Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms

Energy Technology Data Exchange (ETDEWEB)

Ablinger, Jakob; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

2013-01-15

In recent three-loop calculations of massive Feynman integrals within Quantum Chromodynamics (QCD) and, e.g., in recent combinatorial problems the so-called generalized harmonic sums (in short S-sums) arise. They are characterized by rational (or real) numerator weights also different from {+-}1. In this article we explore the algorithmic and analytic properties of these sums systematically. We work out the Mellin and inverse Mellin transform which connects the sums under consideration with the associated Poincare iterated integrals, also called generalized harmonic polylogarithms. In this regard, we obtain explicit analytic continuations by means of asymptotic expansions of the S-sums which started to occur frequently in current QCD calculations. In addition, we derive algebraic and structural relations, like differentiation w.r.t. the external summation index and different multi-argument relations, for the compactification of S-sum expressions. Finally, we calculate algebraic relations for infinite S-sums, or equivalently for generalized harmonic polylogarithms evaluated at special values. The corresponding algorithms and relations are encoded in the computer algebra package HarmonicSums.

Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms

Energy Technology Data Exchange (ETDEWEB)

Ablinger, Jakob; Schneider, Carsten [Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, A-4040, Linz (Austria); Blümlein, Johannes [Deutsches Elektronen–Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen (Germany)

2013-08-15

In recent three-loop calculations of massive Feynman integrals within Quantum Chromodynamics (QCD) and, e.g., in recent combinatorial problems the so-called generalized harmonic sums (in short S-sums) arise. They are characterized by rational (or real) numerator weights also different from ±1. In this article we explore the algorithmic and analytic properties of these sums systematically. We work out the Mellin and inverse Mellin transform which connects the sums under consideration with the associated Poincaré iterated integrals, also called generalized harmonic polylogarithms. In this regard, we obtain explicit analytic continuations by means of asymptotic expansions of the S-sums which started to occur frequently in current QCD calculations. In addition, we derive algebraic and structural relations, like differentiation with respect to the external summation index and different multi-argument relations, for the compactification of S-sum expressions. Finally, we calculate algebraic relations for infinite S-sums, or equivalently for generalized harmonic polylogarithms evaluated at special values. The corresponding algorithms and relations are encoded in the computer algebra package HarmonicSums.

Higher-order harmonics of general limited diffraction Bessel beams

Science.gov (United States)

Ding, De-Sheng; Huang, Jin-Huang

2016-12-01

In this paper, we extensively study the higher-order harmonic generation of the general limited diffraction m-th-order Bessel beam. The analysis is based on successive approximations of the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation. Asymptotic expansions are presented for higher-order harmonic Bessel beams in near and far fields. The validity of asymptotic approximation is also analyzed. The higher-order harmonic of the Bessel beam with the lowest zero-order is taken as a special example. Project supported by the National Natural Science Foundation of China (Grant Nos. 11074038 and 11374051).

Magneto-hydrodynamically stable axisymmetric mirrorsa)

Science.gov (United States)

Ryutov, D. D.; Berk, H. L.; Cohen, B. I.; Molvik, A. W.; Simonen, T. C.

2011-09-01

Making axisymmetric mirrors magnetohydrodynamically (MHD) stable opens up exciting opportunities for using mirror devices as neutron sources, fusion-fission hybrids, and pure-fusion reactors. This is also of interest from a general physics standpoint (as it seemingly contradicts well-established criteria of curvature-driven instabilities). The axial symmetry allows for much simpler and more reliable designs of mirror-based fusion facilities than the well-known quadrupole mirror configurations. In this tutorial, after a summary of classical results, several techniques for achieving MHD stabilization of the axisymmetric mirrors are considered, in particular: (1) employing the favorable field-line curvature in the end tanks; (2) using the line-tying effect; (3) controlling the radial potential distribution; (4) imposing a divertor configuration on the solenoidal magnetic field; and (5) affecting the plasma dynamics by the ponderomotive force. Some illuminative theoretical approaches for understanding axisymmetric mirror stability are described. The applicability of the various stabilization techniques to axisymmetric mirrors as neutron sources, hybrids, and pure-fusion reactors are discussed; and the constraints on the plasma parameters are formulated.

Magneto-hydrodynamically stable axisymmetric mirrors

Energy Technology Data Exchange (ETDEWEB)

Ryutov, D. D.; Cohen, B. I.; Molvik, A. W. [Lawrence Livermore National Laboratory, Livermore, California 94551 (United States); Berk, H. L. [University of Texas, Austin, Texas 78712 (United States); Simonen, T. C. [University of California, Berkeley, California 94720 (United States)

2011-09-15

Making axisymmetric mirrors magnetohydrodynamically (MHD) stable opens up exciting opportunities for using mirror devices as neutron sources, fusion-fission hybrids, and pure-fusion reactors. This is also of interest from a general physics standpoint (as it seemingly contradicts well-established criteria of curvature-driven instabilities). The axial symmetry allows for much simpler and more reliable designs of mirror-based fusion facilities than the well-known quadrupole mirror configurations. In this tutorial, after a summary of classical results, several techniques for achieving MHD stabilization of the axisymmetric mirrors are considered, in particular: (1) employing the favorable field-line curvature in the end tanks; (2) using the line-tying effect; (3) controlling the radial potential distribution; (4) imposing a divertor configuration on the solenoidal magnetic field; and (5) affecting the plasma dynamics by the ponderomotive force. Some illuminative theoretical approaches for understanding axisymmetric mirror stability are described. The applicability of the various stabilization techniques to axisymmetric mirrors as neutron sources, hybrids, and pure-fusion reactors are discussed; and the constraints on the plasma parameters are formulated.

Harmonic Analysis Associated with the Generalized Weinstein Operator

Directory of Open Access Journals (Sweden)

Ahmed Abouelaz

2015-11-01

Full Text Available In this paper we consider a generalized Weinstein operator ∆d,α,n on Rd−1×]0,∞[, which generalizes the Weinstein operator ∆d,α, we define the generalized Weinstein intertwining operator Rα,n which turn out to be transmutation operator between ∆d,α,n and the Laplacian operator ∆d. We build the dual of the generalized Weinstein intertwining operatortRα,n, another hand we prove the formula related Rα,n andtRα,n . We exploit these transmutation operators to develop a new harmonic analysis corresponding to ∆d,α,n.

Coherent states of general time-dependent harmonic oscillator

Indian Academy of Sciences (India)

Abstract. By introducing an invariant operator, we obtain exact wave functions for a general time-dependent quadratic harmonic oscillator. The coherent states, both in x- and p-spaces, are calculated. We confirm that the uncertainty product in coherent state is always larger than Η/2 and is equal to the minimum of the ...

A variational principle for the axisymmetric stability of rotating relativistic stars

International Nuclear Information System (INIS)

Prabhu, Kartik; Wald, Robert M; Schiffrin, Joshua S

2016-01-01

It is well known that all rotating perfect fluid stars in general relativity are unstable to certain non-axisymmetric perturbations via the Chandrasekhar–Friedman–Schutz (CFS) instability. However, the mechanism of the CFS instability requires, in an essential way, the loss of angular momentum by gravitational radiation and, in many instances, it acts on too long a timescale to be physically/astrophysically relevant. It is therefore of interest to examine the stability of rotating, relativistic stars to axisymmetric perturbations, where the CFS instability does not occur. In this paper, we provide a Rayleigh–Ritz-type variational principle for testing the stability of perfect fluid stars to axisymmetric perturbations, which generalizes to axisymmetric perturbations of rotating stars a variational principle given by Chandrasekhar for spherical perturbations of static, spherical stars. Our variational principle provides a lower bound to the rate of exponential growth in the case of instability. The derivation closely parallels the derivation of a recently obtained variational principle for analyzing the axisymmetric stability of black holes. (paper)

Simulations of axisymmetric, Newtonian star clusters - prelude to 2 + 1 general relativistic computations

International Nuclear Information System (INIS)

Shapiro, S.L.; Teukolsky, S.A.

1987-01-01

The dynamical behavior of nonspherical systems in general relativity is analyzed, allowing for rotation and the emission of gravitational waves. An axisymmetric code for solving the Vlasov equation in the Newtonian limit based on a mean-field particle simulation scheme is constructed and tested by reproducing the known evolution of homogeneous spheroids with and without rotation, including the Lin-Kestel-Shu instability. Results for the collapse of homogeneous, nonequilbrium spheroids are described, and stability studies of homogeneous, equilibrium spheroids are summarized. Finally, the code is used to follow the evolution of inhomogeneous, centrally condensed spheroids, and the results are compared with those for homogeneous collapse. 22 references

Nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating embedded in water

Energy Technology Data Exchange (ETDEWEB)

Jiménez, N.; Picó, R. [Instituto de Investigación para la Gestión Integrada de zonas Costeras, Universitat Politècnica de València, Paranimf 1, 46730 Grao de Gandia, València (Spain); Romero-García, V. [LUNAM Université, Université du Maine, LAUM UMR CNRS 6613, Av. O. Messiaen, 72085 Le Mans (France); Garcia-Raffi, L. M. [Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 València (Spain); Staliunas, K. [ICREA, Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Colom, 11, E-08222 Terrassa, Barcelona (Spain)

2015-11-16

We report the nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating immersed in water. In the linear regime, the system presents high focal gain (32 dB), with a narrow beam-width and intense side lobes as it is common in focusing by Fresnel-like lenses. Activating the nonlinearity of the host medium by using high amplitude incident waves, the focusing properties of the lens dramatically change. Theoretical predictions show that the focal gain of the system extraordinary increases in the strongly nonlinear regime (Mach number of 6.1 × 10{sup −4}). Particularly, the harmonic generation is locally activated at the focal spot, and the second harmonic beam is characterized by strongly reduced side-lobes and an excellent beam profile as experiments show in agreement with theory. The results can motivate applications in medical therapy or second harmonic imaging.

Thermal state of the general time-dependent harmonic oscillator

Indian Academy of Sciences (India)

Taking advantage of dynamical invariant operator, we derived quantum mechanical solution of general time-dependent harmonic oscillator. The uncertainty relation of the system is always larger than ħ=2 not only in number but also in the thermal state as expected. We used the diagonal elements of density operator ...

On solution of Maxwell's equations in axisymmetric domains with edges. Part I: Theoretical aspects

International Nuclear Information System (INIS)

Nkemzi, Boniface

2003-10-01

In this paper we present the basic mathematical tools for treating boundary value problems for the Maxwell's equations in three-dimensional axisymmetric domains with reentrant edges by means of partial Fourier analysis. We consider the decomposition of the classical and regularized time-harmonic three-dimensional Maxwell's equations into variational equations in the plane meridian domain of the axisymmetric domain and define suitable weighted Sobolev spaces for their treatment. The trace properties of these spaces on the rotational axis and some properties of the solutions are proved, which are important for further numerical treatment, e.g. by the finite-element method. Particularly, a priori estimates of the solutions of the reduced system are given and the asymptotic behavior of these solutions near reentrant corners of the meridian domain is explicitly described by suitable singular functions. (author)

Harmonic sums, polylogarithms, special numbers, and their generalizations

International Nuclear Information System (INIS)

Ablinger, Jakob

2013-04-01

In these introductory lectures we discuss classes of presently known nested sums, associated iterated integrals, and special constants which hierarchically appear in the evaluation of massless and massive Feynman diagrams at higher loops. These quantities are elements of stuffle and shuffle algebras implying algebraic relations being widely independent of the special quantities considered. They are supplemented by structural relations. The generalizations are given in terms of generalized harmonic sums, (generalized) cyclotomic sums, and sums containing in addition binomial and inverse-binomial weights. To all these quantities iterated integrals and special numbers are associated. We also discuss the analytic continuation of nested sums of different kind to complex values of the external summation bound N.

Harmonic sums, polylogarithms, special numbers, and their generalizations

Energy Technology Data Exchange (ETDEWEB)

Ablinger, Jakob [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

2013-04-15

In these introductory lectures we discuss classes of presently known nested sums, associated iterated integrals, and special constants which hierarchically appear in the evaluation of massless and massive Feynman diagrams at higher loops. These quantities are elements of stuffle and shuffle algebras implying algebraic relations being widely independent of the special quantities considered. They are supplemented by structural relations. The generalizations are given in terms of generalized harmonic sums, (generalized) cyclotomic sums, and sums containing in addition binomial and inverse-binomial weights. To all these quantities iterated integrals and special numbers are associated. We also discuss the analytic continuation of nested sums of different kind to complex values of the external summation bound N.

New construction of coherent states for generalized harmonic oscillators

International Nuclear Information System (INIS)

El Baz, M.; Hassouni, Y.; Madouri, F.

2001-08-01

A dynamical algebra A q , englobing many of the deformed harmonic oscillator algebras is introduced. One of its special cases is extensively developed. A general method for constructing coherent states related to any algebra of the type A q is discussed. The construction following this method is carried out for the special case. (author)

Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillator

Energy Technology Data Exchange (ETDEWEB)

Midya, Bikashkali; Dube, P P; Roychoudhury, Rajkumar, E-mail: bikash.midya@gmail.com, E-mail: ppdube1@gmail.com, E-mail: raj@isical.ac.in [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India)

2011-02-11

The generalized Swanson Hamiltonian H{sub GS}=w(a-tilde a-tilde{sup {dagger}}+1/2)+{alpha}{alpha}-tilde{sup 2}+{beta}a-tilde{sup {dagger}}{sup 2} with a-tilde = A(x) d/dx + B(x) can be transformed into an equivalent Hermitian Hamiltonian with the help of a similarity transformation. It is shown that the equivalent Hermitian Hamiltonian can be further transformed into the harmonic oscillator Hamiltonian so long as [a-ilde,a-tilde{sup {dagger}}]=constant. However, the main objective of this communication is to show that though the commutator of a-tilde and a-tilde{sup {dagger}} is constant, the generalized Swanson Hamiltonian is not necessarily isospectral to the harmonic oscillator. The reason for this anomaly is discussed in the framework of position-dependent mass models by choosing A(x) as the inverse square root of the mass function. (fast track communication)

A Generalized Time-Dependent Harmonic Oscillator at Finite Temperature

International Nuclear Information System (INIS)

Majima, H.; Suzuki, A.

2006-01-01

We show how a generalized time-dependent harmonic oscillator (GTHO) is extended to a finite temperature case by using thermo field dynamics (TFD). We derive the general time-dependent annihilation and creation operators for the system, and obtain the time-dependent quasiparticle annihilation and creation operators for the GTHO by using the temperature-dependent Bogoliubov transformation of TFD. We also obtain the thermal state as a two-mode squeezed vacuum state in the time-dependent case as well as in the time-independent case. The general formula is derived to calculate the thermal expectation value of operators

Effect of electromagnetic waves and higher harmonics in capacitively coupled plasma phenomena

International Nuclear Information System (INIS)

Upadhyay, R R; Sawada, I; Ventzek, P L G; Raja, L L

2013-01-01

High-resolution self-consistent numerical simulation of electromagnetic wave phenomena in an axisymmetric capacitively coupled plasma reactor is reported. A prominent centre-peaked plasma density profile is observed for driving frequencies of 60 MHz and is consistent with observations in the literature and accompanying experimental studies. A power spectrum of the simulated wave electric field reveals the presence of well-resolved high frequency harmonic content up to the 20th harmonic of the excitation frequency; an observation that has also been reported in experiments. Importantly, the simulation results reveal that the occurrence of higher harmonics is strongly correlated with the occurrence of a centre-peaked plasma density profile. (fast track communication)

Theory and computation of general force balance in non-axisymmetric tokamak equilibria

Science.gov (United States)

Park, Jong-Kyu; Logan, Nikolas; Wang, Zhirui; Kim, Kimin; Boozer, Allen; Liu, Yueqiang; Menard, Jonathan

2014-10-01

Non-axisymmetric equilibria in tokamaks can be effectively described by linearized force balance. In addition to the conventional isotropic pressure force, there are three important components that can strongly contribute to the force balance; rotational, anisotropic tensor pressure, and externally given forces, i.e. ∇ --> p + ρv-> . ∇ --> v-> + ∇ --> . Π + f-> = j-> × B-> , especially in, but not limited to, high β and rotating plasmas. Within the assumption of nested flux surfaces, Maxwell equations and energy minimization lead to the modified-generalized Newcomb equation for radial displacements with simple algebraic relations for perpendicular and parallel displacements, including an inhomogeneous term if any of the forces are not explicitly dependent on displacements. The general perturbed equilibrium code (GPEC) solves this force balance consistent with energy and torque given by external perturbations. Local and global behaviors of solutions will be discussed when ∇ --> . Π is solved by the semi-analytic code PENT and will be compared with MARS-K. Any first-principle transport code calculating ∇ --> . Π or f-> , e.g. POCA, can also be incorporated without demanding iterations. This work was supported by DOE Contract DE-AC02-09CH11466.

Stress analysis in a non axisymmetric loaded reactor pressure vessel

International Nuclear Information System (INIS)

Albuquerque, Levi Barcelos; Assis, Gracia Menezes V. de; Miranda, Carlos Alexandre J.; Cruz, Julio Ricardo B.; Mattar Neto, Miguel

1995-01-01

In this work we intend to present the stress analysis of a PWR vessel under postulated concentrated loads. The vessel was modeled with Axisymmetric solid 4 nodes harmonic finite elements with the use of the ANSYS program, version 5.0. The bolts connecting the vessel flanges were modeled with beam elements. Some considerations were made to model the contact between the flanges. The perforated part of the vessel tori spherical head was modeled (with reduced properties due to its holes) to introduce its stiffness and loads but was not within the scope of this work. The loading consists of some usual ones, as pressure, dead weight, bolts preload, seismic load and some postulated ones as concentrated loads, over the vessel, modeled by Fourier Series. The results in the axisymmetric model are taken in terms of linearized stresses, obtained in some circumferential positions and for each position, in some sections along the vessel. Using the ASME Code (Section III, Division 1, Sub-section NB) the stresses are within the allowable limits. In order to draw some conclusions about stress linearization, the membrane plus bending stresses (Pl + Pb) are obtained and compared in some sections, using three different methods. (author)

Freely floating structures trapping time-harmonic water waves (revisited)

OpenAIRE

Kuznetsov, Nikolay; Motygin, Oleg

2014-01-01

We study the coupled small-amplitude motion of the mechanical system consisting of infinitely deep water and a structure immersed in it. The former is bounded above by a free surface, whereas the latter is formed by an arbitrary finite number of surface-piercing bodies floating freely. The mathematical model of time-harmonic motion is a spectral problem in which the frequency of oscillations serves as the spectral parameter. It is proved that there exist axisymmetric structures consisting of ...

Electron cyclotron current drive efficiency in an axisymmetric tokamak

Energy Technology Data Exchange (ETDEWEB)

Gutierrez-Tapia, C.; Beltran-Plata, M. [Instituto Nacional de Investigaciones Nucleares, Dept. de Fisica, Mexico D.F. (Mexico)

2004-07-01

The neoclassical transport theory is applied to calculate electron cyclotron current drive (ECCD) efficiency in an axisymmetric tokamak in the low-collisionality regime. The tokamak ordering is used to obtain a system of equations that describe the dynamics of the plasma where the nonlinear ponderomotive (PM) force due to high-power radio-frequency (RF) waves is included. The PM force is produced around an electron cyclotron resonant surface at a specific poloidal location. The ECCD efficiency is analyzed in the cases of first and second harmonics (for different impinging angles of the RF waves) and it is validated using experimental parameter values from TCV and T-10 tokamaks. The results are in agreement with those obtained by means of Green's function techniques. (authors)

Computer Aided Process Planning for Non-Axisymmetric Deep Drawing Products

Science.gov (United States)

Park, Dong Hwan; Yarlagadda, Prasad K. D. V.

2004-06-01

In general, deep drawing products have various cross-section shapes such as cylindrical, rectangular and non-axisymmetric shapes. The application of the surface area calculation to non-axisymmetric deep drawing process has not been published yet. In this research, a surface area calculation for non-axisymmetric deep drawing products with elliptical shape was constructed for a design of blank shape of deep drawing products by using an AutoLISP function of AutoCAD software. A computer-aided process planning (CAPP) system for rotationally symmetric deep drawing products has been developed. However, the application of the system to non-axisymmetric components has not been reported yet. Thus, the CAPP system for non-axisymmetric deep drawing products with elliptical shape was constructed by using process sequence design. The system developed in this work consists of four modules. The first is recognition of shape module to recognize non-axisymmetric products. The second is a three-dimensional (3-D) modeling module to calculate the surface area for non-axisymmetric products. The third is a blank design module to create an oval-shaped blank with the identical surface area. The forth is a process planning module based on the production rules that play the best important role in an expert system for manufacturing. The production rules are generated and upgraded by interviewing field engineers. Especially, the drawing coefficient, the punch and die radii for elliptical shape products are considered as main design parameters. The suitability of this system was verified by applying to a real deep drawing product. This CAPP system constructed would be very useful to reduce lead-time for manufacturing and improve an accuracy of products.

Axisymmetric Plasma Equilibria in General Relativity

Science.gov (United States)

Elsässer, Klaus

Axisymmetric plasma equilibria near a rotating black hole are considered within the multifluid description. An isothermal two-component plasma with electrons and positrons or ions is determined by four structure functions and the boundary conditions. These structure functions are the Bernoulli function and the toroidal canonical momentum per mass for each species; they remain arbitrary if no gain and loss processes are considered, in close analogy to the free flux functions in ideal magnetohydrodynamics. Several simplifying assumptions allow the reduction of the basic equations to one single scalar equation for the stream function χ of positrons or ions, respectively, playing the rôle of the Grad/Shafranov equation in magnetohydrodynamics; in particular, Maxwell's equations can be solved analytically for a quasineutral plasma when both the charge density and the toroidal electric current density are negligible (in contrast to the Tokamak situation). The basic smallness parameter is the ratio of the skin depth of electrons to the scale length of the metric and fluid quantities, and, in the case of an electron-ion plasma, the mass ratio me/mi. The χ-equation can be solved by standard methods, and simple solutions for a Kerr geometry are available; they show characteristic flow patterns, depending on the structure functions and the boundary conditions.

Efficient molecular density functional theory using generalized spherical harmonics expansions.

