1996-01-01
Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.
Hybrid Finite Element and Volume Integral Methods for Scattering Using Parametric Geometry
DEFF Research Database (Denmark)
Volakis, John L.; Sertel, Kubilay; Jørgensen, Erik
2004-01-01
n this paper we address several topics relating to the development and implementation of volume integral and hybrid finite element methods for electromagnetic modeling. Comparisons of volume integral equation formulations with the finite element-boundary integral method are given in terms of accu...... of vanishing divergence within the element but non-zero curl. In addition, a new domain decomposition is introduced for solving array problems involving several million degrees of freedom. Three orders of magnitude CPU reduction is demonstrated for such applications....
Energy Technology Data Exchange (ETDEWEB)
Aspelund, O; Gustafsson, B
1967-05-15
After an introductory discussion of various methods for correction of experimental left-right ratios for polarized multiple-scattering and finite-geometry effects necessary and sufficient formulas for consistent tracking of polarization effects in successive scattering orders are derived. The simplifying assumptions are then made that the scattering is purely elastic and nuclear, and that in the description of the kinematics of the arbitrary Scattering {mu}, only one triple-parameter - the so-called spin rotation parameter {beta}{sup ({mu})} - is required. Based upon these formulas a general discussion of the importance of the correct inclusion of polarization effects in any scattering order is presented. Special attention is then paid to the question of depolarization of an already polarized beam. Subsequently, the afore-mentioned formulas are incorporated in the comprehensive Monte Carlo program MULTPOL, which has been designed so as to correctly account for finite-geometry effects in the sense that both the scattering sample and the detectors (both having cylindrical shapes) are objects of finite dimensions located at finite distances from each other and from the source of polarized fast-neutrons. A special feature of MULTPOL is the application of the method of correlated sampling for reduction of the standard deviations .of the results of the simulated experiment. Typical data of performance of MULTPOL have been obtained by the application of this program to the correction of experimental polarization data observed in n + '{sup 12}C elastic scattering between 1 and 2 MeV. Finally, in the concluding remarks the possible modification of MULTPOL to other experimental geometries is briefly discussed.
SPANDY: a Monte Carlo program for gas target scattering geometry
International Nuclear Information System (INIS)
Jarmie, N.; Jett, J.H.; Niethammer, A.C.
1977-02-01
A Monte Carlo computer program is presented that simulates a two-slit gas target scattering geometry. The program is useful in estimating effects due to finite geometry and multiple scattering in the target foil. Details of the program are presented and experience with a specific example is discussed
Grassmannian geometry of scattering amplitudes
Arkani-Hamed, Nima; Cachazo, Freddy; Goncharov, Alexander; Postnikov, Alexander; Trnka, Jaroslav
2016-01-01
Outlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang–Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids - in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the...
Polynomials in finite geometries and combinatorics
Blokhuis, A.; Walker, K.
1993-01-01
It is illustrated how elementary properties of polynomials can be used to attack extremal problems in finite and euclidean geometry, and in combinatorics. Also a new result, related to the problem of neighbourly cylinders is presented.
Thermal geometry from CFT at finite temperature
Directory of Open Access Journals (Sweden)
Wen-Cong Gan
2016-09-01
Full Text Available We present how the thermal geometry emerges from CFT at finite temperature by using the truncated entanglement renormalization network, the cMERA. For the case of 2d CFT, the reduced geometry is the BTZ black hole or the thermal AdS as expectation. In order to determine which spacetimes prefer to form, we propose a cMERA description of the Hawking–Page phase transition. Our proposal is in agreement with the picture of the recent proposed surface/state correspondence.
Thermal geometry from CFT at finite temperature
Energy Technology Data Exchange (ETDEWEB)
Gan, Wen-Cong, E-mail: ganwencong@gmail.com [Department of Physics, Nanchang University, Nanchang 330031 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University, Nanchang 330031 (China); Shu, Fu-Wen, E-mail: shufuwen@ncu.edu.cn [Department of Physics, Nanchang University, Nanchang 330031 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University, Nanchang 330031 (China); Wu, Meng-He, E-mail: menghewu.physik@gmail.com [Department of Physics, Nanchang University, Nanchang 330031 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University, Nanchang 330031 (China)
2016-09-10
We present how the thermal geometry emerges from CFT at finite temperature by using the truncated entanglement renormalization network, the cMERA. For the case of 2d CFT, the reduced geometry is the BTZ black hole or the thermal AdS as expectation. In order to determine which spacetimes prefer to form, we propose a cMERA description of the Hawking–Page phase transition. Our proposal is in agreement with the picture of the recent proposed surface/state correspondence.
The geometry of finite equilibrium sets
DEFF Research Database (Denmark)
Balasko, Yves; Tvede, Mich
2009-01-01
We investigate the geometry of finite datasets defined by equilibrium prices, income distributions, and total resources. We show that the equilibrium condition imposes no restrictions if total resources are collinear, a property that is robust to small perturbations. We also show that the set...... of equilibrium datasets is pathconnected when the equilibrium condition does impose restrictions on datasets, as for example when total resources are widely noncollinear....
The Geometry of Finite Equilibrium Datasets
DEFF Research Database (Denmark)
Balasko, Yves; Tvede, Mich
We investigate the geometry of finite datasets defined by equilibrium prices, income distributions, and total resources. We show that the equilibrium condition imposes no restrictions if total resources are collinear, a property that is robust to small perturbations. We also show that the set...... of equilibrium datasets is pathconnected when the equilibrium condition does impose restrictions on datasets, as for example when total resources are widely non collinear....
Finite quantum physics and noncommutative geometry
International Nuclear Information System (INIS)
Balachandran, A.P.; Ercolessi, E.; Landi, G.; Teotonio-Sobrinho, P.; Lizzi, F.; Sparano, G.
1994-04-01
Conventional discrete approximations of a manifold do not preserve its nontrivial topological features. In this article we describe an approximation scheme due to Sorkin which reproduces physically important aspects of manifold topology with striking fidelity. The approximating topological spaces in this scheme are partially ordered sets (posets). Now, in ordinary quantum physics on a manifold M, continuous probability densities generate the commutative C * -algebra C(M) of continuous functions on M. It has a fundamental physical significance, containing the information to reconstruct the topology of M, and serving to specify the domains of observables like the Hamiltonian. For a poset, the role of this algebra is assumed by a noncommutative C * -algebra A. As noncommutative geometries are based on noncommutative C * -algebra, we therefore have a remarkable connection between finite approximations to quantum physics and noncommutative geometries. Varies methods for doing quantum physics using A are explored. Particular attention is paid to developing numerically viable approximation schemes which at the same time preserve important topological features of continuum physics. (author). 21 refs, 13 figs
Scattering Amplitudes via Algebraic Geometry Methods
Søgaard, Mads; Damgaard, Poul Henrik
This thesis describes recent progress in the understanding of the mathematical structure of scattering amplitudes in quantum field theory. The primary purpose is to develop an enhanced analytic framework for computing multiloop scattering amplitudes in generic gauge theories including QCD without Feynman diagrams. The study of multiloop scattering amplitudes is crucial for the new era of precision phenomenology at the Large Hadron Collider (LHC) at CERN. Loop-level scattering amplitudes can be reduced to a basis of linearly independent integrals whose coefficients are extracted from generalized unitarity cuts. We take advantage of principles from algebraic geometry in order to extend the notion of maximal cuts to a large class of two- and three-loop integrals. This allows us to derive unique and surprisingly compact formulae for the coefficients of the basis integrals. Our results are expressed in terms of certain linear combinations of multivariate residues and elliptic integrals computed from products of ...
Finite element and finite difference methods in electromagnetic scattering
Morgan, MA
2013-01-01
This second volume in the Progress in Electromagnetic Research series examines recent advances in computational electromagnetics, with emphasis on scattering, as brought about by new formulations and algorithms which use finite element or finite difference techniques. Containing contributions by some of the world's leading experts, the papers thoroughly review and analyze this rapidly evolving area of computational electromagnetics. Covering topics ranging from the new finite-element based formulation for representing time-harmonic vector fields in 3-D inhomogeneous media using two coupled sca
Cooperative Games, Finite Geometries and Hyperstructures
Directory of Open Access Journals (Sweden)
Antonio Maturo
2003-02-01
Full Text Available In this paper some relations between finite geometric spaces and cooperative games are considered. In particular by some recent results on blocking sets we have new results on blocking coalitions. Finally we introduce a new research field on the possible relations between quasihypergroups and cooperative games.
Scattering Amplitudes via Algebraic Geometry Methods
DEFF Research Database (Denmark)
Søgaard, Mads
Feynman diagrams. The study of multiloop scattering amplitudes is crucial for the new era of precision phenomenology at the Large Hadron Collider (LHC) at CERN. Loop-level scattering amplitudes can be reduced to a basis of linearly independent integrals whose coefficients are extracted from generalized...
Geometry-invariant GRIN lens: finite ray tracing.
Bahrami, Mehdi; Goncharov, Alexander V
2014-11-17
The refractive index distribution of the geometry-invariant gradient refractive index lens (GIGL) model is derived as a function of Cartesian coordinates. The adjustable external geometry of the GIGL model aims to mimic the shape of the human and animal crystalline lens. The refractive index distribution is based on an adjustable power-law profile, which provides additional flexibility of the model. An analytical method for layer-by-layer finite ray tracing through the GIGL model is developed and used to calculate aberrations of the GIGL model. The result of the finite ray tracing aberrations of the GIGL model are compared to those obtained with paraxial ray tracing. The derived analytical expression for the refractive index distribution can be employed in the reconstruction processes of the eye using the conventional ray tracing methods. The layer-by-layer finite ray tracing approach would be an asset in ray tracing through a modified GIGL model, where the refractive index distribution cannot be described analytically. Using the layer-by-layer finite ray-tracing method, the potential of the GIGL model in representing continuous as well as shell-like layered structures is illustrated and the results for both cases are presented and analysed.
Advanced DPSM approach for modeling ultrasonic wave scattering in an arbitrary geometry
Yadav, Susheel K.; Banerjee, Sourav; Kundu, Tribikram
2011-04-01
Several techniques are used to diagnose structural damages. In the ultrasonic technique structures are tested by analyzing ultrasonic signals scattered by damages. The interpretation of these signals requires a good understanding of the interaction between ultrasonic waves and structures. Therefore, researchers need analytical or numerical techniques to have a clear understanding of the interaction between ultrasonic waves and structural damage. However, modeling of wave scattering phenomenon by conventional numerical techniques such as finite element method requires very fine mesh at high frequencies necessitating heavy computational power. Distributed point source method (DPSM) is a newly developed robust mesh free technique to simulate ultrasonic, electrostatic and electromagnetic fields. In most of the previous studies the DPSM technique has been applied to model two dimensional surface geometries and simple three dimensional scatterer geometries. It was difficult to perform the analysis for complex three dimensional geometries. This technique has been extended to model wave scattering in an arbitrary geometry. In this paper a channel section idealized as a thin solid plate with several rivet holes is formulated. The simulation has been carried out with and without cracks near the rivet holes. Further, a comparison study has been also carried out to characterize the crack. A computer code has been developed in C for modeling the ultrasonic field in a solid plate with and without cracks near the rivet holes.
Finite energy sum rules in potential scattering
International Nuclear Information System (INIS)
Graham, N.; Jaffe, R.L.; Quandt, M.; Weige, H.
2001-01-01
We study scattering theory identities previously obtained as consistency conditions in the context of one-loop quantum field theory calculations. We prove the identities using Jost function techniques and study applications
Application of finite element numerical technique to nuclear reactor geometries
Energy Technology Data Exchange (ETDEWEB)
Rouai, N M [Nuclear engineering department faculty of engineering Al-fateh universty, Tripoli (Libyan Arab Jamahiriya)
1995-10-01
Determination of the temperature distribution in nuclear elements is of utmost importance to ensure that the temperature stays within safe limits during reactor operation. This paper discusses the use of Finite element numerical technique (FE) for the solution of the two dimensional heat conduction equation in geometries related to nuclear reactor cores. The FE solution stats with variational calculus which considers transforming the heat conduction equation into an integral equation I(O) and seeks a function that minimizes this integral and hence gives the solution to the heat conduction equation. In this paper FE theory as applied to heat conduction is briefly outlined and a 2-D program is used to apply the theory to simple shapes and to two gas cooled reactor fuel elements. Good results are obtained for both cases with reasonable number of elements. 7 figs.
Application of finite element numerical technique to nuclear reactor geometries
International Nuclear Information System (INIS)
Rouai, N. M.
1995-01-01
Determination of the temperature distribution in nuclear elements is of utmost importance to ensure that the temperature stays within safe limits during reactor operation. This paper discusses the use of Finite element numerical technique (FE) for the solution of the two dimensional heat conduction equation in geometries related to nuclear reactor cores. The FE solution stats with variational calculus which considers transforming the heat conduction equation into an integral equation I(O) and seeks a function that minimizes this integral and hence gives the solution to the heat conduction equation. In this paper FE theory as applied to heat conduction is briefly outlined and a 2-D program is used to apply the theory to simple shapes and to two gas cooled reactor fuel elements. Good results are obtained for both cases with reasonable number of elements. 7 figs
Cosmological solutions and finite time singularities in Finslerian geometry
Paul, Nupur; de, S. S.; Rahaman, Farook
2018-03-01
We consider a very general scenario of our universe where its geometry is characterized by the Finslerian structure on the underlying spacetime manifold, a generalization of the Riemannian geometry. Now considering a general energy-momentum tensor for matter sector, we derive the gravitational field equations in such spacetime. Further, to depict the cosmological dynamics in such spacetime proposing an interesting equation of state identified by a sole parameter γ which for isotropic limit is simply the barotropic equation of state p = (γ ‑ 1)ρ (γ ∈ ℝ being the barotropic index), we solve the background dynamics. The dynamics offers several possibilities depending on this sole parameter as follows: (i) only an exponential expansion, or (ii) a finite time past singularity (big bang) with late accelerating phase, or (iii) a nonsingular universe exhibiting an accelerating scenario at late time which finally predicts a big rip type singularity. We also discuss several energy conditions and the possibility of cosmic bounce. Finally, we establish the first law of thermodynamics in such spacetime.
Compton scattering at finite temperature: thermal field dynamics approach
International Nuclear Information System (INIS)
Juraev, F.I.
2006-01-01
Full text: Compton scattering is a classical problem of quantum electrodynamics and has been studied in its early beginnings. Perturbation theory and Feynman diagram technique enables comprehensive analysis of this problem on the basis of which famous Klein-Nishina formula is obtained [1, 2]. In this work this problem is extended to the case of finite temperature. Finite-temperature effects in Compton scattering is of practical importance for various processes in relativistic thermal plasmas in astrophysics. Recently Compton effect have been explored using closed-time path formalism with temperature corrections estimated [3]. It was found that the thermal cross section can be larger than that for zero-temperature by several orders of magnitude for the high temperature realistic in astrophysics [3]. In our work we use a main tool to account finite-temperature effects, a real-time finite-temperature quantum field theory, so-called thermofield dynamics [4, 5]. Thermofield dynamics is a canonical formalism to explore field-theoretical processes at finite temperature. It consists of two steps, doubling of Fock space and Bogolyubov transformations. Doubling leads to appearing additional degrees of freedom, called tilded operators which together with usual field operators create so-called thermal doublet. Bogolyubov transformations make field operators temperature-dependent. Using this formalism we treat Compton scattering at finite temperature via replacing in transition amplitude zero-temperature propagators by finite-temperature ones. As a result finite-temperature extension of the Klein-Nishina formula is obtained in which differential cross section is represented as a sum of zero-temperature cross section and finite-temperature correction. The obtained result could be useful in quantum electrodynamics of lasers and for relativistic thermal plasma processes in astrophysics where correct account of finite-temperature effects is important. (author)
Lorentz Violation, Möller Scattering, and Finite Temperature
Directory of Open Access Journals (Sweden)
Alesandro F. Santos
2018-01-01
Full Text Available Lorentz and CPT symmetries may be violated in new physics that emerges at very high energy scale, that is, at the Planck scale. The differential cross section of the Möller scattering due to Lorentz violation at finite temperature is calculated. Lorentz-violating effects emerge from an interaction vertex due to a CPT-odd nonminimal coupling in the covariant derivative. The finite temperature effects are determined using the Thermo Field Dynamics (TFD formalism.
Uniqueness in inverse elastic scattering with finitely many incident waves
International Nuclear Information System (INIS)
Elschner, Johannes; Yamamoto, Masahiro
2009-01-01
We consider the third and fourth exterior boundary value problems of linear isotropic elasticity and present uniqueness results for the corresponding inverse scattering problems with polyhedral-type obstacles and a finite number of incident plane elastic waves. Our approach is based on a reflection principle for the Navier equation. (orig.)
Finite-difference modelling of anisotropic wave scattering in discrete ...
Indian Academy of Sciences (India)
2
cells containing equivalent anisotropic medium by the use of the linear slip equivalent model. Our. 16 results show ...... frequency regression predicted by equation (21) can be distorted by the effects of multiple scattering. 337 ..... other seismic attributes, at least for the relatively simple geometries of subsurface structure. 449.
Linear theory of a cold relativistic beam in a strongly magnetized finite-geometry plasma
International Nuclear Information System (INIS)
Gagne, R.R.J.; Shoucri, M.M.
1976-01-01
The linear theory of a finite-geometry cold relativistic beam propagating in a cold homogeneous finite-geometry plasma, is investigated in the case of a strongly magnetized plasma. The beam is assumed to propagate parallel to the external magnetic field. It is shown that the instability which takes place at the Cherenkov resonance ωapprox. =k/subz/v/subb/ is of the convective type. The effect of the finite geometry on the instability growth rate is studied and is shown to decrease the growth rate, with respect to the infinite geometry, by a factor depending on the ratio of the beam-to-plasma radius
SCAP-82, Single Scattering, Albedo Scattering, Point-Kernel Analysis in Complex Geometry
International Nuclear Information System (INIS)
Disney, R.K.; Vogtman, S.E.
1987-01-01
1 - Description of problem or function: SCAP solves for radiation transport in complex geometries using the single or albedo scatter point kernel method. The program is designed to calculate the neutron or gamma ray radiation level at detector points located within or outside a complex radiation scatter source geometry or a user specified discrete scattering volume. Geometry is describable by zones bounded by intersecting quadratic surfaces within an arbitrary maximum number of boundary surfaces per zone. Anisotropic point sources are describable as pointwise energy dependent distributions of polar angles on a meridian; isotropic point sources may also be specified. The attenuation function for gamma rays is an exponential function on the primary source leg and the scatter leg with a build- up factor approximation to account for multiple scatter on the scat- ter leg. The neutron attenuation function is an exponential function using neutron removal cross sections on the primary source leg and scatter leg. Line or volumetric sources can be represented as a distribution of isotropic point sources, with un-collided line-of-sight attenuation and buildup calculated between each source point and the detector point. 2 - Method of solution: A point kernel method using an anisotropic or isotropic point source representation is used, line-of-sight material attenuation and inverse square spatial attenuation between the source point and scatter points and the scatter points and detector point is employed. A direct summation of individual point source results is obtained. 3 - Restrictions on the complexity of the problem: - The SCAP program is written in complete flexible dimensioning so that no restrictions are imposed on the number of energy groups or geometric zones. The geometric zone description is restricted to zones defined by boundary surfaces defined by the general quadratic equation or one of its degenerate forms. The only restriction in the program is that the total
Finite energy bounds for $\\piN$ scattering
Grassberger, P; Schwela, D
1974-01-01
Upper bounds on energy averaged pi N cross sections are given. Using low energy data and data from pi N backward scattering and NN to pi pi annihilation, it is found that sigma /sub tot/
Finite geometry effect on the interaction of a hot beam with a plasma
International Nuclear Information System (INIS)
Shoucri, M.M.; Gagne, R.R.J.
1977-01-01
The effect of finite geometry on the interaction of a hot low-density beam with a uniform plasma filling a circular waveguide is studied. An expression is derived for the growth rate of the instabilities developing at the harmonic of the beam gyrofrequency, taking the finite beam gyroradius into account. The calculations are done in the quasistatic approximation. (author)
Geometry of finite deformations and time-incremental analysis
Czech Academy of Sciences Publication Activity Database
Fiala, Zdeněk
2016-01-01
Roč. 81, May (2016), s. 230-244 ISSN 0020-7462 Institutional support: RVO:68378297 Keywords : solid mechanics * finite deformations * time-incremental analysis * Lagrangian system * evolution equation of Lie type Subject RIV: BE - Theoretical Physics Impact factor: 2.074, year: 2016 http://www.sciencedirect.com/science/article/pii/S0020746216000330
Lorentz violation, gravitoelectromagnetism and Bhabha scattering at finite temperature
Santos, A. F.; Khanna, Faqir C.
2018-04-01
Gravitoelectromagnetism (GEM) is an approach for the gravitation field that is described using the formulation and terminology similar to that of electromagnetism. The Lorentz violation is considered in the formulation of GEM that is covariant in its form. In practice, such a small violation of the Lorentz symmetry may be expected in a unified theory at very high energy. In this paper, a non-minimal coupling term, which exhibits Lorentz violation, is added as a new term in the covariant form. The differential cross-section for Bhabha scattering in the GEM framework at finite temperature is calculated that includes Lorentz violation. The Thermo Field Dynamics (TFD) formalism is used to calculate the total differential cross-section at finite temperature. The contribution due to Lorentz violation is isolated from the total cross-section. It is found to be small in magnitude.
Finite differences versus finite elements in slab geometry, even-parity transport theory
International Nuclear Information System (INIS)
Miller, W.F. Jr.; Noh, T.
1993-01-01
There continues to be considerable interest in the application of the even-parity transport equation to problems of radiation transfer and neutron transport. The motivation for this interest arises from several potential advantages of this equation when compared with the more traditional first-order form of the equation. First, assuming that the scalar flux is of primary interest, the angular domain under consideration is one-half of that required for the first-order equation. Thus, for the same degree of accuracy, one would hopefully require substantiably fewer unknown values of the dependent variable to be determined. Secondly, the elliptic-like nature of the set of even-parity equations should allow certain parallel computer architectures to be used more readily. In a recent paper, it was shown that for neutron transport applications in slab geometry, finite differencing the even-parity equation on the cell edges yields algebraic equations with numerical properties that are superior to the traditional diamond difference approach. Specifically, a positive, second-order method with a rapidly convergent iteration approach emerged from cell-edge differencing. Additionally, for radiation transfer problems that are optically thick, it was shown that cell-edge differencing demonstrates better behavior than does diamond-differencing. However, some problems in accuracy could occur due to vacuum boundaries as well as at interfaces between very different types of material regions. These problems emerge from a boundary-layer analysis of the so called open-quotes thickclose quotes diffusion limit. For neutronics calculations, which are the subject of this paper, however, the open-quotes thickclose quotes diffusion limit analysis has little applicability, and the cell-edge differencing derived previously seems to have considerable promise. 13 refs., 2 figs., 3 tabs
Finite element method for neutron diffusion problems in hexagonal geometry
International Nuclear Information System (INIS)
Wei, T.Y.C.; Hansen, K.F.
1975-06-01
The use of the finite element method for solving two-dimensional static neutron diffusion problems in hexagonal reactor configurations is considered. It is investigated as a possible alternative to the low-order finite difference method. Various piecewise polynomial spaces are examined for their use in hexagonal problems. The central questions which arise in the design of these spaces are the degree of incompleteness permissible and the advantages of using a low-order space fine-mesh approach over that of a high-order space coarse-mesh one. There is also the question of the degree of smoothness required. Two schemes for the construction of spaces are described and a number of specific spaces, constructed with the questions outlined above in mind, are presented. They range from a complete non-Lagrangian, non-Hermite quadratic space to an incomplete ninth order space. Results are presented for two-dimensional problems typical of a small high temperature gas-cooled reactor. From the results it is concluded that the space used should at least include the complete linear one. Complete spaces are to be preferred to totally incomplete ones. Once function continuity is imposed any additional degree of smoothness is of secondary importance. For flux shapes typical of the small high temperature gas-cooled reactor the linear space fine-mesh alternative is to be preferred to the perturbation quadratic space coarse-mesh one and the low-order finite difference method is to be preferred over both finite element schemes
Scattering resonances of ultracold atoms in confined geometries
Energy Technology Data Exchange (ETDEWEB)
Saeidian, Shahpoor
2008-06-18
Subject of this thesis is the investigation of the quantum dynamics of ultracold atoms in confined geometries. We discuss the behavior of ground state atoms inside a 3D magnetic quadrupole field. Such atoms in enough weak magnetic fields can be approximately treated as neutral point-like particles. Complementary to the well-known positive energy resonances, we point out the existence of short-lived negative energy resonances. The latter originate from a fundamental symmetry of the underlying Hamiltonian. We drive a mapping of the two branches of the spectrum. Moreover, we analyze atomic hyperfine resonances in a magnetic quadrupole field. This corresponds to the case for which both the hyperfine and Zeeman interaction, are comparable, and should be taken into account. Finally, we develop a general grid method for multichannel scattering of two atoms in a two-dimensional harmonic confinement. With our approach we analyze transverse excitations/deexcitations in the course of the collisional process (distinguishable or identical atoms) including all important partial waves and their couplings due to the broken spherical symmetry. Special attention is paid to suggest a non-trivial extension of the CIRs theory developed so far only for the single-mode regime and zero-energy limit. (orig.)
Scattering resonances of ultracold atoms in confined geometries
International Nuclear Information System (INIS)
Saeidian, Shahpoor
2008-01-01
Subject of this thesis is the investigation of the quantum dynamics of ultracold atoms in confined geometries. We discuss the behavior of ground state atoms inside a 3D magnetic quadrupole field. Such atoms in enough weak magnetic fields can be approximately treated as neutral point-like particles. Complementary to the well-known positive energy resonances, we point out the existence of short-lived negative energy resonances. The latter originate from a fundamental symmetry of the underlying Hamiltonian. We drive a mapping of the two branches of the spectrum. Moreover, we analyze atomic hyperfine resonances in a magnetic quadrupole field. This corresponds to the case for which both the hyperfine and Zeeman interaction, are comparable, and should be taken into account. Finally, we develop a general grid method for multichannel scattering of two atoms in a two-dimensional harmonic confinement. With our approach we analyze transverse excitations/deexcitations in the course of the collisional process (distinguishable or identical atoms) including all important partial waves and their couplings due to the broken spherical symmetry. Special attention is paid to suggest a non-trivial extension of the CIRs theory developed so far only for the single-mode regime and zero-energy limit. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Calloo, A.; Vidal, J.F.; Le Tellier, R.; Rimpault, G., E-mail: ansar.calloo@cea.fr, E-mail: jean-francois.vidal@cea.fr, E-mail: romain.le-tellier@cea.fr, E-mail: gerald.rimpault@cea.fr [CEA, DEN, DER/SPRC/LEPh, Saint-Paul-lez-Durance (France)
2011-07-01
This paper deals with the solving of the multigroup integro-differential form of the transport equation for fine energy group structure. In that case, multigroup transfer cross sections display strongly peaked shape for light scatterers and the current Legendre polynomial expansion is not well-suited to represent them. Furthermore, even if considering an exact scattering cross sections representation, the scattering source in the discrete ordinates method (also known as the Sn method) being calculated by sampling the angular flux at given directions, may be wrongly computed due to lack of angular support for the angular flux. Hence, following the work of Gerts and Matthews, an angular finite volume solver has been developed for 2D Cartesian geometries. It integrates the multigroup transport equation over discrete volume elements obtained by meshing the unit sphere with a product grid over the polar and azimuthal coordinates and by considering the integrated flux per solid angle element. The convergence of this method has been compared to the S{sub n} method for a highly anisotropic benchmark. Besides, piecewise-average scattering cross sections have been produced for non-bound Hydrogen atoms using a free gas model for thermal neutrons. LWR lattice calculations comparing Legendre representations of the Hydrogen scattering multigroup cross section at various orders and piecewise-average cross sections for this same atom are carried out (while keeping a Legendre representation for all other isotopes). (author)
International Nuclear Information System (INIS)
Calloo, A.; Vidal, J.F.; Le Tellier, R.; Rimpault, G.
2011-01-01
This paper deals with the solving of the multigroup integro-differential form of the transport equation for fine energy group structure. In that case, multigroup transfer cross sections display strongly peaked shape for light scatterers and the current Legendre polynomial expansion is not well-suited to represent them. Furthermore, even if considering an exact scattering cross sections representation, the scattering source in the discrete ordinates method (also known as the Sn method) being calculated by sampling the angular flux at given directions, may be wrongly computed due to lack of angular support for the angular flux. Hence, following the work of Gerts and Matthews, an angular finite volume solver has been developed for 2D Cartesian geometries. It integrates the multigroup transport equation over discrete volume elements obtained by meshing the unit sphere with a product grid over the polar and azimuthal coordinates and by considering the integrated flux per solid angle element. The convergence of this method has been compared to the S_n method for a highly anisotropic benchmark. Besides, piecewise-average scattering cross sections have been produced for non-bound Hydrogen atoms using a free gas model for thermal neutrons. LWR lattice calculations comparing Legendre representations of the Hydrogen scattering multigroup cross section at various orders and piecewise-average cross sections for this same atom are carried out (while keeping a Legendre representation for all other isotopes). (author)
Energy Technology Data Exchange (ETDEWEB)
Lillie, R.A.; Robinson, J.C.
1976-05-01
The discrete ordinates method is the most powerful and generally used deterministic method to obtain approximate solutions of the Boltzmann transport equation. A finite element formulation, utilizing a canonical form of the transport equation, is here developed to obtain both integral and pointwise solutions to neutron transport problems. The formulation is based on the use of linear triangles. A general treatment of anisotropic scattering is included by employing discrete ordinates-like approximations. In addition, multigroup source outer iteration techniques are employed to perform group-dependent calculations. The ability of the formulation to reduce substantially ray effects and its ability to perform streaming calculations are demonstrated by analyzing a series of test problems. The anisotropic scattering and multigroup treatments used in the development of the formulation are verified by a number of one-dimensional comparisons. These comparisons also demonstrate the relative accuracy of the formulation in predicting integral parameters. The applicability of the formulation to nonorthogonal planar geometries is demonstrated by analyzing a hexagonal-type lattice. A small, high-leakage reactor model is analyzed to investigate the effects of varying both the spatial mesh and order of angular quadrature. This analysis reveals that these effects are more pronounced in the present formulation than in other conventional formulations. However, the insignificance of these effects is demonstrated by analyzing a realistic reactor configuration. In addition, this final analysis illustrates the importance of incorporating anisotropic scattering into the finite element formulation. 8 tables, 29 figures.
International Nuclear Information System (INIS)
Lillie, R.A.; Robinson, J.C.
1976-05-01
The discrete ordinates method is the most powerful and generally used deterministic method to obtain approximate solutions of the Boltzmann transport equation. A finite element formulation, utilizing a canonical form of the transport equation, is here developed to obtain both integral and pointwise solutions to neutron transport problems. The formulation is based on the use of linear triangles. A general treatment of anisotropic scattering is included by employing discrete ordinates-like approximations. In addition, multigroup source outer iteration techniques are employed to perform group-dependent calculations. The ability of the formulation to reduce substantially ray effects and its ability to perform streaming calculations are demonstrated by analyzing a series of test problems. The anisotropic scattering and multigroup treatments used in the development of the formulation are verified by a number of one-dimensional comparisons. These comparisons also demonstrate the relative accuracy of the formulation in predicting integral parameters. The applicability of the formulation to nonorthogonal planar geometries is demonstrated by analyzing a hexagonal-type lattice. A small, high-leakage reactor model is analyzed to investigate the effects of varying both the spatial mesh and order of angular quadrature. This analysis reveals that these effects are more pronounced in the present formulation than in other conventional formulations. However, the insignificance of these effects is demonstrated by analyzing a realistic reactor configuration. In addition, this final analysis illustrates the importance of incorporating anisotropic scattering into the finite element formulation. 8 tables, 29 figures
Scattering amplitudes over finite fields and multivariate functional reconstruction
International Nuclear Information System (INIS)
Peraro, Tiziano
2016-01-01
Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their evaluation over finite fields. Calculations over finite fields can in turn be efficiently performed using machine-size integers in statically-typed languages. We then discuss the application of the algorithm to several techniques related to the computation of scattering amplitudes, such as the four- and six-dimensional spinor-helicity formalism, tree-level recursion relations, and multi-loop integrand reduction via generalized unitarity. The method has good efficiency and scales well with the number of variables and the complexity of the problem. As an example combining these techniques, we present the calculation of full analytic expressions for the two-loop five-point on-shell integrands of the maximal cuts of the planar penta-box and the non-planar double-pentagon topologies in Yang-Mills theory, for a complete set of independent helicity configurations.
Scattering amplitudes over finite fields and multivariate functional reconstruction
Energy Technology Data Exchange (ETDEWEB)
Peraro, Tiziano [Higgs Centre for Theoretical Physics,School of Physics and Astronomy, The University of Edinburgh,James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD (United Kingdom)
2016-12-07
Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their evaluation over finite fields. Calculations over finite fields can in turn be efficiently performed using machine-size integers in statically-typed languages. We then discuss the application of the algorithm to several techniques related to the computation of scattering amplitudes, such as the four- and six-dimensional spinor-helicity formalism, tree-level recursion relations, and multi-loop integrand reduction via generalized unitarity. The method has good efficiency and scales well with the number of variables and the complexity of the problem. As an example combining these techniques, we present the calculation of full analytic expressions for the two-loop five-point on-shell integrands of the maximal cuts of the planar penta-box and the non-planar double-pentagon topologies in Yang-Mills theory, for a complete set of independent helicity configurations.
Diffusion of Finite-Size Particles in Confined Geometries
Bruna, Maria
2013-05-10
The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle\\'s dimensions. The result is a nonlinear diffusion equation for the one-particle probability density function, with an overall collective diffusion that depends on both the excluded-volume and the narrow confinement. By including both these effects, the equation is able to interpolate between severe confinement (for example, single-file diffusion) and unconfined diffusion. Numerical solutions of both the effective nonlinear diffusion equation and the stochastic particle system are presented and compared. As an application, the case of diffusion under a ratchet potential is considered, and the change in transport properties due to excluded-volume and confinement effects is examined. © 2013 Society for Mathematical Biology.
Diffusion of Finite-Size Particles in Confined Geometries
Bruna, Maria; Chapman, S. Jonathan
2013-01-01
The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle's dimensions. The result is a nonlinear diffusion equation for the one-particle probability density function, with an overall collective diffusion that depends on both the excluded-volume and the narrow confinement. By including both these effects, the equation is able to interpolate between severe confinement (for example, single-file diffusion) and unconfined diffusion. Numerical solutions of both the effective nonlinear diffusion equation and the stochastic particle system are presented and compared. As an application, the case of diffusion under a ratchet potential is considered, and the change in transport properties due to excluded-volume and confinement effects is examined. © 2013 Society for Mathematical Biology.
Excitation of lower hybrid waves by electron beams in finite geometry plasmas
International Nuclear Information System (INIS)
Shoucri, M.m.; Gagne, R.R.J.
1978-01-01
The quasi-static lower hybrid eigenmodes of a plasma column in a cylindrical waveguide are determined, and their linear excitation by a small density electron beam is discussed for the cases of a hot electron beam as well as for a cold electron beam. It is shown that under certain conditions, finite geometry effects introduce important quantitative and qualitative differences with respect to the results obtained in an infinite geometry. (author)
Finite element modeling of the neuron-electrode interface: stimulus transfer and geometry
Buitenweg, Jan R.; Rutten, Wim; Marani, Enrico
1999-01-01
The relation between stimulus transfer and the geometry of the neuron-electrode interface can not be determined properly using electrical equivalent circuits, since current that flows from the sealing gap through the neuronal membrane is difficult to model in these circuits. Therefore, finite
Mani, Arjun; Benjamin, Colin
2016-04-13
On the surface of 2D topological insulators, 1D quantum spin Hall (QSH) edge modes occur with Dirac-like dispersion. Unlike quantum Hall (QH) edge modes, which occur at high magnetic fields in 2D electron gases, the occurrence of QSH edge modes is due to spin-orbit scattering in the bulk of the material. These QSH edge modes are spin-dependent, and chiral-opposite spins move in opposing directions. Electronic spin has a larger decoherence and relaxation time than charge. In view of this, it is expected that QSH edge modes will be more robust to disorder and inelastic scattering than QH edge modes, which are charge-dependent and spin-unpolarized. However, we notice no such advantage accrues in QSH edge modes when subjected to the same degree of contact disorder and/or inelastic scattering in similar setups as QH edge modes. In fact we observe that QSH edge modes are more susceptible to inelastic scattering and contact disorder than QH edge modes. Furthermore, while a single disordered contact has no effect on QH edge modes, it leads to a finite charge Hall current in the case of QSH edge modes, and thus a vanishing of the pure QSH effect. For more than a single disordered contact while QH states continue to remain immune to disorder, QSH edge modes become more susceptible--the Hall resistance for the QSH effect changes sign with increasing disorder. In the case of many disordered contacts with inelastic scattering included, while quantization of Hall edge modes holds, for QSH edge modes a finite charge Hall current still flows. For QSH edge modes in the inelastic scattering regime we distinguish between two cases: with spin-flip and without spin-flip scattering. Finally, while asymmetry in sample geometry can have a deleterious effect in the QSH case, it has no impact in the QH case.
International Nuclear Information System (INIS)
Mani, Arjun; Benjamin, Colin
2016-01-01
On the surface of 2D topological insulators, 1D quantum spin Hall (QSH) edge modes occur with Dirac-like dispersion. Unlike quantum Hall (QH) edge modes, which occur at high magnetic fields in 2D electron gases, the occurrence of QSH edge modes is due to spin–orbit scattering in the bulk of the material. These QSH edge modes are spin-dependent, and chiral-opposite spins move in opposing directions. Electronic spin has a larger decoherence and relaxation time than charge. In view of this, it is expected that QSH edge modes will be more robust to disorder and inelastic scattering than QH edge modes, which are charge-dependent and spin-unpolarized. However, we notice no such advantage accrues in QSH edge modes when subjected to the same degree of contact disorder and/or inelastic scattering in similar setups as QH edge modes. In fact we observe that QSH edge modes are more susceptible to inelastic scattering and contact disorder than QH edge modes. Furthermore, while a single disordered contact has no effect on QH edge modes, it leads to a finite charge Hall current in the case of QSH edge modes, and thus a vanishing of the pure QSH effect. For more than a single disordered contact while QH states continue to remain immune to disorder, QSH edge modes become more susceptible—the Hall resistance for the QSH effect changes sign with increasing disorder. In the case of many disordered contacts with inelastic scattering included, while quantization of Hall edge modes holds, for QSH edge modes a finite charge Hall current still flows. For QSH edge modes in the inelastic scattering regime we distinguish between two cases: with spin-flip and without spin-flip scattering. Finally, while asymmetry in sample geometry can have a deleterious effect in the QSH case, it has no impact in the QH case. (paper)
Finite element analysis of the neutron transport equation in spherical geometry
International Nuclear Information System (INIS)
Kim, Yong Ill; Kim, Jong Kyung; Suk, Soo Dong
1992-01-01
The Galerkin formulation of the finite element method is applied to the integral law of the first-order form of the one-group neutron transport equation in one-dimensional spherical geometry. Piecewise linear or quadratic Lagrange polynomials are utilized in the integral law for the angular flux to establish a set of linear algebraic equations. Numerical analyses are performed for the scalar flux distribution in a heterogeneous sphere as well as for the criticality problem in a uniform sphere. For the criticality problems in the uniform sphere, the results of the finite element method, with the use of continuous finite elements in space and angle, are compared with the exact solutions. In the heterogeneous problem, the scalar flux distribution obtained by using discontinuous angular and spatical finite elements is in good agreement with that from the ANISN code calculation. (Author)
Finite element analysis of a solar collector plate using two plate geometries
Directory of Open Access Journals (Sweden)
Diego Manuel Medina Carril
2016-09-01
Full Text Available The thermal behavior of an absorber plate in a solar collector is investigated using finite element analysis. The thermal behavior and efficiency of two absorber plate geometries are studied, using a typical solar collector with a rectangular profile as reference, and a proposed absorber plate with curved geometry. An analysis of the most important parameters involved in the design of the absorber plate was carried out, indicating that the curved geometry of the absorber plate yields an average efficiency ~25% higher than the conventional rectangular geometry. The results suggest that a curved profile made of materials such as aluminum with thermal conductivity higher than 200W/m°C, plate thickness of the order of 2-3mm and with a large density of tubes per unit area of the collector´s plate greatly benefits the thermal efficiency of the solar collector.
Application of Mie theory to assess structure of spheroidal scattering in backscattering geometries.
Chalut, Kevin J; Giacomelli, Michael G; Wax, Adam
2008-08-01
Inverse light scattering analysis seeks to associate measured scattering properties with the most probable theoretical scattering distribution. Although Mie theory is a spherical scattering model, it has been used successfully for discerning the geometry of spheroidal scatterers. The goal of this study was an in-depth evaluation of the consequences of analyzing the structure of spheroidal geometries, which are relevant to cell and tissue studies in biology, by employing Mie-theory-based inverse light scattering analysis. As a basis for this study, the scattering from spheroidal geometries was modeled using T-matrix theory and used as test data. In a previous study, we used this technique to investigate the case of spheroidal scatterers aligned with the optical axis. In the present study, we look at a broader scope which includes the effects of aspect ratio, orientation, refractive index, and incident light polarization. Over this wide range of parameters, our results indicate that this method provides a good estimate of spheroidal structure.
International Nuclear Information System (INIS)
El-Wakil, S.A.; Sallah, M.; Degheidy, A.R.
2005-01-01
The time-dependent radiation transfer equation in plane geometry with Rayleigh scattering is studied. The traveling wave transformation is used to obtain the corresponding stationary-like equation. Pomraning-Eddington approximation is then used to calculate the radiation intensity in finite plane-parallel media. Numerical results and shielding calculations are shown for reflectivity and transmissivity at different times. The medium is assumed to have specular-reflecting boundaries. For the sake of comparison, two different weight functions are introduced and to force the boundary conditions to be fulfilled
Effects of Hot-Spot Geometry on Backscattering and Down-Scattering Neutron Spectra
Mohamed, Z. L.; Mannion, O. M.; Forrest, C. J.; Knauer, J. P.; Anderson, K. S.; Radha, P. B.
2017-10-01
The measured neutron spectrum produced by a fusion experiment plays a key role in inferring observable quantities. One important observable is the areal density of an implosion, which is inferred by measuring the scattering of neutrons. This project seeks to use particle-transport simulations to model the effects of hot-spot geometry on backscattering and down-scattering neutron spectra along different lines of sight. Implosions similar to those conducted at the Laboratory of Laser Energetics are modeled by neutron transport through a DT plasma and a DT ice shell using the particle transport codes MCNP and IRIS. Effects of hot-spot geometry are obtained by ``detecting'' scattered neutrons along different lines of sight. This process is repeated for various hot-spot geometries representing known shape distortions between the hot spot and the shell. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944.
A finite element conjugate gradient FFT method for scattering
Collins, Jeffery D.; Ross, Dan; Jin, J.-M.; Chatterjee, A.; Volakis, John L.
1991-01-01
Validated results are presented for the new 3D body of revolution finite element boundary integral code. A Fourier series expansion of the vector electric and mangnetic fields is employed to reduce the dimensionality of the system, and the exact boundary condition is employed to terminate the finite element mesh. The mesh termination boundary is chosen such that is leads to convolutional boundary operatores of low O(n) memory demand. Improvements of this code are discussed along with the proposed formulation for a full 3D implementation of the finite element boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution.
SPIRIT, Plot of Geometry and Results of 2-D Finite Elements Calculation
International Nuclear Information System (INIS)
Lambert, P.
