherical loop quantum gravity black hole

International Nuclear Information System (INIS)

Gambini, Rodolfo; Pullin, Jorge

2014-01-01

We introduce quantum field theory on quantum space-times techniques to characterize the quantum vacua as a first step toward studying black hole evaporation in spherical symmetry in loop quantum gravity and compute the Hawking radiation. We use as quantum space-time the recently introduced exact solution of the quantum Einstein equations in vacuum with spherical symmetry and consider a spherically symmetric test scalar field propagating on it. The use of loop quantum gravity techniques in the background space-time naturally regularizes the matter content, solving one of the main obstacles to back-reaction calculations in more traditional treatments. The discreteness of area leads to modifications of the quantum vacua, eliminating the trans-Planckian modes close to the horizon, which in turn eliminates all singularities from physical quantities, like the expectation value of the stress–energy tensor. Apart from this, the Boulware, Hartle–Hawking and Unruh vacua differ little from the treatment on a classical space-time. The asymptotic modes near scri are reproduced very well. We show that the Hawking radiation can be computed, leading to an expression similar to the conventional one but with a high frequency cutoff. Since many of the conclusions concern asymptotic behavior, where the spherical mode of the field behaves in a similar way as higher multipole modes do, the results can be readily generalized to non spherically symmetric fields. (paper)

Morphing Continuum Theory: A First Order Approximation to the Balance Laws

Science.gov (United States)

Wonnell, Louis; Cheikh, Mohamad Ibrahim; Chen, James

2017-11-01

Morphing Continuum Theory is constructed under the framework of Rational Continuum Mechanics (RCM) for fluid flows with inner structure. This multiscale theory has been successfully emplyed to model turbulent flows. The framework of RCM ensures the mathematical rigor of MCT, but contains new material constants related to the inner structure. The physical meanings of these material constants have yet to be determined. Here, a linear deviation from the zeroth-order Boltzmann-Curtiss distribution function is derived. When applied to the Boltzmann-Curtiss equation, a first-order approximation of the MCT governing equations is obtained. The integral equations are then related to the appropriate material constants found in the heat flux, Cauchy stress, and moment stress terms in the governing equations. These new material properties associated with the inner structure of the fluid are compared with the corresponding integrals, and a clearer physical interpretation of these coefficients emerges. The physical meanings of these material properties is determined by analyzing previous results obtained from numerical simulations of MCT for compressible and incompressible flows. The implications for the physics underlying the MCT governing equations will also be discussed. This material is based upon work supported by the Air Force Office of Scientific Research under Award Number FA9550-17-1-0154.

Internal stray radiation measurement for cryogenic infrared imaging systems using a spherical mirror.

Science.gov (United States)

Tian, Qijie; Chang, Songtao; He, Fengyun; Li, Zhou; Qiao, Yanfeng

2017-06-10

Internal stray radiation is a key factor that influences infrared imaging systems, and its suppression level is an important criterion to evaluate system performance, especially for cryogenic infrared imaging systems, which are highly sensitive to thermal sources. In order to achieve accurate measurement for internal stray radiation, an approach is proposed, which is based on radiometric calibration using a spherical mirror. First of all, the theory of spherical mirror design is introduced. Then, the calibration formula considering the integration time is presented. Following this, the details regarding the measurement method are presented. By placing a spherical mirror in front of the infrared detector, the influence of internal factors of the detector on system output can be obtained. According to the calibration results of the infrared imaging system, the output caused by internal stray radiation can be acquired. Finally, several experiments are performed in a chamber with controllable inside temperatures to validate the theory proposed in this paper. Experimental results show that the measurement results are in good accordance with the theoretical analysis, and demonstrate that the proposed theories are valid and can be employed in practical applications. The proposed method can achieve accurate measurement for internal stray radiation at arbitrary integration time and ambient temperatures. The measurement result can be used to evaluate whether the suppression level meets the system requirement.

Radiative Transfer Equation for Anisotropic Spherical Medium with Specular Reflective Index

International Nuclear Information System (INIS)

Elghazaly, A.

2009-01-01

Radiative transfer problem for anisotropic scattering in a spherical homogeneous, turbid medium with diffuse and angular dependent (specular) reflecting boundaries is solved using the Pomraning-Eddington approximation method. The angular dependent specular reflectivity of the boundary is considered as Fresnel's reflection probability function. The partial heat flux is calculated with anisotropic scattering through a homogeneous solid sphere. The calculations are carried out for spherical media of radii 0.1, 1.0, and 10 mfp and for different scattering albedo. Two different weight functions are used to verify the boundary conditions. Our results are compared with the available data and give an excellent agreement for thick and highly scattering media

Effect of Fresnel Reflectivity in a Spherical Turbid Medium

CERN Document Server

Elghazaly, A

2003-01-01

Radiative transfer problem for anisotropic scattering in a spherical homogeneous, turbid medium with angular dependent (specular) reflecting boundary is solved using the pomraning-Eddington approximation method. The angular dependent reflectivity of the boundary is considered as Fresnel's reflection probability function. The partial heat flux is calculated with anisotropic scattering through a homogeneous solid sphere. our results are compared with the available data and give an excellent agreement.

Effect of Fresnel Reflectivity in a Spherical Turbid Medium

International Nuclear Information System (INIS)

Elghazaly, A.; Attia, M.T.

2003-01-01

Radiative transfer problem for anisotropic scattering in a spherical homogeneous, turbid medium with angular dependent (specular) reflecting boundary is solved using the pomraning-Eddington approximation method. The angular dependent reflectivity of the boundary is considered as Fresnel's reflection probability function. The partial heat flux is calculated with anisotropic scattering through a homogeneous solid sphere. our results are compared with the available data and give an excellent agreement

Effective response and scattering cross section of spherical inclusions in a medium

Energy Technology Data Exchange (ETDEWEB)

Alexopoulos, A., E-mail: Aris.Alexopoulos@dsto.defence.gov.a [Electronic Warfare and Radar Division, Defence Science and Technology Organisation (DSTO), PO Box 1500, Edinburgh 5111 (Australia)

2009-08-24

The Maxwell-Garnett theory for a right-handed homogeneous system is extended in order to investigate the effective response of a medium consisting of low density distributed 3-dimensional inclusions. The polarisability factor is modified to account for inclusions with binary layered volumes and it is shown that such a configuration can yield doubly negative effective permittivity and permeability. Terms representing second-order scattering interactions between binary inclusions in the medium are derived and are used to reformulate conventional effective medium theory. In the appropriate limit, the one-body theory of Maxwell-Garnett is recovered. The scattering cross section of the spherical inclusions is determined and comparison is made to homogeneous dielectric scatterers in the Rayleigh limit. It is found that the scattering resonances can be manipulated using the inclusion parameters. Furthermore, the effect that two-interacting spherical inclusions in a medium have on the scattering cross section is investigated via higher order dipole moments while the issue of reducing the scattering cross section to zero is also examined.

Uniqueness of flat spherically symmetric spacelike hypersurfaces admitted by spherically symmetric static spacetimes

Science.gov (United States)

Beig, Robert; Siddiqui, Azad A.

2007-11-01

It is known that spherically symmetric static spacetimes admit a foliation by flat hypersurfaces. Such foliations have explicitly been constructed for some spacetimes, using different approaches, but none of them have proved or even discussed the uniqueness of these foliations. The issue of uniqueness becomes more important due to suitability of flat foliations for studying black hole physics. Here, flat spherically symmetric spacelike hypersurfaces are obtained by a direct method. It is found that spherically symmetric static spacetimes admit flat spherically symmetric hypersurfaces, and that these hypersurfaces are unique up to translation under the timelike Killing vector. This result guarantees the uniqueness of flat spherically symmetric foliations for such spacetimes.

Theory for site-site pair distribution functions of molecular fluids. II. Approximations for the Percus--Yevick site-site direct correlation functions

International Nuclear Information System (INIS)

Johnson, E.

1977-01-01

A theory for site-site pair distribution functions of molecular fluids is derived from the Ornstein-Zernike equation. Atom-atom pair distribution functions of this theory which were obtained by using different approximations for the Percus-Yevick site-site direct correlation functions are compared

INTEGRATION OF THE ROTATION OF AN EARTH-LIKE BODY AS A PERTURBED SPHERICAL ROTOR

International Nuclear Information System (INIS)

Ferrer, Sebastian; Lara, Martin

2010-01-01

For rigid bodies close to a sphere, we propose an analytical solution that is free from elliptic integrals and functions, and can be fundamental for application to perturbed problems. After reordering the Hamiltonian as a perturbed spherical rotor, the Lie-series solution is generated up to an arbitrary order. Using the inertia parameters of different solar system bodies, the comparison of the approximate series solution with the exact analytical one shows that the precision reached with relatively low orders is at the same level of the observational accuracy for the Earth and Mars. Thus, for instance, the periodic errors of the mathematical solution are confined to the microarcsecond level with a simple second-order truncation for the Earth. On the contrary, higher orders are required for the mathematical solution to reach a precision at the expected level of accuracy of proposed new theories for the rotational dynamics of the Moon.

Self-similar continued root approximants

International Nuclear Information System (INIS)

Gluzman, S.; Yukalov, V.I.

2012-01-01

A novel method of summing asymptotic series is advanced. Such series repeatedly arise when employing perturbation theory in powers of a small parameter for complicated problems of condensed matter physics, statistical physics, and various applied problems. The method is based on the self-similar approximation theory involving self-similar root approximants. The constructed self-similar continued roots extrapolate asymptotic series to finite values of the expansion parameter. The self-similar continued roots contain, as a particular case, continued fractions and Padé approximants. A theorem on the convergence of the self-similar continued roots is proved. The method is illustrated by several examples from condensed-matter physics.

Multiple Scattering of Gamma Radiation in a Spherical Concrete Wall Room

Energy Technology Data Exchange (ETDEWEB)

Leimdoerfer, M

1962-12-15

The Monte Carlo method has been applied for the calculation of the energy flux of scattered gamma radiation in a spherical room surrounded by an infinitely thick spherical wall and with a point source at the centre. Source energies were I, 2, 4, 6, and 10 MeV. The main investigation was carried out at a room radius of 500 cm but, for the 1 MeV source, the influence of varying the room radius down to 1 cm was analysed. The results contain energy distributions of the first four successive reflection components at the centre of the room and at the wall surface, as well as spatial distributions of the successive energy flux components. The neglect of reflection contributions of order five and higher was estimated to introduce an error of less than 0. 2 % of the total scattered energy flux. An analytical approximation is shown to produce a useful and easily applicable method of predicting the amount of scattered radiation in a spherical room.

Multiple Scattering of Gamma Radiation in a Spherical Concrete Wall Room

International Nuclear Information System (INIS)

Leimdoerfer, M.

1962-12-01

The Monte Carlo method has been applied for the calculation of the energy flux of scattered gamma radiation in a spherical room surrounded by an infinitely thick spherical wall and with a point source at the centre. Source energies were I, 2, 4, 6, and 10 MeV. The main investigation was carried out at a room radius of 500 cm but, for the 1 MeV source, the influence of varying the room radius down to 1 cm was analysed. The results contain energy distributions of the first four successive reflection components at the centre of the room and at the wall surface, as well as spatial distributions of the successive energy flux components. The neglect of reflection contributions of order five and higher was estimated to introduce an error of less than 0. 2 % of the total scattered energy flux. An analytical approximation is shown to produce a useful and easily applicable method of predicting the amount of scattered radiation in a spherical room

First results of spherical GEMs

CERN Document Server

Pinto, Serge Duarte; Brock, Ian; Croci, Gabriele; David, Eric; de Oliveira, Rui; Ropelewski, Leszek; van Stenis, Miranda; Taureg, Hans; Villa, Marco

2010-01-01

We developed a method to make GEM foils with a spherical geometry. Tests of this procedure and with the resulting spherical GEMs are presented. Together with a spherical drift electrode, a spherical conversion gap can be formed. This eliminates the parallax error for detection of x-rays, neutrons or UV photons when a gaseous converter is used. This parallax error limits the spatial resolution at wide scattering angles. Besides spherical GEMs, we have developed curved spacers to maintain accurate spacing, and a conical field cage to prevent edge distortion of the radial drift field up to the limit of the angular acceptance of the detector. With these components first tests are done in a setup with a spherical entrance window but a planar readout structure; results will be presented and discussed. A flat readout structure poses difficulties, however. Therefore we will show advanced plans to make a prototype of an entirely spherical double-GEM detector, including a spherical 2D readout structure. This detector w...

A new and self-contained presentation of the theory of boundary operators for slit diffraction and their logarithmic approximations

Energy Technology Data Exchange (ETDEWEB)

Gorenflo, Norbert [Beuth Hochschule fuer Technik Berlin (Germany). Fachbereich II; Kunik, Matthias [Magdeburg Univ. (Germany). Inst. fuer Analysis und Numerik

2009-07-01

We present a new and self-contained theory for mapping properties of the boundary operators for slit diffraction occurring in Sommerfeld's diffraction theory, covering two different cases of the polarisation of the light. This theory is entirely developed in the context of the boundary operators with a Hankel kernel and not based on the corresponding mixed boundary value problem for the Helmholtz equation. For a logarithmic approximation of the Hankel kernel we also study the corresponding mapping properties and derive explicit solutions together with certain regularity results. (orig.)

CONTRIBUTIONS TO RATIONAL APPROXIMATION,

Science.gov (United States)

Some of the key results of linear Chebyshev approximation theory are extended to generalized rational functions. Prominent among these is Haar’s...linear theorem which yields necessary and sufficient conditions for uniqueness. Some new results in the classic field of rational function Chebyshev...Furthermore a Weierstrass type theorem is proven for rational Chebyshev approximation. A characterization theorem for rational trigonometric Chebyshev approximation in terms of sign alternation is developed. (Author)

Spheroidal corrections to the spherical and parabolic bases of the hydrogen atom

International Nuclear Information System (INIS)

Mardyan, L.G.; Pogosyan, G.S.; Sisakyan, A.N.

1986-01-01

This paper introduces the bases of the hydrogen atom and obtains recursion relations that determine the expansion of the spheroidal basis with respect to its parabolic basis. The leading spheroidal corrections to the spherical and parabolic bases are calculated by perturbation theory

Minimal entropy approximation for cellular automata

International Nuclear Information System (INIS)

Fukś, Henryk

2014-01-01

We present a method for the construction of approximate orbits of measures under the action of cellular automata which is complementary to the local structure theory. The local structure theory is based on the idea of Bayesian extension, that is, construction of a probability measure consistent with given block probabilities and maximizing entropy. If instead of maximizing entropy one minimizes it, one can develop another method for the construction of approximate orbits, at the heart of which is the iteration of finite-dimensional maps, called minimal entropy maps. We present numerical evidence that the minimal entropy approximation sometimes outperforms the local structure theory in characterizing the properties of cellular automata. The density response curve for elementary CA rule 26 is used to illustrate this claim. (paper)

Acoustic reciprocity: An extension to spherical harmonics domain.

Science.gov (United States)

Samarasinghe, Prasanga; Abhayapala, Thushara D; Kellermann, Walter

2017-10-01

Acoustic reciprocity is a fundamental property of acoustic wavefields that is commonly used to simplify the measurement process of many practical applications. Traditionally, the reciprocity theorem is defined between a monopole point source and a point receiver. Intuitively, it must apply to more complex transducers than monopoles. In this paper, the authors formulate the acoustic reciprocity theory in the spherical harmonics domain for directional sources and directional receivers with higher order directivity patterns.

Evolution of the spherical clusters

International Nuclear Information System (INIS)

Surdin, V.G.

1978-01-01

The possible processes of the Galaxy spherical clusters formation and evolution are described on a popular level. The orbits of spherical cluster motion and their spatial velocities are determined. Given are the distrbutions of spherical cluster stars according to their velocities and the observed distribution of spherical clusters in the area of the Galaxy slow evolution. The dissipation and dynamic friction processes destructing clusters with the mass less than 10 4 of solar mass and bringing about the reduction of clusters in the Galaxy are considered. The paradox of forming mainly X-ray sources in spherical clusters is explained. The schematic image of possible ways of forming X-ray sources in spherical clusters is given

Usefulness of bound-state approximations in reaction theory

International Nuclear Information System (INIS)

Adhikari, S.K.

1981-01-01

A bound-state approximation when applied to certain operators, such as the many-body resolvent operator for a two-body fragmentation channel, in many-body scattering equations, reduces such equations to equivalent two-body scattering equations which are supposed to provide a good description of the underlying physical process. In this paper we test several variants of bound-state approximations in the soluble three-boson Amado model and find that such approximations lead to weak and unacceptable kernels for the equivalent two-body scattering equations and hence to a poor description of the underlying many-body process

Directivity of Spherical Polyhedron Sound Source Used in Near-Field HRTF Measurements

International Nuclear Information System (INIS)

Yu Guang-Zheng; Xie Bo-Sun; Rao Dan

2010-01-01

The omnidirectional character is one of important requirements for the sound source used in near-field head-related transfer function (HRTF) measurements. Based on the analysis on the radiation sound pressure and directivity character of various spherical polyhedron sound sources, a spherical dodecahedral sound source with radius of 0.035m is proposed and manufactured. Theoretical and measured results indicate that the sound source is approximately omnidirectional below the frequency of 8 kHz. In addition, the sound source has reasonable magnitude response from 350Hz to 20kHz and linear phase characteristics. Therefore, it is suitable for the near-field HRTF measurements. (fundamental areas of phenomenology(including applications))

Origin of the Anomalous Color of Egyptian and Han Blue Historical Pigments: Going beyond the Complex Approximation in Ligand Field Theory

Science.gov (United States)

García-Fernandez, Pablo; Moreno, Miguel; Aramburu, José Antonio

2016-01-01

The complex approximation is widely used in the framework of the Ligand Field Theory for explaining the optical properties of crystalline coordination compounds. Here, we show that there are essential features of these systems that cannot be understood with the usual approximation that only considers an isolated complex at the correct equilibrium…

Total-energy Assisted Tight-binding Method Based on Local Density Approximation of Density Functional Theory

Science.gov (United States)

Fujiwara, Takeo; Nishino, Shinya; Yamamoto, Susumu; Suzuki, Takashi; Ikeda, Minoru; Ohtani, Yasuaki

2018-06-01

A novel tight-binding method is developed, based on the extended Hückel approximation and charge self-consistency, with referring the band structure and the total energy of the local density approximation of the density functional theory. The parameters are so adjusted by computer that the result reproduces the band structure and the total energy, and the algorithm for determining parameters is established. The set of determined parameters is applicable to a variety of crystalline compounds and change of lattice constants, and, in other words, it is transferable. Examples are demonstrated for Si crystals of several crystalline structures varying lattice constants. Since the set of parameters is transferable, the present tight-binding method may be applicable also to molecular dynamics simulations of large-scale systems and long-time dynamical processes.

Modeling the Interaction of Mineral Dust with Solar Radiation: Spherical versus Non-spherical Particles

Science.gov (United States)

Hoshyaripour, A.; Vogel, B.; Vogel, H.

2017-12-01

Mineral dust, emitted from arid and semi-arid regions, is the most dominant atmospheric aerosol by mass. Beside detrimental effect on air quality, airborne dust also influences the atmospheric radiation by absorbing and scattering solar and terrestrial radiation. As a result, while the long-term radiative impacts of dust are important for climate, the short-term effects are significant for the photovoltaic energy production. Therefore, it is a vital requirement to accurately forecast the effects of dust on energy budget of the atmosphere and surface. To this end, a major issue is the fact that dust particles are non-spherical. Thus, the optical properties of such particles cannot be calculated precisely using the conventional methods like Mie theory that are often used in climate and numerical weather forecast models. In this study, T-Matrix method is employed, which is able to treat the non-sphericity of particles. Dust particles are assumed to be prolate spheroids with aspect ratio of 1.5 distributed in three lognormal modes. The wavelength-dependent refractive indices of dust are used in T-Matrix algorithm to calculate the extinction coefficient, single scattering albedo, asymmetry parameter and backscattering ratio at different wavelengths. These parameters are then implemented in ICON-ART model (ICOsahedral Nonhydrostatic model with Aerosols and Reactive Trace gases) to conduct a global simulation with 80 km horizontal resolution and 90 vertical levels. April 2014 is selected as the simulation period during which North African dust plumes reached central Europe and Germany. Results show that treatment of non-sphericity reduces the dust AOD in the range of 10 to 30%/. The impacts on diffuse and direct radiation at global, regional and local scales show strong dependency on the size distribution of the airborne dust. The implications for modeling and remote sensing the dust impacts on solar energy are also discussed.

Diophantine approximation and Dirichlet series

CERN Document Server

Queffélec, Hervé

2013-01-01

This self-contained book will benefit beginners as well as researchers. It is devoted to Diophantine approximation, the analytic theory of Dirichlet series, and some connections between these two domains, which often occur through the Kronecker approximation theorem. Accordingly, the book is divided into seven chapters, the first three of which present tools from commutative harmonic analysis, including a sharp form of the uncertainty principle, ergodic theory and Diophantine approximation to be used in the sequel. A presentation of continued fraction expansions, including the mixing property of the Gauss map, is given. Chapters four and five present the general theory of Dirichlet series, with classes of examples connected to continued fractions, the famous Bohr point of view, and then the use of random Dirichlet series to produce non-trivial extremal examples, including sharp forms of the Bohnenblust-Hille theorem. Chapter six deals with Hardy-Dirichlet spaces, which are new and useful Banach spaces of anal...

Geometric approximation algorithms

CERN Document Server

Har-Peled, Sariel

2011-01-01

Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.

The inverse spatial Laplacian of spherically symmetric spacetimes

International Nuclear Information System (INIS)

Fernandes, Karan; Lahiri, Amitabha

2017-01-01

We derive the inverse spatial Laplacian for static, spherically symmetric backgrounds by solving Poisson’s equation for a point source. This is different from the electrostatic Green function, which is defined on the four dimensional static spacetime, while the equation we consider is defined on the spatial hypersurface of such spacetimes. This Green function is relevant in the Hamiltonian dynamics of theories defined on spherically symmetric backgrounds, and closed form expressions for the solutions we find are absent in the literature. We derive an expression in terms of elementary functions for the Schwarzschild spacetime, and comment on the relation of this solution with the known Green function of the spacetime Laplacian operator. We also find an expression for the Green function on the static pure de-Sitter space in terms of hypergeometric functions. We conclude with a discussion of the constraints of the electromagnetic field. (paper)

Surface multifragmentation investigated with a finite temperature spherical TDHF model

International Nuclear Information System (INIS)

Ngo, H.; Ighezou, F.Z.; Paula, L. De

1992-01-01

A model for multifragmentation caused by heavy ion collision is developed. The initial state is a hot and compressed spherical nucleus in thermal equilibrium. The dynamical evolution of this nucleus is studied. The nuclear density of the system is calculated with mean field approximation. It is shown that, in some cases, the surface of the nucleus breaks up before its volume. (K.A.) 8 refs.; 1 fig

Monoidal categories and topological field theory

CERN Document Server

Turaev, Vladimir

2017-01-01

This monograph is devoted to monoidal categories and their connections with 3-dimensional topological field theories. Starting with basic definitions, it proceeds to the forefront of current research. Part 1 introduces monoidal categories and several of their classes, including rigid, pivotal, spherical, fusion, braided, and modular categories. It then presents deep theorems of Müger on the center of a pivotal fusion category. These theorems are proved in Part 2 using the theory of Hopf monads. In Part 3 the authors define the notion of a topological quantum field theory (TQFT) and construct a Turaev-Viro-type 3-dimensional state sum TQFT from a spherical fusion category. Lastly, in Part 4 this construction is extended to 3-manifolds with colored ribbon graphs, yielding a so-called graph TQFT (and, consequently, a 3-2-1 extended TQFT). The authors then prove the main result of the monograph: the state sum graph TQFT derived from any spherical fusion category is isomorphic to the Reshetikhin-Turaev surgery gr...

Linearized vector radiative transfer model MCC++ for a spherical atmosphere

International Nuclear Information System (INIS)

Postylyakov, O.V.

2004-01-01

Application of radiative transfer models has shown that optical remote sensing requires extra characteristics of radiance field in addition to the radiance intensity itself. Simulation of spectral measurements, analysis of retrieval errors and development of retrieval algorithms are in need of derivatives of radiance with respect to atmospheric constituents under investigation. The presented vector spherical radiative transfer model MCC++ was linearized, which allows the calculation of derivatives of all elements of the Stokes vector with respect to the volume absorption coefficient simultaneously with radiance calculation. The model MCC++ employs Monte Carlo algorithm for radiative transfer simulation and takes into account aerosol and molecular scattering, gas and aerosol absorption, and Lambertian surface albedo. The model treats a spherically symmetrical atmosphere. Relation of the estimated derivatives with other forms of radiance derivatives: the weighting functions used in gas retrieval and the air mass factors used in the DOAS retrieval algorithms, is obtained. Validation of the model against other radiative models is overviewed. The computing time of the intensity for the MCC++ model is about that for radiative models treating sphericity of the atmosphere approximately and is significantly shorter than that for the full spherical models used in the comparisons. The simultaneous calculation of all derivatives (i.e. with respect to absorption in all model atmosphere layers) and the intensity is only 1.2-2 times longer than the calculation of the intensity only

Vanishing Viscosity Approach to the Compressible Euler Equations for Transonic Nozzle and Spherically Symmetric Flows

Science.gov (United States)

Chen, Gui-Qiang G.; Schrecker, Matthew R. I.