Science.gov (United States)

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

2017-09-07

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

Identification of multiple modes of axisymmetric or circularly repetitive structures

International Nuclear Information System (INIS)

Kopff, P.

1983-01-01

The axisymmetric structures, or those composed with circularly repetitive elements, often display multiple modes, which are not easy to separate by modal identification of experimental responses. To be able to solve in situ some problems related to the vibrational behaviour of reactor vessels or other such huge structures, ELECTRICITY DE FRANCE developed a few years ago, experimental capabilities providing heavy harmonic driving forces, and elaborate data acquisition, signal processing and modal identification software, self-contained in an integrated mobile test facility. The modal analysis techniques we have developed with the LABORATOIRE DE MECANIQUE Appliquee of University of BESANCON (FRANCE) were especially suited for identification of multiple or separation of quasi-multiple modes, i.e. very close and strongly coupled resonances. Besides, the curve fitting methods involved, compute the same complex eigen-frequencies for all the vibration pick-ups, for better accuracy of the related eigen-vector components. Moreover, the latest extensions of these algorithms give us the means to deal with non-linear behaviour. The performances of these programs are drawn from some experimental results on axisymmetric or circularly repetitive structure, we tested in our laboratory to validate the computational hypothesis used in models for seismic responses of breeder reactor vessels. (orig.)

Discontinuities in an axisymmetric generalized thermoelastic problem

Directory of Open Access Journals (Sweden)

Moncef Aouadi

2005-06-01

Full Text Available This paper deals with discontinuities analysis in the temperature, displacement, and stress fields of a thick plate whose lower and upper surfaces are traction-free and subjected to a given axisymmetric temperature distribution. The analysis is carried out under three thermoelastic theories. Potential functions together with Laplace and Hankel transform techniques are used to derive the solution in the transformed domain. Exact expressions for the magnitude of discontinuities are computed by using an exact method developed by Boley (1962. It is found that there exist two coupled waves, one of which is elastic and the other is thermal, both propagating with finite speeds with exponential attenuation, and a third which is called shear wave, propagating with constant speed but with no exponential attenuation. The Hankel transforms are inverted analytically. The inversion of the Laplace transforms is carried out using the inversion formula of the transform together with Fourier expansion techniques. Numerical results are presented graphically along with a comparison of the three theories of thermoelasticity.

Elastic-plastic analysis of an axi-symmetric problem by a finite element method

International Nuclear Information System (INIS)

Isozaki, Toshikuni

1984-06-01

Generally speaking, many structures are designed and fabricated on the basis of an axi-symmetric structure. Finite Element Method is the capable method to solve these axi-symmetric problems beyond the elastic limit. As the first step to solve these problems, the computer program for the elastic-plastic analysis of the axi-symmetric problem is composed. The basic program is based upon that described in Zienkiewicz's text book to solve the elastic plane stress problem, taking the plastic stress matrix by Yamada's method into consideration and it is converted to solve the axi-symmetric problem. For the verification of the program, the plane strain problem of a cylindrical tube under internal pressure was solved. The computed results were compared with those shown in ADINA's user's manual. They showed close agreement. (author)

Electromagnetic fields created by a beam in an axisymmetric infinitely thick single-layer resistive pipe: general formulas and low frequency approximations

CERN Document Server

Mounet, Nicolas Frank; CERN. Geneva. ATS Department

2015-01-01

This note provides general and approximate formulas for the electromagnetic fields created by a passing beam in an axisymmetric infinitely thick resistive pipe made of a single homogeneous layer. The full derivations and their resulting approximate expressions at low and intermediate frequencies are given here, as well as the conditions under which those approximations are valid. Beam-coupling impedances are also computed, and examples are shown.

Second harmonic inversion for ultrasound contrast harmonic imaging

Energy Technology Data Exchange (ETDEWEB)

Pasovic, Mirza; Danilouchkine, Mike; Faez, Telli; Van Neer, Paul L M J; Van der Steen, Antonius F W; De Jong, Nico [THORAXCENTER, Department of Biomedical Engineering Ee2302, Erasmus MC, Rotterdam (Netherlands); Cachard, Christian; Basset, Olivier, E-mail: mirza.pasovic@creatis.insa-lyon.fr [CREATIS-LRMN, Universite de Lyon, INSA-Lyon, Universite Lyon 1, Inserm U630, CNRS UMR 5220 (France)

2011-06-07

Ultrasound contrast agents (UCAs) are small micro-bubbles that behave nonlinearly when exposed to an ultrasound wave. This nonlinear behavior can be observed through the generated higher harmonics in a back-scattered echo. In past years several techniques have been proposed to detect or image harmonics produced by UCAs. In these proposed works, the harmonics generated in the medium during the propagation of the ultrasound wave played an important role, since these harmonics compete with the harmonics generated by the micro-bubbles. We present a method for the reduction of the second harmonic generated during nonlinear-propagation-dubbed second harmonic inversion (SHI). A general expression for the suppression signals is also derived. The SHI technique uses two pulses, p' and p'', of the same frequency f{sub 0} and the same amplitude P{sub 0} to cancel out the second harmonic generated by nonlinearities of the medium. Simulations show that the second harmonic is reduced by 40 dB on a large axial range. Experimental SHI B-mode images, from a tissue-mimicking phantom and UCAs, show an improvement in the agent-to-tissue ratio (ATR) of 20 dB compared to standard second harmonic imaging and 13 dB of improvement in harmonic power Doppler.

Second harmonic inversion for ultrasound contrast harmonic imaging

International Nuclear Information System (INIS)

Pasovic, Mirza; Danilouchkine, Mike; Faez, Telli; Van Neer, Paul L M J; Van der Steen, Antonius F W; De Jong, Nico; Cachard, Christian; Basset, Olivier

2011-01-01

Ultrasound contrast agents (UCAs) are small micro-bubbles that behave nonlinearly when exposed to an ultrasound wave. This nonlinear behavior can be observed through the generated higher harmonics in a back-scattered echo. In past years several techniques have been proposed to detect or image harmonics produced by UCAs. In these proposed works, the harmonics generated in the medium during the propagation of the ultrasound wave played an important role, since these harmonics compete with the harmonics generated by the micro-bubbles. We present a method for the reduction of the second harmonic generated during nonlinear-propagation-dubbed second harmonic inversion (SHI). A general expression for the suppression signals is also derived. The SHI technique uses two pulses, p' and p'', of the same frequency f 0 and the same amplitude P 0 to cancel out the second harmonic generated by nonlinearities of the medium. Simulations show that the second harmonic is reduced by 40 dB on a large axial range. Experimental SHI B-mode images, from a tissue-mimicking phantom and UCAs, show an improvement in the agent-to-tissue ratio (ATR) of 20 dB compared to standard second harmonic imaging and 13 dB of improvement in harmonic power Doppler.

Stationary axisymmetric Einstein--Maxwell field equations

International Nuclear Information System (INIS)

Catenacci, R.; Diaz Alonso, J.

1976-01-01

We show the existence of a formal identity between Einstein's and Ernst's stationary axisymmetric gravitational field equations and the Einstein--Maxwell and the Ernst equations for the electrostatic and magnetostatic axisymmetric cases. Our equations are invariant under very simple internal symmetry groups, and one of them appears to be new. We also obtain a method for associating two stationary axisymmetric vacuum solutions with every electrostatic known

Forcing scheme analysis for the axisymmetric lattice Boltzmann method under incompressible limit.

Science.gov (United States)

Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Chen, Jie; Yin, Linmao; Chew, Jia Wei

2017-04-01

Because the standard lattice Boltzmann (LB) method is proposed for Cartesian Navier-Stokes (NS) equations, additional source terms are necessary in the axisymmetric LB method for representing the axisymmetric effects. Therefore, the accuracy and applicability of the axisymmetric LB models depend on the forcing schemes adopted for discretization of the source terms. In this study, three forcing schemes, namely, the trapezium rule based scheme, the direct forcing scheme, and the semi-implicit centered scheme, are analyzed theoretically by investigating their derived macroscopic equations in the diffusive scale. Particularly, the finite difference interpretation of the standard LB method is extended to the LB equations with source terms, and then the accuracy of different forcing schemes is evaluated for the axisymmetric LB method. Theoretical analysis indicates that the discrete lattice effects arising from the direct forcing scheme are part of the truncation error terms and thus would not affect the overall accuracy of the standard LB method with general force term (i.e., only the source terms in the momentum equation are considered), but lead to incorrect macroscopic equations for the axisymmetric LB models. On the other hand, the trapezium rule based scheme and the semi-implicit centered scheme both have the advantage of avoiding the discrete lattice effects and recovering the correct macroscopic equations. Numerical tests applied for validating the theoretical analysis show that both the numerical stability and the accuracy of the axisymmetric LB simulations are affected by the direct forcing scheme, which indicate that forcing schemes free of the discrete lattice effects are necessary for the axisymmetric LB method.

Data harmonization of environmental variables: from simple to general solutions

Science.gov (United States)

Baume, O.

2009-04-01

European data platforms often contain measurements from different regional or national networks. As standards and protocols - e.g. type of measurement devices, sensors or measurement site classification, laboratory analysis and post-processing methods, vary between networks, discontinuities will appear when mapping the target variable at an international scale. Standardisation is generally a costly solution and does not allow classical statistical analysis of previously reported values. As an alternative, harmonization should be envisaged as an integrated step in mapping procedures across borders. In this paper, several harmonization solutions developed under the INTAMAP FP6 project are presented. The INTAMAP FP6 project is currently developing an interoperable framework for real-time automatic mapping of critical environmental variables by extending spatial statistical methods to web-based implementations. Harmonization is often considered as a pre-processing step in statistical data analysis workflow. If biases are assessed with little knowledge about the target variable - in particular when no explanatory covariate is integrated, a harmonization procedure along borders or between regionally overlapping networks may be adopted (Skøien et al., 2007). In this case, bias is estimated as the systematic difference between line or local predictions. On the other hand, when covariates can be included in spatial prediction, the harmonization step is integrated in the whole model estimation procedure, and, therefore, is no longer an independent pre-processing step of the automatic mapping process (Baume et al., 2007). In this case, bias factors become integrated parameters of the geostatistical model and are estimated alongside the other model parameters. The harmonization methods developed within the INTAMAP project were first applied within the field of radiation, where the European Radiological Data Exchange Platform (EURDEP) - http://eurdep.jrc.ec.europa.eu/ - has

The heat flows and harmonic maps from complete manifolds into generalized regular balls

International Nuclear Information System (INIS)

Li Jiayu.

1993-01-01

Let M be a complete Riemannian manifold (compact (with or without boundary) or noncompact). Let N be a complete Riemannian manifold. We generalize the existence result for harmonic maps obtained by Hildebrandt-Kaul-Widman using the heat flow method. (author). 21 refs

Angular momentum in general relativity. 1. Definition and asymptotic behaviour. [axisymmetric space-times, infinity, conservation law, spin coefficient formalism

Energy Technology Data Exchange (ETDEWEB)

Prior, C R [Cambridge Univ. (UK). Dept. of Applied Mathematics and Theoretical Physics

1977-06-27

Angular momentum in axisymmetric space-times is investigated. The conclusions lead to a general definition suitable for all asymptotically-flat spaces which is valid both at infinity and on the event horizon of a black hole. This first paper restricts attention to considerations at infinity. Working in terms of the spin coefficient formalism, the field equations are solved asymptotically at large distances and the definition is evaluated. A conservation law is derived and finally the effect on the angular momentum of a supertranslation of the coordinates is discussed.

Supersonic quasi-axisymmetric vortex breakdown

Science.gov (United States)

Kandil, Osama A.; Kandil, Hamdy A.; Liu, C. H.

1991-01-01

An extensive computational study of supersonic quasi-axisymmetric vortex breakdown in a configured circular duct is presented. The unsteady, compressible, full Navier-Stokes (NS) equations are used. The NS equations are solved for the quasi-axisymmetric flows using an implicit, upwind, flux difference splitting, finite volume scheme. The quasi-axisymmetric solutions are time accurate and are obtained by forcing the components of the flowfield vector to be equal on two axial planes, which are in close proximity of each other. The effect of Reynolds number, for laminar flows, on the evolution and persistence of vortex breakdown, is studied. Finally, the effect of swirl ration at the duct inlet is investigated.

Generalized harmonic, cyclotomic, and binomial sums, their polylogarithms and special numbers

Energy Technology Data Exchange (ETDEWEB)

Ablinger, J.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, J. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

2013-10-15

A survey is given on mathematical structures which emerge in multi-loop Feynman diagrams. These are multiply nested sums, and, associated to them by an inverse Mellin transform, specific iterated integrals. Both classes lead to sets of special numbers. Starting with harmonic sums and polylogarithms we discuss recent extensions of these quantities as cyclotomic, generalized (cyclotomic), and binomially weighted sums, associated iterated integrals and special constants and their relations.

Generalized harmonic, cyclotomic, and binomial sums, their polylogarithms and special numbers

International Nuclear Information System (INIS)

Ablinger, J.; Schneider, C.; Bluemlein, J.

2013-10-01

A survey is given on mathematical structures which emerge in multi-loop Feynman diagrams. These are multiply nested sums, and, associated to them by an inverse Mellin transform, specific iterated integrals. Both classes lead to sets of special numbers. Starting with harmonic sums and polylogarithms we discuss recent extensions of these quantities as cyclotomic, generalized (cyclotomic), and binomially weighted sums, associated iterated integrals and special constants and their relations.

Theoretical analysis of the vibration of axisymmetric liquid bridges of arbitrary shape

Energy Technology Data Exchange (ETDEWEB)

Montanero, J.M. [Departamento de Electronica e Ingenieria Electromecanica, Universidad de Extremadura, 06071 Badajoz (Spain)

2003-01-01

A liquid bridge consists of a mass of liquid sustained by the action of capillary forces between two parallel disks. The dynamics of these liquid columns has been extensively analysed both theoretically and experimentally over the last decades. Many of the studies have focused on the dynamical response of cylindrical liquid bridges subjected to the action of an oscillatory microgravity field due to, for instance, an in-phase vibration of the supporting disks. There have been fewer studies dealing with the vibration of axisymmetric liquid bridges of arbitrary shape. In this paper the dynamics of rotating inviscid axisymmetric liquid bridges is analysed considering the combined effect of residual gravity, the inequality of the disks and the liquid bridge volume. The results are calculated numerically by using the one-dimensional Cosserat model and the full three-dimensional description. The excitation is assumed to be of small amplitude and harmonic, so that the theoretical models are linearized and the analysis is performed in the frequency domain. The details of the numerical methods proposed are discussed. Comparison between the values of the first resonance frequency obtained from both models shows an excellent agreement for long liquid bridges, the discrepancies increasing as the value of the slenderness decreases. (orig.)

Axisymmetric general relativistic hydrodynamics: Long-term evolution of neutron stars and stellar collapse to neutron stars and black holes

International Nuclear Information System (INIS)

Shibata, Masaru

2003-01-01

We report a new implementation for axisymmetric simulation in full general relativity. In this implementation, the Einstein equations are solved using the Nakamura-Shibata formulation with the so-called cartoon method to impose an axisymmetric boundary condition, and the general relativistic hydrodynamic equations are solved using a high-resolution shock-capturing scheme based on an approximate Riemann solver. As tests, we performed the following simulations: (i) long-term evolution of nonrotating and rapidly rotating neutron stars, (ii) long-term evolution of neutron stars of a high-amplitude damping oscillation accompanied with shock formation, (iii) collapse of unstable neutron stars to black holes, and (iv) stellar collapses to neutron stars. Tests (i)-(iii) were carried out with the Γ-law equation of state, and test (iv) with a more realistic parametric equation of state for high-density matter. We found that this new implementation works very well: It is possible to perform the simulations for stable neutron stars for more than 10 dynamical time scales, to capture strong shocks formed at stellar core collapses, and to accurately compute the mass of black holes formed after the collapse and subsequent accretion. In conclusion, this implementation is robust enough to apply to astrophysical problems such as stellar core collapse of massive stars to a neutron star, and black hole, phase transition of a neutron star to a high-density star, and accretion-induced collapse of a neutron star to a black hole. The result for the first simulation of stellar core collapse to a neutron star started from a realistic initial condition is also presented

Numerical simulation of the generation mechanism of axisymmetric supersonic jet screech tones

Science.gov (United States)

Li, X. D.; Gao, J. H.

2005-08-01

In this paper an axisymmetric computational aeroacoustic procedure is developed to investigate the generation mechanism of axisymmetric supersonic jet screech tones. The axisymmetric Navier-Stokes equations and the two equations standard k-ɛ turbulence model modified by Turpin and Troyes ["Validation of a two-equation turbulence model for axisymmetric reacting and non-reaction flows," AIAA Paper No. 2000-3463 (2000)] are solved in the generalized curvilinear coordinate system. A generalized wall function is applied in the nozzle exit wall region. The dispersion-relation-preserving scheme is applied for space discretization. The 2N storage low-dissipation and low-dispersion Runge-Kutta scheme is employed for time integration. Much attention is paid to far-field boundary conditions and turbulence model. The underexpanded axisymmetric supersonic jet screech tones are simulated over the Mach number from 1.05 to 1.2. Numerical results are presented and compared with the experimental data by other researchers. The simulated wavelengths of A0, A1, A2, and B modes and part of simulated amplitudes agree very well with the measurement data by Ponton and Seiner ["The effects of nozzle exit lip thickness on plume resonance," J. Sound Vib. 154, 531 (1992)]. In particular, the phenomena of modes jumping have been captured correctly although the numerical procedure has to be improved to predict the amplitudes of supersonic jet screech tones more accurately. Furthermore, the phenomena of shock motions are analyzed. The predicted splitting and combination of shock cells are similar with the experimental observations of Panda ["Shock oscillation in underexpanded screeching jets," J. Fluid. Mech. 363, 173 (1998)]. Finally, the receptivity process is numerically studied and analyzed. It is shown that the receptivity zone is associated with the initial thin shear layer, and the incoming and reflected sound waves.

Extension of the flow-rate-of-strain tensor formulation of plasma rotation theory to non-axisymmetric tokamaks

Energy Technology Data Exchange (ETDEWEB)

Stacey, W. M. [Georgia Institute of Technology, Atlanta, Georgia 30332 (United States); Bae, C. [National Fusion Research Institute, Daejoen (Korea, Republic of)

2015-06-15

A systematic formalism for the calculation of rotation in non-axisymmetric tokamaks with 3D magnetic fields is described. The Braginskii Ωτ-ordered viscous stress tensor formalism, generalized to accommodate non-axisymmetric 3D magnetic fields in general toroidal flux surface geometry, and the resulting fluid moment equations provide a systematic formalism for the calculation of toroidal and poloidal rotation and radial ion flow in tokamaks in the presence of various non-axisymmetric “neoclassical toroidal viscosity” mechanisms. The relation among rotation velocities, radial ion particle flux, ion orbit loss, and radial electric field is discussed, and the possibility of controlling these quantities by producing externally controllable toroidal and/or poloidal currents in the edge plasma for this purpose is suggested for future investigation.

An Enhanced GINGER Simulation Code with Harmonic Emission and HDF5 IO Capabilities

International Nuclear Information System (INIS)

Fawley, William M.

2006-01-01

GINGER [1] is an axisymmetric, polychromatic (r-z-t) FEL simulation code originally developed in the mid-1980's to model the performance of single-pass amplifiers. Over the past 15 years GINGER's capabilities have been extended to include more complicated configurations such as undulators with drift spaces, dispersive sections, and vacuum chamber wakefield effects; multi-pass oscillators; and multi-stage harmonic cascades. Its coding base has been tuned to permit running effectively on platforms ranging from desktop PC's to massively parallel processors such as the IBM-SP. Recently, we have made significant changes to GINGER by replacing the original predictor-corrector field solver with a new direct implicit algorithm, adding harmonic emission capability, and switching to the HDF5 IO library [2] for output diagnostics. In this paper, we discuss some details regarding these changes and also present simulation results for LCLS SASE emission at λ = 0.15 nm and higher harmonics

Asymptotic properties of axisymmetric Stokes flow of a viscous liquid with intersecting boundaries

International Nuclear Information System (INIS)

Voinov, O.V.

2004-01-01

The general axisymmetric problem on the liquid flow by the low Reynolds number when the boundary surfaces (both of the solid body and free one) are intersecting at the certain angle on the moving line, is considered. The work is aimed at establishing the asymptotic regularities of the behavior of the current function and voltages in the small vicinity of the intersection (contact) line of the boundary surfaces. The asymptotic analysis makes it possible to consider the arbitrary axisymmetric Stokes flow with the intersecting boundaries [ru

Axisymmetric modeling of prestressing tendons in nuclear containment dome

Energy Technology Data Exchange (ETDEWEB)

Jeon, Se-Jin [DAEWOO E and C, Institute of Construction Technology, 60 Songjook-dong, Jangan-gu, Suwon, Kyonggi 440-210 (Korea, Republic of)]. E-mail: jsj@dwconst.co.kr; Chung, Chul-Hun [Department of Civil and Environmental Engineering, Dankook University, San 8, Hannam-dong, Youngsan-gu, Seoul 140-714 (Korea, Republic of)

2005-12-15

Simple axisymmetric modeling of a nuclear containment building has been often employed in practice to estimate structural behavior for the axisymmetric loadings such as internal pressure. In this case, the prestressing tendons placed in the containment dome should be axisymmetrically approximated, since most dome tendons are not arranged in an axisymmetric manner. Some procedures are proposed that can realistically implement the actual three-dimensional tendon stiffness and prestressing effect into the axisymmetric model. Prestressing tendons, which are arranged in two or three ways depending on a containment type, are converted into the equivalent layer to consider the stiffness contribution in meridional and hoop directions. In order to reflect the prestressing effect, the equivalent load method and the initial stress method are devised, respectively, and the corresponding loads or stresses are derived in terms of the axisymmetric model. The proposed schemes are verified through some numerical examples comparing the results of the axisymmetric models to those of the actual three-dimensional model. The examples show that the proper level of the prestressing in the hoop direction of the axisymmetric dome plays an important role in tracing the actual behavior induced by the prestressing. Finally, some correction factors are discussed that can further improve the analysis results.