1977-01-01
1 - Nature of the physical problem solved: SPIRIT plots the geometry and the results from a 2-D finite elements calculation. 2 - Method of solution: SPIRIT uses the Benson-Lehner graph plotter. The programme will draw each separate element of the mesh according to the description supplied and a complete picture of the mesh is therefore built up. The program can also construct an isothermal distribution using straight lines. Each line is constructed considering each element in isolation. 3 - Restrictions on the complexity of the problem: The program deals only with bodies entirely contained in the first quadrant and the x-coordinates should be less than 20.0
High Order Finite Element Method for the Lambda modes problem on hexagonal geometry
International Nuclear Information System (INIS)
Gonzalez-Pintor, S.; Ginestar, D.; Verdu, G.
2009-01-01
A High Order Finite Element Method to approximate the Lambda modes problem for reactors with hexagonal geometry has been developed. This method is based on the expansion of the neutron flux in terms of the modified Dubiner's polynomials on a triangular mesh. This mesh is fixed and the accuracy of the method is improved increasing the degree of the polynomial expansions without the necessity of remeshing. The performance of method has been tested obtaining the dominant Lambda modes of different 2D reactor benchmark problems.
Finite-difference modelling of anisotropic wave scattering in discrete ...
Indian Academy of Sciences (India)
A M Ekanem
2018-04-05
Apr 5, 2018 ... scattering characteristics in fractured media and thus, validate the practical utility of using anisotropic .... to fluid flow. ... account the porosity of the host rock and assumes .... The free surface boundary conditions generally.
Some studies on weld bead geometries for laser spot welding process using finite element analysis
International Nuclear Information System (INIS)
Siva Shanmugam, N.; Buvanashekaran, G.; Sankaranarayanasamy, K.
2012-01-01
Highlights: → In this study, a 2 kW Nd:YAG laser welding system is used to conduct laser spot welding trials. → The size and shape of the laser spot weld is predicted using finite element simulation. → The heat input is assumed to be a three-dimensional conical Gaussian heat source. → The result highlights the effect of beam incident angle on laser spot welds. → The achieved results of numerical simulation are almost identical with a real weldment. -- Abstract: Nd:YAG laser beam welding is a high power density welding process which has the capability to focus the beam to a very small spot diameter of about 0.4 mm. It has favorable characteristics namely, low heat input, narrow heat affected zone and lower distortions, as compared to conventional welding processes. In this study, finite element method (FEM) is applied for predicting the weld bead geometry i.e. bead length (BL), bead width (BW) and depth of penetration (DP) in laser spot welding of AISI 304 stainless steel sheet of thickness 2.5 mm. The input parameters of laser spot welding such as beam power, incident angle of the beam and beam exposure time are varied for conducting experimental trials and numerical simulations. Temperature-dependent thermal properties of AISI 304 stainless steel, the effect of latent heat of fusion, and the convective and radiative aspects of boundary conditions are considered while developing the finite element model. The heat input to the developed model is assumed to be a three-dimensional conical Gaussian heat source. Finite-element simulations of laser spot welding were carried out by using Ansys Parametric Design Language (APDL) available in finite-element code, ANSYS. The results of the numerical analysis provide the shape of the weld beads for different ranges of laser input parameters that are subsequently compared with the results obtained through experimentation and it is found that they are in good agreement.
Finite element method solution of simplified P3 equation for flexible geometry handling
International Nuclear Information System (INIS)
Ryu, Eun Hyun; Joo, Han Gyu
2011-01-01
In order to obtain efficiently core flux solutions which would be much closer to the transport solution than the diffusion solution is, not being limited by the geometry of the core, the simplified P 3 (SP 3 ) equation is solved with the finite element method (FEM). A generic mesh generator, GMSH, is used to generate linear and quadratic mesh data. The linear system resulting from the SP 3 FEM discretization is solved by Krylov subspace methods (KSM). A symmetric form of the SP 3 equation is derived to apply the conjugate gradient method rather than the KSMs for nonsymmetric linear systems. An optional iso-parametric quadratic mapping scheme, which is to selectively model nonlinear shapes with a quadratic mapping to prevent significant mismatch in local domain volume, is also implemented for efficient application of arbitrary geometry handling. The gain in the accuracy attainable by the SP 3 solution over the diffusion solution is assessed by solving numerous benchmark problems having various core geometries including the IAEA PWR problems involving rectangular fuels and the Takeda fast reactor problems involving hexagonal fuels. The reference transport solution is produced by the McCARD Monte Carlo code and the multiplication factor and power distribution errors are assessed. In addition, the effect of quadratic mapping is examined for circular cell problems. It is shown that significant accuracy gain is possible with the SP 3 solution for the fast reactor problems whereas only marginal improvement is noted for thermal reactor problems. The quadratic mapping is also quite effective handling geometries with curvature. (author)
Scattering Theory for Open Quantum Systems with Finite Rank Coupling
International Nuclear Information System (INIS)
Behrndt, Jussi; Malamud, Mark M.; Neidhardt, Hagen
2007-01-01
Quantum systems which interact with their environment are often modeled by maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a single maximal dissipative operator A D in a Hilbert space is used to describe an open quantum system. In this case the minimal self-adjoint dilation of A D can be regarded as the Hamiltonian of a closed system which contains the open system, but since K-tilde is necessarily not semibounded from below, this model is difficult to interpret from a physical point of view. In the second part of the paper an open quantum system is modeled with a family {A(μ)} of maximal dissipative operators depending on energy μ, and it is shown that the open system can be embedded into a closed system where the Hamiltonian is semibounded. Surprisingly it turns out that the corresponding scattering matrix can be completely recovered from scattering matrices of single pseudo-Hamiltonians as in the first part of the paper. The general results are applied to a class of Sturm-Liouville operators arising in dissipative and quantum transmitting Schroedinger-Poisson systems
Sossinsky, A B
2012-01-01
The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal--although some, of course, remain more equal than others. The author concentrates on several of the more distinguished and beautiful ones, which include what he terms "toy geometries", the geometries of Platonic bodies, discrete geometries, and classical continuous geometries. The text is based on first-year semester course lectures delivered at the Independent University of Moscow in 2003 and 2006. It is by no means a formal algebraic or analytic treatment of geometric topics, but rather, a highly visual exposition containing upwards of 200 illustrations. The reader is expected to possess a familiarity with elementary Euclidean geometry, albeit those lacking t...
Emittance of a finite scattering medium with refractive index greater than unity
International Nuclear Information System (INIS)
Crosbie, A.L.
1980-01-01
Refractive index and scattering can significantly influence the transfer of radiation in a semitransparent medium such as water, glass, plastics, or ceramics. In a recent article (1979), the author presented exact numerical results for the emittance of a semiinfinite scattering medium with a refractive index greater than unity. The present investigation extends the analysis to a finite medium. The physical situation consists of a finite planar layer. The isothermal layer emits, absorbs, and isotropically scatters thermal radiation. It is characterized by single scattering albedo, optical thickness, refractive index, and temperature. A formula for the directional emittance is derived, the directional emittance being the emittance of the medium multiplied by the interface transmittance. The ratio of hemispherical to normal emittance is tabulated and discussed
Multiple scattering expansion of the self-energy at finite temperature
International Nuclear Information System (INIS)
Jeon, S.; Ellis, P.J.
1998-01-01
An often used rule that the thermal correction to the self-energy is the thermal phase-space times the forward scattering amplitude from target particles is shown to be the leading term in an exact multiple scattering expansion. Starting from imaginary-time finite-temperature field theory, a rigorous expansion for the retarded self-energy is derived. The relationship to the thermodynamic potential is briefly discussed. copyright 1998 The American Physical Society
Multiple Scattering Expansion of the Self-Energy at Finite Temperature
Jeon, Sangyong; Ellis, Paul J.
1998-01-01
An often used rule that the thermal correction to the self-energy is the thermal phase-space times the forward scattering amplitude from target particles is shown to be the leading term in an exact multiple scattering expansion. Starting from imaginary-time finite-temperature field theory, a rigorous expansion for the retarded self-energy is derived. The relationship to the thermodynamic potential is briefly discussed.
Taking into account of effects of finite geometry in a neutron-physical experiment
International Nuclear Information System (INIS)
Dushin, V.N.; Ippolitov, V.T.
1981-01-01
Problems for account of finite geometry of neutron-physical experiment are considered from the point of view of increasing the determination accuracy of nuclear-physical constants (NPC). A three-equation system, which relates studied nuclear-physical characteristics of the target to experimental results obtained at the output of registering device, is presented. A problem of accurate NPC determination is the solution of the given system in relation to parameters sought for, it is a so-called reverse problem of the irradiation transfer theory. A method of error matrix determination measuring NPC, with the help of the introduction of the sensitivity coefficients is considered. Proposed interpretation of reverse problems of the irradiation transfer theory is effective during the planning of experimental investigations taking into account correlation properties of experimental techniques [ru
Rodriguez, Lucas C; Saba, Juliana N; Meyer, Clark A; Chung, Kwok-Hung; Wadhwani, Chandur; Rodrigues, Danieli C
2016-11-01
Recent literature indicates that the long-term success of dental implants is, in part, attributed to how dental crowns are attached to their associated implants. The commonly utilized method for crown attachment - cementation, has been criticized because of recent links between residual cement and peri-implant disease. Residual cement extrusion from crown-abutment margins post-crown seating is a growing concern. This study aimed at (1) identifying key abutment features, which would improve dental cement flow characteristics, and (2) understanding how these features would impact the mechanical stability of the abutment under functional loads. Computational fluid dynamic modeling was used to evaluate cement flow in novel abutment geometries. These models were then evaluated using 3D-printed surrogate models. Finite element analysis also provided an understanding of how the mechanical stability of these abutments was altered after key features were incorporated into the geometry. The findings demonstrated that the key features involved in improved venting of the abutment during crown seating were (1) addition of vents, (2) diameter of the vents, (3) location of the vents, (4) addition of a plastic screw insert, and (5) thickness of the abutment wall. This study culminated in a novel design for a vented abutment consisting of 8 vents located radially around the abutment neck-margin plus a plastic insert to guide the cement during seating and provide retrievability to the abutment system.Venting of the dental abutment has been shown to decrease the risk of undetected residual dental cement post-cement-retained crown seating. This article will utilize a finite element analysis approach toward optimizing dental abutment designs for improved dental cement venting. Features investigated include (1) addition of vents, (2) diameter of vents, (3) location of vents, (4) addition of plastic screw insert, and (5) thickness of abutment wall.
Rodriguez, Lucas C.; Saba, Juliana N.; Meyer, Clark A.; Chung, Kwok‐Hung; Wadhwani, Chandur
2016-01-01
Abstract Recent literature indicates that the long‐term success of dental implants is, in part, attributed to how dental crowns are attached to their associated implants. The commonly utilized method for crown attachment – cementation, has been criticized because of recent links between residual cement and peri‐implant disease. Residual cement extrusion from crown‐abutment margins post‐crown seating is a growing concern. This study aimed at (1) identifying key abutment features, which would improve dental cement flow characteristics, and (2) understanding how these features would impact the mechanical stability of the abutment under functional loads. Computational fluid dynamic modeling was used to evaluate cement flow in novel abutment geometries. These models were then evaluated using 3D‐printed surrogate models. Finite element analysis also provided an understanding of how the mechanical stability of these abutments was altered after key features were incorporated into the geometry. The findings demonstrated that the key features involved in improved venting of the abutment during crown seating were (1) addition of vents, (2) diameter of the vents, (3) location of the vents, (4) addition of a plastic screw insert, and (5) thickness of the abutment wall. This study culminated in a novel design for a vented abutment consisting of 8 vents located radially around the abutment neck‐margin plus a plastic insert to guide the cement during seating and provide retrievability to the abutment system.Venting of the dental abutment has been shown to decrease the risk of undetected residual dental cement post‐cement‐retained crown seating. This article will utilize a finite element analysis approach toward optimizing dental abutment designs for improved dental cement venting. Features investigated include (1) addition of vents, (2) diameter of vents, (3) location of vents, (4) addition of plastic screw insert, and (5) thickness of abutment wall. PMID
Indian Academy of Sciences (India)
. In the previous article we looked at the origins of synthetic and analytic geometry. More practical minded people, the builders and navigators, were studying two other aspects of geometry- trigonometry and integral calculus. These are actually ...
Electron Raman scattering in semiconductor quantum well wire of cylindrical ring geometry
International Nuclear Information System (INIS)
Betancourt-Riera, Re.; Betancourt-Riera, Ri.; Nieto Jalil, J. M.; Riera, R.
2015-01-01
We study the electron states and the differential cross section for an electron Raman scattering process in a semiconductor quantum well wire of cylindrical ring geometry. The electron Raman scattering developed here can be used to provide direct information about the electron band structures of these confinement systems. We assume that the system grows in a GaAs/Al 0.35 Ga 0.65 As matrix. The system is modeled by considering T = 0 K and also a single parabolic conduction band, which is split into a sub-band system due to the confinement. The emission spectra are discussed for different scattering configurations, and the selection rules for the processes are also studied. Singularities in the spectra are found and interpreted. (paper)
Validation of favor code linear elastic fracture solutions for finite-length flaw geometries
International Nuclear Information System (INIS)
Dickson, T.L.; Keeney, J.A.; Bryson, J.W.
1995-01-01
One of the current tasks within the US Nuclear Regulatory Commission (NRC)-funded Heavy Section Steel Technology Program (HSST) at Oak Ridge National Laboratory (ORNL) is the continuing development of the FAVOR (Fracture, analysis of Vessels: Oak Ridge) computer code. FAVOR performs structural integrity analyses of embrittled nuclear reactor pressure vessels (RPVs) with stainless steel cladding, to evaluate compliance with the applicable regulatory criteria. Since the initial release of FAVOR, the HSST program has continued to enhance the capabilities of the FAVOR code. ABAQUS, a nuclear quality assurance certified (NQA-1) general multidimensional finite element code with fracture mechanics capabilities, was used to generate a database of stress-intensity-factor influence coefficients (SIFICs) for a range of axially and circumferentially oriented semielliptical inner-surface flaw geometries applicable to RPVs with an internal radius (Ri) to wall thickness (w) ratio of 10. This database of SIRCs has been incorporated into a development version of FAVOR, providing it with the capability to perform deterministic and probabilistic fracture analyses of RPVs subjected to transients, such as pressurized thermal shock (PTS), for various flaw geometries. This paper discusses the SIFIC database, comparisons with other investigators, and some of the benchmark verification problem specifications and solutions
International Nuclear Information System (INIS)
Schneider, D.
2001-01-01
The nodal method Minos has been developed to offer a powerful method for the calculation of nuclear reactor cores in rectangular geometry. This method solves the mixed dual form of the diffusion equation and, also of the simplified P N approximation. The discretization is based on Raviart-Thomas' mixed dual finite elements and the iterative algorithm is an alternating direction method, which uses the current as unknown. The subject of this work is to adapt this method to hexagonal geometry. The guiding idea is to construct and test different methods based on the division of a hexagon into trapeze or rhombi with appropriate mapping of these quadrilaterals onto squares in order to take into advantage what is already available in the Minos solver. The document begins with a review of the neutron diffusion equation. Then we discuss its mixed dual variational formulation from a functional as well as from a numerical point of view. We study conformal and bilinear mappings for the two possible meshing of the hexagon. Thus, four different methods are proposed and are completely described in this work. Because of theoretical and numerical difficulties, a particular treatment has been necessary for methods based on the conformal mapping. Finally, numerical results are presented for a hexagonal benchmark to validate and compare the four methods with respect to pre-defined criteria. (authors)
International Nuclear Information System (INIS)
Mickael, M.; Gardner, R.P.; Verghese, K.
1988-01-01
An improved method for calculating the total probability of particle scattering within the solid angle subtended by finite detectors is developed, presented, and tested. The limiting polar and azimuthal angles subtended by the detector are measured from the direction that most simplifies their calculation rather than from the incident particle direction. A transformation of the particle scattering probability distribution function (pdf) is made to match the transformation of the direction from which the limiting angles are measured. The particle scattering probability to the detector is estimated by evaluating the integral of the transformed pdf over the range of the limiting angles measured from the preferred direction. A general formula for transforming the particle scattering pdf is derived from basic principles and applied to four important scattering pdf's; namely, isotropic scattering in the Lab system, isotropic neutron scattering in the center-of-mass system, thermal neutron scattering by the free gas model, and gamma-ray Klein-Nishina scattering. Some approximations have been made to these pdf's to enable analytical evaluations of the final integrals. These approximations are shown to be valid over a wide range of energies and for most elements. The particle scattering probability to spherical, planar circular, and right circular cylindrical detectors has been calculated using the new and previously reported direct approach. Results indicate that the new approach is valid and is computationally faster by orders of magnitude
Lloyd's formula in multiple-scattering calculations with finite temperature
International Nuclear Information System (INIS)
Zeller, Rudolf
2005-01-01
Lloyd's formula is an elegant tool to calculate the number of states directly from the imaginary part of the logarithm of the Korringa-Kohn-Rostoker (KKR) determinant. It is shown how this formula can be used at finite electronic temperatures and how the difficult problem to determine the physically significant correct phase of the complex logarithm can be circumvented by working with the single-valued real part of the logarithm. The approach is based on contour integrations in the complex energy plane and exploits the analytical properties of the KKR Green function and the Fermi-Dirac function. It leads to rather accurate results, which is illustrated by a local-density functional calculation of the temperature dependence of the intrinsic Fermi level in zinc-blende GaN
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
International Nuclear Information System (INIS)
Burger, M. J.
1981-01-01
1 - Description of problem or function: The ZONE program is a finite element mesh generator which produces the nodes and element description of any two-dimensional geometry. The geometry is divided into a mesh of quadrilateral and triangular zones defined by node points taken in a counter-clockwise sequence. The zones are arranged sequentially in an ordered march through the geometry. The order can be chosen so that the minimum bandwidth is obtained. The mesh that is generated can be used as input to any two-dimensional as well as any axisymmetrical structure program. 2 - Method of solution: The basic concept used is the definition of a two-dimensional structure by the intersection of two sets of lines which describe the geometric and material boundaries. A set of lines called meridians define the geometric and material boundaries and generally run in the same direction. Another set of linear line segments called rays which intersect the meridians are also defined at the material and geometric boundaries. The section of the structure between successive rays is called a region. The ray segment between any two consecutive ray-meridian intersections or void area in the structure is called a layer and is described as passing through, or bounding a material. The boundaries can be directly defined as a sequence of straight line segments or can be computed in terms of elliptic segments or circular arcs. A meridian or ray can also be made to follow a previously-defined meridian or ray at a fixed distance by invoking an offset option. 3 - Restrictions on the complexity of the problem: The following are limited only by a DIMENSION statement. The code currently has a maxima of: 100 coordinate points defining a meridian or ray, 40 meridians, 40 layers. There are no limits on the number of zones or nodes for any problems
Prasolov, V V
2015-01-01
This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.
Scattering of E Polarized Plane Wave by Rectangular Cavity With Finite Flanges
Vinogradova, Elena D.
2017-11-01
The rigorous Method of Regularization is implemented for accurate analysis of wave scattering by rectangular cavity with finite flanges. The solution is free from limitations on problem parameters. The calculation of the induced surface current, bistatic radar cross section (RCS) and frequency dependence of monostatic RCS are performed with controlled accuracy in a wide frequency band.
Hadagali, Prasannaah; Peters, James R; Balasubramanian, Sriram
2018-03-12
Personalized Finite Element (FE) models and hexahedral elements are preferred for biomechanical investigations. Feature-based multi-block methods are used to develop anatomically accurate personalized FE models with hexahedral mesh. It is tedious to manually construct multi-blocks for large number of geometries on an individual basis to develop personalized FE models. Mesh-morphing method mitigates the aforementioned tediousness in meshing personalized geometries every time, but leads to element warping and loss of geometrical data. Such issues increase in magnitude when normative spine FE model is morphed to scoliosis-affected spinal geometry. The only way to bypass the issue of hex-mesh distortion or loss of geometry as a result of morphing is to rely on manually constructing the multi-blocks for scoliosis-affected spine geometry of each individual, which is time intensive. A method to semi-automate the construction of multi-blocks on the geometry of scoliosis vertebrae from the existing multi-blocks of normative vertebrae is demonstrated in this paper. High-quality hexahedral elements were generated on the scoliosis vertebrae from the morphed multi-blocks of normative vertebrae. Time taken was 3 months to construct the multi-blocks for normative spine and less than a day for scoliosis. Efforts taken to construct multi-blocks on personalized scoliosis spinal geometries are significantly reduced by morphing existing multi-blocks.
Wang, R T; van de Hulst, H C
1995-05-20
A new algorithm for cylindrical Bessel functions that is similar to the one for spherical Bessel functions allows us to compute scattering functions for infinitely long cylinders covering sizes ka = 2πa/λ up to 8000 through the use of only an eight-digit single-precision machine computation. The scattering function and complex extinction coefficient of a finite cylinder that is seen near perpendicular incidence are derived from those of an infinitely long cylinder by the use of Huygens's principle. The result, which contains no arbitrary normalization factor, agrees quite well with analog microwave measurements of both extinction and scattering for such cylinders, even for an aspect ratio p = l/(2a) as low as 2. Rainbows produced by cylinders are similar to those for spherical drops but are brighter and have a lower contrast.
International Nuclear Information System (INIS)
Wu Hongchun; Xie Zhongsheng; Zhu Xuehua
1994-01-01
The nodal discrete-ordinate transport calculating model of anisotropy scattering problem in three-dimensional cartesian geometry is given. The computing code NOTRAN/3D has been encoded and the satisfied conclusion is gained
Scattering forms and the positive geometry of kinematics, color and the worldsheet
Arkani-Hamed, Nima; Bai, Yuntao; He, Song; Yan, Gongwang
2018-05-01
The search for a theory of the S-Matrix over the past five decades has revealed surprising geometric structures underlying scattering amplitudes ranging from the string worldsheet to the amplituhedron, but these are all geometries in auxiliary spaces as opposed to the kinematical space where amplitudes actually live. Motivated by recent advances providing a reformulation of the amplituhedron and planar N = 4 SYM amplitudes directly in kinematic space, we propose a novel geometric understanding of amplitudes in more general theories. The key idea is to think of amplitudes not as functions, but rather as differential forms on kinematic space. We explore the resulting picture for a wide range of massless theories in general spacetime dimensions. For the bi-adjoint ϕ 3 scalar theory, we establish a direct connection between its "scattering form" and a classic polytope — the associahedron — known to mathematicians since the 1960's. We find an associahedron living naturally in kinematic space, and the tree level amplitude is simply the "canonical form" associated with this "positive geometry". Fundamental physical properties such as locality and unitarity, as well as novel "soft" limits, are fully determined by the combinatorial geometry of this polytope. Furthermore, the moduli space for the open string worldsheet has also long been recognized as an associahedron. We show that the scattering equations act as a diffeomorphism between the interior of this old "worldsheet associahedron" and the new "kinematic associahedron", providing a geometric interpretation and simple conceptual derivation of the bi-adjoint CHY formula. We also find "scattering forms" on kinematic space for Yang-Mills theory and the Non-linear Sigma Model, which are dual to the fully color-dressed amplitudes despite having no explicit color factors. This is possible due to a remarkable fact—"Color is Kinematics"— whereby kinematic wedge products in the scattering forms satisfy the same Jacobi
Morphing methods to parameterize specimen-specific finite element model geometries.
Sigal, Ian A; Yang, Hongli; Roberts, Michael D; Downs, J Crawford
2010-01-19
Shape plays an important role in determining the biomechanical response of a structure. Specimen-specific finite element (FE) models have been developed to capture the details of the shape of biological structures and predict their biomechanics. Shape, however, can vary considerably across individuals or change due to aging or disease, and analysis of the sensitivity of specimen-specific models to these variations has proven challenging. An alternative to specimen-specific representation has been to develop generic models with simplified geometries whose shape is relatively easy to parameterize, and can therefore be readily used in sensitivity studies. Despite many successful applications, generic models are limited in that they cannot make predictions for individual specimens. We propose that it is possible to harness the detail available in specimen-specific models while leveraging the power of the parameterization techniques common in generic models. In this work we show that this can be accomplished by using morphing techniques to parameterize the geometry of specimen-specific FE models such that the model shape can be varied in a controlled and systematic way suitable for sensitivity analysis. We demonstrate three morphing techniques by using them on a model of the load-bearing tissues of the posterior pole of the eye. We show that using relatively straightforward procedures these morphing techniques can be combined, which allows the study of factor interactions. Finally, we illustrate that the techniques can be used in other systems by applying them to morph a femur. Morphing techniques provide an exciting new possibility for the analysis of the biomechanical role of shape, independently or in interaction with loading and material properties. Copyright 2009 Elsevier Ltd. All rights reserved.
Influence of first proximal phalanx geometry on hallux valgus deformity: a finite element analysis.
Morales-Orcajo, Enrique; Bayod, Javier; Becerro-de-Bengoa-Vallejo, Ricardo; Losa-Iglesias, Marta; Doblare, Manuel
2015-07-01
Hallux abducto valgus (HAV), one of the most common forefoot deformities, occurs primarily in elderly women. HAV is a complex disease without a clearly identifiable cause for its higher prevalence in women compared with men. Several studies have reported various skeletal parameters related to HAV. This study examined the geometry of the proximal phalanx of the hallux (PPH) as a potential etiologic factor in this deformity. A total of 43 cadaver feet (22 males and 21 females) were examined by means of cadaveric dissection. From these data, ten representative PPHs for both genders were selected, corresponding to five percentiles for males (0, 25, 50, 75, and 100%) and five for females. These ten different PPHs were modeled and inserted in ten foot models. Stress distribution patterns within these ten PPH models were qualitatively compared using finite element analysis. In the ten cases analyzed, tensile stresses were larger on the lateral side, whereas compressive stresses were larger on the medial side. The bones of males were larger than female bones for each of the parameters examined; however, the mean difference between lateral and medial sides of the PPH (mean ± SD) was larger in women. Also the shallower the concavity at the base of the PPH, the larger the compressive stresses predicted. Internal forces on the PPH, due to differences in length between its medial and lateral sides, may force the PPH into a less-stressful position. The geometry of the PPH is a significant factor in HAV development influencing the other reported skeletal parameters and, thus, should be considered during preoperative evaluation. Clinical assessment should evaluate the first ray as a whole and not as isolated factors.
Atom-dimer scattering in a heteronuclear mixture with a finite intraspecies scattering length
Gao, Chao; Zhang, Peng
2018-04-01
We study the three-body problem of two ultracold identical bosonic atoms (denoted by B ) and one extra atom (denoted by X ), where the scattering length aB X between each bosonic atom and atom X is resonantly large and positive. We calculate the scattering length aad between one bosonic atom and the shallow dimer formed by the other bosonic atom and atom X , and investigate the effect induced by the interaction between the two bosonic atoms. We find that even if this interaction is weak (i.e., the corresponding scattering length aB B is of the same order of the van der Waals length rvdW or even smaller), it can still induce a significant effect for the atom-dimer scattering length aad. Explicitly, an atom-dimer scattering resonance can always occur when the value of aB B varies in the region with | aB B|≲ rvdW . As a result, both the sign and the absolute value of aad, as well as the behavior of the aad-aB X function, depends sensitively on the exact value of aB B. Our results show that, for a good quantitative theory, the intraspecies interaction is required to be taken into account for this heteronuclear system, even if this interaction is weak.
Neutron Transport in Finite Random Media with Pure-Triplet Scattering
International Nuclear Information System (INIS)
Sallaha, M.; Hendi, A.A.
2008-01-01
The solution of the one-speed neutron transport equation in a finite slab random medium with pure-triplet anisotropic scattering is studied. The stochastic medium is assumed to consist of two randomly mixed immiscible fluids. The cross section and the scattering kernel are treated as discrete random variables, which obey the same statistics as Markovian processes and exponential chord length statistics. The medium boundaries are considered to have specular reflectivities with angular-dependent externally incident flux. The deterministic solution is obtained by using Pomraning-Eddington approximation. Numerical results are calculated for the average reflectivity and average transmissivity for different values of the single scattering albedo and varying the parameters which characterize the random medium. Compared to the results obtained by Adams et al. in case of isotropic scattering that based on the Monte Carlo technique, it can be seen that we have good comparable data
International Nuclear Information System (INIS)
Bourassa, A.E.; Degenstein, D.A.; Llewellyn, E.J.
2008-01-01
The inversion of satellite-based observations of limb scattered sunlight for the retrieval of constituent species requires an efficient and accurate modelling of the measurement. We present the development of the SASKTRAN radiative transfer model for the prediction of limb scatter measurements at optical wavelengths by method of successive orders along rays traced in a spherical atmosphere. The component of the signal due to the first two scattering events of the solar beam is accounted for directly along rays traced in the three-dimensional geometry. Simplifying assumptions in successive scattering orders provide computational optimizations without severely compromising the accuracy of the solution. SASKTRAN is designed for the analysis of measurements from the OSIRIS instrument and the implementation of the algorithm is efficient such that the code is suitable for the inversion of OSIRIS profiles on desktop computers. SASKTRAN total limb radiance profiles generally compare better with Monte-Carlo reference models over a large range of solar conditions than the approximate spherical and plane-parallel models typically used for inversions
International Nuclear Information System (INIS)
Kobayashi, Keisuke; Kikuchi, Hirohiko; Tsutsuguchi, Ken
1993-01-01
A neutron multigroup transport equation in x-y-z geometry is solved by the spherical harmonics method using finite Fourier transformation. Using the first term of the Fourier series for the space variables of spherical harmonics moments, three-point finite difference like equations are derived for x-, y- and z-axis directions, which are more consistent and accurate than those derived using the usual finite difference approximation, and these equations are solved by the iteration method in each axis direction alternatively. A method to find an optimum acceleration factor for this inner iteration is described. It is shown in the numerical examples that the present method gives higher accuracy with less mesh points that the usual finite difference method. (author)
«Paralipomena» on uniqueness in inverse scattering from a finite number of data
Directory of Open Access Journals (Sweden)
R. Persico
2007-06-01
Full Text Available This paper shows new proof of non-uniqueness of the solution for the retrieving of a compact-supported function starting from a finite number of samples of its spectrum. As will be shown, this is relevant for linear inverse scattering problems, that in many cases can be recast as the reconstruction of a compact supported function from a finite set of samples of its spectrum. Since this reconstruction is not unique, from a practical point of view, any linear inverse scattering algorithm that can be recast in terms of a Fourier relationship between unknowns and data necessarily «trusts» on the absence of invisible objects in the particular situation at hand.
A Non-Perturbative, Finite Particle Number Approach to Relativistic Scattering Theory
Energy Technology Data Exchange (ETDEWEB)
Lindesay, James V
2001-05-11
We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these equations, which have been demonstrated to be calculable, provide a non-perturbative way of obtaining relativistic scattering amplitudes for any finite number of particles that are Lorentz invariant, unitary, cluster decomposable and reduce unambiguously in the non-relativistic limit to the non-relativistic Faddeev equations. The aim of this program is to develop equations which explicitly depend upon physically observable input variables, and do not require ''renormalization'' or ''dressing'' of these parameters to connect them to the boundary states.
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Cambon, S.; Lacoste, P.
2011-01-01
We propose a finite element method to solve the axisymmetric scattering problem posed on a regular bounded domain. Here we shall show how to reduce the initial 3D problem into a truncated sum of 2D independent problems posed into a meridian plane of the object. Each of these problem results in the coupling of a partial differential equation into the interior domain and an integral equation on the surface simulating the free space. Then variational volume and boundary integral formulations of Maxwell's equation on regular surfaces are derived. We introduce some general finite element adapted to cylindrical coordinates and constructed from nodal and mixed finite element both for the interior (volume) and for the integral equation (surface). (authors)
TWOTRAN-2, 2-D Multigroup Transport in X-Y, R-Z, R-Theta Geometry with Anisotropic Scattering
International Nuclear Information System (INIS)
Lathrop, K.D.; Brinkley, F.W.
1995-01-01
1 - Description of problem or function: TWOTRAN2 solves the two-dimensional multigroup transport equation in (x,y), (r,theta), and (r,z) geometries. Both regular and adjoint, inhomogeneous and homogeneous (k eff and eigenvalue searches) problems subject to vacuum, reflective, periodic, white or input-specified 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 in finite difference form which is solved with the central (diamond) difference approximation. Negative fluxes are eliminated by a local set-to zero and correct algorithm. Standard inner (within-group) and outer iterative cycles are accelerated by a coarse-mesh re-balancing on a coarse mesh which may be independent of the material mesh. 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 MAXLEN can be accommodated. On IBM machines, TWOTRAN2 will execute in the 4-byte mode so that any combination of problem parameters leading to a container array less than MAXLEN can be accommodated. MAXLEN can be several hundred thousand and most problems can be core-contained. On the CDC machines MAXLEN can be slightly greater than 40,000 words and peripheral storage is used for most group-dependent data
Pedoe, Dan
1988-01-01
""A lucid and masterly survey."" - Mathematics Gazette Professor Pedoe is widely known as a fine teacher and a fine geometer. His abilities in both areas are clearly evident in this self-contained, well-written, and lucid introduction to the scope and methods of elementary geometry. It covers the geometry usually included in undergraduate courses in mathematics, except for the theory of convex sets. Based on a course given by the author for several years at the University of Minnesota, the main purpose of the book is to increase geometrical, and therefore mathematical, understanding and to he
Gluon scattering in N=4 super Yang-Mills at finite temperature
International Nuclear Information System (INIS)
Ito, Katsushi; Iwasaki, Koh; Nastase, Horatiu
2008-01-01
We extend the AdS/CFT prescription of Alday and Maldacena to finite temperature T, defining an amplitude for gluon scattering in N=4 Super Yang-Mills at strong coupling from string theory. It is defined by a lightlike 'Wilson loop' living at the horizon of the T-dual to the black hole in AdS space. Unlike the zero temperature case, this is different from the Wilson loop contour defined at the boundary of the AdS black hole metric. Thus at nonzero T there is no relation between gluon scattering amplitudes and the Wilson loop. We calculate a gauge theory observable that can be interpreted as the amplitude at strong coupling for forward scattering of a low energy gluon (E >T) in both cutoff and generalized dimensional regularization. The generalized dimensional regularization is defined in string theory as an IR modified dimensional reduction. For this calculation, the corresponding usual Wilson loop of the same boundary shape was argued to be related to the jet quenching parameter of the finite temperature N=4 SYM plasma, while the gluon scattering amplitude is related to the viscosity coefficient. (author)
A time-domain finite element boundary integral approach for elastic wave scattering
Shi, F.; Lowe, M. J. S.; Skelton, E. A.; Craster, R. V.
2018-04-01
The response of complex scatterers, such as rough or branched cracks, to incident elastic waves is required in many areas of industrial importance such as those in non-destructive evaluation and related fields; we develop an approach to generate accurate and rapid simulations. To achieve this we develop, in the time domain, an implementation to efficiently couple the finite element (FE) method within a small local region, and the boundary integral (BI) globally. The FE explicit scheme is run in a local box to compute the surface displacement of the scatterer, by giving forcing signals to excitation nodes, which can lie on the scatterer itself. The required input forces on the excitation nodes are obtained with a reformulated FE equation, according to the incident displacement field. The surface displacements computed by the local FE are then projected, through time-domain BI formulae, to calculate the scattering signals with different modes. This new method yields huge improvements in the efficiency of FE simulations for scattering from complex scatterers. We present results using different shapes and boundary conditions, all simulated using this approach in both 2D and 3D, and then compare with full FE models and theoretical solutions to demonstrate the efficiency and accuracy of this numerical approach.
International Nuclear Information System (INIS)
Gado, J.
1986-02-01
The four group, 2D and 3D hexagonal geometry HTGR benchmark problems and a 2D hexagonal geometry PWR (WWER) benchmark problem have been solved by using the finite element diffusion code DIFGEN. The hexagons (or hexagonal prisms) were subdivided into first order or second order triangles or quadrilaterals (or triangular or quadrilateral prisms). In the 2D HTGR case of the number of the inserted absorber rods was also varied (7, 6, 0 or 37 rods). The calculational results are in a good agreement with the results of other calculations. The larger systematic series of DIFGEN calculations have given a quantitative picture on the convergence properties of various finite element modellings of hexagonal grids in DIFGEN. (orig.)
Directory of Open Access Journals (Sweden)
Matthew R. McCurry
2015-06-01
Full Text Available The reliability of finite element analysis (FEA in biomechanical investigations depends upon understanding the influence of model assumptions. In producing finite element models, surface mesh resolution is influenced by the resolution of input geometry, and influences the resolution of the ensuing solid mesh used for numerical analysis. Despite a large number of studies incorporating sensitivity studies of the effects of solid mesh resolution there has not yet been any investigation into the effect of surface mesh resolution upon results in a comparative context. Here we use a dataset of crocodile crania to examine the effects of surface resolution on FEA results in a comparative context. Seven high-resolution surface meshes were each down-sampled to varying degrees while keeping the resulting number of solid elements constant. These models were then subjected to bite and shake load cases using finite element analysis. The results show that incremental decreases in surface resolution can result in fluctuations in strain magnitudes, but that it is possible to obtain stable results using lower resolution surface in a comparative FEA study. As surface mesh resolution links input geometry with the resulting solid mesh, the implication of these results is that low resolution input geometry and solid meshes may provide valid results in a comparative context.
International Nuclear Information System (INIS)
Sallah, M.; Margeanu, C. A.
2016-01-01
The space-fractional neutron transport equation is used to describe the neutrons transport in finite disturbed reactors. It is approximated using the Pomraning-Eddington technique to yield two space-fractional differential equations, in terms of neutron density and net neutron flux. These resultant equations are coupled into a fractional diffusion-like equation for the neutron density whose solution is obtained by using Laplace transformation method. The solution is represented in terms of the Mittag-Leffler function and its different orders. The scattering is considered as quadratic scattering to offer a more realistic, compact representation of the system, and to increase the accuracy of the estimated neutronic parameters. The results are presented graphically to illustrate the fractional parameter effect in addition to the effect of radiative-transfer properties on the physical parameters of interest (reflection coefficient, transmission coefficient, neutron energy, and net neutron flux). The neutron transport problem in finite disturbed reactor with quadratic scattering is considered in investigating the shielding effectiveness, by using MAVRIC shielding module from SCALE6 programs package. The fractional parameter can be used to adjust the analysed data on neutron energy and flux, both for the theoretical model and the neutron transport application. (authors)
Analysis of a finite PML approximation to the three dimensional elastic wave scattering problem
Bramble, James H.
2010-01-01
We consider the application of a perfectly matched layer (PML) technique to approximate solutions to the elastic wave scattering problem in the frequency domain. The PML is viewed as a complex coordinate shift in spherical coordinates which leads to a variable complex coefficient equation for the displacement vector posed on an infinite domain (the complement of the scatterer). The rapid decay of the PML solution suggests truncation to a bounded domain with a convenient outer boundary condition and subsequent finite element approximation (for the truncated problem). We prove existence and uniqueness of the solutions to the infinite domain and truncated domain PML equations (provided that the truncated domain is sufficiently large). We also show exponential convergence of the solution of the truncated PML problem to the solution of the original scattering problem in the region of interest. We then analyze a Galerkin numerical approximation to the truncated PML problem and prove that it is well posed provided that the PML damping parameter and mesh size are small enough. Finally, computational results illustrating the efficiency of the finite element PML approximation are presented. © 2010 American Mathematical Society.
Solution of the Cox-Thompson inverse scattering problem using finite set of phase shifts
Apagyi, B; Scheid, W
2003-01-01
A system of nonlinear equations is presented for the solution of the Cox-Thompson inverse scattering problem (1970 J. Math. Phys. 11 805) at fixed energy. From a given finite set of phase shifts for physical angular momenta, the nonlinear equations determine related sets of asymptotic normalization constants and nonphysical (shifted) angular momenta from which all quantities of interest, including the inversion potential itself, can be calculated. As a first application of the method we use input data consisting of a finite set of phase shifts calculated from Woods-Saxon and box potentials representing interactions with diffuse or sharp surfaces, respectively. The results for the inversion potentials, their first moments and asymptotic properties are compared with those provided by the Newton-Sabatier quantum inversion procedure. It is found that in order to achieve inversion potentials of similar quality, the Cox-Thompson method requires a smaller set of phase shifts than the Newton-Sabatier procedure.
Solution of the Cox-Thompson inverse scattering problem using finite set of phase shifts
International Nuclear Information System (INIS)
Apagyi, Barnabas; Harman, Zoltan; Scheid, Werner
2003-01-01
A system of nonlinear equations is presented for the solution of the Cox-Thompson inverse scattering problem (1970 J. Math. Phys. 11 805) at fixed energy. From a given finite set of phase shifts for physical angular momenta, the nonlinear equations determine related sets of asymptotic normalization constants and nonphysical (shifted) angular momenta from which all quantities of interest, including the inversion potential itself, can be calculated. As a first application of the method we use input data consisting of a finite set of phase shifts calculated from Woods-Saxon and box potentials representing interactions with diffuse or sharp surfaces, respectively. The results for the inversion potentials, their first moments and asymptotic properties are compared with those provided by the Newton-Sabatier quantum inversion procedure. It is found that in order to achieve inversion potentials of similar quality, the Cox-Thompson method requires a smaller set of phase shifts than the Newton-Sabatier procedure
Scattering analysis of periodic structures using finite-difference time-domain
ElMahgoub, Khaled; Elsherbeni, Atef Z
2012-01-01
Periodic structures are of great importance in electromagnetics due to their wide range of applications such as frequency selective surfaces (FSS), electromagnetic band gap (EBG) structures, periodic absorbers, meta-materials, and many others. The aim of this book is to develop efficient computational algorithms to analyze the scattering properties of various electromagnetic periodic structures using the finite-difference time-domain periodic boundary condition (FDTD/PBC) method. A new FDTD/PBC-based algorithm is introduced to analyze general skewed grid periodic structures while another algor
International Nuclear Information System (INIS)
Hutchinson, S.; Costillo, S.; Dalton, K.; Hensel, E.
1990-01-01
A study is conducted of the finite element solution of the partial differential equations governing two-dimensional electromagnetic field scattering problems on a SIMD computer. A nodal assembly technique is introduced which maps a single node to a single processor. The physical domain is first discretized in parallel to yield the node locations of an O-grid mesh. Next, the system of equations is assembled and then solved in parallel using a conjugate gradient algorithm for complex-valued, non-symmetric, non-positive definite systems. Using this technique and Thinking Machines Corporation's Connection Machine-2 (CM-2), problems with more than 250k nodes are solved. Results of electromagnetic scattering, governed by the 2-d scalar Hemoholtz wave equations are presented in this paper. Solutions are demonstrated for a wide range of objects. A summary of performance data is given for the set of test problems
International Nuclear Information System (INIS)
Lindesay, James V
2002-01-01
Starting from a unitary, Lorentz invariant two-particle scattering amplitude, we show how to use an identification and replacement process to construct a unique, unitary particle-antiparticle amplitude. This process differs from conventional on-shell Mandelstam s,t,u crossing in that the input and constructed amplitudes can be off-diagonal and off-energy shell. Further, amplitudes are constructed using the invariant parameters which are appropriate to use as driving terms in the multi-particle, multichannel nonperturbative, cluster decomposable, relativistic scattering equations of the Faddeev-type integral equations recently presented by Alfred, Kwizera, Lindesay and Noyes. It is therefore anticipated that when so employed, the resulting multi-channel solutions will also be unitary. The process preserves the usual particle-antiparticle symmetries. To illustrate this process, we construct a J=0 scattering length model chosen for simplicity. We also exhibit a class of physical models which contain a finite quantum mass parameter and are Lorentz invariant. These are constructed to reduce in the appropriate limits, and with the proper choice of value and sign of the interaction parameter, to the asymptotic solution of the nonrelativistic Coulomb problem, including the forward scattering singularity , the essential singularity in the phase, and the Bohr bound-state spectrum
International Nuclear Information System (INIS)
Kraus, H.G.