2018-04-01

We are concerned with globally defined entropy solutions to the Euler equations for compressible fluid flows in transonic nozzles with general cross-sectional areas. Such nozzles include the de Laval nozzles and other more general nozzles whose cross-sectional area functions are allowed at the nozzle ends to be either zero (closed ends) or infinity (unbounded ends). To achieve this, in this paper, we develop a vanishing viscosity method to construct globally defined approximate solutions and then establish essential uniform estimates in weighted L p norms for the whole range of physical adiabatic exponents γ\\in (1, ∞) , so that the viscosity approximate solutions satisfy the general L p compensated compactness framework. The viscosity method is designed to incorporate artificial viscosity terms with the natural Dirichlet boundary conditions to ensure the uniform estimates. Then such estimates lead to both the convergence of the approximate solutions and the existence theory of globally defined finite-energy entropy solutions to the Euler equations for transonic flows that may have different end-states in the class of nozzles with general cross-sectional areas for all γ\\in (1, ∞) . The approach and techniques developed here apply to other problems with similar difficulties. In particular, we successfully apply them to construct globally defined spherically symmetric entropy solutions to the Euler equations for all γ\\in (1, ∞).

Calculation of the Huang-Rhys parameter in spherical quantum dots: the optical deformation potential effect

International Nuclear Information System (INIS)

Hamma, M; Miranda, R P; Vasilevskiy, M I; Zorkani, I

2007-01-01

An accurate calculation of the exciton-phonon interaction matrix elements and Huang-Rhys parameter for nearly spherical nanocrystals (NCs) of polar semiconductor materials is presented. The theoretical approach is based on a continuum lattice dynamics model and the effective mass approximation for electronic states in the NCs. A strong confinement regime is considered for both excitons and optical phonons, taking into account both the Froehlich-type and optical deformation potential (ODP) mechanisms of the exciton-phonon interaction. The effects of exchange electron-hole interaction and possible hexagonal crystal structure of the underlying material are also taken into account. The theory is applied to CdSe and InP quantum dots. It is shown that the ODP mechanism, almost unimportant for CdSe, dominates the exciton-phonon coupling in small InP dots. The effect of the non-diagonal interaction, not included in the Huang-Rhys parameter, is briefly discussed

Extension of the KLI approximation toward the exact optimized effective potential.

Science.gov (United States)

Iafrate, G J; Krieger, J B

2013-03-07

The integral equation for the optimized effective potential (OEP) is utilized in a compact form from which an accurate OEP solution for the spin-unrestricted exchange-correlation potential, Vxcσ, is obtained for any assumed orbital-dependent exchange-correlation energy functional. The method extends beyond the Krieger-Li-Iafrate (KLI) approximation toward the exact OEP result. The compact nature of the OEP equation arises by replacing the integrals involving the Green's function terms in the traditional OEP equation by an equivalent first-order perturbation theory wavefunction often referred to as the "orbital shift" function. Significant progress is then obtained by solving the equation for the first order perturbation theory wavefunction by use of Dalgarno functions which are determined from well known methods of partial differential equations. The use of Dalgarno functions circumvents the need to explicitly address the Green's functions and the associated problems with "sum over states" numerics; as well, the Dalgarno functions provide ease in dealing with inherent singularities arising from the origin and the zeros of the occupied orbital wavefunctions. The Dalgarno approach for finding a solution to the OEP equation is described herein, and a detailed illustrative example is presented for the special case of a spherically symmetric exchange-correlation potential. For the case of spherical symmetry, the relevant Dalgarno function is derived by direct integration of the appropriate radial equation while utilizing a user friendly method which explicitly treats the singular behavior at the origin and at the nodal singularities arising from the zeros of the occupied states. The derived Dalgarno function is shown to be an explicit integral functional of the exact OEP Vxcσ, thus allowing for the reduction of the OEP equation to a self-consistent integral equation for the exact exchange-correlation potential; the exact solution to this integral equation can be

World Gravity Map: a set of global complete spherical Bouguer and isostatic anomaly maps and grids

Science.gov (United States)

Bonvalot, S.; Balmino, G.; Briais, A.; Kuhn, M.; Peyrefitte, A.; Vales, N.; Biancale, R.; Gabalda, G.; Reinquin, F.

2012-04-01

We present here a set of digital maps of the Earth's gravity anomalies (surface free air, Bouguer and isostatic), computed at Bureau Gravimetric International (BGI) as a contribution to the Global Geodetic Observing Systems (GGOS) and to the global geophysical maps published by the Commission for the Geological Map of the World (CGMW) with support of UNESCO and other institutions. The Bouguer anomaly concept is extensively used in geophysical interpretation to investigate the density distributions in the Earth's interior. Complete Bouguer anomalies (including terrain effects) are usually computed at regional scales by integrating the gravity attraction of topography elements over and beyond a given area (under planar or spherical approximations). Here, we developed and applied a worldwide spherical approach aimed to provide a set of homogeneous and high resolution gravity anomaly maps and grids computed at the Earth's surface, taking into account a realistic Earth model and reconciling geophysical and geodetic definitions of gravity anomalies. This first version (1.0) has been computed by spherical harmonics analysis / synthesis of the Earth's topography-bathymetry up to degree 10800. The detailed theory of the spherical harmonics approach is given in Balmino et al., (Journal of Geodesy, 2011). The Bouguer and terrain corrections have thus been computed in spherical geometry at 1'x1' resolution using the ETOPO1 topography/bathymetry, ice surface and bedrock models from the NOAA (National Oceanic and Atmospheric Administration) and taking into account precise characteristics (boundaries and densities) of major lakes, inner seas, polar caps and of land areas below sea level. Isostatic corrections have been computed according to the Airy-Heiskanen model in spherical geometry for a constant depth of compensation of 30km. The gravity information given here is provided by the Earth Geopotential Model (EGM2008), developed at degree 2160 by the National Geospatial

Spherical CNNs

OpenAIRE

Cohen, Taco S.; Geiger, Mario; Koehler, Jonas; Welling, Max

2018-01-01

Convolutional Neural Networks (CNNs) have become the method of choice for learning problems involving 2D planar images. However, a number of problems of recent interest have created a demand for models that can analyze spherical images. Examples include omnidirectional vision for drones, robots, and autonomous cars, molecular regression problems, and global weather and climate modelling. A naive application of convolutional networks to a planar projection of the spherical signal is destined t...

Self-consistent Random Phase Approximation applied to a schematic model of the field theory

International Nuclear Information System (INIS)

Bertrand, Thierry

1998-01-01

The self-consistent Random Phase Approximation (SCRPA) is a method allowing in the mean-field theory inclusion of the correlations in the ground and excited states. It has the advantage of not violating the Pauli principle in contrast to RPA, that is based on the quasi-bosonic approximation; in addition, numerous applications in different domains of physics, show a possible variational character. However, the latter should be formally demonstrated. The first model studied with SCRPA is the anharmonic oscillator in the region where one of its symmetries is spontaneously broken. The ground state energy is reproduced by SCRPA more accurately than RPA, with no violation of the Ritz variational principle, what is not the case for the latter approximation. The success of SCRPA is the the same in case of ground state energy for a model mixing bosons and fermions. At the transition point the SCRPA is correcting RPA drastically, but far from this region the correction becomes negligible, both methods being of similar precision. In the deformed region in the case of RPA a spurious mode occurred due to the microscopical character of the model.. The SCRPA may also reproduce this mode very accurately and actually it coincides with an excitation in the exact spectrum

Buckling strength of spherical shells under combined loads

International Nuclear Information System (INIS)

Nagashima, H.; Kokubo, K.; Takayanagi, M.; Hayasaka, Y.; Kume, T.; Nagata, T.

1995-01-01

Many studies on buckling of cylindrical shells have been conducted, and many buckling evaluation equations have been proposed for actual plant designs; however, buckling of spherical shells under combined horizontal and vertical loads cannot be evaluated due to insufficient data. There is a particular lack of buckling data for spherical shells under lateral loads. To establish a method for estimating the buckling strength of spherical shells, we investigate the interactions between horizontal and vertical (compressive tensile) loads by conducting buckling tests. Applying several combinations of these loads in tests and using computer linear analysis, we obtain interaction curves. This study reports on the buckling tests conducted using spherical shell 1120 mm in dia., 0.7 mm thick and 696 mm high, which are shaped individually by press-forming and finally joined together by four meridional welds, using a specially made jig. Initial imperfections before testing and local deformations after each loading increment during testing are measured with special measuring equipment, and the interaction curve of horizontal and vertical loads and effect of imperfection on the buckling strength of spherical shells are obtained. Nonlinear FEM programs are developed using an 8-node isoparametric shell element and a four-node quadrilateral element of C 0 type with reduced integration based upon a Mindlin-Reissner theory which includes transverse shear. Actual initial imperfections are generally in irregular patterns. Thus, there may be several definitions of the equivalent magnitudes of initial imperfections related to buckling loads. Equivalent magnitudes have no practical meaning unless they can be obtained easily not only for small structures such as test shells but also for large actual structures. In the present study, we define the equivalent magnitude of initial imperfections as the maximum local ruggedness measured radially from a circular temperature having a radius equal

Porous spherical shells and microspheres by electrodispersion precipitation

International Nuclear Information System (INIS)

Harris, M.T.; Sisson, W.G.; Basaran, O.A.; Hayes, S.M.; Bobrowski, S.J.

1994-01-01

The ability to reproduce the synthesis of dense- and porous-microspheres and micron-sized spherical shells is very important in (a) the development of ceramics for structural, electronic, catalyst and thermal applications; and (b) the encapsulation of products for controlled-release of drugs, flavors and perfumes, and inks and dyes, and the protection of light-sensitive components and mechanical support of fragile materials. Larger metallic- and ceramic-spherical shells have been used in inertial confinement fusion (ICF) experiments and as catalyst supports. The current paper will focus on a recent technique that has been developed for synthesizing ceramic microspheres and micro-shells. Pulsed electric fields have been used to enhance the dispersion of aqueous metal (Zr and Al) salt solutions from a nozzle and into a nonconducting liquid continuous phase that is immiscible with the aqueous phase. The diameter of the resulting microdroplets ranged in size from approximately 0.1 to 10 μm. Precipitation of hydrous metal oxides occurred as ammonia, which was dissolved in varying amounts in the continuous phase, diffused into the aqueous microdroplets. Spherical shells were formed at higher ammonia concentrations and microspheres were produced at lower ammonia concentrations. Upon drying, dimples appeared in the particles that were synthesized at higher ammonia concentrations. The latter result accords with the well known fact that under certain conditions spherical shells collapse when a fluid is extracted from the core of the particle. No dimples were observed in the microspheres that were produced at lower ammonia concentrations. Analog X-ray dot maps for aluminum and zirconium were done to determine the spatial distribution of each metal in the particles

General solution of the multigroup spherical harmonics equations in R-Z geometry

International Nuclear Information System (INIS)

Matausek, M.

1983-01-01

In the present paper the generalization is performed of the procedure to solve multigroup spherical harmonics equations, which has originally been proposed and developed foe one-dimensional systems in cylindrical or spherical geometry, and later extended for special case of a two-dimensional system in r-z geometry. The expressions are derived for the axial and the radial dependence of the group values of the neutron flux moments, in the P-3 approximation of the spherical harmonics method, in a cylindrically symmetrical system with an arbitrary number of material regions in both r and z directions. In the special case of an axially homogeneous system, these expressions reduce to the relations derived previously. The analysis is performed of the possibilities to satisfy the boundary conditions in the case when the system considered represents an elementary reactor lattice cell and in the case when the system represents a reactor as a whole. The computational effort is estimated for system of a given configuration. (author)

On Born approximation in black hole scattering

Science.gov (United States)

Batic, D.; Kelkar, N. G.; Nowakowski, M.

2011-12-01

A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner-Nordström and Reissner-Nordström-de Sitter backgrounds is considered. In particular, explicit formulae in terms of transcendental functions for the scattering of massless scalar particles off black holes are derived within a Born approximation. It is shown that the conditions on the existence of the Born integral forbid a straightforward extraction of the quasi normal modes using the Born approximation for the scattering amplitude. Such a method has been used in literature. We suggest a novel, well defined method, to extract the large imaginary part of quasinormal modes via the Coulomb-like phase shift. Furthermore, we compare the numerically evaluated exact scattering amplitude with the Born one to find that the approximation is not very useful for the scattering of massless scalar, electromagnetic as well as gravitational waves from black holes.

Multiple spatial scaling and the weak-coupling approximation. I. General formulation and equilibrium theory

Energy Technology Data Exchange (ETDEWEB)

Kleinsmith, P E [Carnegie-Mellon Univ., Pittsburgh, Pa. (USA)

1976-04-01

Multiple spatial scaling is incorporated in a modified form of the Bogoliubov plasma cluster expansion; then this proposed reformulation of the plasma weak-coupling approximation is used to derive, from the BBGKY Hierarchy, a decoupled set of equations for the one-and two-particle distribution functions in the limit as the plasma parameter goes to zero. Because the reformulated cluster expansion permits retention of essential two-particle collisional information in the limiting equations, while simultaneously retaining the well-established Debye-scale relative ordering of the correlation functions, decoupling of the Hierarchy is accomplished without introduction of the divergence problems encountered in the Bogoliubov theory, as is indicated by an exact solution of the limiting equations for the equilibrium case. To establish additional links with existing plasma equilibrium theories, the two-particle equilibrium correlation function is used to calculate the interaction energy and the equation of state. The limiting equation for the equilibrium three-particle correlation function is then developed, and a formal solution is obtained.

Combined analytical-numerical procedure to solve multigroup spherical harmonics equations in two-dimensional r-z geometry

International Nuclear Information System (INIS)

Matausek, M.V.; Milosevic, M.

1986-01-01

In the present paper a generalization is performed of a procedure to solve multigroup spherical harmonics equations, which has originally been proposed and developed for one-dimensional systems in cylindrical or spherical geometry, and later extended for a special case of a two-dimensional system in r-z geometry. The expressions are derived for the axial and the radial dependence of the group values of the neutron flux moments, in the P-3 approximation of the spherical harmonics method, in a cylindrically symmetrical system with an arbitrary number of material regions in both r- and z-directions. In the special case of an axially homogeneous system, these expressions reduce to the relations derived previously. (author)

Galileon radiation from a spherical collapsing shell

Energy Technology Data Exchange (ETDEWEB)

Martín-García, Javier [Instituto de Física Teórica UAM/CSIC,C/ Nicolás Cabrera 15, E-28049 Madrid (Spain); Vázquez-Mozo, Miguel Á. [Instituto Universitario de Física Fundamental y Matemáticas (IUFFyM),Universidad de Salamanca, Plaza de la Merced s/n, E-37008 Salamanca (Spain)

2017-01-17

Galileon radiation in the collapse of a thin spherical shell of matter is analyzed. In the framework of a cubic Galileon theory, we compute the field profile produced at large distances by a short collapse, finding that the radiated field has two peaks traveling ahead of light fronts. The total energy radiated during the collapse follows a power law scaling with the shell’s physical width and results from two competing effects: a Vainshtein suppression of the emission and an enhancement due to the thinness of the shell.

Preparation and Optical Properties of Spherical Inverse Opals by Liquid Phase Deposition Using Spherical Colloidal Crystals

International Nuclear Information System (INIS)

Aoi, Y; Tominaga, T

2013-01-01

Titanium dioxide (TiO 2 ) inverse opals in spherical shape were prepared by liquid phase deposition (LPD) using spherical colloidal crystals as templates. Spherical colloidal crystals were produced by ink-jet drying technique. Aqueous emulsion droplets that contain polystyrene latex particles were ejected into air and dried. Closely packed colloidal crystals with spherical shape were obtained. The obtained spherical colloidal crystals were used as templates for the LPD. The templates were dispersed in the deposition solution of the LPD, i.e. a mixed solution of ammonium hexafluorotitanate and boric acid and reacted for 4 h at 30 °C. After the LPD process, the interstitial spaces of the spherical colloidal crystals were completely filled with titanium oxide. Subsequent heat treatment resulted in removal of templates and spherical titanium dioxide inverse opals. The spherical shape of the template was retained. SEM observations indicated that the periodic ordered voids were surrounded by titanium dioxide. The optical reflectance spectra indicated that the optical properties of the spherical titanium dioxide inverse opals were due to Bragg diffractions from the ordered structure. Filling in the voids of the inverse opals with different solvents caused remarkable changes in the reflectance peak.

Polarization effects on spectra of spherical core/shell nanostructures: Perturbation theory against finite difference approach

International Nuclear Information System (INIS)

Ibral, Asmaa; Zouitine, Asmaa; Assaid, El Mahdi

2015-01-01

Poisson equation is solved analytically in the case of a point charge placed anywhere in a spherical core/shell nanostructure, immersed in aqueous or organic solution or embedded in semiconducting or insulating matrix. Conduction and valence band-edge alignments between core and shell are described by finite height barriers. Influence of polarization charges induced at the surfaces where two adjacent materials meet is taken into account. Original expressions of electrostatic potential created everywhere in the space by a source point charge are derived. Expressions of self-polarization potential describing the interaction of a point charge with its own image–charge are deduced. Contributions of double dielectric constant mismatch to electron and hole ground state energies as well as nanostructure effective gap are calculated via first order perturbation theory and also by finite difference approach. Dependencies of electron, hole and gap energies against core to shell radii ratio are determined in the case of ZnS/CdSe core/shell nanostructure immersed in water or in toluene. It appears that finite difference approach is more efficient than first order perturbation method and that the effect of polarization charge may in no case be neglected as its contribution can reach a significant proportion of the value of nanostructure gap

Polarization effects on spectra of spherical core/shell nanostructures: Perturbation theory against finite difference approach

Energy Technology Data Exchange (ETDEWEB)

Ibral, Asmaa [Equipe d' Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida principale, El Jadida, Royaume du Maroc (Morocco); Laboratoire d' Instrumentation, Mesure et Contrôle, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida principale, El Jadida, Royaume du Maroc (Morocco); Zouitine, Asmaa [Département de Physique, Ecole Nationale Supérieure d' Enseignement Technique, Université Mohammed V Souissi, B. P. 6207 Rabat-Instituts, Rabat, Royaume du Maroc (Morocco); Assaid, El Mahdi, E-mail: eassaid@yahoo.fr [Equipe d' Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida principale, El Jadida, Royaume du Maroc (Morocco); Laboratoire d' Instrumentation, Mesure et Contrôle, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida principale, El Jadida, Royaume du Maroc (Morocco); and others

2015-02-01

Poisson equation is solved analytically in the case of a point charge placed anywhere in a spherical core/shell nanostructure, immersed in aqueous or organic solution or embedded in semiconducting or insulating matrix. Conduction and valence band-edge alignments between core and shell are described by finite height barriers. Influence of polarization charges induced at the surfaces where two adjacent materials meet is taken into account. Original expressions of electrostatic potential created everywhere in the space by a source point charge are derived. Expressions of self-polarization potential describing the interaction of a point charge with its own image–charge are deduced. Contributions of double dielectric constant mismatch to electron and hole ground state energies as well as nanostructure effective gap are calculated via first order perturbation theory and also by finite difference approach. Dependencies of electron, hole and gap energies against core to shell radii ratio are determined in the case of ZnS/CdSe core/shell nanostructure immersed in water or in toluene. It appears that finite difference approach is more efficient than first order perturbation method and that the effect of polarization charge may in no case be neglected as its contribution can reach a significant proportion of the value of nanostructure gap.

Fourier analysis of spherically averaged momentum densities for some gaseous molecules

International Nuclear Information System (INIS)

Tossel, J.A.; Moore, J.H.

1981-01-01

The spherically averaged autocorrelation function, B(r), of the position-space wavefunction, psi(anti r), is calculated by numerical Fourier transformation from spherically averaged momentum densities, rho(p), obtained from either theoretical wavefunctions or (e,2e) electron-impact ionization experiments. Inspection of B(r) for the π molecular orbitals of C 4 H 6 established that autocorrelation function differences, ΔB(r), can be qualitatively related to bond lengths and numbers of bonding interactions. Differences between B(r) functions obtained from different approximate wavefunctions for a given orbital can be qualitatively understood in terms of wavefunction difference, Δpsi(1anti r), maps for these orbitals. Comparison of the B(r) function for the 1αsub(u) orbital of C 4 H 6 obtained from (e,2e) momentum densities with that obtained from an ab initio SCF MO wavefunction shows differences consistent with expected correlation effects. Thus, B(r) appears to be a useful quantity for relating spherically averaged momentum distributions to position-space wavefunction differences. (orig.)

Friction factor for water flow through packed beds of spherical and non-spherical particles

Directory of Open Access Journals (Sweden)

Kaluđerović-Radoičić Tatjana

2017-01-01

Full Text Available The aim of this work was the experimental evaluation of different friction factor correlations for water flow through packed beds of spherical and non-spherical particles at ambient temperature. The experiments were performed by measuring the pressure drop across the bed. Packed beds made of monosized glass spherical particles of seven different diameters were used, as well as beds made of 16 fractions of quartz filtration sand obtained by sieving (polydisperse non-spherical particles. The range of bed voidages was 0.359–0.486, while the range of bed particle Reynolds numbers was from 0.3 to 286 for spherical particles and from 0.1 to 50 for non-spherical particles. The obtained results were compared using a number of available literature correlations. In order to improve the correlation results for spherical particles, a new simple equation was proposed in the form of Ergun’s equation, with modified coefficients. The new correlation had a mean absolute deviation between experimental and calculated values of pressure drop of 9.04%. For non-spherical quartz filtration sand particles the best fit was obtained using Ergun’s equation, with a mean absolute deviation of 10.36%. Surface-volume diameter (dSV necessary for correlating the data for filtration sand particles was calculated based on correlations for dV = f(dm and Ψ = f(dm. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. ON172022

Spherical collapse of small masses in the ghost-free gravity

International Nuclear Information System (INIS)

Frolov, Valeri P.; Zelnikov, Andrei; Netto, Tibério de Paula

2015-01-01

We discuss some properties of recently proposed models of a ghost-free gravity. For this purpose we study solutions of linearized gravitational equations in the framework of such a theory. We mainly focus on the version of the ghost-free theory with the exponential modification exp (◻/μ 2 )◻ −1 of the free propagator. The following three problems are discussed: (i) gravitational field of a point mass; (ii) Penrose limit of a point source boosted to the speed of light; and (iii) spherical gravitational collapse of null fluid. For the first problem we demonstrate that it can be solved by using the method of heat kernels and obtain a solution in a spacetime with arbitrary number of dimensions. For the second problem we also find the corresponding gyraton-type solutions of the ghost-free gravitational equations for any number of dimensions. For the third problem we obtain solutions for the gravitational field for the collapse of both “thin" and “thick" spherical null shells. We demonstrate how the ghost-free modification of the gravitational equations regularize the solutions of the linearized Einstein equations and smooth out their singularities.

Spherical collapse of small masses in the ghost-free gravity

Energy Technology Data Exchange (ETDEWEB)

Frolov, Valeri P.; Zelnikov, Andrei [Theoretical Physics Institute, Department of Physics, University of Alberta,Edmonton, AB, T6G 2E1 (Canada); Netto, Tibério de Paula [Theoretical Physics Institute, Department of Physics, University of Alberta,Edmonton, AB, T6G 2E1 (Canada); Departamento de Fisica - ICE, Universidade Federal de Juiz de Fora,Campus da UFJF, CEP: 36036-900, Juiz de Fora, MG (Brazil)

2015-06-17

We discuss some properties of recently proposed models of a ghost-free gravity. For this purpose we study solutions of linearized gravitational equations in the framework of such a theory. We mainly focus on the version of the ghost-free theory with the exponential modification exp (◻/μ{sup 2})◻{sup −1} of the free propagator. The following three problems are discussed: (i) gravitational field of a point mass; (ii) Penrose limit of a point source boosted to the speed of light; and (iii) spherical gravitational collapse of null fluid. For the first problem we demonstrate that it can be solved by using the method of heat kernels and obtain a solution in a spacetime with arbitrary number of dimensions. For the second problem we also find the corresponding gyraton-type solutions of the ghost-free gravitational equations for any number of dimensions. For the third problem we obtain solutions for the gravitational field for the collapse of both “thin' and “thick' spherical null shells. We demonstrate how the ghost-free modification of the gravitational equations regularize the solutions of the linearized Einstein equations and smooth out their singularities.