Axisymmetric modeling of prestressing tendons in nuclear containment dome

International Nuclear Information System (INIS)

Jeon, Se-Jin; Chung, Chul-Hun

2005-01-01

Simple axisymmetric modeling of a nuclear containment building has been often employed in practice to estimate structural behavior for the axisymmetric loadings such as internal pressure. In this case, the prestressing tendons placed in the containment dome should be axisymmetrically approximated, since most dome tendons are not arranged in an axisymmetric manner. Some procedures are proposed that can realistically implement the actual three-dimensional tendon stiffness and prestressing effect into the axisymmetric model. Prestressing tendons, which are arranged in two or three ways depending on a containment type, are converted into the equivalent layer to consider the stiffness contribution in meridional and hoop directions. In order to reflect the prestressing effect, the equivalent load method and the initial stress method are devised, respectively, and the corresponding loads or stresses are derived in terms of the axisymmetric model. The proposed schemes are verified through some numerical examples comparing the results of the axisymmetric models to those of the actual three-dimensional model. The examples show that the proper level of the prestressing in the hoop direction of the axisymmetric dome plays an important role in tracing the actual behavior induced by the prestressing. Finally, some correction factors are discussed that can further improve the analysis results

Exact Solutions to Several Nonlinear Cases of Generalized Grad-Shafranov Equation for Ideal Magnetohydrodynamic Flows in Axisymmetric Domain

Science.gov (United States)

Adem, Abdullahi Rashid; Moawad, Salah M.

2018-05-01

In this paper, the steady-state equations of ideal magnetohydrodynamic incompressible flows in axisymmetric domains are investigated. These flows are governed by a second-order elliptic partial differential equation as a type of generalized Grad-Shafranov equation. The problem of finding exact equilibria to the full governing equations in the presence of incompressible mass flows is considered. Two different types of constraints on position variables are presented to construct exact solution classes for several nonlinear cases of the governing equations. Some of the obtained results are checked for their applications to magnetic confinement plasma. Besides, they cover many previous configurations and include new considerations about the nonlinearity of magnetic flux stream variables.

Numerical Investigation of Pressure Losses in Axisymmetric Sudden Expansion with a Chamfer

Energy Technology Data Exchange (ETDEWEB)

Bae, Youngmin; Kim, Youngin; Kim, Keung Koo [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

2014-05-15

In this paper, the pressure losses through axisymmetric sudden expansions with a chamfer are analyzed by means of numerical simulation, with an emphasis on the effect of the Reynolds number. In this study, we investigate numerically the turbulent flow in axisymmetric sudden expansions having a slight chamfer on the edge. With the aim of investigating the impact of Reynolds number on the expansion losses in a time-averaged sense, an extensive set of simulations is carried out. On the basis of numerical results, we also propose a general correlation to estimate the local loss coefficient in sudden expansions with a chamfer.

Numerical Investigation of Pressure Losses in Axisymmetric Sudden Expansion with a Chamfer

International Nuclear Information System (INIS)

Bae, Youngmin; Kim, Youngin; Kim, Keung Koo

2014-01-01

In this paper, the pressure losses through axisymmetric sudden expansions with a chamfer are analyzed by means of numerical simulation, with an emphasis on the effect of the Reynolds number. In this study, we investigate numerically the turbulent flow in axisymmetric sudden expansions having a slight chamfer on the edge. With the aim of investigating the impact of Reynolds number on the expansion losses in a time-averaged sense, an extensive set of simulations is carried out. On the basis of numerical results, we also propose a general correlation to estimate the local loss coefficient in sudden expansions with a chamfer

Second harmonic generation in generalized Thue-Morse ferroelectric superlattices

International Nuclear Information System (INIS)

Wang Longxiang; Yang Xiangbo; Chen Tongsheng

2009-01-01

In this paper the second harmonic generation (SHG) in generalized Thue-Morse (GTM(m, n)) ferroelectric superlattices is studied. Under the small-signal approximation, the SHG spectra in both real and reciprocal spaces are investigated. It is found that: (1) only when the structure parameters l, l A , and l B are all chosen to be proper, can SHG in GTM(m, n) ferroelectric superlattices be generated; (2) for Family A of generalized Thue-Morse, GTM(m, 1) ferroelectric systems, with the increase of parameter m, the intense peaks of SHG concentrate on the long wavelength 1.4-1.5μm (the fundamental beam (FB) wavelength is within 0.8-1.5μm), but for Family B of generalized Thue-Morse, GTM(1, n) ferroelectric superlattices, with the increase of parameter n, the intense peaks of SHG concentrate on the middle wavelength 1.1-1.2μm; and (3) for GTM(m, 1) ferroelectric superlattices, the bigger the m, the stronger the relative integral intensity (RII) of SHG would be, but for GTM(1, n) ferroelectric systems, the bigger the n, the weaker the RII of SHG would be.

Ideal magnetohydrodynamic stability of axisymmetric mirrors

International Nuclear Information System (INIS)

D'Ippolito, D.A.; Hafizi, B.; Myra, J.R.

1982-01-01

The governing partial differential equation for general mode-number pressure-driven ballooning modes in a long-thin, axisymmetric plasma is derived within the context of ideal magnetohydrodynamics. It is shown that the equation reduces in special limits to the Hain--Luest equation, the high-m diffuse p(psi) ballooning equation, and the low-m sharp-boundary equation. A low-β analytic solution of the full partial differential equation is presented for quasiflute modes in an idealized tandem mirror model to elucidate the relationship of the various limiting cases

Topological fluid mechanics of Axisymmetric Flow

DEFF Research Database (Denmark)

Brøns, Morten

1998-01-01

Topological fluid mechanics in the sense of the present paper is the study and classification of flow patterns close to a critical point. Here we discuss the topology of steady viscous incompressible axisymmetric flows in the vicinity of the axis. Following previous studies the velocity field v...... to the authors knowledge has not been used systematically to high orders in topological fluid mechanics. We compare the general results with experimental and computational results on the Vogel-Ronneberg flow. We show that the topology changes observed when recirculating bubbles on the vortex axis are created...

Axisymmetric MHD stability of sharp-boundary Tokamaks

International Nuclear Information System (INIS)

Rebhan, E.; Salat, A.

1976-09-01

For a sharp-boundary, constant pressure plasma model of axisymmetric equilibria the MHD stability problem of axisymmetric perturbations is solved by analytic reduction to a one-dimensional problem on the boundary and subsequent numerical treatment, using the energy principle. The stability boundaries are determined for arbitrary aspect ratio, arbitrary βsub(p) and elliptical, triangular and rectangular plasma cross-sections, wall stabilization not being taken into account. It is found that the axisymmetric stability strongly depends on the plasma shape and is almost independent of the safety factor q. (orig.) [de

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

International Nuclear Information System (INIS)

Matausek, M.

1983-01-01

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

Numerical artifacts in the Generalized Porous Medium Equation: Why harmonic averaging itself is not to blame

Science.gov (United States)

Maddix, Danielle C.; Sampaio, Luiz; Gerritsen, Margot

2018-05-01

The degenerate parabolic Generalized Porous Medium Equation (GPME) poses numerical challenges due to self-sharpening and its sharp corner solutions. For these problems, we show results for two subclasses of the GPME with differentiable k (p) with respect to p, namely the Porous Medium Equation (PME) and the superslow diffusion equation. Spurious temporal oscillations, and nonphysical locking and lagging have been reported in the literature. These issues have been attributed to harmonic averaging of the coefficient k (p) for small p, and arithmetic averaging has been suggested as an alternative. We show that harmonic averaging is not solely responsible and that an improved discretization can mitigate these issues. Here, we investigate the causes of these numerical artifacts using modified equation analysis. The modified equation framework can be used for any type of discretization. We show results for the second order finite volume method. The observed problems with harmonic averaging can be traced to two leading error terms in its modified equation. This is also illustrated numerically through a Modified Harmonic Method (MHM) that can locally modify the critical terms to remove the aforementioned numerical artifacts.

Harmonic supergraphs

International Nuclear Information System (INIS)

Galperin, A.; Ivanov, E.; Ogievetsky, V.; Sokatchev, E.

1985-01-01

This paper completes a descrption of the quantization procedure in the harmonic superspace approach. The Feynman rules for N=2 matter and Yang-Mills theories are derived and the various examples of harmonic supergraph calculations are given. Calculations appear to be not more difficult than those in the N=1 case. The integration over harmonic variables does not lead to any troubles, a non-locality in these disappears on-shell. The important property is that the quantum corrections are always writen as integrals over the full harmonic superspace even though the initial action is an integral over the analytic subspace. As a by-product our results imply a very simple proof of finiteness of a wide class of the N=4, d=2 non-linear Σ-models. The most general self-couplings of hypermultiplets including those with broken SU(2) are considered.The duality relations among the N=2 linear multiplet and both kinds of hypermultiplet are established

Axi-symmetric generalized thermoelastic diffusion problem with two-temperature and initial stress under fractional order heat conduction

International Nuclear Information System (INIS)

Deswal, Sunita; Kalkal, Kapil Kumar; Sheoran, Sandeep Singh

2016-01-01

A mathematical model of fractional order two-temperature generalized thermoelasticity with diffusion and initial stress is proposed to analyze the transient wave phenomenon in an infinite thermoelastic half-space. The governing equations are derived in cylindrical coordinates for a two dimensional axi-symmetric problem. The analytical solution is procured by employing the Laplace and Hankel transforms for time and space variables respectively. The solutions are investigated in detail for a time dependent heat source. By using numerical inversion method of integral transforms, we obtain the solutions for displacement, stress, temperature and diffusion fields in physical domain. Computations are carried out for copper material and displayed graphically. The effect of fractional order parameter, two-temperature parameter, diffusion, initial stress and time on the different thermoelastic and diffusion fields is analyzed on the basis of analytical and numerical results. Some special cases have also been deduced from the present investigation.

A multi-harmonic generalized energy balance method for studying autonomous oscillations of nonlinear conservative systems

Science.gov (United States)

Balaji, Nidish Narayanaa; Krishna, I. R. Praveen; Padmanabhan, C.

2018-05-01

The Harmonic Balance Method (HBM) is a frequency-domain based approximation approach used for obtaining the steady state periodic behavior of forced dynamical systems. Intrinsically these systems are non-autonomous and the method offers many computational advantages over time-domain methods when the fundamental period of oscillation is known (generally fixed as the forcing period itself or a corresponding sub-harmonic if such behavior is expected). In the current study, a modified approach, based on He's Energy Balance Method (EBM), is applied to obtain the periodic solutions of conservative systems. It is shown that by this approach, periodic solutions of conservative systems on iso-energy manifolds in the phase space can be obtained very efficiently. The energy level provides the additional constraint on the HBM formulation, which enables the determination of the period of the solutions. The method is applied to the linear harmonic oscillator, a couple of nonlinear oscillators, the elastic pendulum and the Henon-Heiles system. The approach is used to trace the bifurcations of the periodic solutions of the last two, being 2 degree-of-freedom systems demonstrating very rich dynamical behavior. In the process, the advantages offered by the current formulation of the energy balance is brought out. A harmonic perturbation approach is used to evaluate the stability of the solutions for the bifurcation diagram.

Fast digital envelope detector based on generalized harmonic wavelet transform for BOTDR performance improvement

International Nuclear Information System (INIS)

Yang, Wei; Yang, Yuanhong; Yang, Mingwei

2014-01-01

We propose a fast digital envelope detector (DED) based on the generalized harmonic wavelet transform to improve the performance of coherent heterodyne Brillouin optical time domain reflectometry. The proposed DED can obtain undistorted envelopes due to the zero phase-shift ideal bandpass filter (BPF) characteristics of the generalized harmonic wavelet (GHW). Its envelope average ability benefits from the passband designing flexibility of the GHW, and its demodulation speed can be accelerated by using a fast algorithm that only analyses signals of interest within the passband of the GHW with reduced computational complexity. The feasibility and advantage of the proposed DED are verified by simulations and experiments. With an optimized bandwidth, Brillouin frequency shift accuracy improvements of 19.4% and 11.14%, as well as envelope demodulation speed increases of 39.1% and 24.9%, are experimentally attained by the proposed DED over Hilbert transform (HT) and Morlet wavelet transform (MWT) based DEDs, respectively. Spatial resolution by the proposed DED is undegraded, which is identical to the undegraded value by HT-DED with an allpass filter characteristic and better than the degraded value by MWT-DED with a Gaussian BPF characteristic. (paper)

Global stability analysis of axisymmetric boundary layer over a circular cylinder

Science.gov (United States)

Bhoraniya, Ramesh; Vinod, Narayanan

2018-05-01

This paper presents a linear global stability analysis of the incompressible axisymmetric boundary layer on a circular cylinder. The base flow is parallel to the axis of the cylinder at inflow boundary. The pressure gradient is zero in the streamwise direction. The base flow velocity profile is fully non-parallel and non-similar in nature. The boundary layer grows continuously in the spatial directions. Linearized Navier-Stokes (LNS) equations are derived for the disturbance flow quantities in the cylindrical polar coordinates. The LNS equations along with homogeneous boundary conditions forms a generalized eigenvalues problem. Since the base flow is axisymmetric, the disturbances are periodic in azimuthal direction. Chebyshev spectral collocation method and Arnoldi's iterative algorithm is used for the solution of the general eigenvalues problem. The global temporal modes are computed for the range of Reynolds numbers and different azimuthal wave numbers. The largest imaginary part of the computed eigenmodes is negative, and hence, the flow is temporally stable. The spatial structure of the eigenmodes shows that the disturbance amplitudes grow in size and magnitude while they are moving towards downstream. The global modes of axisymmetric boundary layer are more stable than that of 2D flat-plate boundary layer at low Reynolds number. However, at higher Reynolds number they approach 2D flat-plate boundary layer. Thus, the damping effect of transverse curvature is significant at low Reynolds number. The wave-like nature of the disturbance amplitudes is found in the streamwise direction for the least stable eigenmodes.

On spherical harmonic representation of transient waves in dispersive media

International Nuclear Information System (INIS)

Borisov, Victor V

2003-01-01

Axisymmetric transient solutions to the inhomogeneous telegraph equation are constructed in terms of spherical harmonics. Explicit solutions of the initial-value problem are derived in the spacetime domain by means of the Smirnov method of incomplete separation of variables and the Riemann formula. The corresponding Riemann function is constructed with the help of the Olevsky theorem. Solutions for some source distributions on a sphere expanding with a velocity greater than the wavefront velocity are obtained. This allows an analogous solution in the case of a circle belonging to a sphere expanding with the wavefront velocity to be written at once. Application of the scalar solution to a description of electromagnetic waves is also discussed

Streamline topology of axisymmetric flows

DEFF Research Database (Denmark)

Brøns, Morten

Topological fluid mechanics in the sense of the present paper is the study and classification of flow patterns close to a critical point. Here we discuss the topology of steady viscous incompressible axisymmetric flows in the vicinity of the axis. Following previous studies the velocity field $v...... to the authors knowledge has not been used systematically to high orders in topological fluid mechanics. We compare the general results with experimental and computational results on the Vogel-Ronneberg flow. We show that the topology changes observed when recirculating bubbles on the vortex axis are created...... and interact follow the topological classification and that the complete set of patterns found is contained in a codimension-4 unfolding of the most simple singular configuration....

Non-Axisymmetric Shaping of Tokamaks Preserving Quasi-Axisymmetry

Energy Technology Data Exchange (ETDEWEB)

Long-Poe Ku and Allen H. Boozer

2009-06-05

If quasi-axisymmetry is preserved, non-axisymmetric shaping can be used to design tokamaks that do not require current drive, are resilient to disruptions, and have robust plasma stability without feedback. Suggestions for addressing the critical issues of tokamaks can only be validated when presented with sufficient specificity that validating experiments can be designed. The purpose of this paper is provide that specificity for non-axisymmetric shaping. To our knowledge, no other suggestions for the solution of a number of tokamak issues, such as disruptions, have reached this level of specificity. Sequences of three-field-period quasi-axisymmetric plasmas are studied. These sequences address the questions: (1) What can be achieved at various levels of non-axisymmetric shaping? (2) What simplifications to the coils can be achieved by going to a larger aspect ratio? (3) What range of shaping can be achieved in a single experimental facility? The sequences of plasmas found in this study provide a set of interesting and potentially important configurations.

Development of axisymmetric lattice Boltzmann flux solver for complex multiphase flows

Science.gov (United States)

Wang, Yan; Shu, Chang; Yang, Li-Ming; Yuan, Hai-Zhuan

2018-05-01

This paper presents an axisymmetric lattice Boltzmann flux solver (LBFS) for simulating axisymmetric multiphase flows. In the solver, the two-dimensional (2D) multiphase LBFS is applied to reconstruct macroscopic fluxes excluding axisymmetric effects. Source terms accounting for axisymmetric effects are introduced directly into the governing equations. As compared to conventional axisymmetric multiphase lattice Boltzmann (LB) method, the present solver has the kinetic feature for flux evaluation and avoids complex derivations of external forcing terms. In addition, the present solver also saves considerable computational efforts in comparison with three-dimensional (3D) computations. The capability of the proposed solver in simulating complex multiphase flows is demonstrated by studying single bubble rising in a circular tube. The obtained results compare well with the published data.

Multitude scaling laws in axisymmetric turbulent wake

Science.gov (United States)

Layek, G. C.; Sunita

2018-03-01

We establish theoretically multitude scaling laws of a self-similar (statistical) axisymmetric turbulent wake. At infinite Reynolds number limit, the flow evolves as general power law and a new exponential law of streamwise distance, consistent with the criterion of equilibrium similarity hypothesis. We found power law scalings for components of the homogeneous dissipation rate (ɛ) obeying the non-Richardson-Kolmogorov cascade as ɛu˜ku3 /2/(l R elm ) , ɛv˜kv3 /2/l , kv˜ku/R el2 m, 0 stress, l is the local length scale, and Rel is the Reynolds number. The Richardson-Kolmogorov cascade corresponds to m = 0. For m ≈ 1, the power law agrees with non-equilibrium scaling laws observed in recent experiments of the axisymmetric wake. On the contrary, the exponential scaling law follows the above dissipation law with different regions of existence for power index m = 3. At finite Reynolds number with kinematic viscosity ν, scalings obey the dissipation laws ɛu ˜ νku/l2 and ɛv ˜ νkv/l2 with kv˜ku/R eln. The value of n is preferably 0 and 2. Different possibilities of scaling laws and symmetry breaking process are discussed at length.

Superstrings and harmonic superspace

International Nuclear Information System (INIS)

Kallosh, R.E.; AN SSSR, Moscow. Fizicheskij Inst.)

1987-01-01

The paper on superstrings and harmonic superspace is a contribution to the book dedicated to E.S. Fradkin on his sixtieth birthday. The purpose of the paper is to propose a description of N = 2,3 superspace which could be used for the investigation of the effective d = 10 harmonic superspace corresponding to the heterotic superstring. A description is given of the structure of semi-simple Lie algebras in the Cartan-Weyl basis, as well as the general properties of the even, compact part of harmonic superspace. The main properties of the four-dimensional N = 2 SYM theory are discussed, along with the N = 3, d = 4 super Yang-Mills theory. Finally the relation between the harmonic superspace and the heterotic E 8 x E 8 superstring is examined. (U.K.)

Marginal Stability Boundaries for Infinite-n Ballooning Modes in a Quasi-axisymmetric Stellarator

International Nuclear Information System (INIS)

Hudson, S.R.; Hegna, C.C.

2003-01-01

A method for computing the ideal-MHD stability boundaries in three-dimensional equilibria is employed. Following Hegna and Nakajima [Phys. Plasmas 5 (May 1998) 1336], a two-dimensional family of equilibria are constructed by perturbing the pressure and rotational-transform profiles in the vicinity of a flux surface for a given stellarator equilibrium. The perturbations are constrained to preserve the magnetohydrodynamic equilibrium condition. For each perturbed equilibrium, the infinite-n ballooning stability is calculated. Marginal stability diagrams are thus constructed that are analogous to (s; a) diagrams for axisymmetric configurations. A quasi-axisymmetric stellarator is considered. Calculations of stability boundaries generally show regions of instability can occur for either sign of the average magnetic shear. Additionally, regions of second-stability are present

Non-axisymmetric line-driven disc winds - I. Disc perturbations

Science.gov (United States)

Dyda, Sergei; Proga, Daniel

2018-04-01

We study mass outflows driven from accretion discs by radiation pressure due to spectral lines. To investigate non-axisymmetric effects, we use the ATHENA++ code and develop a new module to account for radiation pressure driving. In 2D, our new simulations are consistent with previous 2D axisymmetric solutions by Proga et al., who used the ZEUS 2D code. Specifically, we find that the disc winds are time dependent, characterized by a dense stream confined to ˜45° relative to the disc mid-plane and bounded on the polar side by a less dense, fast stream. In 3D, we introduce a vertical, ϕ-dependent, subsonic velocity perturbation in the disc mid-plane. The perturbation does not change the overall character of the solution but global outflow properties such as the mass, momentum, and kinetic energy fluxes are altered by up to 100 per cent. Non-axisymmetric density structures develop and persist mainly at the base of the wind. They are relatively small, and their densities can be a few times higher than the azimuthal average. The structure of the non-axisymmetric and axisymmetric solutions differ also in other ways. Perhaps most importantly from the observational point of view are the differences in the so-called clumping factors, that serve as a proxy for emissivity due to two body processes. In particular, the spatially averaged clumping factor over the entire fast stream, while it is of a comparable value in both solutions, it varies about 10 times faster in the non-axisymmetric case.

Computation of compressible quasi-axisymmetric slender vortex flow and breakdown

Science.gov (United States)

Kandil, Osama A.; Kandil, Hamdy A.

1991-01-01

The unsteady, compressible Navier-Stokes equations are used to compute and analyze compressible quasi-axisymmetric isolated vortices. The Navier-Stokes equations are solved using an implicit, upwind, flux difference splitting finite volume scheme. The developed three dimensional solver was verified by comparing its solution profiles with those of a slender, quasi-axisymmetric vortex solver for a subsonic, quasi-axisymmetric vortex in an unbounded domain. The Navier-Stokes solver is then used to solve for a supersonic, quasi-axisymmetric vortex flow in a configured circular duct. Steady and unsteady vortex-shock interactions and breakdown were captured. The problem was also calculated using the Euler solver of the same code; the results were compared with those of the Navier-Stokes solver. The effect of the initial swirl was investigated.