1991-01-01
This paper discusses methods for calculating Fraunhofer intensity fields resulting from diffraction through one- and two-dimensional apertures are presented. These methods are based on the geometric concept of finite elements and on Fourier and Abbe transforms. The geometry of the two-dimensional diffracting aperture(s) is based on biquadratic isoparametric elements, which are used to define aperture(s) of complex geometry. These elements are also used to build complex amplitude and phase functions across the aperture(s) which may be of continuous or discontinuous form. The transform integrals are accurately and efficiently integrated numerically using Gaussian quadrature. The power of these methods is most evident in two dimensions, where several examples are presented which include secondary obstructions, straight and curved secondary spider supports, multiple-mirror arrays, synthetic aperture arrays, segmented mirrors, apertures covered by screens, apodization, and phase plates. Typically, the finite element Abbe transform method results in significant gains in computational efficiency over the finite element Fourier transform method, but is also subject to some loss in generality
International Nuclear Information System (INIS)
Ganguli, G.; Palmadesso, P.
1984-01-01
Finite geometry effects on the stability properties of a charged beam propagating through an intense relativistic annular electron beam have been studied. The stability of the system under transverse oscillation has been examined in detail in a parameter domain pertinent to the collective particle accelerator, currently under development at the Naval Research Laboratory. Both the normal mode and the convective aspects of this instability have been investigated. Despite a substantial temporal growth rate as predicted by the normal mode approach, this instability does not prevent successful acceleration of a portion of the axial beam. Thus the transverse oscillation is not fatal to the collective particle accelerator operation
Finite beta and compressibility effects on stability of resistive modes in toroidal geometry
International Nuclear Information System (INIS)
Leboeuf, J-N.G.; Kurita, Gen-ichi.
1998-03-01
Linear resistive stability results obtained from the toroidal magnetohydrodynamic codes FAR developed at the Oak Ridge National Laboratory in United States of America and AEOLUS developed at the Japan Atomic Energy Research Institute are compared for carefully constructed benchmark profiles and parameters. These are unstable to a tearing mode with toroidal mode number n=1. The eigenvalues and eigenfunctions calculated with both codes are in close agreement and show that the effect of compressibility is weak for these modes. The effect of finite plasma beta is considered, and the eigenvalues calculated by the FAR and AEOLUS codes also show good agreement. It is shown that the finite beta has a stabilizing effect on the toroidal tearing mode, but that the compressibility also has little effect on finite beta tearing modes. (author)
Extraction of neutron-neutron scattering length from nn coincidence-geometry nd breakup data
Directory of Open Access Journals (Sweden)
E. S. Konobeevski
2011-03-01
Full Text Available We report preliminary results of a kinematically complete experiment on measurement of nd breakup reaction yield at neutron beam RADEX of Institute for Nuclear Research (Moscow, Russia. In the experiment two secondary neutrons are detected in geometry of neutron-neutron final-state interaction. Data are obtained at energy of incident neutrons En = 40 - 60 MeV for various divergence angles of two neutrons ΔΘ = 4, 6, 8º. 1S0 neutron-neutron scattering length ann were determined by comparison of the experimental dependence of reaction yield on the relative energy of two secondary neutrons with results of simulation depending on ann. For En = 40 MeV and ΔΘ = 6º (the highest statistics in the experiment the value ann = -17.9 ± 1.0 fm is obtained. The further improving of accuracy of the experiment and more rigorous theoretical analysis will allow one to remove the existing difference in ann values obtained in different experiments.
The effect of finite geometry on the three-dimensional transfer of solar irradiance in clouds
Davies, R.
1978-01-01
Results are presented for a Monte Carlo model applied to a wide range of cloud widths and heights, and for an analytical model restricted in its application to cuboidally shaped clouds whose length, breadth, and depth may be varied independently; the clouds must be internally homogeneous with respect to their intrinsic radiative properties. Comparative results from the Monte Carlo method and the derived analytical model are presented for a wide range of cloud sizes, with special emphasis on the effects of varying the single scatter albedo, the solar zenith angle, and the scattering phase angle.
International Nuclear Information System (INIS)
Schoefs, Franck; Chevreuil, Mathilde; Pasqualini, Olivier; Cazuguel, Mikaël
2016-01-01
Welded joints are used in various structures and infrastructures like bridges, ships and offshore structures, and are submitted to cyclic stresses. Their fatigue behaviour is an industrial key issue to deal with and still offers original research subjects. One of the available methods relies on the computing of the stress concentration factor. Even if some studies were previously driven to evaluate this factor onto some cases of welded structures, the shape of the weld joint is generally idealized through a deterministic parametric geometry. Previous experimental works however have shown that this shape plays a key role in the lifetime assessment. We propose in this paper a methodology for computing the stress concentration factor in presence of random geometries of welded joints. In view to make the results available by engineers, this method merges stochastic computation and semi-probabilistic analysis by computing partial safety factors with a dedicated method. - Highlights: • Numerical computation of stress concentration factor with random geometry of weld. • Real data are used for probabilistic modelling. • Identification of partial safety factor from SFEM computation in case of random geometries.
International Nuclear Information System (INIS)
Núñez, Jóse; Ramos, Eduardo; Lopez, Juan M
2012-01-01
We describe a hybrid method based on the combined use of the Fourier Galerkin and finite-volume techniques to solve the fluid dynamics equations in cylindrical geometries. A Fourier expansion is used in the angular direction, partially translating the problem to the Fourier space and then solving the resulting equations using a finite-volume technique. We also describe an algorithm required to solve the coupled mass and momentum conservation equations similar to a pressure-correction SIMPLE method that is adapted for the present formulation. Using the Fourier–Galerkin method for the azimuthal direction has two advantages. Firstly, it has a high-order approximation of the partial derivatives in the angular direction, and secondly, it naturally satisfies the azimuthal periodic boundary conditions. Also, using the finite-volume method in the r and z directions allows one to handle boundary conditions with discontinuities in those directions. It is important to remark that with this method, the resulting linear system of equations are band-diagonal, leading to fast and efficient solvers. The benefits of the mixed method are illustrated with example problems. (paper)
Solution of multi-group diffusion equation in x-y-z geometry by finite Fourier transformation
International Nuclear Information System (INIS)
Kobayashi, Keisuke
1975-01-01
The multi-group diffusion equation in three-dimensional x-y-z geometry is solved by finite Fourier transformation. Applying the Fourier transformation to a finite region with constant nuclear cross sections, the fluxes and currents at the material boundaries are obtained in terms of the Fourier series. Truncating the series after the first term, and assuming that the source term is piecewise linear within each mesh box, a set of coupled equations is obtained in the form of three-point equations for each coordinate. These equations can be easily solved by the alternative direction implicit method. Thus a practical procedure is established that could be applied to replace the currently used difference equation. This equation is used to solve the multi-group diffusion equation by means of the source iteration method; and sample calculations for thermal and fast reactors show that the present method yields accurate results with a smaller number of mesh points than the usual finite difference equations. (auth.)
Finite difference time domain solution of electromagnetic scattering on the hypercube
International Nuclear Information System (INIS)
Calalo, R.H.; Lyons, J.R.; Imbriale, W.A.
1988-01-01
Electromagnetic fields interacting with a dielectric or conducting structure produce scattered electromagnetic fields. To model the fields produced by complicated, volumetric structures, the finite difference time domain (FDTD) method employs an iterative solution to Maxwell's time dependent curl equations. Implementations of the FDTD method intensively use memory and perform numerous calculations per time step iteration. The authors have implemented an FDTD code on the California Institute of Technology/Jet Propulsion Laboratory Mark III Hypercube. This code allows to solve problems requiring as many as 2,048,000 unit cells on a 32 node Hypercube. For smaller problems, the code produces solutions in a fraction of the time to solve the same problems on sequential computers
The Geometry Optimisation of a Triple Branch Pipe Using Finite Element Method
Directory of Open Access Journals (Sweden)
Dorian Nedelcu
2008-01-01
Full Text Available The paper presents the geometrical optimization of a triple branch pipesubmitted to an internal pressure. The goal of the optimization was todetermine the optimum thickness of piping and branch pipe ribs, in thecondition of reaching admissible values of the stress and displacement.The resistance calculus was realized with Cosmos DesignStar softwareand the geometry was modeled with Microstation Modeler software.
International Nuclear Information System (INIS)
Kılıç, Emre; Eibert, Thomas F.
2015-01-01
An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained
Energy Technology Data Exchange (ETDEWEB)
Kılıç, Emre, E-mail: emre.kilic@tum.de; Eibert, Thomas F.
2015-05-01
An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.
Traoré, Philippe; Ahipo, Yves Marcel; Louste, Christophe
2009-08-01
In this paper an improved finite volume scheme to discretize diffusive flux on a non-orthogonal mesh is proposed. This approach, based on an iterative technique initially suggested by Khosla [P.K. Khosla, S.G. Rubin, A diagonally dominant second-order accurate implicit scheme, Computers and Fluids 2 (1974) 207-209] and known as deferred correction, has been intensively utilized by Muzaferija [S. Muzaferija, Adaptative finite volume method for flow prediction using unstructured meshes and multigrid approach, Ph.D. Thesis, Imperial College, 1994] and later Fergizer and Peric [J.H. Fergizer, M. Peric, Computational Methods for Fluid Dynamics, Springer, 2002] to deal with the non-orthogonality of the control volumes. Using a more suitable decomposition of the normal gradient, our scheme gives accurate solutions in geometries where the basic idea of Muzaferija fails. First the performances of both schemes are compared for a Poisson problem solved in quadrangular domains where control volumes are increasingly skewed in order to test their robustness and efficiency. It is shown that convergence properties and the accuracy order of the solution are not degraded even on extremely skewed mesh. Next, the very stable behavior of the method is successfully demonstrated on a randomly distorted grid as well as on an anisotropically distorted one. Finally we compare the solution obtained for quadrilateral control volumes to the ones obtained with a finite element code and with an unstructured version of our finite volume code for triangular control volumes. No differences can be observed between the different solutions, which demonstrates the effectiveness of our approach.
Phononic thermal resistance due to a finite periodic array of nano-scatterers
Energy Technology Data Exchange (ETDEWEB)
Trang Nghiêm, T. T.; Chapuis, Pierre-Olivier [Univ. Lyon, CNRS, INSA-Lyon, Université Claude Bernard Lyon 1, CETHIL UMR5008, F-69621 Villeurbanne (France)
2016-07-28
The wave property of phonons is employed to explore the thermal transport across a finite periodic array of nano-scatterers such as circular and triangular holes. As thermal phonons are generated in all directions, we study their transmission through a single array for both normal and oblique incidences, using a linear dispersionless time-dependent acoustic frame in a two-dimensional system. Roughness effects can be directly considered within the computations without relying on approximate analytical formulae. Analysis by spatio-temporal Fourier transform allows us to observe the diffraction effects and the conversion of polarization. Frequency-dependent energy transmission coefficients are computed for symmetric and asymmetric objects that are both subject to reciprocity. We demonstrate that the phononic array acts as an efficient thermal barrier by applying the theory of thermal boundary (Kapitza) resistances to arrays of smooth scattering holes in silicon for an exemplifying periodicity of 10 nm in the 5–100 K temperature range. It is observed that the associated thermal conductance has the same temperature dependence as that without phononic filtering.
Finite elements for the calculation of turbulent flows in three-dimensional complex geometries
Ruprecht, A.
A finite element program for the calculation of incompressible turbulent flows is presented. In order to reduce the required storage an iterative algorithm is used which solves the necessary equations sequentially. The state of turbulence is defined by the k-epsilon model. In addition to the standard k-epsilon model, the modification of Bardina et al., taking into account the rotation of the mean flow, is investigated. With this program, the flow in the draft tube of a Kaplan turbine is examined. Calculations are carried out for swirling and nonswirling entrance flow. The results are compared with measurements.
Dilz, R.J.; van Beurden, M.C.
2016-01-01
We propose a mixed spatial spectral method aimed directly at aperiodic, finite scatterers in a layered medium. By using a Gabor frame to discretize the problem a straightforward and fast way to Fourier transform is available. The poles and branchcuts in the spectral-domain Green function can be
Holographic geometry of cMERA for quantum quenches and finite temperature
International Nuclear Information System (INIS)
Mollabashi, Ali; Naozaki, Masahiro; Ryu, Shinsei; Takayanagi, Tadashi
2014-01-01
We study the time evolution of cMERA (continuous MERA) under quantum quenches in free field theories. We calculate the corresponding holographic metric using the proposal in http://arxiv.org/abs/1208.3469 and confirm that it qualitatively agrees with its gravity dual given by a half of the AdS black hole spacetime, argued by Hartman and Maldacena in http://arxiv.org/abs/1303.1080. By doubling the cMERA for the quantum quench, we give an explicit construction of finite temperature cMERA. We also study cMERA in the presence of chemical potential and show that there is an enhancement of metric in the infrared region corresponding to the Fermi energy
Gerke, Kirill M.
2018-01-17
Permeability is one of the fundamental properties of porous media and is required for large-scale Darcian fluid flow and mass transport models. Whilst permeability can be measured directly at a range of scales, there are increasing opportunities to evaluate permeability from pore-scale fluid flow simulations. We introduce the free software Finite-Difference Method Stokes Solver (FDMSS) that solves Stokes equation using a finite-difference method (FDM) directly on voxelized 3D pore geometries (i.e. without meshing). Based on explicit convergence studies, validation on sphere packings with analytically known permeabilities, and comparison against lattice-Boltzmann and other published FDM studies, we conclude that FDMSS provides a computationally efficient and accurate basis for single-phase pore-scale flow simulations. By implementing an efficient parallelization and code optimization scheme, permeability inferences can now be made from 3D images of up to 109 voxels using modern desktop computers. Case studies demonstrate the broad applicability of the FDMSS software for both natural and artificial porous media.
Directory of Open Access Journals (Sweden)
Hassan Badreddine
2017-01-01
Full Text Available The current work focuses on the development and application of a new finite volume immersed boundary method (IBM to simulate three-dimensional fluid flows and heat transfer around complex geometries. First, the discretization of the governing equations based on the second-order finite volume method on Cartesian, structured, staggered grid is outlined, followed by the description of modifications which have to be applied to the discretized system once a body is immersed into the grid. To validate the new approach, the heat conduction equation with a source term is solved inside a cavity with an immersed body. The approach is then tested for a natural convection flow in a square cavity with and without circular cylinder for different Rayleigh numbers. The results computed with the present approach compare very well with the benchmark solutions. As a next step in the validation procedure, the method is tested for Direct Numerical Simulation (DNS of a turbulent flow around a surface-mounted matrix of cubes. The results computed with the present method compare very well with Laser Doppler Anemometry (LDA measurements of the same case, showing that the method can be used for scale-resolving simulations of turbulence as well.
Gerke, Kirill M.; Vasilyev, Roman V.; Khirevich, Siarhei; Collins, Daniel; Karsanina, Marina V.; Sizonenko, Timofey O.; Korost, Dmitry V.; Lamontagne, Sébastien; Mallants, Dirk
2018-05-01
Permeability is one of the fundamental properties of porous media and is required for large-scale Darcian fluid flow and mass transport models. Whilst permeability can be measured directly at a range of scales, there are increasing opportunities to evaluate permeability from pore-scale fluid flow simulations. We introduce the free software Finite-Difference Method Stokes Solver (FDMSS) that solves Stokes equation using a finite-difference method (FDM) directly on voxelized 3D pore geometries (i.e. without meshing). Based on explicit convergence studies, validation on sphere packings with analytically known permeabilities, and comparison against lattice-Boltzmann and other published FDM studies, we conclude that FDMSS provides a computationally efficient and accurate basis for single-phase pore-scale flow simulations. By implementing an efficient parallelization and code optimization scheme, permeability inferences can now be made from 3D images of up to 109 voxels using modern desktop computers. Case studies demonstrate the broad applicability of the FDMSS software for both natural and artificial porous media.
International Nuclear Information System (INIS)
Fujii, A; Hayashi, S; Fujii, S; Yanagi, K
2014-01-01
This paper deals with the functional performance of optical surface texture measuring instruments on the market. It is well known that their height response curves against certain referential geometry are not always identical to each other. So, a more precise study on the optical instrument's characteristics is greatly needed. Firstly, we developed a new simulation tool using a finite-difference time-domain technique, which enables the prediction of the height response curve against the fundamental surface geometry in the case of the confocal laser scanning microscope. Secondly, by utilizing this new simulation tool, measurement results, including outliers, were compared with the analytical simulation results. The comparison showed the consistency, which indicates that necessary conditions of surface measurement standards for verifying the instrument performance can be established. Consequently, we suggest that the maximum measurable slope angle must be added to evaluation subjects as significant metrological characteristics of measuring instruments, along with the lateral period limit. Finally, we propose a procedure to determine the lateral period limit in an ISO standard. (paper)
Finite difference modelling of scattered hydrates and its implications in gas-hydrate exploration
Digital Repository Service at National Institute of Oceanography (India)
Dewangan, P.; Ramprasad, T.; Ramana, M.V.
coming from individual scatterers 12 . However, the scatterers which lie within the first Fresnel zone interfere constructively. Therefore, the BSR ampli- tude in a zero-offset section represents all the scatterers lying within the first Fresnel zone...
Non-Gaussian Stochastic Radiation Transfer in Finite Planar Media with Quadratic Scattering
International Nuclear Information System (INIS)
Sallah, M.
2016-01-01
The stochastic radiation transfer is considered in a participating planar finite continuously fluctuating medium characterized by non-Gaussian variability. The problem is considered for diffuse-reflecting boundaries with quadratic Rayleigh scattering. Random variable transformation (RVT) technique is used to get the complete average for the solution functions that are represented by the probability-density function (PDF) of the solution process. RVT algorithm applies a simple integral transformation to the input stochastic process (the extinction function of the medium). This linear transformation enables us to rewrite the stochastic transport equations in terms of the optical random variable (x) and the optical random thickness (L). Then the radiation transfer equation is solved deterministically to get a closed form for the solution as a function of x and L. So, the solution is used to obtain the PDF of the solution functions applying the RVT technique among the input random variable (L) and the output process (the solution functions). The obtained averages of the solution functions are used to get the complete analytical averages for some interesting physical quantities, namely, reflectivity, transmissivity and partial heat fluxes at the medium boundaries. Numerical results are represented graphically for different non-Gaussian probability distribution functions that compared with the corresponding Gaussian PDF.
A Framework for Coxeter Spectral Classification of Finite Posets and Their Mesh Geometries of Roots
Directory of Open Access Journals (Sweden)
Daniel Simson
2013-01-01
Full Text Available Following our paper [Linear Algebra Appl. 433(2010, 699–717], we present a framework and computational tools for the Coxeter spectral classification of finite posets J≡(J,⪯. One of the main motivations for the study is an application of matrix representations of posets in representation theory explained by Drozd [Funct. Anal. Appl. 8(1974, 219–225]. We are mainly interested in a Coxeter spectral classification of posets J such that the symmetric Gram matrix GJ:=(1/2[CJ+CJtr]∈J(ℚ is positive semidefinite, where CJ∈J(ℤ is the incidence matrix of J. Following the idea of Drozd mentioned earlier, we associate to J its Coxeter matrix CoxJ:=-CJ·CJ-tr, its Coxeter spectrum speccJ, a Coxeter polynomial coxJ(t∈ℤ[t], and a Coxeter number cJ. In case GJ is positive semi-definite, we also associate to J a reduced Coxeter number čJ, and the defect homomorphism ∂J:ℤJ→ℤ. In this case, the Coxeter spectrum speccJ is a subset of the unit circle and consists of roots of unity. In case GJ is positive semi-definite of corank one, we relate the Coxeter spectral properties of the posets J with the Coxeter spectral properties of a simply laced Euclidean diagram DJ∈{̃n,̃6,̃7,̃8} associated with J. Our aim of the Coxeter spectral analysis of such posets J is to answer the question when the Coxeter type CtypeJ:=(speccJ,cJ, čJ of J determines its incidence matrix CJ (and, hence, the poset J uniquely, up to a ℤ-congruency. In connection with this question, we also discuss the problem studied by Horn and Sergeichuk [Linear Algebra Appl. 389(2004, 347–353], if for any ℤ-invertible matrix A∈n(ℤ, there is B∈n(ℤ such that Atr=Btr·A·B and B2=E is the identity matrix.
Determination of the gamma radiation scattering with geometry changes in the system
International Nuclear Information System (INIS)
Albuquerque, M. da P.P.; Xavier, M.; Caldas, L.V.E.
1988-07-01
Three different experimental systems were used for the determination of the radiation scattering due to the walls, ceiling and floor of the Calibration Laboratory. The radiation detection was made with a portable ionization chamber Victoreen model Panoramic 470. The measurements were taken with and without the use of a lead shield block between the detector and the radioactive source. The results showed that the scattering contribution increased about 80%, as the distance between detector and source was varied from 1,0 to 2,0 m. Therefore the scattering contribution determination is very important for the establishment of the standard radiation fields for instruments calibration. (author) [pt
International Nuclear Information System (INIS)
Canpolat, M.; Mourant, J.R.
2000-01-01
Measurement of light transport in tissue has the potential to be an inexpensive and practical tool for non-invasive tissue diagnosis in medical applications because it can provide information on both morphological and biochemical properties. To capitalize on the potential of light transport as a diagnostic tool, an understanding of what information can be gleaned from light transport measurements is needed. We present data concerning the sensitivity of light transport measurements, made in clinically relevant geometries, to scattering properties. The intensity of the backscattered light at small source-detector separations is shown to be sensitive to the phase function, and furthermore the collected light intensity is found to be correlated with the amount of high-angle scattering in the medium. (author)
International Nuclear Information System (INIS)
Tayal, M.
1987-01-01
Structures often operate at elevated temperatures. Temperature calculations are needed so that the design can accommodate thermally induced stresses and material changes. A finite element computer called FEAT has been developed to calculate temperatures in solids of arbitrary shapes. FEAT solves the classical equation for steady state conduction of heat. The solution is obtained for two-dimensional (plane or axisymmetric) or for three-dimensional problems. Gap elements are use to simulate interfaces between neighbouring surfaces. The code can model: conduction; internal generation of heat; prescribed convection to a heat sink; prescribed temperatures at boundaries; prescribed heat fluxes on some surfaces; and temperature-dependence of material properties like thermal conductivity. The user has a option of specifying the detailed variation of thermal conductivity with temperature. For convenience to the nuclear fuel industry, the user can also opt for pre-coded values of thermal conductivity, which are obtained from the MATPRO data base (sponsored by the U.S. Nuclear Regulatory Commission). The finite element method makes FEAT versatile, and enables it to accurately accommodate complex geometries. The optional link to MATPRO makes it convenient for the nuclear fuel industry to use FEAT, without loss of generality. Special numerical techniques make the code inexpensive to run, for the type of material non-linearities often encounter in the analysis of nuclear fuel. The code, however, is general, and can be used for other components of the reactor, or even for non-nuclear systems. The predictions of FEAT have been compared against several analytical solutions. The agreement is usually better than 5%. Thermocouple measurements show that the FEAT predictions are consistent with measured changes in temperatures in simulated pressure tubes. FEAT was also found to predict well, the axial variations in temperatures in the end-pellets(UO 2 ) of two fuel elements irradiated
International Nuclear Information System (INIS)
Kumar, V.; Sahni, D.C.
1983-01-01
In this paper, the authors present the mathematical techniques that were developed for solving the integral transport equation for the criticality of a homogeneous cylinder of finite height with general anisotropic scattering. They present the integral transport equations for the Fourier transformed spherical harmonic moments of the angular flux. These moments are also represented by a series of products of spherical Bessel functions. The criticality problem is, then, posed by the matrix eigenvalue problem whose eigenvector is composed of the expansion coefficients mentioned above. An methodology of calculating the general matrix element is discussed by using the recursion relations derived in this paper. Finally, for the one-group criticality of finite cylinders, the benchmark results are generated when scattering is linearly anisotropic. Also, these benchmarks are solved and compared with the S/sub N/ method of TWOTRAN
LSHINSE, Air Scattering Neutron and Gamma Dose rates for Complex Shielding Geometry
International Nuclear Information System (INIS)
Baran, A.; Gruen, M.; Leicht, R.
1991-01-01
1 - Description of program or function: The program LSHINSE is used to calculate the flux and the dose rate caused by gamma radiation emanating from a point source and being scattered in surrounding air. The program considers all forms of single scattering. Multiple scattering is taken into account in an approximate way by use of buildup factors. 2 - Method of solution: The program LSHINSE solves the equations for skyshine by use of Simpson integration. The integration limits are chosen such that the partial shielding is approximated by rectangular walls around the source. In addition, the attenuation of the primary radiation by a room ceiling can be calculated for several materials. By giving the height of the ceiling, the scattering in the air of the room can be calculated. By specifying energy groups the spectrum of the scattered radiation can be obtained. Valid energy range is 0.1 - 0.2 MeV, where the lower limit is due to uncertainties in the buildup factors. 3 - Restrictions on the complexity of the problem: The program is restricted to rectangular shielding problems involving gamma radiation in the range of 0.1 to 2.0 MeV
International Nuclear Information System (INIS)
Sanchez, Richard.
1975-11-01
The Integral Transform Method for the neutron transport equation has been developed in last years by Asaoka and others. The method uses Fourier transform techniques in solving isotropic one-dimensional transport problems in homogeneous media. The method has been extended to linearly anisotropic transport in one-dimensional homogeneous media. Series expansions were also obtained using Hembd techniques for the new anisotropic matrix elements in cylindrical geometry. Carlvik spatial-spherical harmonics method was generalized to solve the same problem. By applying a relation between the isotropic and anisotropic one-dimensional kernels, it was demonstrated that anisotropic matrix elements can be calculated by a linear combination of a few isotropic matrix elements. This means in practice that the anisotropic problem of order N with the N+2 isotropic matrix for the plane and spherical geometries, and N+1 isotropic matrix for cylindrical geometries can be solved. A method of solving linearly anisotropic one-dimensional transport problems in homogeneous media was defined by applying Mika and Stankiewicz observations: isotropic matrix elements were computed by Hembd series and anisotropic matrix elements then calculated from recursive relations. The method has been applied to albedo and critical problems in cylindrical geometries. Finally, a number of results were computed with 12-digit accuracy for use as benchmarks [fr
International Nuclear Information System (INIS)
Lisichkin, Yu.V.; Dovbenko, A.G.; Efimenko, B.A.; Novikov, A.G.; Smirenkina, L.D.; Tikhonova, S.I.
1979-01-01
Described is a method of taking account of finite sample dimensions in processing measurement results of double differential cross sections (DDCS) of slow neutron scattering. A necessity of corrective approach to the account taken of the effect of sample finite dimensions is shown, and, in particular, the necessity to conduct preliminary processing of DDCS, the account being taken of attenuation coefficients of single scattered neutrons (SSN) for measurements on the sample with a container, and on the container. Correction for multiple scattering (MS) calculated on the base of the dynamic model should be obtained, the account being taken of resolution effects. To minimize the effect of the dynamic model used in calculations it is preferred to make absolute measurements of DDCS and to use the subraction method. The above method was realized in the set of programs for the BESM-5 computer. The FISC program computes the coefficients of SSN attenuation and correction for MS. The DDS program serves to compute a model DDCS averaged as per the resolution function of an instrument. The SCATL program is intended to prepare initial information necessary for the FISC program, and permits to compute the scattering law for all materials. Presented are the results of using the above method while processing experimental data on measuring DDCS of water by the DIN-1M spectrometer
Langmack, Christian; Schmidt, Richard; Zwerger, Wilhelm
2018-03-01
We calculate the spectrum of three-body Efimov bound states near a Feshbach resonance within a model which accounts both for the finite range of interactions and the presence of background scattering. The latter may be due to direct interactions in an open channel or a second overlapping Feshbach resonance. It is found that background scattering gives rise to substantial changes in the trimer spectrum as a function of the detuning away from a Feshbach resonance, in particular in the regime where the background channel supports Efimov states on its own. Compared to the situation with negligible background scattering, the regime where van der Waals universality applies is shifted to larger values of the resonance strength if the background scattering length is positive. For negative background scattering lengths, in turn, van der Waals universality extends to even small values of the resonance strength parameter, consistent with experimental results on Efimov states in 39K. Within a simple model, we show that short-range three-body forces do not affect van der Waals universality significantly. Repulsive three-body forces may, however, explain the observed variation between around -8 and -10 of the ratio between the scattering length where the first Efimov trimer appears and the van der Waals length.
Geometry Survey of the Time-of-Flight Neutron-Elastic Scattering (Antonella) Experiment
Energy Technology Data Exchange (ETDEWEB)
Oshinowo, Babatunde O. [Fermilab; Izraelevitch, Federico [Buenos Aires U.
2016-10-17
The Antonella experiment is a measurement of the ionization efficiency of nuclear recoils in silicon at low energies [1]. It is a neutron elastic scattering experiment motivated by the search for dark matter particles. In this experiment, a proton beam hits a lithium target and neutrons are produced. The neutron shower passes through a collimator that produces a neutron beam. The beam illuminates a silicon detector. With a certain probability, a neutron interacts with a silicon nucleus of the detector producing elastic scattering. After the interaction, a fraction of the neutron energy is transferred to the silicon nucleus which acquires kinetic energy and recoils. This kinetic energy is then dissipated in the detector producing ionization and thermal energy. The ionization produced is measured with the silicon detector electronics. On the other hand, the neutron is scattered out of the beam. A neutron-detector array (made of scintillator bars) registers the neutron arrival time and the scattering angle to reconstruct the kinematics of the neutron-nucleus interaction with the time-of-flight technique [2]. In the reconstruction equations, the energy of the nuclear recoil is a function of the scattering angle with respect to the beam direction, the time-of-flight of the neutron and the geometric distances between components of the setup (neutron-production target, silicon detector, scintillator bars). This paper summarizes the survey of the different components of the experiment that made possible the off-line analysis of the collected data. Measurements were made with the API Radian Laser Tracker and I-360 Probe Wireless. The survey was completed at the University of Notre Dame, Indiana, USA in February 2015.
Directory of Open Access Journals (Sweden)
Alexandre Bambina
2018-01-01
Full Text Available Limitation of the cloak-size reduction is investigated numerically by a finite-difference time-domain (FDTD method. A metallic pole that imitates an antenna is cloaked with an anisotropic and parameter-gradient medium against electromagnetic-wave propagation in microwave range. The cloaking structure is a metamaterial submerged in a plasma confined in a vacuum chamber made of glass. The smooth-permittivity plasma can be compressed in the radial direction, which enables us to decrease the size of the cloak. Theoretical analysis is performed numerically by comparing scattering waves in various cases; there exists a high reduction of the scattering wave when the radius of the cloak is larger than a quarter of one wavelength. This result indicates that the required size of the cloaking layer is more than an object scale in the Rayleigh scattering regime.
DEFF Research Database (Denmark)
Kristensen, Philip Trøst; Lodahl, Peter; Mørk, Jesper
2010-01-01
We present an accurate, stable, and efficient solution to the Lippmann–Schwinger equation for electromagnetic scattering in two dimensions. The method is well suited for multiple scattering problems and may be applied to problems with scatterers of arbitrary shape or non-homogenous background mat...
International Nuclear Information System (INIS)
Telling, M.T.F.; Campbell, S.I.
1999-01-01
This report describes the upgrade of the pyrolytic graphite (PG) analyser bank on the IRIS high-resolution inelastic spectrometer at ISIS from 1350 graphite pieces (6 rows by 225 columns) to 4212 crystal pieces (18 rows by 234 columns). The analyser array will achieve a three-fold increase in area and in addition the graphite crystals will be cooled close to liquid helium temperature to reduce thermal diffuse scattering, thereby further improving the sensitivity of the spectrometer. For an instrument such as IRIS, with its analyser out of exact back-scattering geometry, optical aberration and variation in the time-of-flight of the analysed neutrons is introduced as one moves out from the horizontal scattering plane. To minimise such effects, the profile of the analyser array has been redesigned. The concept behind the design of the new analyser bank and the factors that effect the overall resolution of the instrument are discussed. Results of Monte Carlo simulations of the expected resolution and intensity of the complete instrument are presented and compared to the current instrument performance. (author)
Directory of Open Access Journals (Sweden)
Stefania Ferri
1996-02-01
Full Text Available Si fa vedere come si può costruire la geometria analitica su un piano affìne finito. Vengono riportati risultati classici che però sono stati esposti in modo da essere compresi dagli alunni delle Scuole Medie Secondarie.
International Nuclear Information System (INIS)
Sanchez G, J.
2015-09-01
The solution of the so-called Canonical problems of neutron transport theory has been given by Case, who developed a method akin to the classical eigenfunction expansion procedure, extended to admit singular eigenfunctions. The solution is given as a set consisting of a Fredholm integral equation coupled with a transcendental equation, which has to be solved for the expansion coefficients by iteration. CASE's method make extensive use of the results of the theory of functions of a complex variable and many successful approaches to solve in an approximate form the above mentioned set have been reported in the literature. We present here an entirely different approach which deals with the canonical problems in a more direct and elementary manner. As far as we know, the original idea for the latter method is due to Carlvik who devised the escape probability approximation to the solution of the neutron transport equation in its integral form. In essence, the procedure consists in assuming a sectionally constant form of the neutron density that in turn yields a set of linear algebraic equations obeyed by the assumed constant values of the density. Very well established techniques of numerical analysis for the solution of integral equations consist in independent approaches that generalize the sectionally constant approach by assuming a sectionally low degree polynomial for the unknown function. This procedure also known as the arbitrary quadratures method is especially suited to deal with cases where the kernel of the integral equation is singular. The author wishes to present the results obtained with the arbitrary quadratures method for the numerical calculation of the monoenergetic neutron density in a critical, homogeneous sphere of finite radius with isotropic scattering. The singular integral equation obeyed by the neutron density in the critical sphere is introduced, an outline of the method's main features is given, and tables and graphs of the density
Energy Technology Data Exchange (ETDEWEB)
Sanchez G, J., E-mail: julian.sanchez@inin.gob.mx [ININ, Carretera Mexico-Toluca s/n, 52750 Ocoyoacac, Estado de Mexico (Mexico)
2015-09-15
The solution of the so-called Canonical problems of neutron transport theory has been given by Case, who developed a method akin to the classical eigenfunction expansion procedure, extended to admit singular eigenfunctions. The solution is given as a set consisting of a Fredholm integral equation coupled with a transcendental equation, which has to be solved for the expansion coefficients by iteration. CASE's method make extensive use of the results of the theory of functions of a complex variable and many successful approaches to solve in an approximate form the above mentioned set have been reported in the literature. We present here an entirely different approach which deals with the canonical problems in a more direct and elementary manner. As far as we know, the original idea for the latter method is due to Carlvik who devised the escape probability approximation to the solution of the neutron transport equation in its integral form. In essence, the procedure consists in assuming a sectionally constant form of the neutron density that in turn yields a set of linear algebraic equations obeyed by the assumed constant values of the density. Very well established techniques of numerical analysis for the solution of integral equations consist in independent approaches that generalize the sectionally constant approach by assuming a sectionally low degree polynomial for the unknown function. This procedure also known as the arbitrary quadratures method is especially suited to deal with cases where the kernel of the integral equation is singular. The author wishes to present the results obtained with the arbitrary quadratures method for the numerical calculation of the monoenergetic neutron density in a critical, homogeneous sphere of finite radius with isotropic scattering. The singular integral equation obeyed by the neutron density in the critical sphere is introduced, an outline of the method's main features is given, and tables and graphs of the density
International Nuclear Information System (INIS)
Goncalves, G.A.; Bogado Leite, S.Q.; Vilhena, M.T. de
2009-01-01
An analytical solution has been obtained for the one-speed stationary neutron transport problem, in an infinitely long cylinder with anisotropic scattering by the decomposition method. Series expansions of the angular flux distribution are proposed in terms of suitably constructed functions, recursively obtainable from the isotropic solution, to take into account anisotropy. As for the isotropic problem, an accurate closed-form solution was chosen for the problem with internal source and constant incident radiation, obtained from an integral transformation technique and the F N method
Directory of Open Access Journals (Sweden)
W.R. Azzam
2015-08-01
Full Text Available This paper reports the application of using a skirted foundation system to study the behavior of foundations with structural skirts adjacent to a sand slope and subjected to earthquake loading. The effect of the adopted skirts to safeguard foundation and slope from collapse is studied. The skirts effect on controlling horizontal soil movement and decreasing pore water pressure beneath foundations and beside the slopes during earthquake is investigated. This technique is investigated numerically using finite element analysis. A four story reinforced concrete building that rests on a raft foundation is idealized as a two-dimensional model with and without skirts. A two dimensional plain strain program PLAXIS, (dynamic version is adopted. A series of models for the problem under investigation were run under different skirt depths and lactation from the slope crest. The effect of subgrade relative density and skirts thickness is also discussed. Nodal displacement and element strains were analyzed for the foundation with and without skirts and at different studied parameters. The research results showed a great effectiveness in increasing the overall stability of the slope and foundation. The confined soil footing system by such skirts reduced the foundation acceleration therefore it can be tended to damping element and relieved the transmitted disturbance to the adjacent slope. This technique can be considered as a good method to control the slope deformation and decrease the slope acceleration during earthquakes.
DEFF Research Database (Denmark)
Tanev, Stoyan; Sun, Wenbo
2012-01-01
for particle and surface scattering calculations and the uniaxial perfectly matched layer (UPML) absorbing boundary conditions for truncation of the FDTD grid. We show that the FDTD approach has a significant potential for studying the light scattering by cloud, dust, and biological particles. The applications...
International Nuclear Information System (INIS)
Nielsen, Tim; Brendel, Bernhard; Ziegler, Ronny; Beek, Michiel van; Uhlemann, Falk; Bontus, Claas; Koehler, Thomas
2009-01-01
Diffuse optical tomography (DOT) is a potential new imaging modality to detect or monitor breast lesions. Recently, Philips developed a new DOT system capable of transmission and fluorescence imaging, where the investigated breast is hanging freely into the measurement cup containing scattering fluid. We present a fast and robust image reconstruction algorithm that is used for the transmission measurements. The algorithm is based on the Rytov approximation. We show that this algorithm can be used over a wide range of tissue optical properties if the reconstruction is adapted to each patient. We use estimates of the breast shape and average tissue optical properties to initialize the reconstruction, which improves the image quality significantly. We demonstrate the capability of the measurement system and reconstruction to image breast lesions by clinical examples
International Nuclear Information System (INIS)
Lautard, J.J.; Flumiani, T.
2003-01-01
The mixed dual finite element method is usually used for the resolution of the SPN transport equations (simplified PN equations) in 3D homogenized geometries (composed by homogenized rectangles or hexagons). This method produces fast results with little memory requirements. We have extended the previous method to the treatment of unstructured geometries composed by quadrilaterals (for the moment limited to 2D), allowing us to treat geometries where fuel pins are exactly represented. The iterative resolution of the resulting matrix system is a generalization of the one already developed for the cartesian and the hexagonal geometries. In order to illustrate and to show the efficiency of this method, results on the NEA-C5G7-MOX benchmark are given. The previous benchmark has been extended for the hexagonal geometry and we provide here some results. This method is a first step towards the treatment of pin by pin core calculations without homogenization. The present solver is a prototype. It shows the efficiency of the method and it has to be extended to 3D calculations as well as to exact transport calculations. We also intend to extend the method to the treatment of unstructured geometries composed by quadrilaterals with curved edges (sectors of a circle).The iterative algorithm has yet to be accelerated using multigrid techniques through a coupling with the present homogenized solver (MINOS). In the future, it will be included in the next generation neutronic toolbox DESCARTES currently under development
International Nuclear Information System (INIS)
Adams, Jamie C.; Joyce, Malcolm J.; Mellor, Matthew
2009-01-01
The aim of this paper is to further validate the physical capability of N-Visage TM under more challenging shielding geometries, when the number of mean free paths is greater than one. N-Visage TM is a recently established technique developed at REACT Engineering Ltd. The software locates radionuclide sources and contours radiation magnitude. The N-Visage TM software uses a geometric computer model combined with measured spectra. The software is able to estimate source locations through shielding materials by using mass attenuation coefficients to calculate the number of unscattered gamma photons arriving at the detector, and build-up factors to estimate scatter contribution to dose rate. The experiments described in this paper were carried out in a high-scatter environment using cobalt-60 and cesium- 137 sources, these two sources are the primary sources of radiological contamination found in the nuclear industry. It is hoped that this will further assist in the identification, characterisation and removal of buried radiologically contaminated waste. (authors)
DEFF Research Database (Denmark)
Freltoft, T.; Kjems, Jørgen; Sinha, S. K.
1986-01-01
Small-angle neutron scattering from normal, compressed, and water-suspended powders of aggregates of fine silica particles has been studied. The samples possessed average densities ranging from 0.008 to 0.45 g/cm3. Assuming power-law correlations between particles and a finite correlation length ξ......, the authors derive the scattering function S(q) from specific models for particle-particle correlation in these systems. S(q) was found to provide a satisfactory fit to the data for all samples studied. The fractal dimension df corresponding to the power-law correlation was 2.61±0.1 for all dry samples, and 2...
International Nuclear Information System (INIS)
Soric, J C; Chen, P Y; Alù, A; Kerkhoff, A; Rainwater, D; Melin, K
2013-01-01
We present the first experimental realization and verification of a three-dimensional stand-alone mantle cloak designed to suppress the total scattering of a finite-length dielectric rod of moderate cross-section. Mantle cloaking has been proposed to realize ultralow-profile conformal covers that may achieve substantial camouflage, transparency and high-performance non-invasive near-field sensing. Here, we realize and verify a mantle cloak for radio-waves. We report an extensive campaign of far- and near-field free-space measurements demonstrating that conformal cloaks can indeed produce strong scattering suppression in all directions and over a relatively broad bandwidth of operation. (paper)
Li, Ning; Wu, Ya-Jie; Liu, Zhan-Wei
2018-01-01
The relations between the baryon-baryon elastic scattering phase shifts and the two-particle energy spectrum in the elongated box are established. We studied the cases with both the periodic boundary condition and twisted boundary condition in the center of mass frame. The framework is also extended to the system of nonzero total momentum with periodic boundary condition in the moving frame. Moreover, we discussed the sensitivity functions σ (q ) that represent the sensitivity of higher scattering phases. Our analytical results will be helpful to extract the baryon-baryon elastic scattering phase shifts in the continuum from lattice QCD data by using elongated boxes.
Elastic scattering and transport coefficients for a quark plasma in SUf(3) at finite temperatures
Rehberg, P.; Klevansky, S. P.; Hüfner, J.
1996-02-01
The temperature dependence of the elastic-scattering processes qq' → qq' and q overlineq' → q overlineq' , with q, q' = u, d, s is studied as a function of the scattering angle and the center-of-mass energy of the collision within the framework of the SUf(3) Nambu-Jona-Lasinio model. Critical scattering at threshold is observed in the q overlineq' → q overlineq' process, leading to an enhancement of the cross section as occurs in the phenomenon of critical opalescence. Transport properties such as viscosity, mean free paths and thermal relaxation times are calculated. Strangeness enhancement is investigated via the chemical relaxation times, which are found to be considerably higher than those calculated via perturbative QCD. A comparison with the experimental values for the strangeness enhancement in S + S collisions leads to an upper limit of 4 fm/ c for the lifetime of the plasma.
International Nuclear Information System (INIS)
Singh, Sukhpal; Kumar, Ashok; Singh, Charanjeet; Thind, Kulwant Singh; Mudahar, Gurmel S.