Progress in octahedral spherical hohlraum study

Directory of Open Access Journals (Sweden)

Ke Lan

2016-01-01

Full Text Available In this paper, we give a review of our theoretical and experimental progress in octahedral spherical hohlraum study. From our theoretical study, the octahedral spherical hohlraums with 6 Laser Entrance Holes (LEHs of octahedral symmetry have robust high symmetry during the capsule implosion at hohlraum-to-capsule radius ratio larger than 3.7. In addition, the octahedral spherical hohlraums also have potential superiority on low backscattering without supplementary technology. We studied the laser arrangement and constraints of the octahedral spherical hohlraums, and gave a design on the laser arrangement for ignition octahedral hohlraums. As a result, the injection angle of laser beams of 50°–60° was proposed as the optimum candidate range for the octahedral spherical hohlraums. We proposed a novel octahedral spherical hohlraum with cylindrical LEHs and LEH shields, in order to increase the laser coupling efficiency and improve the capsule symmetry and to mitigate the influence of the wall blowoff on laser transport. We studied on the sensitivity of the octahedral spherical hohlraums to random errors and compared the sensitivity among the octahedral spherical hohlraums, the rugby hohlraums and the cylindrical hohlraums, and the results show that the octahedral spherical hohlraums are robust to these random errors while the cylindrical hohlraums are the most sensitive. Up till to now, we have carried out three experiments on the spherical hohlraum with 2 LEHs on Shenguang(SG laser facilities, including demonstration of improving laser transport by using the cylindrical LEHs in the spherical hohlraums, spherical hohlraum energetics on the SGIII prototype laser facility, and comparisons of laser plasma instabilities between the spherical hohlraums and the cylindrical hohlraums on the SGIII laser facility.

Synthesis of Thermally Spherical CuO Nanoparticles

Directory of Open Access Journals (Sweden)

Nittaya Tamaekong

2014-01-01

Full Text Available Copper oxide (CuO nanoparticles were successfully synthesized by a thermal method. The CuO nanoparticles were further characterized by thermogravimetric analysis (TGA, differential thermal analysis (DTA, X-ray diffraction (XRD, scanning electron microscopy (SEM, energy dispersive X-ray spectrometry (EDS, and high resolution transmission electron microscopy (HRTEM, respectively. The specific surface area (SSABET of CuO nanoparticles was determined by nitrogen adsorption. The SSABET was found to be 99.67 m2/g (dBET of 9.5 nm. The average diameter of the spherical CuO nanoparticles was approximately 6–9 nm.

Full-potential multiple scattering theory with space-filling cells for bound and continuum states.

Science.gov (United States)

Hatada, Keisuke; Hayakawa, Kuniko; Benfatto, Maurizio; Natoli, Calogero R

2010-05-12

We present a rigorous derivation of a real-space full-potential multiple scattering theory (FP-MST) that is free from the drawbacks that up to now have impaired its development (in particular the need to expand cell shape functions in spherical harmonics and rectangular matrices), valid both for continuum and bound states, under conditions for space partitioning that are not excessively restrictive and easily implemented. In this connection we give a new scheme to generate local basis functions for the truncated potential cells that is simple, fast, efficient, valid for any shape of the cell and reduces to the minimum the number of spherical harmonics in the expansion of the scattering wavefunction. The method also avoids the need for saturating 'internal sums' due to the re-expansion of the spherical Hankel functions around another point in space (usually another cell center). Thus this approach provides a straightforward extension of MST in the muffin-tin (MT) approximation, with only one truncation parameter given by the classical relation l(max) = kR(b), where k is the electron wavevector (either in the excited or ground state of the system under consideration) and R(b) is the radius of the bounding sphere of the scattering cell. Moreover, the scattering path operator of the theory can be found in terms of an absolutely convergent procedure in the l(max) --> ∞ limit. Consequently, this feature provides a firm ground for the use of FP-MST as a viable method for electronic structure calculations and makes possible the computation of x-ray spectroscopies, notably photo-electron diffraction, absorption and anomalous scattering among others, with the ease and versatility of the corresponding MT theory. Some numerical applications of the theory are presented, both for continuum and bound states.

Structure of neutron star crusts from new Skyrme effective interactions constrained by chiral effective field theory

Science.gov (United States)

Lim, Yeunhwan; Holt, Jeremy W.

2017-06-01

We investigate the structure of neutron star crusts, including the crust-core boundary, based on new Skyrme mean field models constrained by the bulk-matter equation of state from chiral effective field theory and the ground-state energies of doubly-magic nuclei. Nuclear pasta phases are studied using both the liquid drop model as well as the Thomas-Fermi approximation. We compare the energy per nucleon for each geometry (spherical nuclei, cylindrical nuclei, nuclear slabs, cylindrical holes, and spherical holes) to obtain the ground state phase as a function of density. We find that the size of the Wigner-Seitz cell depends strongly on the model parameters, especially the coefficients of the density gradient interaction terms. We employ also the thermodynamic instability method to check the validity of the numerical solutions based on energy comparisons.

Power maximization of a spheric reflected reactor with optimized fuel distribution

International Nuclear Information System (INIS)

Reade, Joamar Rodrigues Vincent

1979-01-01

The maximum power of a spheric reflected reactor was determined using the theory of optimal control. The control variable employed was the fuel distribution, in accordance to constraints on the power density and on the concentration fuel. It was considered a thermal reactor with a fixed radius. The reactor was fuelled with U-235 and moderated with light water. The nuclear reactor was described by a diffusion theory model. The analytical solution was obtained for both two and four groups of energy and a FORTRAN program was developed to obtain the numerical results. (author)

S-wave Qanti Qqanti q states in the adiabatic approximation

Energy Technology Data Exchange (ETDEWEB)

Chao, K T [Oxford Univ. (UK). Dept. of Theoretical Physics

1981-06-01

The static potential energy for an S-wave Qanti Qqanti q system is discussed in an adiabatic (Born-Oppenheimer) approximation. Both spherical bag and arbitrary bag are considered. We concentrate on those Qanti Qqanti q states in which both (Qanti Q) and (qanti q) are colour singlets. Their energy level, wave function, and possible experimental observation are studied.

SANS [small-angle neutron scattering] evaluation of the RPA [random phase approximation] theory for binary homopolymer mixtures

International Nuclear Information System (INIS)

Bates, F.S.; Koehler, W.C.; Wignall, G.D.; Fetters, L.J.

1986-12-01

A well characterized binary mixture of normal (protonated) and perdeuterated monodisperse 1,2 polybutenes has been studied by small-angle neutron scattering (SANS). For scattering wavevectors q greater than the inverse radius-of-gyration R/sub g/ -1 , the SANS intensity is quantitatively predicted by the random phase approximation (RPA) theory of deGennes over all measured values of the segment-segment interaction parameter Chi. In the region (Chi s-Chi)Chi s -1 > 0.5 the interaction parameter determined using the RPA theory for q > R/sub g/ -1 is greater than that calculated from the zero-angle intensity based on an Ornstein-Zernike plot, where Chi s represents the limit of single phase stability. These findings indicate a correlation between the critical fluctuation length ξ and R/sub g/ which is not accounted for by the RPA theory

Spherical harmonics analysis of surface density fluctuations of spherical ionic SDS and nonionic C12E8 micelles: A molecular dynamics study.

Science.gov (United States)

Yoshii, Noriyuki; Nimura, Yuki; Fujimoto, Kazushi; Okazaki, Susumu

2017-07-21

The surface structure and its fluctuation of spherical micelles were investigated using a series of density correlation functions newly defined by spherical harmonics and Legendre polynomials based on the molecular dynamics calculations. To investigate the influence of head-group charges on the micelle surface structure, ionic sodium dodecyl sulfate and nonionic octaethyleneglycol monododecylether (C 12 E 8 ) micelles were investigated as model systems. Large-scale density fluctuations were observed for both micelles in the calculated surface static structure factor. The area compressibility of the micelle surface evaluated by the surface static structure factor was tens-of-times larger than a typical value of a lipid membrane surface. The structural relaxation time, which was evaluated from the surface intermediate scattering function, indicates that the relaxation mechanism of the long-range surface structure can be well described by the hydrostatic approximation. The density fluctuation on the two-dimensional micelle surface has similar characteristics to that of three-dimensional fluids near the critical point.

Breakdown of the single-exchange approximation in third-order symmetry-adapted perturbation theory.

Science.gov (United States)

Lao, Ka Un; Herbert, John M

2012-03-22

We report third-order symmetry-adapted perturbation theory (SAPT) calculations for several dimers whose intermolecular interactions are dominated by induction. We demonstrate that the single-exchange approximation (SEA) employed to derive the third-order exchange-induction correction (E(exch-ind)((30))) fails to quench the attractive nature of the third-order induction (E(ind)((30))), leading to one-dimensional potential curves that become attractive rather than repulsive at short intermolecular separations. A scaling equation for (E(exch-ind)((30))), based on an exact formula for the first-order exchange correction, is introduced to approximate exchange effects beyond the SEA, and qualitatively correct potential energy curves that include third-order induction are thereby obtained. For induction-dominated systems, our results indicate that a "hybrid" SAPT approach, in which a dimer Hartree-Fock calculation is performed in order to obtain a correction for higher-order induction, is necessary not only to obtain quantitative binding energies but also to obtain qualitatively correct potential energy surfaces. These results underscore the need to develop higher-order exchange-induction formulas that go beyond the SEA. © 2012 American Chemical Society

Approximate and renormgroup symmetries

International Nuclear Information System (INIS)

Ibragimov, Nail H.; Kovalev, Vladimir F.

2009-01-01

''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)

Theoretical investigation of stark effect on shallow donor binding energy in InGaN spherical QD-QW

International Nuclear Information System (INIS)

El Ghazi, Haddou; Jorio, Anouar; Zorkani, Izeddine

2013-01-01

In this paper, a simultaneous study of electric field and impurity's position effects on the ground-state shallow-donor binding energy in GaN|InGaN|GaN spherical quantum dot-quantum well (SQD-QW) as a function of the ratio of the inner and the outer radius is reported. The calculations are investigated using variational approach within the framework of the effective-mass approximation. The numerical results show that: (i) the binding energy is strongly affected by the external electric field and the SQD-QW dimension, (ii) a critical value of spherical system's radius is obtained constituting the limit of three dimension confinement and spherical thin layer confinement and (iii) the Stark shift increases with increasing electric field and it is more pronounced around the position of the impurity corresponding to the binding energy maxima than in the spherical layer extremities

Spherically symmetric near-critical accretion onto neutron stars

International Nuclear Information System (INIS)

Miller, G.S.

1990-01-01

Numerical and approximate analytic solutions for time-independent, spherically symmetric, radiation pressure-dominated accretion flows are presented. For flows with luminosities at infinity, L-infinity, sufficiently close to the Eddington limit L-crit, the flow velocity profile is qualitatively different from the modified free-fall profile v(r) = (1 - L-infinity/L-crit)exp 1/2 (2GM/r)exp 1/2. Advective contributions to the comoving radiation flux decelerate the flow within a criical radius, and, in this settling region, the velocity of the flow decreases linearly with decreasing radius. 14 refs

Approximate reasoning in physical systems

International Nuclear Information System (INIS)

Mutihac, R.

1991-01-01

The theory of fuzzy sets provides excellent ground to deal with fuzzy observations (uncertain or imprecise signals, wavelengths, temperatures,etc.) fuzzy functions (spectra and depth profiles) and fuzzy logic and approximate reasoning. First, the basic ideas of fuzzy set theory are briefly presented. Secondly, stress is put on application of simple fuzzy set operations for matching candidate reference spectra of a spectral library to an unknown sample spectrum (e.g. IR spectroscopy). Thirdly, approximate reasoning is applied to infer an unknown property from information available in a database (e.g. crystal systems). Finally, multi-dimensional fuzzy reasoning techniques are suggested. (Author)

Chiral pion dynamics for spherical nucleon bags

International Nuclear Information System (INIS)

Vento, V.; Rho, M.; Nyman, E.M.; Jun, J.H.; Brown, G.E.; CEA Centre d'Etudes Nucleaires de Saclay, 91 - Gif-sur-Yvette

1980-01-01

A chirally symmetric quark-bag model for the nucleon is obtained by introducing an explicit, classical, pion field exterior to the bag. The coupling at the bag surface is determined by the requirement of a conserved axial-vector current. The pion field satisfies equations of motion corresponding to the non-linear sigma-model. We study on this paper the simplified case where the bag and the pion field are spherically symmetric. Corrections due to gluon exchange between the quarks are ignored along with other interactions which split the N- and Δ-masses. The equations of motion for the pion field are solved and we find a substantial pion pressure at the bag surface, along with an attractive contribution to the nucleon self-energy. The total energy of the system, bag plus meson cloud, turns out to be approximately Msub(n)c 2 for a wide range of bag radii, from 1.5 fm down to about 0.5 fm. Introduction of a form factor for the pion would extend the range of possible radii to even smaller values. We propose that the bag with the smallest allowed radius be identified with the 'little bag' discussed before. One surprising result of the paper is that as long as one restricts to spherically symmetric bags, restoring chiral symmetry to the bag model makes the axial-vector current coupling constant gsub(A) to be always too large compared with the experimental value for any bag radius, suggesting a deviation from spherical symmetry for the intrinsic bag wave functions of the 'ground-state' hadrons. (orig.)

Approximate and renormgroup symmetries

Energy Technology Data Exchange (ETDEWEB)

Ibragimov, Nail H. [Blekinge Institute of Technology, Karlskrona (Sweden). Dept. of Mathematics Science; Kovalev, Vladimir F. [Russian Academy of Sciences, Moscow (Russian Federation). Inst. of Mathematical Modeling

2009-07-01

''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)

A no-hair theorem for stars in Horndeski theories

Energy Technology Data Exchange (ETDEWEB)

Lehébel, A.; Babichev, E.; Charmousis, C., E-mail: antoine.lehebel@th.u-psud.fr, E-mail: eugeny.babichev@th.u-psud.fr, E-mail: christos.charmousis@th.u-psud.fr [Laboratoire de Physique Théorique, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay (France)

2017-07-01

We consider a generic scalar-tensor theory involving a shift-symmetric scalar field and minimally coupled matter fields. We prove that the Noether current associated with shift-symmetry vanishes in regular, spherically symmetric and static spacetimes. We use this fact to prove the absence of scalar hair for spherically symmetric and static stars in Horndeski and beyond theories. We carefully detail the validity of this no-hair theorem.

Kinetic theory of a spherical probe in a stationary collision-dominated isothermal plasma

International Nuclear Information System (INIS)

Brailsford, A.D.

1977-01-01

Constitutive equations for the charge carrier fluxes in a stationary collision-dominated isothermal plasma surrounding a spherical electrode are derived, from the Boltzmann equation, by a moment method using a two-stream Maxwellian distribution of the type introduced by Lees. In contrast to previous treatments, the constraint of uniform temperature is imposed and its importance emphasized. This condition, together with particle conservation, is shown to necessitate the use of a four-parameter Lees distribution and leads to generalized hydrodynamic equations. These are shown to reduce to conventional flux equations in terms of diffusion and mobility components only when the fields are spatially slowly varying. In addition, boundary conditions are derived by the same formalism. They are formulated for typical physical processes which may be operative at a real probe surface. As an example, the effect of the nonlinearity on the pure diffusion problem is analyzed in detail in the Appendix. A semiquantitative discussion of the current-voltage characteristics for negative probe potentials is also presented. It is shown that the charge carrier distribution around the probe conforms to the ''free-fall'' model only at low probe voltages. Otherwise, the model proposed by Su and Lam holds. The domain covered by the present analysis is determined by the following conditions on the probe radius r/sub p/, mean free path l, and Debye length lambda: (i) l 3 very-much-less-thanlambda 2 r/sub p/, (ii) (e vertical-barphi/sub p/ vertical-barl/kTr/sub p/) 2 /l 2 for l>lambda, where phi/sub p/ is the probe voltage. Analytic approximations to the current-voltage characteristics in both these regimes are presented

Spherical and planar three-dimensional anti-de Sitter black holes

International Nuclear Information System (INIS)

Zanchin, Vilson T; Miranda, Alex S

2004-01-01

The technique of dimensional reduction was used in a recent paper (Zanchin V T, Kleber A and Lemos J P S 2002 Phys. Rev. D 66 064022) where a three-dimensional (3D) Einstein-Maxwell-dilaton theory was built from the usual four-dimensional (4D) Einstein-Maxwell-Hilbert action for general relativity. Starting from a class of 4D toroidal black holes in asymptotically anti-de Sitter (AdS) spacetimes several 3D black holes were obtained and studied in such a context. In the present work we choose a particular case of the 3D action which presents Maxwell field, dilaton field and an extra scalar field, besides gravity field and a negative cosmological constant, and obtain new 3D static black hole solutions whose horizons may have spherical or planar topology. We show that there is a 3D static spherically symmetric solution analogous to the 4D Reissner-Nordstroem-AdS black hole, and obtain other new 3D black holes with planar topology. From the static spherical solutions, new rotating 3D black holes are also obtained and analysed in some detail

Conference on Abstract Spaces and Approximation

CERN Document Server

Szökefalvi-Nagy, B; Abstrakte Räume und Approximation; Abstract spaces and approximation

1969-01-01

The present conference took place at Oberwolfach, July 18-27, 1968, as a direct follow-up on a meeting on Approximation Theory [1] held there from August 4-10, 1963. The emphasis was on theoretical aspects of approximation, rather than the numerical side. Particular importance was placed on the related fields of functional analysis and operator theory. Thirty-nine papers were presented at the conference and one more was subsequently submitted in writing. All of these are included in these proceedings. In addition there is areport on new and unsolved problems based upon a special problem session and later communications from the partici­ pants. A special role is played by the survey papers also presented in full. They cover a broad range of topics, including invariant subspaces, scattering theory, Wiener-Hopf equations, interpolation theorems, contraction operators, approximation in Banach spaces, etc. The papers have been classified according to subject matter into five chapters, but it needs littl...

Self-consistent generalized Langevin-equation theory for liquids of nonspherically interacting particles

Science.gov (United States)

Elizondo-Aguilera, L. F.; Zubieta Rico, P. F.; Ruiz-Estrada, H.; Alarcón-Waess, O.

2014-11-01

A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, Fl m ,l m(k ,t ) and Flm ,l m S(k ,t ) , are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density nl m(k ,t ) and the translational (α =T ) and rotational (α =R ) current densities jlm α(k ,t ) . Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by Sl m ,l m(k ) . Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, γT and γR, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters η (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states.

Self-consistent generalized Langevin-equation theory for liquids of nonspherically interacting particles.

Science.gov (United States)

Elizondo-Aguilera, L F; Zubieta Rico, P F; Ruiz-Estrada, H; Alarcón-Waess, O

2014-11-01

A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, F_{lm,lm}(k,t) and F_{lm,lm}^{S}(k,t), are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density n_{lm}(k,t) and the translational (α=T) and rotational (α=R) current densities j_{lm}^{α}(k,t). Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by S_{lm,lm}(k). Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, γ_{T} and γ_{R}, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters η (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states.

Some results in Diophantine approximation

DEFF Research Database (Denmark)

Pedersen, Steffen Højris

the basic concepts on which the papers build. Among other it introduces metric Diophantine approximation, Mahler’s approach on algebraic approximation, the Hausdorff measure, and properties of the formal Laurent series over Fq. The introduction ends with a discussion on Mahler’s problem when considered......This thesis consists of three papers in Diophantine approximation, a subbranch of number theory. Preceding these papers is an introduction to various aspects of Diophantine approximation and formal Laurent series over Fq and a summary of each of the three papers. The introduction introduces...

Are Nanoparticles Spherical or Quasi-Spherical?

Science.gov (United States)

Sokolov, Stanislav V; Batchelor-McAuley, Christopher; Tschulik, Kristina; Fletcher, Stephen; Compton, Richard G

2015-07-20

The geometry of quasi-spherical nanoparticles is investigated. The combination of SEM imaging and electrochemical nano-impact experiments is demonstrated to allow sizing and characterization of the geometry of single silver nanoparticles. © 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim.

Spherical cows in the sky with fab four

Energy Technology Data Exchange (ETDEWEB)

Kaloper, Nemanja; Sandora, McCullen, E-mail: kaloper@physics.ucdavis.edu, E-mail: mesandora@ucdavis.edu [Department of Physics, University of California, Davis, CA 95616 (United States)

2014-05-01

We explore spherically symmetric static solutions in a subclass of unitary scalar-tensor theories of gravity, called the 'Fab Four' models. The weak field large distance solutions may be phenomenologically viable, but only if the Gauss-Bonnet term is negligible. Only in this limit will the Vainshtein mechanism work consistently. Further, classical constraints and unitarity bounds constrain the models quite tightly. Nevertheless, in the limits where the range of individual terms at large scales is respectively Kinetic Braiding, Horndeski, and Gauss-Bonnet, the horizon scale effects may occur while the theory satisfies Solar system constraints and, marginally, unitarity bounds. On the other hand, to bring the cutoff down to below a millimeter constrains all the couplings scales such that 'Fab Fours' can't be heard outside of the Solar system.

Theoretical investigation of stark effect on shallow donor binding energy in InGaN spherical QD-QW

Energy Technology Data Exchange (ETDEWEB)

El Ghazi, Haddou, E-mail: hadghazi@gmail.com [Solid State Physics Laboratory, Faculty of Science, Dhar EL Mehrez, BP 1796 Fes-Atlas (Morocco); Mathématiques spéciales, CPGE Kénitra, Chakib Arsalane Street (Morocco); Jorio, Anouar; Zorkani, Izeddine [Solid State Physics Laboratory, Faculty of Science, Dhar EL Mehrez, BP 1796 Fes-Atlas (Morocco)

2013-08-01

In this paper, a simultaneous study of electric field and impurity's position effects on the ground-state shallow-donor binding energy in GaN|InGaN|GaN spherical quantum dot-quantum well (SQD-QW) as a function of the ratio of the inner and the outer radius is reported. The calculations are investigated using variational approach within the framework of the effective-mass approximation. The numerical results show that: (i) the binding energy is strongly affected by the external electric field and the SQD-QW dimension, (ii) a critical value of spherical system's radius is obtained constituting the limit of three dimension confinement and spherical thin layer confinement and (iii) the Stark shift increases with increasing electric field and it is more pronounced around the position of the impurity corresponding to the binding energy maxima than in the spherical layer extremities.

Gravitational perturbation theory and synchrotron radiation

Energy Technology Data Exchange (ETDEWEB)

Breuer, R A [Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (F.R. Germany). Inst. fuer Astrophysik

1975-01-01

This article presents methods and results for a gravitational perturbation theory which treats massless fields as linearized perturbations of an arbitrary gravitational vacuum background spacetime. The formalism is outlined for perturbations of type (22) spacetimes. As an application, high-frequency radiation emitted by particles moving approximately on relativistic circular geodesic orbits is computed. More precisely, the test particle assumption is made; throughout it is therefore assumed that the reaction of the radiation on the particle motion is negligible. In particular, these orbits are studied in the gravitational field of a spherically symmetric (Schwarzschild-) black hole as well as of a rotating (Kerr-) black hole. In this model, the outgoing radiation is highly focussed and of much higher fequency than the orbital frequency, i.e. one is dealing with 'gravitational synchrotron radiation'.

High-energy, twelve-channel laser facility (DEFIN) for spherical irradiation of thermonuclear targets

International Nuclear Information System (INIS)

Basov, N.G.; Danilov, A.E.; Krokhin, O.N.; Kruglov, B.V.; Mikhailov, Yu.A.; Sklizkov, G.V.; Fedotov, S.I.; Fedorov, A.N.

This paper describes a high-energy, twelve-channel laser facility (DELFIN) intended for high-temperature heating of thermonuclear targets with spherical symmetry. The facility includes a neodymium-glass laser with the ultimate radiation energy of 10 kJ, a pulse length of approximately 10 -10 to 10 -9 s, beam divergence of 5 x 10 -4 radians, a vacuum chamber in which laser radiation interacts with the plasma, and a system of diagnostic instrumentation for the observation of laser beam and plasma parameters. Described are the optical scheme and construction details of the laser facility. Presented is an analysis of focusing schemes for target irradiation and described is the focusing scheme of the DELFIN facility, which is capable of attaining a high degree of spherical symmetry in irradiating targets with maximum beam intensity at the target surface of approximately 10 15 W/cm 2 . This paper examines the most important problems connected with the physical investigations of thermonuclear laser plasma and the basic diagnostic problems involved in their solution

Fifth International Conference on "Approximation and Optimization in the Caribbean"

CERN Document Server

Approximation, Optimization and Mathematical Economic

2001-01-01

The articles in this proceedings volume reflect the current trends in the theory of approximation, optimization and mathematical economics, and include numerous applications. The book will be of interest to researchers and graduate students involved in functional analysis, approximation theory, mathematical programming and optimization, game theory, mathematical finance and economics.

Ordered cones and approximation

CERN Document Server

Keimel, Klaus

1992-01-01

This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.

A constrained approximation for nuclear barrier penetration and fission

International Nuclear Information System (INIS)

Tang, H.H.K.; Negele, J.W.; Massachusetts Inst. of Tech., Cambridge; Massachusetts Inst. of Tech., Cambridge

1983-01-01

An approximation to the time-dependent mean-field theory for barrier penetration by a nucleus is obtained in terms of constrained Hartree-Fock wave functions and a coherent velocity field. A discrete approximation to the continuum theory suitable for practical numerical calculations is presented and applied to three illustrative models. Potential application of the theory to the study of nuclear fission is discussed. (orig.)