Two examples of escaping harmonic maps

International Nuclear Information System (INIS)

Pereira do Valle, A.; Verjovsky, A.

1988-12-01

This paper is part of a study on the existence of special harmonic maps on complete non-compact Riemannian manifolds. We generalize the notion of escaping geodesic and prove some results on the existence of escaping harmonic maps. 11 refs, 6 figs

An approach for spherical harmonic analysis of non-smooth data

Science.gov (United States)

Wang, Hansheng; Wu, Patrick; Wang, Zhiyong

2006-12-01

A method is proposed to evaluate the spherical harmonic coefficients of a global or regional, non-smooth, observable dataset sampled on an equiangular grid. The method is based on an integration strategy using new recursion relations. Because a bilinear function is used to interpolate points within the grid cells, this method is suitable for non-smooth data; the slope of the data may be piecewise continuous, with extreme changes at the boundaries. In order to validate the method, the coefficients of an axisymmetric model are computed, and compared with the derived analytical expressions. Numerical results show that this method is indeed reasonable for non-smooth models, and that the maximum degree for spherical harmonic analysis should be empirically determined by several factors including the model resolution and the degree of non-smoothness in the dataset, and it can be several times larger than the total number of latitudinal grid points. It is also shown that this method is appropriate for the approximate analysis of a smooth dataset. Moreover, this paper provides the program flowchart and an internet address where the FORTRAN code with program specifications are made available.

Nonstandard conserved Hamiltonian structures in dissipative/damped systems: Nonlinear generalizations of damped harmonic oscillator

International Nuclear Information System (INIS)

Pradeep, R. Gladwin; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.

2009-01-01

In this paper we point out the existence of a remarkable nonlocal transformation between the damped harmonic oscillator and a modified Emden-type nonlinear oscillator equation with linear forcing, xe+αxx+βx 3 +γx=0, which preserves the form of the time independent integral, conservative Hamiltonian, and the equation of motion. Generalizing this transformation we prove the existence of nonstandard conservative Hamiltonian structure for a general class of damped nonlinear oscillators including Lienard-type systems. Further, using the above Hamiltonian structure for a specific example, namely, the generalized modified Emden equation xe+αx q x+βx 2q+1 =0, where α, β, and q are arbitrary parameters, the general solution is obtained through appropriate canonical transformations. We also present the conservative Hamiltonian structure of the damped Mathews-Lakshmanan oscillator equation. The associated Lagrangian description for all the above systems is also briefly discussed.

Harmonic mappings into manifolds with boundary

International Nuclear Information System (INIS)

Chen Yunmei; Musina, R.

1989-08-01

In this paper we deal with harmonic maps from a compact Riemannian manifold into a manifold with boundary. In this case, a weak harmonic map is by definition a solution to a differential inclusion. In the first part of the paper we investigate the general properties of weak harmonic maps, which can be seen as solutions to a system of elliptic differential equations. In the second part we concentrate our attention on the heat flow method for harmonic maps. The result we achieve in this context extends a result by Chen and Struwe. (author). 21 refs

The spherical harmonics method, 1 (general development of the theory)

International Nuclear Information System (INIS)

Mark, C.

1957-02-01

A method of obtaining approximate solutions of the transport equation is presented in a form applicable in principle to any geometry. The approximation will give good results in cases where the angular distribution is not very anisotropic. The basis of the approximation is to expand the density per unit solid angle Ψ(→/r, →/Ω) in spherical harmonic tensors formed from →/Ω the unit vector in the direction of velocity, and to break off the expansion. A differential equation whose degree increases with the order of the approximation is obtained for the total density Ψ (o) (r). This equation has the form where the numbers ν i depend on the order of the approximation and on the value of the parameter a of the medium, but not at all on the geometry. When the equation for the total density is an ordinary equation, we simulate the physical condition of continuity of Ψ(→/r, →/Ω) at a boundary in a multi-medium problem by requiring that the spherical harmonic moments of Ψ(→/r, →/Ω) which we retain be continuous; and this determines the constants in the solution for Ψ (o) (→/r. The form of the solution for the total density and the necessary moments in an approximation of general order is given explicitly for plane and spherical symmetry; and for cylindrical symmetry the solution is given for two low-order approximations. In a later report (CRT-338, Revised) the application of the method to several problems involving plane and spherical symmetry will be discussed in detail and the results of a number of examples already worked will also be given. (author)

Stellar dynamics around a massive black hole - III. Resonant relaxation of razor-thin axisymmetric discs

Science.gov (United States)

Sridhar, S.; Touma, Jihad R.

2017-02-01

We study the resonant relaxation (RR) of an axisymmetric, low-mass (or Keplerian) stellar disc orbiting a more massive black hole (MBH). Our recent work on the general kinetic theory of RR is simplified in the standard manner by the neglect of 'gravitational polarization' and applied to a razor-thin axisymmetric disc. The wake of a stellar orbit is expressed in terms of the angular momenta exchanged with other orbits, and used to derive a kinetic equation for RR under the combined actions of self-gravity, 1 PN and 1.5 PN general relativistic effects of the MBH and an arbitrary external axisymmetric potential. This is a Fokker-Planck equation for the stellar distribution function (DF), wherein the diffusion coefficients are given self-consistently in terms of contributions from apsidal resonances between pairs of stellar orbits. The physical kinetics is studied for the two main cases of interest. (1) 'Lossless' discs in which the MBH is not a sink of stars, and disc mass, angular momentum and energy are conserved: we prove that general H-functions can increase or decrease during RR, but the Boltzmann entropy is (essentially) unique in being a non-decreasing function of time. Therefore, secular thermal equilibria are maximum entropy states, with DFs of the Boltzmann form; the two-ring correlation function at equilibrium is computed. (2) Discs that lose stars to the MBH through an 'empty loss cone': we derive expressions for the MBH feeding rates of mass, angular momentum and energy in terms of the diffusive fluxes at the loss-cone boundaries.

Numerical computation of gravitational field of general extended body and its application to rotation curve study of galaxies

Science.gov (United States)

Fukushima, Toshio

2017-06-01

Reviewed are recently developed methods of the numerical integration of the gravitational field of general two- or three-dimensional bodies with arbitrary shape and mass density distribution: (i) an axisymmetric infinitely-thin disc (Fukushima 2016a, MNRAS, 456, 3702), (ii) a general infinitely-thin plate (Fukushima 2016b, MNRAS, 459, 3825), (iii) a plane-symmetric and axisymmetric ring-like object (Fukushima 2016c, AJ, 152, 35), (iv) an axisymmetric thick disc (Fukushima 2016d, MNRAS, 462, 2138), and (v) a general three-dimensional body (Fukushima 2016e, MNRAS, 463, 1500). The key techniques employed are (a) the split quadrature method using the double exponential rule (Takahashi and Mori, 1973, Numer. Math., 21, 206), (b) the precise and fast computation of complete elliptic integrals (Fukushima 2015, J. Comp. Appl. Math., 282, 71), (c) Ridder's algorithm of numerical differentiaion (Ridder 1982, Adv. Eng. Softw., 4, 75), (d) the recursive computation of the zonal toroidal harmonics, and (e) the integration variable transformation to the local spherical polar coordinates. These devices succesfully regularize the Newton kernel in the integrands so as to provide accurate integral values. For example, the general 3D potential is regularly integrated as Φ (\\vec{x}) = - G \\int_0^∞ ( \\int_{-1}^1 ( \\int_0^{2π} ρ (\\vec{x}+\\vec{q}) dψ ) dγ ) q dq, where \\vec{q} = q (√{1-γ^2} cos ψ, √{1-γ^2} sin ψ, γ), is the relative position vector referred to \\vec{x}, the position vector at which the potential is evaluated. As a result, the new methods can compute the potential and acceleration vector very accurately. In fact, the axisymmetric integration reproduces the Miyamoto-Nagai potential with 14 correct digits. The developed methods are applied to the gravitational field study of galaxies and protoplanetary discs. Among them, the investigation on the rotation curve of M33 supports a disc-like structure of the dark matter with a double-power-law surface

Quantum harmonic Brownian motion in a general environment: A modified phase-space approach

International Nuclear Information System (INIS)

Yeh, L.

1993-01-01

After extensive investigations over three decades, the linear-coupling model and its equivalents have become the standard microscopic models for quantum harmonic Brownian motion, in which a harmonically bound Brownian particle is coupled to a quantum dissipative heat bath of general type modeled by infinitely many harmonic oscillators. The dynamics of these models have been studied by many authors using the quantum Langevin equation, the path-integral approach, quasi-probability distribution functions (e.g., the Wigner function), etc. However, the quantum Langevin equation is only applicable to some special problems, while other approaches all involve complicated calculations due to the inevitable reduction (i.e., contraction) operation for ignoring/eliminating the degrees of freedom of the heat bath. In this dissertation, the author proposes an improved methodology via a modified phase-space approach which employs the characteristic function (the symplectic Fourier transform of the Wigner function) as the representative of the density operator. This representative is claimed to be the most natural one for performing the reduction, not only because of its simplicity but also because of its manifestation of geometric meaning. Accordingly, it is particularly convenient for studying the time evolution of the Brownian particle with an arbitrary initial state. The power of this characteristic function is illuminated through a detailed study of several physically interesting problems, including the environment-induced damping of quantum interference, the exact quantum Fokker-Planck equations, and the relaxation of non-factorizable initial states. All derivations and calculations axe shown to be much simplified in comparison with other approaches. In addition to dynamical problems, a novel derivation of the fluctuation-dissipation theorem which is valid for all quantum linear systems is presented

Tides and tidal harmonics at Umbharat, Gujarat

Digital Repository Service at National Institute of Oceanography (India)

Suryanarayana, A.; Swamy, G.N.

A part of the data on tides recorded at Machiwada near Umbharat, Gulf of Cambay during April 1978 was subjected to harmonic analysis following the Admiralty procedure. The general tidal characteristics and the value of four major harmonic...

Boundary element method for internal axisymmetric flow

Directory of Open Access Journals (Sweden)

Gokhman Alexander

1999-01-01

Full Text Available We present an accurate fast method for the computation of potential internal axisymmetric flow based on the boundary element technique. We prove that the computed velocity field asymptotically satisfies reasonable boundary conditions at infinity for various types of inlet/exit. Computation of internal axisymmetric potential flow is an essential ingredient in the three-dimensional problem of computation of velocity fields in turbomachines. We include the results of a practical application of the method to the computation of flow in turbomachines of Kaplan and Francis types.

Radiating axisymmetric metric

International Nuclear Information System (INIS)

Patel, M.D.

1978-01-01

The Einstein's field equations for an enveloping radiating zone surrounding rotating axisymmetric collapsing source are studied. The solution has singularity along the axis of rotation. It is proved that on null hyper surface u = 0, the solution of the field equation for the radiating zone match with solution of axially symmetric vacuum field equations obtained by the author. Landau Lifshitz complex is used to obtain conserved total mass. (author)

Relativistic equations for axisymmetric gravitational collapse with escaping neutrinos

International Nuclear Information System (INIS)

Patel, M.D.

1979-01-01

Einstein's field equations for the dynamics of a self-gravitating axially symmetric source of a perfect fluid, presented by Chandrasekhar and Friedman (1964), are modified to allow emission of neutrinos. The boundary conditions at the outer surface of the radiating axisymmetric source are obtained by matching to an exterior solution of an axisymmetric rotating, radiating core. (auth.)

Axisymmetric multiphase lattice Boltzmann method for generic equations of state

NARCIS (Netherlands)

Reijers, S.A.; Gelderblom, H.; Toschi, F.

2016-01-01

We present an axisymmetric lattice Boltzmann model based on the Kupershtokh et al. multiphase model that is capable of solving liquid–gas density ratios up to 103. Appropriate source terms are added to the lattice Boltzmann evolution equation to fully recover the axisymmetric multiphase conservation

Explaining the harmonic sequence paradox.

Science.gov (United States)

Schmidt, Ulrich; Zimper, Alexander

2012-05-01

According to the harmonic sequence paradox, an expected utility decision maker's willingness to pay for a gamble whose expected payoffs evolve according to the harmonic series is finite if and only if his marginal utility of additional income becomes zero for rather low payoff levels. Since the assumption of zero marginal utility is implausible for finite payoff levels, expected utility theory - as well as its standard generalizations such as cumulative prospect theory - are apparently unable to explain a finite willingness to pay. This paper presents first an experimental study of the harmonic sequence paradox. Additionally, it demonstrates that the theoretical argument of the harmonic sequence paradox only applies to time-patient decision makers, whereas the paradox is easily avoided if time-impatience is introduced. ©2011 The British Psychological Society.

The spherical harmonics method, 1 (general development of the theory)

Energy Technology Data Exchange (ETDEWEB)

Mark, C

1957-02-15

A method of obtaining approximate solutions of the transport equation is presented in a form applicable in principle to any geometry. The approximation will give good results in cases where the angular distribution is not very anisotropic. The basis of the approximation is to expand the density per unit solid angle {Psi}({yields}/r, {yields}/{Omega}) in spherical harmonic tensors formed from {yields}/{Omega} the unit vector in the direction of velocity, and to break off the expansion. A differential equation whose degree increases with the order of the approximation is obtained for the total density {Psi}{sup (o)}(r). This equation has the form where the numbers {nu}{sub i} depend on the order of the approximation and on the value of the parameter a of the medium, but not at all on the geometry. When the equation for the total density is an ordinary equation, we simulate the physical condition of continuity of {Psi}({yields}/r, {yields}/{Omega}) at a boundary in a multi-medium problem by requiring that the spherical harmonic moments of {Psi}({yields}/r, {yields}/{Omega}) which we retain be continuous; and this determines the constants in the solution for {Psi}{sup (o)}({yields}/r. The form of the solution for the total density and the necessary moments in an approximation of general order is given explicitly for plane and spherical symmetry; and for cylindrical symmetry the solution is given for two low-order approximations. In a later report (CRT-338, Revised) the application of the method to several problems involving plane and spherical symmetry will be discussed in detail and the results of a number of examples already worked will also be given. (author)

Axisymmetric ideal magnetohydrodynamic equilibria with incompressible flows

International Nuclear Information System (INIS)

Tasso, H.; Throumoulopoulos, G.N.

1997-12-01

It is shown that the ideal MHD equilibrium states of an axisymmetric plasma with incompressible flows are governed by an elliptic partial differential equation for the poloidal magnetic flux function ψ containing five surface quantities along with a relation for the pressure. Exact equilibria are constructed including those with non vanishing poloidal and toroidal flows and differentially varying radial electric fields. Unlike the case in cylindrical incompressible equilibria with isothermal magnetic surfaces which should have necessarily circular cross sections [G. N. Throumoulopoulos and H. Tasso, Phys. Plasmas 4, 1492 (1997)], no restriction appears on the shapes of the magnetic surfaces in the corresponding axisymmetric equilibria. The latter equilibria satisfy a set of six ordinary differential equations which for flows parallel to the magnetic field B can be solved semianalytically. In addition, it is proved the non existence of incompressible axisymmetric equilibria with (a) purely poloidal flows and (b) non-parallel flows with isothermal magnetic surfaces and vertical stroke B vertical stroke = vertical stroke B vertical stroke (ψ) (omnigenous equilibria). (orig.)

Efficiency of the generation of impulsion by cyclotron waves currents of the electrons in an Axisymmetric Tokamak

International Nuclear Information System (INIS)

Gutierrez T, C.; Beltran P, M.

2004-01-01

The neoclassical theory of transport is used to calculate the current efficiency of electronic cyclotron impulsion (ECCD) in an axisymmetric tokamak in the few collisions regime. The standard parameter of the tokamak is used to obtain a system of equations that describe the hydrodynamic of the plasma, where the ponderomotive force (PM) due to high power radio frequency waves is taken in account. The PM force is produced in the proximity of electron cyclotron resonance surface in a specific poloidal localization. The efficiency ECCD is analyzed in the cases of first and second harmonic (for different angles of injection of radio frequency waves) and it is validated using the experimental values of the TCV and T-10 tokamaks. The results are according to those obtained by means of the techniques of the Green functions. (Author)

Experimental investigation about the effect of non-axisymmetric wake impact on a low speed axial compressor

Science.gov (United States)

Liu, Jianyong; Lu, Yajun; Li, Zhiping

2010-05-01

Non-axisymmetric wake impact experiments were carried out after the best exciting frequency for a low speed axial compressor had been found by axisymmetric wake impact experiments. When the number and circumferential distribution of inlet guide vanes (IGV) are logical the wakes of non-axisymmetric IGVs can exert beneficial unsteady exciting effect on their downstream rotor flow fields and improve the compressor’s performance. In the present paper, four non-axisymmetric wake impact plans were found working better than the axisymmetric wake impact plan. Compared with the base plan, the best non-axisymmetric plan increased the compressor’s peak efficiency, and the total pressure rise by 1.1 and 2%, and enhanced the stall margin by 4.4%. The main reason why non-axisymmetric plans worked better than the axisymmetric plan was explained as the change of the unsteady exciting signal arising from IGV wakes. Besides the high-frequency components, the non-axisymmetric plan generated a beneficial low-frequency square-wave exciting signal and other secondary frequency components. Compared with the axisymmetric plan, multi-frequency exciting wakes arising from the non-axisymmetric plans are easier to get coupling relation with complex vortices such as clearance vortices, passage vortices and shedding vortices.

Potential formation in axisymmetrized tandem mirror GAMMA 10

International Nuclear Information System (INIS)

Cho, T.; Ichimura, M.; Inutake, M.

1985-01-01

The paper reports experimental results on potential formation and end plugging in the axisymmetrized tandem mirror GAMMA 10. The plugging at both ends has been achieved by a combination of neutral beams and gyrotrons. The presence of a plug potential with a thermal barrier in an axisymmetric mirror has been confirmed by direct measurement of the axial potential profile. Enhancement of axial particle confinement has been observed during the end plugging. Non-ambipolar radial transport has been greatly reduced in the axisymmetrized magnetic configuration. The potentials measured by beam probes and end loss analysers are 0.7, 0.4 and 1.1 kV in the central, barrier and plug regions, respectively. Strong end plugging is observed when the central-cell density is higher than the densities in the plug and the barrier, and the plug density remains higher than the barrier density. The plug electron temperature is higher than the central temperature. Hot electrons forming a football-shaped profile have been stably produced in the axisymmetric mirror. The beta value and the fraction of the hot electrons reach up to 5% and 0.8, respectively. Central-cell ion-cyclotron resonance heating can sustain a stable plasma with higher density and ion temperature when resonance surfaces exist in both the anchor and the central cells. (author)

Two-dimensional generalized harmonic oscillators and their Darboux partners

International Nuclear Information System (INIS)

Schulze-Halberg, Axel

2011-01-01

We construct two-dimensional Darboux partners of the shifted harmonic oscillator potential and of an isotonic oscillator potential belonging to the Smorodinsky–Winternitz class of superintegrable systems. The transformed solutions, their potentials and the corresponding discrete energy spectra are computed in explicit form. (paper)

Building a Joint Force on the Fly: The Relationship of Admiral Aubrey W. Fitch and Lieutenant General Millard F. Harmon

Science.gov (United States)

2017-06-01

REQUIREMENTS SCHOOL OF ADVANCED AIR AND SPACE STUDIES AIR UNIVERSITY MAXWELL AIR FORCE BASE , ALABAMA JUNE 2017...World War II, led by two flag officers of different services. This campaign was pivotal to the allied advance in the Pacific theater but has...leading all land- based aviation in the theater, and Lieutenant General Millard Harmon, Commanding General, South Pacific, the overall land component

Explicit formulas for generalized harmonic perturbations of the infinite quantum well with an application to Mathieu equations

International Nuclear Information System (INIS)

García-Ravelo, J.; Trujillo, A. L.; Schulze-Halberg, A.

2012-01-01

We obtain explicit formulas for perturbative corrections of the infinite quantum well model. The formulas we obtain are based on a class of matrix elements that we construct by means of two-parameter ladder operators associated with the infinite quantum well system. Our approach can be used to construct solutions to Schrödinger-type equations that involve generalized harmonic perturbations of their potentials, such as cosine powers, Fourier series, and more general functions. As a particular case, we obtain characteristic values for odd periodic solutions of the Mathieu equation.

Explicit formulas for generalized harmonic perturbations of the infinite quantum well with an application to Mathieu equations

Energy Technology Data Exchange (ETDEWEB)

Garcia-Ravelo, J.; Trujillo, A. L. [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Unidad Profesional Adolfo Lopez Mateos, Zacatenco, 07738 Mexico D.F. (Mexico); Schulze-Halberg, A. [Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)

2012-10-15

We obtain explicit formulas for perturbative corrections of the infinite quantum well model. The formulas we obtain are based on a class of matrix elements that we construct by means of two-parameter ladder operators associated with the infinite quantum well system. Our approach can be used to construct solutions to Schroedinger-type equations that involve generalized harmonic perturbations of their potentials, such as cosine powers, Fourier series, and more general functions. As a particular case, we obtain characteristic values for odd periodic solutions of the Mathieu equation.