2008-01-01
The simultaneous variation of gamma ray buildup factors with absorber thickness (up to 6.5 mfp) and total scatter acceptance angle (which is the sum of incidence and exit beam divergence) in the media of high volume flyash concrete and water was studied experimentally using a point isotropic 137 Cs source
Energy Technology Data Exchange (ETDEWEB)
Oliva, Amaury M.; Filho, Hermes A.; Silva, Davi M.; Garcia, Carlos R., E-mail: aoliva@iprj.uerj.br, E-mail: halves@iprj.uerj.br, E-mail: davijmsilva@yahoo.com.br, E-mail: cgh@instec.cu [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Instituto Politecnico. Departamento de Modelagem Computacional; Instituto Superior de Tecnologias y Ciencias Aplicadas (InSTEC), La Habana (Cuba)
2017-07-01
In this paper, we propose a numerical methodology for the development of a method of the spectral nodal class that will generate numerical solutions free from spatial truncation errors. This method, denominated Spectral Deterministic Method (SDM), is tested as an initial study of the solutions (spectral analysis) of neutron transport equations in the discrete ordinates (S{sub N}) formulation, in one-dimensional slab geometry, multigroup approximation, with linearly anisotropic scattering, considering homogeneous and heterogeneous domains with fixed source. The unknowns in the methodology are the cell-edge, and cell average angular fluxes, the numerical values calculated for these quantities coincide with the analytic solution of the equations. These numerical results are shown and compared with the traditional ne- mesh method Diamond Difference (DD) and the coarse-mesh method spectral Green's function (SGF) to illustrate the method's accuracy and stability. The solution algorithms problems are implemented in a computer simulator made in C++ language, the same that was used to generate the results of the reference work. (author)
International Nuclear Information System (INIS)
Hennart, J.P.; Valle, E. del.
1995-01-01
A generalized nodal finite element formalism is presented, which covers virtually all known finit difference approximation to the discrete ordinates equations in slab geometry. This paper (Part 1) presents the theory of the so called open-quotes continuous moment methodsclose quotes, which include such well-known methods as the open-quotes diamond differenceclose quotes and the open-quotes characteristicclose quotes schemes. In a second paper (hereafter referred to as Part II), the authors will present the theory of the open-quotes discontinuous moment methodsclose quotes, consisting in particular of the open-quotes linear discontinuousclose quotes scheme as well as of an entire new class of schemes. Corresponding numerical results are available for all these schemes and will be presented in a third paper (Part III). 12 refs
Time-dependent Second Order Scattering Theory for Weather Radar with a Finite Beam Width
Kobayashi, Satoru; Tanelli, Simone; Im, Eastwood; Ito, Shigeo; Oguchi, Tomohiro
2006-01-01
Multiple scattering effects from spherical water particles of uniform diameter are studied for a W-band pulsed radar. The Gaussian transverse beam-profile and the rectangular pulse-duration are used for calculation. An second-order analytical solution is derived for a single layer structure, based on a time-dependent radiative transfer theory as described in the authors' companion paper. When the range resolution is fixed, increase in footprint radius leads to increase in the second order reflectivity that is defined as the ratio of the second order return to the first order one. This feature becomes more serious as the range increases. Since the spaceborne millimeter-wavelength radar has a large footprint radius that is competitive to the mean free path, the multiple scattering effect must be taken into account for analysis.
International Nuclear Information System (INIS)
Gazdallah, Moncef; Feldheim, Véronique; Claramunt, Kilian; Hirsch, Charles
2012-01-01
This paper presents the implementation of the finite volume method to solve the radiative transfer equation in a commercial code. The particularity of this work is that the method applied on unstructured hexahedral meshes does not need a pre-processing step establishing a particular marching order to visit all the control volumes. The solver simply visits the faces of the control volumes as numbered in the hexahedral unstructured mesh. A cell centred mesh and a spatial differencing step scheme to relate facial radiative intensities to nodal intensities is used. The developed computer code based on FVM has been integrated in the CFD solver FINE/Open from NUMECA Int. Radiative heat transfer can be evaluated within systems containing uniform, grey, emitting, absorbing and/or isotropically or linear anisotropically scattering medium bounded by diffuse grey walls. This code has been validated for three test cases. The first one is a three dimensional rectangular enclosure filled with emitting, absorbing and anisotropically scattering media. The second is the differentially heated cubic cavity. The third one is the L-shaped enclosure. For these three test cases a good agreement has been observed when temperature and heat fluxes predictions are compared with references taken, from literature.
Energy Technology Data Exchange (ETDEWEB)
Warehime, Mick [Chemical Physics Program, University of Maryland, College Park, Maryland 20742-2021 (United States); Kłos, Jacek; Alexander, Millard H., E-mail: mha@umd.edu [Department of Chemistry and Biochemistry and Institute of Physical Science and Technology, University of Maryland, College Park, Maryland 20742-2021 (United States)
2015-01-21
This is the second in a series of papers detailing a MATLAB based implementation of the finite element method applied to collinear triatomic reactions. Here, we extend our previous work to reactions on coupled potential energy surfaces. The divergence of the probability current density field associated with the two electronically adiabatic states allows us to visualize in a novel way where and how nonadiabaticity occurs. A two-dimensional investigation gives additional insight into nonadiabaticity beyond standard one-dimensional models. We study the F({sup 2}P) + HCl and F({sup 2}P) + H{sub 2} reactions as model applications. Our publicly available code (http://www2.chem.umd.edu/groups/alexander/FEM) is general and easy to use.
International Nuclear Information System (INIS)
Forkl, A.; Kronmueller, H.
1995-01-01
The distribution of the critical current density j c (r) in hard type-II superconductors depends strongly on their sample geometry. Rules are given for the construction of j c (r). Samples with homogeneous thickness are divided into cakelike regions with a unique current direction. The spatial magnetic flux density distribution and the magnetic polarization of such a cakelike unit cell with homogeneous current density are calculated analytically. The magnetic polarization and magnetic flux density distribution of a superconductor in the mixed state is then given by an adequate superposition of the unit cell solutions. The theoretical results show good agreement with magneto-optically determined magnetic flux density distributions of a quadratic thin superconducting YBa 2 Cu 3 O 7-x film. The current density distribution is discussed for several sample geometries
Marques, Alexandre; Nave, Jean-Christophe; Rosales, Ruben
2011-11-01
The Poisson equation is of central importance in the description of fluid flows and other physical phenomena. In prior work, Marques, Nave, and Rosales introduced the Correction Function Method (CFM) to obtain fourth-order accurate solutions for the constant coefficient Poisson problem with prescribed jump conditions for the solution and its normal derivative across arbitrary interfaces. Here we combine this method with the ideas introduced by Mayo to solve other Poisson problems involving complex geometries. In summary, we are able to rewrite the problem as a boundary integral equation in terms of a potential distribution over the boundary or interface. The solution of this integral equation is discontinuous across the boundary or interface. Hence, after this integral equation is solved using standard techniques, the potential distribution can be used to determine the jump discontinuities. We are then able to use the CFM to solve the resulting Poisson equation with jump discontinuities. The outcome is a fourth-order accurate scheme to solve general Poisson problems which, over arbitrary geometries, has a cost that is approximately twice that of a fast Poisson solver using FFT on a rectangular geometry of the same size. Details of the method and applications will be presented.
International Nuclear Information System (INIS)
Menezes, Welton A.; Filho, Hermes Alves; Barros, Ricardo C.
2014-01-01
Highlights: • Fixed-source S N transport problems. • Energy multigroup model. • Anisotropic scattering. • Slab-geometry spectral nodal method. - Abstract: A generalization of the spectral Green’s function (SGF) method is developed for multigroup, fixed-source, slab-geometry discrete ordinates (S N ) problems with anisotropic scattering. The offered SGF method with the one-node block inversion (NBI) iterative scheme converges numerical solutions that are completely free from spatial truncation errors for multigroup, slab-geometry S N problems with scattering anisotropy of order L, provided L < N. As a coarse-mesh numerical method, the SGF method generates numerical solutions that generally do not give detailed information on the problem solution profile, as the grid points can be located considerably away from each other. Therefore, we describe in this paper a technique for the spatial reconstruction of the coarse-mesh solution generated by the multigroup SGF method. Numerical results are given to illustrate the method’s accuracy
Acoustic scattering from a contrast agent microbubble near an elastic wall of finite thickness
International Nuclear Information System (INIS)
Doinikov, Alexander A; Aired, Leila; Bouakaz, Ayache
2011-01-01
Interest in the problem under consideration in this study is motivated by targeted ultrasound imaging where one has to deal with microbubble contrast agents pulsating near blood vessel walls. A modified Rayleigh–Plesset equation is derived that describes the oscillation of a contrast agent microbubble near an elastic wall of finite thickness. It is assumed that the medium behind the wall is a fluid but it is shown that the equation obtained is easily transformable to the case that the medium behind the wall is an elastic solid. In contrast to the model of a rigid wall, which predicts decreasing natural frequency of a bubble near the wall, the elastic wall model reveals that the bubble natural frequency can both decrease and increase, and in cases of interest for medical applications, the bubble natural frequency usually increases. It is found that the influence of an elastic wall on the acoustic response of a bubble is determined by the ratio between a cumulative parameter, which integrally characterizes the mechanical properties of the wall and has the dimension of density, and the density of the liquid surrounding the bubble. It is shown that the acoustic influence of the arterial wall on the bubble is weak and apparently cannot be used to recognize the moment when the bubble approaches the wall. However, in experiments where the behavior of bubbles near various plastic walls is observed, changes in the bubble response, such as increasing natural frequency and decreasing oscillation amplitude, are detectable.
Caouette, Christiane; Ikin, Nicole; Villemure, Isabelle; Arnoux, Pierre-Jean; Rauch, Frank; Aubin, Carl-Éric
2017-04-01
Lower limb deformation in children with osteogenesis imperfecta (OI) impairs ambulation and may lead to fracture. Corrective surgery is based on empirical assessment criteria. The objective was to develop a reconstruction method of the tibia for OI patients that could be used as input of a comprehensive finite element model to assess fracture risks. Data were obtained from three children with OI and tibia deformities. Four pQCT scans were registered to biplanar radiographs, and a template mesh was deformed to fit the bone outline. Cortical bone thickness was computed. Sensitivity of the model to missing slices of pQCT was assessed by calculating maximal von Mises stress for a vertical hopping load case. Sensitivity of the model to ±5 % of cortical thickness measurements was assessed by calculating loads at fracture. Difference between the mesh contour and bone outline on the radiographs was below 1 mm. Removal of one pQCT slice increased maximal von Mises stress by up to 10 %. Simulated ±5 % variation of cortical bone thickness leads to variations of up to 4.1 % on predicted fracture loads. Using clinically available tibia imaging from children with OI, the developed reconstruction method allowed the building of patient-specific finite element models.
Heumann, Holger; Rapetti, Francesca
2017-04-01
Existing finite element implementations for the computation of free-boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard lowest order continuous finite elements with discontinuous gradients. As a consequence, the location of critical points of the poloidal flux, that are of paramount importance in tokamak engineering, is constrained to nodes of the mesh leading to undesired jumps in transient problems. Moreover, recent numerical results for the self-consistent coupling of equilibrium with resistive diffusion and transport suggest the necessity of higher regularity when approximating the flux map. In this work we propose a mortar element method that employs two overlapping meshes. One mesh with Cartesian quadrilaterals covers the vacuum chamber domain accessible by the plasma and one mesh with triangles discretizes the region outside. The two meshes overlap in a narrow region. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the domain covered by the plasma, while preserving accurate meshing of the geometric details outside this region. The continuity of the numerical solution in the region of overlap is weakly enforced by a mortar-like mapping.
Energy Technology Data Exchange (ETDEWEB)
Schneider, D
2001-07-01
The nodal method Minos has been developed to offer a powerful method for the calculation of nuclear reactor cores in rectangular geometry. This method solves the mixed dual form of the diffusion equation and, also of the simplified P{sub N} approximation. The discretization is based on Raviart-Thomas' mixed dual finite elements and the iterative algorithm is an alternating direction method, which uses the current as unknown. The subject of this work is to adapt this method to hexagonal geometry. The guiding idea is to construct and test different methods based on the division of a hexagon into trapeze or rhombi with appropriate mapping of these quadrilaterals onto squares in order to take into advantage what is already available in the Minos solver. The document begins with a review of the neutron diffusion equation. Then we discuss its mixed dual variational formulation from a functional as well as from a numerical point of view. We study conformal and bilinear mappings for the two possible meshing of the hexagon. Thus, four different methods are proposed and are completely described in this work. Because of theoretical and numerical difficulties, a particular treatment has been necessary for methods based on the conformal mapping. Finally, numerical results are presented for a hexagonal benchmark to validate and compare the four methods with respect to pre-defined criteria. (authors)
Energy Technology Data Exchange (ETDEWEB)
Schneider, D
2001-07-01
The nodal method Minos has been developed to offer a powerful method for the calculation of nuclear reactor cores in rectangular geometry. This method solves the mixed dual form of the diffusion equation and, also of the simplified P{sub N} approximation. The discretization is based on Raviart-Thomas' mixed dual finite elements and the iterative algorithm is an alternating direction method, which uses the current as unknown. The subject of this work is to adapt this method to hexagonal geometry. The guiding idea is to construct and test different methods based on the division of a hexagon into trapeze or rhombi with appropriate mapping of these quadrilaterals onto squares in order to take into advantage what is already available in the Minos solver. The document begins with a review of the neutron diffusion equation. Then we discuss its mixed dual variational formulation from a functional as well as from a numerical point of view. We study conformal and bilinear mappings for the two possible meshing of the hexagon. Thus, four different methods are proposed and are completely described in this work. Because of theoretical and numerical difficulties, a particular treatment has been necessary for methods based on the conformal mapping. Finally, numerical results are presented for a hexagonal benchmark to validate and compare the four methods with respect to pre-defined criteria. (authors)
International Nuclear Information System (INIS)
Souza, Altivo Monteiro de
2008-12-01
The world energy consumption has been increasing strongly in recent years. Nuclear energy has been regarded as a suitable option to supply this growing energy demand in industrial scale. In view of the need of improving the understanding and capacity of analysis of nuclear power plants, modern simulation techniques for flow and heat transfer problems are gaining greater importance. A large number of problems found in nuclear reactor engineering can be dealt assuming axial symmetry. Thus, in this work a stabilized finite element formulation for the solution of the Navier-Stokes and energy equations for axisymmetric problems have been developed and tested. The formulation has been implemented in the NS S OLVER M PI 2 D A program developed at the Parallel Computation Laboratory of the Instituto de Engenharia Nuclear (LCP/IEN) and is now available either for safety analysis or design of nuclear systems. (author)
International Nuclear Information System (INIS)
Broome, J.
1965-11-01
The programme SCATTER is a KDF9 programme in the Egtran dialect of Fortran to generate normalized angular distributions for elastically scattered neutrons from data input as the coefficients of a Legendre polynomial series, or from differential cross-section data. Also, differential cross-section data may be analysed to produce Legendre polynomial coefficients. Output on cards punched in the format of the U.K. A. E. A. Nuclear Data Library is optional. (author)
Hamilton, Mark F.
1989-08-01
Four projects are discussed in this annual summary report, all of which involve basic research in nonlinear acoustics: Scattering of Sound by Sound, a theoretical study of two nonconlinear Gaussian beams which interact to produce sum and difference frequency sound; Parametric Receiving Arrays, a theoretical study of parametric reception in a reverberant environment; Nonlinear Effects in Asymmetric Sound Beams, a numerical study of two dimensional finite amplitude sound fields; and Pulsed Finite Amplitude Sound Beams, a numerical time domain solution of the KZK equation.
Ay, Nihat; Lê, Hông Vân; Schwachhöfer, Lorenz
2017-01-01
The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, inf...
International Nuclear Information System (INIS)
Shum, D.K.; Bryson, J.W.; Merkle, J.G.
1993-09-01
This study presents preliminary estimates on whether an shallow, axially oriented, inner-surface finite-length flaw in a PWR-RPV would tend to elongate in the axial direction and/or deepen into the wall of the vessel during a postulated PTS transient. Analysis results obtained based on the assumptions of (1) linear-elastic material response, and (2) cladding with same toughness as the base metal, indicate that a nearly semicircular flaw would likely propagate in the axial direction followed by propagation into the wall of the vessel. Note that these results correspond to initiation within the lower-shelf fracture toughness temperature range, and that their general validity within the lower-transition temperature range remains to be determined. The sensitivity of the numerical results aid conclusions to the following analysis assumptions are evaluated: (1) reference flaw geometry along the entire crack front and especially within the cladding region; (2) linear-elastic vs elastic-plastic description of material response; and (3) base-material-only vs bimaterial cladding-base vessel-model assumption. The sensitivity evaluation indicates that the analysis results are very sensitive to the above assumptions
Energy Technology Data Exchange (ETDEWEB)
Maruyama, R., E-mail: ryuji.maruyama@j-parc.jp [J-PARC Center, Japan Atomic Energy Agency, 2-4 Shirakata Shirane, Tokai, Ibaraki 319-1195 (Japan); Bigault, T.; Wildes, A.R.; Dewhurst, C.D. [Institut Laue Langevin, 71 avenue des Martyrs, 38042 Grenoble (France); Soyama, K. [J-PARC Center, Japan Atomic Energy Agency, 2-4 Shirakata Shirane, Tokai, Ibaraki 319-1195 (Japan); Courtois, P. [Institut Laue Langevin, 71 avenue des Martyrs, 38042 Grenoble (France)
2016-05-21
The in-plane magnetic structure of a layered system with a polycrystalline grain size less than the ferromagnetic exchange length was investigated using polarized neutron off-specular scattering and grazing incidence small angle scattering measurements to gain insight into the mechanism that controls the magnetic properties which are different from the bulk. These complementary measurements with different length scales and the data analysis based on the distorted wave Born approximation revealed the lateral correlation on a length scale of sub- μm due to the fluctuating orientation of the magnetization in the layer. The obtained in-plane magnetic structure is consistent with the random anisotropy model, i.e. competition between the exchange interactions between neighboring spins and the local magnetocrystalline anisotropy.
Optimizing Nanoscale Quantitative Optical Imaging of Subfield Scattering Targets
Henn, Mark-Alexander; Barnes, Bryan M.; Zhou, Hui; Sohn, Martin; Silver, Richard M.
2016-01-01
The full 3-D scattered field above finite sets of features has been shown to contain a continuum of spatial frequency information, and with novel optical microscopy techniques and electromagnetic modeling, deep-subwavelength geometrical parameters can be determined. Similarly, by using simulations, scattering geometries and experimental conditions can be established to tailor scattered fields that yield lower parametric uncertainties while decreasing the number of measurements and the area of such finite sets of features. Such optimized conditions are reported through quantitative optical imaging in 193 nm scatterfield microscopy using feature sets up to four times smaller in area than state-of-the-art critical dimension targets. PMID:27805660
International Nuclear Information System (INIS)
Liu Shaobin; Zhang Guangfu; Yuan Naichang
2004-01-01
A PLJERC-FDTD algorithm is applied to the study of the scattering of perfectly conducting cube covered with homogeneous isotropic plasmas. The effects of plasma thickness, density and collision frequency on the radar cross section (RCS) of the conducting cube scatterer have been obtained. The results illustrate that the plasma cloaking can greatly reduce the RCS of radar targets, and the RCS of the perfectly conducting cube scatterer decreases with increasing plasma thickness when the plasma frequency is greatly less than the electromagnetic (EM) wave frequency; the RCS of the perfectly conducting cube scatterer decreases with increasing plasma thickness and plasma collision frequency when the plasma frequency is almost half as much as the EM wave frequency; the effects of plasma thickness and collision frequency on the RCS of the perfectly conducting cube scatterer is small when the plasma frequency is close to the EM wave frequency
Collins, Jeffery D.; Volakis, John L.; Jin, Jian-Ming
1990-01-01
A new technique is presented for computing the scattering by 2-D structures of arbitrary composition. The proposed solution approach combines the usual finite element method with the boundary-integral equation to formulate a discrete system. This is subsequently solved via the conjugate gradient (CG) algorithm. A particular characteristic of the method is the use of rectangular boundaries to enclose the scatterer. Several of the resulting boundary integrals are therefore convolutions and may be evaluated via the fast Fourier transform (FFT) in the implementation of the CG algorithm. The solution approach offers the principal advantage of having O(N) memory demand and employs a 1-D FFT versus a 2-D FFT as required with a traditional implementation of the CGFFT algorithm. The speed of the proposed solution method is compared with that of the traditional CGFFT algorithm, and results for rectangular bodies are given and shown to be in excellent agreement with the moment method.
International Nuclear Information System (INIS)
Murray, A.J.; Read, F.H.
1993-01-01
Experimentally determined differential cross sections are presented for the (e,2e) process in helium, in which the two outgoing electrons have the same energy and the same scattering angle with respect to the incident beam. At four incident energies from 20 to 50 eV above the ionization threshold the detection plane defined by the outgoing electrons was varied from being coplanar with the incident beam to being perpendicular to the beam. The differential cross section evolves from a two-peak structure in coplanar geometry to a three-peak structure in the perpendicular plane. At the lowest energy the forward-scattering coplanar peak is smaller than the backscatter peak, in contrast to the results at higher energies. A deep minimum is seen at an intermediate plane angle of 67.5 degree, this minimum being deepest at 40 eV above the ionization threshold. The results are normalized to an absolute scale using previous coplanar measurements as discussed in the text. The spectrometer used to collect these results is fully computer controlled and real-time computer optimized
Spinning geometry = Twisted geometry
International Nuclear Information System (INIS)
Freidel, Laurent; Ziprick, Jonathan
2014-01-01
It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries are not continuous across the faces. Here we show that this phase space can also be represented by continuous, piecewise-flat three-geometries called spinning geometries. These are composed of metric-flat three-cells glued together consistently. The geometry of each cell and the manner in which they are glued is compatible with the choice of fluxes and holonomies. We first remark that the fluxes provide each edge with an angular momentum. By studying the piecewise-flat geometries which minimize edge lengths, we show that these angular momenta can be literally interpreted as the spin of the edges: the geometries of all edges are necessarily helices. We also show that the compatibility of the gluing maps with the holonomy data results in the same conclusion. This shows that a spinning geometry represents a way to glue together the three-cells of a twisted geometry to form a continuous geometry which represents a point in the loop gravity phase space. (paper)
Petersen, Peter
2016-01-01
Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with posit...
International Nuclear Information System (INIS)
Dang, N.D.
1986-01-01
The discovery of giant resonances in reactions of nuclei with heavy ions and in deep inelastic processes has stimulated interest in the study of the properties of highly excited nuclei. By taking into account exactly the population numbers of the single-phonon levels, the authors obtain a system of equations describing the interaction with the configurations in even-even spherical nuclei at a finite temperature. The Pauli principle is taken into account for the two-phonon components of the wave function of the excited states in accordance with an approximate procedure. The new diagrams associated with the introduction of the temperature are analyzed, and a comparison is made with the diagrams of nuclear field theory and the results of the theory of finite Fermi systems
Hirakawa, E. T.; Pitarka, A.; Mellors, R. J.
2015-12-01
Evan Hirakawa, Arben Pitarka, and Robert Mellors One challenging task in explosion seismology is development of physical models for explaining the generation of S-waves during underground explosions. Pitarka et al. (2015) used finite difference simulations of SPE-3 (part of Source Physics Experiment, SPE, an ongoing series of underground chemical explosions at the Nevada National Security Site) and found that while a large component of shear motion was generated directly at the source, additional scattering from heterogeneous velocity structure and topography are necessary to better match the data. Large-scale features in the velocity model used in the SPE simulations are well constrained, however, small-scale heterogeneity is poorly constrained. In our study we used a stochastic representation of small-scale variability in order to produce additional high-frequency scattering. Two methods for generating the distributions of random scatterers are tested. The first is done in the spatial domain by essentially smoothing a set of random numbers over an ellipsoidal volume using a Gaussian weighting function. The second method consists of filtering a set of random numbers in the wavenumber domain to obtain a set of heterogeneities with a desired statistical distribution (Frankel and Clayton, 1986). This method is capable of generating distributions with either Gaussian or von Karman autocorrelation functions. The key parameters that affect scattering are the correlation length, the standard deviation of velocity for the heterogeneities, and the Hurst exponent, which is only present in the von Karman media. Overall, we find that shorter correlation lengths as well as higher standard deviations result in increased tangential motion in the frequency band of interest (0 - 10 Hz). This occurs partially through S-wave refraction, but mostly by P-S and Rg-S waves conversions. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore
Geometry of multihadron production
Energy Technology Data Exchange (ETDEWEB)
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions.
Geometry of multihadron production
International Nuclear Information System (INIS)
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions
Bhunia, Snehasis; Forster, Stefan; Vyas, Nidhi; Schmitt, Hans-Christian; Ojha, Animesh K
2015-12-05
Fourier transform Raman (FT-Raman) spectra of neat pyridine (Py) and surface enhanced Raman scattering (SERS) spectra of Py with silver nanoparticles (AgNPs) solution at different molar concentrations (X=1.5M, 1.0M, 0.50 M, 0.25 M, and 0.125 M) were recorded using 1064 nm excitation wavelength. The intensity of Raman bands at ∼1003 (ν11) and ∼1035 (ν21) cm(-1) of Py is enhanced in the SERS spectra. Two new Raman bands were observed at ∼1009 (ν12) and ∼1038 (ν22) cm(-1) in the SERS spectra. These bands correspond to the ring breathing vibrations of Py molecules adsorbed at the AgNPs surface. The value of intensity ratios (I12/I11) and (I21/I22) is increased with dilution and attains a maximum value at X=0.5M and upon further dilution (0.25 and 0.125 M) it drops gradually. The theoretically calculated Raman spectra were found to be in good agreement with experimentally observed Raman spectra. Both, experimental and theoretical investigations have confirmed that the Py interacts with AgNPs via the end-on geometry. Copyright © 2015 Elsevier B.V. All rights reserved.
Double-grid finite-difference frequency-domain (DG-FDFD) method for scattering from chiral objects
Alkan, Erdogan; Elsherbeni, Atef
2013-01-01
This book presents the application of the overlapping grids approach to solve chiral material problems using the FDFD method. Due to the two grids being used in the technique, we will name this method as Double-Grid Finite Difference Frequency-Domain (DG-FDFD) method. As a result of this new approach the electric and magnetic field components are defined at every node in the computation space. Thus, there is no need to perform averaging during the calculations as in the aforementioned FDFD technique [16]. We formulate general 3D frequency-domain numerical methods based on double-grid
Hoenders, B. J.
2011-01-01
The theory for scattering of electromagnetic waves is developed for scattering objects for which the natural modes of the field inside the object do not couple one-to-one with those outside the scatterer. Key feature of the calculation of the scattered fields is the introduction of a new set of
Arridge, S R; Dehghani, H; Schweiger, M; Okada, E
2000-01-01
We present a method for handling nonscattering regions within diffusing domains. The method develops from an iterative radiosity-diffusion approach using Green's functions that was computationally slow. Here we present an improved implementation using a finite element method (FEM) that is direct. The fundamental idea is to introduce extra equations into the standard diffusion FEM to represent nondiffusive light propagation across a nonscattering region. By appropriate mesh node ordering the computational time is not much greater than for diffusion alone. We compare results from this method with those from a discrete ordinate transport code, and with Monte Carlo calculations. The agreement is very good, and, in addition, our scheme allows us to easily model time-dependent and frequency domain problems.
International Nuclear Information System (INIS)
O'Dell, R.D.; Stepanek, J.; Wagner, M.R.
1983-01-01
The aim of the present work is to compare and discuss the three of the most advanced two dimensional transport methods, the finite difference and nodal discrete ordinates and surface flux method, incorporated into the transport codes TWODANT, TWOTRAN-NODAL, MULTIMEDIUM and SURCU. For intercomparison the eigenvalue and the neutron flux distribution are calculated using these codes in the LWR pool reactor benchmark problem. Additionally the results are compared with some results obtained by French collision probability transport codes MARSYAS and TRIDENT. Because the transport solution of this benchmark problem is close to its diffusion solution some results obtained by the finite element diffusion code FINELM and the finite difference diffusion code DIFF-2D are included
International Nuclear Information System (INIS)
Fernandes, A.; Maiorino, J.R.
1989-01-01
This work presents a method to solve the neutron transport equation in thre space dimensions. The angular flux is aproximated by spherical harmonics and the finite element method is applied to the space component. The program originated by the analytical development is being tested and some results are presented. (author) [pt
DEFF Research Database (Denmark)
Kokkendorff, Simon Lyngby
2002-01-01
The subject of this Ph.D.-thesis is somewhere in between continuous and discrete geometry. Chapter 2 treats the geometry of finite point sets in semi-Riemannian hyperquadrics,using a matrix whose entries are a trigonometric function of relative distances in a given point set. The distance...... to the geometry of a simplex in a semi-Riemannian hyperquadric. In chapter 3 we study which finite metric spaces that are realizable in a hyperbolic space in the limit where curvature goes to -∞. We show that such spaces are the so called leaf spaces, the set of degree 1 vertices of weighted trees. We also...... establish results on the limiting geometry of such an isometrically realized leaf space simplex in hyperbolic space, when curvature goes to -∞. Chapter 4 discusses negative type of metric spaces. We give a measure theoretic treatment of this concept and related invariants. The theory developed...
Sartkulvanich, Partchapol; Al-Zkeri, Ibrahim; Yen, Yung-Chang; Altan, Taylan
2004-06-01
This paper summarizes some of the progress made on FEM simulations of metal cutting processes conducted at the Engineering Research Center (ERC/NSM). Presented research focuses on the performance of various cutting edge geometries (hone and chamfer edges) for different tool materials and specifically on: 1) the effect of round and chamfer edge geometries on the cutting variables in machining carbon steels and 2) the effect of the edge hone size upon the flank wear and burr formation behavior in face milling of A356-T6 aluminum alloy. In the second task, an innovative design of edge preparation with varying hone size around the tool nose is also explored using FEM. In order to model three-dimensional conventional turning and face milling with two-dimensional orthogonal cutting simulations, 2D simulation cross-sections consisting of the cutting speed direction and chip flow direction are selected at different locations along the tool nose radius. Then the geometries of the hone and chamfer edges and their associated tool angles as well as uncut chip thickness are determined on these planes and employed in cutting simulations. The chip flow direction on the tool rake face are obtained by examining the wear grooves on the experimental inserts or estimated by using Oxley's approximation theory of oblique cutting. Simulation results are compared with the available experimental results (e.g. cutting forces) both qualitatively and quantitatively.
International Nuclear Information System (INIS)
Sartkulvanich, Partchapol; Al-Zkeri, Ibrahim; Yen Yungchang; Altan, Taylan
2004-01-01
This paper summarizes some of the progress made on FEM simulations of metal cutting processes conducted at the Engineering Research Center (ERC/NSM). Presented research focuses on the performance of various cutting edge geometries (hone and chamfer edges) for different tool materials and specifically on: 1) the effect of round and chamfer edge geometries on the cutting variables in machining carbon steels and 2) the effect of the edge hone size upon the flank wear and burr formation behavior in face milling of A356-T6 aluminum alloy. In the second task, an innovative design of edge preparation with varying hone size around the tool nose is also explored using FEM.In order to model three-dimensional conventional turning and face milling with two-dimensional orthogonal cutting simulations, 2D simulation cross-sections consisting of the cutting speed direction and chip flow direction are selected at different locations along the tool nose radius. Then the geometries of the hone and chamfer edges and their associated tool angles as well as uncut chip thickness are determined on these planes and employed in cutting simulations. The chip flow direction on the tool rake face are obtained by examining the wear grooves on the experimental inserts or estimated by using Oxley's approximation theory of oblique cutting. Simulation results are compared with the available experimental results (e.g. cutting forces) both qualitatively and quantitatively
DISCUS, Neutron Single to Double Scattering Ratio in Inelastic Scattering Experiment by Monte-Carlo
International Nuclear Information System (INIS)
Johnson, M.W.
1993-01-01
1 - Description of problem or function: DISCUS calculates the ratio of once-scattered to twice-scattered neutrons detected in an inelastic neutron scattering experiment. DISCUS also calculates the flux of once-scattered neutrons that would have been observed if there were no absorption in the sample and if, once scattered, the neutron would emerge without further re-scattering or absorption. Three types of sample geometry are used: an infinite flat plate, a finite flat plate or a finite length cylinder. (The infinite flat plate is included for comparison with other multiple scattering programs.) The program may be used for any sample for which the scattering law is of the form S(/Q/, omega). 2 - Method of solution: Monte Carlo with importance sampling is used. Neutrons are 'forced' both into useful angular trajectories, and useful energy bins. Biasing of the collision point according to the point of entry of the neutron into the sample is also utilised. The first and second order scattered neutron fluxes are calculated in independent histories. For twice-scattered neutron histories a square distribution in Q-omega space is used to sample the neutron coming from the first scattering event, whilst biasing is used for the second scattering event. (A square distribution is used so as to obtain reasonable inelastic-inelastic statistics.) 3 - Restrictions on the complexity of the problem: Unlimited number of detectors. Max. size of (Q, omega) matrix is 39*149. Max. number of points in momentum space for the scattering cross section is 199
Multiple scattering in closely packed systems of arbitrary non-overlapping shapes
International Nuclear Information System (INIS)
Keister, B.D.
1982-11-01
It has long been known that the multiple scattering of waves from a system of obstacles of finite extent can be described completely with a knowledge of the on-shell amplitudes of the individual scatterers, provided that the minimally enclosing spheres concentric with the scattering centers do not overlap. In this paper, it is shown that on-shell amplitudes alone suffice for a wider class of scattering configurations, in which the individual scatterers do not overlap, but their geometries do not satisfy the above condition. These extended geometries require a careful treatment of certain partial wave sums. An example is also discussed in which a pair of non-overlapping scatterers requires more than the on-shell amplitudes for a solution
Childress, Stephen; Gilbert, Andrew D.
2018-02-01
A theory of an eroding ‘hairpin’ vortex dipole structure in three-dimensions is developed, extending our previous study of an axisymmetric eroding dipole without swirl. The axisymmetric toroidal dipole was found to lead to maximal growth of vorticity, as {t}4/3. The hairpin is here similarly proposed as a model to produce large ‘self-stretching’ of vorticity, with the possibility of finite-time blow-up. We derive a system of partial differential equations of ‘generalized’ form, involving contour averaging of a locally two-dimensional Euler flow. We do not attempt here to solve the system exactly, but point out that non-existence of physically acceptable solutions would most probably be a result of the axial flow. Because of the axial flow the vorticity distribution within the dipole eddies is no longer of the simple Sadovskii type (vorticity constant over a cross-section) obtained in the axisymmetric problem. Thus the solution of the system depends upon the existence of a larger class of propagating two-dimensional dipoles. The hairpin model is obtained by formal asymptotic analysis. As in the axisymmetric problem a local transformation to ‘shrinking’ coordinates is introduced, but now in a self-similar form appropriate to the study of a possible finite-time singularity. We discuss some properties of the model, including a study of the helicity and a first step in iterating toward a solution from the Sadovskii structure. We also present examples of two-dimensional propagating dipoles not previously studied, which have a vorticity profile consistent with our model. Although no rigorous results can be given, and analysis of the system is only partial, the formal calculations are consistent with the possibility of a finite time blowup of vorticity at a point of vanishing circulation of the dipole eddies, but depending upon the existence of the necessary two-dimensional propagating dipole. Our results also suggest that conservation of kinetic energy as
Multiplicity in difference geometry
Tomasic, Ivan
2011-01-01
We prove a first principle of preservation of multiplicity in difference geometry, paving the way for the development of a more general intersection theory. In particular, the fibres of a \\sigma-finite morphism between difference curves are all of the same size, when counted with correct multiplicities.
Modelling Hyperboloid Sound Scattering
DEFF Research Database (Denmark)
Burry, Jane; Davis, Daniel; Peters, Brady
2011-01-01
The Responsive Acoustic Surfaces workshop project described here sought new understandings about the interaction between geometry and sound in the arena of sound scattering. This paper reports on the challenges associated with modelling, simulating, fabricating and measuring this phenomenon using...... both physical and digital models at three distinct scales. The results suggest hyperboloid geometry, while difficult to fabricate, facilitates sound scattering....
Watanabe, Kenichi; Kyomoto, Masayuki; Saiga, Kenichi; Taketomi, Shuji; Inui, Hiroshi; Kadono, Yuho; Takatori, Yoshio; Tanaka, Sakae; Ishihara, Kazuhiko; Moro, Toru
2015-01-01
The wear and creep deformation resistances of polymeric orthopedic bearing materials are both important for extending their longevity. In this study, we evaluated the wear and creep deformation resistances, including backside damage, of different polyethylene (PE) materials, namely, conventional PE, cross-linked PE (CLPE), and poly(2-methacryloyloxyethyl phosphorylcholine)- (PMPC-) grafted CLPE, through wear tests and finite element analysis. The gravimetric and volumetric degrees of wear of disks (3 or 6 mm in thickness) of these materials against a cobalt-chromium-molybdenum alloy pin were examined using a multidirectional pin-on-disk tester. Cross-linking and PMPC grafting decreased the gravimetric wear of the PE disks significantly. The volumetric wear at the bearing surface and the volumetric penetration in the backside of the 3-mm thick PE disk were higher than those of the 6-mm thick PE disk, regardless of the bearing material. The geometrical changes induced in the PE disks consisted of creep, because the calculated internal von Mises stress at the bearing side of all disks and that at the backside of the 3-mm thick disks exceeded their actual yield strengths. A highly hydrated bearing surface layer, formed by PMPC grafting, and a cross-linking-strengthened substrate of adequate thickness are essential for increasing the wear and creep deformation resistances.
Directory of Open Access Journals (Sweden)
Kenichi Watanabe
2015-01-01
phosphorylcholine- (PMPC- grafted CLPE, through wear tests and finite element analysis. The gravimetric and volumetric degrees of wear of disks (3 or 6 mm in thickness of these materials against a cobalt-chromium-molybdenum alloy pin were examined using a multidirectional pin-on-disk tester. Cross-linking and PMPC grafting decreased the gravimetric wear of the PE disks significantly. The volumetric wear at the bearing surface and the volumetric penetration in the backside of the 3-mm thick PE disk were higher than those of the 6-mm thick PE disk, regardless of the bearing material. The geometrical changes induced in the PE disks consisted of creep, because the calculated internal von Mises stress at the bearing side of all disks and that at the backside of the 3-mm thick disks exceeded their actual yield strengths. A highly hydrated bearing surface layer, formed by PMPC grafting, and a cross-linking-strengthened substrate of adequate thickness are essential for increasing the wear and creep deformation resistances.
Directory of Open Access Journals (Sweden)
Kikinis Ron
2006-03-01
Full Text Available Abstract Introduction Mitral Valve (MV 3D structural data can be easily obtained using standard transesophageal echocardiography (TEE devices but quantitative pre- and intraoperative volume analysis of the MV is presently not feasible in the cardiac operation room (OR. Finite element method (FEM modelling is necessary to carry out precise and individual volume analysis and in the future will form the basis for simulation of cardiac interventions. Method With the present retrospective pilot study we describe a method to transfer MV geometric data to 3D Slicer 2 software, an open-source medical visualization and analysis software package. A newly developed software program (ROIExtract allowed selection of a region-of-interest (ROI from the TEE data and data transformation for use in 3D Slicer. FEM models for quantitative volumetric studies were generated. Results ROI selection permitted the visualization and calculations required to create a sequence of volume rendered models of the MV allowing time-based visualization of regional deformation. Quantitation of tissue volume, especially important in myxomatous degeneration can be carried out. Rendered volumes are shown in 3D as well as in time-resolved 4D animations. Conclusion The visualization of the segmented MV may significantly enhance clinical interpretation. This method provides an infrastructure for the study of image guided assessment of clinical findings and surgical planning. For complete pre- and intraoperative 3D MV FEM analysis, three input elements are necessary: 1. time-gated, reality-based structural information, 2. continuous MV pressure and 3. instantaneous tissue elastance. The present process makes the first of these elements available. Volume defect analysis is essential to fully understand functional and geometrical dysfunction of but not limited to the valve. 3D Slicer was used for semi-automatic valve border detection and volume-rendering of clinical 3D echocardiographic
Lindquist Liljeqvist, Moritz; Hultgren, Rebecka; Siika, Antti; Gasser, T Christian; Roy, Joy
2017-04-01
Finite element analysis (FEA) has been suggested to be superior to maximal diameter measurements in predicting rupture of abdominal aortic aneurysms (AAAs). Our objective was to investigate to what extent previously described rupture risk factors were associated with FEA-estimated rupture risk. One hundred forty-six patients with an asymptomatic AAA of a 40- to 60-mm diameter were retrospectively identified and consecutively included. The patients' computed tomography angiograms were analyzed by FEA without (neutral) and with (specific) input of patient-specific mean arterial pressure (MAP), gender, family history, and age. The maximal wall stress/wall strength ratio was described as a rupture risk equivalent diameter (RRED), which translated this ratio into an average aneurysm diameter of corresponding rupture risk. In multivariate linear regression, RRED neutral increased with female gender (3.7 mm; 95% confidence interval [CI], 0.13-7.3) and correlated with patient height (0.27 mm/cm; 95% CI, 0.11-0.43) and body surface area (BSA, 16 mm/m 2 ; 95% CI, 8.3-24) and inversely with body mass index (BMI, -0.40 mm/kg m -2 ; 95% CI, -0.75 to -0.054) in a wall stress-dependent manner. Wall stress-adjusted RRED neutral was raised if the patient was currently smoking (1.1 mm; 95% CI, 0.21-1.9). Age, MAP, family history, and patient weight were unrelated to RRED neutral . In specific FEA, RRED specific increased with female gender, MAP, family history positive for AAA, height, and BSA, whereas it was inversely related to BMI. All results were independent of aneurysm diameter. Peak wall stress and RRED correlated with aneurysm diameter and lumen volume. Female gender, current smoking, increased patient height and BSA, and low BMI were found to increase the mechanical rupture risk of AAAs. Previously described rupture risk factors may in part be explained by patient characteristic-dependent variations in aneurysm biomechanics. Copyright © 2016 Society for Vascular
International Nuclear Information System (INIS)
Doll, P.
1990-02-01
Neutron-proton scattering as fundamental interaction process below and above hundred MeV is discussed. Quark model inspired interactions and phenomenological potential models are described. The seminar also indicates the experimental improvements for achieving new precise scattering data. Concluding remarks indicate the relevance of nucleon-nucleon scattering results to finite nuclei. (orig.) [de
Iversen, Birger
1992-01-01
Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics
Discrete differential geometry. Consistency as integrability
Bobenko, Alexander I.; Suris, Yuri B.
2005-01-01
A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra), the discrete differential geometry aims at the development of discrete equivalents of notions and methods of smooth surface theory. Current interest in this field derives not ...
Molecular motion in restricted geometries
Indian Academy of Sciences (India)
Molecular dynamics in restricted geometries is known to exhibit anomalous behaviour. Diffusion, translational or rotational, of molecules is altered significantly on confinement in restricted geometries. Quasielastic neutron scattering (QENS) offers a unique possibility of studying molecular motion in such systems. Both time ...
International Nuclear Information System (INIS)
Santos, Frederico P.; Alves Filho, Hermes; Barros, Ricardo C.; Xavier, Vinicius S.
2011-01-01
The scattering source iterative (SI) scheme is traditionally applied to converge fine-mesh numerical solutions to fixed-source discrete ordinates (S N ) neutron transport problems. The SI scheme is very simple to implement under a computational viewpoint. However, the SI scheme may show very slow convergence rate, mainly for diffusive media (low absorption) with several mean free paths in extent. In this work we describe an acceleration technique based on an improved initial guess for the scattering source distribution within the slab. In other words, we use as initial guess for the fine-mesh scattering source, the coarse-mesh solution of the neutron diffusion equation with special boundary conditions to account for the classical S N prescribed boundary conditions, including vacuum boundary conditions. Therefore, we first implement a spectral nodal method that generates coarse-mesh diffusion solution that is completely free from spatial truncation errors, then we reconstruct this coarse-mesh solution within each spatial cell of the discretization grid, to further yield the initial guess for the fine-mesh scattering source in the first S N transport sweep (μm > 0 and μm < 0, m = 1:N) across the spatial grid. We consider a number of numerical experiments to illustrate the efficiency of the offered diffusion synthetic acceleration (DSA) technique. (author)
van den Broek, P.M.