Approximate spin projected spin-unrestricted density functional theory method: Application to diradical character dependences of second hyperpolarizabilities

Energy Technology Data Exchange (ETDEWEB)

Nakano, Masayoshi, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Minami, Takuya, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Fukui, Hitoshi, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Yoneda, Kyohei, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Shigeta, Yasuteru, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Kishi, Ryohei, E-mail: mnaka@cheng.es.osaka-u.ac.jp [Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531 (Japan); Champagne, Benoît; Botek, Edith [Laboratoire de Chimie Théorique, Facultés Universitaires Notre-Dame de la Paix (FUNDP), rue de Bruxelles, 61, 5000 Namur (Belgium)

2015-01-22

We develop a novel method for the calculation and the analysis of the one-electron reduced densities in open-shell molecular systems using the natural orbitals and approximate spin projected occupation numbers obtained from broken symmetry (BS), i.e., spin-unrestricted (U), density functional theory (DFT) calculations. The performance of this approximate spin projection (ASP) scheme is examined for the diradical character dependence of the second hyperpolarizability (γ) using several exchange-correlation functionals, i.e., hybrid and long-range corrected UDFT schemes. It is found that the ASP-LC-UBLYP method with a range separating parameter μ = 0.47 reproduces semi-quantitatively the strongly-correlated [UCCSD(T)] result for p-quinodimethane, i.e., the γ variation as a function of the diradical character.

Rainbows: Mie computations and the Airy approximation.

Science.gov (United States)

Wang, R T; van de Hulst, H C

1991-01-01

Efficient and accurate computation of the scattered intensity pattern by the Mie formulas is now feasible for size parameters up to x = 50,000 at least, which in visual light means spherical drops with diameters up to 6 mm. We present a method for evaluating the Mie coefficients from the ratios between Riccati-Bessel and Neumann functions of successive order. We probe the applicability of the Airy approximation, which we generalize to rainbows of arbitrary p (number of internal reflections = p - 1), by comparing the Mie and Airy intensity patterns. Millimeter size water drops show a match in all details, including the position and intensity of the supernumerary maxima and the polarization. A fairly good match is still seen for drops of 0.1 mm. A small spread in sizes helps to smooth out irrelevant detail. The dark band between the rainbows is used to test more subtle features. We conclude that this band contains not only externally reflected light (p = 0) but also a sizable contribution f rom the p = 6 and p = 7 rainbows, which shift rapidly with wavelength. The higher the refractive index, the closer both theories agree on the first primary rainbow (p = 2) peak for drop diameters as small as 0.02 mm. This may be useful in supporting experimental work.

Theory of a spherical emissive probe in a low-density isotropic plasma

International Nuclear Information System (INIS)

Din, A.

2010-01-01

Emissive probes are widely being used by plasma experimentalists to determine plasma parameters. Here, a fairly general spherical-emissive-probe scenario based on trajectory integration of the Vlasov equation is formulated and specialized to the particular non-emissive situation considered by Bernstein and Rabinowitz (1959), which is monoenergetic isotropic ions and Boltzmann-distributed electrons originating from the plasma. Then, this formalism together with our newly developed analytic-numerical matching procedure is used for finding the potential profile in the entire plasma-probe transition (PPT) region, consisting of the 'inward' and 'outward' sheath solutions, and the quasineutral (plasma) solution. The analytically expanded outward sheath and plasma solutions, the quasineutral solution and the related matching procedure represent genuinely new results in the context of this particular non-emissive probe scenario, however with the underlying methodology also applicable to other probe scenarios in the future. For the emissive case we consider, in addition to the plasma ions and electrons of the Bernstein and Rabinowitz scenario, electrons emitted from the probe surface with zero tangential velocity and a 'waterbag' distribution with respect to the radial velocity. Using our newly developed numerical matching procedure, we calculate the entire potential profile also for this emissive case. Comparison of the potential profiles for the emissive and non-emissive cases shows visible differences, thus demonstrating the effect of electron emission from the probe. To our knowledge, the present work represents the first attempt at systematically developing a kinetic approach for spherical emissive probes. (author)

Spherical sila- and germa-homoaromaticity.

Science.gov (United States)

Chen, Zhongfang; Hirsch, Andreas; Nagase, Shigeru; Thiel, Walter; Schleyer, Paul von Ragué

2003-12-17

Guided by the 2(N + 1)2 electron-counting rule for spherical aromatic molecules, we have designed various spherical sila- and germa-homoaromatic systems rich in group 14 elements. Their aromaticity is revealed by density-functional computations of their structures and the nucleus-independent chemical shifts (NICS). Besides the formerly used endohedral inclusion strategy, spherical homoaromaticity is another way to stabilize silicon and germanium clusters.

Oscillations of spherical fullerenes interacting with graphene sheet

Energy Technology Data Exchange (ETDEWEB)

Ghavanloo, Esmaeal, E-mail: ghavanloo@shirazu.ac.ir; Fazelzadeh, S. Ahmad

2017-01-01

In the present study, the oscillations of spherical fullerenes in the vicinity of a fully constrained graphene sheet are investigated. Using the continuous approximation and Lennard-Jones potential, the van der Waals (vdW) potential energy and interaction forces are obtained. The equation of motion is derived and directly solved based on the actual force distribution between the fullerene molecules and the graphene sheet. Numerical results are obtained and shown that the oscillation is sensitive to the size of the fullerene as well as the distance between the center of the fullerene and the graphene sheet.

Relativistic theory of tidal Love numbers

International Nuclear Information System (INIS)

Binnington, Taylor; Poisson, Eric

2009-01-01

In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body's internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neutron star can be measured by Earth-based gravitational-wave detectors. We consider a spherical body deformed by an external tidal field, and provide precise and meaningful definitions for electric-type and magnetic-type Love numbers; and these are computed for polytropic equations of state. The theory applies to black holes as well, and we find that the relativistic Love numbers of a nonrotating black hole are all zero.

Coulomb potentials between spherical heavy ions

International Nuclear Information System (INIS)

Iwe, H.

1982-01-01

The Coulomb interaction between spherical nuclei having arbitrary radial nuclear charge distributions is calculated. All these realistic Coulomb potentials are given in terms of analytical expressions and are available for immediate application. So in no case a numerical computation of the Coulomb integral is required. The parameters of the charge distributions are taken from electron scattering analysis. The Coulomb self-energies of the charge distributions used are also calculated analytically in a closed form. For a number of nucleus-nucleus pairs, the Coulomb potentials derived from realistic charge distributions are compared with those normally used in various nucleus-nucleus optical model calculations. In this connection a detailed discussion of the problem how to choose consistently Coulomb parameters for different approximations is given. (orig.)

Self-similar factor approximants

International Nuclear Information System (INIS)

Gluzman, S.; Yukalov, V.I.; Sornette, D.

2003-01-01

The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving an improved type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approximants, because of their form, are called self-similar factor approximants. These complement the obtained earlier self-similar exponential approximants and self-similar root approximants. The specific feature of self-similar factor approximants is that their control functions, providing convergence of the computational algorithm, are completely defined from the accuracy-through-order conditions. These approximants contain the Pade approximants as a particular case, and in some limit they can be reduced to the self-similar exponential approximants previously introduced by two of us. It is proved that the self-similar factor approximants are able to reproduce exactly a wide class of functions, which include a variety of nonalgebraic functions. For other functions, not pertaining to this exactly reproducible class, the factor approximants provide very accurate approximations, whose accuracy surpasses significantly that of the most accurate Pade approximants. This is illustrated by a number of examples showing the generality and accuracy of the factor approximants even when conventional techniques meet serious difficulties

Quark and gluon propagators in the spherical bag model

Energy Technology Data Exchange (ETDEWEB)

Kulish, Yu V [AN Ukrainskoj SSR, Fiziko-Tekhnicheskij Inst., Kharkov

1983-12-01

The quark and gluon propagators in a spherical cavity have been obtained by summation of the quark field modes (J-1/2, J is the total moment) and gluon field modes (J=1). The requirements for the spatial components of the gluon propagator Gsub(ik)(x, x') and the quark propagator S(x, x') to be Green functions of the wave equations result in the coincidence of directions for anti x and anti x' vectors. Relations have been derived which allow verification of the self-consistency of approximations used to calculate dynamic values.

Quark and gluon propagators in the spherical bag model

International Nuclear Information System (INIS)

Kulish, Yu.V.

1983-01-01

The quark and gluon propagators in a spherical cavity have been obtained by summation of the quark field modes (J-1/2, J is the total moment) and gluon field modes (J=1). The requirements for the spatial components of the gluon propagator Gsub(ik)(x, x') and the quark propagator S(x, x') to be Green functions of the wave equations result in the coincidence of directions for anti x and anti x' vectors. Relations have been derived which allow verification of the self-consistency of approximations used to calculate dynamic values

An improved filtered spherical harmonic method for transport calculations

International Nuclear Information System (INIS)

Ahrens, C.; Merton, S.

2013-01-01

Motivated by the work of R. G. McClarren, C. D. Hauck, and R. B. Lowrie on a filtered spherical harmonic method, we present a new filter for such numerical approximations to the multi-dimensional transport equation. In several test problems, we demonstrate that the new filter produces results with significantly less Gibbs phenomena than the filter used by McClarren, Hauck and Lowrie. This reduction in Gibbs phenomena translates into propagation speeds that more closely match the correct propagation speed and solutions that have fewer regions where the scalar flux is negative. (authors)

Pade approximants in field theory: pion and kaon systems; Approximants de pade en theorie des champs: systeme de pions et de kaons

Energy Technology Data Exchange (ETDEWEB)

Zinn-Justin, J. [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1969-07-01

We construct the Pade approximants of the S-matrix, starting from the perturbation series, in the case of two body pion and kaon systems. We have three parameters. The seven lowest lying two body resonances ({rho}, K{sup *}(890), {phi}, K{sup *}(1420), f{sub 0}, f', A{sub 2}) are obtained within a few per cent of their actual masses. The Regge trajectories are rising, the intercepts of the {rho} and f{sub 0} agree well with the experimental values. In the appendices we give some properties and applications of the Pade approximants. (author) [French] Nous avons construit les approximants de Pade de la matrice S a partir de la serie formelle des perturbations, dans le cas des systemes a deux corps de pions et de kaons. Le probleme depend de trois parametres. Nous avons obtenu les sept resonances meson-meson a deux corps ({rho}, K{sup *}(890), {phi}, K{sup *}(1420), f{sub 0}, f', A{sub 2}) a quelques pour cent de leurs masses experimentales. Les trajectoires de Regge sont trouvees croissantes, les intercepts du {rho} et du f{sub 0} sont en bon accord avec l'experience. Dans les appendices nous donnons quelques proprietes et applications des approximants de Pade. (auteur)

Pade approximants in field theory: pion and kaon systems; Approximants de pade en theorie des champs: systeme de pions et de kaons

Energy Technology Data Exchange (ETDEWEB)

Zinn-Justin, J [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1969-07-01

We construct the Pade approximants of the S-matrix, starting from the perturbation series, in the case of two body pion and kaon systems. We have three parameters. The seven lowest lying two body resonances ({rho}, K{sup *}(890), {phi}, K{sup *}(1420), f{sub 0}, f', A{sub 2}) are obtained within a few per cent of their actual masses. The Regge trajectories are rising, the intercepts of the {rho} and f{sub 0} agree well with the experimental values. In the appendices we give some properties and applications of the Pade approximants. (author) [French] Nous avons construit les approximants de Pade de la matrice S a partir de la serie formelle des perturbations, dans le cas des systemes a deux corps de pions et de kaons. Le probleme depend de trois parametres. Nous avons obtenu les sept resonances meson-meson a deux corps ({rho}, K{sup *}(890), {phi}, K{sup *}(1420), f{sub 0}, f', A{sub 2}) a quelques pour cent de leurs masses experimentales. Les trajectoires de Regge sont trouvees croissantes, les intercepts du {rho} et du f{sub 0} sont en bon accord avec l'experience. Dans les appendices nous donnons quelques proprietes et applications des approximants de Pade. (auteur)

Spin-adapted open-shell random phase approximation and time-dependent density functional theory. I. Theory.

Science.gov (United States)

Li, Zhendong; Liu, Wenjian

2010-08-14

The spin-adaptation of single-reference quantum chemical methods for excited states of open-shell systems has been nontrivial. The primary reason is that the configuration space, generated by a truncated rank of excitations from only one component of a reference multiplet, is spin-incomplete. Those "missing" configurations are of higher ranks and can, in principle, be recaptured by a particular class of excitation operators. However, the resulting formalisms are then quite involved and there are situations [e.g., time-dependent density functional theory (TD-DFT) under the adiabatic approximation] that prevent one from doing so. To solve this issue, we propose here a tensor-coupling scheme that invokes all the components of a reference multiplet (i.e., a tensor reference) rather than increases the excitation ranks. A minimal spin-adapted n-tuply excited configuration space can readily be constructed by tensor products between the n-tuple tensor excitation operators and the chosen tensor reference. Further combined with the tensor equation-of-motion formalism, very compact expressions for excitation energies can be obtained. As a first application of this general idea, a spin-adapted open-shell random phase approximation is first developed. The so-called "translation rule" is then adopted to formulate a spin-adapted, restricted open-shell Kohn-Sham (ROKS)-based TD-DFT (ROKS-TD-DFT). Here, a particular symmetry structure has to be imposed on the exchange-correlation kernel. While the standard ROKS-TD-DFT can access only excited states due to singlet-coupled single excitations, i.e., only some of the singly excited states of the same spin (S(i)) as the reference, the new scheme can capture all the excited states of spin S(i)-1, S(i), or S(i)+1 due to both singlet- and triplet-coupled single excitations. The actual implementation and computation are very much like the (spin-contaminated) unrestricted Kohn-Sham-based TD-DFT. It is also shown that spin-contaminated spin

LLE-LLNL progress report on studies in nonlocal heat transport in spherical plasmas using the Fokker-Planck code SPARK

International Nuclear Information System (INIS)

Epperlein, E.M.

1992-01-01

Preliminary 1-D studies of nonlocal heat transport in spherical plasmas based on the Fokker-Planck code SPARK indicate significant levels of electron preheat and radial heat flux across a spherical heat sink surface kept at fixed temperature. However, the diffusive approximation to the Fokker-Planck equation is shown to be particularly sensitive to the nature of the inner surface boundary condition chosen. A suggested remedy is the inclusion of a target capsule in future simulations studies with SPARK

Spherical Harmonics Treatment of Epithermal Neutron Spectra in Reactor lattices

International Nuclear Information System (INIS)

Matausek, M.V.

1972-04-01

A procedure has been developed to solve the slowing down transport equation for neutrons in a cylindrized reactor lattice cell. Treating the anisotropy of the epithermal neutron flux by the spherical harmonics formalism, which reduces the space-angle-lethargy-dependent transport equation to the matrix integrodifferential equation in space and lethargy, and replacing the lethargy transfer integrals by finite-difference forms, a set of matrix ordinary differential equations, with lethargy and space dependent coefficients, is obtained. In the resonance region this set takes a lower block triangular form and can be directly solved by forward block substitution; in the lethargy range, where the fast fission effects have to be considered, the iterative procedure is introduced. A simple and efficient approximation is then proposed, making possible the analytical solution for the spatial dependence of the spherical harmonics flux moments. The proposed procedure has been numerically examined and approved. Some typical results are presented and discussed. (author)

Spherical bootstrap calculation of qqq-baryon and multiquark-hadron masses

International Nuclear Information System (INIS)

Balazs, L.A.P.; Nicolescu, B.

1979-12-01

Recently a way of implementing the dual-topological unitarization program has been found, in which baryons and other multiquark hadrons are put on the sphere and appear at the same topological-complexity level as ordinary anti-qq mesons. This permits one to have a lowest-order 'spherical bootstrap', within which unitarity, duality and crossing can be consistently satisfied. In the present paper, this framework to calculate hadron masses has been used by imposing duality on an infinite sum of ladder graphs generated from spherical unitarity. By making a certain simple dynamical approximation, an explicit generic Regge-trajectory formula is derived for any given process. If one then makes certain reasonable dynamical assumptions and requires simultaneous consistency for entire sets of processes, it is possible to calculate the masses of all the lowest states and the Regge trajectories associated with each of them. The only arbitrary parameter is the mass of the rho which merely serves to set the mass scale

An Origami Approximation to the Cosmic Web

Science.gov (United States)

Neyrinck, Mark C.

2016-10-01

The powerful Lagrangian view of structure formation was essentially introduced to cosmology by Zel'dovich. In the current cosmological paradigm, a dark-matter-sheet 3D manifold, inhabiting 6D position-velocity phase space, was flat (with vanishing velocity) at the big bang. Afterward, gravity stretched and bunched the sheet together in different places, forming a cosmic web when projected to the position coordinates. Here, I explain some properties of an origami approximation, in which the sheet does not stretch or contract (an assumption that is false in general), but is allowed to fold. Even without stretching, the sheet can form an idealized cosmic web, with convex polyhedral voids separated by straight walls and filaments, joined by convex polyhedral nodes. The nodes form in `polygonal' or `polyhedral' collapse, somewhat like spherical/ellipsoidal collapse, except incorporating simultaneous filament and wall formation. The origami approximation allows phase-space geometries of nodes, filaments, and walls to be more easily understood, and may aid in understanding spin correlations between nearby galaxies. This contribution explores kinematic origami-approximation models giving velocity fields for the first time.

Spherical tokamak development in Brazil

Energy Technology Data Exchange (ETDEWEB)

Ludwig, Gerson Otto; Bosco, Edson Del; Ferreira, Julio Guimaraes [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Lab. Associado de Plasma] (and others)

2003-07-01

The general characteristics of spherical tokamaks, or spherical tori, with a brief view of work in this area already performed or in progress at several institutions worldwide are described. The paper presents also the steps in the development of the ETE (Experiment Tokamak spheric) project, its research program, technical characteristics and operating conditions as of December, 2002 a the Associated Plasma Laboratory (LAP) of the National Space Research Institute (INPE) in Brazil. (author)

Spherical tokamak development in Brazil

International Nuclear Information System (INIS)

Ludwig, Gerson Otto; Bosco, Edson Del; Ferreira, Julio Guimaraes

2003-01-01

The general characteristics of spherical tokamaks, or spherical tori, with a brief view of work in this area already performed or in progress at several institutions worldwide are described. The paper presents also the steps in the development of the ETE (Experiment Tokamak spheric) project, its research program, technical characteristics and operating conditions as of December, 2002 a the Associated Plasma Laboratory (LAP) of the National Space Research Institute (INPE) in Brazil. (author)

Approximate analytical solution of two-dimensional multigroup P-3 equations

International Nuclear Information System (INIS)

Matausek, M.V.; Milosevic, M.

1981-01-01

Iterative solution of multigroup spherical harmonics equations reduces, in the P-3 approximation and in two-dimensional geometry, to a problem of solving an inhomogeneous system of eight ordinary first order differential equations. With appropriate boundary conditions, these equations have to be solved for each energy group and in each iteration step. The general solution of the corresponding homogeneous system of equations is known in analytical form. The present paper shows how the right-hand side of the system can be approximated in order to derive a particular solution and thus an approximate analytical expression for the general solution of the inhomogeneous system. This combined analytical-numerical approach was shown to have certain advantages compared to the finite-difference method or the Lie-series expansion method, which have been used to solve similar problems. (author)

Quasilinear theory without the random phase approximation

International Nuclear Information System (INIS)

Weibel, E.S.; Vaclavik, J.

1980-08-01

The system of quasilinear equations is derived without making use of the random phase approximation. The fluctuating quantities are described by the autocorrelation function of the electric field using the techniques of Fourier analysis. The resulting equations posses the necessary conservation properties, but comprise new terms which hitherto have been lost in the conventional derivations

A theoretical-electron-density databank using a model of real and virtual spherical atoms.

Science.gov (United States)

Nassour, Ayoub; Domagala, Slawomir; Guillot, Benoit; Leduc, Theo; Lecomte, Claude; Jelsch, Christian

2017-08-01

A database describing the electron density of common chemical groups using combinations of real and virtual spherical atoms is proposed, as an alternative to the multipolar atom modelling of the molecular charge density. Theoretical structure factors were computed from periodic density functional theory calculations on 38 crystal structures of small molecules and the charge density was subsequently refined using a density model based on real spherical atoms and additional dummy charges on the covalent bonds and on electron lone-pair sites. The electron-density parameters of real and dummy atoms present in a similar chemical environment were averaged on all the molecules studied to build a database of transferable spherical atoms. Compared with the now-popular databases of transferable multipolar parameters, the spherical charge modelling needs fewer parameters to describe the molecular electron density and can be more easily incorporated in molecular modelling software for the computation of electrostatic properties. The construction method of the database is described. In order to analyse to what extent this modelling method can be used to derive meaningful molecular properties, it has been applied to the urea molecule and to biotin/streptavidin, a protein/ligand complex.

Approximating the physical inner product of loop quantum cosmology

International Nuclear Information System (INIS)

Bahr, Benjamin; Thiemann, Thomas

2007-01-01

In this paper, we investigate the possibility of approximating the physical inner product of constrained quantum theories. In particular, we calculate the physical inner product of a simple cosmological model in two ways: firstly, we compute it analytically via a trick; secondly, we use the complexifier coherent states to approximate the physical inner product defined by the master constraint of the system. We find that the approximation is able to recover the analytic solution of the problem, which consolidates hopes that coherent states will help to approximate solutions of more complicated theories, like loop quantum gravity

Diophantine approximation

CERN Document Server

Schmidt, Wolfgang M

1980-01-01

"In 1970, at the U. of Colorado, the author delivered a course of lectures on his famous generalization, then just established, relating to Roth's theorem on rational approxi- mations to algebraic numbers. The present volume is an ex- panded and up-dated version of the original mimeographed notes on the course. As an introduction to the author's own remarkable achievements relating to the Thue-Siegel-Roth theory, the text can hardly be bettered and the tract can already be regarded as a classic in its field."(Bull.LMS) "Schmidt's work on approximations by algebraic numbers belongs to the deepest and most satisfactory parts of number theory. These notes give the best accessible way to learn the subject. ... this book is highly recommended." (Mededelingen van het Wiskundig Genootschap)

Static spherically symmetric wormholes in f(R, T) gravity

Energy Technology Data Exchange (ETDEWEB)

Zubair, M.; Ahmad, Yasir [Institute Of Information Technology, Department of Mathematics, COMSATS, Lahore (Pakistan); Waheed, Saira [Prince Mohammad Bin Fahd University, Al Khobar (Saudi Arabia)

2016-08-15

In this work, we explore wormhole solutions in f(R, T) theory of gravity, where R is the scalar curvature and T is the trace of stress-energy tensor of matter. To investigate this, we consider a static spherically symmetric geometry with matter contents as anisotropic, isotropic, and barotropic fluids in three separate cases. By taking into account the Starobinsky f(R) model, we analyze the behavior of energy conditions for these different kinds of fluids. It is shown that the wormhole solutions can be constructed without exotic matter in few regions of space-time. We also give the graphical illustration of the results obtained and discuss the equilibrium picture for the anisotropic case only. It is concluded that the wormhole solutions with anisotropic matter are realistic and stable in this theory of gravity. (orig.)

Estimation of added-mass and damping coefficients of a tethered spherical float using potential flow theory

Digital Repository Service at National Institute of Oceanography (India)

Vethamony, P.; Chandramohan, P.; Sastry, J.S.; Narasimhan, S.

Added-mass (alpha) and damping coefficients (beta) of a tethered spherical float, undergoing oscillatory motion in sinusoidal waves, have been derived from the motion generated velocity potential for one degree-of-freedom (surge) using potential...

Collisionless ion drag force on a spherical grain

International Nuclear Information System (INIS)

Hutchinson, I H

2006-01-01

The ion drag force on a spherical grain situated in a flowing collisionless plasma is obtained from the specialized coordinate electrostatic particle and thermals in cell simulation code (SCEPTIC) (Hutchinson 2002 Plasma Phys. Control. Fusion 44 1953, Hutchinson 2003 Plasma Phys. Control. Fusion 45 1477, Hutchinson 2005 Plasma Phys. Control. Fusion 47 71) and compared with recent analytic approximate treatments in the interesting and relevant case when the Debye length is only moderately larger than the sphere radius. There is a substantial complex structure in the results for transonic flows, which is explained in terms of the details of ion orbits. Naturally the prior analytic approximations miss this structure, and as a result they seriously underestimate the drag for speeds near the sound speed. An easy-to-evaluate expression for force is provided that fits the comprehensive results of the code. This expression, with minor modification, also fits the results even for Debye length much smaller than the sphere radius

Spherical perturbations of hairy black holes in designer gravity theories

International Nuclear Information System (INIS)

Battarra, Lorenzo

2012-01-01

We study the spectrum of the scalar l = 0 quasi-normal frequencies of anti-de Sitter hairy black holes in four- and five-dimensional designer gravity theories of the Einstein-scalar type, arising as consistent truncations of N= 8 gauged supergravity. In the dual field theory, such hairy black holes represent thermal states in which the operator corresponding to the bulk scalar field is condensed, due to the multi-trace deformation associated with non-standard boundary conditions. We show that, in a particular class of models, the effective potential describing the vacua of the deformed dual theory can be identified, at large values of the condensate, with the deformation plus the conformal coupling of the condensate to the curvature of the boundary geometry. In this limit, we show that the least damped quasi-normal frequency of the corresponding hairy black holes can be accurately predicted by the curvature of the effective potential describing the field theory at finite entropy. (paper)

Topology, calculus and approximation

CERN Document Server

Komornik, Vilmos

2017-01-01

Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...