Axisymmetric flow and heat transfer to modified second grade fluid over a radially stretching sheet

Directory of Open Access Journals (Sweden)

Masood Khan

Full Text Available In the present work, an analysis is made to the two-dimensional axisymmetric flow and heat transfer of a modified second grade fluid over an isothermal non-linear radially stretching sheet. The momentum and energy equations are modelled and the boundary layer equations are derived. The governing equations for velocity and temperature are turned down into a system of ordinary differential equations by invoking appropriate transformations which are then solved numerically via fourth and fifth order Runge-Kutta Fehlberg method. Moreover, the influence of the pertinent parameters namely the generalized second grade parameter, stretching parameter, the power-law index and the generalized Prandtl number is graphically portrayed. It is inferred that the generalized second grade parameter uplifted the momentum boundary layer while lessened the thermal boundary layer. Furthermore, the impact of stretching parameter is more pronounced for the second grade fluid (m = 0 in contrast with the power-law fluid (k = 0. For some special cases, comparisons are made with previously reported results and an excellent agreement is established. Keywords: Modified second grade fluid, Axisymmetric flow, Heat transfer, Non-linear stretching sheet

Axisymmetric Lattice Boltzmann Model of Droplet Impact on Solid Surfaces

Science.gov (United States)

Dalgamoni, Hussein; Yong, Xin

2017-11-01

Droplet impact is a ubiquitous fluid phenomena encountered in scientific and engineering applications such as ink-jet printing, coating, electronics manufacturing, and many others. It is of great technological importance to understand the detailed dynamics of drop impact on various surfaces. The lattice Boltzmann method (LBM) emerges as an efficient method for modeling complex fluid systems involving rapidly evolving fluid-fluid and fluid-solid interfaces with complex geometries. In this work, we model droplet impact on flat solid substrates with well-defined wetting behavior using a two-phase axisymmetric LBM with high density and viscosity contrasts. We extend the two-dimensional Lee and Liu model to capture axisymmetric effect in the normal impact. First we compare the 2D axisymmetric results with the 2D and 3D results reported by Lee and Liu to probe the effect of axisymmetric terms. Then, we explore the effects of Weber number, Ohnesorge number, and droplet-surface equilibrium contact angle on the impact. The dynamic contact angle and spreading factor of the droplet during impact are investigated to qualitatively characterize the impact dynamics.

Harmonically excited orbital variations

International Nuclear Information System (INIS)

Morgan, T.

1985-01-01

Rephrasing the equations of motion for orbital maneuvers in terms of Lagrangian generalized coordinates instead of Newtonian rectangular cartesian coordinates can make certain harmonic terms in the orbital angular momentum vector more readily apparent. In this formulation the equations of motion adopt the form of a damped harmonic oscillator when torques are applied to the orbit in a variationally prescribed manner. The frequencies of the oscillator equation are in some ways unexpected but can nonetheless be exploited through resonant forcing functions to achieve large secular variations in the orbital elements. Two cases are discussed using a circular orbit as the control case: (1) large changes in orbital inclination achieved by harmonic excitation rather than one impulsive velocity change, and (2) periodic and secular changes to the longitude of the ascending node using both stable and unstable excitation strategies. The implications of these equations are also discussed for both artificial satellites and natural satellites. For the former, two utilitarian orbits are suggested, each exploiting a form of harmonic excitation. 5 refs

NOVA: a nonvariational code for solving MHD stability of axisymmetric toroidal plasmas

International Nuclear Information System (INIS)

Cheng, C.Z.; Chance, M.S.

1986-04-01

A nonvariational approach for determining the ideal MHD stability of axisymmetric toroidal confinement systems is presented. The code (NOVA) employs cubic B-spline finite elements and Fourier expansion in a general flux coordinate (psi, theta, zeta) system. Better accuracy and faster convergence were obtained in comparison with the variational PEST and ERATO codes. The nonvariational approach can be extended to problems having non-Hermitian eigenmode equations where variational energy principles cannot be obtained

Harmonic sums and polylogarithms generated by cyclotomic polynomials

Energy Technology Data Exchange (ETDEWEB)

Ablinger, Jakob; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

2011-05-15

The computation of Feynman integrals in massive higher order perturbative calculations in renormalizable Quantum Field Theories requires extensions of multiply nested harmonic sums, which can be generated as real representations by Mellin transforms of Poincare-iterated integrals including denominators of higher cyclotomic polynomials. We derive the cyclotomic harmonic polylogarithms and harmonic sums and study their algebraic and structural relations. The analytic continuation of cyclotomic harmonic sums to complex values of N is performed using analytic representations. We also consider special values of the cyclotomic harmonic polylogarithms at argument x=1, resp., for the cyclotomic harmonic sums at N{yields}{infinity}, which are related to colored multiple zeta values, deriving various of their relations, based on the stuffle and shuffle algebras and three multiple argument relations. We also consider infinite generalized nested harmonic sums at roots of unity which are related to the infinite cyclotomic harmonic sums. Basis representations are derived for weight w=1,2 sums up to cyclotomy l=20. (orig.)

The Dispersion of the Axisymmetric Longitudinal Waves in the Pre-Strained Bi-Material Hollow Cylinder with the Imperfect Interface Conditions

Science.gov (United States)

Akbarov, S. D.; Ipek, C.

This work studies the influence of the imperfectness of the interface conditions on the dispersion of the axisymmetric longitudinal waves in the pre-strained bi-material hollow cylinder. The investigations are made within the 3D linearized theory of elastic waves in elastic bodies with initial stresses. It is assumed that the materials of the layers of the hollow cylinder are made from hyper elastic compressible materials and the elasticity relations of those are given through the harmonic potential. The shear spring type imperfectness of the interface conditions is considered and the degree of this imperfectness is estimated by the shear-spring parameter. Numerical results on the influence of this parameter on the behavior of the dispersion curves are presented and discussed.

Harmonic manifolds with minimal horospheres are flat

Indian Academy of Sciences (India)

Abstract. In this note we reprove the known theorem: Harmonic manifolds with minimal horospheres are flat. It turns out that our proof is simpler and more direct than the original one. We also reprove the theorem: Ricci flat harmonic manifolds are flat, which is generally affirmed by appealing to Cheeger–Gromov splitting ...

Harmonic Manifolds with Minimal Horospheres are Flat

Indian Academy of Sciences (India)

In this note we reprove the known theorem: Harmonic manifolds with minimal horospheres are flat. It turns out that our proof is simpler and more direct than the original one. We also reprove the theorem: Ricci flat harmonic manifolds are flat, which is generally affirmed by appealing to Cheeger–Gromov splitting theorem.

Variational problems with obstacles and harmonic maps

International Nuclear Information System (INIS)

Musina, R.

1990-08-01

Our first purpose is to find a generalization of the usual definition of a harmonic map between two Riemannian manifolds in order to consider less regular target spaces. Our second aim was to extend a result by Chen and Struwe about the heat flow of harmonic mappings into manifolds with boundary. 19 refs

Computation of steady and unsteady compressible quasi-axisymmetric vortex flow and breakdown

Science.gov (United States)

Kandil, Osama A.; Kandil, Hamdy A.; Liu, C. H.

1991-01-01

The unsteady, compressible Navier-Stokes equations are used to compute and analyze compressible quasi-axisymmetric isolated vortices. The Navier-Stokes equations are solved using an implicit, upwind, flux-difference splitting finite-volume scheme. The developed three-dimensional solver has been verified by comparing its solution profiles with those of a slender, quasi-axisymmetric vortex solver for a subsonic, isolated quasi-axisymmetric vortex in an unbounded domain. The Navier-Stokes solver is then used to solve for a supersonic quasi-axisymmetric vortex flow in a configured circular duct. Steady and unsteady vortex-shock interactions and breakdown have been captured. The problem has also been calculated using the Euler solver of the same code and the results are compared with those of the Navier-Stokes solver. The effect of the initial swirl has been tentatively studied.

Lyapunov stability analysis of magnetohydrodynamic plasma equilibria with axisymmetric toroidal flow

International Nuclear Information System (INIS)

Almaguer, J.A.; Hameiri, E.; Herrera, J.; Holm, D.D.

1988-01-01

Lyapunov stability conditions for ideal magnetohydrodynamic (MHD) plasmas with mass flow in axisymmetric toroidal geometry are determined in the Eulerian representation. Axisymmetric equilibrium solutions of ideal MHD are associated to critical points of a nonlinearly conserved Lyapunov functional consisting of the sum of the total energy and the following flux-weighted quantities: the circulation along field lines, the angular momentum, the toroidal flux, and the mass content within each flux tube. Conditions sufficient for Lyapunov stability of these equilibria against axisymmetric perturbations are found by taking advantage of the Hamiltonian formalism for ideal MHD. In particular [see Eq. (60)], it is sufficient for Lyapunov stability under linearized dynamics that an axisymmetric equilibrium be subsonic in the appropriate rotating frame, lie in the first elliptic regime of the Bernoulli--Grad--Shafranov (BGS) system of equations, and satisfy one additional, more complicated, condition. Effects of boundary conditions, nonlinearity, and three-dimensionality on MHD stability are also discussed

HARMONIZATION OF TAX POLICIES: REVIEWING MACEDONIA AND CROATIA

Directory of Open Access Journals (Sweden)

Sasho Kozuharov

2015-12-01

Full Text Available The tax harmonization is a complex issue in the process of European integration. The tax harmonization is a process of convergence of the tax system based on mutual set of rules and, in general, it means existence of identical or similar tax rates for the tax payers in European Union, i.e. Euro zone. In case there are identical tax rates, then we are talking about a, so called, total explicit tax harmonization, whereas, if there are similar tax rates, we are talking about partial explicit tax harmonization, which refers to determination of the highest and the lowest tax rates. Thus, countries can determine the tax rates of certain taxes. The total harmonization, besides tax rates harmonization, means structural harmonization or harmonization of the tax structure. The harmonization of direct taxes mainly relies on the following main objectives: avoiding tax evasion and elimination of double taxation. The harmonization of regulations and directives in the field of indirect taxes is necessary in terms of establishing a single market, or removal of barriers to the free movement of goods, people, services and capital.

Adaptative mixed methods to axisymmetric shells

International Nuclear Information System (INIS)

Malta, S.M.C.; Loula, A.F.D.; Garcia, E.L.M.

1989-09-01

The mixed Petrov-Galerkin method is applied to axisymmetric shells with uniform and non uniform meshes. Numerical experiments with a cylindrical shell showed a significant improvement in convergence and accuracy with adaptive meshes. (A.C.A.S.) [pt

Axisymmetric vibrations of thin shells of revolution

International Nuclear Information System (INIS)

Suzuki, Katsuyoshi; Kikuchi, Norio; Kosawada, Tadashi; Takahashi, Shin

1983-01-01

The problem of free vibration of axisymmetric shells of revolution is important in connection with the design of pressure vessels, chemical equipment, aircrafts, structures and so on. In this study, the axisymmetrical vibration of a thin shell of revolution having a constant curvature in meridian direction was analyzed by thin shell theory. First, the Lagrangian during one period of the vibration of a shell of revolution was determined by the primary approximate theory of Love, and the vibration equations and boundary conditions were derived from its stopping condition. The vibration equations were strictly analyzed by using the series solution. The basic equations for the strain and strain energy of a shell were based on those of Novozhilov. As the examples of numerical calculation, the natural frequency and vibration mode of the symmetrical shells of revolution fixed at both ends and supported at both ends were determined, and their characteristics were clarified. The theory and the numerical calculation ore described. Especially in the frequency curves, the waving phenomena were observed frequently, which were not seen in non-axisymmetric vibration, accordingly also the vibration mode changed in complex state on the frequency curves of same order. The numerical calculation was carried out in the large computer center in Tohoku University. (Kako, I.)

Options for axisymmetric operation of MFTF-B

International Nuclear Information System (INIS)

Fenstermacher, M.E.; Devoto, R.S.; Thomassen, K.I.

1986-01-01

The flexibility of MFTF-B for axisymmetric experiments has been investigated. Interhcanging the axicell coils and increasing their separation results in an axisymmetric plug cell with 12:1 and 6:1 inner and outer mirror ratios, respectively. For axisymmetric operation, the sloshing-ion neutral beams, ECRH gyrotrons, and the pumping system would be moved to the axicell. Stabilization by E-rings could be explored in this configuration. With the addition of octopole magnets, off-axis multipole stabilization could also be tested. Operating points for octopole and E-ring-stabilized configurations with properties similar to those of the quadrupole MFTF-B, namely T/sub ic/ = 10 - 15 keV and n/sub c/ approx. = 3 x 10 13 cm -3 , have been obtained. Because of the negligible radial transport of central-cell ions, the required neutral-beam power in the central cell has been dramatically reduced. In addition, because MHD stabilization is achieved by off-axis hot electrons in both cases, much lower barrier beta is possible, which aids in reducing the barrier ECRH power. Total ECRH power in the end cell is projected to be approx. =1 MW. Possible operating points for both octopole and E-ring configurations are described along with the stability considerations involved

A time-dependent dusty gas dynamic model of axisymmetric cometary jets

International Nuclear Information System (INIS)

Korosmezey, A.; Gombosi, T.I.

1990-01-01

The present time-dependent, axisymmetric dusty gas dynamical model of inner cometary atmospheres solves the coupled and time-dependent equations of continuity, momentum, and energy for a gas-dust mixture between the surface of the nucleus and 100 km, using an axisymmetric 40 x 40 grid structure. A novel numerical method employing a second-order accurate Godunov-type scheme with dimensional splitting is used to solve the time-dependent pde system. It is established that a subsolar dust spike not predicted by previous calculations is generated by narrow axisymmetric jets, together with a jet cone whose opening angle depends on the jet length. 28 refs

Edge Plasma Response to Non-Axisymmetric Fields in Tokamaks

Energy Technology Data Exchange (ETDEWEB)

Ferraro, N. M.; Lao, L. L.; Buttery, R. J.; Evans, T. E.; Snyder, P. B.; Wade, M.R., E-mail: ferraro@fusion.gat.com [General Atomics, San Diego (United States); Moyer, R. A.; Orlov, D. M. [University of California San Diego, La Jolla (United States); Lanctot, M. J. [Lawrence Livermore National Laboratory, Livermore (United States)

2012-09-15

Full text: The application of non-axisymmetric fields is found to have significant effects on the transport and stability of H-mode tokamak plasmas. These effects include dramatic changes in rotation and particle transport, and may lead to the partial or complete suppression of edge-localized modes (ELMs) under some circumstances. The physical mechanism underlying these effects is presently not well understood, in large part because the response of the plasma to non- axisymmetric fields is significant and complex. Here, recent advances in modeling the plasma response to non-axisymmetric fields are discussed. Calculations using a resistive two-fluid model in diverted toroidal geometry confirm the special role of the perpendicular electron velocity in suppressing the formation of islands in the plasma. The possibility that islands form near the top of the pedestal, where the zero-crossing of the perpendicular electron velocity may coincide with a mode-rational surface, is explored, and the implications for ELM suppression are discussed. Modeling results are compared with empirical data. It is shown that numerical modeling is successful in reproducing some experimentally observed effects of applied non-axisymmetric fields on the edge temperature and density profiles. The numerical model self-consistently includes the plasma, separatrix, and scrape-off layer. Rotation and diamagnetic effects are also included self-consistently. Solutions are calculated using the M3D-C1 extended-MHD code. (and others)

Regulations for marine microalgal toxins: Towards harmonization of ...

African Journals Online (AJOL)

The World Trade Organization and the General Agreements on Tariffs and Trade encourage the harmonization of regulations on food safety requirements. The current policy on trade liberalization of seafood is presented, together with a review of the regulations for marine microalgal toxins. Activities on harmonization of ...

Modeling axisymmetric flows dynamics of films, jets, and drops

CERN Document Server

Middleman, Stanley

1995-01-01

This concise book is intended to fulfill two purposes: to provide an important supplement to classic texts by carrying fluid dynamics students on into the realm of free boundary flows; and to demonstrate the art of mathematical modeling based on knowledge, intuition, and observation. In the authors words, the overall goal is make the complex simple, without losing the essence--the virtue--of the complexity.Modeling Axisymmetric Flows: Dynamics of Films, Jets, and Drops is the first book to cover the topics of axisymmetric laminar flows; free-boundary flows; and dynamics of drops, jets, and films. The text also features comparisons of models to experiments, and it includes a large selection of problems at the end of each chapter.Key Features* Contains problems at the end of each chapter* Compares real-world experimental data to theory* Provides one of the first comprehensive examinations of axisymmetric laminar flows, free-boundary flows, and dynamics of drops, jets, and films* Includes development of basic eq...

A toolbox for Harmonic Sums and their analytic continuations

Energy Technology Data Exchange (ETDEWEB)

Ablinger, Jakob; Schneider, Carsten [RISC, J. Kepler University, Linz (Austria); Bluemlein, Johannes [DESY, Zeuthen (Germany)

2010-07-01

The package HarmonicSums implemented in the computer algebra system Mathematica is presented. It supports higher loop calculations in QCD and QED to represent single-scale quantities like anomalous dimensions and Wilson coefficients. The package allows to reduce general harmonic sums due to their algebraic and different structural relations. We provide a general framework for these reductions and the explicit representations up to weight w=8. For the use in experimental analyzes we also provide an analytic formalism to continue the harmonic sums form their integer arguments into the complex plane, which includes their recursions and asymptotic representations. The main ideas are illustrated by specific examples.

Dynamic analysis of reactor containment building using axisymmetric finite element model

International Nuclear Information System (INIS)

Thakkar, S.K.; Dubey, R.N.

1989-01-01

The structural safety of nuclear reactor building during earthquake is of great importance in view of possibility of radiation hazards. The rational evaluation of forces and displacements in various portions of structure and foundation during strong ground motion is most important for safe performance and economic design of the reactor building. The accuracy of results of dynamic analysis is naturally dependent on the type of mathematical model employed. Three types of mathematical models are employed for dynamic analysis of reactor building beam model axisymmetric finite element model and three dimensional model. In this paper emphasis is laid on axisymmetric model. This model of containment building is considered a reinfinement over conventional beam model of the structure. The nuclear reactor building on a rocky foundation is considered herein. The foundation-structure interaction is relatively less in this condition. The objective of the paper is to highlight the significance of modelling of non-axisymmetric portion of building, such as reactor internals by equivalent axisymmetric body, on the structural response of the building

Topological Fluid Mechanics with Applications to Free Surfaces and Axisymmetric Flows

DEFF Research Database (Denmark)

Brøns, Morten

1996-01-01

Topological fluid mechanics is the study of qualitative features of fluid patterns. We discuss applications to the flow beneath a stagnant surface film, and to patterns in axisymmetric flow.......Topological fluid mechanics is the study of qualitative features of fluid patterns. We discuss applications to the flow beneath a stagnant surface film, and to patterns in axisymmetric flow....

Linking high harmonics from gases and solids.

Science.gov (United States)

Vampa, G; Hammond, T J; Thiré, N; Schmidt, B E; Légaré, F; McDonald, C R; Brabec, T; Corkum, P B

2015-06-25

When intense light interacts with an atomic gas, recollision between an ionizing electron and its parent ion creates high-order harmonics of the fundamental laser frequency. This sub-cycle effect generates coherent soft X-rays and attosecond pulses, and provides a means to image molecular orbitals. Recently, high harmonics have been generated from bulk crystals, but what mechanism dominates the emission remains uncertain. To resolve this issue, we adapt measurement methods from gas-phase research to solid zinc oxide driven by mid-infrared laser fields of 0.25 volts per ångström. We find that when we alter the generation process with a second-harmonic beam, the modified harmonic spectrum bears the signature of a generalized recollision between an electron and its associated hole. In addition, we find that solid-state high harmonics are perturbed by fields so weak that they are present in conventional electronic circuits, thus opening a route to integrate electronics with attosecond and high-harmonic technology. Future experiments will permit the band structure of a solid to be tomographically reconstructed.

Three-Dimensional Electromagnetic High Frequency Axisymmetric Cavity Scars.

Energy Technology Data Exchange (ETDEWEB)

Warne, Larry Kevin; Jorgenson, Roy Eberhardt

2014-10-01

This report examines the localization of high frequency electromagnetic fi elds in three-dimensional axisymmetric cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This report treats both the case where the opposing sides, or mirrors, are convex, where there are no interior foci, and the case where they are concave, leading to interior foci. The scalar problem is treated fi rst but the approximations required to treat the vector fi eld components are also examined. Particular att ention is focused on the normalization through the electromagnetic energy theorem. Both projections of the fi eld along the scarred orbit as well as point statistics are examined. Statistical comparisons are m ade with a numerical calculation of the scars run with an axisymmetric simulation. This axisymmetric cas eformstheoppositeextreme(wherethetwomirror radii at each end of the ray orbit are equal) from the two -dimensional solution examined previously (where one mirror radius is vastly di ff erent from the other). The enhancement of the fi eldontheorbitaxiscanbe larger here than in the two-dimensional case. Intentionally Left Blank

Generation of new solutions of the stationary axisymmetric Einstein equations by a double complex function method

International Nuclear Information System (INIS)

Zhong, Z.

1985-01-01

A new approach to the solution of certain differential equations, the double complex function method, is developed, combining ordinary complex numbers and hyperbolic complex numbers. This method is applied to the theory of stationary axisymmetric Einstein equations in general relativity. A family of exact double solutions, double transformation groups, and n-soliton double solutions are obtained

Characterization of Harmonic Signal Acquisition with Parallel Dipole and Multipole Detectors

Science.gov (United States)

Park, Sung-Gun; Anderson, Gordon A.; Bruce, James E.

2018-04-01

Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS) is a powerful instrument for the study of complex biological samples due to its high resolution and mass measurement accuracy. However, the relatively long signal acquisition periods needed to achieve high resolution can serve to limit applications of FTICR-MS. The use of multiple pairs of detector electrodes enables detection of harmonic frequencies present at integer multiples of the fundamental cyclotron frequency, and the obtained resolving power for a given acquisition period increases linearly with the order of harmonic signal. However, harmonic signal detection also increases spectral complexity and presents challenges for interpretation. In the present work, ICR cells with independent dipole and harmonic detection electrodes and preamplifiers are demonstrated. A benefit of this approach is the ability to independently acquire fundamental and multiple harmonic signals in parallel using the same ions under identical conditions, enabling direct comparison of achieved performance as parameters are varied. Spectra from harmonic signals showed generally higher resolving power than spectra acquired with fundamental signals and equal signal duration. In addition, the maximum observed signal to noise (S/N) ratio from harmonic signals exceeded that of fundamental signals by 50 to 100%. Finally, parallel detection of fundamental and harmonic signals enables deconvolution of overlapping harmonic signals since observed fundamental frequencies can be used to unambiguously calculate all possible harmonic frequencies. Thus, the present application of parallel fundamental and harmonic signal acquisition offers a general approach to improve utilization of harmonic signals to yield high-resolution spectra with decreased acquisition time. [Figure not available: see fulltext.

Computational study of axisymmetric modes in noncircular cross section tokamaks

International Nuclear Information System (INIS)

Johnson, J.L.; Chance, M.S.; Greene, J.M.; Grimm, R.C.; Jardin, S.C.; Kerner, W.; Manickam, J.; Weimer, K.E.