1984-01-01
The aim of this paper is to give a detailed exposition of the relation between the geometry of twistor space and the geometry of Minkowski space. The paper has a didactical purpose; no use has been made of differential geometry and cohomology.
Kobayashi, Satoru; Tanelli, Simone; Im, Eastwood
2005-01-01
Effects of multiple scattering on reflectivity are studied for millimeter wavelength weather radars. A time-independent vector theory, including up to second-order scattering, is derived for a single layer of hydrometeors of a uniform density and a uniform diameter. In this theory, spherical waves with a Gaussian antenna pattern are used to calculate ladder and cross terms in the analytical scattering theory. The former terms represent the conventional multiple scattering, while the latter terms cause backscattering enhancement in both the copolarized and cross-polarized components. As the optical thickness of the hydrometeor layer increases, the differences from the conventional plane wave theory become more significant, and essentially, the reflectivity of multiple scattering depends on the ratio of mean free path to radar footprint radius. These results must be taken into account when analyzing radar reflectivity for use in remote sensing.
Energy Technology Data Exchange (ETDEWEB)
Bore, C; Dandeu, Y; Saint-Amand, Ch [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1965-07-01
MUDE is a nuclear code written in FORTRAN II for IBM 7090-7094. It resolves a system of difference equations approximating to the one-dimensional multigroup neutron scattering problem. More precisely, this code makes it possible to: 1. Calculate the critical condition of a reactor (k{sub eff}, critical radius, critical composition) and the corresponding fluxes; 2. Calculate the associated fluxes and various subsidiary results; 3. Carry out perturbation calculations; 4. Study the propagation of fluxes at a distance; 5. Estimate the relative contributions of the cross sections (macroscopic or microscopic); 6. Study the changes with time of the composition of the reactor. (authors) [French] MUDE est un code nucleaire ecrit en FORTRAN II pour IBM 7090-7094. Il resout un systeme d'equations aux differences approchant le probleme de diffusion neutronique multigroupe a une dimension. Plus precisement ce code permet de: 1. Calculer la condition critique d'un reacteur (k{sub eff}, rayon critique, composition critique) et les flux correspondants; 2. Calculer les flux adjoints et divers resultats connexes; 3. Effectuer des calculs de perturbation; 4. Etudier la propagation des flux a longue distance; 5. Ponderer des sections efficaces (macroscopiques ou microscopiques); 6. Etudier l'evolution de la composition du reacteur au cours du temps. (auteurs)
Rodger, Alison
1995-01-01
Molecular Geometry discusses topics relevant to the arrangement of atoms. The book is comprised of seven chapters that tackle several areas of molecular geometry. Chapter 1 reviews the definition and determination of molecular geometry, while Chapter 2 discusses the unified view of stereochemistry and stereochemical changes. Chapter 3 covers the geometry of molecules of second row atoms, and Chapter 4 deals with the main group elements beyond the second row. The book also talks about the complexes of transition metals and f-block elements, and then covers the organometallic compounds and trans
2002-01-01
Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...
Scattering of electromagnetic waves by obstacles
Kristensson, Gerhard
2016-01-01
The main purpose of Scattering of Electromagnetic Waves by Obstacles is to give a theoretical treatment of the scattering phenomena, and to illustrate numerical computations of some canonical scattering problems for different geometries and materials.
Black hole entropy and finite geometry
Czech Academy of Sciences Publication Activity Database
Levay, P.; Saniga, M.; Vrana, P.; Pracna, Petr
2009-01-01
Roč. 79, č. 8 (2009), 084036 ISSN 1550-7998 Institutional research plan: CEZ:AV0Z40400503 Keywords : Maxwell-Einstein supergravity * attractors * black hole entropy Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 4.922, year: 2009
Combinatorics of block designs and finite geometries
Indian Academy of Sciences (India)
2013-11-10
Nov 10, 2013 ... example, it is not known whether there is a projective plane of order twelve but it is known, ..... is just the same thing as saying that Γ is a regular graph. .... It is strange and pathetic that not too many tools are available for the.
International Nuclear Information System (INIS)
Robinson, I.; Trautman, A.
1988-01-01
The geometry of classical physics is Lorentzian; but weaker geometries are often more appropriate: null geodesics and electromagnetic fields, for example, are well known to be objects of conformal geometry. To deal with a single null congruence, or with the radiative electromagnetic fields associated with it, even less is needed: flag geometry for the first, optical geometry, with which this paper is chiefly concerned, for the second. The authors establish a natural one-to-one correspondence between optical geometries, considered locally, and three-dimensional Cauchy-Riemann structures. A number of Lorentzian geometries are shown to be equivalent from the optical point of view. For example the Goedel universe, the Taub-NUT metric and Hauser's twisting null solution have an optical geometry isomorphic to the one underlying the Robinson congruence in Minkowski space. The authors present general results on the problem of lifting a CR structure to a Lorentz manifold and, in particular, to Minkowski space; and exhibit the relevance of the deviation form to this problem
Pottmann, Helmut; Eigensatz, Michael; Vaxman, Amir; Wallner, Johannes
2014-01-01
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.
Pottmann, Helmut
2014-11-26
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.
Maor, Eli
2014-01-01
If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configur
International Nuclear Information System (INIS)
Ueki, T.; Larsen, E.W.
1998-01-01
The authors show that Monte Carlo simulations of neutral particle transport in planargeometry anisotropically scattering media, using the exponential transform with angular biasing as a variance reduction device, are governed by a new Boltzman Monte Carlo (BMC) equation, which includes particle weight as an extra independent variable. The weight moments of the solution of the BMC equation determine the moments of the score and the mean number of collisions per history in the nonanalog Monte Carlo simulations. Therefore, the solution of the BMC equation predicts the variance of the score and the figure of merit in the simulation. Also, by (1) using an angular biasing function that is closely related to the ''asymptotic'' solution of the linear Boltzman equation and (2) requiring isotropic weight changes as collisions, they derive a new angular biasing scheme. Using the BMC equation, they propose a universal ''safe'' upper limit of the transform parameter, valid for any type of exponential transform. In numerical calculations, they demonstrate that the behavior of the Monte Carlo simulations and the performance predicted by deterministically solving the BMC equation agree well, and that the new angular biasing scheme is always advantageous
Kemnitz, Arnfried
Der Grundgedanke der Analytischen Geometrie besteht darin, dass geometrische Untersuchungen mit rechnerischen Mitteln geführt werden. Geometrische Objekte werden dabei durch Gleichungen beschrieben und mit algebraischen Methoden untersucht.
Lefschetz, Solomon
2005-01-01
An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
Hilbert's Nullstellensatz and the Beginning of Algebraic Geometry
Indian Academy of Sciences (India)
The objects of study in algebraic geometry are the loci, or zero sets of polynomials. ... of polynomials in n-variables with real coefficients, indexed by some (finite or ... complex, can defined by only finitely many polynomials.) _ _ _ _ _ _ _ _ ...
Optical geometry across the horizon
International Nuclear Information System (INIS)
Jonsson, Rickard
2006-01-01
In a recent paper (Jonsson and Westman 2006 Class. Quantum Grav. 23 61), a generalization of optical geometry, assuming a non-shearing reference congruence, is discussed. Here we illustrate that this formalism can be applied to (a finite four-volume) of any spherically symmetric spacetime. In particular we apply the formalism, using a non-static reference congruence, to do optical geometry across the horizon of a static black hole. While the resulting geometry in principle is time dependent, we can choose the reference congruence in such a manner that an embedding of the geometry always looks the same. Relative to the embedded geometry the reference points are then moving. We discuss the motion of photons, inertial forces and gyroscope precession in this framework
Burdette, A C
1971-01-01
Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus.This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes.This book will prove useful to undergraduate trigonometric st
Berger, Marcel
2010-01-01
Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces,
Robinson, Gilbert de B
2011-01-01
This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geom
Connes, Alain
1994-01-01
This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathemat
Devrient, M.; Da, X.; Frick, T.; Schmidt, M.
Laser transmission welding is a well known joining technology for thermoplastics. Because of the needs of lightweight, cost effective and green production thermoplastics are usually filled with glass fibers. These lead to higher absorption and more scattering within the upper joining partner with a negative influence on the welding process. Here an experimental method for the characterization of the scattering behavior of semi crystalline thermoplastics filled with short glass fibers and a finite element model of the welding process capable to consider scattering as well as an analytical model are introduced. The experimental data is used for the numerical and analytical investigation of laser transmission welding under consideration of scattering. The scattering effects of several thermoplastics onto the calculated temperature fields as well as weld seam geometries are quantified.
FDTD scattered field formulation for scatterers in stratified dispersive media.
Olkkonen, Juuso
2010-03-01
We introduce a simple scattered field (SF) technique that enables finite difference time domain (FDTD) modeling of light scattering from dispersive objects residing in stratified dispersive media. The introduced SF technique is verified against the total field scattered field (TFSF) technique. As an application example, we study surface plasmon polariton enhanced light transmission through a 100 nm wide slit in a silver film.
International Nuclear Information System (INIS)
Fletcher, J.K.
1987-12-01
The computer code MARC/PN provides a solution of the multigroup transport equation by expanding the flux in spherical harmonics. The coefficients of the series so obtained satisfy linked first order differential equations, and on eliminating terms associated with odd parity harmonics a second order system results which can be solved by established finite difference or finite element techniques. This report describes modifications incorporated in MARC/PN to allow for anisotropic scattering, and the modelling of irregular exterior boundaries in the finite element option. The latter development leads to substantial reductions in problem size, particularly for three dimensions. Also, links to an interactive graphics mesh generator (SUPERTAB) have been added. The final section of the report contains results from problems showing the effects of anisotropic scatter and the ability of the code to model irregular geometries. (author)
Indian Academy of Sciences (India)
mathematicians are trained to use very precise language, and so find it hard to simplify and state .... thing. If you take a plane on which there are two such triangles which enjoy the above ... within this geometry to simplify things if needed.
Geometry -----------~--------------RESONANCE
Indian Academy of Sciences (India)
Parallel: A pair of lines in a plane is said to be parallel if they do not meet. Mathematicians were at war ... Subsequently, Poincare, Klein, Beltrami and others refined non-. Euclidean geometry. ... plane divides the plane into two half planes and.
International Nuclear Information System (INIS)
Strominger, A.
1990-01-01
A special manifold is an allowed target manifold for the vector multiplets of D=4, N=2 supergravity. These manifolds are of interest for string theory because the moduli spaces of Calabi-Yau threefolds and c=9, (2,2) conformal field theories are special. Previous work has given a local, coordinate-dependent characterization of special geometry. A global description of special geometries is given herein, and their properties are studied. A special manifold M of complex dimension n is characterized by the existence of a holomorphic Sp(2n+2,R)xGL(1,C) vector bundle over M with a nowhere-vanishing holomorphic section Ω. The Kaehler potential on M is the logarithm of the Sp(2n+2,R) invariant norm of Ω. (orig.)
Structural modeling techniques by finite element method
International Nuclear Information System (INIS)
Kang, Yeong Jin; Kim, Geung Hwan; Ju, Gwan Jeong
1991-01-01
This book includes introduction table of contents chapter 1 finite element idealization introduction summary of the finite element method equilibrium and compatibility in the finite element solution degrees of freedom symmetry and anti symmetry modeling guidelines local analysis example references chapter 2 static analysis structural geometry finite element models analysis procedure modeling guidelines references chapter 3 dynamic analysis models for dynamic analysis dynamic analysis procedures modeling guidelines and modeling guidelines.
General Geometry and Geometry of Electromagnetism
Shahverdiyev, Shervgi S.
2002-01-01
It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwell equations are derived from curvature function of geometry underlying Electromagnetism. And it is shown that equation of motion for a particle interacting with electromagnetic...
Integral geometry and valuations
Solanes, Gil
2014-01-01
Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented...
Ciarlet, Philippe G
2007-01-01
This book gives the basic notions of differential geometry, such as the metric tensor, the Riemann curvature tensor, the fundamental forms of a surface, covariant derivatives, and the fundamental theorem of surface theory in a selfcontained and accessible manner. Although the field is often considered a classical one, it has recently been rejuvenated, thanks to the manifold applications where it plays an essential role. The book presents some important applications to shells, such as the theory of linearly and nonlinearly elastic shells, the implementation of numerical methods for shells, and
Application of the 2-D discrete-ordinates method to multiple scattering of laser radiation
International Nuclear Information System (INIS)
Zardecki, A.; Gerstl, S.A.W.; Embury, J.F.
1983-01-01
The discrete-ordinates finite-element radiation transport code twotran is applied to describe the multiple scattering of a laser beam from a reflecting target. For a model scenario involving a 99% relative humidity rural aerosol we compute the average intensity of the scattered radiation and correction factors to the Beer-Lambert law arising from multiple scattering. As our results indicate, 2-D x-y and r-z geometry modeling can reliably describe a realistic 3-D scenario. Specific results are presented for the two visual ranges of 1.52 and 0.76 km which show that, for sufficiently high aerosol concentrations (e.g., equivalent to V = 0.76 km), the target signature in a distant detector becomes dominated by multiply scattered radiation from interactions of the laser light with the aerosol environment. The merits of the scaling group and the delta-M approximation for the transfer equation are also explored
Groups and Geometries : Siena Conference
Kantor, William; Lunardon, Guglielmo; Pasini, Antonio; Tamburini, Maria
1998-01-01
On September 1-7, 1996 a conference on Groups and Geometries took place in lovely Siena, Italy. It brought together experts and interested mathematicians from numerous countries. The scientific program centered around invited exposi tory lectures; there also were shorter research announcements, including talks by younger researchers. The conference concerned a broad range of topics in group theory and geometry, with emphasis on recent results and open problems. Special attention was drawn to the interplay between group-theoretic methods and geometric and combinatorial ones. Expanded versions of many of the talks appear in these Proceedings. This volume is intended to provide a stimulating collection of themes for a broad range of algebraists and geometers. Among those themes, represented within the conference or these Proceedings, are aspects of the following: 1. the classification of finite simple groups, 2. the structure and properties of groups of Lie type over finite and algebraically closed fields of f...
Energy Technology Data Exchange (ETDEWEB)
Yilbas, Bekir Sami; Akhtar, Syed Sohail [King Fahd University of Petroleum and Minerals, Dhahran (Saudi Arabia); Keles, Omer; Boran, Kurtulus [Gazi University, Ankara (Turkmenistan)
2015-08-15
Laser cutting of a triangular geometry into aluminum 2024 alloy is carried out. Thermal stress field in the cutting section is predicted using the finite element code ABAQUS. Surface temperature predictions are validated through the thermocouple data. Morphological changes in the cut section are examined incorporating optical and electron scanning microscopes. The effects of the size of the triangular geometry on thermal stress field are also examined. It is found that surface temperature predictions agree well with thermocouple data. von Mises stress remains high in the region close to the corners of the triangular geometry, which is more pronounced for the small size triangle. This behavior is associated with the occurrence of the high cooling rates in this region. Laser cut edges are free from large scale sideways burning and large size burr attachments. However, some locally scattered dross attachments are observed at the kerf exit.
Guide to Computational Geometry Processing
DEFF Research Database (Denmark)
Bærentzen, Jakob Andreas; Gravesen, Jens; Anton, François
be processed before it is useful. This Guide to Computational Geometry Processing reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. This is balanced with an introduction...... to the theoretical and mathematical underpinnings of each technique, enabling the reader to not only implement a given method, but also to understand the ideas behind it, its limitations and its advantages. Topics and features: Presents an overview of the underlying mathematical theory, covering vector spaces......, metric space, affine spaces, differential geometry, and finite difference methods for derivatives and differential equations Reviews geometry representations, including polygonal meshes, splines, and subdivision surfaces Examines techniques for computing curvature from polygonal meshes Describes...
Alpha particle collective Thomson scattering in TFTR
International Nuclear Information System (INIS)
Machuzak, J.S.; Woskov, P.P.; Rhee, D.Y.; Gilmore, J.; Bindslev, H.
1993-01-01
A collective Thomson scattering diagnostic is being implemented on TFTR to measure alpha particle, energetic and thermal ion densities and velocity distributions. A 60 GHz, 0.1-1 kW gyrotron will be used as the transmitter source, and the scattering geometry will be perpendicular to the magnetic field in the extraordinary mode polarization. An enhanced scattered signal is anticipated from fluctuations in the lower hybrid frequency range with this scattering geometry. Millimeter wave collective Thomson scattering diagnostics have the advantage of larger scattering angles to decrease the amount of stray light, and long, high power, modulated pulses to obtain improved signal to noise through synchronous detection techniques
Functional integration over geometries
International Nuclear Information System (INIS)
Mottola, E.
1995-01-01
The geometric construction of the functional integral over coset spaces M/G is reviewed. The inner product on the cotangent space of infinitesimal deformations of M defines an invariant distance and volume form, or functional integration measure on the full configuration space. Then, by a simple change of coordinates parameterizing the gauge fiber G, the functional measure on the coset space M/G is deduced. This change of integration variables leads to a Jacobian which is entirely equivalent to the Faddeev--Popov determinant of the more traditional gauge fixed approach in non-abelian gauge theory. If the general construction is applied to the case where G is the group of coordinate reparameterizations of spacetime, the continuum functional integral over geometries, i.e. metrics modulo coordinate reparameterizations may be defined. The invariant functional integration measure is used to derive the trace anomaly and effective action for the conformal part of the metric in two and four dimensional spacetime. In two dimensions this approach generates the Polyakov--Liouville action of closed bosonic non-critical string theory. In four dimensions the corresponding effective action leads to novel conclusions on the importance of quantum effects in gravity in the far infrared, and in particular, a dramatic modification of the classical Einstein theory at cosmological distance scales, signaled first by the quantum instability of classical de Sitter spacetime. Finite volume scaling relations for the functional integral of quantum gravity in two and four dimensions are derived, and comparison with the discretized dynamical triangulation approach to the integration over geometries are discussed. Outstanding unsolved problems in both the continuum definition and the simplicial approach to the functional integral over geometries are highlighted
Lectures on zeta functions over finite fields
Wan, Daqing
2007-01-01
These are the notes from the summer school in G\\"ottingen sponsored by NATO Advanced Study Institute on Higher-Dimensional Geometry over Finite Fields that took place in 2007. The aim was to give a short introduction on zeta functions over finite fields, focusing on moment zeta functions and zeta functions of affine toric hypersurfaces.
Nonlinear finite element modeling of corrugated board
A. C. Gilchrist; J. C. Suhling; T. J. Urbanik
1999-01-01
In this research, an investigation on the mechanical behavior of corrugated board has been performed using finite element analysis. Numerical finite element models for corrugated board geometries have been created and executed. Both geometric (large deformation) and material nonlinearities were included in the models. The analyses were performed using the commercial...
Finite-volume spectra of the Lee-Yang model
Energy Technology Data Exchange (ETDEWEB)
Bajnok, Zoltan [MTA Lendület Holographic QFT Group, Wigner Research Centre for Physics,H-1525 Budapest 114, P.O.B. 49 (Hungary); Deeb, Omar el [MTA Lendület Holographic QFT Group, Wigner Research Centre for Physics,H-1525 Budapest 114, P.O.B. 49 (Hungary); Physics Department, Faculty of Science, Beirut Arab University (BAU),Beirut (Lebanon); Pearce, Paul A. [School of Mathematics and Statistics, University of Melbourne,Parkville, Victoria 3010 (Australia)
2015-04-15
We consider the non-unitary Lee-Yang minimal model M(2,5) in three different finite geometries: (i) on the interval with integrable boundary conditions labelled by the Kac labels (r,s)=(1,1),(1,2), (ii) on the circle with periodic boundary conditions and (iii) on the periodic circle including an integrable purely transmitting defect. We apply φ{sub 1,3} integrable perturbations on the boundary and on the defect and describe the flow of the spectrum. Adding a Φ{sub 1,3} integrable perturbation to move off-criticality in the bulk, we determine the finite size spectrum of the massive scattering theory in the three geometries via Thermodynamic Bethe Ansatz (TBA) equations. We derive these integral equations for all excitations by solving, in the continuum scaling limit, the TBA functional equations satisfied by the transfer matrices of the associated A{sub 4} RSOS lattice model of Forrester and Baxter in Regime III. The excitations are classified in terms of (m,n) systems. The excited state TBA equations agree with the previously conjectured equations in the boundary and periodic cases. In the defect case, new TBA equations confirm previously conjectured transmission factors.
Brillouin scattering at high pressures
International Nuclear Information System (INIS)
Grimsditch, M.; Polian, A.
1988-02-01
Technical advances which have made Brillouin scattering a useful tool in high pressure diamond anvil cell (DAC) studies, viz. multipassing and tandem operation of Fabry-Perot interferometers, are reviewed. Experimental aspects, such as allowed scattering geometries, are outlined and the data analysis required to transform Brillouin spectra into sound velocities and elastic constants is presented. Experimental results on H 2 , N 2 , Ar, and He are presented, and the close relationship between the Brillouin scattering results and equations of state is highlighted
A Monte Carlo modeling on charging effect for structures with arbitrary geometries
Li, C.; Mao, S. F.; Zou, Y. B.; Li, Yong Gang; Zhang, P.; Li, H. M.; Ding, Z. J.
2018-04-01
Insulating materials usually suffer charging effects when irradiated by charged particles. In this paper, we present a Monte Carlo study on the charging effect caused by electron beam irradiation for sample structures with any complex geometry. When transporting in an insulating solid, electrons encounter elastic and inelastic scattering events; the Mott cross section and a Lorentz-type dielectric function are respectively employed to describe such scatterings. In addition, the band gap and the electron–long optical phonon interaction are taken into account. The electronic excitation in inelastic scattering causes generation of electron–hole pairs; these negative and positive charges establish an inner electric field, which in turn induces the drift of charges to be trapped by impurities, defects, vacancies etc in the solid, where the distributions of trapping sites are assumed to have uniform density. Under charging conditions, the inner electric field distorts electron trajectories, and the surface electric potential dynamically alters secondary electron emission. We present, in this work, an iterative modeling method for a self-consistent calculation of electric potential; the method has advantages in treating any structure with arbitrary complex geometry, in comparison with the image charge method—which is limited to a quite simple boundary geometry. Our modeling is based on: the combination of the finite triangle mesh method for an arbitrary geometry construction; a self-consistent method for the spatial potential calculation; and a full dynamic description for the motion of deposited charges. Example calculations have been done to simulate secondary electron yield of SiO2 for a semi-infinite solid, the charging for a heterostructure of SiO2 film grown on an Au substrate, and SEM imaging of a SiO2 line structure with rough surfaces and SiO2 nanoparticles with irregular shapes. The simulations have explored interesting interlaced charge layer distribution
Silva, Alessandro
1993-01-01
The papers in this wide-ranging collection report on the results of investigations from a number of linked disciplines, including complex algebraic geometry, complex analytic geometry of manifolds and spaces, and complex differential geometry.
Eisenhart, Luther Pfahler
2005-01-01
This concise text by a prominent mathematician deals chiefly with manifolds dominated by the geometry of paths. Topics include asymmetric and symmetric connections, the projective geometry of paths, and the geometry of sub-spaces. 1927 edition.
Energy Technology Data Exchange (ETDEWEB)
Souza, Altivo Monteiro de
2008-12-15
The world energy consumption has been increasing strongly in recent years. Nuclear energy has been regarded as a suitable option to supply this growing energy demand in industrial scale. In view of the need of improving the understanding and capacity of analysis of nuclear power plants, modern simulation techniques for flow and heat transfer problems are gaining greater importance. A large number of problems found in nuclear reactor engineering can be dealt assuming axial symmetry. Thus, in this work a stabilized finite element formulation for the solution of the Navier-Stokes and energy equations for axisymmetric problems have been developed and tested. The formulation has been implemented in the NS{sub S}OLVER{sub M}PI{sub 2}D{sub A} program developed at the Parallel Computation Laboratory of the Instituto de Engenharia Nuclear (LCP/IEN) and is now available either for safety analysis or design of nuclear systems. (author)
International Nuclear Information System (INIS)
Gurevich, L.Eh.; Gliner, Eh.B.
1978-01-01
Problems of investigating the Universe space-time geometry are described on a popular level. Immediate space-time geometries, corresponding to three cosmologic models are considered. Space-time geometry of a closed model is the spherical Riemann geonetry, of an open model - is the Lobachevskij geometry; and of a plane model - is the Euclidean geometry. The Universe real geometry in the contemporary epoch of development is based on the data testifying to the fact that the Universe is infinitely expanding
Energy Technology Data Exchange (ETDEWEB)
Cwik, T. [California Institute of Technology, Pasadena, CA (United States); Katz, D.S. [Cray Research, El Segundo, CA (United States)
1996-12-31
Finite element modeling has proven useful for accurately simulating scattered or radiated electromagnetic fields from complex three-dimensional objects whose geometry varies on the scale of a fraction of an electrical wavelength. An unstructured finite element model of realistic objects leads to a large, sparse, system of equations that needs to be solved efficiently with regard to machine memory and execution time. Both factorization and iterative solvers can be used to produce solutions to these systems of equations. Factorization leads to high memory requirements that limit the electrical problem size of three-dimensional objects that can be modeled. An iterative solver can be used to efficiently solve the system without excessive memory use and in a minimal amount of time if the convergence rate is controlled.
Neutron Elastic Scattering Cross Sections of Iron and Zinc in the Energy Region 2.5 to 8.1 MeV
International Nuclear Information System (INIS)
Holmqvist, B.; Johansson, S.G.; Lodin, G.; Wiedling, T.; Kiss, A.
1966-12-01
Angular distributions were measured for the elastic scattering of neutrons from iron at five energies between 3.0 and 8. 1 MeV and from zinc at eight energies between 2.5 and 8.1 MeV. Time-of-flight technique was used. Corrections for neutron flux attenuation, multiple elastic scattering, and the finite geometry of the source-sample detector system were made by using a Monte Carlo program. An optical model potential with Saxon-Woods form factors was used to fit theoretical angular distributions to the experimental ones. The parameter values giving the best fits to the experimental distributions were calculated by a computer
Neutron Elastic Scattering Cross Sections of Iron and Zinc in the Energy Region 2.5 to 8.1 MeV
Energy Technology Data Exchange (ETDEWEB)
Holmqvist, B; Johansson, S G; Lodin, G; Wiedling, T [AB Atomenergi, Nyko eping (Sweden); Kiss, A [Inst. for Experimental Physics, Univ. of Debrecen, De brecen (Hungary)
1966-12-15
Angular distributions were measured for the elastic scattering of neutrons from iron at five energies between 3.0 and 8. 1 MeV and from zinc at eight energies between 2.5 and 8.1 MeV. Time-of-flight technique was used. Corrections for neutron flux attenuation, multiple elastic scattering, and the finite geometry of the source-sample detector system were made by using a Monte Carlo program. An optical model potential with Saxon-Woods form factors was used to fit theoretical angular distributions to the experimental ones. The parameter values giving the best fits to the experimental distributions were calculated by a computer.
Nozzle geometry variations on the discharge coefficient
Directory of Open Access Journals (Sweden)
M.M.A. Alam
2016-03-01
Full Text Available Numerical works have been conducted to investigate the effect of nozzle geometries on the discharge coefficient. Several contoured converging nozzles with finite radius of curvatures, conically converging nozzles and conical divergent orifices have been employed in this investigation. Each nozzle and orifice has a nominal exit diameter of 12.7×10−3 m. A 3rd order MUSCL finite volume method of ANSYS Fluent 13.0 was used to solve the Reynolds-averaged Navier–Stokes equations in simulating turbulent flows through various nozzle inlet geometries. The numerical model was validated through comparison between the numerical results and experimental data. The results obtained show that the nozzle geometry has pronounced effect on the sonic lines and discharge coefficients. The coefficient of discharge was found differ from unity due to the non-uniformity of flow parameters at the nozzle exit and the presence of boundary layer as well.
Polarized Elastic Fast-Neutron Scattering off {sup 12}C in the Lower MeV-Range. I. Experimental Part
Energy Technology Data Exchange (ETDEWEB)
Aspelund, O
1967-05-15
Practical as well as more fundamental interest in low-energy n-{sup 12}C elastic scattering motivated the execution of comprehensive polarization studies between 1.062 and 2.243 MeV. Seven complete polarization angular distributions were obtained from experimental finite-geometry left-right ratios at each energy observed at six or seven laboratory scattering angles between 30 and 129 deg, using polarized fast-neutrons emitted at {theta}{sub i} 50 (lab. syst.) from the {sup 7}Li(p, n) {sup 7}Be-reaction. Proper corrections were applied for finite geometry and polarized multiple-scattering effects as well as for the presence of the first-excited state group of fast-neutrons in the incident beams. The magnitude of the polarization effects are sufficiently large to ensure the potentialities of {sup 12}C as an acceptable fast-neutron polarization analyser in the energy range under consideration. Furthermore, on the basis of the above-mentioned polarization data as well as on the basis of total and differential scattering cross section data available in current literature reliable phase shifts were determined. These phase shifts are only in partial agreement with the ones of Wills, Jr. et al. , and in definite disagreement with the extrapolated phases of Meier, Scherrer, and Trumpy. Their energy variations will be predicted in the theoretical part of this contribution.
Schreyer, W.; Kikawa, T.; Losekamm, M. J.; Paul, S.; Picker, R.
2017-06-01
Modern precision experiments trapping low-energy particles require detailed simulations of particle trajectories and spin precession to determine systematic measurement limitations and apparatus deficiencies. We developed PENTrack, a tool that allows to simulate trajectories of ultracold neutrons and their decay products-protons and electrons-and the precession of their spins in complex geometries and electromagnetic fields. The interaction of ultracold neutrons with matter is implemented with the Fermi-potential formalism and diffuse scattering using Lambert and microroughness models. The results of several benchmark simulations agree with STARucn v1.2, uncovered several flaws in Geant4 v10.2.2, and agree with experimental data. Experiment geometry and electromagnetic fields can be imported from commercial computer-aided-design and finite-element software. All simulation parameters are defined in simple text files allowing quick changes. The simulation code is written in C++ and is freely available at github.com/wschreyer/PENTrack.git.
Energy Technology Data Exchange (ETDEWEB)
Schreyer, W., E-mail: w.schreyer@tum.de [Technical University of Munich, James-Franck-Str. 1, 85748 Garching (Germany); Kikawa, T. [TRIUMF, 4004 Wesbrook Mall, Vancouver (Canada); Losekamm, M.J.; Paul, S. [Technical University of Munich, James-Franck-Str. 1, 85748 Garching (Germany); Picker, R. [TRIUMF, 4004 Wesbrook Mall, Vancouver (Canada); Simon Fraser University, 8888 University Drive, Burnaby (Canada)
2017-06-21
Modern precision experiments trapping low-energy particles require detailed simulations of particle trajectories and spin precession to determine systematic measurement limitations and apparatus deficiencies. We developed PENTrack, a tool that allows to simulate trajectories of ultracold neutrons and their decay products—protons and electrons—and the precession of their spins in complex geometries and electromagnetic fields. The interaction of ultracold neutrons with matter is implemented with the Fermi-potential formalism and diffuse scattering using Lambert and microroughness models. The results of several benchmark simulations agree with STARucn v1.2, uncovered several flaws in Geant4 v10.2.2, and agree with experimental data. Experiment geometry and electromagnetic fields can be imported from commercial computer-aided-design and finite-element software. All simulation parameters are defined in simple text files allowing quick changes. The simulation code is written in C++ and is freely available at (github.com/wschreyer/PENTrack.git).
Scattered X-ray beam nondestructive testing
International Nuclear Information System (INIS)
Harding, G.; Kosanetzky, J.
1988-01-01
X-ray scatter interactions generally dominate the linear attenuation coefficient at the photon energies typical of medical and industrial radiography. Specific advantages of X-ray scatter imaging, including a flexible choice of measurement geometry, direct 3D-imaging capability (tomography) and improved information for material characterization, are illustrated with results from Compton and coherent scatter devices. Applications of a Compton backscatter scanner (ComScan) in the aerospace industry and coherent scatter imaging in security screening are briefly considered [pt
International Nuclear Information System (INIS)
Oliveira, C.R.E. de; Goddard, A.
1991-01-01
In this paper we review the current status of the finite element method applied to the solution of the neutron transport equation and we discuss its potential role in the field of criticality safety. We show that the method's ability in handling complex, irregular geometry in two- and three-dimensions coupled with its accurate solutions potentially renders it an attractive alternative to the longer-established Monte Carlo method. Details of the most favoured form of the method - that which combines finite elements in space and spherical harmonics in angle - are presented. This form of the method, which has been extensively investigated over the last decade by research groups at the University of London, has been numerically implemented in the finite element code EVENT. The code has among its main features the capability of solving fixed source eigenvalue and time-dependent complex geometry problems in two- and three-dimensions. Other features of the code include anisotropic up- and down-scatter, direct and/or adjoint solutions and access to standard data libraries. Numerical examples, ranging from simple criticality benchmark studies to the analysis of idealised three-dimensional reactor cores, are presented to demonstrate the potential of the method. (author)
Application of the finite element method to the neutron transport equation
International Nuclear Information System (INIS)
Martin, W.R.
1976-01-01
This paper examines the theoretical and practical application of the finite element method to the neutron transport equation. It is shown that in principle the system of equations obtained by application of the finite element method can be solved with certain physical restrictions concerning the criticality of the medium. The convergence of this approximate solution to the exact solution with mesh refinement is examined, and a non-optical estimate of the convergence rate is obtained analytically. It is noted that the numerical results indicate a faster convergence rate and several approaches to obtain this result analytically are outlined. The practical application of the finite element method involved the development of a computer code capable of solving the neutron transport equation in 1-D plane geometry. Vacuum, reflecting, or specified incoming boundary conditions may be analyzed, and all are treated as natural boundary conditions. The time-dependent transport equation is also examined and it is shown that the application of the finite element method in conjunction with the Crank-Nicholson time discretization method results in a system of algebraic equations which is readily solved. Numerical results are given for several critical slab eigenvalue problems, including anisotropic scattering, and the results compare extremely well with benchmark results. It is seen that the finite element code is more efficient than a standard discrete ordinates code for certain problems. A problem with severe heterogeneities is considered and it is shown that the use of discontinuous spatial and angular elements results in a marked improvement in the results. Finally, time-dependent problems are examined and it is seen that the phenomenon of angular mode separation makes the numerical treatment of the transport equation in slab geometry a considerable challenge, with the result that the angular mesh has a dominant effect on obtaining acceptable solutions
International Nuclear Information System (INIS)
Buescher, R.
2005-01-01
density of states in terms of the S-matrix of quantum scattering at potentials, the new trace formula is applied to the free Green function, evaluated at the boundary surfaces of the confining geometry. This latter formulation is non-approximative and hence exact. (Orig.)
Meyer, Walter J
2006-01-01
Meyer''s Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry''s usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers.* Realistic applications integrated throughout the text, including (but not limited to): - Symmetries of artistic patterns- Physics- Robotics- Computer vision- Computer graphics- Stability of architectural structures- Molecular biology- Medicine- Pattern recognition* Historical notes included in many chapters...
Indian Academy of Sciences (India)
algebraic geometry but also in related fields like number theory. ... every vector bundle on the affine space is trivial. (equivalently ... les on a compact Riemann surface to unitary rep- ... tial geometry and topology and was generalised in.
International Nuclear Information System (INIS)
Sloane, Peter
2007-01-01
We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)
Energy Technology Data Exchange (ETDEWEB)
Sloane, Peter [Department of Mathematics, King' s College, University of London, Strand, London WC2R 2LS (United Kingdom)
2007-09-15
We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)
International Nuclear Information System (INIS)
Ozgener, B.; Azgener, H.A.
1991-01-01
In finite element formulations for the solution of the within-group neutron diffusion equation, two different treatments are possible for the group source term: the consistent source approximation (CSA) and the lumped source approximation (LSA). CSA results in intra-group scattering and fission matrices which have the same nondiagonal structure as the global coefficient matrix. This situation might be regarded as a disadvantage, compared to the conventional (i.e. finite difference) methods where the intra-group scattering and fission matrices are diagonal. To overcome this disadvantage, LSA could be used to diagonalize these matrices. LSA is akin to the lumped mass approximation of continuum mechanics. We concentrate on two different aspects of the source approximations. Although it has been reported that LSA does not modify the asymptotic h 2 convergence behaviour for linear elements, the effect of LSA on convergence of higher degree elements has not been investigated. Thus, we would be interested in determining, p, the asymptotic order of convergence, in: Δk |k eff (analytical) -k eff (finite element)| = Ch p (1) for finite element approximations of varying degree (N) with both of the source approximations. Since (1) is valid in the asymptotic limit, we must use ultra-fine meshes and quadruple precision arithmetic. For our order of convergence study, we used infinite cylindrical geometry with azimuthal symmetry. Hence, the effects of singularities remain uninvestigated. The second aspect we dwell on is the performance of LSA in bilinear 3-D finite element calculations, compared to CSA. LSA has been used quite extensively in 1- and 2-D even-parity transport and diffusion calculations. In this work, we will try to assess the relative merits of LSA and CSA in 3-D problems. (author)
Scattering phase functions of horizontally oriented hexagonal ice crystals
International Nuclear Information System (INIS)
Chen Guang; Yang Ping; Kattawar, George W.; Mishchenko, Michael I.
2006-01-01
Finite-difference time domain (FDTD) solutions are first compared with the corresponding T-matrix results for light scattering by circular cylinders with specific orientations. The FDTD method is then utilized to study the scattering properties of horizontally oriented hexagonal ice plates at two wavelengths, 0.55 and 12 μm. The phase functions of horizontally oriented ice plates deviate substantially from their counterparts obtained for randomly oriented particles. Furthermore, we compute the phase functions of horizontally oriented ice crystal columns by using the FDTD method along with two schemes for averaging over the particle orientations. It is shown that the phase functions of hexagonal ice columns with horizontal orientations are not sensitive to the rotation about the principal axes of the particles. Moreover, hexagonal ice crystals and circular cylindrical ice particles have similar optical properties, particularly, at a strongly absorbing wavelength, if the two particle geometries have the same length and aspect ratio defined as the ratio of the radius or semi-width of the cross section of a particle to its length. The phase functions for the two particle geometries are slightly different in the case of weakly absorbing plates with large aspect ratios. However, the solutions for circular cylinders agree well with their counterparts for hexagonal columns
Directory of Open Access Journals (Sweden)
Na Liu
2015-10-01
Full Text Available Hadron production in semi-inclusive deep-inelastic scattering of leptons from nuclei is an ideal tool to determine and constrain the transport coefficient in cold nuclear matter. The leading-order computations for hadron multiplicity ratios are performed by means of the SW quenching weights and the analytic parameterizations of quenching weights based on BDMPS formalism. The theoretical results are compared to the HERMES positively charged pions production data with the quarks hadronization occurring outside the nucleus. With considering the nuclear geometry effect on hadron production, our predictions are in good agreement with the experimental measurements. The extracted transport parameter from the global fit is shown to be qˆ=0.74±0.03 GeV2/fm for the SW quenching weight without the finite energy corrections. As for the analytic parameterization of BDMPS quenching weight without the quark energy E dependence, the computed transport coefficient is qˆ=0.20±0.02 GeV2/fm. It is found that the nuclear geometry effect has a significant impact on the transport coefficient in cold nuclear matter. It is necessary to consider the detailed nuclear geometry in studying the semi-inclusive hadron production in deep inelastic scattering on nuclear targets.
Geometry essentials for dummies
Ryan, Mark
2011-01-01
Just the critical concepts you need to score high in geometry This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams. Get down to the basics - get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals Conque
The finite element method in electromagnetics
Jin, Jianming
2014-01-01
A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetics The finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration. The
Arithmetic noncommutative geometry
Marcolli, Matilde
2005-01-01
Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...
Solutions of the finite type of Sine-Gordon equation
International Nuclear Information System (INIS)
Zhao Guosong
1998-01-01
We use the technique of differential geometry to prove that the solutions of finite type of the sine-Gordon equation φ xx - φ yy = sin φ cosφ can be obtained from a system of ordinary differential equations
An introduction to finite projective planes
Albert, Abraham Adrian
2015-01-01
Geared toward both beginning and advanced undergraduate and graduate students, this self-contained treatment offers an elementary approach to finite projective planes. Following a review of the basics of projective geometry, the text examines finite planes, field planes, and coordinates in an arbitrary plane. Additional topics include central collineations and the little Desargues' property, the fundamental theorem, and examples of finite non-Desarguesian planes.Virtually no knowledge or sophistication on the part of the student is assumed, and every algebraic system that arises is defined and
Study of the sensitivity of the radiation transport problem in a scattering medium
International Nuclear Information System (INIS)
Nunes, Rogerio Chaffin
2002-03-01
In this work, the system of differential equations obtained by the angular approach of the two-dimensional transport equation by the discrete ordinates method is solved through the formulation of finite elements with the objective of investigating the sensitivity of the outgoing flux of radiation with the incoming flux and the properties of absorption and scattering of the medium. The variational formulation for the system of differential equations of second order with the generalized boundary conditions of Neumann (third type) allows an easy implementation of the method of the finite elements with triangular mesh and approximation space of first order. The geometry chosen for the simulations is a circle with a non homogeneous circular form in its interior. The mapping of Dirichlet-Neumann is studied through various simulations involving the incoming flux, the outgoing flux and the properties of the medium. (author)
An introduction to finite tight frames
Waldron, Shayne F D
2018-01-01
This textbook is an introduction to the theory and applications of finite tight frames, an area that has developed rapidly in the last decade. Stimulating much of this growth are the applications of finite frames to diverse fields such as signal processing, quantum information theory, multivariate orthogonal polynomials, and remote sensing. Key features and topics: * First book entirely devoted to finite frames * Extensive exercises and MATLAB examples for classroom use * Important examples, such as harmonic and Heisenberg frames, are presented in preliminary chapters, encouraging readers to explore and develop an intuitive feeling for tight frames * Later chapters delve into general theory details and recent research results * Many illustrations showing the special aspects of the geometry of finite frames * Provides an overview of the field of finite tight frames * Discusses future research directions in the field Featuring exercises and MATLAB examples in each chapter, the book is well suited as a textbook ...
Introduction to global variational geometry
Krupka, Demeter
2015-01-01
The book is devoted to recent research in the global variational theory on smooth manifolds. Its main objective is an extension of the classical variational calculus on Euclidean spaces to (topologically nontrivial) finite-dimensional smooth manifolds; to this purpose the methods of global analysis of differential forms are used. Emphasis is placed on the foundations of the theory of variational functionals on fibered manifolds - relevant geometric structures for variational principles in geometry, physical field theory and higher-order fibered mechanics. The book chapters include: - foundations of jet bundles and analysis of differential forms and vector fields on jet bundles, - the theory of higher-order integral variational functionals for sections of a fibred space, the (global) first variational formula in infinitesimal and integral forms- extremal conditions and the discussion of Noether symmetries and generalizations,- the inverse problems of the calculus of variations of Helmholtz type- variational se...
Some Progress in Conformal Geometry
Directory of Open Access Journals (Sweden)
Sun-Yung A. Chang
2007-12-01
Full Text Available This is a survey paper of our current research on the theory of partial differential equations in conformal geometry. Our intention is to describe some of our current works in a rather brief and expository fashion. We are not giving a comprehensive survey on the subject and references cited here are not intended to be complete. We introduce a bubble tree structure to study the degeneration of a class of Yamabe metrics on Bach flat manifolds satisfying some global conformal bounds on compact manifolds of dimension 4. As applications, we establish a gap theorem, a finiteness theorem for diffeomorphism type for this class, and diameter bound of the $sigma_2$-metrics in a class of conformal 4-manifolds. For conformally compact Einstein metrics we introduce an eigenfunction compactification. As a consequence we obtain some topological constraints in terms of renormalized volumes.