Validity of the Aluminum Equivalent Approximation in Space Radiation Shielding

Science.gov (United States)

Badavi, Francis F.; Adams, Daniel O.; Wilson, John W.

2009-01-01

The origin of the aluminum equivalent shield approximation in space radiation analysis can be traced back to its roots in the early years of the NASA space programs (Mercury, Gemini and Apollo) wherein the primary radiobiological concern was the intense sources of ionizing radiation causing short term effects which was thought to jeopardize the safety of the crew and hence the mission. Herein, it is shown that the aluminum equivalent shield approximation, although reasonably well suited for that time period and to the application for which it was developed, is of questionable usefulness to the radiobiological concerns of routine space operations of the 21 st century which will include long stays onboard the International Space Station (ISS) and perhaps the moon. This is especially true for a risk based protection system, as appears imminent for deep space exploration where the long-term effects of Galactic Cosmic Ray (GCR) exposure is of primary concern. The present analysis demonstrates that sufficiently large errors in the interior particle environment of a spacecraft result from the use of the aluminum equivalent approximation, and such approximations should be avoided in future astronaut risk estimates. In this study, the aluminum equivalent approximation is evaluated as a means for estimating the particle environment within a spacecraft structure induced by the GCR radiation field. For comparison, the two extremes of the GCR environment, the 1977 solar minimum and the 2001 solar maximum, are considered. These environments are coupled to the Langley Research Center (LaRC) deterministic ionized particle transport code High charge (Z) and Energy TRaNsport (HZETRN), which propagates the GCR spectra for elements with charges (Z) in the range I aluminum equivalent approximation for a good polymeric shield material such as genetic polyethylene (PE). The shield thickness is represented by a 25 g/cm spherical shell. Although one could imagine the progression to greater

Spherical collapse in quintessence models with zero speed of sound

CERN Document Server

Creminelli, Paolo; Noreña, Jorge; Senatore, Leonardo; Vernizzi, Filippo

2010-01-01

We study the spherical collapse model in the presence of quintessence with zero speed of sound. This case is particularly motivated for w<-1 as it is required by stability. As pressure gradients are negligible, quintessence follows dark matter during the collapse. The spherical overdensity behaves as a separate closed FLRW universe, so that its evolution can be studied exactly. We derive the critical overdensity for collapse and we use the extended Press-Schechter theory to study how the clustering of quintessence affects the dark matter mass function. The effect is dominated by the modification of the linear dark matter growth function. A larger effect occurs on the total mass function, which includes the quintessence overdensities. Indeed, here quintessence constitutes a third component of virialized objects, together with baryons and dark matter, and contributes to the total halo mass by a fraction ~ (1+w) Omega_Q / Omega_m. This gives a distinctive modification of the total mass function at low redshif...

Structure of the strongly coupled classical plasma in the self-consistent mean spherical approximation

International Nuclear Information System (INIS)

Chaturvedi, D.K.; Senatore, G.; Tosi, M.P.

1980-10-01

An analytic theory is presented for the static structure factor of the one-component classical plasma at strong couplings. The theory combines the hard-core model of Gillan for short-range correlations in the Coulomb fluid with a semiempirical representation of intermediate-range correlations, through which the requirement of thermodynamic consistency on the ''compressibility'' and the known equation of state of the system are satisfied. Excellent agreement is found with the available computer simulation data on the structure of the fluid. The approach becomes inapplicable at intermediate and weak couplings where effects of penetration in the Coulomb hole of each particle become important. (author)

Gauge theories as string theories: the first results

International Nuclear Information System (INIS)

Gorsky, Aleksandr S

2005-01-01

The gauge/string theory duality in curved space is discussed mainly using a non-Abelian conformal N = 4 supersymmetric gauge theory and the theory of a closed superstring in the AdS 5 x S 5 metric as an example. It is shown that in the supergravity approximation, string duality yields the characteristics of a strong-coupling gauge theory. For a special shape of the contour, a Wilson loop expression is derived in the classical superstring approximation. The role of the hidden integrability in lower-loop calculations in gauge theory and in different approximations of string theory is discussed. It is demonstrated that in the large quantum-number limit, gauge theory operators can be described in terms of the dual string picture. Examples of metrics providing the dual description of gauge theories with broken conformal symmetry are presented, and formulations of the vacuum structure of such theories in terms of gravity are discussed. (reviews of topical problems)

The spherical harmonics method, II (application to problems with plane and spherical symmetry)

Energy Technology Data Exchange (ETDEWEB)

Mark, C

1958-12-15

The application of the spherical harmonic method to problems with plane or spherical symmetry is discussed in detail. The numerical results of some applications already made are included to indicate the degree of convergence obtained. Formulae for dealing with distributions of isotropic sources are developed. Tables useful in applying the method are given in Section 11. (author)

The relation between degree-2160 spectral models of Earth's gravitational and topographic potential: a guide on global correlation measures and their dependency on approximation effects

Science.gov (United States)

Hirt, Christian; Rexer, Moritz; Claessens, Sten; Rummel, Reiner

2017-10-01

Comparisons between high-degree models of the Earth's topographic and gravitational potential may give insight into the quality and resolution of the source data sets, provide feedback on the modelling techniques and help to better understand the gravity field composition. Degree correlations (cross-correlation coefficients) or reduction rates (quantifying the amount of topographic signal contained in the gravitational potential) are indicators used in a number of contemporary studies. However, depending on the modelling techniques and underlying levels of approximation, the correlation at high degrees may vary significantly, as do the conclusions drawn. The present paper addresses this problem by attempting to provide a guide on global correlation measures with particular emphasis on approximation effects and variants of topographic potential modelling. We investigate and discuss the impact of different effects (e.g., truncation of series expansions of the topographic potential, mass compression, ellipsoidal versus spherical approximation, ellipsoidal harmonic coefficient versus spherical harmonic coefficient (SHC) representation) on correlation measures. Our study demonstrates that the correlation coefficients are realistic only when the model's harmonic coefficients of a given degree are largely independent of the coefficients of other degrees, permitting degree-wise evaluations. This is the case, e.g., when both models are represented in terms of SHCs and spherical approximation (i.e. spherical arrangement of field-generating masses). Alternatively, a representation in ellipsoidal harmonics can be combined with ellipsoidal approximation. The usual ellipsoidal approximation level (i.e. ellipsoidal mass arrangement) is shown to bias correlation coefficients when SHCs are used. Importantly, gravity models from the International Centre for Global Earth Models (ICGEM) are inherently based on this approximation level. A transformation is presented that enables a

Self consistent field theory of virus assembly

Science.gov (United States)

Li, Siyu; Orland, Henri; Zandi, Roya

2018-04-01

The ground state dominance approximation (GSDA) has been extensively used to study the assembly of viral shells. In this work we employ the self-consistent field theory (SCFT) to investigate the adsorption of RNA onto positively charged spherical viral shells and examine the conditions when GSDA does not apply and SCFT has to be used to obtain a reliable solution. We find that there are two regimes in which GSDA does work. First, when the genomic RNA length is long enough compared to the capsid radius, and second, when the interaction between the genome and capsid is so strong that the genome is basically localized next to the wall. We find that for the case in which RNA is more or less distributed uniformly in the shell, regardless of the length of RNA, GSDA is not a good approximation. We observe that as the polymer-shell interaction becomes stronger, the energy gap between the ground state and first excited state increases and thus GSDA becomes a better approximation. We also present our results corresponding to the genome persistence length obtained through the tangent-tangent correlation length and show that it is zero in case of GSDA but is equal to the inverse of the energy gap when using SCFT.

Approximate analytical solution of two-dimensional multigroup P-3 equations

International Nuclear Information System (INIS)

Matausek, M.V.; Milosevic, M.

1981-01-01

Iterative solution of multigroup spherical harmonics equations reduces, in the P-3 approximation and in two-dimensional geometry, to a problem of solving an inhomogeneous system of eight ordinary first order differential equations. With appropriate boundary conditions, these equations have to be solved for each energy group and in each iteration step. The general solution of the corresponding homogeneous system of equations is known in analytical form. The present paper shows how the right-hand side of the system can be approximated in order to derive a particular solution and thus an approximate analytical expression for the general solution of the inhomogeneous system. This combined analytical-numerical approach was shown to have certain advantages compared to the finite-difference method or the Lie-series expansion method, which have been used to solve similar problems. (orig./RW) [de

Solutions for the conductivity of multi-coated spheres and spherically symmetric inclusion problems

Science.gov (United States)

Pham, Duc Chinh

2018-02-01

Variational results on the macroscopic conductivity (thermal, electrical, etc.) of the multi-coated sphere assemblage have been used to derive the explicit expression of the respective field (thermal, electrical, etc.) within the spheres in d dimensions (d=2,3). A differential substitution approach has been developed to construct various explicit expressions or determining equations for the effective spherically symmetric inclusion problems, which include those with radially variable conductivity, different radially variable transverse and normal conductivities, and those involving imperfect interfaces, in d dimensions. When the volume proportion of the outermost spherical shell increases toward 1, one obtains the respective exact results for the most important specific cases: the dilute solutions for the compound inhomogeneities suspended in a major matrix phase. Those dilute solution results are also needed for other effective medium approximation schemes.

A non-conforming 3D spherical harmonic transport solver

Energy Technology Data Exchange (ETDEWEB)

Van Criekingen, S. [Commissariat a l' Energie Atomique CEA-Saclay, DEN/DM2S/SERMA/LENR Bat 470, 91191 Gif-sur-Yvette, Cedex (France)

2006-07-01

A new 3D transport solver for the time-independent Boltzmann transport equation has been developed. This solver is based on the second-order even-parity form of the transport equation. The angular discretization is performed through the expansion of the angular neutron flux in spherical harmonics (PN method). The novelty of this solver is the use of non-conforming finite elements for the spatial discretization. Such elements lead to a discontinuous flux approximation. This interface continuity requirement relaxation property is shared with mixed-dual formulations such as the ones based on Raviart-Thomas finite elements. Encouraging numerical results are presented. (authors)

A non-conforming 3D spherical harmonic transport solver

International Nuclear Information System (INIS)

Van Criekingen, S.

2006-01-01

A new 3D transport solver for the time-independent Boltzmann transport equation has been developed. This solver is based on the second-order even-parity form of the transport equation. The angular discretization is performed through the expansion of the angular neutron flux in spherical harmonics (PN method). The novelty of this solver is the use of non-conforming finite elements for the spatial discretization. Such elements lead to a discontinuous flux approximation. This interface continuity requirement relaxation property is shared with mixed-dual formulations such as the ones based on Raviart-Thomas finite elements. Encouraging numerical results are presented. (authors)

On coordinates and coordinate transformation in Einstein's theory of gravitation

International Nuclear Information System (INIS)

Chou Peiyuan

1983-01-01

This investigation is a further exposition of the significance of coordinates and their transformation in Einstein's theory of gravitation. The author considers the static axisymmetric field as an example, starts with its metric in the cylindrical coordinates, transforms this metric and the field equations into the Weyl-Levi-Civita system of coordinates, and supplements them with the harmonic condition. Both of the field equations and the harmonic condition are then transformed back to the original Cartesian system. Solutions for the static fields of an infinite plane with uniform surface density and an infinite rod with uniform linear density of matter, and of a body with spherical symmetry, are obtained again to show the necessity of the harmonic condition in their solutions. The fact that under the harmonic condition the solutions of the field equations for these problems contain their corresponding Newtonian potentials as approximations, is a strong support to the argument that the harmonic condition should be a physical supplement to Einstein's theory of gravitation. (Auth.)

Free vibration analysis of delaminated composite shells using different shell theories

International Nuclear Information System (INIS)

Nanda, Namita; Sahu, S.K.

2012-01-01

Free vibration response of laminated composite shells with delamination is presented using the finite element method based on first order shear deformation theory. The shell theory used is the extension of dynamic, shear deformable theory according to the Sanders' first approximation for doubly curved shells, which can be reduced to Love's and Donnell's theories by means of tracers. An eight-noded C 0 continuity, isoparametric quadrilateral element with five degrees of freedom per node is used in the formulation. For modeling the delamination, multipoint constraint algorithm is incorporated in the finite element code. The natural frequencies of the delaminated cylindrical (CYL), spherical (SPH) and hyperbolic paraboloid (HYP) shells are determined by using the above mentioned shell theories, namely Sanders', Love's, and Donnell's. The validity of the present approach is established by comparing the authors' results with those available in the literature. Additional studies on free vibration response of CYL, SPH and HYP shells are conducted to assess the effects of delamination size and number of layers considering all three shell theories. It is shown that shell theories according to Sanders and Love always predict practically identical frequencies. Donnell's theory gives reliable results only for shallow shells. Moreover, the natural frequency is found to be very sensitive to delamination size and number of layers in the shell.

Angular shift in scattering the spherical analogous of the Goos-Hanchen effect

International Nuclear Information System (INIS)

Ferrari Junior, N.F.; Nussenzveig, H.M.

1983-01-01

A generalization of the time and spatial delay concept is obtained, for the scattering of transversaly incident beam restricted by a spherically symmetric scatterer using the methods of the complex angular momentum, valid for the angular momentum and angle conjufated variable pair. The result obtained is known validity domain, within the semiclassical approximation. Applied to the scttering problem in the high frequency limit by a transparent sphere with refractive index N [pt

On Covering Approximation Subspaces

Directory of Open Access Journals (Sweden)

Xun Ge

2009-06-01

Full Text Available Let (U';C' be a subspace of a covering approximation space (U;C and X⊂U'. In this paper, we show that and B'(X⊂B(X∩U'. Also, iff (U;C has Property Multiplication. Furthermore, some connections between outer (resp. inner definable subsets in (U;C and outer (resp. inner definable subsets in (U';C' are established. These results answer a question on covering approximation subspace posed by J. Li, and are helpful to obtain further applications of Pawlak rough set theory in pattern recognition and artificial intelligence.

Spherical tuned liquid damper for vibration control in wind turbines

DEFF Research Database (Denmark)

Chen, Jun-Ling; Georgakis, Christos T.

2015-01-01

table. The experimental results indicated that the spherical TLD could effectively improve the damping capacity of the test model. The standard deviation of the dynamic response could be effectively reduced when the excitation frequency was approximately equal to its fundamental frequency. For overspeed...... and extreme operating gust load cases, the standard deviations of the dynamic responses were reduced more than 40% when the liquid mass was about 2% of the generalized mass; for parking load cases, the corresponding standard deviation was reduced more than 50% when the liquid mass was only 1...

Improved streaming analysis technique: spherical harmonics expansion of albedo data

International Nuclear Information System (INIS)

Albert, T.E.; Simmons, G.L.

1979-01-01

An improved albedo scattering technique was implemented with a three-dimensional Monte Carlo transport code for use in analyzing radiation streaming problems. The improvement was based on a shifted spherical Harmonics expansion of the doubly differential albedo data base. The result of the improvement was a factor of 3 to 10 reduction in data storage requirements and approximately a factor of 3 to 6 increase in computational speed. Comparisons of results obtained using the technique with measurements are shown for neutron streaming in one- and two-legged square concrete ducts

Analytic approximations to hamiltonian lattice field theories. Pt. 2

International Nuclear Information System (INIS)

Surany, P.

1983-01-01

It is shown that at weak coupling physical quantities in hamiltonian U(1) lattice gauge (or global symmetric) theories of arbitrary dimension are provided as expectation values in a d - 1 dimensional lagrangian Z(2) gauge (or spin) theory with calculable long-range interactions. Confinement and the existence of a magnetic mass gap are equivalent to the existence of infinite-range plaquette-plaquette (or link-link) correlations in the spin field. The existence of infinite range correlations is simply related to the dimension of the lattice and the transformation property of the order parameter. As expected, only the d = 2 + 1 U(1) gauge theory confines electric charges at all non-vanishing coupling. (orig.)

The Hartree-Fock seniority approximation

International Nuclear Information System (INIS)

Gomez, J.M.G.; Prieto, C.

1986-01-01

A new self-consistent method is used to take into account the mean-field and the pairing correlations in nuclei at the same time. We call it the Hartree-Fock seniority approximation, because the long-range and short-range correlations are treated in the frameworks of Hartree-Fock theory and the seniority scheme. The method is developed in detail for a minimum-seniority variational wave function in the coordinate representation for an effective interaction of the Skyrme type. An advantage of the present approach over the Hartree-Fock-Bogoliubov theory is the exact conservation of angular momentum and particle number. Furthermore, the computational effort required in the Hartree-Fock seniority approximation is similar to that ofthe pure Hartree-Fock picture. Some numerical calculations for Ca isotopes are presented. (orig.)

Some properties of the statistical models of the spherical Friedman world

International Nuclear Information System (INIS)

Rumyantseva, E.N.

1981-01-01

Considered are some properties of the statistical model of the spherical Friedman world filled with quantum gas of massless particles the spin of which can be equal to 0, 1/2, 1. Obtained are approximate expressions for a number of particles of Fermi- and Bose-gas and for the radius of the world taking into account mainly the dependence on the spin. The dependence of the number of particles on the radius of the world and temperature of the gas is illustrated [ru

Nonlinear theory of magnetohydrodynamic flows of a compressible fluid in the shallow water approximation

Energy Technology Data Exchange (ETDEWEB)

Klimachkov, D. A., E-mail: klimchakovdmitry@gmail.com; Petrosyan, A. S., E-mail: apetrosy@iki.rssi.ru [Russian Academy of Sciences, Space Research Institute (Russian Federation)

2016-09-15

Shallow water magnetohydrodynamic (MHD) theory describing incompressible flows of plasma is generalized to the case of compressible flows. A system of MHD equations is obtained that describes the flow of a thin layer of compressible rotating plasma in a gravitational field in the shallow water approximation. The system of quasilinear hyperbolic equations obtained admits a complete simple wave analysis and a solution to the initial discontinuity decay problem in the simplest version of nonrotating flows. In the new equations, sound waves are filtered out, and the dependence of density on pressure on large scales is taken into account that describes static compressibility phenomena. In the equations obtained, the mass conservation law is formulated for a variable that nontrivially depends on the shape of the lower boundary, the characteristic vertical scale of the flow, and the scale of heights at which the variation of density becomes significant. A simple wave theory is developed for the system of equations obtained. All self-similar discontinuous solutions and all continuous centered self-similar solutions of the system are obtained. The initial discontinuity decay problem is solved explicitly for compressible MHD equations in the shallow water approximation. It is shown that there exist five different configurations that provide a solution to the initial discontinuity decay problem. For each configuration, conditions are found that are necessary and sufficient for its implementation. Differences between incompressible and compressible cases are analyzed. In spite of the formal similarity between the solutions in the classical case of MHD flows of an incompressible and compressible fluids, the nonlinear dynamics described by the solutions are essentially different due to the difference in the expressions for the squared propagation velocity of weak perturbations. In addition, the solutions obtained describe new physical phenomena related to the dependence of the

Dynamic response of sand particles impacted by a rigid spherical object

Science.gov (United States)

Youplao, P.; Takita, A.; Nasbey, H.; Yupapin, P. P.; Fujii, Y.

2018-06-01

A method for measuring the dynamic impact responses that acting on a spherical object while dropping and colliding with dried sand, such as the velocity, displacement, acceleration, and resultant force, is presented and discussed. In the experiment, a Michelson-type laser interferometer is employed to obtain the velocity of the spherical stainless steel object. Then the obtained time velocity profile is used to calculate the acceleration, the displacement, and the inertial force acting on the observed sand particles. Furthermore, a high-speed camera is employed to observe the behavior of the sand during the collision. From the experimental results with the sampling interval for frequencies calculation of 1 ms, the combined standard uncertainty in the instantaneous value of the impact force acts on the observed object is obtained and approximated to 0.49 N, which is related to a corresponding 4.07% of the maximum value at 12.05 N of the impact force.

Cylindrical and spherical solitary waves in an electron-acoustic plasma with vortex electron distribution

Science.gov (United States)

Demiray, Hilmi; El-Zahar, Essam R.

2018-04-01

We consider the nonlinear propagation of electron-acoustic waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions. The basic nonlinear equations of the above described plasma are re-examined in the cylindrical (spherical) coordinates by employing the reductive perturbation technique. The modified cylindrical (spherical) KdV equation with fractional power nonlinearity is obtained as the evolution equation. Due to the nature of nonlinearity, this evolution equation cannot be reduced to the conventional KdV equation. A new family of closed form analytical approximate solution to the evolution equation and a comparison with numerical solution are presented and the results are depicted in some 2D and 3D figures. The results reveal that both solutions are in good agreement and the method can be used to obtain a new progressive wave solution for such evolution equations. Moreover, the resulting closed form analytical solution allows us to carry out a parametric study to investigate the effect of the physical parameters on the solution behavior of the modified cylindrical (spherical) KdV equation.

Molecular Excitation Energies from Time-Dependent Density Functional Theory Employing Random-Phase Approximation Hessians with Exact Exchange.

Science.gov (United States)

Heßelmann, Andreas

2015-04-14

Molecular excitation energies have been calculated with time-dependent density-functional theory (TDDFT) using random-phase approximation Hessians augmented with exact exchange contributions in various orders. It has been observed that this approach yields fairly accurate local valence excitations if combined with accurate asymptotically corrected exchange-correlation potentials used in the ground-state Kohn-Sham calculations. The inclusion of long-range particle-particle with hole-hole interactions in the kernel leads to errors of 0.14 eV only for the lowest excitations of a selection of three alkene, three carbonyl, and five azabenzene molecules, thus surpassing the accuracy of a number of common TDDFT and even some wave function correlation methods. In the case of long-range charge-transfer excitations, the method typically underestimates accurate reference excitation energies by 8% on average, which is better than with standard hybrid-GGA functionals but worse compared to range-separated functional approximations.

Approximate Controllability of Semilinear Neutral Stochastic Integrodifferential Inclusions with Infinite Delay

Directory of Open Access Journals (Sweden)

Meili Li

2015-01-01

Full Text Available The approximate controllability of semilinear neutral stochastic integrodifferential inclusions with infinite delay in an abstract space is studied. Sufficient conditions are established for the approximate controllability. The results are obtained by using the theory of analytic resolvent operator, the fractional power theory, and the theorem of nonlinear alternative for Kakutani maps. Finally, an example is provided to illustrate the theory.

On the mathematical treatment of the Born-Oppenheimer approximation

International Nuclear Information System (INIS)

Jecko, Thierry

2014-01-01

Motivated by the paper by Sutcliffe and Woolley [“On the quantum theory of molecules,” J. Chem. Phys. 137, 22A544 (2012)], we present the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation for molecules. Based on mathematical works on this approximation for molecular bound states, in scattering theory, in resonance theory, and for short time evolution, we give an overview of some rigorous results obtained up to now. We also point out the main difficulties mathematicians are trying to overcome and speculate on further developments. The mathematical approach does not fit exactly to the common use of the approximation in Physics and Chemistry. We criticize the latter and comment on the differences, contributing in this way to the discussion on the Born-Oppenheimer approximation initiated by Sutcliffe and Woolley. The paper neither contains mathematical statements nor proofs. Instead, we try to make accessible mathematically rigourous results on the subject to researchers in Quantum Chemistry or Physics

On the mathematical treatment of the Born-Oppenheimer approximation

Energy Technology Data Exchange (ETDEWEB)

Jecko, Thierry, E-mail: thierry.jecko@u-cergy.fr [AGM, UMR 8088 du CNRS, Université de Cergy-Pontoise, Département de mathématiques, site de Saint Martin, 2 avenue Adolphe Chauvin, F-95000 Pontoise (France)

2014-05-15

Motivated by the paper by Sutcliffe and Woolley [“On the quantum theory of molecules,” J. Chem. Phys. 137, 22A544 (2012)], we present the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation for molecules. Based on mathematical works on this approximation for molecular bound states, in scattering theory, in resonance theory, and for short time evolution, we give an overview of some rigorous results obtained up to now. We also point out the main difficulties mathematicians are trying to overcome and speculate on further developments. The mathematical approach does not fit exactly to the common use of the approximation in Physics and Chemistry. We criticize the latter and comment on the differences, contributing in this way to the discussion on the Born-Oppenheimer approximation initiated by Sutcliffe and Woolley. The paper neither contains mathematical statements nor proofs. Instead, we try to make accessible mathematically rigourous results on the subject to researchers in Quantum Chemistry or Physics.