1976-09-01

A major computational program to investigate the MHD equilibrium, stability, and nonlinear evolution properties of realistic tokamak configurations is proceeding. Preliminary application is made to the Princeton PDX device. Both axisymmetric (n = 0) modes and kink (n = 1) modes are found; the growth rates depend sensitively on the configuration. A study of the nonlinear evolution of axisymmetric modes in such a device shows that flux conservation in the vacuum region can limit their growth

Operator Arithmetic-Harmonic Mean Inequality on Krein Spaces

Directory of Open Access Journals (Sweden)

M. Dehghani

2014-03-01

Full Text Available We prove an operator arithmetic-harmonic mean type inequality in Krein space setting, by using some block matrix techniques of indefinite type. We also give an example which shows that the operator arithmetic-geometric-harmonic mean inequality for two invertible selfadjoint operators on Krein spaces is not valid, in general.

Invariance of the Berry phase under unitary transformations: application to the time-dependent generalized harmonic oscillator

International Nuclear Information System (INIS)

Kobe, D.H.

1989-01-01

The Berry phase is derived in a manifestly gauge-invariant way, without adiabatic or cyclic requirements. It is invariant under unitary transformations, contrary to recent assertions. A time-dependent generalized harmonic oscillator is taken as an example. The energy of the system is not in general the Hamiltonian. An energy, the time derivative of which is the power, is obtained from the equation of motion. When the system is quantized, the Berry phase is zero, and is invariant under unitary transformations. If the energy is chosen incorrectly to be the Hamiltonian, a nonzero Berry phase is obtained. In this case the total phase, the sun of the dynamical and Berry phases, is equal to the correct total phase through first order in perturbation theory. (author)

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

Directory of Open Access Journals (Sweden)

Rong Xiao

2014-01-01

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

Harmonic Analyzing of the Double PWM Converter in DFIG Based on Mathematical Model

Directory of Open Access Journals (Sweden)

Jing Liu

2017-12-01

Full Text Available Harmonic pollution of double fed induction generators (DFIGs has become a vital concern for its undesirable effects on power quality issues of wind generation systems and grid-connected system, and the double pulse width modulation (PWMconverter is one of the main harmonic sources in DFIGs. Thus the harmonic analysis of the converter in DFIGs is a necessary step to evaluate their harmonic pollution of DFIGs. This paper proposes a detailed harmonic modeling method to discuss the main harmonic components in a converter. In general the harmonic modeling could be divided into the low-order harmonic part (up to 30th order and the high-order harmonic part (greater than order 30 parts in general. The low-order harmonics are produced by the circuit topology and control algorithm, and the harmonic component will be different if the control strategy changes. The high-order harmonics are produced by the modulation of the switching function to the dc variable. In this paper, the low-order harmonic modeling is established according to the directions of power flow under the vector control (VC, and the high-order harmonic modeling is established by the switching function of space vector PWM and dc currents. Meanwhile, the simulations of harmonic a components in a converter are accomplished in a real time digital simulation system. The results indicate that the proposed modeling could effectively show the harmonics distribution of the converter in DFIGs.

78 FR 13835 - Harmonization of Airworthiness Standards-Miscellaneous Structures Requirements

Science.gov (United States)

2013-03-01

... Airworthiness Standards--Miscellaneous Structures Requirements AGENCY: Federal Aviation Administration (FAA... and Dynamics Harmonization Working Group (LDHWG) and the General Structures Harmonization Working Group (GSHWG) to review existing structures regulations and recommend changes that would eliminate...

Dipole mechanism of spontaneous breaking of N = 2 supersymmetry. II. Reformulation and generalization in harmonic superspace

International Nuclear Information System (INIS)

Ohta, N.

1985-01-01

After elucidating the component structure of N = 2 supersymmetric gauge theories in the harmonic superspace formalism with central charges, we reformulate our previous dipole mechanism of spontaneous breaking of N = 2 supersymmetry free from the Nambu-Goldstone-fermion difficulties in this formalism. This allows a generalization of our previous model of generating finiteness-preserving mass terms for scalar hypermultiplets; we can also obtain the gauge-fermion and scalar mass terms together with specific cubic interactions for scalar fields. The mechanism is equivalent to the so-called spurion method

Axisymmetric control in tokamaks

International Nuclear Information System (INIS)

Humphreys, D.A.

1991-02-01

Vertically elongated tokamak plasmas are intrinsically susceptible to vertical axisymmetric instabilities as a result of the quadrupole field which must be applied to produce the elongation. The present work analyzes the axisymmetric control necessary to stabilize elongated equilibria, with special application to the Alcator C-MOD tokamak. A rigid current-conserving filamentary plasma model is applied to Alcator C-MOD stability analysis, and limitations of the model are addressed. A more physically accurate nonrigid plasma model is developed using a perturbed equilibrium approach to estimate linearized plasma response to conductor current variations. This model includes novel flux conservation and vacuum vessel stabilization effects. It is found that the nonrigid model predicts significantly higher growth rates than predicted by the rigid model applied to the same equilibria. The nonrigid model is then applied to active control system design. Multivariable pole placement techniques are used to determine performance optimized control laws. Formalisms are developed for implementing and improving nominal feedback laws using the C-MOD digital-analog hybrid control system architecture. A proportional-derivative output observer which does not require solution of the nonlinear Ricatti equation is developed to help accomplish this implementation. The nonrigid flux conserving perturbed equilibrium plasma model indicates that equilibria with separatrix elongation of at least κ sep = 1.85 can be stabilized robustly with the present control architecture and conductor/sensor configuration

Ideal, steady-state, axisymmetric magnetohydrodynamic equations with flow

International Nuclear Information System (INIS)

Baransky, Y.A.

1987-01-01

The motivation of this study is to gain additional understanding of the effect of rotation on the equilibrium of a plasma. The axisymmetric equilibria of ideal magnetohydrodynamics (MHD) with flow have been studied numerically and analytically. A general discussion is provided of previous work on plasmas with flow and comparisons are made to the static model. A variational principle has been derived for the two dimensional problem with comments as to appropriate boundary conditions. An inverse aspect ratio expansion has been used for a study of the toroidal flow equation for both low- and high-β. The inverse aspect ratio expansion has also been used for a study of equations with both poloidal and toroidal flow. An overview is provided of the adaptive finite-difference code which was developed to solve the full equations. (FI)

Axisymmetric magnetohydrodynamic equilibria in local polar coordinates

International Nuclear Information System (INIS)

Clemente, R.A.

1982-01-01

The Grad--Shafranov equation for an ideal magnetohydrodynamic axisymmetric toroidal configuration is solved analytically in a local polar coordinate system using a novel method which produces solutions valid up to the second order in the inverse aspect ratio expansion

Comparative study of turbulence model performance for axisymmetric sudden expansion flow

International Nuclear Information System (INIS)

Bae, Youngmin; Kim, Young In; Kim, Keung Koo; Yoon, Juhyeon

2013-01-01

In this study, the performance of turbulence models in predicting the turbulent flow in an axisymmetric sudden expansion with an expansion ratio of 4 is assessed for a Reynolds number of 5.6 Χ 10 4 . The comparisons show that the standard k-ε and RSM models provide the best agreement with the experimental data, whereas the standard k-ω model gives poor predictions. Owing to its computational efficiency, the Reynolds Averaged Navier-Stokes (RANS) approach has been widely used for the prediction of turbulent flows and associated pressure losses in a variety of internal flow systems such as a diffuser, orifice, converging nozzle, and pipes with sudden expansion. However, the lack of a general turbulence model often leads to limited applications of a RANS approach, i. e., the accuracy and validity of solutions obtained from RANS equations vary with the turbulence model, flow regime, near-wall treatment, and configuration of the problem. In light of the foregoing, a large amount of turbulence research has been conducted to assess the performance of existing turbulence models for different flow fields. In this paper, the turbulent flow in an axisymmetric sudden expansion is numerically investigated for a Reynolds number of 5.6 Χ 10 4 , with the aim of examining the performance of several turbulence models

General exact harmonic analysis of in-plane timoshenko beam structures

Directory of Open Access Journals (Sweden)

C. A. N. Dias

Full Text Available The exact solution for the problem of damped, steady state response, of in-plane Timoshenko frames subjected to harmonically time varying external forces is here described. The solution is obtained by using the classical dynamic stiffness matrix (DSM, which is non-linear and transcendental in respect to the excitation frequency, and by performing the harmonic analysis using the Laplace transform. As an original contribution, the partial differential coupled governing equations, combining displacements and forces, are directly subjected to Laplace transforms, leading to the member DSM and to the equivalent load vector formulations. Additionally, the members may have rigid bodies attached at any of their ends where, optionally, internal forces can be released. The member matrices are then used to establish the global matrices that represent the dynamic equilibrium of the overall framed structure, preserving close similarity to the finite element method. Several application examples prove the certainty of the proposed method by comparing the model results with the ones available in the literature or with finite element analyses.

Determination of two dimensional axisymmetric finite element model for reactor coolant piping nozzles

International Nuclear Information System (INIS)

Choi, S. N.; Kim, H. N.; Jang, K. S.; Kim, H. J.

2000-01-01

The purpose of this paper is to determine a two dimensional axisymmetric model through a comparative study between a three dimensional and an axisymmetric finite element analysis of the reactor coolant piping nozzle subject to internal pressure. The finite element analysis results show that the stress adopting the axisymmetric model with the radius of equivalent spherical vessel are well agree with that adopting the three dimensional model. The radii of equivalent spherical vessel are 3.5 times and 7.3 times of the radius of the reactor coolant piping for the safety injection nozzle and for the residual heat removal nozzle, respectively

Local solutions of harmonical and Bi-harmonical equations, universal field equation and self-dual configurations of Yang-Mills fields in four dimensions

International Nuclear Information System (INIS)

Leznov, A.N.

1994-01-01

A general method for the construction of solutions of the d'Alamberian and double d'Alamberian (harmonic and bi-harmonic) equations with local dependence of arbitrary functions upon two independent arguments is proposed. The connection between solutions of this kind and self-dual configurations of gauge fields having no singularities is established. 5 refs

Surface pressure drag for hydrostatic two-layer flow over axisymmetric mountains

Energy Technology Data Exchange (ETDEWEB)

Leutbecher, M.

2000-07-01

The effect of partial reflections on surface pressure drag is investigated for hydrostatic gravity waves in two-layer flow with piecewise constant buoyancy frequency. The variation of normalized surface pressure drag with interface height is analyzed for axisymmetric mountains. The results are compared with the familiar solution for infinitely long ridges. The drag for the two-layer flow is normalized with the drag of one-layer flow, which has the buoyancy frequency of the lower layer. An analytical expression for the normalized drag of axisymmetric mountains is derived from linear theory of steady flow. Additionally, two-layer flow over finite-height axisymmetric mountains is simulated numerically for flow with higher stability in the upper layer. The temporal evolution of the surface pressure drag is examined in a series of experiments with different interface and mountain heights. The focus is on the linear regime and the nonlinear regime of nonbreaking gravity waves. The dispersion of gravity waves in flow over isolated mountains prevents that the entire wave spectrum is in resonance at the same interface height, which is the case in hydrostatic flow over infinitely long ridges. In consequence, the oscillation of the normalized drag with interface height is smaller for axisymmetric mountains than for infinitely long ridges. However, even for a reflection coefficient as low as 1/3 the drag of an axisymmetric mountain can be amplified by 50% and reduced by 40%. The nonlinear drag becomes steady in the numerical experiments in which no wave breaking occurs. The steady state nonlinear drag agrees quite well with the prediction of linear theory if the linear drag is computed for a slightly lowered interface. (orig.)

Harmonic statistics

International Nuclear Information System (INIS)

Eliazar, Iddo

2017-01-01

The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.

Harmonic statistics

Energy Technology Data Exchange (ETDEWEB)

Eliazar, Iddo, E-mail: eliazar@post.tau.ac.il

2017-05-15

The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.

Prediction of the vibroacoustic behavior of a submerged shell with non-axisymmetric internal substructures by a condensed transfer function method

Science.gov (United States)

Meyer, V.; Maxit, L.; Guyader, J.-L.; Leissing, T.

2016-01-01

The vibroacoustic behavior of axisymmetric stiffened shells immersed in water has been intensively studied in the past. On the contrary, little attention has been paid to the modeling of these shells coupled to non-axisymmetric internal frames. Indeed, breaking the axisymmetry couples the circumferential orders of the Fourier series and considerably increases the computational costs. In order to tackle this issue, we propose a sub-structuring approach called the Condensed Transfer Function (CTF) method that will allow assembling a model of axisymmetric stiffened shell with models of non-axisymmetric internal frames. The CTF method is developed in the general case of mechanical subsystems coupled along curves. A set of orthonormal functions called condensation functions, which depend on the curvilinear abscissa along the coupling line, is considered. This set is then used as a basis for approximating and decomposing the displacements and the applied forces at the line junctions. Thanks to the definition and calculation of condensed transfer functions for each uncoupled subsystem and by using the superposition principle for passive linear systems, the behavior of the coupled subsystems can be deduced. A plane plate is considered as a test case to study the convergence of the method with respect to the type and the number of condensation functions taken into account. The CTF method is then applied to couple a submerged non-periodically stiffened shell described using the Circumferential Admittance Approach (CAA) with internal substructures described by Finite Element Method (FEM). The influence of non-axisymmetric internal substructures can finally be studied and it is shown that it tends to increase the radiation efficiency of the shell and can modify the vibrational and acoustic energy distribution.

Microfluidic step-emulsification in axisymmetric geometry.

Science.gov (United States)

Chakraborty, I; Ricouvier, J; Yazhgur, P; Tabeling, P; Leshansky, A M

2017-10-25

Biphasic step-emulsification (Z. Li et al., Lab Chip, 2015, 15, 1023) is a promising microfluidic technique for high-throughput production of μm and sub-μm highly monodisperse droplets. The step-emulsifier consists of a shallow (Hele-Shaw) microchannel operating with two co-flowing immiscible liquids and an abrupt expansion (i.e., step) to a deep and wide reservoir. Under certain conditions the confined stream of the disperse phase, engulfed by the co-flowing continuous phase, breaks into small highly monodisperse droplets at the step. Theoretical investigation of the corresponding hydrodynamics is complicated due to the complex geometry of the planar device, calling for numerical approaches. However, direct numerical simulations of the three dimensional surface-tension-dominated biphasic flows in confined geometries are computationally expensive. In the present paper we study a model problem of axisymmetric step-emulsification. This setup consists of a stable core-annular biphasic flow in a cylindrical capillary tube connected co-axially to a reservoir tube of a larger diameter through a sudden expansion mimicking the edge of the planar step-emulsifier. We demonstrate that the axisymmetric setup exhibits similar regimes of droplet generation to the planar device. A detailed parametric study of the underlying hydrodynamics is feasible via inexpensive (two dimensional) simulations owing to the axial symmetry. The phase diagram quantifying the different regimes of droplet generation in terms of governing dimensionless parameters is presented. We show that in qualitative agreement with experiments in planar devices, the size of the droplets generated in the step-emulsification regime is independent of the capillary number and almost insensitive to the viscosity ratio. These findings confirm that the step-emulsification regime is solely controlled by surface tension. The numerical predictions are in excellent agreement with in-house experiments with the axisymmetric

A Method for Harmonic Sources Detection based on Harmonic Distortion Power Rate

Science.gov (United States)

Lin, Ruixing; Xu, Lin; Zheng, Xian

2018-03-01

Harmonic sources detection at the point of common coupling is an essential step for harmonic contribution determination and harmonic mitigation. The harmonic distortion power rate index is proposed for harmonic source location based on IEEE Std 1459-2010 in the paper. The method only based on harmonic distortion power is not suitable when the background harmonic is large. To solve this problem, a threshold is determined by the prior information, when the harmonic distortion power is larger than the threshold, the customer side is considered as the main harmonic source, otherwise, the utility side is. A simple model of public power system was built in MATLAB/Simulink and field test results of typical harmonic loads verified the effectiveness of proposed method.

Compact formulas for bounce/transit averaging in axisymmetric tokamak geometry

Energy Technology Data Exchange (ETDEWEB)

Duthoit, F.-X. [SNU Division of Graduate Education for Sustainabilization of Foundation Energy, Seoul National University, Seoul 151-742 (Korea, Republic of); Brizard, A. J. [Department of Physics, Saint Michael' s College, Colchester, Vermont 05439 (United States); Hahm, T. S. [Department of Nuclear Engineering, Seoul National University, Seoul 151-742 (Korea, Republic of)

2014-12-15

Compact formulas for bounce and transit orbit averaging of the fluctuation-amplitude eikonal factor in axisymmetric tokamak geometry, which is frequently encountered in bounce-gyrokinetic description of microturbulence, are given in terms of the Jacobi elliptic functions and elliptic integrals. These formulas are readily applicable to the calculation of the neoclassical susceptibility in the framework of modern bounce-gyrokinetic theory. In the long-wavelength limit for axisymmetric electrostatic perturbations, we recover the expression for the Rosenbluth-Hinton residual zonal flow [M. N. Rosenbluth and F. L. Hinton, Phys. Rev. Lett. 80, 724 (1998)] accurately.

Static third-harmonic lines in widely variable fiber continuum generation

Science.gov (United States)

Tu, Haohua; Zhao, Youbo; Liu, Yuan; Boppart, Stephen A.

2014-01-01

An intriguing phenomenon of third-harmonic generation under fiber continuum generation is the emission of an anharmonic signal. One popular interpretation of this effect has developed into a general theory of fiber third-harmonic generation. Here we produce "static" third-harmonic lines dictated fully by fiber properties independent of pump parameters, in contrast to the signals of all known phase-matched nonlinear optical processes that vary dynamically with these parameters. We argue that the anharmonic signal is an illusion of the continuum generation, that it is in fact harmonic, and that this theory should be reevaluated.

Seismic analysis of axisymmetric shells

International Nuclear Information System (INIS)

Jospin, R.J.; Toledo, E.M.; Feijoo, R.A.

1984-01-01

Axisymmetric shells subjected to multiple support excitation are studied. The shells are spatialy discretized by the finite element method and in order to obtain estimates for the maximum values of displacements and stresses the response spectrum tecnique is used. Finally, some numerical results are presented and discussed in the case of a shell of revolution with vertical symmetry axis, subjected to seismic ground motions in the horizontal, vertical and rocking directions. (Author) [pt

Multispecies transport theory for axisymmetric rotating plasmas

International Nuclear Information System (INIS)

Tessarotto, M.; White, R.B.

1992-01-01

A reduced gyrokinetic equation is derived for a multi-species toroidal axisymmetric plasma with arbitrary toroidal differential rotation speeds and in the presence of a finite induced electric field. The kinetic equation obtained, extending previous results obtained by Hinton and Wong and by Catto, Bernstein and Tessarotto, has a form suited for transport applications, via variational techniques; in particular it exhibits the feature that all source terms, including the Spitzer source term, carrying the contribution due to the inductive electric field, appear to be acted upon by the collision operator. Moreover, the equation displays a new contribution due to ''explicit'' velocity perturbations, here proven to be consistent with transport ordering, whose evaluation appears relevant for transport calculations. In addition, general expressions are obtained for the neoclassical fluxes in terms of a variational principle, as well as for the classical ones, retaining, in both cases, the contributions due to the Spitzer's inductive terms

Covariant quantization of the d=4 Brink-Schwarz superparticle using Lorentz harmonics

International Nuclear Information System (INIS)

Zima, V.G.; Fedoryuk, S.A.

1995-01-01

Covariant first and second quantizations of the free d=4 massless superparticle are implemented with the introduction of purely gauge auxiliary spinor Lorentz harmonics. It is shown that the general solution of the condition of masslessness is a sum of two independent chiral superfields with each of them corresponding to finite superspin. A translationally covariant, in general bijective correspondence between harmonic and massless superfields is constructed. By calculation of the commutation function it is shown that in the considered approach only harmonic fields with the correct connection between spin and statistics and with integer negative homogeneity index satisfy the microcausality condition. It is emphasized that the harmonic fields that arise are reducible at integer points. The index spinor technique is used to describe infinite-component fields of finite spin; the equations of motion of such fields are obtained, and for them Weinberg's theorem on the connection between massless helicity particles and the type of nongauge field that describes them is generalized

Analysis of Even Harmonics Generation in an Isolated Electric Power System

Science.gov (United States)

Kanao, Norikazu; Hayashi, Yasuhiro; Matsuki, Junya

Harmonics bred from loads are mainly odd order because the current waveform has half-wave symmetry. Since the even harmonics are negligibly small, those are not generally measured in electric power systems. However, even harmonics were measured at a 500/275/154kV substation in Hokuriku Electric Power Company after removal of a transmission line fault. The even harmonics caused malfunctions of protective digital relays because the relays used 4th harmonics at the input filter as automatic supervisory signal. This paper describes the mechanism of generation of the even harmonics by comparing measured waveforms with ATP-EMTP simulation results. As a result of analysis, it is cleared that even harmonics are generated by three causes. The first cause is a magnetizing current of transformers due to flux deviation by DC component of a fault current. The second one is due to harmonic conversion of a synchronous machine which generates even harmonics when direct current component or even harmonic current flow into the machine. The third one is that increase of harmonic impedance due to an isolated power system produces harmonic voltages. The design of the input filter of protective digital relays should consider even harmonics generation in an isolated power system.

Harmonizing power cables and power lines. Harmonisierung der Starkstromkabel und -leitungen

Energy Technology Data Exchange (ETDEWEB)

Heinhold, L [Siemens A.G., Erlangen (Germany, F.R.); Retzlaff, E; Warner, A [Verband Deutscher Elektrotechniker (VDE) e.V., Frankfurt am Main (Germany, F.R.)

1976-01-01

The article gives a summarizing view of the present level of harmonization in the field of power cables and lines. Special attention is paid to problems referring to using harmonized designs for flexible lines and using lines for solid layout with PVC and rubber insulation in the German standards DIN 57281/VDE 0281 and DIN 57282/VDE 0282 and problems of taking the types used until today out of use. A general view of the power lines fully harmonized is given and a harmonization-labelling (common labelling) for cables and lines is described.