The circle equation over finite fields
DEFF Research Database (Denmark)
Aabrandt, Andreas; Hansen, Vagn Lundsgaard
2017-01-01
Interesting patterns in the geometry of a plane algebraic curve C can be observed when the defining polynomial equation is solved over the family of finite fields. In this paper, we examine the case of C the classical unit circle defined by the circle equation x2 + y2 = 1. As a main result, we es...
Modelling drawbeads with finite elements and verification
Carleer, B.D.; Carleer, B.D.; Vreede, P.T.; Vreede, P.T.; Louwes, M.F.M.; Louwes, M.F.M.; Huetink, Han
1994-01-01
Drawbeads are commonly used in deep drawing processes to control the flow of the blank during the forming operation. In finite element simulations of deep drawing the drawbead geometries are seldom included because of the small radii; because of these small radii a very large number of elements is
Bárány, Imre; Vilcu, Costin
2016-01-01
This volume presents easy-to-understand yet surprising properties obtained using topological, geometric and graph theoretic tools in the areas covered by the Geometry Conference that took place in Mulhouse, France from September 7–11, 2014 in honour of Tudor Zamfirescu on the occasion of his 70th anniversary. The contributions address subjects in convexity and discrete geometry, in distance geometry or with geometrical flavor in combinatorics, graph theory or non-linear analysis. Written by top experts, these papers highlight the close connections between these fields, as well as ties to other domains of geometry and their reciprocal influence. They offer an overview on recent developments in geometry and its border with discrete mathematics, and provide answers to several open questions. The volume addresses a large audience in mathematics, including researchers and graduate students interested in geometry and geometrical problems.
Pattern formation in reaction diffusion systems with finite geometry
International Nuclear Information System (INIS)
Borzi, C.; Wio, H.
1990-04-01
We analyze the one-component, one-dimensional, reaction-diffusion equation through a simple inverse method. We confine the system and fix the boundary conditions as to induce pattern formation. We analyze the stability of those patterns. Our goal is to get information about the reaction term out of the preknowledgment of the pattern. (author). 5 refs
An algebraic approach to the scattering equations
Energy Technology Data Exchange (ETDEWEB)
Huang, Rijun; Rao, Junjie [Zhejiang Institute of Modern Physics, Zhejiang University,Hangzhou, 310027 (China); Feng, Bo [Zhejiang Institute of Modern Physics, Zhejiang University,Hangzhou, 310027 (China); Center of Mathematical Science, Zhejiang University,Hangzhou, 310027 (China); He, Yang-Hui [School of Physics, NanKai University,Tianjin, 300071 (China); Department of Mathematics, City University,London, EC1V 0HB (United Kingdom); Merton College, University of Oxford,Oxford, OX14JD (United Kingdom)
2015-12-10
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using simple linear algebra and is amenable to an algorithmic approach. Certain identities in the amplitudes as well as rationality of the final integrand become immediate in this formalism.
An algebraic approach to the scattering equations
International Nuclear Information System (INIS)
Huang, Rijun; Rao, Junjie; Feng, Bo; He, Yang-Hui
2015-01-01
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using simple linear algebra and is amenable to an algorithmic approach. Certain identities in the amplitudes as well as rationality of the final integrand become immediate in this formalism.
Inverse acoustic problem of N homogeneous scatterers
DEFF Research Database (Denmark)
Berntsen, Svend
2002-01-01
The three-dimensional inverse acoustic medium problem of N homogeneous objects with known geometry and location is considered. It is proven that one scattering experiment is sufficient for the unique determination of the complex wavenumbers of the objects. The mapping from the scattered fields...
Algorithms in Algebraic Geometry
Dickenstein, Alicia; Sommese, Andrew J
2008-01-01
In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its
O'Leary, Michael
2010-01-01
Guides readers through the development of geometry and basic proof writing using a historical approach to the topic. In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfull
Fundamental concepts of geometry
Meserve, Bruce E
1983-01-01
Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.
Developments in special geometry
International Nuclear Information System (INIS)
Mohaupt, Thomas; Vaughan, Owen
2012-01-01
We review the special geometry of N = 2 supersymmetric vector and hypermultiplets with emphasis on recent developments and applications. A new formulation of the local c-map based on the Hesse potential and special real coordinates is presented. Other recent developments include the Euclidean version of special geometry, and generalizations of special geometry to non-supersymmetric theories. As applications we discuss the proof that the local r-map and c-map preserve geodesic completeness, and the construction of four- and five-dimensional static solutions through dimensional reduction over time. The shared features of the real, complex and quaternionic version of special geometry are stressed throughout.
Leamer, Micah J.
2004-01-01
Let K be a field and Q a finite directed multi-graph. In this paper I classify all path algebras KQ and admissible orders with the property that all of their finitely generated ideals have finite Groebner bases. MS
Locally Finite Root Supersystems
Yousofzadeh, Malihe
2013-01-01
We introduce the notion of locally finite root supersystems as a generalization of both locally finite root systems and generalized root systems. We classify irreducible locally finite root supersystems.
Geometric Monte Carlo and black Janus geometries
Energy Technology Data Exchange (ETDEWEB)
Bak, Dongsu, E-mail: dsbak@uos.ac.kr [Physics Department, University of Seoul, Seoul 02504 (Korea, Republic of); B.W. Lee Center for Fields, Gravity & Strings, Institute for Basic Sciences, Daejeon 34047 (Korea, Republic of); Kim, Chanju, E-mail: cjkim@ewha.ac.kr [Department of Physics, Ewha Womans University, Seoul 03760 (Korea, Republic of); Kim, Kyung Kiu, E-mail: kimkyungkiu@gmail.com [Department of Physics, Sejong University, Seoul 05006 (Korea, Republic of); Department of Physics, College of Science, Yonsei University, Seoul 03722 (Korea, Republic of); Min, Hyunsoo, E-mail: hsmin@uos.ac.kr [Physics Department, University of Seoul, Seoul 02504 (Korea, Republic of); Song, Jeong-Pil, E-mail: jeong_pil_song@brown.edu [Department of Chemistry, Brown University, Providence, RI 02912 (United States)
2017-04-10
We describe an application of the Monte Carlo method to the Janus deformation of the black brane background. We present numerical results for three and five dimensional black Janus geometries with planar and spherical interfaces. In particular, we argue that the 5D geometry with a spherical interface has an application in understanding the finite temperature bag-like QCD model via the AdS/CFT correspondence. The accuracy and convergence of the algorithm are evaluated with respect to the grid spacing. The systematic errors of the method are determined using an exact solution of 3D black Janus. This numerical approach for solving linear problems is unaffected initial guess of a trial solution and can handle an arbitrary geometry under various boundary conditions in the presence of source fields.
Simulation on scattering features of biological tissue based on generated refractive-index model
International Nuclear Information System (INIS)
Wang Baoyong; Ding Zhihua
2011-01-01
Important information on morphology of biological tissue can be deduced from elastic scattering spectra, and their analyses are based on the known refractive-index model of tissue. In this paper, a new numerical refractive-index model is put forward, and its scattering properties are intensively studied. Spectral decomposition [1] is a widely used method to generate random medium in geology, but it is never used in biology. Biological tissue is different from geology in the sense of random medium. Autocorrelation function describe almost all of features in geology, but biological tissue is not as random as geology, its structure is regular in the sense of fractal geometry [2] , and fractal dimension can be used to describe its regularity under random. Firstly scattering theories of this fractal media are reviewed. Secondly the detailed generation process of refractive-index is presented. Finally the scattering features are simulated in FDTD (Finite Difference Time Domain) Solutions software. From the simulation results, we find that autocorrelation length and fractal dimension controls scattering feature of biological tissue.
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
ZONE: a finite element mesh generator
International Nuclear Information System (INIS)
Burger, M.J.
1976-05-01
The ZONE computer program is a finite-element mesh generator which produces the nodes and element description of any two-dimensional geometry. The geometry is subdivided into a mesh of quadrilateral and triangular zones arranged sequentially in an ordered march through the geometry. The order of march can be chosen so that the minimum bandwidth is obtained. The node points are defined in terms of the x and y coordinates in a global rectangular coordinate system. The zones generated are quadrilaterals or triangles defined by four node points in a counterclockwise sequence. Node points defining the outside boundary are generated to describe pressure boundary conditions. The mesh that is generated can be used as input to any two-dimensional as well as any axisymmetrical structure program. The output from ZONE is essentially the input file to NAOS, HONDO, and other axisymmetric finite element programs. 14 figures
Tearing modes in toroidal geometry
International Nuclear Information System (INIS)
Connor, J.W.; Cowley, S.C.; Hastie, R.J.; Hender, T.C.; Hood, A.; Martin, T.J.
1988-01-01
The separation of the cylindrical tearing mode stability problem into a resistive resonant layer calculation and an external marginal ideal magnetohydrodynamic (MHD) calculation (Δ' calculation) is generalized to axisymmetric toroidal geometry. The general structure of this separation is analyzed and the marginal ideal MHD information (the toroidal generalization of Δ') required to discuss stability is isolated. This can then, in principle, be combined with relevant resonant layer calculations to determine tearing mode growth rates in realistic situations. Two examples are given: the first is an analytic treatment of toroidally coupled (m = 1, n = 1) and (m = 2, n = 1) tearing modes in a large aspect ratio torus; the second, a numerical treatment of the toroidal coupling of three tearing modes through finite pressure effects in a large aspect ratio torus. In addition, the use of a coupling integral approach for determining the stability of coupled tearing modes is discussed. Finally, the possibility of using initial value resistive MHD codes in realistic toroidal geometry to determine the necessary information from the ideal MHD marginal solution is discussed
Differential geometry of group lattices
International Nuclear Information System (INIS)
Dimakis, Aristophanes; Mueller-Hoissen, Folkert
2003-01-01
In a series of publications we developed ''differential geometry'' on discrete sets based on concepts of noncommutative geometry. In particular, it turned out that first-order differential calculi (over the algebra of functions) on a discrete set are in bijective correspondence with digraph structures where the vertices are given by the elements of the set. A particular class of digraphs are Cayley graphs, also known as group lattices. They are determined by a discrete group G and a finite subset S. There is a distinguished subclass of ''bicovariant'' Cayley graphs with the property ad(S)S subset of S. We explore the properties of differential calculi which arise from Cayley graphs via the above correspondence. The first-order calculi extend to higher orders and then allow us to introduce further differential geometric structures. Furthermore, we explore the properties of ''discrete'' vector fields which describe deterministic flows on group lattices. A Lie derivative with respect to a discrete vector field and an inner product with forms is defined. The Lie-Cartan identity then holds on all forms for a certain subclass of discrete vector fields. We develop elements of gauge theory and construct an analog of the lattice gauge theory (Yang-Mills) action on an arbitrary group lattice. Also linear connections are considered and a simple geometric interpretation of the torsion is established. By taking a quotient with respect to some subgroup of the discrete group, generalized differential calculi associated with so-called Schreier diagrams are obtained
Volakis, J. L.; Gong, J.; Alexanian, A.; Woo, A.
1992-01-01
A new hybrid method is presented for the analysis of the scattering and radiation by conformal antennas and arrays comprised of circular or rectangular elements. In addition, calculations for cavity-backed spiral antennas are given. The method employs a finite element formulation within the cavity and the boundary integral (exact boundary condition) for terminating the mesh. By virtue of the finite element discretization, the method has no restrictions on the geometry and composition of the cavity or its termination. Furthermore, because of the convolutional nature of the boundary integral and the inherent sparseness of the finite element matrix, the storage requirement is kept very low at O(n). These unique features of the method have already been exploited in other scattering applications and have permitted the analysis of large-size structures with remarkable efficiency. In this report, we describe the method's formulation and implementation for circular and rectangular patch antennas in different superstrate and substrate configurations which may also include the presence of lumped loads and resistive sheets/cards. Also, various modelling approaches are investigated and implemented for characterizing a variety of feed structures to permit the computation of the input impedance and radiation pattern. Many computational examples for rectangular and circular patch configurations are presented which demonstrate the method's versatility, modeling capability and accuracy.
Effective permittivity of finite inhomogeneous objects
Raghunathan, S.B.; Budko, N.V.
2010-01-01
A generalization of the S-parameter retrieval method for finite three-dimensional inhomogeneous objects under arbitrary illumination and observation conditions is presented. The effective permittivity of such objects may be rigorously defined as a solution of a nonlinear inverse scattering problem.
Morris, Barbara H.
2004-01-01
This article describes a geometry project that used the beauty of stained-glass-window designs to teach middle school students about geometric figures and concepts. Three honors prealgebra teachers and a middle school mathematics gifted intervention specialist created a geometry project that covered the curriculum and also assessed students'…
Energy Technology Data Exchange (ETDEWEB)
Grotz, Andreas
2011-10-07
In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.
Methods of information geometry
Amari, Shun-Ichi
2000-01-01
Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the \\alpha-connections. The duality between the \\alpha-connection and the (-\\alpha)-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective. The first half of this book is devoted to a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability d...
International Nuclear Information System (INIS)
Grotz, Andreas
2011-01-01
In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.
Multiple-scattering analysis of laser-beam propagation in the atmosphere and through obscurants
International Nuclear Information System (INIS)
Zardecki, A.; Gerstl, S.A.W.
1983-01-01
The general purpose, discrete-ordinates transport code TWOTRAN is applied to describe the propagation and multiple scattering of a laser beam in a nonhomogeneous aerosol medium. For the medium composed of smoke, haze, and a rain cloud, the problem of the target detectability in a realistic atmospheric scenario is addressed and solved. The signals reflected from the target vs the signals scattered from the smoke cloud are analyzed as a function of the smoke concentration. By calculating the average intensity and a correction factor in the x-y and r-z geometries, the consistency of the rectangular and cylindrical geometry models is assessed. Received power for a detector with a small field of view is computed on a sphere of 1-km radius around the laser source for the Air Force Geophysics Laboratory rural aerosol model with extinction coefficients of 4 km - 1 and 10 km - 1 . This computation allows us to study the received power as a function of the angle between the detector and source axes. The correction factor describing the multiple-scattering enhancement with respect to the simple Lambert-Beer law is introduced, and its calculation is employed to validate the use of the small-angle approximation for the transmissometer configuration. An outline of the theory for a finite field of view detector is followed by numerical results pertaining to the received power and intensity for various aerosol models. Recommendations regarding future work are also formulated
Geometry on the space of geometries
International Nuclear Information System (INIS)
Christodoulakis, T.; Zanelli, J.
1988-06-01
We discuss the geometric structure of the configuration space of pure gravity. This is an infinite dimensional manifold, M, where each point represents one spatial geometry g ij (x). The metric on M is dictated by geometrodynamics, and from it, the Christoffel symbols and Riemann tensor can be found. A ''free geometry'' tracing a geodesic on the manifold describes the time evolution of space in the strong gravity limit. In a regularization previously introduced by the authors, it is found that M does not have the same dimensionality, D, everywhere, and that D is not a scalar, although it is covariantly constant. In this regularization, it is seen that the path integral measure can be absorbed in a renormalization of the cosmological constant. (author). 19 refs
Propagation of liquid surface waves over finite graphene structured arrays of cylinders
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
Based on the multiple scattering method,this paper investigates a benchmark problem of the propagation of liquid surface waves over finite graphene (or honeycomb) structured arrays of cylinders.Comparing the graphene structured array with the square structured and with triangle structured arrays,it finds that the finite graphene structure can produce more complete band gaps than the other finite structures,and the finite graphene structure has less localized ability than the other finite structures.
International Nuclear Information System (INIS)
Hategan, Cornel; Comisel, Horia; Ionescu, Remus A.
2004-01-01
The quasiresonant scattering consists from a single channel resonance coupled by direct interaction transitions to some competing reaction channels. A description of quasiresonant Scattering, in terms of generalized reduced K-, R- and S- Matrix, is developed in this work. The quasiresonance's decay width is, due to channels coupling, smaller than the width of the ancestral single channel resonance (resonance's direct compression). (author)
Donne, A. J. H.
1994-01-01
Thomson scattering is a very powerful diagnostic which is applied at nearly every magnetic confinement device. Depending on the experimental conditions different plasma parameters can be diagnosed. When the wave vector is much larger than the plasma Debye length, the total scattered power is
DIGA/NSL new calculational model in slab geometry
International Nuclear Information System (INIS)
Makai, M.; Gado, J.; Kereszturi, A.
1987-04-01
A new calculational model is presented based on a modified finite-difference algorithm, in which the coefficients are determined by means of the so-called gamma matrices. The DIGA program determines the gamma matrices and the NSL program realizes the modified finite difference model. Both programs assume slab cell geometry, DIGA assumes 2 energy groups and 3 diffusive regions. The DIGA/NSL programs serve to study the new calculational model. (author)
Complex and symplectic geometry
Medori, Costantino; Tomassini, Adriano
2017-01-01
This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.
Kulczycki, Stefan
2008-01-01
This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of suff
Classical- and quantum mechanical Coulomb scattering
International Nuclear Information System (INIS)
Gratzl, W.
1987-01-01
Because in textbooks the quantum mechanical Coulomb scattering is either ignored or treated unsatisfactory, the present work attempts to present a physically plausible, mathematically correct but elementary treatment in a way that it can be used in textbooks and lectures on quantum mechanics. Coulomb scattering is derived as a limiting case of a screened Coulomb potential (finite range) within a time dependent quantum scattering theory. The difference in the asymptotic conditions for potentials of finite versus infinite range leads back to the classical Coulomb scattering. In the classical framework many concepts of the quantum theory can be introduced and are useful in an intuitive understanding of the quantum theory. The differences between classical and quantum scattering theory are likewise useful for didactic purposes. (qui)
Discrete-ordinates finite-element method for atmospheric radiative transfer and remote sensing
International Nuclear Information System (INIS)
Gerstl, S.A.W.; Zardecki, A.
1985-01-01
Advantages and disadvantages of modern discrete-ordinates finite-element methods for the solution of radiative transfer problems in meteorology, climatology, and remote sensing applications are evaluated. After the common basis of the formulation of radiative transfer problems in the fields of neutron transport and atmospheric optics is established, the essential features of the discrete-ordinates finite-element method are described including the limitations of the method and their remedies. Numerical results are presented for 1-D and 2-D atmospheric radiative transfer problems where integral as well as angular dependent quantities are compared with published results from other calculations and with measured data. These comparisons provide a verification of the discrete-ordinates results for a wide spectrum of cases with varying degrees of absorption, scattering, and anisotropic phase functions. Accuracy and computational speed are also discussed. Since practically all discrete-ordinates codes offer a builtin adjoint capability, the general concept of the adjoint method is described and illustrated by sample problems. Our general conclusion is that the strengths of the discrete-ordinates finite-element method outweight its weaknesses. We demonstrate that existing general-purpose discrete-ordinates codes can provide a powerful tool to analyze radiative transfer problems through the atmosphere, especially when 2-D geometries must be considered
Measurement of proton momentum distributions using a direct geometry instrument
International Nuclear Information System (INIS)
Senesi, R; Andreani, C; Kolesnikov, A I
2014-01-01
We report the results of inelastic neutron scattering measurements on bulk water and ice using the direct geometry SEQUOIA chopper spectrometer at the Spallation Neutron Source (USA), with incident energy E i = 6 eV. In this set up the measurements allow to access the Deep Inelastic Neutron Scattering regime. The scattering is centred at the proton recoil energy given by the impulse approximation, and the shape of the recoil peak conveys information on the proton momentum distribution in the system. The comparison with the performance of inverse geometry instruments, such as VESUVIO at the ISIS source (UK), shows that complementary information can be accessed by the use of direct and inverse geometry instruments. Analysis of the neutron Compton profiles shows that the proton kinetic energy in ice at 271 K is larger than in room temperature liquid water, in agreement with previous measurements on VESUVIO
Roe, John
2003-01-01
Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This point of view is effective because it is often true that the relevant geometric properties of metric spaces are determined by their coarse geometry. Two examples of important uses of coarse geometry are Gromov's beautiful notion of a hyperbolic group and Mostow's proof of his famous rigidity theorem. The first few chapters of the book provide a general perspective on coarse structures. Even when only metric coarse structures are in view, the abstract framework brings the same simplification as does the passage from epsilons and deltas to open sets when speaking of continuity. The middle section reviews notions of negative curvature and rigidity. Modern interest in large scale geometry derives in large part from Mostow's rigidity theorem and from Gromov's subsequent 'large scale' rendition of the crucial properties of n...
Lectures on Symplectic Geometry
Silva, Ana Cannas
2001-01-01
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and cl...
Kollár, János
1997-01-01
This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.
Busemann, Herbert
2005-01-01
A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.
Tabachnikov, Serge
2005-01-01
Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. The topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course (but contains more material than can be realistically taught in one semester). Although the minimum prerequisit...
Introduction to tropical geometry
Maclagan, Diane
2015-01-01
Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of t...
Rudiments of algebraic geometry
Jenner, WE
2017-01-01
Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.
Implosions and hypertoric geometry
DEFF Research Database (Denmark)
Dancer, A.; Kirwan, F.; Swann, A.
2013-01-01
The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion.......The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion....
Intermediate algebra & analytic geometry
Gondin, William R
1967-01-01
Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system
Ceresole, Anna; Gnecchi, Alessandra; Marrani, Alessio
2013-01-01
We analyze some properties of the four dimensional supergravity theories which originate from five dimensions upon reduction. They generalize to N>2 extended supersymmetries the d-geometries with cubic prepotentials, familiar from N=2 special K\\"ahler geometry. We emphasize the role of a suitable parametrization of the scalar fields and the corresponding triangular symplectic basis. We also consider applications to the first order flow equations for non-BPS extremal black holes.
International Nuclear Information System (INIS)
Sitenko, A.
1991-01-01
This book emerged out of graduate lectures given by the author at the University of Kiev and is intended as a graduate text. The fundamentals of non-relativistic quantum scattering theory are covered, including some topics, such as the phase-function formalism, separable potentials, and inverse scattering, which are not always coverded in textbooks on scattering theory. Criticisms of the text are minor, but the reviewer feels an inadequate index is provided and the citing of references in the Russian language is a hindrance in a graduate text
Neutron transfer with anisotropic scattering
International Nuclear Information System (INIS)
El Wakil, S.A.; Haggag, M.H.; Saad, E.A.
1979-01-01
The finite slab problem is reduced to a semi-infinite one by adding an infinitesimally thick layer such that both the added layer and the total layer are semi-infinite. The relation between the reflection and transmission functions for a finite slab and those for an infinite one are obtained in terms of an operator which satisfies a semigroup equation. The method is applied to anisotropic scattering with azimuthal dependence. Numerical calculations are made and the results compared with those of other workers. (author)
International Nuclear Information System (INIS)
Osborne, I; Brownson, E; Eulisse, G; Jones, C D; Sexton-Kennedy, E; Lange, D J
2014-01-01
CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.
Software Geometry in Simulations
Alion, Tyler; Viren, Brett; Junk, Tom
2015-04-01
The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).
Introduction to combinatorial geometry
International Nuclear Information System (INIS)
Gabriel, T.A.; Emmett, M.B.
1985-01-01
The combinatorial geometry package as used in many three-dimensional multimedia Monte Carlo radiation transport codes, such as HETC, MORSE, and EGS, is becoming the preferred way to describe simple and complicated systems. Just about any system can be modeled using the package with relatively few input statements. This can be contrasted against the older style geometry packages in which the required input statements could be large even for relatively simple systems. However, with advancements come some difficulties. The users of combinatorial geometry must be able to visualize more, and, in some instances, all of the system at a time. Errors can be introduced into the modeling which, though slight, and at times hard to detect, can have devastating effects on the calculated results. As with all modeling packages, the best way to learn the combinatorial geometry is to use it, first on a simple system then on more complicated systems. The basic technique for the description of the geometry consists of defining the location and shape of the various zones in terms of the intersections and unions of geometric bodies. The geometric bodies which are generally included in most combinatorial geometry packages are: (1) box, (2) right parallelepiped, (3) sphere, (4) right circular cylinder, (5) right elliptic cylinder, (6) ellipsoid, (7) truncated right cone, (8) right angle wedge, and (9) arbitrary polyhedron. The data necessary to describe each of these bodies are given. As can be easily noted, there are some subsets included for simplicity
Global aspects of complex geometry
Catanese, Fabrizio; Huckleberry, Alan T
2006-01-01
Present an overview of developments in Complex Geometry. This book covers topics that range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry.
More on microstate geometries of 4d black holes
International Nuclear Information System (INIS)
Bianchi, M.; Morales, J.F.; Pieri, L.; Zinnato, N.
2017-01-01
We construct explicit examples of microstate geometries of four-dimensional black holes that lift to smooth horizon-free geometries in five dimensions. Solutions consist of half-BPS D-brane atoms distributed in ℝ 3 . Charges and positions of the D-brane centers are constrained by the bubble equations and boundary conditions ensuring the regularity of the metric and the match with the black hole geometry. In the case of three centers, we find that the moduli spaces of solutions includes disjoint one-dimensional components of (generically) finite volume.
More on microstate geometries of 4d black holes
Energy Technology Data Exchange (ETDEWEB)
Bianchi, M. [Università di Roma Tor Vergata and I.N.F.N, Dipartimento di Fisica,Via della Ricerca Scientifica, I-00133 Rome (Italy); Morales, J.F. [I.N.F.N. - Sezione di Roma 2 and Università di Roma Tor Vergata, Dipartimento di Fisica,Via della Ricerca Scientifica, I-00133 Roma (Italy); Pieri, L. [Università di Roma Tor Vergata and I.N.F.N, Dipartimento di Fisica,Via della Ricerca Scientifica, I-00133 Rome (Italy); Center for Research in String Theory, School of Physics and Astronomy,Queen Mary University of London, Mile End Road, London, E1 4NS (United Kingdom); Zinnato, N. [Università di Roma Tor Vergata and I.N.F.N, Dipartimento di Fisica,Via della Ricerca Scientifica, I-00133 Rome (Italy)
2017-05-29
We construct explicit examples of microstate geometries of four-dimensional black holes that lift to smooth horizon-free geometries in five dimensions. Solutions consist of half-BPS D-brane atoms distributed in ℝ{sup 3}. Charges and positions of the D-brane centers are constrained by the bubble equations and boundary conditions ensuring the regularity of the metric and the match with the black hole geometry. In the case of three centers, we find that the moduli spaces of solutions includes disjoint one-dimensional components of (generically) finite volume.
An introduction to algebraic geometry and algebraic groups
Geck, Meinolf
2003-01-01
An accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles.Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie type.The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups
International Nuclear Information System (INIS)
Stirling, W.G.; Perry, S.C.
1996-01-01
We outline the theoretical and experimental background to neutron scattering studies of critical phenomena at magnetic and structural phase transitions. The displacive phase transition of SrTiO 3 is discussed, along with examples from recent work on magnetic materials from the rare-earth (Ho, Dy) and actinide (NpAs, NpSb, USb) classes. The impact of synchrotron X-ray scattering is discussed in conclusion. (author) 13 figs., 18 refs
Computational modeling of geometry dependent phonon transport in silicon nanostructures
Cheney, Drew A.
Recent experiments have demonstrated that thermal properties of semiconductor nanostructures depend on nanostructure boundary geometry. Phonons are quantized mechanical vibrations that are the dominant carrier of heat in semiconductor materials and their aggregate behavior determine a nanostructure's thermal performance. Phonon-geometry scattering processes as well as waveguiding effects which result from coherent phonon interference are responsible for the shape dependence of thermal transport in these systems. Nanoscale phonon-geometry interactions provide a mechanism by which nanostructure geometry may be used to create materials with targeted thermal properties. However, the ability to manipulate material thermal properties via controlling nanostructure geometry is contingent upon first obtaining increased theoretical understanding of fundamental geometry induced phonon scattering processes and having robust analytical and computational models capable of exploring the nanostructure design space, simulating the phonon scattering events, and linking the behavior of individual phonon modes to overall thermal behavior. The overall goal of this research is to predict and analyze the effect of nanostructure geometry on thermal transport. To this end, a harmonic lattice-dynamics based atomistic computational modeling tool was created to calculate phonon spectra and modal phonon transmission coefficients in geometrically irregular nanostructures. The computational tool is used to evaluate the accuracy and regimes of applicability of alternative computational techniques based upon continuum elastic wave theory. The model is also used to investigate phonon transmission and thermal conductance in diameter modulated silicon nanowires. Motivated by the complexity of the transmission results, a simplified model based upon long wavelength beam theory was derived and helps explain geometry induced phonon scattering of low frequency nanowire phonon modes.
Hydrothermal analysis in engineering using control volume finite element method
Sheikholeslami, Mohsen
2015-01-01
Control volume finite element methods (CVFEM) bridge the gap between finite difference and finite element methods, using the advantages of both methods for simulation of multi-physics problems in complex geometries. In Hydrothermal Analysis in Engineering Using Control Volume Finite Element Method, CVFEM is covered in detail and applied to key areas of thermal engineering. Examples, exercises, and extensive references are used to show the use of the technique to model key engineering problems such as heat transfer in nanofluids (to enhance performance and compactness of energy systems),
International Nuclear Information System (INIS)
1982-01-01
1 - Description of problem or function: ONETRAN solves the one- dimensional multigroup transport equation in plane, cylindrical, spherical, and two-angle plane geometries. Both regular and adjoint, inhomogeneous and homogeneous (K-eff and eigenvalue searches) 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. Standard inner (within-group) iteration cycles are accelerated by system re-balance, coarse mesh re-balance, or Chebyshev acceleration. Outer iteration cycles are accelerated by coarse-mesh re-balance. 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. On CDC machines MAXCOR can be about 25 000 words and peripheral storage is used for most group-dependent data
Regularization of the Coulomb scattering problem
International Nuclear Information System (INIS)
Baryshevskii, V.G.; Feranchuk, I.D.; Kats, P.B.
2004-01-01
The exact solution of the Schroedinger equation for the Coulomb potential is used within the scope of both stationary and time-dependent scattering theories in order to find the parameters which determine the regularization of the Rutherford cross section when the scattering angle tends to zero but the distance r from the center remains finite. The angular distribution of the particles scattered in the Coulomb field is studied on rather a large but finite distance r from the center. It is shown that the standard asymptotic representation of the wave functions is inapplicable in the case when small scattering angles are considered. The unitary property of the scattering matrix is analyzed and the 'optical' theorem for this case is discussed. The total and transport cross sections for scattering the particle by the Coulomb center proved to be finite values and are calculated in the analytical form. It is shown that the effects under consideration can be important for the observed characteristics of the transport processes in semiconductors which are determined by the electron and hole scattering by the field of charged impurity centers
CHOLESK, Diffusion Calculation with 2-D Source in X-Y or R-Z Geometry
International Nuclear Information System (INIS)
1988-01-01
1 - Description of problem or function: Solution of the diffusion equation with source in two-dimensional geometries x-y or r-z. 2 - Method of solution: The finite-element method of Ritz-Galerkin is applied
Sources of hyperbolic geometry
Stillwell, John
1996-01-01
This book presents, for the first time in English, the papers of Beltrami, Klein, and Poincaré that brought hyperbolic geometry into the mainstream of mathematics. A recognition of Beltrami comparable to that given the pioneering works of Bolyai and Lobachevsky seems long overdue-not only because Beltrami rescued hyperbolic geometry from oblivion by proving it to be logically consistent, but because he gave it a concrete meaning (a model) that made hyperbolic geometry part of ordinary mathematics. The models subsequently discovered by Klein and Poincaré brought hyperbolic geometry even further down to earth and paved the way for the current explosion of activity in low-dimensional geometry and topology. By placing the works of these three mathematicians side by side and providing commentaries, this book gives the student, historian, or professional geometer a bird's-eye view of one of the great episodes in mathematics. The unified setting and historical context reveal the insights of Beltrami, Klein, and Po...
International Nuclear Information System (INIS)
Jonsson, Rickard; Westman, Hans
2006-01-01
We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz M A and Lasota J-P 1997 Class. Quantum Grav. A 14 23-30). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson R 2006 Class. Quantum Grav. 23 1)) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity
Energy Technology Data Exchange (ETDEWEB)
Pettit, J. R.; Lowe, M. J. S. [UK Research Centre for NDE, Imperial College London, Exhibition Road, London, SW7 2AZ (United Kingdom); Walker, A. E. [Rolls-Royce Nuclear, PO BOX 2000, Derby, DE21 7XX (United Kingdom)
2015-03-31
Pulse-echo ultrasonic NDE examination of large pressure vessel forgings is a design and construction code requirement in the power generation industry. Such inspections aim to size and characterise potential defects that may have formed during the forging process. Typically these defects have a range of orientations and surface roughnesses which can greatly affect ultrasonic wave scattering behaviour. Ultrasonic modelling techniques can provide insight into defect response and therefore aid in characterisation. However, analytical approaches to solving these scattering problems can become inaccurate, especially when applied to increasingly complex defect geometries. To overcome these limitations a elastic Finite Element (FE) method has been developed to simulate pulse-echo inspections of embedded planar defects. The FE model comprises a significantly reduced spatial domain allowing for a Monte-Carlo based approach to consider multiple realisations of defect orientation and surface roughness. The results confirm that defects aligned perpendicular to the path of beam propagation attenuate ultrasonic signals according to the level of surface roughness. However, for defects orientated away from this plane, surface roughness can increase the magnitude of the scattered component propagating back along the path of the incident beam. This study therefore highlights instances where defect roughness increases the magnitude of ultrasonic scattered signals, as opposed to attenuation which is more often assumed.
Scattering of guided waves at delaminations in composite plates.
Murat, Bibi I S; Khalili, Pouyan; Fromme, Paul
2016-06-01
Carbon fiber laminate composites are increasingly employed for aerospace structures as they offer advantages, such as a good strength to weight ratio. However, impact during the operation and servicing of the aircraft can lead to barely visible and difficult to detect damage. Depending on the severity of the impact, fiber and matrix breakage or delaminations can occur, reducing the load carrying capacity of the structure. Efficient nondestructive testing and structural health monitoring of composite panels can be achieved using guided ultrasonic waves propagating along the structure. The scattering of the A0 Lamb wave mode at delaminations was investigated using a full three-dimensional (3D) finite element (FE) analysis. The influence of the delamination geometry (size and depth) was systematically evaluated. In addition to the depth dependency, a significant influence of the delamination width due to sideways reflection of the guided waves within the delamination area was found. Mixed-mode defects were simulated using a combined model of delamination with localized material degradation. The guided wave scattering at cross-ply composite plates with impact damage was measured experimentally using a non-contact laser interferometer. Good agreement between experiments and FE predictions using the mixed-mode model for an approximation of the impact damage was found.
Flow of viscoplastic fluids in eccentric annular geometries
DEFF Research Database (Denmark)
Szabo, Peter; Hassager, Ole
1992-01-01
A classification of flowfields for the flow of a Bingham fluid in general eccentric annular geometries is presented. Simple arguments show that a singularity can exist in the stress gradient on boundaries between zones with yielded and un-yielded fluid respectively. A Finite Element code is used...
International Nuclear Information System (INIS)
Acharya, B.S.; Douglas, M.R.
2006-06-01
We present evidence that the number of string/M theory vacua consistent with experiments is finite. We do this both by explicit analysis of infinite sequences of vacua and by applying various mathematical finiteness theorems. (author)
Nilpotent -local finite groups
Cantarero, José; Scherer, Jérôme; Viruel, Antonio
2014-10-01
We provide characterizations of -nilpotency for fusion systems and -local finite groups that are inspired by known result for finite groups. In particular, we generalize criteria by Atiyah, Brunetti, Frobenius, Quillen, Stammbach and Tate.
Computational synthetic geometry
Bokowski, Jürgen
1989-01-01
Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to stud...
Discrete and computational geometry
Devadoss, Satyan L
2011-01-01
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also fe...
Ochiai, T.; Nacher, J. C.
2011-09-01
Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.
Zheng, Fangyang
2002-01-01
The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classifi...
International Nuclear Information System (INIS)
Lee, Byeong Hae
1992-02-01
This book gives descriptions of basic finite element method, which includes basic finite element method and data, black box, writing of data, definition of VECTOR, definition of matrix, matrix and multiplication of matrix, addition of matrix, and unit matrix, conception of hardness matrix like spring power and displacement, governed equation of an elastic body, finite element method, Fortran method and programming such as composition of computer, order of programming and data card and Fortran card, finite element program and application of nonelastic problem.
Information theory, spectral geometry, and quantum gravity.
Kempf, Achim; Martin, Robert
2008-01-18
We show that there exists a deep link between the two disciplines of information theory and spectral geometry. This allows us to obtain new results on a well-known quantum gravity motivated natural ultraviolet cutoff which describes an upper bound on the spatial density of information. Concretely, we show that, together with an infrared cutoff, this natural ultraviolet cutoff beautifully reduces the path integral of quantum field theory on curved space to a finite number of ordinary integrations. We then show, in particular, that the subsequent removal of the infrared cutoff is safe.
Scattering of Non-Relativistic Charged Particles by Electromagnetic Radiation
Apostol, M.
2017-11-01
The cross-section is computed for non-relativistic charged particles (like electrons and ions) scattered by electromagnetic radiation confined to a finite region (like the focal region of optical laser beams). The cross-section exhibits maxima at scattering angles given by the energy and momentum conservation in multi-photon absorption or emission processes. For convenience, a potential scattering is included and a comparison is made with the well-known Kroll-Watson scattering formula. The scattering process addressed in this paper is distinct from the process dealt with in previous studies, where the scattering is immersed in the radiation field.
Direct Calculation of the Scattering Amplitude Without Partial Wave Analysis
Shertzer, J.; Temkin, A.; Fisher, Richard R. (Technical Monitor)
2001-01-01
Two new developments in scattering theory are reported. We show, in a practical way, how one can calculate the full scattering amplitude without invoking a partial wave expansion. First, the integral expression for the scattering amplitude f(theta) is simplified by an analytic integration over the azimuthal angle. Second, the full scattering wavefunction which appears in the integral expression for f(theta) is obtained by solving the Schrodinger equation with the finite element method (FEM). As an example, we calculate electron scattering from the Hartree potential. With minimal computational effort, we obtain accurate and stable results for the scattering amplitude.
Yale, Paul B
2012-01-01
This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on ""practical geometry,"" emphasi
Alabdulmohsin, Ibrahim M.
2018-01-01
In this chapter, we extend the previous results of Chap. 2 to the more general case of composite finite sums. We describe what composite finite sums are and how their analysis can be reduced to the analysis of simple finite sums using the chain rule. We apply these techniques, next, on numerical integration and on some identities of Ramanujan.
Alabdulmohsin, Ibrahim M.
2018-03-07
In this chapter, we extend the previous results of Chap. 2 to the more general case of composite finite sums. We describe what composite finite sums are and how their analysis can be reduced to the analysis of simple finite sums using the chain rule. We apply these techniques, next, on numerical integration and on some identities of Ramanujan.
Groups, combinatorics and geometry
Ivanov, A A; Saxl, J
2003-01-01
Over the past 20 years, the theory of groups in particular simplegroups, finite and algebraic has influenced a number of diverseareas of mathematics. Such areas include topics where groups have beentraditionally applied, such as algebraic combinatorics, finitegeometries, Galois theory and permutation groups, as well as severalmore recent developments.
Scattering of electromagnetic waves by a traversable wormhole
Directory of Open Access Journals (Sweden)
B. Nasr Esfahani
2005-09-01
Full Text Available Replacing the wormhole geometry with an equivalent medium using the perturbation theory of scattering and the Born approximation, we have calculated the differential scattering cross section of electromagnetic waves by a traversable wormhole. It is shown that scattering at long wavelenghts can essentially distinguish wormhole from ordinary scattering object. Some of the zeros of the scattering cross section are determined which can be used for estimating the radius of the throat of wormholes. The known result that in this kind of scattering the linear polarization remains unchanged is verified here.
International Nuclear Information System (INIS)
Botto, D.J.; Pratt, R.H.
1979-05-01
The current status of Compton scattering, both experimental observations and the theoretical predictions, is examined. Classes of experiments are distinguished and the results obtained are summarized. The validity of the incoherent scattering function approximation and the impulse approximation is discussed. These simple theoretical approaches are compared with predictions of the nonrelativistic dipole formula of Gavrila and with the relativistic results of Whittingham. It is noted that the A -2 based approximations fail to predict resonances and an infrared divergence, both of which have been observed. It appears that at present the various available theoretical approaches differ significantly in their predictions and that further and more systematic work is required
Energy Technology Data Exchange (ETDEWEB)
Botto, D.J.; Pratt, R.H.
1979-05-01
The current status of Compton scattering, both experimental observations and the theoretical predictions, is examined. Classes of experiments are distinguished and the results obtained are summarized. The validity of the incoherent scattering function approximation and the impulse approximation is discussed. These simple theoretical approaches are compared with predictions of the nonrelativistic dipole formula of Gavrila and with the relativistic results of Whittingham. It is noted that the A/sup -2/ based approximations fail to predict resonances and an infrared divergence, both of which have been observed. It appears that at present the various available theoretical approaches differ significantly in their predictions and that further and more systematic work is required.
Towards relativistic quantum geometry
Energy Technology Data Exchange (ETDEWEB)
Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)
2015-12-17
We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.
Spacetime and Euclidean geometry
Brill, Dieter; Jacobson, Ted
2006-04-01
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.
International Nuclear Information System (INIS)
Konopleva, N.P.
2009-01-01
The basic ideas of description methods of physical fields and elementary particle interactions are discussed. One of such ideas is the conception of space-time geometry. In this connection experimental measurement methods are analyzed. It is shown that measure procedures are the origin of geometrical axioms. The connection between space symmetry properties and the conservation laws is considered
Wares, Arsalan; Elstak, Iwan
2017-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…
MacKeown, P. K.
1984-01-01
Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm
2011-01-01
This paper applies I.M. Gelfand's distinction between adequate and non-adequate use of mathematical language in different contexts to the newly opened window of model-based measurements of intracellular dynamics. The specifics of geometry and dynamics on the mesoscale of cell physiology are elabo...
Diophantine geometry an introduction
Hindry, Marc
2000-01-01
This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.
Sliding vane geometry turbines
Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R
2014-12-30
Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.
Boyer, Carl B
2012-01-01
Designed as an integrated survey of the development of analytic geometry, this study presents the concepts and contributions from before the Alexandrian Age through the eras of the great French mathematicians Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850.
Coxeter, HSM
1965-01-01
This textbook introduces non-Euclidean geometry, and the third edition adds a new chapter, including a description of the two families of 'mid-lines' between two given lines and an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, and other new material.
International Nuclear Information System (INIS)
Ezin, J.P.
1988-08-01
The lectures given at the ''5th Symposium of Mathematics in Abidjan: Differential Geometry and Mechanics'' are presented. They are divided into four chapters: Riemannian metric on a differential manifold, curvature tensor fields on a Riemannian manifold, some classical functionals on Riemannian manifolds and questions. 11 refs
Hartshorne, Robin
2000-01-01
In recent years, I have been teaching a junior-senior-level course on the classi cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa rately. The remainder of the book is an exploration of questions that arise natu rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And ...
Alonso, Rodrigo; Manohar, Aneesh V.