Spherical cavity-expansion forcing function in PRONTO 3D for application to penetration problems

Energy Technology Data Exchange (ETDEWEB)

Warren, T.L.; Tabbara, M.R.

1997-05-01

In certain penetration events the primary mode of deformation of the target can be approximated by known analytical expressions. In the context of an analysis code, this approximation eliminates the need for modeling the target as well as the need for a contact algorithm. This technique substantially reduces execution time. In this spirit, a forcing function which is derived from a spherical-cavity expansion analysis has been implemented in PRONTO 3D. This implementation is capable of computing the structural and component responses of a projectile due to three dimensional penetration events. Sample problems demonstrate good agreement with experimental and analytical results.

High beta, Long Pulse, Bootstrap Sustained Scenarios on the National Spherical Torus Experiment (NSTX)

International Nuclear Information System (INIS)

Gates, D.A.

2003-01-01

Long-pulse, high-beta scenarios have been established on the National Spherical Torus Experiment (NSTX). Beta(sub)t(always equal to 2μ(sub)0· /B 2 (sub)t0) ∼ 35% has been achieved during transient discharges. The machine improvements that lead to these results, including error field reduction and high-temperature bakeout of plasma-facing components are described. The highest Beta(sub)t plasmas have high triangularity (delta = 0.8) and elongation (k = 2.0) at low-aspect ratio A always equal to R/a = 1.4. The strong shaping permits large values of normalized current, I(sub)N(always equal to I(sub)p /(aB(sub)t0)) approximately equal to 6 while maintaining moderate values of q(sub)95 = 4. Long-pulse discharges up to 1 sec in duration have been achieved with substantial bootstrap current. The total noninductive current drive can be as high as 60%, comprised of 50% bootstrap current and ∼10% neutral-beam current drive. The confinement enhancement factor H89P is in excess of 2.7. Beta(sub)N * H(sub)89P approximately or greater than 15 has been maintained for 8 * tau(sub)E ∼ 1.6 * tau(sub)CR, where tau(sub)CR is the relaxation time of the first radial moment of the toroidal current density. The ion temperature for these plasmas is significantly higher than that predicted by neoclassical theory

Stellar wind theory

International Nuclear Information System (INIS)

Summers, D.

1980-01-01

The theory of stellar winds as given by the equations of classical fluid dynamics is considered. The equations of momentum and energy describing a steady, spherically symmetric, heat-conducting, viscous stellar wind are cast in a dimensionless form which involves a thermal conduction parameter E and a viscosity parameter γ. An asymptotic analysis is carried out, for fixed γ, in the cases E→O and E→infinity (corresponding to small and large thermal conductivity, respectively), and it is found that it is possible to construct critical solutions for the wind velocity and temperature over the entire flow. The E→O solution represents a wind which emanates from the star at low, subsonic speeds, accelerates through a sonic point, and then approaches a constant asymptotic speed, with its temperature varying as r/sup -4/3/ at large distances r from the star; the E→infinity solution represents a wind which, after reaching an approximately constant speed, with temperature varying as r/sup -2/7/, decelerates through a diffuse shock and approaches a finite pressure at infinity. A categorization is made of all critical stellar wind solutions for given values of γ and E, and actual numerical examples are given. Numerical solutions are obtained by integrating upstream 'from infinity' from initial values of the flow parameters given by appropriate asymptotic expansions. The role of viscosity in stellar wind theory is discussed, viscous and inviscid stellar wind solutions are compared, and it is suggested that with certain limitations, the theory presented may be useful in analyzing winds from solar-type stars

Theory and observation of compressional Alfven eigenmodes in low aspect ratio plasma

International Nuclear Information System (INIS)

Gorelenkov, N.N.

2002-01-01

A new theory of radially and poloidally localized Compressional Alfven Eigenmodes (CAE) in low aspect ratio plasma is reported. The theory is applied to identify recently observed instabilities in the MHz frequency range in National Spherical Torus experiments (NSTX). The frequency of observed CAEs is correlated with the characteristic Alfven velocity of the plasma. The observed high frequency modes are explained as CAEs driven by energetic beam ions. The CAE frequency is determined by the Alfven frequency at the mode location on the low field side of the plasma and is given approximately by ω CAE v A m=r, where m is the poloidal mode number, and r is the local minor radius. CAEs are destabilized by free energy in the energetic ion velocity space gradient via Doppler shifted cyclotron resonance with beam ions. Properties of the CAE instability driven by different NBI ion distributions are presented. (author)

Polarizability and binding energy of a shallow donor in spherical quantum dot-quantum well (QD-QW)

Science.gov (United States)

Rahmani, K.; Chrafih, Y.; M’Zred, S.; Janati, S.; Zorkani, I.; Jorio, A.; Mmadi, A.

2018-03-01

The polarizability and the binding energy is estimated for a shallow donor confined to move in inhomogeneous quantum dots (CdS/HgS/CdS). In this work, the Hass variational method within the effective mass approximation in used in the case of an infinitely deep well. The polarizability and the binding energy depend on the inner and the outer radius of the QDQW, also it depends strongly on the donor position. It’s found that the stark effect is more important when the impurity is located at the center of the (QDQW) and becomes less important when the donor moves toward the extremities of the spherical layer. When the electric field increases, the binding energy and the polarizability decreases. Its effects is more pronounced when the impurity is placed on the center of the spherical layer and decrease when the donor move toward extremities of this spherical layer. We have demonstrated the existence of a critical value {≤ft( {{{{R_1}} \\over {{R_2}}}} \\right)cri} which can be used to distinguish the tree dimension confinement from the spherical surface confinement and it’s may be important for the nanofabrication techniques.

Computation of higher spherical harmonics moments of the angular flux for neutron transport problems in spherical geometry

International Nuclear Information System (INIS)

Sahni, D.C.; Sharma, A.

2000-01-01

The integral form of one-speed, spherically symmetric neutron transport equation with isotropic scattering is considered. Two standard problems are solved using normal mode expansion technique. The expansion coefficients are obtained by solving their singular integral equations. It is shown that these expansion coefficients provide a representation of all spherical harmonics moments of the angular flux as a superposition of Bessel functions. It is seen that large errors occur in the computation of higher moments unless we take certain precautions. The reasons for this phenomenon are explained. They throw some light on the failure of spherical harmonics method in treating spherical geometry problems as observed by Aronsson

Statistical Mechanics of Thin Spherical Shells

Directory of Open Access Journals (Sweden)

Andrej Košmrlj

2017-01-01

Full Text Available We explore how thermal fluctuations affect the mechanics of thin amorphous spherical shells. In flat membranes with a shear modulus, thermal fluctuations increase the bending rigidity and reduce the in-plane elastic moduli in a scale-dependent fashion. This is still true for spherical shells. However, the additional coupling between the shell curvature, the local in-plane stretching modes, and the local out-of-plane undulations leads to novel phenomena. In spherical shells, thermal fluctuations produce a radius-dependent negative effective surface tension, equivalent to applying an inward external pressure. By adapting renormalization group calculations to allow for a spherical background curvature, we show that while small spherical shells are stable, sufficiently large shells are crushed by this thermally generated “pressure.” Such shells can be stabilized by an outward osmotic pressure, but the effective shell size grows nonlinearly with increasing outward pressure, with the same universal power-law exponent that characterizes the response of fluctuating flat membranes to a uniform tension.

Pade approximants in field theory: pion and kaon systems

International Nuclear Information System (INIS)

Zinn-Justin, J.

1969-01-01

We construct the Pade approximants of the S-matrix, starting from the perturbation series, in the case of two body pion and kaon systems. We have three parameters. The seven lowest lying two body resonances (ρ, K * (890), φ, K * (1420), f 0 , f', A 2 ) are obtained within a few per cent of their actual masses. The Regge trajectories are rising, the intercepts of the ρ and f 0 agree well with the experimental values. In the appendices we give some properties and applications of the Pade approximants. (author) [fr

New methods in linear transport theory. Part of a coordinated programme on methods in neutron transport theory

International Nuclear Information System (INIS)

Mika, J.

1975-09-01

Originally the work was oriented towards two main topics: a) difference and integral methods in neutron transport theory. Two computers were used for numerical calculations GIER and CYBER-72. During the first year the main effort was shifted towards basic theoretical investigations. At the first step the ANIS code was adopted and later modified to check various finite difference approaches against each other. Then the general finite element method and the singular perturbation method were developed. The analysis of singularities of the one-dimensional neutron transport equation in spherical geometry has been done and presented. Later the same analysis for the case of cylindrical symmetry has been carried out. The second and the third year programme included the following topics: 1) finite difference methods in stationary neutron transport theory; 2)mathematical fundamentals of approximate methods for solving the transport equation; 3) singular perturbation method for the time-dependent transport equation; 4) investigation of various iterative procedures in reactor calculations. This investigation will help to better understanding of the mathematical basis for existing and developed numerical methods resulting in more effective algorithms for reactor computer codes

The discrete Planck spectrum of a spherical cavity

International Nuclear Information System (INIS)

Vlad, V.I.; Ionescu-Pallas, N.

1999-03-01

The energy spectrum of black body radiation at the absolute temperature, T, in an ideal spherical cavity of radius, R, is studied. The departures from the classical predictions of Planck's theory, due to the discrete energies of the radiation quanta confined inside the cavity, depend on the adiabatic invariant RT and are significant for RT ≤ 40 cm · K. Special attention was paid to evidence strong changes in the spectrum intensities, forbidden bands of frequency, as well as major modifications of the total energy for RT ≤ 2 cm · K. Similar effects were present in the case of a cubic cavity. (author)

The free energy of spherical bubbles in lattice SU(3) gauge theory

CERN Document Server

Kajantie, Keijo; Rummukainen, K; Karkkainen, Leo

1992-01-01

We study the coefficients of the expansion $F(R) = 1/3 c_3 R^3 + 1/2 c_2 R^2 + c_1 R$ of the free energy of spherical bubbles at $T=T_c$ in pure glue QCD using lattice Monte Carlo techniques. The coefficient $c_3$ vanishes at $T=T_c$ and our results suggest that the sign and the order of magnitude of $c_1$ is in agreement with the value $c_1=\\pm 32\\pi T_c^2/9$ (- for hadronic bubbles in quark phase, + for quark bubbles in hadronic phase) computed by Mardor and Svetitsky from the MIT bag model. The parameter $c_2$ is small in agreement with earlier determinations.

Relativistic properties of spherical diodes with a radial electron flux

International Nuclear Information System (INIS)

Chetvertkov, V.I.

1987-01-01

Forward and backward electron diodes with concentric spherical electrodes (inner cathode, outer anode or vice versa) are considered under the assumption that the emission is limited by the space charge and the guiding magnetic field is predominantly radial within a region of solid angle α f < 4π bounding the electron flux. The Poisson equations for the relativistic factor γ are solved for generalized model dependences. Ultrarelativistic and new nonrelativistic solutions are found, and analytic approximations to the solution near the cathode are used to carry out numerical calculations. The characteristics of forward and backward diodes turn out to be related to the exact solutions for a planar diode. Accurate approximations are found for calculating the diode parameters in a wide range of voltages; they can also be used to check the validity of the 3/2 laws and the ultrarelativistic solutions

Quantum mean-field approximations for nuclear bound states and tunneling

International Nuclear Information System (INIS)

Negele, J.W.; Levit, S.; Paltiel, Z.; Massachusetts Inst. of Tech., Cambridge

1979-01-01

A conceptual framework has been presented in which observables are approximated in terms of a self-consistent quantum mean-field theory. Since the SPA (Stationary Phase Approximation) determines the optimal mean field to approximate a given observable, it is natural that when one changes the observable, the best mean field to describe it changes as well. Although the theory superficially appears applicable to any observable expressible in terms of an evolution operator, for example an S-matrix element, one would have to go far beyond the SPA to adequately approximate the overlap of two many-body wave functions. The most salient open problems thus concern quantitative assessment of the accuracy of the SPA, reformulation of the theory to accomodate hard cores, and selection of sensible expectation values of few-body operators to address in scattering problems

Comparison of calculations of a reflected reactor with diffusion, SN and Monte Carlo codes

International Nuclear Information System (INIS)

McGregor, B.

1975-01-01

A diffusion theory code, POW, was compared with a Monte Carlo transport theory code, KENO, for the calculation of a small C/ 235 U cylindrical core with a graphite reflector. The calculated multiplication factors were in good agreement but differences were noted in region-averaged group fluxes. A one-dimensional spherical geometry was devised to approximate cylindrical geometry. Differences similar to those already observed were noted when the region-averaged fluxes from a diffusion theory (POW) calculation were compared with an SN transport theory (ANAUSN) calculation for the spherical model. Calculations made with SN and Monte Carlo transport codes were in good agreement. It was concluded that observed flux differences were attributable to the POW code, and were not inconsistent with inherent diffusion theory approximations. (author)

Tight-binding approximations to time-dependent density functional theory — A fast approach for the calculation of electronically excited states

Energy Technology Data Exchange (ETDEWEB)

Rüger, Robert, E-mail: rueger@scm.com [Scientific Computing & Modelling NV, De Boelelaan 1083, 1081 HV Amsterdam (Netherlands); Department of Theoretical Chemistry, Vrije Universiteit Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam (Netherlands); Wilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie, Linnéstr. 2, 04103 Leipzig (Germany); Lenthe, Erik van [Scientific Computing & Modelling NV, De Boelelaan 1083, 1081 HV Amsterdam (Netherlands); Heine, Thomas [Wilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie, Linnéstr. 2, 04103 Leipzig (Germany); Visscher, Lucas [Department of Theoretical Chemistry, Vrije Universiteit Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam (Netherlands)

2016-05-14

We propose a new method of calculating electronically excited states that combines a density functional theory based ground state calculation with a linear response treatment that employs approximations used in the time-dependent density functional based tight binding (TD-DFTB) approach. The new method termed time-dependent density functional theory TD-DFT+TB does not rely on the DFTB parametrization and is therefore applicable to systems involving all combinations of elements. We show that the new method yields UV/Vis absorption spectra that are in excellent agreement with computationally much more expensive TD-DFT calculations. Errors in vertical excitation energies are reduced by a factor of two compared to TD-DFTB.

Parabolic versus spherical partial cross sections for photoionization excitation of He near threshold

International Nuclear Information System (INIS)

Bouri, C.; Selles, P.; Malegat, L.; Kwato Njock, M. G.

2006-01-01

Spherical and parabolic partial cross sections and asymmetry parameters, defined in the ejected electron frame, are presented for photoionization excitation of the helium atom at 0.1 eV above its double ionization threshold. A quantitative law giving the dominant spherical partial wave l dom for each excitation level n is obtained. The parabolic partial cross sections are shown to satisfy the same approximate selection rules as the related Rydberg series of doubly excited states (K,T) n A . The analysis of radial and angular correlations reveals the close relationship between double excitation, ionization excitation, and double ionization. Opposite to a widespread belief, the observed value of the asymmetry parameter is shown to result from the interplay of radial correlations and symmetry constraints, irrespective of angular correlations. Finally, the measurement of parabolic partial cross sections is proposed as a challenge to experimentalists

Unified field theory on the basis of the projective theory of relativity

International Nuclear Information System (INIS)

Lessner, G.

1982-01-01

A unified field theory is developed on the basis of the five-dimensional vacuum equations R/sub munu/ = 0 in the projective theory of relativity. The four-dimensional field equations following from R/sub munu/ = 0 by projection are a generalized Einstein-Maxwell theory, for which the generalization is given by a scalar field. The particle concept based on these equations represents the intrinsic particle properties, which are the rest mass, or the energy in case of photons and neutrinos, the charge and the spin by integrals of the field distribution extended over spacelike hypersurfaces. The energy concept is based on Moller's energy-momentum complex. Moller's argument against his energy-momentum complex is discussed and refuted. The spin concept is derived from the axial symmetry of the field distribution. The stationary axially symmetric field is studied in detail. In the spherically symmetric static case the solutions of the field equations are given and investigated for their particle properties. It is shown that one and only one type of solution yields a good approach to the distribution of charge and rest mass in the proton. However, none of the spherically symmetric solutions represents the electron

Spherical spacelike geometries in static spherically symmetric spacetimes: Generalized Painlevè–Gullstrand coordinates, foliation, and embedding

Energy Technology Data Exchange (ETDEWEB)

Akbar, M.M., E-mail: akbar@utdallas.edu

2017-06-10

It is well known that static spherically symmetric spacetimes can admit foliations by flat spacelike hypersurfaces, which are best described in terms of the Painlevè–Gullstrand coordinates. The uniqueness and existence of such foliations were addressed earlier. In this paper, we prove, purely geometrically, that any possible foliation of a static spherically symmetric spacetime by an arbitrary codimension-one spherical spacelike geometry, up to time translation and rotation, is unique, and we find the algebraic condition under which it exists. This leads us to what can be considered as the most natural generalization of the Painlevè–Gullstrand coordinate system for static spherically symmetric metrics, which, in turn, makes it easy to derive generic conclusions on foliation and to study specific cases as well as to easily reproduce previously obtained generalizations as special cases. In particular, we note that the existence of foliation by flat hypersurfaces guarantees the existence of foliation by hypersurfaces whose Ricci curvature tensor is everywhere non-positive (constant negative curvature is a special case). The study of uniqueness and the existence concurrently solves the question of embeddability of a spherical spacelike geometry in one-dimensional higher static spherically symmetric spacetimes, and this produces known and new results geometrically, without having to go through the momentum and Hamiltonian constraints.

Optical Response of CeB_6 Nanoparticles with Different Sizes and Shapes from Discrete-Dipole Approximation

International Nuclear Information System (INIS)

Chao Luo-Meng; Bao Li-Hong; Tegus, O.

2015-01-01

The discrete dipole approximation is used to investigate the optical response of CeB_6 nanoparticles with different sizes and different shapes. The extinction valley in the visible light range becomes narrower and the extinction peak at the near infrared region (NIR) is red-shifted with the increasing particle size. In addition, the extinction peak value of the spherical particle decreases more rapidly than that of cubic-shaped particle with an increase in the particle size, and the cubic-shaped particles exhibit better performance on blocking NIR radiation than spherical-shaped particles. The calculation results coincide well with the reported experimental results. (paper)

Charging of nonspherical macroparticles in a plasma

Science.gov (United States)

Holgate, J. T.; Coppins, M.

2016-03-01

The current theories of macroparticle charging in a plasma are limited to spheres, and are unsuitable for the multitude of nonspherical objects existing in astrophysical, atmospheric, laboratory, and fusion plasmas. This paper extends the most widely used spherical charging theory, orbit motion limited theory, to spheroids and, as such, provides a comprehensive study of the charging of nonspherical objects in a plasma. The spherical charging theory is shown to be a reasonable approximation for a considerable range of spheroids. However, the electric potential of highly elongated spheroids can be almost twice the spherical value. Furthermore, the total charge on the spheroids increases by a significantly larger factor than their potential.

Spiral CT manifestations of spherical pneumonia

International Nuclear Information System (INIS)

Li Xiaohong; Yang Hongwei; Xu Chunmin; Qin Xiu

2008-01-01

Objective: To explore the Spiral CT manifestations and differential diagnosis of spherical pneumonia. Methods: 18 cases of spherical pneumonia and 20 cases of peripheral pulmonary carcinoma were selected, both of them were confirmed by clinic and/or pathology. The SCT findings of both groups were compared retrospectively. Results: Main spiral CT findings of spherical pneumonia were showed as followings: square or triangular lesions adjacent to pleura; with irregular shape, blurry, slightly lobulated margin, sometimes with halo sign. Small inflammatory patches and intensified vascular markings around the lesions were seen. Lesions became smaller or vanished after short-term anti-inflammatory treatment. Conclusion: Spherical pneumonia showed some characteristics on Spiral CT scan, which are helpful in diagnosis and differential diagnosis of this disease. (authors)

Non-conformal contact mechanical characteristic analysis on spherical components

Energy Technology Data Exchange (ETDEWEB)

Zhen-zhi, G.; Bin, H.; Zheng-ming, G.; Feng-mei, Y.; Jin, Q [The 2. Artillery Engineering Univ., Xi' an (China)

2017-03-15

Non-conformal spherical-contact mechanical problems is a three-dimensional coordination or similar to the coordination spherical contact. Due to the complexity of the problem of spherical-contact and difficulties of solving higher-order partial differential equations, problems of three-dimensional coordination or similar to the coordination spherical-contact is still no exact analytical method for solving. It is based on three-dimensional taper model is proposed a model based on the contour surface of the spherical contact and concluded of the formula of the contact pressure and constructed of finite element model by contact pressure distribution under the non-conformal spherical. The results shows spherical contact model can reflect non-conformal spherical-contacting mechanical problems more than taper-contacting model, and apply for the actual project.

Nonlinear many-body reaction theories from nuclear mean field approximations

International Nuclear Information System (INIS)

Griffin, J.J.

1983-01-01

Several methods of utilizing nonlinear mean field propagation in time to describe nuclear reaction have been studied. The property of physical asymptoticity is analyzed in this paper, which guarantees that the prediction by a reaction theory for the physical measurement of internal fragment properties shall not depend upon the precise location of the measuring apparatus. The physical asymptoticity is guaranteed in the Schroedinger collision theory of a scuttering system with translationally invariant interaction by the constancy of the S-matrix elements and by the translational invariance of the internal motion for well-separated fragments. Both conditions are necessary for the physical asymptoticity. The channel asymptotic single-determinantal propagation can be described by the Dirac-TDHF (time dependent Hartree-Fock) time evolution. A new asymptotic Hartree-Fock stationary phase (AHFSP) description together with the S-matrix time-dependent Hartree-Fock (TD-S-HF) theory constitute the second example of a physically asymptotic nonlinear many-body reaction theory. A review of nonlinear mean field many-body reaction theories shows that initial value TDHF is non-asymptotic. The TD-S-HF theory is asymptotic by the construction. The gauge invariant periodic quantized solution of the exact Schroedinger problem has been considered to test whether it includes all of the exact eigenfunctions as it ought to. It did, but included as well an infinity of all spurions solutions. (Kato, T.)

Application of the nuclear field theory to superfluid nuclei

International Nuclear Information System (INIS)

Reinhardt, H.

1980-01-01

The quasiparticle-phonon multiplet of superfluid spherical nuclei is investigated in the framework of the nuclear field theory (NFT), using the pairing plus quadrupole force. In leading order of the NFT expansion there exists a simple relation between the energy splitting of the multiplet and the ground state B(E lambda) transitions from the multiplet. This relation states that the reduced matrix elements for the B(E lambda) transition decrease linearly with increasing energies of the multiplet states. The extent to which this relation is fulfilled by available experimental data is checked. The influence of the spurious correlations involved in the NFT treatment due to the BCS approximation is estimated. The numerical calculations are performed for 93 Nb where the ground state B(E lambda) transitions are measured for all multiplet states. (orig.)

Connection between strong and weak coupling in the mean spherical model in 1 + 1 dimensions

International Nuclear Information System (INIS)

Banks, J.L.

1980-01-01

I extend the strong-coupling expansion obtained by Srednicki, for the β-function of the mean spherical model in 1 + 1 dimensions, in the hamiltonian formulation. I use ordinary and two-point Pade approximants to extrapolate this result to weak coupling. I find a reasonably smooth connection between strong and weak coupling, and good numerical agreement with the exact solution. (orig.)

Pawlak algebra and approximate structure on fuzzy lattice.

Science.gov (United States)

Zhuang, Ying; Liu, Wenqi; Wu, Chin-Chia; Li, Jinhai

2014-01-01

The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to rough set theory. We also investigate molecule Pawlak algebra and obtain some related properties.

Scaling of a fast spherical discharge

Energy Technology Data Exchange (ETDEWEB)

Antsiferov, P. S., E-mail: Ants@isan.troitsk.ru; Dorokhin, L. A. [Russian Academy of Sciences, Institute of Spectroscopy (Russian Federation)

2017-02-15

The influence of the discharge cavity dimensions on the properties of the spherical plasma formed in a fast discharge was studied experimentally. The passage of a current pulse with an amplitude of 30–40 kA and a rise rate of ~10{sup 12} A/s (a fast discharge) through a spherical ceramic (Al{sub 2}O{sub 3}) cavity with an inner diameter of 11 mm filled with argon at a pressure of 80 Pa results in the formation of a 1- to 2-mm-diameter spherical plasma with an electron temperature of several tens of electronvolts and a density of 10{sup 18}–10{sup 19} cm{sup –3}. It is shown that an increase in the inner diameter of the discharge cavity from 11 to 21 mm leads to the fourfold increase in the formation time of the spherical plasma and a decrease in the average ion charge. A decrease in the cavity diameter to 7 mm makes the spherical plasma unstable.

Spherical aberrations of human astigmatic corneas.