Simulation study of generalized electron cyclotron harmonic waves and nonlinear scattering in a magnetized plasma

International Nuclear Information System (INIS)

Martinez, R.M.

1983-01-01

Part One examines the properties of electron cyclotron harmonic waves by means of computer simulation. The electromagnetic cyclotron harmonic modes not previously observed in simulation are emphasized and compared with the better known electrostatic (Bernstein) modes for perpendicular propagation. The investigation is performed by a spectrum analysis (both wavelength and frequency) of the thermal equilibrium electromagnetic fluctuation fields present in the simulation. A numerical solution of the fully electromagnetic dispersion relation shows that extreme frequency resolution is necessary to discern shifts of the electromagnetic mode frequencies from the cyclotron harmonics except at high plasma density or temperature. The simulation results show that at high plasma pressure the amplitude of the electromagnetic modes can become greater than that of the electrostatic modes. Part Two examines the interaction of an external electromagnetic wave with the electrostatic cylotron harmonic modes. The stimulated Raman scattering with an extraordinary wave as the pump is observed to occur in a wavelength regime where it would be prevented by Landau damping in an unmagnetized plasma

Analysis of axisymmetric shells subjected to asymmetric loads using field consistent shear flexible curved element

Energy Technology Data Exchange (ETDEWEB)

Balakrishna, C; Sarma, B S [Defence Research and Development Laboratory, Hyderabad (India)

1989-02-01

A formulation for axisymmetric shell analysis under asymmetric load based on Fourier series representation and using field consistent 3 noded curved axisymmetric shell element is presented. Different field inconsistent/consistent interpolations for an element based on shear flexible theory have been studied for thick and thin shells under asymmetric loads. Various examples covering axisymmetric as well as asymmetric loading cases have been analyzed and numerical results show a good agreement with the available results in the case of thin shells. 12 refs.

RESONANT ABSORPTION OF AXISYMMETRIC MODES IN TWISTED MAGNETIC FLUX TUBES

Energy Technology Data Exchange (ETDEWEB)

Giagkiozis, I.; Verth, G. [Solar Plasma Physics Research Centre, School of Mathematics and Statistics, University of Sheffield, Hounsfield Road, Hicks Building, Sheffield, S3 7RH (United Kingdom); Goossens, M.; Doorsselaere, T. Van [Centre for mathematical Plasma Astrophysics, Mathematics Department, KU Leuven, Celestijnenlaan 200B bus 2400, B-3001 Leuven (Belgium); Fedun, V. [Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Amy Johnson Building, Sheffield, S1 3JD (United Kingdom)

2016-06-01

It has been shown recently that magnetic twist and axisymmetric MHD modes are ubiquitous in the solar atmosphere, and therefore the study of resonant absorption for these modes has become a pressing issue because it can have important consequences for heating magnetic flux tubes in the solar atmosphere and the observed damping. In this investigation, for the first time, we calculate the damping rate for axisymmetric MHD waves in weakly twisted magnetic flux tubes. Our aim is to investigate the impact of resonant damping of these modes for solar atmospheric conditions. This analytical study is based on an idealized configuration of a straight magnetic flux tube with a weak magnetic twist inside as well as outside the tube. By implementing the conservation laws derived by Sakurai et al. and the analytic solutions for weakly twisted flux tubes obtained recently by Giagkiozis et al. we derive a dispersion relation for resonantly damped axisymmetric modes in the spectrum of the Alfvén continuum. We also obtain an insightful analytical expression for the damping rate in the long wavelength limit. Furthermore, it is shown that both the longitudinal magnetic field and the density, which are allowed to vary continuously in the inhomogeneous layer, have a significant impact on the damping time. Given the conditions in the solar atmosphere, resonantly damped axisymmetric modes are highly likely to be ubiquitous and play an important role in energy dissipation. We also suggest that, given the character of these waves, it is likely that they have already been observed in the guise of Alfvén waves.

An axisymmetric method of creep analysis for primary and secondary creep

International Nuclear Information System (INIS)

Jahed, Hamid; Bidabadi, Jalal

2003-01-01

A general axisymmetric method for elastic-plastic analysis was previously proposed by Jahed and Dubey [ASME J Pressure Vessels Technol 119 (1997) 264]. In the present work the method is extended to the time domain. General rate type governing equations are derived and solved in terms of rate of change of displacement as a function of rate of change in loading. Different types of loading, such as internal and external pressure, centrifugal loading and temperature gradient, are considered. To derive specific equations and employ the proposed formulation, the problem of an inhomogeneous non-uniform rotating disc is worked out. Primary and secondary creep behaviour is predicted using the proposed method and results are compared to FEM results. The problem of creep in pressurized vessels is also solved. Several numerical examples show the effectiveness and robustness of the proposed method

Effect of compressibility on the global stability of axisymmetric wake flows

OpenAIRE

Meliga , Philippe; Sipp , D.; Chomaz , Jean-Marc

2010-01-01

International audience; We study the linear dynamics of global eigenmodes in compressible axisymmetric wake flows, up to the high subsonic regime. We consider both an afterbody flow at zero angle of attack and a sphere, and find that the sequence of bifurcations destabilizing the axisymmetric steady flow is independent of the Mach number and reminiscent of that documented in the incompressible wake past a sphere and a disk (Natarajan & Acrivos, J. Fluid Mech., vol. 254, 1993, p. 323), hence s...

Two-point boundary value and Cauchy formulations in an axisymmetrical MHD equilibrium problem

International Nuclear Information System (INIS)

Atanasiu, C.V.; Subbotin, A.A.

1999-01-01

In this paper we present two equilibrium solvers for axisymmetrical toroidal configurations, both based on the expansion in poloidal angle method. The first one has been conceived as a two-point boundary value solver in a system of coordinates with straight field lines, while the second one uses a well-conditioned Cauchy formulation of the problem in a general curvilinear coordinate system. In order to check the capability of our moment methods to describe equilibrium accurately, a comparison of the moment solutions with analytical solutions obtained for a Solov'ev equilibrium has been performed. (author)

One dimension harmonic oscillator

International Nuclear Information System (INIS)

Cohen-Tannoudji, Claude; Diu, Bernard; Laloe, Franck.

1977-01-01

The importance of harmonic oscillator in classical and quantum physics, eigenvalues and eigenstates of hamiltonian operator are discussed. In complement are presented: study of some physical examples of harmonic oscillators; study of stationnary states in the /x> representation; Hermite polynomials; resolution of eigenvalue equation of harmonic oscillator by polynomial method; isotope harmonic oscillator with three dimensions; charged harmonic oscillator in uniform electric field; quasi classical coherent states of harmonic oscillator; eigenmodes of vibration of two coupled harmonic oscillators; vibration modus of a continuous physical system (application to radiation: photons); vibration modus of indefinite linear chain of coupled harmonic oscillators (phonons); one-dimensional harmonic oscillator in thermodynamic equilibrium at temperature T [fr

Comparative study of turbulence model performance for axisymmetric sudden expansion flow

Energy Technology Data Exchange (ETDEWEB)

Bae, Youngmin; Kim, Young In; Kim, Keung Koo; Yoon, Juhyeon [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

2013-10-15

In this study, the performance of turbulence models in predicting the turbulent flow in an axisymmetric sudden expansion with an expansion ratio of 4 is assessed for a Reynolds number of 5.6 Χ 10{sup 4}. The comparisons show that the standard k-ε and RSM models provide the best agreement with the experimental data, whereas the standard k-ω model gives poor predictions. Owing to its computational efficiency, the Reynolds Averaged Navier-Stokes (RANS) approach has been widely used for the prediction of turbulent flows and associated pressure losses in a variety of internal flow systems such as a diffuser, orifice, converging nozzle, and pipes with sudden expansion. However, the lack of a general turbulence model often leads to limited applications of a RANS approach, i. e., the accuracy and validity of solutions obtained from RANS equations vary with the turbulence model, flow regime, near-wall treatment, and configuration of the problem. In light of the foregoing, a large amount of turbulence research has been conducted to assess the performance of existing turbulence models for different flow fields. In this paper, the turbulent flow in an axisymmetric sudden expansion is numerically investigated for a Reynolds number of 5.6 Χ 10{sup 4}, with the aim of examining the performance of several turbulence models.

Axisymmetric thermoviscoelastoplastic state of branched laminar shells, taking account of transverse-shear and torsional deformation

International Nuclear Information System (INIS)

Galishin, A.Z.

1995-01-01

The nonaxisymmetric thermoelastic stress-strain state (SSS) of branched laminar orthotropic shells was considered; the axisymmetric thermoviscoelastic SSS of branched laminar orthotropic shells was considered; and the axisymmetric thermoviscoelastoplastic SSS of branched laminar isotropic shells was considered, taking into account of the transverse-shear deformation. In the present work, in contrast, the axisymmetric thermoviscoelastoplastic SSS of branched laminar isotropic shells is considered, taking account of transverse-shear and torsional deformation. Layers that are made from orthotropic materials and deform in the elastic region may be present

HARMONIC DRIVE SELECTION

Directory of Open Access Journals (Sweden)

Piotr FOLĘGA

2014-03-01

Full Text Available The variety of types and sizes currently in production harmonic drive is a problem in their rational choice. Properly selected harmonic drive must meet certain requirements during operation, and achieve the anticipated service life. The paper discusses the problems associated with the selection of the harmonic drive. It also presents the algorithm correct choice of harmonic drive. The main objective of this study was to develop a computer program that allows the correct choice of harmonic drive by developed algorithm.

The su(1, 1) dynamical algebra from the Schroedinger ladder operators for N-dimensional systems: hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator

International Nuclear Information System (INIS)

Martinez, D; Flores-Urbina, J C; Mota, R D; Granados, V D

2010-01-01

We apply the Schroedinger factorization to construct the ladder operators for the hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator in arbitrary dimensions. By generalizing these operators we show that the dynamical algebra for these problems is the su(1, 1) Lie algebra.

Dynamics of harmonically-confined systems: Some rigorous results

Energy Technology Data Exchange (ETDEWEB)

Wu, Zhigang, E-mail: zwu@physics.queensu.ca; Zaremba, Eugene, E-mail: zaremba@sparky.phy.queensu.ca

2014-03-15

In this paper we consider the dynamics of harmonically-confined atomic gases. We present various general results which are independent of particle statistics, interatomic interactions and dimensionality. Of particular interest is the response of the system to external perturbations which can be either static or dynamic in nature. We prove an extended Harmonic Potential Theorem which is useful in determining the damping of the centre of mass motion when the system is prepared initially in a highly nonequilibrium state. We also study the response of the gas to a dynamic external potential whose position is made to oscillate sinusoidally in a given direction. We show in this case that either the energy absorption rate or the centre of mass dynamics can serve as a probe of the optical conductivity of the system. -- Highlights: •We derive various rigorous results on the dynamics of harmonically-confined atomic gases. •We derive an extension of the Harmonic Potential Theorem. •We demonstrate the link between the energy absorption rate in a harmonically-confined system and the optical conductivity.

Nonlinear electromagnetic gyrokinetic equations for rotating axisymmetric plasmas

International Nuclear Information System (INIS)

Artun, M.; Tang, W.M.

1994-03-01

The influence of sheared equilibrium flows on the confinement properties of tokamak plasmas is a topic of much current interest. A proper theoretical foundation for the systematic kinetic analysis of this important problem has been provided here by presented the derivation of a set of nonlinear electromagnetic gyrokinetic equations applicable to low frequency microinstabilities in a rotating axisymmetric plasma. The subsonic rotation velocity considered is in the direction of symmetry with the angular rotation frequency being a function of the equilibrium magnetic flux surface. In accordance with experimental observations, the rotation profile is chosen to scale with the ion temperature. The results obtained represent the shear flow generalization of the earlier analysis by Frieman and Chen where such flows were not taken into account. In order to make it readily applicable to gyrokinetic particle simulations, this set of equations is cast in a phase-space-conserving continuity equation form

Axisymmetric instability in a noncircular tokamak

International Nuclear Information System (INIS)

Lipschultz, B.

1979-10-01

The stability of dee, inverse-dee and square cross section plasmas to axisymmetric modes has been investigated experimentally in Tokapole II, a tokamak with a four-null poloidal divertor. Experimental results are closely compared with predictions of two numerical stability codes - the PEST code (ideal MHD, linear stability) adapted to tokapole geometry and a code which follows the nonlinear evolution of shapes similar to tokapole equilibria

The Local Stellar Velocity Field via Vector Spherical Harmonics

Science.gov (United States)

Markarov, V. V.; Murphy, D. W.

2007-01-01

We analyze the local field of stellar tangential velocities for a sample of 42,339 nonbinary Hipparcos stars with accurate parallaxes, using a vector spherical harmonic formalism. We derive simple relations between the parameters of the classical linear model (Ogorodnikov-Milne) of the local systemic field and low-degree terms of the general vector harmonic decomposition. Taking advantage of these relationships, we determine the solar velocity with respect to the local stars of (V(sub X), V(sub Y), V(sub Z)) (10.5, 18.5, 7.3) +/- 0.1 km s(exp -1) not corrected for the asymmetric drift with respect to the local standard of rest. If only stars more distant than 100 pc are considered, the peculiar solar motion is (V(sub X), V(sub Y), V(sub Z)) (9.9, 15.6, 6.9) +/- 0.2 km s(exp -1). The adverse effects of harmonic leakage, which occurs between the reflex solar motion represented by the three electric vector harmonics in the velocity space and higher degree harmonics in the proper-motion space, are eliminated in our analysis by direct subtraction of the reflex solar velocity in its tangential components for each star. The Oort parameters determined by a straightforward least-squares adjustment in vector spherical harmonics are A=14.0 +/- 1.4, B=13.1 +/- 1.2, K=1.1 +/- 1.8, and C=2.9 +/- 1.4 km s(exp -1) kpc(exp -1). The physical meaning and the implications of these parameters are discussed in the framework of a general linear model of the velocity field. We find a few statistically significant higher degree harmonic terms that do not correspond to any parameters in the classical linear model. One of them, a third-degree electric harmonic, is tentatively explained as the response to a negative linear gradient of rotation velocity with distance from the Galactic plane, which we estimate at approximately -20 km s(exp -1) kpc(exp -1). A similar vertical gradient of rotation velocity has been detected for more distant stars representing the thick disk (z greater than 1 kpc

Secondary magnetic field harmonics dependence on vacuum beam chamber geometry

Directory of Open Access Journals (Sweden)

S. Y. Shim

2013-08-01

Full Text Available The harmonic magnetic field properties due to eddy currents have been studied with respect to the geometry of the vacuum beam chamber. We derived a generalized formula enabling the precise prediction of any field harmonics generated by eddy currents in beam tubes with different cross-sectional geometries. Applying our model to study the properties of field harmonics in beam tubes with linear dipole magnetic field ramping clearly proved that the circular cross section tube generates only a dipole field from eddy currents. The elliptic tube showed noticeable magnitudes of sextupole and dipole fields. We demonstrate theoretically that it is feasible to suppress the generation of the sextupole field component by appropriately varying the tube wall thickness as a function of angle around the tube circumference. This result indicates that it is possible to design an elliptical-shaped beam tube that generates a dipole field component with zero magnitude of sextupole. In a rectangular-shaped beam tube, one of the selected harmonic fields can be prevented if an appropriate wall thickness ratio between the horizontal and vertical tube walls is properly chosen. Our generalized formalism can be used for optimization of arbitrarily complex-shaped beam tubes, with respect to suppression of detrimental field harmonics.

Automated detection and characterization of harmonic tremor in continuous seismic data

Science.gov (United States)

Roman, Diana C.

2017-06-01

Harmonic tremor is a common feature of volcanic, hydrothermal, and ice sheet seismicity and is thus an important proxy for monitoring changes in these systems. However, no automated methods for detecting harmonic tremor currently exist. Because harmonic tremor shares characteristics with speech and music, digital signal processing techniques for analyzing these signals can be adapted. I develop a novel pitch-detection-based algorithm to automatically identify occurrences of harmonic tremor and characterize their frequency content. The algorithm is applied to seismic data from Popocatepetl Volcano, Mexico, and benchmarked against a monthlong manually detected catalog of harmonic tremor events. During a period of heightened eruptive activity from December 2014 to May 2015, the algorithm detects 1465 min of harmonic tremor, which generally precede periods of heightened explosive activity. These results demonstrate the algorithm's ability to accurately characterize harmonic tremor while highlighting the need for additional work to understand its causes and implications at restless volcanoes.

An object-oriented approach for harmonization of multimedia markup languages

Science.gov (United States)

Chen, Yih-Feng; Kuo, May-Chen; Sun, Xiaoming; Kuo, C.-C. Jay

2003-12-01

An object-oriented methodology is proposed to harmonize several different markup languages in this research. First, we adopt the Unified Modelling Language (UML) as the data model to formalize the concept and the process of the harmonization process between the eXtensible Markup Language (XML) applications. Then, we design the Harmonization eXtensible Markup Language (HXML) based on the data model and formalize the transformation between the Document Type Definitions (DTDs) of the original XML applications and HXML. The transformation between instances is also discussed. We use the harmonization of SMIL and X3D as an example to demonstrate the proposed methodology. This methodology can be generalized to various application domains.

Integrable motion of a vortex dipole in an axisymmetric flow

International Nuclear Information System (INIS)

Sutyrin, G.G.; Perrot, X.; Carton, X.

2008-01-01

The evolution of a self-propelling vortex dipole, embedded in an external nondivergent flow with constant potential vorticity, is studied in an equivalent-barotropic model commonly used in geophysical, astrophysical and plasma studies. In addition to the conservation of the Hamiltonian for an arbitrary point vortex dipole, it is found that the angular momentum is also conserved when the external flow is axisymmetric. This reduces the original four degrees of freedom to only two, so that the solution is expressed in quadratures. In particular, the scattering of antisymmetric dipoles approaching from the infinity is analyzed in the presence of an axisymmetric oceanic flow typical for the vicinity of isolated seamounts

Nonlinearly driven harmonics of Alfvén modes

Science.gov (United States)

Zhang, B.; Breizman, B. N.; Zheng, L. J.; Berk, H. L.

2014-01-01

In order to study the leading order nonlinear magneto-hydrodynamic (MHD) harmonic response of a plasma in realistic geometry, the AEGIS code has been generalized to account for inhomogeneous source terms. These source terms are expressed in terms of the quadratic corrections that depend on the functional form of a linear MHD eigenmode, such as the Toroidal Alfvén Eigenmode. The solution of the resultant equation gives the second order harmonic response. Preliminary results are presented here.

Nonlinearly driven harmonics of Alfvén modes

Energy Technology Data Exchange (ETDEWEB)

Zhang, B., E-mail: bozhang@austin.utexas.edu; Breizman, B. N.; Zheng, L. J.; Berk, H. L. [Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (United States)

2014-01-15

In order to study the leading order nonlinear magneto-hydrodynamic (MHD) harmonic response of a plasma in realistic geometry, the AEGIS code has been generalized to account for inhomogeneous source terms. These source terms are expressed in terms of the quadratic corrections that depend on the functional form of a linear MHD eigenmode, such as the Toroidal Alfvén Eigenmode. The solution of the resultant equation gives the second order harmonic response. Preliminary results are presented here.

Axisymmetric accretion flows very near black holes and Rosen-collapsed objects

International Nuclear Information System (INIS)

Stoeger, W.R.

1979-01-01

Motivated by the need for stronger observational leverage on the black hole hypothesis and for a more detailed characterization of axisymmetric accretion flows across the marginally stable circular orbit rsub(ms), a general approach for describing the non-Keplerian accretion in the region rsub(H) 0 , where rsub(H) = radius of the event horizon and r 0 > = rsub(ms) is developed. The procedure possesses many advantages, including easily imposed consistency with the Keplerian for r > rsub(o), the avoidance of ad hoc boundary conditions at rsub(ms) and/or at rsub(H) and its application also to accretion in Rosen's bimetric theory, whose spherically symmetric solution has the same qualitative orbital topography as that of general relativity. It becomes apparent, furthermore, that the particular viscosity law chosen in this procedure will have a crucial bearing on the flow in the region rsub(ms) 0 . (author)

GATO: an MHD stability code for axisymmetric plasmas with internal separatrices

International Nuclear Information System (INIS)

Bernard, L.C.; Helton, F.J.; Moore, R.W.

1981-07-01

The GATO code computes the growth rate of ideal magnetohydrodynamic instabilities in axisymmetric geometries with internal separatrices such as doublet and expanded spheromak. The basic method, which uses a variational principle and a Galerkin procedure to obtain a matrix eigenvalue problem, is common to the ERATO and PEST codes. A new coordinate system has been developed to handle the internal separatrix. Efficient algorithms have been developed to solve the matrix eigenvalue problem for matrices of rank as large as 40,000. Further improvement is expected using graph theoretical techniques to reorder the matrices. Using judicious mesh repartition, the marginal point can be determined with great precision. The code has been extensively used to optimize doublet and general tokamak plasmas

Optimal convergence recovery for the Fourier-finite-element approximation of Maxwell's equations in non-smooth axisymmetric domains

International Nuclear Information System (INIS)

Nkemzi, B.

2005-10-01

Three-dimensional time-harmonic Maxwell's problems in axisymmetric domains Ω-circumflex with edges and conical points on the boundary are treated by means of the Fourier-finite-element method. The Fourier-fem combines the approximating Fourier series expansion of the solution with respect to the rotational angle using trigonometric polynomials of degree N (N → ∞), with the finite element approximation of the Fourier coefficients on the plane meridian domain Ω a is a subset of R + 2 of Ω-circumflex with mesh size h (h → 0). The singular behaviors of the Fourier coefficients near angular points of the domain Ω a are fully described by suitable singular functions and treated numerically by means of the singular function method with the finite element method on graded meshes. It is proved that the rate of convergence of the mixed approximations in H 1 (Ω-circumflex) 3 is of the order O (h+N -1 ) as known for the classical Fourier-finite-element approximation of problems with regular solutions. (author)

High-order harmonic generation in solid slabs beyond the single-active-electron approximation

Science.gov (United States)

Hansen, Kenneth K.; Deffge, Tobias; Bauer, Dieter

2017-11-01

High-harmonic generation by a laser-driven solid slab is simulated using time-dependent density functional theory. Multiple harmonic plateaus up to very high harmonic orders are observed already at surprisingly low field strengths. The full all-electron harmonic spectra are, in general, very different from those of any individual Kohn-Sham orbital. Freezing the Kohn-Sham potential instead is found to be a good approximation for the laser intensities and harmonic orders considered. The origins of the plateau cutoffs are explained in terms of band gaps that can be reached by Kohn-Sham electrons and holes moving through the band structure.