2016-01-01
The $S$-matrix of a quantum field theory is unchanged by field redefinitions, and so only depends on geometric quantities such as the curvature of field space. Whether the Higgs multiplet transforms linearly or non-linearly under electroweak symmetry is a subtle question since one can make a coordinate change to convert a field that transforms linearly into one that transforms non-linearly. Renormalizability of the Standard Model (SM) does not depend on the choice of scalar fields or whether the scalar fields transform linearly or non-linearly under the gauge group, but only on the geometric requirement that the scalar field manifold ${\\mathcal M}$ is flat. We explicitly compute the one-loop correction to scalar scattering in the SM written in non-linear Callan-Coleman-Wess-Zumino (CCWZ) form, where it has an infinite series of higher dimensional operators, and show that the $S$-matrix is finite. Standard Model Effective Field Theory (SMEFT) and Higgs Effective Field Theory (HEFT) have curved ${\\mathcal M}$, ...
Brillouin scatter in laser-produced plasmas
International Nuclear Information System (INIS)
Phillion, D.W.; Kruer, W.L.; Rupert, V.C.
1977-01-01
The absorption of intense laser light is found to be reduced when targets are irradiated by 1.06 μm light with long pulse widths (150-400 psec) and large focal spots (100-250 μm). Estimates of Brillouin scatter which account for the finite heat capacity of the underdense plasma predict this reduction. Spectra of the back reflected light show red shifts indicative of Brillouin scattering
Diffuse scattering from crystals with point defects
International Nuclear Information System (INIS)
Andrushevsky, N.M.; Shchedrin, B.M.; Simonov, V.I.; Malakhova, L.F.
2002-01-01
The analytical expressions for calculating the intensities of X-ray diffuse scattering from a crystal of finite dimensions and monatomic substitutional, interstitial, or vacancy-type point defects have been derived. The method for the determination of the three-dimensional structure by experimental diffuse-scattering data from crystals with point defects having various concentrations is discussed and corresponding numerical algorithms are suggested
International Nuclear Information System (INIS)
Vernon, M.F.
1983-07-01
The molecular-beam technique has been used in three different experimental arrangements to study a wide range of inter-atomic and molecular forces. Chapter 1 reports results of a low-energy (0.2 kcal/mole) elastic-scattering study of the He-Ar pair potential. The purpose of the study was to accurately characterize the shape of the potential in the well region, by scattering slow He atoms produced by expanding a mixture of He in N 2 from a cooled nozzle. Chapter 2 contains measurements of the vibrational predissociation spectra and product translational energy for clusters of water, benzene, and ammonia. The experiments show that most of the product energy remains in the internal molecular motions. Chapter 3 presents measurements of the reaction Na + HCl → NaCl + H at collision energies of 5.38 and 19.4 kcal/mole. This is the first study to resolve both scattering angle and velocity for the reaction of a short lived (16 nsec) electronic excited state. Descriptions are given of computer programs written to analyze molecular-beam expansions to extract information characterizing their velocity distributions, and to calculate accurate laboratory elastic-scattering differential cross sections accounting for the finite apparatus resolution. Experimental results which attempted to determine the efficiency of optically pumping the Li(2 2 P/sub 3/2/) and Na(3 2 P/sub 3/2/) excited states are given. A simple three-level model for predicting the steady-state fraction of atoms in the excited state is included
An algorithm for solving thermalhydraulic equations in complex geometries: the Astec code
International Nuclear Information System (INIS)
Lonsdale, R.D.
1987-01-01
By applying a finite volume approach to a finite element mesh, the ASTEC computer code allows three-dimensional incompressible fluid flow and heat transfer in complex geometries to be simulated realistically, without making excessive demands on computing resources. The methods used in the code are described, and examples of the application of the code are presented
Hard scattering and gauge/string duality
International Nuclear Information System (INIS)
Polchinski, Joseph; Strassler, Matthew J.
2002-01-01
We consider high-energy fixed-angle scattering of glueballs in confining gauge theories that have supergravity duals. Although the effective description is in terms of the scattering of strings, we find that the amplitudes are hard (power law). This is a consequence of the warped geometry of the dual theory, which has the effect that in an inertial frame the string process is never in the soft regime. At small angle we find hard and Regge behaviors in different kinematic regions
Modeling the bidirectional reflectance distribution function of mixed finite plant canopies and soil
Schluessel, G.; Dickinson, R. E.; Privette, J. L.; Emery, W. J.; Kokaly, R.
1994-01-01
An analytical model of the bidirectional reflectance for optically semi-infinite plant canopies has been extended to describe the reflectance of finite depth canopies contributions from the underlying soil. The model depends on 10 independent parameters describing vegetation and soil optical and structural properties. The model is inverted with a nonlinear minimization routine using directional reflectance data for lawn (leaf area index (LAI) is equal to 9.9), soybeans (LAI, 2.9) and simulated reflectance data (LAI, 1.0) from a numerical bidirectional reflectance distribution function (BRDF) model (Myneni et al., 1988). While the ten-parameter model results in relatively low rms differences for the BRDF, most of the retrieved parameters exhibit poor stability. The most stable parameter was the single-scattering albedo of the vegetation. Canopy albedo could be derived with an accuracy of less than 5% relative error in the visible and less than 1% in the near-infrared. Sensitivity were performed to determine which of the 10 parameters were most important and to assess the effects of Gaussian noise on the parameter retrievals. Out of the 10 parameters, three were identified which described most of the BRDF variability. At low LAI values the most influential parameters were the single-scattering albedos (both soil and vegetation) and LAI, while at higher LAI values (greater than 2.5) these shifted to the two scattering phase function parameters for vegetation and the single-scattering albedo of the vegetation. The three-parameter model, formed by fixing the seven least significant parameters, gave higher rms values but was less sensitive to noise in the BRDF than the full ten-parameter model. A full hemispherical reflectance data set for lawn was then interpolated to yield BRDF values corresponding to advanced very high resolution radiometer (AVHRR) scan geometries collected over a period of nine days. The resulting parameters and BRDFs are similar to those for the
Multivariate calculus and geometry
Dineen, Seán
2014-01-01
Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.
Transformational plane geometry
Umble, Ronald N
2014-01-01
Axioms of Euclidean Plane Geometry The Existence and Incidence Postulates The Distance and Ruler Postulates The Plane Separation Postulate The Protractor Postulate The Side-Angle-Side Postulate and the Euclidean Parallel Postulate Theorems of Euclidean Plane Geometry The Exterior Angle Theorem Triangle Congruence Theorems The Alternate Interior Angles Theorem and the Angle Sum Theorem Similar Triangles Introduction to Transformations, Isometries, and Similarities Transformations Isometries and SimilaritiesAppendix: Proof of Surjectivity Translations, Rotations, and Reflections Translations Rotations Reflections Appendix: Geometer's Sketchpad Commands Required by Exploratory Activities Compositions of Translations, Rotations, and Reflections The Three Points Theorem Rotations as Compositions of Two Reflections Translations as Compositions of Two Halfturns or Two Reflections The Angle Addition Theorem Glide Reflections Classification of Isometries The Fundamental Theorem and Congruence Classification of Isometr...
Multilevel geometry optimization
Rodgers, Jocelyn M.; Fast, Patton L.; Truhlar, Donald G.
2000-02-01
Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol.
Multilevel geometry optimization
Energy Technology Data Exchange (ETDEWEB)
Rodgers, Jocelyn M. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Fast, Patton L. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Truhlar, Donald G. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States)
2000-02-15
Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol. (c) 2000 American Institute of Physics.
Finite element solution of two dimensional time dependent heat equation
International Nuclear Information System (INIS)
Maaz
1999-01-01
A Microsoft Windows based computer code, named FHEAT, has been developed for solving two dimensional heat problems in Cartesian and Cylindrical geometries. The programming language is Microsoft Visual Basic 3.0. The code makes use of Finite element formulation for spatial domain and Finite difference formulation for time domain. Presently the code is capable of solving two dimensional steady state and transient problems in xy- and rz-geometries. The code is capable excepting both triangular and rectangular elements. Validation and benchmarking was done against hand calculations and published results. (author)
High accuracy 3D electromagnetic finite element analysis
International Nuclear Information System (INIS)
Nelson, E.M.
1996-01-01
A high accuracy 3D electromagnetic finite element field solver employing quadratic hexahedral elements and quadratic mixed-order one-form basis functions will be described. The solver is based on an object-oriented C++ class library. Test cases demonstrate that frequency errors less than 10 ppm can be achieved using modest workstations, and that the solutions have no contamination from spurious modes. The role of differential geometry and geometrical physics in finite element analysis will also be discussed
High accuracy 3D electromagnetic finite element analysis
International Nuclear Information System (INIS)
Nelson, Eric M.
1997-01-01
A high accuracy 3D electromagnetic finite element field solver employing quadratic hexahedral elements and quadratic mixed-order one-form basis functions will be described. The solver is based on an object-oriented C++ class library. Test cases demonstrate that frequency errors less than 10 ppm can be achieved using modest workstations, and that the solutions have no contamination from spurious modes. The role of differential geometry and geometrical physics in finite element analysis will also be discussed
Krauss, Lawrence M.; Turner, Michael S.
1999-01-01
The recognition that the cosmological constant may be non-zero forces us to re-evaluate standard notions about the connection between geometry and the fate of our Universe. An open Universe can recollapse, and a closed Universe can expand forever. As a corollary, we point out that there is no set of cosmological observations we can perform that will unambiguously allow us to determine what the ultimate destiny of the Universe will be.
DEFF Research Database (Denmark)
Tamke, Martin; Ramsgaard Thomsen, Mette; Riiber Nielsen, Jacob
2009-01-01
The versatility of wood constructions and traditional wood joints for the production of non standard elements was in focus of a design based research. Herein we established a seamless process from digital design to fabrication. A first research phase centered on the development of a robust...... parametric model and a generic design language a later explored the possibilities to construct complex shaped geometries with self registering joints on modern wood crafting machines. The research was carried out as collaboration with industrial partners....
International Nuclear Information System (INIS)
Lepora, N.; Kibble, T.
1999-01-01
We analyse symmetry breaking in the Weinberg-Salam model paying particular attention to the underlying geometry of the theory. In this context we find two natural metrics upon the vacuum manifold: an isotropic metric associated with the scalar sector, and a squashed metric associated with the gauge sector. Physically, the interplay between these metrics gives rise to many of the non-perturbative features of Weinberg-Salam theory. (author)
Quantum scattering in two black hole moduli space
International Nuclear Information System (INIS)
Sakamoto, Kenji; Shiraishi, Kiyoshi
2003-01-01
We discuss the quantum scattering process in a moduli space consisting of two maximally charged dilaton black holes. The black hole moduli space geometry has different structures for arbitrary dimensions and various values of the dilaton coupling. We study the quantum effects of the different moduli space geometries with scattering process. Then, it is found that there is a resonance state on certain moduli spaces
International Nuclear Information System (INIS)
Hull, C.M.
1993-01-01
The geometric structure of theories with gauge fields of spins two and higher should involve a higher spin generalisation of Riemannian geometry. Such geometries are discussed and the case of W ∝ -gravity is analysed in detail. While the gauge group for gravity in d dimensions is the diffeomorphism group of the space-time, the gauge group for a certain W-gravity theory (which is W ∝ -gravity in the case d=2) is the group of symplectic diffeomorphisms of the cotangent bundle of the space-time. Gauge transformations for W-gravity gauge fields are given by requiring the invariance of a generalised line element. Densities exist and can be constructed from the line element (generalising √detg μν ) only if d=1 or d=2, so that only for d=1,2 can actions be constructed. These two cases and the corresponding W-gravity actions are considered in detail. In d=2, the gauge group is effectively only a subgroup of the symplectic diffeomorphisms group. Some of the constraints that arise for d=2 are similar to equations arising in the study of self-dual four-dimensional geometries and can be analysed using twistor methods, allowing contact to be made with other formulations of W-gravity. While the twistor transform for self-dual spaces with one Killing vector reduces to a Legendre transform, that for two Killing vectors gives a generalisation of the Legendre transform. (orig.)
CBM RICH geometry optimization
Energy Technology Data Exchange (ETDEWEB)
Mahmoud, Tariq; Hoehne, Claudia [II. Physikalisches Institut, Giessen Univ. (Germany); Collaboration: CBM-Collaboration
2016-07-01
The Compressed Baryonic Matter (CBM) experiment at the future FAIR complex will investigate the phase diagram of strongly interacting matter at high baryon density and moderate temperatures in A+A collisions from 2-11 AGeV (SIS100) beam energy. The main electron identification detector in the CBM experiment will be a RICH detector with a CO{sub 2} gaseous-radiator, focusing spherical glass mirrors, and MAPMT photo-detectors being placed on a PMT-plane. The RICH detector is located directly behind the CBM dipole magnet. As the final magnet geometry is now available, some changes in the RICH geometry become necessary. In order to guarantee a magnetic field of 1 mT at maximum in the PMT plane for effective operation of the MAPMTs, two measures have to be taken: The PMT plane is moved outwards of the stray field by tilting the mirrors by 10 degrees and shielding boxes have been designed. In this contribution the results of the geometry optimization procedure are presented.
Introducing geometry concept based on history of Islamic geometry
Maarif, S.; Wahyudin; Raditya, A.; Perbowo, K. S.
2018-01-01
Geometry is one of the areas of mathematics interesting to discuss. Geometry also has a long history in mathematical developments. Therefore, it is important integrated historical development of geometry in the classroom to increase’ knowledge of how mathematicians earlier finding and constructing a geometric concept. Introduction geometrical concept can be started by introducing the Muslim mathematician who invented these concepts so that students can understand in detail how a concept of geometry can be found. However, the history of mathematics development, especially history of Islamic geometry today is less popular in the world of education in Indonesia. There are several concepts discovered by Muslim mathematicians that should be appreciated by the students in learning geometry. Great ideas of mathematicians Muslim can be used as study materials to supplement religious character values taught by Muslim mathematicians. Additionally, by integrating the history of geometry in teaching geometry are expected to improve motivation and geometrical understanding concept.
Scattering Correction For Image Reconstruction In Flash Radiography
International Nuclear Information System (INIS)
Cao, Liangzhi; Wang, Mengqi; Wu, Hongchun; Liu, Zhouyu; Cheng, Yuxiong; Zhang, Hongbo
2013-01-01
Scattered photons cause blurring and distortions in flash radiography, reducing the accuracy of image reconstruction significantly. The effect of the scattered photons is taken into account and an iterative deduction of the scattered photons is proposed to amend the scattering effect for image restoration. In order to deduct the scattering contribution, the flux of scattered photons is estimated as the sum of two components. The single scattered component is calculated accurately together with the uncollided flux along the characteristic ray, while the multiple scattered component is evaluated using correction coefficients pre-obtained from Monte Carlo simulations.The arbitrary geometry pretreatment and ray tracing are carried out based on the customization of AutoCAD. With the above model, an Iterative Procedure for image restORation code, IPOR, is developed. Numerical results demonstrate that the IPOR code is much more accurate than the direct reconstruction solution without scattering correction and it has a very high computational efficiency
Scattering Correction For Image Reconstruction In Flash Radiography
Energy Technology Data Exchange (ETDEWEB)
Cao, Liangzhi; Wang, Mengqi; Wu, Hongchun; Liu, Zhouyu; Cheng, Yuxiong; Zhang, Hongbo [Xi' an Jiaotong Univ., Xi' an (China)
2013-08-15
Scattered photons cause blurring and distortions in flash radiography, reducing the accuracy of image reconstruction significantly. The effect of the scattered photons is taken into account and an iterative deduction of the scattered photons is proposed to amend the scattering effect for image restoration. In order to deduct the scattering contribution, the flux of scattered photons is estimated as the sum of two components. The single scattered component is calculated accurately together with the uncollided flux along the characteristic ray, while the multiple scattered component is evaluated using correction coefficients pre-obtained from Monte Carlo simulations.The arbitrary geometry pretreatment and ray tracing are carried out based on the customization of AutoCAD. With the above model, an Iterative Procedure for image restORation code, IPOR, is developed. Numerical results demonstrate that the IPOR code is much more accurate than the direct reconstruction solution without scattering correction and it has a very high computational efficiency.
Energy Technology Data Exchange (ETDEWEB)
Nunes, Rogerio Chaffin
2002-03-15
In this work, the system of differential equations obtained by the angular approach of the two-dimensional transport equation by the discrete ordinates method is solved through the formulation of finite elements with the objective of investigating the sensitivity of the outgoing flux of radiation with the incoming flux and the properties of absorption and scattering of the medium. The variational formulation for the system of differential equations of second order with the generalized boundary conditions of Neumann (third type) allows an easy implementation of the method of the finite elements with triangular mesh and approximation space of first order. The geometry chosen for the simulations is a circle with a non homogeneous circular form in its interior. The mapping of Dirichlet-Neumann is studied through various simulations involving the incoming flux, the outgoing flux and the properties of the medium. (author)
Scattering effect on entanglement propagation in RCFTs
Energy Technology Data Exchange (ETDEWEB)
Numasawa, Tokiro [Yukawa Institute for Theoretical Physics, Kyoto University,Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto, 606-8502 (Japan); Kavli Institute for Theoretical Physics, University of California Santa Barbara,Santa Barbara, CA, 93106 (United States)
2016-12-14
In this paper we discuss the scattering effect on entanglement propagation in RCFTs. In our setup, we consider the time evolution of excited states created by the insertion of many local operators. Our results show that because of the finiteness of quantum dimension, entanglement is not changed after the scattering in RCFTs. In this mean, entanglement is conserved after the scattering event in RCFTs, which reflects the integrability of the system. Our results are also consistent with the free quasiparticle picture after the global quenches.
Twistor diagrams and massless Moeller scattering
International Nuclear Information System (INIS)
Hodges, A.P.
1983-01-01
The theory of twistor diagrams, as devised by Penrose, is intended to lead to a manifestly finite account of scattering amplitudes in quantum field theory. The theory is here extended to a more general type of interaction between massless fields than has hitherto been described. It is applied to the example of first-order massless Moeller scattering in quantum electrodynamics. It is shown that earlier studies of this example have failed to render a correct account, in particular by overlooking an infrared divergency, but that the scattering data can nevertheless be represented within the twistor formalism. (author)
International Nuclear Information System (INIS)
Leader, Elliot
1991-01-01
With very few unexplained results to challenge conventional ideas, physicists have to look hard to search for gaps in understanding. An area of physics which offers a lot more than meets the eye is elastic and diffractive scattering where particles either 'bounce' off each other, emerging unscathed, or just graze past, emerging relatively unscathed. The 'Blois' workshops provide a regular focus for this unspectacular, but compelling physics, attracting highly motivated devotees
MM99.81 Projection welding of complex geometries
DEFF Research Database (Denmark)
Kristensen, Lars
The objective of this work has been to establish a profound knowledge about design rules for projection welding geometries dependent of the actual material combination.Design rules and recommendations for geometries and projections in projection welding given in literature is summarised...... and these are catalogued into geometry-classes. A simulation software, SORPAS, based on the finite element method (FEM) is chosen as tool to investigate projection weld quality. SORPAS needs input of the material flow stress as function of strain, strain rate and temperature. Flow stress experiments are performed using...... been investigated.Two different welding geometries, disc with triangular ring projection welded to ring and hat welded to inside hole in ring, are both experimentally and numerically used to investigate the influence of different geometric parameters (thicknesses and angles) on weldability and weld...
International Nuclear Information System (INIS)
1991-02-01
The annual report on hand gives an overview of the research work carried out in the Laboratory for Neutron Scattering (LNS) of the ETH Zuerich in 1990. Using the method of neutron scattering, it is possible to examine in detail the static and dynamic properties of the condensed material. In accordance with the multidisciplined character of the method, the LNS has for years maintained a system of intensive co-operation with numerous institutes in the areas of biology, chemistry, solid-state physics, crystallography and materials research. In 1990 over 100 scientists from more than 40 research groups both at home and abroad took part in the experiments. It was again a pleasure to see the number of graduate students present, who were studying for a doctorate and who could be introduced into the neutron scattering during their stay at the LNS and thus were in the position to touch on central ways of looking at a problem in their dissertation using this modern experimental method of solid-state research. In addition to the numerous and interesting ways of formulating the questions to explain the structure, nowadays the scientific programme increasingly includes particularly topical studies in connection with high temperature-supraconductors and materials research
Friedrich, Harald
2016-01-01
This corrected and updated second edition of "Scattering Theory" presents a concise and modern coverage of the subject. In the present treatment, special attention is given to the role played by the long-range behaviour of the projectile-target interaction, and a theory is developed, which is well suited to describe near-threshold bound and continuum states in realistic binary systems such as diatomic molecules or molecular ions. It is motivated by the fact that experimental advances have shifted and broadened the scope of applications where concepts from scattering theory are used, e.g. to the field of ultracold atoms and molecules, which has been experiencing enormous growth in recent years, largely triggered by the successful realization of Bose-Einstein condensates of dilute atomic gases in 1995. The book contains sections on special topics such as near-threshold quantization, quantum reflection, Feshbach resonances and the quantum description of scattering in two dimensions. The level of abstraction is k...
Finite element coiled cochlea model
Isailovic, Velibor; Nikolic, Milica; Milosevic, Zarko; Saveljic, Igor; Nikolic, Dalibor; Radovic, Milos; Filipović, Nenad
2015-12-01
Cochlea is important part of the hearing system, and thanks to special structure converts external sound waves into neural impulses which go to the brain. Shape of the cochlea is like snail, so geometry of the cochlea model is complex. The simplified cochlea coiled model was developed using finite element method inside SIFEM FP7 project. Software application is created on the way that user can prescribe set of the parameters for spiral cochlea, as well as material properties and boundary conditions to the model. Several mathematical models were tested. The acoustic wave equation for describing fluid in the cochlea chambers - scala vestibuli and scala timpani, and Newtonian dynamics for describing vibrations of the basilar membrane are used. The mechanical behavior of the coiled cochlea was analyzed and the third chamber, scala media, was not modeled because it does not have a significant impact on the mechanical vibrations of the basilar membrane. The obtained results are in good agreement with experimental measurements. Future work is needed for more realistic geometry model. Coiled model of the cochlea was created and results are compared with initial simplified coiled model of the cochlea.
Two lectures on D-geometry and noncommutative geometry
International Nuclear Information System (INIS)
Douglas, M.R.
1999-01-01
This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has appeared in D-brane and Matrix theory physics. (author)
Taheri, H.; Koester, L.; Bigelow, T.; Bond, L. J.
2018-04-01
Industrial applications of additively manufactured components are increasing quickly. Adequate quality control of the parts is necessary in ensuring safety when using these materials. Base material properties, surface conditions, as well as location and size of defects are some of the main targets for nondestructive evaluation of additively manufactured parts, and the problem of adequate characterization is compounded given the challenges of complex part geometry. Numerical modeling can allow the interplay of the various factors to be studied, which can lead to improved measurement design. This paper presents a finite element simulation verified by experimental results of ultrasonic waves scattering from flat bottom holes (FBH) in additive manufacturing materials. A focused beam immersion ultrasound transducer was used for both the modeling and simulations in the additive manufactured samples. The samples were SS17 4 PH steel samples made by laser sintering in a powder bed.
Fractional finite Fourier transform.
Khare, Kedar; George, Nicholas
2004-07-01
We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.
International Nuclear Information System (INIS)
Lucha, W.; Neufeld, H.
1986-01-01
We investigate the relation between finiteness of a four-dimensional quantum field theory and global supersymmetry. To this end we consider the most general quantum field theory and analyse the finiteness conditions resulting from the requirement of the absence of divergent contributions to the renormalizations of the parameters of the theory. In addition to the gauge bosons, both fermions and scalar bosons turn out to be a necessary ingredient in a non-trivial finite gauge theory. In all cases discussed, the supersymmetric theory restricted by two well-known constraints on the dimensionless couplings proves to be the unique solution of the finiteness conditions. (Author)
International Nuclear Information System (INIS)
Surya Mohan, P.; Tarvainen, Tanja; Schweiger, Martin; Pulkkinen, Aki; Arridge, Simon R.
2011-01-01
Highlights: → We developed a variable order global basis scheme to solve light transport in 3D. → Based on finite elements, the method can be applied to a wide class of geometries. → It is computationally cheap when compared to the fixed order scheme. → Comparisons with local basis method and other models demonstrate its accuracy. → Addresses problems encountered n modeling of light transport in human brain. - Abstract: We propose the P N approximation based on a finite element framework for solving the radiative transport equation with optical tomography as the primary application area. The key idea is to employ a variable order spherical harmonic expansion for angular discretization based on the proximity to the source and the local scattering coefficient. The proposed scheme is shown to be computationally efficient compared to employing homogeneously high orders of expansion everywhere in the domain. In addition the numerical method is shown to accurately describe the void regions encountered in the forward modeling of real-life specimens such as infant brains. The accuracy of the method is demonstrated over three model problems where the P N approximation is compared against Monte Carlo simulations and other state-of-the-art methods.
Neutron density decay constant in a non-multiplying lattice of finite size
International Nuclear Information System (INIS)
Deniz, V.C.
1965-01-01
This report presents a general theory, using the integral transport method, for obtaining the neutron density decay constant in a finite non-multiplying lattice. The theory is applied to obtain the expression for the diffusion coefficient. The case of a homogeneous medium with 1/v absorption and of finite size in all directions is treated in detail, assuming an isotropic scattering law. The decay constant is obtained up to the B 6 term. The expressions for the diffusion coefficient and for the diffusion cooling coefficient are the same as those obtained for a slab geometry by Nelkin, using the expansion in spherical harmonics of the Fourier transform in the spatial variable. Furthermore, explicit forms are obtained for the flux and the current. It is shown that the deviation of the actual flux from a Maxwellian is the flux generated in the medium, extended to infinity and deprived of its absorbing power, by various sources, each of which has a zero integral over all velocities. The study of the current permits the generalization of Fick's law. An independent integral method, valid for homogeneous media, is also presented. (author) [fr
Neutron Elastic Scattering Cross Sections of the Elements Ni, Co, and Cu between 1.5 and 8.0 MeV
Energy Technology Data Exchange (ETDEWEB)
Holmqvist, B; Wiedling, T
1967-12-15
Angular distributions of elastically scattered neutrons have been measured for natural nickel at seven energies between 3.0 and 8.1 MeV and for cobalt and copper at ten energies between 1.5 and 8.1 MeV, by using time-of-flight technique. The observed angular distributions were corrected for neutron flux attenuation, multiple elastic scattering, and the finite geometry of the source-sample-detector system by using a Monte Carlo computer program. Theoretical angular distributions have been fitted to the experimental angular distributions by using an optical model potential with Saxon-Woods form factors. A computer program was used to find parameter values of the potential giving the best fittings to the experimental angular distributions.
Lé tourneau, Pierre-David; Wu, Ying; Papanicolaou, George; Garnier, Josselin; Darve, Eric
2016-01-01
We present a wideband fast algorithm capable of accurately computing the full numerical solution of the problem of acoustic scattering of waves by multiple finite-sized bodies such as spherical scatterers in three dimensions. By full solution, we
International Nuclear Information System (INIS)
Hook, D W
2008-01-01
A geometric framework for quantum mechanics arose during the mid 1970s when authors such as Cantoni explored the notion of generalized transition probabilities, and Kibble promoted the idea that the space of pure quantum states provides a natural quantum mechanical analogue for classical phase space. This central idea can be seen easily since the projection of Schroedinger's equation from a Hilbert space into the space of pure spaces is a set of Hamilton's equations. Over the intervening years considerable work has been carried out by a variety of authors and a mature description of quantum mechanics in geometric terms has emerged with many applications. This current offering would seem ideally placed to review the last thirty years of progress and relate this to the most recent work in quantum entanglement. Bengtsson and Zyczkowski's beautifully illustrated volume, Geometry of Quantum States (referred to as GQS from now on) attempts to cover considerable ground in its 466 pages. Its topics range from colour theory in Chapter 1 to quantum entanglement in Chapter 15-to say that this is a whirlwind tour is, perhaps, no understatement. The use of the work 'introduction' in the subtitle of GQS, might suggest to the reader that this work be viewed as a textbook and I think that this interpretation would be incorrect. The authors have chosen to present a survey of different topics with the specific aim to introduce entanglement in geometric terms-the book is not intended as a pedagogical introduction to the geometric approach to quantum mechanics. Each of the fifteen chapters is a short, and mostly self-contained, essay on a particular aspect or application of geometry in the context of quantum mechanics with entanglement being addressed specifically in the final chapter. The chapters fall into three classifications: those concerned with the mathematical background, those which discuss quantum theory and the foundational aspects of the geometric framework, and
A finite element model for independent wire rope core with double ...
Indian Academy of Sciences (India)
1Istanbul Technical University, Institute of Informatics, Computational Science and ... a little work has been done using the double helical geometry and real ... Finite element approach has been embedded in wire rope analysis since 1999.
Advances in 3D electromagnetic finite element modeling
International Nuclear Information System (INIS)
Nelson, E.M.
1997-01-01
Numerous advances in electromagnetic finite element analysis (FEA) have been made in recent years. The maturity of frequency domain and eigenmode calculations, and the growth of time domain applications is briefly reviewed. A high accuracy 3D electromagnetic finite element field solver employing quadratic hexahedral elements and quadratic mixed-order one-form basis functions will also be described. The solver is based on an object-oriented C++ class library. Test cases demonstrate that frequency errors less than 10 ppm can be achieved using modest workstations, and that the solutions have no contamination from spurious modes. The role of differential geometry and geometrical physics in finite element analysis is also discussed
Dooner, David B
2012-01-01
Building on the first edition published in 1995 this new edition of Kinematic Geometry of Gearing has been extensively revised and updated with new and original material. This includes the methodology for general tooth forms, radius of torsure', cylinder of osculation, and cylindroid of torsure; the author has also completely reworked the '3 laws of gearing', the first law re-written to better parallel the existing 'Law of Gearing" as pioneered by Leonard Euler, expanded from Euler's original law to encompass non-circular gears and hypoid gears, the 2nd law of gearing describing a unique relat
Flegg, H Graham
2001-01-01
This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4-12 give a largely intuitive presentation of selected topics.
Torsional heterotic geometries
International Nuclear Information System (INIS)
Becker, Katrin; Sethi, Savdeep
2009-01-01
We construct new examples of torsional heterotic backgrounds using duality with orientifold flux compactifications. We explain how duality provides a perturbative solution to the type I/heterotic string Bianchi identity. The choice of connection used in the Bianchi identity plays an important role in the construction. We propose the existence of a much larger landscape of compact torsional geometries using string duality. Finally, we present some quantum exact metrics that correspond to NS5-branes placed on an elliptic space. These metrics describe how torus isometries are broken by NS flux.
Geometrie verstehen: statisch - kinematisch
Kroll, Ekkehard
Dem Allgemeinen steht begrifflich das Besondere gegenüber. In diesem Sinne sind allgemeine Überlegungen zum Verstehen von Mathematik zu ergänzen durch Untersuchungen hinsichtlich des Verstehens der einzelnen mathematischen Disziplinen, insbesondere der Geometrie. Hier haben viele Schülerinnen und Schüler Probleme. Diese rühren hauptsächlich daher, dass eine fertige geometrische Konstruktion in ihrer statischen Präsentation auf Papier nicht mehr die einzelnen Konstruktionsschritte erkennen lässt; zum Nachvollzug müssen sie daher ergänzend in einer Konstruktionsbeschreibung festgehalten werden.
Kendig, Keith
2015-01-01
Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator. An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring th
Abhyankar, Shreeram Shankar
1964-01-01
This book provides, for use in a graduate course or for self-study by graduate students, a well-motivated treatment of several topics, especially the following: (1) algebraic treatment of several complex variables; (2) geometric approach to algebraic geometry via analytic sets; (3) survey of local algebra; (4) survey of sheaf theory. The book has been written in the spirit of Weierstrass. Power series play the dominant role. The treatment, being algebraic, is not restricted to complex numbers, but remains valid over any complete-valued field. This makes it applicable to situations arising from
Akopyan, A V
2007-01-01
The book is devoted to the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, the authors move to less trivial results, both classical and contemporary. In particular, the chapter on projective properties of conics contains a detailed analysis of the polar correspondence, pencils of conics, and the Poncelet theorem. In the chapter on metric properties of conics the authors discuss, in particular, inscribed conics, normals to conics, and the Poncelet theorem for confoca
2015-01-01
This stimulating volume offers a broad collection of the principles of geometry and trigonometry and contains colorful diagrams to bring mathematical principles to life. Subjects are enriched by references to famous mathematicians and their ideas, and the stories are presented in a very comprehensible way. Readers investigate the relationships of points, lines, surfaces, and solids. They study construction methods for drawing figures, a wealth of facts about these figures, and above all, methods to prove the facts. They learn about triangle measure for circular motion, sine and cosine, tangent
REA, The Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Geometry I includes methods of proof, points, lines, planes, angles, congruent angles and line segments, triangles, parallelism, quadrilaterals, geometric inequalities, and geometric
Graded geometry and Poisson reduction
Cattaneo, A S; Zambon, M
2009-01-01
The main result of [2] extends the Marsden-Ratiu reduction theorem [4] in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof in [2]. Further, we provide an alternative algebraic proof for the main result. ©2009 American Institute of Physics
A hybrid finite element - statistical energy analysis approach to robust sound transmission modeling
Reynders, Edwin; Langley, Robin S.; Dijckmans, Arne; Vermeir, Gerrit
2014-09-01
When considering the sound transmission through a wall in between two rooms, in an important part of the audio frequency range, the local response of the rooms is highly sensitive to uncertainty in spatial variations in geometry, material properties and boundary conditions, which have a wave scattering effect, while the local response of the wall is rather insensitive to such uncertainty. For this mid-frequency range, a computationally efficient modeling strategy is adopted that accounts for this uncertainty. The partitioning wall is modeled deterministically, e.g. with finite elements. The rooms are modeled in a very efficient, nonparametric stochastic way, as in statistical energy analysis. All components are coupled by means of a rigorous power balance. This hybrid strategy is extended so that the mean and variance of the sound transmission loss can be computed as well as the transition frequency that loosely marks the boundary between low- and high-frequency behavior of a vibro-acoustic component. The method is first validated in a simulation study, and then applied for predicting the airborne sound insulation of a series of partition walls of increasing complexity: a thin plastic plate, a wall consisting of gypsum blocks, a thicker masonry wall and a double glazing. It is found that the uncertainty caused by random scattering is important except at very high frequencies, where the modal overlap of the rooms is very high. The results are compared with laboratory measurements, and both are found to agree within the prediction uncertainty in the considered frequency range.
Sman, van der R.G.M.
2006-01-01
In the special case of relaxation parameter = 1 lattice Boltzmann schemes for (convection) diffusion and fluid flow are equivalent to finite difference/volume (FD) schemes, and are thus coined finite Boltzmann (FB) schemes. We show that the equivalence is inherent to the homology of the
Supersymmetric theories and finiteness
International Nuclear Information System (INIS)
Helayel-Neto, J.A.
1989-01-01
We attempt here to present a short survey of the all-order finite Lagrangian field theories known at present in four-and two-dimensional space-times. The question of the possible relevance of these ultraviolet finite models in the formulation of consistent unified frameworks for the fundamental forces is also addressed to. (author)
Regularization method for solving the inverse scattering problem
International Nuclear Information System (INIS)
Denisov, A.M.; Krylov, A.S.
1985-01-01
The inverse scattering problem for the Schroedinger radial equation consisting in determining the potential according to the scattering phase is considered. The problem of potential restoration according to the phase specified with fixed error in a finite range is solved by the regularization method based on minimization of the Tikhonov's smoothing functional. The regularization method is used for solving the problem of neutron-proton potential restoration according to the scattering phases. The determined potentials are given in the table
Semi-analytical solution to arbitrarily shaped beam scattering
Wang, Wenjie; Zhang, Huayong; Sun, Yufa
2017-07-01
Based on the field expansions in terms of appropriate spherical vector wave functions and the method of moments scheme, an exact semi-analytical solution to the scattering of an arbitrarily shaped beam is given. For incidence of a Gaussian beam, zero-order Bessel beam and Hertzian electric dipole radiation, numerical results of the normalized differential scattering cross section are presented to a spheroid and a circular cylinder of finite length, and the scattering properties are analyzed concisely.
Scattering of Lamb waves in a composite plate
Bratton, Robert; Datta, Subhendu; Shah, Arvind
1991-01-01
A combined analytical and finite element technique is developed to gain a better understanding of the scattering of elastic waves by defects. This hybrid method is capable of predicting scattered displacements from arbitrary shaped defects as well as inclusions of different material. The continuity of traction and displacements at the boundaries of the two areas provided the necessary equations to find the nodal displacements and expansion coefficients. Results clearly illustrate the influence of increasing crack depth on the scattered signal.
De Wolf, E.A.
2002-01-01
We discuss basic concepts and properties of diffractive phenomena in soft hadron collisions and in deep-inelastic scattering at low Bjorken-x. The paper is not a review of the rapidly developing field but presents an attempt to show in simple terms the close inter-relationship between the dynamics of high-energy hadronic and deep-inelastic diffraction. Using the saturation model of Golec-Biernat and Wusthoff as an example, a simple explanation of geometrical scaling is presented. The relation between the QCD anomalous multiplicity dimension and the Pomeron intercept is discussed.
International Nuclear Information System (INIS)
Wolf, E.A. de
2002-01-01
We discuss basic concepts and properties of diffractive phenomena in soft hadron collisions and in deep-inelastic scattering at low Bjorken - x. The paper is not a review of the rapidly developing field but presents an attempt to show in simple terms the close inter-relationship between the dynamics of high-energy hadronic and deep-inelastic diffraction. Using the saturation model of Golec-Biernat and Wuesthoff as an example, a simple explanation of geometrical scaling is presented. The relation between the QCD anomalous multiplicity dimension and the Pomeron intercept is discussed. (author)
Alabdulmohsin, Ibrahim M.
2018-03-07
We will begin our treatment of summability calculus by analyzing what will be referred to, throughout this book, as simple finite sums. Even though the results of this chapter are particular cases of the more general results presented in later chapters, they are important to start with for a few reasons. First, this chapter serves as an excellent introduction to what summability calculus can markedly accomplish. Second, simple finite sums are encountered more often and, hence, they deserve special treatment. Third, the results presented in this chapter for simple finite sums will, themselves, be used as building blocks for deriving the most general results in subsequent chapters. Among others, we establish that fractional finite sums are well-defined mathematical objects and show how various identities related to the Euler constant as well as the Riemann zeta function can actually be derived in an elementary manner using fractional finite sums.
Alabdulmohsin, Ibrahim M.
2018-01-01
We will begin our treatment of summability calculus by analyzing what will be referred to, throughout this book, as simple finite sums. Even though the results of this chapter are particular cases of the more general results presented in later chapters, they are important to start with for a few reasons. First, this chapter serves as an excellent introduction to what summability calculus can markedly accomplish. Second, simple finite sums are encountered more often and, hence, they deserve special treatment. Third, the results presented in this chapter for simple finite sums will, themselves, be used as building blocks for deriving the most general results in subsequent chapters. Among others, we establish that fractional finite sums are well-defined mathematical objects and show how various identities related to the Euler constant as well as the Riemann zeta function can actually be derived in an elementary manner using fractional finite sums.
Finite fields and applications
Mullen, Gary L
2007-01-01
This book provides a brief and accessible introduction to the theory of finite fields and to some of their many fascinating and practical applications. The first chapter is devoted to the theory of finite fields. After covering their construction and elementary properties, the authors discuss the trace and norm functions, bases for finite fields, and properties of polynomials over finite fields. Each of the remaining chapters details applications. Chapter 2 deals with combinatorial topics such as the construction of sets of orthogonal latin squares, affine and projective planes, block designs, and Hadamard matrices. Chapters 3 and 4 provide a number of constructions and basic properties of error-correcting codes and cryptographic systems using finite fields. Each chapter includes a set of exercises of varying levels of difficulty which help to further explain and motivate the material. Appendix A provides a brief review of the basic number theory and abstract algebra used in the text, as well as exercises rel...
Time-dependent scattering in resonance lines
International Nuclear Information System (INIS)
Kunasz, P.B.
1983-01-01
A numerical finite-difference method is presented for the problem of time-dependent line transfer in a finite slab in which material density is sufficiently low that the time of flight between scatterings greatly exceeds the relaxation time of the upper state of the scattering transition. The medium is assumed to scatter photons isotropically, with complete frequency redistribution. Numerical solutions are presented for a homogeneous, time-independent slab illuminated by an externally imposed radiation field which enters the slab at t = 0. Graphical results illustrate relaxation to steady state of trapped internal radiation, emergent energy, and emergent profiles. A review of the literature is also given in which the time-dependent line transfer problem is discussed in the context of recent analytical work
Turbulence studies in tokamak boundary plasmas with realistic divertor geometry
International Nuclear Information System (INIS)
Xu, X.Q.; Cohen, R.H.; Por, G.D. ter; Rognlien, T.D.; Ryutov, D.D.; Myra, J.R.; D'Ippolito, D.A.; Moyer, R.; Groebner, R.J.
1999-01-01
Results are presented from the 3D nonlocal electromagnetic turbulence code BOUT and the linearized shooting code BAL for studies of turbulence in tokamak boundary plasmas and its relationship to the L-H transition, in a realistic divertor plasma geometry. The key results include: (1) the identification of the dominant resistive X-point mode in divertor geometry and (2) turbulence suppression in the L-H transition by shear in the E x B drift speed, ion diamagnetism and finite polarization. Based on the simulation results, a parameterization of the transport is given that includes the dependence on the relevant physical parameters. (author)
Energy Technology Data Exchange (ETDEWEB)
Sun Wenbo E-mail: w.sun@larc.nasa.gov; Loeb, Norman G.; Fu Qiang
2004-02-01
A recently developed finite-difference time domain scheme is examined using the exact analytic solutions for light scattering by a coated sphere immersed in an absorbing medium. The relative differences are less than 1% in the extinction, scattering, and absorption efficiencies and less than 5% in the scattering phase functions. The definition of apparent single-scattering properties is also discussed.
Acoustic scattering of a Bessel vortex beam by a rigid fixed spheroid
Mitri, F. G.
2015-12-01
Partial-wave series representation of the acoustic scattering field of high-order Bessel vortex beams by rigid oblate and prolate spheroids using the modal matching method is developed. The method, which is applicable to slightly elongated objects at low-to-moderate frequencies, requires solving a system of linear equations which depends on the partial-wave index n and the order of the Bessel vortex beam m using truncated partial-wave series expansions (PWSEs), and satisfying the Neumann boundary condition for a rigid immovable surface in the least-squares sense. This original semi-analytical approach developed for Bessel vortex beams is demonstrated for finite oblate and prolate spheroids, where the mathematical functions describing the spheroidal geometry are written in a form involving single angular (polar) integrals that are numerically computed. The transverse (θ = π / 2) and 3D scattering directivity patterns are evaluated in the far-field for both prolate and oblate spheroids, with particular emphasis on the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid) not exceeding 3:1, the half-cone angle β and order m of the Bessel vortex beam, as well as the dimensionless size parameter kr0. Periodic oscillations in the magnitude plots of the far-field scattering form function are observed, which result from the interference of the reflected waves with the circumferential (Franz') waves circumnavigating the surface of the spheroid in the surrounding fluid. Moreover, the 3D directivity patterns illustrate the far-field scattering from the spheroid, that vanishes in the forward (θ = 0) and backward (θ = π) directions. Particular applications in underwater acoustics and scattering, acoustic levitation and the detection of submerged elongated objects using Bessel vortex waves to name a few, would benefit from the results of the present investigation.