Science.gov (United States)

Zhao, Huawei; Dai, Guang-Ming; Chen, Li; Weeber, Henk A; Piers, Patricia A

2011-11-01

To evaluate whether the average spherical aberration of human astigmatic corneas is statistically equivalent to human nonastigmatic corneas. Spherical aberrations of 445 astigmatic corneas prior to laser vision correction were retrospectively investigated to determine Zernike coefficients for central corneal areas 6 mm in diameter using CTView (Sarver and Associates). Data were divided into groups according to cylinder power (0.01 to 0.25 diopters [D], 0.26 to 0.75 D, 0.76 to 1.06 D, 1.07 to 1.53 D, 1.54 to 2.00 D, and >2.00 D) and according to age by decade. Spherical aberrations were correlated with age and astigmatic power among groups and the entire population. Statistical analyses were conducted, and P.05 for all tested groups). Mean spherical aberration of astigmatic corneas was not correlated significantly with cylinder power or age (P>.05). Spherical aberrations are similar to those of nonastigmatic corneas, permitting the use of these additional data in the design of aspheric toric intra-ocular lenses. Copyright 2011, SLACK Incorporated.

Mean-field approximation minimizes relative entropy

International Nuclear Information System (INIS)

Bilbro, G.L.; Snyder, W.E.; Mann, R.C.

1991-01-01

The authors derive the mean-field approximation from the information-theoretic principle of minimum relative entropy instead of by minimizing Peierls's inequality for the Weiss free energy of statistical physics theory. They show that information theory leads to the statistical mechanics procedure. As an example, they consider a problem in binary image restoration. They find that mean-field annealing compares favorably with the stochastic approach

The impact of the form of the Euler equations for radial flow in cylindrical and spherical coordinates on numerical conservation and accuracy

Science.gov (United States)

Crittenden, P. E.; Balachandar, S.

2018-03-01

The radial one-dimensional Euler equations are often rewritten in what is known as the geometric source form. The differential operator is identical to the Cartesian case, but source terms result. Since the theory and numerical methods for the Cartesian case are well-developed, they are often applied without modification to cylindrical and spherical geometries. However, numerical conservation is lost. In this article, AUSM^+ -up is applied to a numerically conservative (discrete) form of the Euler equations labeled the geometric form, a nearly conservative variation termed the geometric flux form, and the geometric source form. The resulting numerical methods are compared analytically and numerically through three types of test problems: subsonic, smooth, steady-state solutions, Sedov's similarity solution for point or line-source explosions, and shock tube problems. Numerical conservation is analyzed for all three forms in both spherical and cylindrical coordinates. All three forms result in constant enthalpy for steady flows. The spatial truncation errors have essentially the same order of convergence, but the rate constants are superior for the geometric and geometric flux forms for the steady-state solutions. Only the geometric form produces the correct shock location for Sedov's solution, and a direct connection between the errors in the shock locations and energy conservation is found. The shock tube problems are evaluated with respect to feature location using an approximation with a very fine discretization as the benchmark. Extensions to second order appropriate for cylindrical and spherical coordinates are also presented and analyzed numerically. Conclusions are drawn, and recommendations are made. A derivation of the steady-state solution is given in the Appendix.

Statistical significance approximation in local trend analysis of high-throughput time-series data using the theory of Markov chains.

Science.gov (United States)

Xia, Li C; Ai, Dongmei; Cram, Jacob A; Liang, Xiaoyi; Fuhrman, Jed A; Sun, Fengzhu

2015-09-21

Local trend (i.e. shape) analysis of time series data reveals co-changing patterns in dynamics of biological systems. However, slow permutation procedures to evaluate the statistical significance of local trend scores have limited its applications to high-throughput time series data analysis, e.g., data from the next generation sequencing technology based studies. By extending the theories for the tail probability of the range of sum of Markovian random variables, we propose formulae for approximating the statistical significance of local trend scores. Using simulations and real data, we show that the approximate p-value is close to that obtained using a large number of permutations (starting at time points >20 with no delay and >30 with delay of at most three time steps) in that the non-zero decimals of the p-values obtained by the approximation and the permutations are mostly the same when the approximate p-value is less than 0.05. In addition, the approximate p-value is slightly larger than that based on permutations making hypothesis testing based on the approximate p-value conservative. The approximation enables efficient calculation of p-values for pairwise local trend analysis, making large scale all-versus-all comparisons possible. We also propose a hybrid approach by integrating the approximation and permutations to obtain accurate p-values for significantly associated pairs. We further demonstrate its use with the analysis of the Polymouth Marine Laboratory (PML) microbial community time series from high-throughput sequencing data and found interesting organism co-occurrence dynamic patterns. The software tool is integrated into the eLSA software package that now provides accelerated local trend and similarity analysis pipelines for time series data. The package is freely available from the eLSA website: http://bitbucket.org/charade/elsa.

Simultaneous approximation in scales of Banach spaces

International Nuclear Information System (INIS)

Bramble, J.H.; Scott, R.

1978-01-01

The problem of verifying optimal approximation simultaneously in different norms in a Banach scale is reduced to verification of optimal approximation in the highest order norm. The basic tool used is the Banach space interpolation method developed by Lions and Peetre. Applications are given to several problems arising in the theory of finite element methods

Dynamic deformation theory of spherical and deformed light and heavy nuclei with A = 12-240

International Nuclear Information System (INIS)

Kumar, Krishna.

1979-01-01

Deformation dependent wave functions are calculated for different types of even-even nuclei (spherical, transitional, deformed; light, medium, heavy) without any fitting parameters. These wave functions are employed for the energies, B(E2)'s, quadrupole and magnetic moments of selected nuclei with A = 12-240 (with special emphasis on 56 Fe, 154 Gd), and for neutron cross sections of 148 Sm, 152 Sm

Stellar explosion in the weak field approximation of the Brans-Dicke theory

International Nuclear Information System (INIS)

Hamity, Victor H; Barraco, Daniel E

2005-01-01

We treat a very crude model of an exploding star, in the weak field approximation of the Brans-Dicke theory, in a scenario that resembles some characteristic data of a type Ia supernova. The most noticeable feature, in the electromagnetic component, is the relationship between the absolute magnitude at maximum brightness of the star and the decline rate in one magnitude from that maximum. This characteristic has become one of the most accurate methods to measure luminosity distances to objects at cosmological distances (Phillips M M 1993 Astrophys. J. 413 L105; see www.all-science-fair-projects.com/ science f air p rojects e ncyclopedia/Supernova, for a brief description of supernovae types). An interesting result is that the active mass associated with the scalar field is totally radiated to infinity, representing a mass loss in the ratio of the 'tensor' component to the scalar component of 1 to (2ω + 3) (ω is the Brans-Dicke parameter), in agreement with a general result of Hawking (1972 Commun. Math. Phys. 25 167). Then, this model shows explicitly, in a dynamical case, the mechanism of the radiation of a scalar field, which is necessary to understand the Hawking result

The Application of Approximate Entropy Theory in Defects Detecting of IGBT Module

Directory of Open Access Journals (Sweden)

Shengqi Zhou

2012-01-01

Full Text Available Defect is one of the key factors in reducing the reliability of the insulated gate bipolar transistor (IGBT module, so developing the diagnostic method for defects inside the IGBT module is an important measure to avoid catastrophic failure and improves the reliability of power electronic converters. For this reason, a novel diagnostic method based on the approximate entropy (ApEn theory is presented in this paper, which can provide statistical diagnosis and allow the operator to replace defective IGBT modules timely. The proposed method is achieved by analyzing the cross ApEn of the gate voltages before and after the occurring of defects. Due to the local damage caused by aging, the intrinsic parasitic parameters of packaging materials or silicon chips inside the IGBT module such as parasitic inductances and capacitances may change over time, which will make remarkable variation in the gate voltage. That is to say the gate voltage is close coupled with the defects. Therefore, the variation is quantified and used as a precursor parameter to evaluate the health status of the IGBT module. Experimental results validate the correctness of the proposed method.

Stress intensity factors for complete internal and external cracks in spherical shells

International Nuclear Information System (INIS)

Chao, Y.J.; Chen, H.

1989-01-01

Cracks or flows found in the nuclear structure must be fully evaluated to assure the safety of the plant. The weight function method has been widely used in the determination of stress intensity factors for cracks under stress gradient e.g. for thermal shock loading. The unique features of the weight function method is that once the weight function for a particular cracked geometry is determined the stress intensity factors at the crack tip for any loading applied to the flawed structure can be calculated by a simple integration. In this paper the stress intensity factors of the complete, part-through internal and external cracks in a spherical shell are determined. The finite element method was used to develop the weight functions for the flawed geometry. The approximate crack surface profile was used to derive the weight functions. The stress intensity factors associated with the cracks in spherical shells under internal pressure are determined by both the weight functions and the direct finite element method

A new perturbative approximation applied to supersymmetric quantum field theory

International Nuclear Information System (INIS)

Bender, C.M.; Milton, K.A.; Pinsky, S.S.; Simmons, L.M. Jr.; Los Alamos National Lab.

1988-01-01

We show that a recently proposed graphical perturbative calculational scheme in quantum field theory is consistent with global supersymmetry invariance. We examine a two-dimensional supersymmetric quantum field theory in which we do not known of any other means for doing analytical calculations. We illustrate the power of this new technique by computing the ground-state energy density E to second order in this new perturbation theory. We show that there is a beautiful and delicate cancellation between infinite classes of graphs which leads to the result that E=0. (orig.)

Relevance of capsid structure in the buckling and maturation of spherical viruses

International Nuclear Information System (INIS)

Aznar, María; Luque, Antoni; Reguera, David

2012-01-01

The shape and mechanical properties of viral capsids play an important role in several biological processes during the virus life cycle. In particular, to become infective, many viruses require a maturation stage where the capsid undergoes a buckling transition, from an initial spherical procapsid into a final icosahedral faceted shell. Here we study, using a minimal physical model, how the capsid shape and the buckling transition depend on the triangulation number T and the icosahedral class P of the virus structure. We find that, for small shells, capsids with P = 1 are most likely to produce polyhedral shapes that minimize their energy and accumulated stress, whereas viruses with P = 3 prefer to remain spherical. For big capsids, all shells are more stable adopting an icosahedral shape, in agreement with continuum elastic theory. Moreover, spherical viruses show a buckling transition to polyhedral shells under expansion, in consonance with virus maturation. The resulting icosahedral shell is mechanically stiffer, tolerates larger expansions and withstands higher internal pressures before failing, which could explain why some dsDNA viruses, which rely on the pressurization of their genetic material to facilitate the infection, undergo a buckling transition. We emphasize that the results are general and could also be applied to non-biological systems. (paper)

Spherically symmetric analysis on open FLRW solution in non-linear massive gravity

Energy Technology Data Exchange (ETDEWEB)

Chiang, Chien-I; Izumi, Keisuke; Chen, Pisin, E-mail: chienichiang@berkeley.edu, E-mail: izumi@phys.ntu.edu.tw, E-mail: chen@slac.stanford.edu [Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei 10617, Taiwan (China)

2012-12-01

We study non-linear massive gravity in the spherically symmetric context. Our main motivation is to investigate the effect of helicity-0 mode which remains elusive after analysis of cosmological perturbation around an open Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. The non-linear form of the effective energy-momentum tensor stemming from the mass term is derived for the spherically symmetric case. Only in the special case where the area of the two sphere is not deviated away from the FLRW universe, the effective energy momentum tensor becomes completely the same as that of cosmological constant. This opens a window for discriminating the non-linear massive gravity from general relativity (GR). Indeed, by further solving these spherically symmetric gravitational equations of motion in vacuum to the linear order, we obtain a solution which has an arbitrary time-dependent parameter. In GR, this parameter is a constant and corresponds to the mass of a star. Our result means that Birkhoff's theorem no longer holds in the non-linear massive gravity and suggests that energy can probably be emitted superluminously (with infinite speed) on the self-accelerating background by the helicity-0 mode, which could be a potential plague of this theory.

F-centers in alkaline-earth fluorides. Inadequacy of the muffin-tin approximation

International Nuclear Information System (INIS)

Oliveira, L.E.; Oliveira, P.M.; Maffeo, B.

1977-01-01

The SCF-MSXα (Self Consisting F-centers-Multiple Scattering Xα) method has been applied in the study of the electronic structure of F centers in CaF 2 , SrF 2 and BaF 2 . The predicted optical transition energies are in disagreement with the experimental data. An explanation for the discrepancy is provided showing the inadequacy of the spherical averaging of the potential within the muffin-tin approximation [pt

Non-hard sphere thermodynamic perturbation theory.

Science.gov (United States)

Zhou, Shiqi

2011-08-21

A non-hard sphere (HS) perturbation scheme, recently advanced by the present author, is elaborated for several technical matters, which are key mathematical details for implementation of the non-HS perturbation scheme in a coupling parameter expansion (CPE) thermodynamic perturbation framework. NVT-Monte Carlo simulation is carried out for a generalized Lennard-Jones (LJ) 2n-n potential to obtain routine thermodynamic quantities such as excess internal energy, pressure, excess chemical potential, excess Helmholtz free energy, and excess constant volume heat capacity. Then, these new simulation data, and available simulation data in literatures about a hard core attractive Yukawa fluid and a Sutherland fluid, are used to test the non-HS CPE 3rd-order thermodynamic perturbation theory (TPT) and give a comparison between the non-HS CPE 3rd-order TPT and other theoretical approaches. It is indicated that the non-HS CPE 3rd-order TPT is superior to other traditional TPT such as van der Waals/HS (vdW/HS), perturbation theory 2 (PT2)/HS, and vdW/Yukawa (vdW/Y) theory or analytical equation of state such as mean spherical approximation (MSA)-equation of state and is at least comparable to several currently the most accurate Ornstein-Zernike integral equation theories. It is discovered that three technical issues, i.e., opening up new bridge function approximation for the reference potential, choosing proper reference potential, and/or using proper thermodynamic route for calculation of f(ex-ref), chiefly decide the quality of the non-HS CPE TPT. Considering that the non-HS perturbation scheme applies for a wide variety of model fluids, and its implementation in the CPE thermodynamic perturbation framework is amenable to high-order truncation, the non-HS CPE 3rd-order or higher order TPT will be more promising once the above-mentioned three technological advances are established. © 2011 American Institute of Physics

Spherical and cylindrical cavity expansion models based prediction of penetration depths of concrete targets.

Directory of Open Access Journals (Sweden)

Xiaochao Jin

Full Text Available The cavity expansion theory is most widely used to predict the depth of penetration of concrete targets. The main purpose of this work is to clarify the differences between the spherical and cylindrical cavity expansion models and their scope of application in predicting the penetration depths of concrete targets. The factors that influence the dynamic cavity expansion process of concrete materials were first examined. Based on numerical results, the relationship between expansion pressure and velocity was established. Then the parameters in the Forrestal's formula were fitted to have a convenient and effective prediction of the penetration depth. Results showed that both the spherical and cylindrical cavity expansion models can accurately predict the depth of penetration when the initial velocity is lower than 800 m/s. However, the prediction accuracy decreases with the increasing of the initial velocity and diameters of the projectiles. Based on our results, it can be concluded that when the initial velocity is higher than the critical velocity, the cylindrical cavity expansion model performs better than the spherical cavity expansion model in predicting the penetration depth, while when the initial velocity is lower than the critical velocity the conclusion is quite the contrary. This work provides a basic principle for selecting the spherical or cylindrical cavity expansion model to predict the penetration depth of concrete targets.

Asymptotically flat black holes in Horndeski theory and beyond

Energy Technology Data Exchange (ETDEWEB)

Babichev, E.; Charmousis, C.; Lehébel, A., E-mail: eugeny.babichev@th.u-psud.fr, E-mail: christos.charmousis@th.u-psud.fr, E-mail: antoine.lehebel@th.u-psud.fr [Laboratoire de Physique Théorique, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay (France)

2017-04-01

We find spherically symmetric and static black holes in shift-symmetric Horndeski and beyond Horndeski theories. They are asymptotically flat and sourced by a non trivial static scalar field. The first class of solutions is constructed in such a way that the Noether current associated with shift symmetry vanishes, while the scalar field cannot be trivial. This in certain cases leads to hairy black hole solutions (for the quartic Horndeski Lagrangian), and in others to singular solutions (for a Gauss-Bonnet term). Additionally, we find the general spherically symmetric and static solutions for a pure quartic Lagrangian, the metric of which is Schwarzschild. We show that under two requirements on the theory in question, any vacuum GR solution is also solution to the quartic theory. As an example, we show that a Kerr black hole with a non-trivial scalar field is an exact solution to these theories.

The preparation of high-adsorption, spherical, hexagonal boron nitride by template method

Energy Technology Data Exchange (ETDEWEB)

Zhang, Ning, E-mail: zhangning5832@163.com; Liu, Huan; Kan, Hongmin; Wang, Xiaoyang; Long, Haibo; Zhou, Yonghui

2014-11-15

Highlights: • The high-adsorption, spherical, hexagonal boron nitride powders were prepared. • The influence mechanism of template content on the micro-morphology and adsorption was explored. • At appropriate synthesis temperature, higher adsorption mesoporous spheres h-BN began to form. - Abstract: This research used low-cost boric acid and borax as a source of boron, urea as a nitrogen source, dodecyl-trimethyl ammonium chloride (DTAC) as a template, and thus prepared different micro-morphology hexagonal boron nitride powders under a flowing ammonia atmosphere at different nitriding temperatures. The effects of the template content and nitriding temperature on the micro-morphology of hexagonal boron nitride were studied and the formation mechanism analysed. The influences of the template content and nitriding temperature on adsorption performance were also explored. The results showed that at a nitriding temperature of 675 °C, the micro-morphologies of h-BN powder were orderly, inhomogeneous spherical, uniform spherical, beam, and pie-like with increasing template content. The micro-morphology was inhomogeneous spherical at a DTAC dose of 7.5%. The micro-morphology was uniform spherical at a DTAC dose of 10%. At a DTAC dose of 12%, the micro-morphology was a mixture of beam and pie-like shapes. At a certain template content (DTAC at 10%) and at lower nitriding temperatures (625 °C and 650 °C), spherical shell structures with surface subsidence began to form. The porous spheres would appear at a nitriding temperature of 675 °C, and the ball diameter thus formed was approximately 500–600 nm. The ball diameter was about 600–700 nm when the nitriding temperature was 700 °C. At a nitriding temperature of 725 °C, the ball diameter was between 800 and 1000 nm and sintering necking started to form. When the relative pressure was higher, previously closed pores opened and connected with the outside world: the adsorption then increased significantly. The

Unified Treatment of a Class of Spherically Symmetric Potentials: Quasi-Exact Solution

International Nuclear Information System (INIS)

Baradaran, M.; Panahi, H.

2016-01-01

We investigate the Schrödinger equation for a class of spherically symmetric potentials in a simple and unified manner using the Lie algebraic approach within the framework of quasi-exact solvability. We illustrate that all models give rise to the same basic differential equation, which is expressible as an element of the universal enveloping algebra of sl(2). Then, we obtain the general exact solutions of the problem by employing the representation theory of sl(2) Lie algebra.

Assessment of time-dependent density functional theory with the restricted excitation space approximation for excited state calculations of large systems

Science.gov (United States)

Hanson-Heine, Magnus W. D.; George, Michael W.; Besley, Nicholas A.

2018-06-01

The restricted excitation subspace approximation is explored as a basis to reduce the memory storage required in linear response time-dependent density functional theory (TDDFT) calculations within the Tamm-Dancoff approximation. It is shown that excluding the core orbitals and up to 70% of the virtual orbitals in the construction of the excitation subspace does not result in significant changes in computed UV/vis spectra for large molecules. The reduced size of the excitation subspace greatly reduces the size of the subspace vectors that need to be stored when using the Davidson procedure to determine the eigenvalues of the TDDFT equations. Furthermore, additional screening of the two-electron integrals in combination with a reduction in the size of the numerical integration grid used in the TDDFT calculation leads to significant computational savings. The use of these approximations represents a simple approach to extend TDDFT to the study of large systems and make the calculations increasingly tractable using modest computing resources.

Inertial modes and their transition to turbulence in a differentially rotating spherical gap flow

Science.gov (United States)

Hoff, Michael; Harlander, Uwe; Andrés Triana, Santiago; Egbers, Christoph

2016-04-01

dominant mode (l,m,ˆω) = (3,2,˜ 0.71) is increasing with increasing |Ro| until a critical Rossby number Rocrit. Accompanying with this is an increase of the zonal mean flow outside the tangent cylinder, leading to enhanced angular momentum transport. At the particular Rocrit, the wave mode, and the entire flow, breaks up into smaller-scale turbulence [6], together with a strong increase of the zonal mean flow inside the tangent cylinder. We found that the critical Rossby number scales approximately with E1/5. References [1] Aldridge, K. D.; Lumb, L. I. (1987): Inertial waves identified in the Earth's fluid outer core. Nature 325 (6103), S. 421-423. DOI: 10.1038/325421a0. [2] Greenspan, H. P. (1968): The theory of rotating fluids. London: Cambridge U.P. (Cambridge monographs on mechanics and applied mathematics). [3] Kelley, D. H.; Triana, S. A.; Zimmerman, D. S.; Lathrop, D. P. (2010): Selection of inertial modes in spherical Couette flow. Phys. Rev. E 81 (2), 26311. DOI: 10.1103/PhysRevE.81.026311. [4] Rieutord, M.; Triana, S. A.; Zimmerman, D. S.; Lathrop, D. P. (2012): Excitation of inertial modes in an experimental spherical Couette flow. Phys. Rev. E 86 (2), 026304. DOI: 10.1103/PhysRevE.86.026304. [5] Hoff, M., Harlander, U., Egbers, C. (2016): Experimental survey of linear and nonlinear inertial waves and wave instabilities in a spherical shell. J. Fluid Mech., (in print) [6] Kerswell, R. R. (1999): Secondary instabilities in rapidly rotating fluids: inertial wave breakdown. Journal of Fluid Mechanics 382, S. 283-306. DOI: 10.1017/S0022112098003954.

ELSA- The European Levitated Spherical Actruator

Science.gov (United States)

Ruiz, M.; Serin, J.; Telteu-Nedelcu, D.; De La Vallee Poussin, H.; Onillon, E.; Rossini, L.

2014-08-01

The reaction sphere is a magnetic bearing spherical actuator consisting of a permanent magnet spherical rotor that can be accelerated in any direction. It consists of an 8-pole permanent magnet spherical rotor that is magnetically levitated and can be accelerated about any axis by a 20-pole stator with electromagnets. The spherical actuator is proposed as a potential alternative to traditional momentum exchange devices such as reaction wheels (RWs) or control moment gyroscopes (CMGs). This new actuator provides several benefits such as reduced mass and power supply allocated to the attitude and navigation unit, performance gain, and improved reliability due to the absence of mechanical bearings. The paper presents the work done on the levitated spherical actuator and more precisely the electrical drive including its control unit and power parts. An elegant breadboard is currently being manufactured within the frame of an FP7 project. This project also comprises a feasibility study to show the feasibility of integrating such a system on a flight platform and to identify all the challenges to be solved in terms of technology or components to be developed.

Improved lumped models for transient combined convective and radiative cooling of a two-layer spherical fuel element

International Nuclear Information System (INIS)

Silva, Alice Cunha da; Su, Jian

2013-01-01

The High Temperature Gas cooled Reactor (HTGR) is a fourth generation thermal nuclear reactor, graphite-moderated and helium cooled. The HTGRs have important characteristics making essential the study of these reactors, as well as its fuel element. Examples of these are: high thermal efficiency,low operating costs and construction, passive safety attributes that allow implication of the respective plants. The Pebble Bed Modular Reactor (PBMR) is a HTGR with spherical fuel elements that named the reactor. This fuel element is composed by a particulate region with spherical inclusions, the fuel UO2 particles, dispersed in a graphite matrix and a convective heat transfer by Helium happens on the outer surface of the fuel element. In this work, the transient heat conduction in a spherical fuel element of a pebble-bed high temperature reactor was studied in a transient situation of combined convective and radiative cooling. Improved lumped parameter model was developed for the transient heat conduction in the two-layer composite sphere subjected to combined convective and radiative cooling. The improved lumped model was obtained through two-point Hermite approximations for integrals. Transient combined convective and radiative cooling of the two-layer spherical fuel element was analyzed to illustrate the applicability of the proposed lumped model, with respect to die rent values of the Biot number, the radiation-conduction parameter, the dimensionless thermal contact resistance, the dimensionless inner diameter and coating thickness, and the dimensionless thermal conductivity. It was shown by comparison with numerical solution of the original distributed parameter model that the improved lumped model, with H2,1/H1,1/H0,0 approximation yielded significant improvement of average temperature prediction over the classical lumped model. (author)

Dynamic response of sand particles impacted by a rigid spherical object

Directory of Open Access Journals (Sweden)

P. Youplao

2018-06-01

Full Text Available A method for measuring the dynamic impact responses that acting on a spherical object while dropping and colliding with dried sand, such as the velocity, displacement, acceleration, and resultant force, is presented and discussed. In the experiment, a Michelson-type laser interferometer is employed to obtain the velocity of the spherical stainless steel object. Then the obtained time velocity profile is used to calculate the acceleration, the displacement, and the inertial force acting on the observed sand particles. Furthermore, a high-speed camera is employed to observe the behavior of the sand during the collision. From the experimental results with the sampling interval for frequencies calculation of 1 ms, the combined standard uncertainty in the instantaneous value of the impact force acts on the observed object is obtained and approximated to 0.49 N, which is related to a corresponding 4.07% of the maximum value at 12.05 N of the impact force. Keywords: Sand particle, Collision response, Dynamic force, Inertial mass, Optical interferometer

Anomalous diffraction approximation for light scattering cross section: Case of random clusters of non-absorbent spheres

Energy Technology Data Exchange (ETDEWEB)

Jacquier, Sandra [Ecole Nationale Superieure des Mines de Saint-Etienne, 158 Cours Fauriel, 42023 F-St. Etienne (France); Gruy, Frederic [Ecole Nationale Superieure des Mines de Saint-Etienne, 158 Cours Fauriel, 42023 F-St. Etienne (France)], E-mail: fgruy@emse.fr

2008-11-15

We previously [Jacquier S, Gruy F. Approximation of the light scattering cross-section for aggregated spherical non-absorbent particles. JQSRT 2008;109:789-810] reformulated the anomalous diffraction (AD) approximation to calculate the light scattering cross section of aggregates by introducing their chord length distribution (CLD). It was applied to several ordered aggregates. This new method is entitled ADr, with the r for rapid because this one is at least 100 times faster than the standard AD method. In this article, we are searching for an approximated expression for CLD suitable all at once for ordered and disordered aggregates. The corresponding scattering cross-section values are compared to the ones coming from the standard AD approximation.

Anomalous diffraction approximation for light scattering cross section: Case of random clusters of non-absorbent spheres

International Nuclear Information System (INIS)

Jacquier, Sandra; Gruy, Frederic

2008-01-01

We previously [Jacquier S, Gruy F. Approximation of the light scattering cross-section for aggregated spherical non-absorbent particles. JQSRT 2008;109:789-810] reformulated the anomalous diffraction (AD) approximation to calculate the light scattering cross section of aggregates by introducing their chord length distribution (CLD). It was applied to several ordered aggregates. This new method is entitled ADr, with the r for rapid because this one is at least 100 times faster than the standard AD method. In this article, we are searching for an approximated expression for CLD suitable all at once for ordered and disordered aggregates. The corresponding scattering cross-section values are compared to the ones coming from the standard AD approximation

The high intensity approximation applied to multiphoton ionization

International Nuclear Information System (INIS)

Brandi, H.S.; Davidovich, L.; Zagury, N.

1980-08-01

It is shown that the most commonly used high intensity approximations as applied to ionization by strong electromagnetic fields are related. The applicability of the steepest descent method in these approximations, and the relation between them and first-order perturbation theory, are also discussed. (Author) [pt

A unified approach to the Darwin approximation

International Nuclear Information System (INIS)

Krause, Todd B.; Apte, A.; Morrison, P. J.

2007-01-01

There are two basic approaches to the Darwin approximation. The first involves solving the Maxwell equations in Coulomb gauge and then approximating the vector potential to remove retardation effects. The second approach approximates the Coulomb gauge equations themselves, then solves these exactly for the vector potential. There is no a priori reason that these should result in the same approximation. Here, the equivalence of these two approaches is investigated and a unified framework is provided in which to view the Darwin approximation. Darwin's original treatment is variational in nature, but subsequent applications of his ideas in the context of Vlasov's theory are not. We present here action principles for the Darwin approximation in the Vlasov context, and this serves as a consistency check on the use of the approximation in this setting

Spherical Torus Center Stack Design

International Nuclear Information System (INIS)

C. Neumeyer; P. Heitzenroeder; C. Kessel; M. Ono; M. Peng; J. Schmidt; R. Woolley; I. Zatz

2002-01-01

The low aspect ratio spherical torus (ST) configuration requires that the center stack design be optimized within a limited available space, using materials within their established allowables. This paper presents center stack design methods developed by the National Spherical Torus Experiment (NSTX) Project Team during the initial design of NSTX, and more recently for studies of a possible next-step ST (NSST) device

Simulations of the Penetration of 6061-T6511 Aluminum Targets by Spherical-Nosed VAR 4340 Steel Projectiles

Energy Technology Data Exchange (ETDEWEB)

Tabbara, M.R.; Warren, T.L.

1998-10-21

In certain penetration events it is proposed that the primary mode of deformation of the target can be approximated by known analytical expressions. In the context of an analysis code, this approximation eliminates the need for discretizing the target as well as the need for a contact algorithm. Thus, this method substantially reduces the computer time and memory requirements. In this paper a forcing function which is derived from a spherical-cavity expansion (SCE) analysis has been implemented in a transient dynamic finite element code. This irnplementation is capable of computing the structural and component responses of a projectile due to a three dimensional penetration event. Simulations are presented for 7.1 l-mm-diameter, 74.7-mm-long, spherical-nose, vacuum- arc-remelted (VAR) 4340 steel projectiles that penetrate 6061-T6511 aluminum targets. Final projectile configurations obtained from the simulations are compared with post-test radiographs obtained from the corresponding experiments. It is shown that the simulations accurately predict the permanent projectile deformation for three dimensional loadings due to incident pitch and yaw over a wide range of striking velocities.

Special treatment of the optical potential of a spherical attractive fermi gas as a Saxon-Woods potential

International Nuclear Information System (INIS)

Grado-Caffaro, M.A.; Grado-Caffaro, M.

2015-01-01

Within a special scheme providing significant new results, we show that the (attractive) optical potential due to a spherical (non-relativistic) dilute and degenerate Fermi-Dirac gas becomes a Saxon-Woods potential which, in turn, is approximated by a truncated Dirac delta function near the center of the above spherical gas. This approximation is suitable to investigate phenomena in which fermions are restricted to move in relatively small spatial domains. In relation to this, we determine the corresponding fermion stationary wavefunctions which are found to be proportional to the aforementioned delta function if twice the fermion rest-mass multiplied by the total electron energy is much larger than the square of the reduced Planck constant. If this relationship is not fulfilled, the above fermion system is found to be roughly equivalent to fermions in an infinite one-dimensional potential well. In addition, the force field derived from the optical potential in question is determined as well as the chemical potential of the gas. Finally, application of our formulation to study electron transport in nanostructures is outlined

All spherically symmetric charged anisotropic solutions for compact stars

Energy Technology Data Exchange (ETDEWEB)

Maurya, S.K. [University of Nizwa, Department of Mathematical and Physical Sciences, College of Arts and Science, Nizwa (Oman); Gupta, Y.K. [Raj Kumar Goel Institute of Technology, Department of Mathematics, Ghaziabad, UP (India); Ray, Saibal [Government College of Engineering and Ceramic Technology, Department of Physics, Kolkata, West Bengal (India)

2017-06-15

In the present paper we develop an algorithm for all spherically symmetric anisotropic charged fluid distributions. Considering a new source function ν(r) we find a set of solutions which is physically well behaved and represents compact stellar models. A detailed study specifically shows that the models actually correspond to strange stars in terms of their mass and radius. In this connection we investigate several physical properties like energy conditions, stability, mass-radius ratio, electric charge content, anisotropic nature and surface redshift through graphical plots and mathematical calculations. All the features from these studies are in excellent agreement with the already available evidence in theory as well as observations. (orig.)

Spherically symmetric solution and a satisfactory energy-momentum complex

International Nuclear Information System (INIS)

Nashed, G.G.L.

2005-01-01

Mikhail et al. obtained two spherically symmetric solution in Moeller tetrad theory of gravitation. They calculated their energy content and obtained a strange value for the second solution, in spite that the associated metric of these solutions is the same (the Schwarzschild metric). We use another method given bu Gibbons and Hawking to calculate the energy content of these solutions. We also obtained a strange value of energy for the second solution. Studying the requirements of the satisfactory energy-momentum complex given by Moeller we find that the second solution which behaves as 1/√r does not transform as a four-vector under Lorentz transformation

An approach for spherical harmonic analysis of non-smooth data

Science.gov (United States)

Wang, Hansheng; Wu, Patrick; Wang, Zhiyong

2006-12-01

A method is proposed to evaluate the spherical harmonic coefficients of a global or regional, non-smooth, observable dataset sampled on an equiangular grid. The method is based on an integration strategy using new recursion relations. Because a bilinear function is used to interpolate points within the grid cells, this method is suitable for non-smooth data; the slope of the data may be piecewise continuous, with extreme changes at the boundaries. In order to validate the method, the coefficients of an axisymmetric model are computed, and compared with the derived analytical expressions. Numerical results show that this method is indeed reasonable for non-smooth models, and that the maximum degree for spherical harmonic analysis should be empirically determined by several factors including the model resolution and the degree of non-smoothness in the dataset, and it can be several times larger than the total number of latitudinal grid points. It is also shown that this method is appropriate for the approximate analysis of a smooth dataset. Moreover, this paper provides the program flowchart and an internet address where the FORTRAN code with program specifications are made available.

Kinetics of growth of semi-spheric pittings in the vicinity repassivation potential depending on bulk concentration of activator anions

International Nuclear Information System (INIS)

Frejman, L.I.

1985-01-01

A general case of semi-spheric pittings development in aqueous solutions of electrolyte of NaCl or LiCl type at different values of C 0 , usually studied in the range approximately equal to 10 -5 -10 -3 g-ionxcm -3 (approximately equal to 10 -2 -10 0 g-ionxl -1 ), has been analyzed. On the basis of experimental data on participation of anion-activators and water molecules in the process of metal dissolution in pitting, and using the previously obtained equations, kinetics of open and closed semi-spheric pittings during galvanostatic anode polarization in neutral chloride solutions with different volumetric concentration of Cl - -ions (C 0 ) has been considered. In a general case the process kinetics is described by a complex equation, the boundary, more simple forms of which, correspond to the initial (A) and subsequent (B) stages of open pitting development, or to certain stable conditions of closed pitting development

Strain mapping under spherical indentations using transmission Kikuchi diffraction

International Nuclear Information System (INIS)

Cackett, A.; Hardie, C.; Wilkinson, A.; Dicks, K.

2015-01-01

Due to restrictions on both the specimen volumes available and the activity levels research facilities can handle, testing techniques on the micron-scale are very attractive for the study of irradiated material. However, the results of such small tests are convoluted by plasticity size-effects. Spherical nano-indentation is increasingly used to probe irradiated material, but to characterise the area of plastic deformation surrounding indentations a method capable of providing crystallographic information at extremely high spatial resolution is required. Transmission Kikuchi Diffraction (TKD) is a novel diffraction technique that can be performed in a scanning electron microscope. Using this technique, spatial resolutions below 10 nm have been achieved. Initial results, shown here, demonstrate the use of TKD in mapping the lattice rotations caused by indentation produced with a spherical diamond tip. With the addition of strain mapping software the plastic zone size was also evaluated for the first time using diffraction patterns generated via TKD. For a tip of radius 15 μm, inserted into Fe to a strain of 0.07, the plastic zone was observed to extend 1.3 μm to either side of the incident location of indentation and the deformation depth was approximately 0.5 μm. (authors)

3DRISM-HI-D2MSA: an improved analytic theory to compute solvent structure around hydrophobic solutes with proper treatment of solute–solvent electrostatic interactions

KAUST Repository

Cao, Siqin

2017-12-22

The 3D reference interaction site model (3DRISM) is a powerful tool to study the thermodynamic and structural properties of liquids. However, for hydrophobic solutes, the inhomogeneity of the solvent density around them poses a great challenge to the 3DRISM theory. To address this issue, we have previously introduced the hydrophobic-induced density inhomogeneity theory (HI) for purely hydrophobic solutes. To further consider the complex hydrophobic solutes containing partial charges, here we propose the D2MSA closure to incorporate the short-range and long-range interactions with the D2 closure and the mean spherical approximation, respectively. We demonstrate that our new theory can compute the solvent distributions around real hydrophobic solutes in water and complex organic solvents that agree well with the explicit solvent molecular dynamics simulations.

3DRISM-HI-D2MSA: an improved analytic theory to compute solvent structure around hydrophobic solutes with proper treatment of solute–solvent electrostatic interactions

KAUST Repository

Cao, Siqin; Zhu, Lizhe; Huang, Xuhui

2017-01-01

The 3D reference interaction site model (3DRISM) is a powerful tool to study the thermodynamic and structural properties of liquids. However, for hydrophobic solutes, the inhomogeneity of the solvent density around them poses a great challenge to the 3DRISM theory. To address this issue, we have previously introduced the hydrophobic-induced density inhomogeneity theory (HI) for purely hydrophobic solutes. To further consider the complex hydrophobic solutes containing partial charges, here we propose the D2MSA closure to incorporate the short-range and long-range interactions with the D2 closure and the mean spherical approximation, respectively. We demonstrate that our new theory can compute the solvent distributions around real hydrophobic solutes in water and complex organic solvents that agree well with the explicit solvent molecular dynamics simulations.

3DRISM-HI-D2MSA: an improved analytic theory to compute solvent structure around hydrophobic solutes with proper treatment of solute–solvent electrostatic interactions

Science.gov (United States)

Cao, Siqin; Zhu, Lizhe; Huang, Xuhui

2018-04-01

The 3D reference interaction site model (3DRISM) is a powerful tool to study the thermodynamic and structural properties of liquids. However, for hydrophobic solutes, the inhomogeneity of the solvent density around them poses a great challenge to the 3DRISM theory. To address this issue, we have previously introduced the hydrophobic-induced density inhomogeneity theory (HI) for purely hydrophobic solutes. To further consider the complex hydrophobic solutes containing partial charges, here we propose the D2MSA closure to incorporate the short-range and long-range interactions with the D2 closure and the mean spherical approximation, respectively. We demonstrate that our new theory can compute the solvent distributions around real hydrophobic solutes in water and complex organic solvents that agree well with the explicit solvent molecular dynamics simulations.

Analysis for extraction and bunching of ion beam from spherical reflex triode

International Nuclear Information System (INIS)

Kawata, Shigeo; Abe, Takashi; Kasuya, Koichi; Niu, Keishiro.

1978-11-01

Since an ion beam is hoped to impinge on a target in a spherically symmetric way for inertial confinement fusion, an analysis is developed here for the intense ion beam which is extracted from a spherical reflex triode. The basic equations are the Poisson equation for the electric potential and the conservation equations of energies for the ion and electron velocities. According to the asymptotic solution, the extracted ion-beam-current density is proportional to the power of 3/2 of the voltage imposed on the triode. This dependence of the current density on the voltage is improved to be the power of 1.6 by the numerical analysis. A special time-dependence of the ion-beam power at the target surface is required for an optimal implosion of the target. Using the bunching theory for the ion beam, we derive numerically an optimal time-dependence of the voltage imposed on the triode. Asymptotic forms are also obtained analytically for the voltage. (author)

A benign property of the ghost mode in massive theory of gravitation

Science.gov (United States)

Chugreev, Yu. V.

2018-01-01

It was shown in the frameworks of massive gravitational theories having in linear approximation mass term {m^2}( {φ ^{α β }}{φ_{α β }} - 1/2{φ ^2}} ) in the lagrangian, that created some time ago spherically-symmetric static sources should possess inside their light cone not only Yukawa potential, but also nonstationary component. It leads to the long ( 1/ m) period of gravitational evaporation of such sources with the mass loss Ṁ m 2 M 2 The magnitude of the flux is c 4/ v 4 times ( c—speed of light, v—velocity of the source particles) bigger then negative gravitational radiation flux corresponding to the ghost scalar mode in the spectrum of such gravitational field, with stabilizing the source.

Sums over geometries and improvements on the mean field approximation

International Nuclear Information System (INIS)

Sacksteder, Vincent E. IV

2007-01-01

The saddle points of a Lagrangian due to Efetov are analyzed. This Lagrangian was originally proposed as a tool for calculating systematic corrections to the Bethe approximation, a mean-field approximation which is important in statistical mechanics, glasses, coding theory, and combinatorial optimization. Detailed analysis shows that the trivial saddle point generates a sum over geometries reminiscent of dynamically triangulated quantum gravity, which suggests new possibilities to design sums over geometries for the specific purpose of obtaining improved mean-field approximations to D-dimensional theories. In the case of the Efetov theory, the dominant geometries are locally treelike, and the sum over geometries diverges in a way that is similar to quantum gravity's divergence when all topologies are included. Expertise from the field of dynamically triangulated quantum gravity about sums over geometries may be able to remedy these defects and fulfill the Efetov theory's original promise. The other saddle points of the Efetov Lagrangian are also analyzed; the Hessian at these points is nonnormal and pseudo-Hermitian, which is unusual for bosonic theories. The standard formula for Gaussian integrals is generalized to nonnormal kernels

Solution of two-dimensional equations of neutron transport in 4P0-approximation of spherical harmonics method

International Nuclear Information System (INIS)

Polivanskij, V.P.

1989-01-01

The method to solve two-dimensional equations of neutron transport using 4P 0 -approximation is presented. Previously such approach was efficiently used for the solution of one-dimensional problems. New an attempt is made to apply the approach to solution of two-dimensional problems. Algorithm of the solution is given, as well as results of test neutron-physical calculations. A considerable as compared with diffusion approximation is shown. 11 refs

PRECONDITIONED BI-CONJUGATE GRADIENT METHOD FOR RADIATIVE TRANSFER IN SPHERICAL MEDIA

International Nuclear Information System (INIS)

Anusha, L. S.; Nagendra, K. N.; Paletou, F.; Leger, L.

2009-01-01

A robust numerical method called the Preconditioned Bi-Conjugate Gradient (Pre-BiCG) method is proposed for the solution of the radiative transfer equation in spherical geometry. A variant of this method called Stabilized Preconditioned Bi-Conjugate Gradient (Pre-BiCG-STAB) is also presented. These are iterative methods based on the construction of a set of bi-orthogonal vectors. The application of the Pre-BiCG method in some benchmark tests shows that the method is quite versatile, and can handle difficult problems that may arise in astrophysical radiative transfer theory.

Neutron-optical effects at very cold neutrons scattering on the spherical particles of different sizes

International Nuclear Information System (INIS)

Grinev, V.G.; Kudinova, O.I.; Novokshonova, L.A.; Kuznetsov, S.P.; Udovenko, A.I.; Shelagin, A.V.

2006-01-01

Very cold neutrons (VCN) with the wavelength λ > 4.0 ran are convenient tool for investigating the super molecular structures of different nature. Using a Born approximation (BA) to the analysis of dependencies on the wavelength of the VCN scattering cross sections, it is possible to obtain information about average sizes (R) and concentrations of the scattering particles with R∼ λ. However, with an increasing the sizes of scatterers the conditions for BA applicability can be disrupted. In this work we investigated the possibilities of BA, eikonal and geometric-optical approximations for the analysis of VCN scattering on the spherical particles with R ≥ λ

The failure behavior of duplex 316 L steel-TA6V titanium alloy spherical pressure vessels

International Nuclear Information System (INIS)

Miannay, D.

1980-05-01

The purpose of this paper is to compare the experimental residual stresses of spherical vessels made of TA6V alloy which exhibits plasticity before failure in toughness testing and cracked with several configurations, with stresses estimated according to the afore mentioned theories. An internal austenitic 316 L steel is used to prevent 'leak before break' [fr

The prediction of spherical aberration with schematic eyes.

Science.gov (United States)

Liou, H L; Brennan, N A

1996-07-01

Many model eyes have been proposed; they differ in optical characteristics and therefore have different aberrations and image quality. In predicting the visual performance of the eye, we are most concerned with the central foveal vision. Spherical aberration is the only on-axis monochromatic aberration and can be used as a criterion to assess the degree of resemblance of eye models to the human eye. We reviewed and compiled experimental values of the spherical aberration of the eye, calculated the spherical aberration of several different categories of model eyes and compared the calculated results to the experimental data. Results show an over-estimation of spherical aberration by all models, the finite schematic eyes predicting values of spherical aberration closest to the experimental data. Current model eyes do not predict the average experimental values of the spherical aberration of the eye. A new model eye satisfying this assessment criterion is required for investigations of the visual performance of the eye.

Measurement of Turbulence Modulation by Non-Spherical Particles

DEFF Research Database (Denmark)

Mandø, Matthias; Rosendahl, Lasse

2010-01-01

The change in the turbulence intensity of an air jet resulting from the addition of particles to the flow is measured using Laser Doppler Anemometry. Three distinct shapes are considered: the prolate spheroid, the disk and the sphere. Measurements of the carrier phase and particle phase velocities...... at the centerline of the jet are carried out for mass loadings of 0.5, 1, 1.6 and particle sizes 880μm, 1350μm, 1820μm for spherical particles. For each non-spherical shape only a single size and loading are considered. The turbulence modulation of the carrier phase is found to highly dependent on the turbulence......, the particle mass flow and the integral length scale of the flow. The expression developed on basis of spherical particles only is applied on the data for the non-spherical particles. The results suggest that non-spherical particles attenuate the carrier phase turbulence significantly more than spherical...

The ETE spherical Tokamak project. IAEA report

Energy Technology Data Exchange (ETDEWEB)

Ludwig, Gerson Otto; Del Bosco, E.; Berni, L.A.; Ferreira, J.G.; Oliveira, R.M.; Andrade, M.C.R.; Shibata, C.S.; Barroso, J.J.; Castro, P.J.; Patire Junior, H. [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Lab. Associado de Plasma]. E-mail: ludwig@plasma.inpe.br

2002-07-01

This paper describes the general characteristics of spherical tokamaks, or spherical tori, with a brief overview of work in this area already performed or in progress at several institutions worldwide. The paper presents also the historical development of the ETE (Spherical Tokamak Experiment) project, its research program, technical characteristics and operating conditions as of October, 2002 at the Associated Plasma Laboratory (LAP) of the National Space Research Institute (INPE) in Brazil. (author)

Spherical solitons in Earth’S mesosphere plasma

International Nuclear Information System (INIS)

Annou, K.; Annou, R.

2016-01-01

Soliton formation in Earth’s mesosphere plasma is described. Nonlinear acoustic waves in plasmas with two-temperature ions and a variable dust charge where transverse perturbation is dealt with are studied in bounded spherical geometry. Using the perturbation method, a spherical Kadomtsev–Petviashvili equation that describes dust acoustic waves is derived. It is found that the parameters taken into account have significant effects on the properties of nonlinear waves in spherical geometry

An Angular Leakage Correction for Modeling a Hemisphere, Using One-Dimensional Spherical Coordinates

International Nuclear Information System (INIS)

Schwinkendorf, K.N.; Eberle, C.S.

2003-01-01

A radially dependent, angular leakage correction was applied to a one-dimensional, multigroup neutron diffusion theory computer code to accurately model hemispherical geometry. This method allows the analyst to model hemispherical geometry, important in nuclear criticality safety analyses, with one-dimensional computer codes, which execute very quickly. Rapid turnaround times for scoping studies thus may be realized. This method uses an approach analogous to an axial leakage correction in a one-dimensional cylinder calculation. The two-dimensional Laplace operator was preserved in spherical geometry using a leakage correction proportional to 1/r 2 , which was folded into the one-dimensional spherical calculation on a mesh-by-mesh basis. Hemispherical geometry is of interest to criticality safety because of its similarity to piles of spilled fissile material and accumulations of fissile material in process containers. A hemisphere also provides a more realistic calculational model for spilled fissile material than does a sphere

Lattice quantum chromodynamics with approximately chiral fermions

International Nuclear Information System (INIS)

Hierl, Dieter

2008-05-01

In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the Θ + pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)

Lattice quantum chromodynamics with approximately chiral fermions

Energy Technology Data Exchange (ETDEWEB)

Hierl, Dieter

2008-05-15

In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the {theta}{sup +} pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)

Dissolution of spherical cap CO2 bubbles attached to flat surfaces in air-saturated water

Science.gov (United States)

Peñas, Pablo; Parrales, Miguel A.; Rodriguez-Rodriguez, Javier

2014-11-01

Bubbles attached to flat surfaces immersed in quiescent liquid environments often display a spherical cap (SC) shape. Their dissolution is a phenomenon commonly observed experimentally. Modelling these bubbles as fully spherical may lead to an inaccurate estimate of the bubble dissolution rate. We develop a theoretical model for the diffusion-driven dissolution or growth of such multi-component SC gas bubbles under constant pressure and temperature conditions. Provided the contact angle of the bubble with the surface is large, the concentration gradients in the liquid may be approximated as spherically symmetric. The area available for mass transfer depends on the instantaneous bubble contact angle, whose dynamics is computed from the adhesion hysteresis model [Hong et al., Langmuir, vol. 27, 6890-6896 (2011)]. Numerical simulations and experimental measurements on the dissolution of SC CO2 bubbles immersed in air-saturated water support the validity of our model. We verify that contact line pinning slows down the dissolution rate, and the fact that any bubble immersed in a saturated gas-liquid solution eventually attains a final equilibrium size. Funded by the Spanish Ministry of Economy and Competitiveness through Grant DPI2011-28356-C03-0.

Laplacian eigenmodes for spherical spaces

International Nuclear Information System (INIS)

Lachieze-Rey, M; Caillerie, S