Compton scatter tomography in TOF-PET
Hemmati, Hamidreza; Kamali-Asl, Alireza; Ay, Mohammadreza; Ghafarian, Pardis
2017-10-01
Scatter coincidences contain hidden information about the activity distribution on the positron emission tomography (PET) imaging system. However, in conventional reconstruction, the scattered data cause the blurring of images and thus are estimated and subtracted from detected coincidences. List mode format provides a new aspect to use time of flight (TOF) and energy information of each coincidence in the reconstruction process. In this study, a novel approach is proposed to reconstruct activity distribution using the scattered data in the PET system. For each single scattering coincidence, a scattering angle can be determined by the recorded energy of the detected photons, and then possible locations of scattering can be calculated based on the scattering angle. Geometry equations show that these sites lie on two arcs in 2D mode or the surface of a prolate spheroid in 3D mode, passing through the pair of detector elements. The proposed method uses a novel and flexible technique to estimate source origin locations from the possible scattering locations, using the TOF information. Evaluations were based on a Monte-Carlo simulation of uniform and non-uniform phantoms at different resolutions of time and detector energy. The results show that although the energy uncertainties deteriorate the image spatial resolution in the proposed method, the time resolution has more impact on image quality than the energy resolution. With progress of the TOF system, the reconstruction using the scattered data can be used in a complementary manner, or to improve image quality in the next generation of PET systems.
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
International Nuclear Information System (INIS)
Basta, C.
1982-01-01
Using the method of orthogonal colocation the boundary problem for a fix bed with cylindrical geometry was solved. The axial disposal term was despicable and the results were compared with those the explicit finite difference method. (E.G.) [pt
Bochnak, Jacek; Roy, Marie-Françoise
1998-01-01
This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Géometrie algébrique réelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.
Critique of information geometry
International Nuclear Information System (INIS)
Skilling, John
2014-01-01
As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples
International Nuclear Information System (INIS)
Correa, Diego H.; Silva, Guillermo A.
2008-01-01
We discuss how geometrical and topological aspects of certain (1/2)-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents
Emergent geometry of membranes
Energy Technology Data Exchange (ETDEWEB)
Badyn, Mathias Hudoba de; Karczmarek, Joanna L.; Sabella-Garnier, Philippe; Yeh, Ken Huai-Che [Department of Physics and Astronomy, University of British Columbia,6224 Agricultural Road, Vancouver (Canada)
2015-11-13
In work http://dx.doi.org/10.1103/PhysRevD.86.086001, a surface embedded in flat ℝ{sup 3} is associated to any three hermitian matrices. We study this emergent surface when the matrices are large, by constructing coherent states corresponding to points in the emergent geometry. We find the original matrices determine not only shape of the emergent surface, but also a unique Poisson structure. We prove that commutators of matrix operators correspond to Poisson brackets. Through our construction, we can realize arbitrary noncommutative membranes: for example, we examine a round sphere with a non-spherically symmetric Poisson structure. We also give a natural construction for a noncommutative torus embedded in ℝ{sup 3}. Finally, we make remarks about area and find matrix equations for minimal area surfaces.
Analysis of a Cartesian PML approximation to acoustic scattering problems in and
Bramble, James H.
2013-08-01
We consider the application of a perfectly matched layer (PML) technique applied in Cartesian geometry to approximate solutions of the acoustic scattering problem in the frequency domain. The PML is viewed as a complex coordinate shift ("stretching") and leads to a variable complex coefficient equation for the acoustic wave posed on an infinite domain, the complement of the bounded scatterer. The use of Cartesian geometry leads to a PML operator with simple coefficients, although, still complex symmetric (non-Hermitian). The PML reformulation results in a problem whose solution coincides with the original solution inside the PML layer while decaying exponentially outside. The rapid decay of the PML solution suggests truncation to a bounded domain with a convenient outer boundary condition and subsequent finite element approximation (for the truncated problem). This paper provides new stability estimates for the Cartesian PML approximations both on the infinite and the truncated domain. We first investigate the stability of the infinite PML approximation as a function of the PML strength σ0. This is done for PML methods which involve continuous piecewise smooth stretching as well as piecewise constant stretching functions. We next introduce a truncation parameter M which determines the size of the PML layer. Our analysis shows that the truncated PML problem is stable provided that the product of Mσ0 is sufficiently large, in which case the solution of the problem on the truncated domain converges exponentially to that of the original problem in the domain of interest near the scatterer. This justifies the simple computational strategy of selecting a fixed PML layer and increasing σ0 to obtain the desired accuracy. The results of numerical experiments varying M and σ0 are given which illustrate the theoretically predicted behavior. © 2013 Elsevier B.V. All rights reserved.
Geometry through history Euclidean, hyperbolic, and projective geometries
Dillon, Meighan I
2018-01-01
Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the...
Energy Technology Data Exchange (ETDEWEB)
Fernandes, Julio Cesar L.; Vilhena, Marco Tullio, E-mail: julio.lombaldo@ufrgs.b, E-mail: vilhena@pq.cnpq.b [Universidade Federal do Rio Grande do Sul (DMPA/UFRGS), Porto Alegre, RS (Brazil). Dept. de Matematica Pura e Aplicada. Programa de Pos Graduacao em Matematica Aplicada; Borges, Volnei; Bodmann, Bardo Ernest, E-mail: bardo.bodmann@ufrgs.b, E-mail: borges@ufrgs.b [Universidade Federal do Rio Grande do Sul (PROMEC/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica
2011-07-01
The principal idea of this work, consist on formulate an analytical method to solved problems for diffusion of neutrons with isotropic scattering in one-dimensional cylindrical geometry. In this area were develop many works that study the same problem in different system of coordinates as well as cartesian system, nevertheless using numerical methods to solve the shielding problem. In view of good results in this works, we starting with the idea that we can represent a source in the origin of the cylindrical system by a Delta Dirac distribution, we describe the physical modeling and solved the neutron diffusion equation inside of cylinder of radius R. For the case of transport equation, the formulation of discrete ordinates S{sub N} consists in discretize the angular variables in N directions and in using a quadrature angular set for approximate the sources of scattering, where the Diffusion equation consist on S{sub 2} approximated transport equation in discrete ordinates. We solved the neutron diffusion equation with an analytical form by the finite Hankel transform. Was presented also the build-up factor for the case that we have neutron flux inside the cylinder. (author)
International Nuclear Information System (INIS)
Fernandes, Julio Cesar L.; Vilhena, Marco Tullio; Borges, Volnei; Bodmann, Bardo Ernest
2011-01-01
The principal idea of this work, consist on formulate an analytical method to solved problems for diffusion of neutrons with isotropic scattering in one-dimensional cylindrical geometry. In this area were develop many works that study the same problem in different system of coordinates as well as cartesian system, nevertheless using numerical methods to solve the shielding problem. In view of good results in this works, we starting with the idea that we can represent a source in the origin of the cylindrical system by a Delta Dirac distribution, we describe the physical modeling and solved the neutron diffusion equation inside of cylinder of radius R. For the case of transport equation, the formulation of discrete ordinates S N consists in discretize the angular variables in N directions and in using a quadrature angular set for approximate the sources of scattering, where the Diffusion equation consist on S 2 approximated transport equation in discrete ordinates. We solved the neutron diffusion equation with an analytical form by the finite Hankel transform. Was presented also the build-up factor for the case that we have neutron flux inside the cylinder. (author)
Finite elements and approximation
Zienkiewicz, O C
2006-01-01
A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o
A finite difference, multipoint flux numerical approach to flow in porous media: Numerical examples
Osman, Hossam Omar; Salama, Amgad; Sun, Shuyu; Bao, Kai
2012-01-01
It is clear that none of the current available numerical schemes which may be adopted to solve transport phenomena in porous media fulfill all the required robustness conditions. That is while the finite difference methods are the simplest of all, they face several difficulties in complex geometries and anisotropic media. On the other hand, while finite element methods are well suited to complex geometries and can deal with anisotropic media, they are more involved in coding and usually require more execution time. Therefore, in this work we try to combine some features of the finite element technique, namely its ability to work with anisotropic media with the finite difference approach. We reduce the multipoint flux, mixed finite element technique through some quadrature rules to an equivalent cell-centered finite difference approximation. We show examples on using this technique to single-phase flow in anisotropic porous media.
A finite difference, multipoint flux numerical approach to flow in porous media: Numerical examples
Osman, Hossam Omar
2012-06-17
It is clear that none of the current available numerical schemes which may be adopted to solve transport phenomena in porous media fulfill all the required robustness conditions. That is while the finite difference methods are the simplest of all, they face several difficulties in complex geometries and anisotropic media. On the other hand, while finite element methods are well suited to complex geometries and can deal with anisotropic media, they are more involved in coding and usually require more execution time. Therefore, in this work we try to combine some features of the finite element technique, namely its ability to work with anisotropic media with the finite difference approach. We reduce the multipoint flux, mixed finite element technique through some quadrature rules to an equivalent cell-centered finite difference approximation. We show examples on using this technique to single-phase flow in anisotropic porous media.
International Nuclear Information System (INIS)
Yee, K.S.
1980-01-01
It has been observed that the exposure of dielectrics to electron beams can produce an electric field of sufficient magnitude to cause dielectric breakdown. The present investigations will be directed to calculate the electric field intensity in dielectrics under spherical and cylindrical geometries. In the spherical geometry the method of multiple images renders the full numerical calculation unnecessary, whereas in a finite length cylindrical geometry the full numerical calculation seems to be inevitable. A description and results of the spherical geometry are presented and a more detailed presentation of the finite cylinder geometry is given
On Finsler Geometry and Applications in Mechanics: Review and New Perspectives
Directory of Open Access Journals (Sweden)
J. D. Clayton
2015-01-01
direction as well as position, and a number of connections emerge associated with various covariant derivatives involving affine and nonlinear coefficients. Finsler geometry encompasses Riemannian, Euclidean, and Minkowskian geometries as special cases, and thus it affords great generality for describing a number of phenomena in physics. Here, descriptions of finite deformation of continuous media are of primary focus. After a review of necessary mathematical definitions and derivations, prior work involving application of Finsler geometry in continuum mechanics of solids is reviewed. A new theoretical description of continua with microstructure is then outlined, merging concepts from Finsler geometry and phase field theories of materials science.
Application of finite Fourier transformation for the solution of the diffusion equation
International Nuclear Information System (INIS)
Kobayashi, Keisuke
1991-01-01
The application of the finite Fourier transformation to the solution of the neutron diffusion equation in one dimension, two dimensional x-y and triangular geometries is discussed. It can be shown that the equation obtained by the Nodal Green's function method in Cartesian coordinates can be derived as a special case of the finite Fourier transformation method. (author)
Evaluation of a cone beam computed tomography geometry for image guided small animal irradiation
International Nuclear Information System (INIS)
Yang, Yidong; Armour, Michael; Wang, Ken Kang-Hsin; Gandhi, Nishant; Wong, John; Iordachita, Iulian; Siewerdsen, Jeffrey
2015-01-01
The conventional imaging geometry for small animal cone beam computed tomography (CBCT) is that a detector panel rotates around the head-to-tail axis of an imaged animal (‘tubular’ geometry). Another unusual but possible imaging geometry is that the detector panel rotates around the anterior-to-posterior axis of the animal (‘pancake’ geometry). The small animal radiation research platform developed at Johns Hopkins University employs the pancake geometry where a prone-positioned animal is rotated horizontally between an x-ray source and detector panel. This study is to assess the CBCT image quality in the pancake geometry and investigate potential methods for improvement. We compared CBCT images acquired in the pancake geometry with those acquired in the tubular geometry when the phantom/animal was placed upright simulating the conventional CBCT geometry. Results showed signal-to-noise and contrast-to-noise ratios in the pancake geometry were reduced in comparison to the tubular geometry at the same dose level. But the overall spatial resolution within the transverse plane of the imaged cylinder/animal was better in the pancake geometry. A modest exposure increase to two folds in the pancake geometry can improve image quality to a level close to the tubular geometry. Image quality can also be improved by inclining the animal, which reduces streak artifacts caused by bony structures. The major factor resulting in the inferior image quality in the pancake geometry is the elevated beam attenuation along the long axis of the phantom/animal and consequently increased scatter-to-primary ratio in that orientation. Not withstanding, the image quality in the pancake-geometry CBCT is adequate to support image guided animal positioning, while providing unique advantages of non-coplanar and multiple mice irradiation. This study also provides useful knowledge about the image quality in the two very different imaging geometries, i.e. pancake and tubular geometry
Evaluation of a cone beam computed tomography geometry for image guided small animal irradiation.
Yang, Yidong; Armour, Michael; Wang, Ken Kang-Hsin; Gandhi, Nishant; Iordachita, Iulian; Siewerdsen, Jeffrey; Wong, John
2015-07-07
The conventional imaging geometry for small animal cone beam computed tomography (CBCT) is that a detector panel rotates around the head-to-tail axis of an imaged animal ('tubular' geometry). Another unusual but possible imaging geometry is that the detector panel rotates around the anterior-to-posterior axis of the animal ('pancake' geometry). The small animal radiation research platform developed at Johns Hopkins University employs the pancake geometry where a prone-positioned animal is rotated horizontally between an x-ray source and detector panel. This study is to assess the CBCT image quality in the pancake geometry and investigate potential methods for improvement. We compared CBCT images acquired in the pancake geometry with those acquired in the tubular geometry when the phantom/animal was placed upright simulating the conventional CBCT geometry. Results showed signal-to-noise and contrast-to-noise ratios in the pancake geometry were reduced in comparison to the tubular geometry at the same dose level. But the overall spatial resolution within the transverse plane of the imaged cylinder/animal was better in the pancake geometry. A modest exposure increase to two folds in the pancake geometry can improve image quality to a level close to the tubular geometry. Image quality can also be improved by inclining the animal, which reduces streak artifacts caused by bony structures. The major factor resulting in the inferior image quality in the pancake geometry is the elevated beam attenuation along the long axis of the phantom/animal and consequently increased scatter-to-primary ratio in that orientation. Not withstanding, the image quality in the pancake-geometry CBCT is adequate to support image guided animal positioning, while providing unique advantages of non-coplanar and multiple mice irradiation. This study also provides useful knowledge about the image quality in the two very different imaging geometries, i.e. pancake and tubular geometry, respectively.
Fluorescent and Raman scattering by molecules embedded in small particles: Final report
International Nuclear Information System (INIS)
Chew, H.; McNulty, P.J.
1987-02-01
The model takes into account the physical properties and the morphology of the particles, as well as the locations of the scatter(s). Brief descriptions of various applications of the model are presented. Brief descriptions of experimental studies of scattering by finite dielectric and cylindrical microstructures in plastic track detector plane surfaces are given
Simplified solutions of the Cox-Thompson inverse scattering method at fixed energy
International Nuclear Information System (INIS)
Palmai, Tamas; Apagyi, Barnabas; Horvath, Miklos
2008-01-01
Simplified solutions of the Cox-Thompson inverse quantum scattering method at fixed energy are derived if a finite number of partial waves with only even or odd angular momenta contribute to the scattering process. Based on new formulae various approximate methods are introduced which also prove applicable to the generic scattering events
System theory as applied differential geometry. [linear system
Hermann, R.
1979-01-01
The invariants of input-output systems under the action of the feedback group was examined. The approach used the theory of Lie groups and concepts of modern differential geometry, and illustrated how the latter provides a basis for the discussion of the analytic structure of systems. Finite dimensional linear systems in a single independent variable are considered. Lessons of more general situations (e.g., distributed parameter and multidimensional systems) which are increasingly encountered as technology advances are presented.
A nonlinear resistive MHD-code in cylindrical geometry
International Nuclear Information System (INIS)
Jakoby, A.
1987-11-01
A computer code has been developed which solves the full compressible resistive magnetohydrodynamic (MHD) equations in cylindrical geometry. The variables are expanded in Fourier series in the poloidal and axial directions while finite differences are used in the radial direction. The time advance is accomplished by using a semi-implicit predictor-corrector-scheme. Applications to the ideal m=1 ideal kink saturation in the nonlinear regime and the subsequent decay of the singular current layer due to resistivity are presented. (orig.)
Certain theories of multiple scattering in random media of discrete scatterers
International Nuclear Information System (INIS)
Olsen, R.L.; Kharadly, M.M.Z.; Corr, D.G.
1976-01-01
New information is presented on the accuracy of the heuristic approximations in two important theories of multiple scattering in random media of discrete scatterers: Twersky's ''free-space'' and ''two-space scatterer'' formalisms. Two complementary approaches, based primarily on a one-dimensional model and the one-dimensional forms of the theories, are used. For scatterer distributions of low average density, the ''heuristic'' asymptotic forms for the coherent field and the incoherent intensity are compared with asymptotic forms derived from a systematic analysis of the multiple scattering processes. For distributions of higher density, both in the average number of scatterers per wavelength and in the degree of packing of finite-size scatterers, the analysis is carried out ''experimentally'' by means of a Monte Carlo computer simulation. Approximate series expressions based on the systematic approach are numerically evaluated along with the heuristic expressions. The comparison (for both forward- and back-scattered field moments) is made for the worst-case conditions of strong multiple scattering for which the theories have not previously been evaluated. Several significant conclusions are drawn which have certain practical implications: in application of the theories to describe some of the scattering phenomena which occur in the troposphere, and in the further evaluation of the theories using experiments on physical models
On organizing principles of discrete differential geometry. Geometry of spheres
International Nuclear Information System (INIS)
Bobenko, Alexander I; Suris, Yury B
2007-01-01
Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. This survey contains a discussion of the following two fundamental discretization principles: the transformation group principle (smooth geometric objects and their discretizations are invariant with respect to the same transformation group) and the consistency principle (discretizations of smooth parametrized geometries can be extended to multidimensional consistent nets). The main concrete geometric problem treated here is discretization of curvature-line parametrized surfaces in Lie geometry. Systematic use of the discretization principles leads to a discretization of curvature-line parametrization which unifies circular and conical nets.
Higher geometry an introduction to advanced methods in analytic geometry
Woods, Frederick S
2005-01-01
For students of mathematics with a sound background in analytic geometry and some knowledge of determinants, this volume has long been among the best available expositions of advanced work on projective and algebraic geometry. Developed from Professor Woods' lectures at the Massachusetts Institute of Technology, it bridges the gap between intermediate studies in the field and highly specialized works.With exceptional thoroughness, it presents the most important general concepts and methods of advanced algebraic geometry (as distinguished from differential geometry). It offers a thorough study
Difference sets connecting algebra, combinatorics, and geometry
Moore, Emily H
2013-01-01
Difference sets belong both to group theory and to combinatorics. Studying them requires tools from geometry, number theory, and representation theory. This book lays a foundation for these topics, including a primer on representations and characters of finite groups. It makes the research literature on difference sets accessible to students who have studied linear algebra and abstract algebra, and it prepares them to do their own research. This text is suitable for an undergraduate capstone course, since it illuminates the many links among topics that the students have already studied. To this end, almost every chapter ends with a coda highlighting the main ideas and emphasizing mathematical connections. This book can also be used for self-study by anyone interested in these connections and concrete examples. An abundance of exercises, varying from straightforward to challenging, invites the reader to solve puzzles, construct proofs, and investigate problems--by hand or on a computer. Hints and solutions are...
Hydrodynamics of compressible superfluids in confined geometries
International Nuclear Information System (INIS)
Malmi-Kakkada, Abdul N; Valls, Oriol T; Dasgupta, Chandan
2014-01-01
We present a study of the hydrodynamics of compressible superfluids in confined geometries. We use a perturbative procedure in terms of the dimensionless expansion parameter (v/v s ) 2 where v is the typical speed of the flow and v s is the speed of sound. A zero value of this parameter corresponds to the incompressible limit. We apply the procedure to two specific problems: the case of a trapped superfluid with a Gaussian profile of the local density, and that of a superfluid confined in a rotating obstructed cylinder. We find that the corrections due to finite compressibility which are, as expected, negligible for liquid He, are important but amenable to the perturbative treatment for typical ultracold atomic systems. (paper)
Discrete approach to complex planar geometries
International Nuclear Information System (INIS)
Cupini, E.; De Matteis, A.
1974-01-01
Planar regions in Monte Carlo transport problems have been represented by a finite set of points with a corresponding region index for each. The simulation of particle free-flight reduces then to the simple operations necessary for scanning appropriate grid points to determine whether a region other than the starting one is encountered. When the complexity of the geometry is restricted to only some regions of the assembly examined, a mixed discrete-continuous philosophy may be adopted. By this approach, the lattice of a thermal reactor has been treated, discretizing only the central regions of the cell containing the fuel rods. Excellent agreement with experimental results has been obtained in the computation of cell parameters in the energy range from fission to thermalization through the 238 U resonance region. (U.S.)
Indian Academy of Sciences (India)
IAS Admin
wavelength, they are called shallow water waves. In the ... Deep and intermediate water waves are dispersive as the velocity of these depends on wavelength. This is not the ..... generation processes, the finite amplitude wave theories are very ...
Finite Discrete Gabor Analysis
DEFF Research Database (Denmark)
Søndergaard, Peter Lempel
2007-01-01
frequency bands at certain times. Gabor theory can be formulated for both functions on the real line and for discrete signals of finite length. The two theories are largely the same because many aspects come from the same underlying theory of locally compact Abelian groups. The two types of Gabor systems...... can also be related by sampling and periodization. This thesis extends on this theory by showing new results for window construction. It also provides a discussion of the problems associated to discrete Gabor bases. The sampling and periodization connection is handy because it allows Gabor systems...... on the real line to be well approximated by finite and discrete Gabor frames. This method of approximation is especially attractive because efficient numerical methods exists for doing computations with finite, discrete Gabor systems. This thesis presents new algorithms for the efficient computation of finite...
International Nuclear Information System (INIS)
Rittenberg, V.
1983-01-01
Fischer's finite-size scaling describes the cross over from the singular behaviour of thermodynamic quantities at the critical point to the analytic behaviour of the finite system. Recent extensions of the method--transfer matrix technique, and the Hamiltonian formalism--are discussed in this paper. The method is presented, with equations deriving scaling function, critical temperature, and exponent v. As an application of the method, a 3-states Hamiltonian with Z 3 global symmetry is studied. Diagonalization of the Hamiltonian for finite chains allows one to estimate the critical exponents, and also to discover new phase transitions at lower temperatures. The critical points lambda, and indices v estimated for finite-scaling are given
Scattering theory and orthogonal polynomials
International Nuclear Information System (INIS)
Geronimo, J.S.
1977-01-01
The application of the techniques of scattering theory to the study of polynomials orthogonal on the unit circle and a finite segment of the real line is considered. The starting point is the recurrence relations satisfied by the polynomials instead of the orthogonality condition. A set of two two terms recurrence relations for polynomials orthogonal on the real line is presented and used. These recurrence relations play roles analogous to those satisfied by polynomials orthogonal on unit circle. With these recurrence formulas a Wronskian theorem is proved and the Christoffel-Darboux formula is derived. In scattering theory a fundamental role is played by the Jost function. An analogy is deferred of this function and its analytic properties and the locations of its zeros investigated. The role of the analog Jost function in various properties of these orthogonal polynomials is investigated. The techniques of inverse scattering theory are also used. The discrete analogues of the Gelfand-Levitan and Marchenko equations are derived and solved. These techniques are used to calculate asymptotic formulas for the orthogonal polynomials. Finally Szego's theorem on toeplitz and Hankel determinants is proved using the recurrence formulas and some properties of the Jost function. The techniques of inverse scattering theory are used to calculate the correction terms
Blocks of finite groups and their invariants
Sambale, Benjamin
2014-01-01
Providing a nearly complete selection of up-to-date methods and results on block invariants with respect to their defect groups, this book covers the classical theory pioneered by Brauer, the modern theory of fusion systems introduced by Puig, the geometry of numbers developed by Minkowski, the classification of finite simple groups, and various computer assisted methods. In a powerful combination, these tools are applied to solve many special cases of famous open conjectures in the representation theory of finite groups. Most of the material is drawn from peer-reviewed journal articles, but there are also new previously unpublished results. In order to make the text self-contained, detailed proofs are given whenever possible. Several tables add to the text's usefulness as a reference. The book is aimed at experts in group theory or representation theory who may wish to make use of the presented ideas in their research.
Finite Blaschke products and their connections
Garcia, Stephan Ramon; Ross, William T
2018-01-01
This monograph offers an introduction to finite Blaschke products and their connections to complex analysis, linear algebra, operator theory, matrix analysis, and other fields. Old favorites such as the Carathéodory approximation and the Pick interpolation theorems are featured, as are many topics that have never received a modern treatment, such as the Bohr radius and Ritt's theorem on decomposability. Deep connections to hyperbolic geometry are explored, as are the mapping properties, zeros, residues, and critical points of finite Blaschke products. In addition, model spaces, rational functions with real boundary values, spectral mapping properties of the numerical range, and the Darlington synthesis problem from electrical engineering are also covered. Topics are carefully discussed, and numerous examples and illustrations highlight crucial ideas. While thorough explanations allow the reader to appreciate the beauty of the subject, relevant exercises following each chapter improve technical fluency with t...
An introduction to incidence geometry
De Bruyn, Bart
2016-01-01
This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among others the generalized polygons, near polygons, polar spaces, dual polar spaces and designs. Also the various relationships between these geometries are investigated. Ovals and ovoids of projective spaces are studied and some applications to particular geometries will be given. A separate chapter introduces the necessary mathematical tools and techniques from graph theory. This chapter itself can be regarded as a self-contained introduction to strongly regular and distance-regular graphs. This book is essentially self-contained, only assuming the knowledge of basic notions from (linear) algebra and projective and affine geometry. Almost all theorems are accompanied with proofs and a list of exercises with full solutions is given at the end...
Supersymmetry at finite temperature
International Nuclear Information System (INIS)
Clark, T.E.; Love, S.T.
1983-01-01
Finite-temperature supersymmetry (SUSY) is characterized by unbroken Ward identities for SUSY variations of ensemble averages of Klein-operator inserted imaginary time-ordered products of fields. Path-integral representations of these products are defined and the Feynman rules in superspace are given. The finite-temperature no-renormalization theorem is derived. Spontaneously broken SUSY at zero temperature is shown not to be restored at high temperature. (orig.)
International Nuclear Information System (INIS)
Brueckel, Thomas; Heger, Gernot; Richter, Dieter; Roth, Georg; Zorn, Reiner
2012-01-01
The following topics are dealt with: Neutron scattering in contemporary research, neutron sources, symmetry of crystals, diffraction, nanostructures investigated by small-angle neutron scattering, the structure of macromolecules, spin dependent and magnetic scattering, structural analysis, neutron reflectometry, magnetic nanostructures, inelastic scattering, strongly correlated electrons, dynamics of macromolecules, applications of neutron scattering. (HSI)
Planetary Image Geometry Library
Deen, Robert C.; Pariser, Oleg
2010-01-01
The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A
Finite difference time domain modelling of particle accelerators
International Nuclear Information System (INIS)
Jurgens, T.G.; Harfoush, F.A.
1989-03-01
Finite Difference Time Domain (FDTD) modelling has been successfully applied to a wide variety of electromagnetic scattering and interaction problems for many years. Here the method is extended to incorporate the modelling of wake fields in particle accelerators. Algorithmic comparisons are made to existing wake field codes, such as MAFIA T3. 9 refs., 7 figs
FINELM: a multigroup finite element diffusion code
International Nuclear Information System (INIS)
Higgs, C.E.; Davierwalla, D.M.
1981-06-01
FINELM is a FORTRAN IV program to solve the Neutron Diffusion Equation in X-Y, R-Z, R-theta, X-Y-Z and R-theta-Z geometries using the method of Finite Elements. Lagrangian elements of linear or higher degree to approximate the spacial flux distribution have been provided. The method of dissections, coarse mesh rebalancing and Chebyshev acceleration techniques are available. Simple user defined input is achieved through extensive input subroutines. The input preparation is described followed by a program structure description. Sample test cases are provided. (Auth.)
Initiation to global Finslerian geometry
Akbar-Zadeh, Hassan
2006-01-01
After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry. The first three chapters develop the basic notions and methods, introduced by the author, to reach the global problems in Finslerian Geometry. The next five chapters are independent of each other, and deal with among others the geometry of generalized Einstein manifolds, the classification of Finslerian manifolds of constant sectional curvatures. They also give a treatment of isometric, affine, p
International Nuclear Information System (INIS)
Palmiotti, G.; Carrico, C.B.; Lewis, E.E.
1995-10-01
The theoretical basis, implementation information and numerical results are presented for VARIANT (VARIational Anisotropic Neutron Transport), a FORTRAN module of the DIF3D code system at Argonne National Laboratory. VARIANT employs the variational nodal method to solve multigroup steady-state neutron diffusion and transport problems. The variational nodal method is a hybrid finite element method that guarantees nodal balance and permits spatial refinement through the use of hierarchical complete polynomial trial functions. Angular variables are expanded with complete or simplified P 1 , P 3 or P 5 5 spherical harmonics approximations with full anisotropic scattering capability. Nodal response matrices are obtained, and the within-group equations are solved by red-black or four-color iteration, accelerated by a partitioned matrix algorithm. Fission source and upscatter iterations strategies follow those of DIF3D. Two- and three-dimensional Cartesian and hexagonal geometries are implemented. Forward and adjoint eigenvalue, fixed source, gamma heating, and criticality (concentration) search problems may be performed
Directory of Open Access Journals (Sweden)
Šárka Nedomová
2013-01-01
Full Text Available Precise quantification of the profile of egg can provide a powerful tool for the analysis of egg shape for various biological problems. A new approach to the geometry of a Ostrich’s egg profile is presented here using an analysing the egg’s digital photo by edge detection techniques. The obtained points on the eggshell counter are fitted by the Fourier series. The obtained equations describing an egg profile have been used to calculate radii of curvature. The radii of the curvature at the important point of the egg profile (sharp end, blunt end and maximum thickness are independent on the egg shape index. The exact values of the egg surface and the egg volume have been obtained. These quantities are also independent on the egg shape index. These quantities can be successively estimated on the basis of simplified equations which are expressed in terms of the egg length, L¸ and its width, B. The surface area of the eggshells also exhibits good correlation with the egg long circumference length. Some limitations of the most used procedures have been also shown.
Nonperturbative quantum geometries
International Nuclear Information System (INIS)
Jacobson, T.; California Univ., Santa Barbara; Smolin, L.; California Univ., Santa Barbara
1988-01-01
Using the self-dual representation of quantum general relativity, based on Ashtekar's new phase space variables, we present an infinite dimensional family of quantum states of the gravitational field which are exactly annihilated by the hamiltonian constraint. These states are constructed from Wilson loops for Ashtekar's connection (which is the spatial part of the left handed spin connection). We propose a new regularization procedure which allows us to evaluate the action of the hamiltonian constraint on these states. Infinite linear combinations of these states which are formally annihilated by the diffeomorphism constraints as well are also described. These are explicit examples of physical states of the gravitational field - and for the compact case are exact zero eigenstates of the hamiltonian of quantum general relativity. Several different approaches to constructing diffeomorphism invariant states in the self dual representation are also described. The physical interpretation of the states described here is discussed. However, as we do not yet know the physical inner product, any interpretation is at this stage speculative. Nevertheless, this work suggests that quantum geometry at Planck scales might be much simpler when explored in terms of the parallel transport of left-handed spinors than when explored in terms of the three metric. (orig.)
Bhatia, Rajendra
2013-01-01
This book is an outcome of the Indo-French Workshop on Matrix Information Geometries (MIG): Applications in Sensor and Cognitive Systems Engineering, which was held in Ecole Polytechnique and Thales Research and Technology Center, Palaiseau, France, in February 23-25, 2011. The workshop was generously funded by the Indo-French Centre for the Promotion of Advanced Research (IFCPAR). During the event, 22 renowned invited french or indian speakers gave lectures on their areas of expertise within the field of matrix analysis or processing. From these talks, a total of 17 original contribution or state-of-the-art chapters have been assembled in this volume. All articles were thoroughly peer-reviewed and improved, according to the suggestions of the international referees. The 17 contributions presented are organized in three parts: (1) State-of-the-art surveys & original matrix theory work, (2) Advanced matrix theory for radar processing, and (3) Matrix-based signal processing applications.
Mathematical model of geometry and fibrous structure of the heart.
Nielsen, P M; Le Grice, I J; Smaill, B H; Hunter, P J
1991-04-01
We developed a mathematical representation of ventricular geometry and muscle fiber organization using three-dimensional finite elements referred to a prolate spheroid coordinate system. Within elements, fields are approximated using basis functions with associated parameters defined at the element nodes. Four parameters per node are used to describe ventricular geometry. The radial coordinate is interpolated using cubic Hermite basis functions that preserve slope continuity, while the angular coordinates are interpolated linearly. Two further nodal parameters describe the orientation of myocardial fibers. The orientation of fibers within coordinate planes bounded by epicardial and endocardial surfaces is interpolated linearly, with transmural variation given by cubic Hermite basis functions. Left and right ventricular geometry and myocardial fiber orientations were characterized for a canine heart arrested in diastole and fixed at zero transmural pressure. The geometry was represented by a 24-element ensemble with 41 nodes. Nodal parameters fitted using least squares provided a realistic description of ventricular epicardial [root mean square (RMS) error less than 0.9 mm] and endocardial (RMS error less than 2.6 mm) surfaces. Measured fiber fields were also fitted (RMS error less than 17 degrees) with a 60-element, 99-node mesh obtained by subdividing the 24-element mesh. These methods provide a compact and accurate anatomic description of the ventricles suitable for use in finite element stress analysis, simulation of cardiac electrical activation, and other cardiac field modeling problems.
Performance of Halbach magnet arrays with finite coercivity
International Nuclear Information System (INIS)
Insinga, A.R.; Bahl, C.R.H.; Bjørk, R.; Smith, A.
2016-01-01
A numerical method to study the effect of finite coercivity on the Halbach cylinder geometry is presented. Despite the fact that the analytical solution available for this geometry does not set any limit to the maximum air gap flux density achievable, in real life the non-linear response of the magnetic material and the fact that the coercivity is not infinite will limit the attainable field. The presented method is able to predict when and where demagnetization will occur, and these predictions are compared with the analytical solution for the case of infinite coercivity. However, the approach presented here also allows quantification of the decrease in flux density and homogeneity for a partially demagnetized magnet. Moreover, the problem of how to realize a Halbach cylinder geometry using a mix of materials with different coercivities without altering the overall performance is addressed. Being based on a numerical approach, the presented method can be employed to analyze the demagnetization effects due to coercivity for any geometry, even when the analytical solution is not available. - Highlights: • The effect of the finite coercivity on the performance of the Halbach cylinder geometry is analyzed • FEM predictions of demagnetization are in agreement with the analytical calculations. • Performance in the non-linear regime is quantified by the average and uniformity of the field • We show which regions in the geometry are more likely to experience non-linear behavior. • We provide a recipe for the fabrication of a multi-material Halbach cylinder
Cieslinski, Jan L.; Ferapontov, Eugene V.; Kitaev, Alexander V.; Nimmo, Jonathan J. C.
2009-10-01
equations. Some integrable systems still await successful application of the twistor approach. This review, although concerned with advanced differential geometry, is quite elementary and self-contained. F Nijhoff, J Atkinson and J Hietarinta review the construction of soliton solutions for the KdV type lattice equations and derive N-soliton solutions for all lattice equations in the Adler-Bobenko-Suris list except for the generic elliptic case. The same problem is addressed in the contribution by J Hietarinta and D J Zhang based on the more traditional direct Hirota method. This leads to Casoratians and bilinear difference equations. Regular contributions include the following. H Baran and M Marvan launch a project to classify integrable classes of surfaces based on a novel deformation procedure of the equations of the embedding. This leads to a remarkable new integrable equation describing a class of Weingarten surfaces which seems to be overlooked in the literature. A Doliwa shows that the τ-function of the quadrilateral lattice can be identified with the Fredholm determinant of the integral equation inverting the nonlocal problem. This result is expected because its continuous counterpart (the case of conjugate nets, Darboux equations and the multicomponent KP hierarchy) is already known. Here one can find an explicit proof. P Gaillard and V B Matveev consider special reductions of the generic Darboux-Crum dressing procedure, leading to new formulas for Darboux-Pöschl-Teller potentials, their difference deformations and the related eigenfunctions. A Gouberman and K Leschke develop the theory of (generalized) Darboux transformations for conformal immersions of a Riemann surface into the 4-sphere. Applying this construction to the Clifford torus, they obtain a family of Willmore tori parametrized by Pythagorean triples. V Kiselev and J W van de Leur construct compatible nontrivial finite deformations of the Lie algebra structure in the symmetry algebra of the 3
Ultraviolet finiteness of N = 8 supergravity, spontaneously broken by dimensional reduction
International Nuclear Information System (INIS)
Sezgin, E.; Nieuwenhuizen, P. van
1982-06-01
The one-loop corrections to scalar-scalar scattering in N = 8 supergravity with 4 masses from dimensional reduction, are finite. We discuss various mechanisms that cancel the cosmological constant and infra-red divergences due to finite but non-vanishing tadpoles. (author)
Advanced geometries for ballistic neutron guides
International Nuclear Information System (INIS)
Schanzer, Christian; Boeni, Peter; Filges, Uwe; Hils, Thomas
2004-01-01
Sophisticated neutron guide systems take advantage of supermirrors being used to increase the neutron flux. However, the finite reflectivity of supermirrors becomes a major loss mechanism when many reflections occur, e.g. in long neutron guides and for long wavelengths. In order to reduce the number of reflections, ballistic neutron guides have been proposed. Usually linear tapered sections are used to enlarge the cross-section and finally, focus the beam to the sample. The disadvantages of linear tapering are (i) an inhomogeneous phase space at the sample position and (ii) a decreasing flux with increasing distance from the exit of the guide. We investigate the properties of parabolic and elliptic tapering for ballistic neutron guides, using the Monte Carlo program McStas with a new guide component dedicated for such geometries. We show that the maximum flux can indeed be shifted away from the exit of the guide. In addition we explore the possibilities of parabolic and elliptic geometries to create point like sources for dedicated experimental demands
The analytic nodal method in cylindrical geometry
International Nuclear Information System (INIS)
Prinsloo, Rian H.; Tomasevic, Djordje I.
2008-01-01
Nodal diffusion methods have been used extensively in nuclear reactor calculations, specifically for their performance advantage, but also for their superior accuracy. More specifically, the Analytic Nodal Method (ANM), utilising the transverse integration principle, has been applied to numerous reactor problems with much success. In this work, a nodal diffusion method is developed for cylindrical geometry. Application of this method to three-dimensional (3D) cylindrical geometry has never been satisfactorily addressed and we propose a solution which entails the use of conformal mapping. A set of 1D-equations with an adjusted, geometrically dependent, inhomogeneous source, is obtained. This work describes the development of the method and associated test code, as well as its application to realistic reactor problems. Numerical results are given for the PBMR-400 MW benchmark problem, as well as for a 'cylindrisized' version of the well-known 3D LWR IAEA benchmark. Results highlight the improved accuracy and performance over finite-difference core solutions and investigate the applicability of nodal methods to 3D PBMR type problems. Results indicate that cylindrical nodal methods definitely have a place within PBMR applications, yielding performance advantage factors of 10 and 20 for 2D and 3D calculations, respectively, and advantage factors of the order of 1000 in the case of the LWR problem
The geometry of on-shell diagrams
Franco, Sebastián; Galloni, Daniele; Mariotti, Alberto
2014-08-01
The fundamental role of on-shell diagrams in quantum field theory has been recently recognized. On-shell diagrams, or equivalently bipartite graphs, provide a natural bridge connecting gauge theory to powerful mathematical structures such as the Grassmannian. We perform a detailed investigation of the combinatorial and geometric objects associated to these graphs. We mainly focus on their relation to polytopes and toric geometry, the Grassmannian and its stratification. Our work extends the current understanding of these connections along several important fronts, most notably eliminating restrictions imposed by planarity, positivity, reducibility and edge removability. We illustrate our ideas with several explicit examples and introduce concrete methods that considerably simplify computations. We consider it highly likely that the structures unveiled in this article will arise in the on-shell study of scattering amplitudes beyond the planar limit. Our results can be conversely regarded as an expansion in the understanding of the Grassmannian in terms of bipartite graphs.
Cloaking through cancellation of diffusive wave scattering
Farhat, Mohamed
2016-08-10
A new cloaking mechanism, which makes enclosed objects invisible to diffusive photon density waves, is proposed. First, diffusive scattering from a basic core-shell geometry, which represents the cloaked structure, is studied. The conditions of scattering cancellation in a quasi-static scattering regime are derived. These allow for tailoring the diffusivity constant of the shell enclosing the object so that the fields scattered from the shell and the object cancel each other. This means that the photon flow outside the cloak behaves as if the cloaked object were not present. Diffusive light invisibility may have potential applications in hiding hot spots in infrared thermography or tissue imaging. © 2016 The Author(s) Published by the Royal Society. All rights reserved.
Emergent Geometry from Entropy and Causality
Engelhardt, Netta
In this thesis, we investigate the connections between the geometry of spacetime and aspects of quantum field theory such as entanglement entropy and causality. This work is motivated by the idea that spacetime geometry is an emergent phenomenon in quantum gravity, and that the physics responsible for this emergence is fundamental to quantum field theory. Part I of this thesis is focused on the interplay between spacetime and entropy, with a special emphasis on entropy due to entanglement. In general spacetimes, there exist locally-defined surfaces sensitive to the geometry that may act as local black hole boundaries or cosmological horizons; these surfaces, known as holographic screens, are argued to have a connection with the second law of thermodynamics. Holographic screens obey an area law, suggestive of an association with entropy; they are also distinguished surfaces from the perspective of the covariant entropy bound, a bound on the total entropy of a slice of the spacetime. This construction is shown to be quite general, and is formulated in both classical and perturbatively quantum theories of gravity. The remainder of Part I uses the Anti-de Sitter/ Conformal Field Theory (AdS/CFT) correspondence to both expand and constrain the connection between entanglement entropy and geometry. The AdS/CFT correspondence posits an equivalence between string theory in the "bulk" with AdS boundary conditions and certain quantum field theories. In the limit where the string theory is simply classical General Relativity, the Ryu-Takayanagi and more generally, the Hubeny-Rangamani-Takayanagi (HRT) formulae provide a way of relating the geometry of surfaces to entanglement entropy. A first-order bulk quantum correction to HRT was derived by Faulkner, Lewkowycz and Maldacena. This formula is generalized to include perturbative quantum corrections in the bulk at any (finite) order. Hurdles to spacetime emergence from entanglement entropy as described by HRT and its quantum
Modal Ring Method for the Scattering of Electromagnetic Waves
Baumeister, Kenneth J.; Kreider, Kevin L.
1993-01-01
The modal ring method for electromagnetic scattering from perfectly electric conducting (PEC) symmetrical bodies is presented. The scattering body is represented by a line of finite elements (triangular) on its outer surface. The infinite computational region surrounding the body is represented analytically by an eigenfunction expansion. The modal ring method effectively reduces the two dimensional scattering problem to a one-dimensional problem similar to the method of moments. The modal element method is capable of handling very high frequency scattering because it has a highly banded solution matrix.
GPS: Geometry, Probability, and Statistics
Field, Mike
2012-01-01
It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…
Surrogate Modeling for Geometry Optimization
DEFF Research Database (Denmark)
Rojas Larrazabal, Marielba de la Caridad; Abraham, Yonas; Holzwarth, Natalie
2009-01-01
A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used.......A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used....
Kaehler geometry and SUSY mechanics
International Nuclear Information System (INIS)
Bellucci, Stefano; Nersessian, Armen
2001-01-01
We present two examples of SUSY mechanics related with Kaehler geometry. The first system is the N = 4 supersymmetric one-dimensional sigma-model proposed in hep-th/0101065. Another system is the N = 2 SUSY mechanics whose phase space is the external algebra of an arbitrary Kaehler manifold. The relation of these models with antisymplectic geometry is discussed
A prediction for bubbling geometries
Okuda, Takuya
2007-01-01
We study the supersymmetric circular Wilson loops in N=4 Yang-Mills theory. Their vacuum expectation values are computed in the parameter region that admits smooth bubbling geometry duals. The results are a prediction for the supergravity action evaluated on the bubbling geometries for Wilson loops.
Bidirectional optical scattering facility
Federal Laboratory Consortium — Goniometric optical scatter instrument (GOSI)The bidirectional reflectance distribution function (BRDF) quantifies the angular distribution of light scattered from a...