Tokamak equilibria with non-parallel flow in a triangularity-deformed axisymmetric toroidal coordinate system

Directory of Open Access Journals (Sweden)

Ap Kuiroukidis

2018-01-01

Full Text Available We consider a generalized Grad–Shafranov equation (GGSE in a triangularity-deformed axisymmetric toroidal coordinate system and solve it numerically for the generic case of ITER-like and JET-like equilibria with non-parallel flow. It turns out that increase of the triangularity improves confinement by leading to larger values of the toroidal beta and the safety factor. This result is supported by the application of a criterion for linear stability valid for equilibria with flow parallel to the magnetic field. Also, the parallel flow has a weaker stabilizing effect.

Axisymmetric general relativistic simulations of the accretion-induced collapse of white dwarfs

International Nuclear Information System (INIS)

Abdikamalov, E. B.; Ott, C. D.; Rezzolla, L.; Dessart, L.; Dimmelmeier, H.; Marek, A.; Janka, H.-T.

2010-01-01

The accretion-induced collapse (AIC) of a white dwarf may lead to the formation of a protoneutron star and a collapse-driven supernova explosion. This process represents a path alternative to thermonuclear disruption of accreting white dwarfs in type Ia supernovae. In the AIC scenario, the supernova explosion energy is expected to be small and the resulting transient short-lived, making it hard to detect by electromagnetic means alone. Neutrino and gravitational-wave (GW) observations may provide crucial information necessary to reveal a potential AIC. Motivated by the need for systematic predictions of the GW signature of AIC, we present results from an extensive set of general-relativistic AIC simulations using a microphysical finite-temperature equation of state and an approximate treatment of deleptonization during collapse. Investigating a set of 114 progenitor models in axisymmetric rotational equilibrium, with a wide range of rotational configurations, temperatures and central densities, and resulting white dwarf masses, we extend previous Newtonian studies and find that the GW signal has a generic shape akin to what is known as a 'type III' signal in the literature. Despite this reduction to a single type of waveform, we show that the emitted GWs carry information that can be used to constrain the progenitor and the postbounce rotation. We discuss the detectability of the emitted GWs, showing that the signal-to-noise ratio for current or next-generation interferometer detectors could be high enough to detect such events in our Galaxy. Furthermore, we contrast the GW signals of AIC and rotating massive star iron core collapse and find that they can be distinguished, but only if the distance to the source is known and a detailed reconstruction of the GW time series from detector data is possible. Some of our AIC models form massive quasi-Keplerian accretion disks after bounce. The disk mass is very sensitive to progenitor mass and angular momentum

Matrix inequalities for the difference between arithmetic mean and harmonic mean

OpenAIRE

Liao, Wenshi; Wu, Junliang

2015-01-01

Motivated by the refinements and reverses of arithmetic-geometric mean and arithmetic-harmonic mean inequalities for scalars and matrices, in this article, we generalize the scalar and matrix inequalities for the difference between arithmetic mean and harmonic mean. In addition, relevant inequalities for the Hilbert-Schmidt norm and determinant are established.

Axisymmetric instability in a noncircular tokamak: experiment and theory

International Nuclear Information System (INIS)

Lipschultz, B.; Prager, S.C.; Todd, A.M.M.; Delucia, J.

1979-09-01

The stability of dee, inverse-dee and square cross section plasmas to axisymmetric modes has been investigated experimentally in Tokapole II, a tokamak with a four-null poloidal divertor. Experimental results are closely compared with predictions of two numerical stability codes -- the PEST code (ideal MHD, linear stability) adapted to tokapole geometry and a code which follows the nonlinear evolution of shapes similar to tokapole equilibria. Experimentally, the square is vertically stable and both dee's unstable to a vertical nonrigid axisymmetric shift. The central magnetic axis displacement grows exponentially with a growth time approximately 10 3 poloidal Alfven times plasma time. Proper initial positioning of the plasma on the midplane allows passive feedback to nonlinearly restore vertical motion to a small stable oscillation. Experimental poloidal flux plots are produced directly from internal magnetic probe measurements

Statistical Analysis and Comparison of Harmonics Measured in Offshore Wind Farms

DEFF Research Database (Denmark)

Kocewiak, Lukasz Hubert; Hjerrild, Jesper; Bak, Claus Leth

2011-01-01

The paper shows statistical analysis of harmonic components measured in different offshore wind farms. Harmonic analysis is a complex task and requires many aspects, such as measurements, data processing, modeling, validation, to be taken into consideration. The paper describes measurement process...... and shows sophisticated analysis on representative harmonic measurements from Avedøre Holme, Gunfleet Sands and Burbo Bank wind farms. The nature of generation and behavior of harmonic components in offshore wind farms clearly presented and explained based on probabilistic approach. Some issues regarding...... commonly applied standards are also put forward in the discussion. Based on measurements and data analysis it is shown that a general overview about wind farm harmonic behaviour cannot be fully observed only based on single-value measurements as suggested in the standards but using more descriptive...

Quantization of a 3D Nonstationary Harmonic plus an Inverse Harmonic Potential System

Directory of Open Access Journals (Sweden)

Salim Medjber

2016-01-01

Full Text Available The Schrödinger solutions for a three-dimensional central potential system whose Hamiltonian is composed of a time-dependent harmonic plus an inverse harmonic potential are investigated. Because of the time-dependence of parameters, we cannot solve the Schrödinger solutions relying only on the conventional method of separation of variables. To overcome this difficulty, special mathematical methods, which are the invariant operator method, the unitary transformation method, and the Nikiforov-Uvarov method, are used when we derive solutions of the Schrödinger equation for the system. In particular, the Nikiforov-Uvarov method with an appropriate coordinate transformation enabled us to reduce the eigenvalue equation of the invariant operator, which is a second-order differential equation, to a hypergeometric-type equation that is convenient to treat. Through this procedure, we derived exact Schrödinger solutions (wave functions of the system. It is confirmed that the wave functions are represented in terms of time-dependent radial functions, spherical harmonics, and general time-varying global phases. Such wave functions are useful for studying various quantum properties of the system. As an example, the uncertainty relations for position and momentum are derived by taking advantage of the wave functions.

Neoclassical resonant-plateau transport calculation in an effectively axisymmetrized tandem mirror with finite end plate resistance

International Nuclear Information System (INIS)

Katanuma, I.; Kiwamoto, Y.; Adachi, S.; Inutake, M.; Ishii, K.; Yatsu, K.; Sawada, K.; Miyoshi, S.

1987-05-01

Calculations are made for neoclassical resonant-plateau transports in the geometry of the effectively axisymmetrized tandem mirror GAMMA 10 magnetic field, which has minimum B inbord anchors inside the axisymmetric plug/barrier mirror cells. Azimuthal drifts at the local non-axisymmetric regions are included. The radial potential profile is determined by solving selfconsistently the charge neutrality equation. A finite resistance connecting end plate to machine ground provides appropriate boundary conditions on the radial electrostatic potential distribution so that it can be determined uniquely. The calculation is consistent with experimental results of GAMMA 10. (author)

Low Cost Method of Manufacturing Cooled Axisymmetric Scramjets, Phase I

Data.gov (United States)

National Aeronautics and Space Administration — Scramjet engine developers are working on advanced axisymmetric engine concepts that may not be feasible due to limitations of currently available manufacturing...

The spherical-harmonics representation for the interaction between diatomic molecules: The general case and applications to COsbnd CO and COsbnd HF

Science.gov (United States)

Barreto, Patricia R. P.; Cruz, Ana Claudia P. S.; Barreto, Rodrigo L. P.; Palazzetti, Federico; Albernaz, Alessandra F.; Lombardi, Andrea; Maciel, Glauciete S.; Aquilanti, Vincenzo

2017-07-01

The spherical-harmonics expansion is a mathematically rigorous procedure and a powerful tool for the representation of potential energy surfaces of interacting molecular systems, determining their spectroscopic and dynamical properties, specifically in van der Waals clusters, with applications also to classical and quantum molecular dynamics simulations. The technique consists in the construction (by ab initio or semiempirical methods) of the expanded potential interaction up to terms that provide the generation of a number of leading configurations sufficient to account for faithful geometrical representations. This paper reports the full general description of the method of the spherical-harmonics expansion as applied to diatomic-molecule - diatomic-molecule systems of increasing complexity: the presentation of the mathematical background is given for providing both the application to the prototypical cases considered previously (O2sbnd O2, N2sbnd N2, and N2sbnd O2 systems) and the generalization to: (i) the COsbnd CO system, where a characteristic feature is the lower symmetry order with respect to the cases studied before, requiring a larger number of expansion terms necessary to adequately represent the potential energy surface; and (ii) the COsbnd HF system, which exhibits the lowest order of symmetry among this class of aggregates and therefore the highest number of leading configurations.

Feedback stabilization of axisymmetric modes in tokamaks

International Nuclear Information System (INIS)

Jardin, S.C.; Larrabee, D.A.

1982-01-01

Noncircular tokamak plasmas can be unstable to ideal MHD axisymmetric instabilities. Passive conductors with finite resistivity will at best slow down these instabilities to the resistive (L/R) time of the conductors. An active feedback system far from the plasma which responds on this resistive time can stabilize the system provided its mutual inductance with the passive coils is small enough

The spectrum of axisymmetric torsional Alfven waves

International Nuclear Information System (INIS)

Sy, W.N.

1977-03-01

The spectrum of axisymmetric torsional Alfven waves propagating in a cylindrical, non-uniform, resistive plasma waveguide has been analysed by a method of singular perturbations. A simple condition has been derived which predicts whether the spectrum is continuous or discrete under given physical conditions. Application of this result to resolve an apparent discrepancy in experimental observations is briefly discussed. (Author)

Almost-sure identifiability of multidimensional harmonic retrieval

NARCIS (Netherlands)

Jiang, T; Sidiropoulos, ND; ten Berge, JMF

Two-dimensional (2-D) and, more generally, multidimensional harmonic retrieval is of interest in a variety of applications, including transmitter localization and joint time and frequency offset estimation in wireless communications. The associated identifiability problem is key in understanding the

RESEARCH ON THE INTERNATIONAL ACCOUNTING HARMONIZATION PROCESS

Directory of Open Access Journals (Sweden)

Tatiana Danescu

2016-12-01

Full Text Available During the last decades, the need of harmonization of the financial reporting frameworks has become more acute, mostly because the capital markets are not restricted anymore by country borders and capital movement has outlined the phenomenon of globalization and internationalism. A significant step in harmonizing the financial reporting was done in the process of normalization through different sets of rules and principles, recognized and applied in many states are the International Financial Reporting Standards (IFRS. The process of international recognition of these standards continues along with conceptual development which is based on epistemological research on specific markets, industries, economies open to international capital flows. In this context it becomes of interest to identify and understand generally accepted and applied accounting elements which carry forward the accounting harmonization process along with factors and circumstances that create diversity in nationally applied financial reporting frameworks.

GATO: An MHD stability code for axisymmetric plasmas with internal separatrices

International Nuclear Information System (INIS)

Bernard, L.C.; Helton, F.J.; Moore, R.W.

1981-01-01

The GATO code computes the growth rate of ideal magnetohydrodynamic instabilities in axisymmetric geometries with internal separatrices such as doublet and expanded spheromak. The basic method, which uses a variational principle and a Galerkin procedure to obtain a matrix eigenvalue problem, is common to the ERATO and PEST codes. A new coordinate system has been developed to handle the internal separatrix. Efficient algorithms have been developed to solve the matrix eigenvalue problem for matrices of rank as large as 40 000. Further improvement is expected using graph theoretical techniques to reorder the matrices. Using judicious mesh repartition, the marginal point can be determined with great precision. The code has been extensively used to optimize doublet and general tokamak plasmas. (orig.)

ASCOT-1, Thermohydraulics of Axisymmetric PWR Core with Homogeneous Flow During LOCA

International Nuclear Information System (INIS)

1978-01-01

1 - Nature of the physical problem solved: ASCOT-1 is used to analyze the thermo-hydraulic behaviour in a PWR core during a loss-of-coolant accident. 2 - Method of solution: The core is assumed to be axisymmetric two-dimensional and the conservation laws are solved by the method of characteristics. For the temperature response of fuel in the annular regions into which the core is divided, the heat conduction equations are solved by an explicit method with averaged flow conditions. 3 - Restrictions on the complexity of the problem: Axisymmetric two-dimensional homogeneous flows

Harmonics and energy management

International Nuclear Information System (INIS)

Andresen, M.

1993-01-01

To summarize what this paper has presented: Voltage and current non-sinusoidal wave shapes exist in our power system. These harmonics result from the prolific use of non-linear loads. The use of these types of loads is increasing dramatically, partly due to the push to implement energy management techniques involving harmonic generating equipment. Harmonic analysis can identify specific harmonics, their frequency, magnitude, and phase shift referenced to the fundamental. Harmonic distortion forces the use of true RMS multimeters for measurement accuracy. High levels of neutral current and N-G voltages are now possible. Transformers may overheat and fail even though they are below rated capacity. Low power factors due to harmonics cannot be corrected by the installation of capacitors, and knowledge of the fundamental VARs or the displacement power factor is needed to use capacitors alone for power factor correction. The harmonic related problems presented are by no means an exhaustive list. Many other concerns arise when harmonics are involved in the power system. The critical issue behind these problems is that many of the devices being recommended from an energy management point of view are contributing to the harmonic levels, and thus to the potential for harmonic problems. We can no longer live in the sinusoidal mentality if we are to be effective in saving energy and reducing costs

Axisymmetrical separator for separating particulate matter from a fluid carrying medium

Science.gov (United States)

Linhardt, Hans D.

1984-09-04

A separator for separating particles carried in a fluid carrying medium is disclosed. The separator includes an elongated duct and associated openings incorporated in a solid body. The duct is axisymmetrical relative to its longitudinal axis, and includes a curved wall portion having a curved cross-section taken along the longitudinal axis. An axisymmetrical opening located downstream of the curved wall portion leads from the duct into an axisymmetrical channel which is substantially radially disposed relative to the longitudinal axis. Continuation of the duct downstream of the opening is a discharge portion which is substantially colinear with the longitudinal axis. In operation, a substantial majority of the fluid carrying medium leaves the duct radially through the opening and channel in a state substantially free of particles. A remaining small portion of the fluid carrying medium and a substantial majority of the particles are channelled into the discharge portion by centrifugal forces arising due to travel of the particles along the curved walls. For industrial scale separation of particles from a fluid carrying medium, such as for the clean-up of stack gases, an array of several hundred to several thousand of the separators is provided.

Theory of plasma confinement in non-axisymmetric magnetic fields.

Science.gov (United States)

Helander, Per

2014-08-01

The theory of plasma confinement by non-axisymmetric magnetic fields is reviewed. Such fields are used to confine fusion plasmas in stellarators, where in contrast to tokamaks and reversed-field pinches the magnetic field generally does not possess any continuous symmetry. The discussion is focussed on magnetohydrodynamic equilibrium conditions, collisionless particle orbits, and the kinetic theory of equilbrium and transport. Each of these topics is fundamentally affected by the absence of symmetry in the magnetic field: the field lines need not trace out nested flux surfaces, the particle orbits may not be confined, and the cross-field transport can be very large. Nevertheless, by tailoring the magnetic field appropriately, well-behaved equilibria with good confinement can be constructed, potentially offering an attractive route to magnetic fusion. In this article, the mathematical apparatus to describe stellarator plasmas is developed from first principles and basic elements underlying confinement optimization are introduced.

Hyper-spherical harmonics and anharmonics in m-dimensional space

International Nuclear Information System (INIS)

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

2008-01-01

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

Experimental studies on an axisymmetric divertor in DIVA(JFT-2a)

International Nuclear Information System (INIS)

Yamamoto, Shin

1979-03-01

DIVA(JFT-2a) is the first tokamak with an axisymmetric divertor in the world. Objectives of the experiments were i) Plasma production and confinement in a tokamak with a separatrix magnetic surface, and ii) divertor effects on radiation loss and plasma confinement. The results so far are as follows: i) The equilibrium with a separatrix magnetic surface is stable during the discharge. ii) There is an ergodic region near the separatrix magnetic surface due to non-axisymmetric magnetic perturbations. iii) The divertor reduces radiation loss and increases energy confinement time. iv) The divertor does not affect the transport process in the main plasma. (author)

Stable operation of an effectively axisymmetric neutral beam driven tandem mirror

International Nuclear Information System (INIS)

Molvik, A.W.; Barter, J.D.; Buchenauer, D.A.; Casper, T.A.; Correll, D.L.; Dimonte, G.; Falabella, S.; Foote, J.H.; Pincosy, P.A.

1990-01-01

A quiescent plasma is sustained for 80 energy confinement times by only gas fuelling and neutral beam heating in an axisymmetric region of the Tandem Mirror Experiment Upgrade (TMX-U). This plasma should be unstable because of the bad magnetic curvature and the absence of ion cyclotron heating which previously provided ponderomotive stabilization to sustain plasmas in bad-curvature regions of other axisymmetric mirror experiments. The TMX-U data are consistent with stabilization by a symbiosis between two mechanisms - line tying, which reduces the growth rate, and finite Larmor radius edge stabilization, which can result in quiescent operation. (author). 42 refs, 8 figs, 1 tab

Finite volume approximation of the three-dimensional flow equation in axisymmetric, heterogeneous porous media based on local analytical solution

KAUST Repository

Salama, Amgad

2013-09-01

In this work the problem of flow in three-dimensional, axisymmetric, heterogeneous porous medium domain is investigated numerically. For this system, it is natural to use cylindrical coordinate system, which is useful in describing phenomena that have some rotational symmetry about the longitudinal axis. This can happen in porous media, for example, in the vicinity of production/injection wells. The basic feature of this system is the fact that the flux component (volume flow rate per unit area) in the radial direction is changing because of the continuous change of the area. In this case, variables change rapidly closer to the axis of symmetry and this requires the mesh to be denser. In this work, we generalize a methodology that allows coarser mesh to be used and yet yields accurate results. This method is based on constructing local analytical solution in each cell in the radial direction and moves the derivatives in the other directions to the source term. A new expression for the harmonic mean of the hydraulic conductivity in the radial direction is developed. Apparently, this approach conforms to the analytical solution for uni-directional flows in radial direction in homogeneous porous media. For the case when the porous medium is heterogeneous or the boundary conditions is more complex, comparing with the mesh-independent solution, this approach requires only coarser mesh to arrive at this solution while the traditional methods require more denser mesh. Comparisons for different hydraulic conductivity scenarios and boundary conditions have also been introduced. © 2013 Elsevier B.V.

Means of Harmonization in Religious Discourse

Directory of Open Access Journals (Sweden)

Irina Ščukina

2012-12-01

Full Text Available Means of harmonization of religious discourse are considered by studying communicational behaviour (verbal and nonverbal between the religion institution and believers. The following factors defining specificity of realization of harmonization in Orthodox and other religious texts are taken into account: the communication channel between the author and the reader, a defining speech genre, the command of language (communication code, and extra-linguistic factors. It is shown that sharing the general social, historical and national experience, as well as a lexical overlapping of actors on both sides of the communication channel are the deciding elements of the harmonization process. The analysis also shows that usage of rational argumentation is more likely to lead to harmonisation in comparison to other rhetoric tools (i. e. affective ones or story-telling. Rational and unemotional sermonic discourse is perceived as a sign of respect (namely, for the listener's intelligence. Another successful and much-applied way seems to be evoking a feeling of equality, unity and/or identity between clerics and their flocks.

Influence of Axisymmetrically Deformed Explosions in Type II Supernovae on the Reproduction of the Solar System Abundances

Science.gov (United States)

Nagataki, Shigehiro

1999-01-01

We have tried to reproduce the solar system abundances using the nucleosynthesis products of Type Ia and Type II supernovae. In particular, we examined the effects of axisymmetrically deformed explosions in Type II supernovae. 44Ca and 47,48Ti are enhanced considerably in axisymmetrically deformed explosion models because of the active alpha-rich freezeout. The enhancement of nuclei around A=45 is a welcome result since it solves the problem of the nuclei shortage. Moreover, 59Co, 63,65Cu, and 66Zn are enhanced enough to reproduce the solar system abundances. The enhancement of Cu and Zn means the possibility that these nuclei, which have been said to be produced by the slow process, can be synthesized fairly well during the explosive nucleosynthesis. To discuss their origin quantitatively, the position of the mass cut is a very important parameter that is very difficult to determine numerically at present. We also stress that an axisymmetrically deformed explosion of Type II supernovae of the degree that is considered in this analysis is not excluded by the results of calculations of explosive nucleosynthesis, that is, the nucleosynthesis products are not extremely disturbed and the solar system abundances can be reproduced fairly well by the axisymmetrically deformed explosion models. This conclusion will be good for the theory of core collapse including the rotation of an iron core, magnetic field, and axisymmetrically modified neutrino radiation from a rotating protoneutron star, which possibly can cause an axisymmetrically deformed explosion.

Harmonic mapping character of Rosen's bimetric theory of gravity and the geometry of its harmonic mapping space

International Nuclear Information System (INIS)

Stoeger, W.R.; Whitman, A.P.; Knill, R.J.

1985-01-01

After showing that Rosen's bimetric theory of gravity is a harmonic map, the geometry of the ten-dimensional harmonic mapping space (HMS), and of its nine-dimensional symmetric submanifolds, which are the leaves of the codimension one foliation of the HMS, is detailed. Both structures are global affinely symmetric spaces. For each, the metric, connections, and Riemann, Ricci, and scalar curvatures are given. The Killing vectors in each case are also worked out and related to the ''conserved quantities'' naturally associated with the harmonic mapping character of the theory. The structure of the Rosen HMS is very much like that determined by the DeWitt metric on the six-dimensional Wheeler superspace of all positive definite three-dimensional metrics. It is clear that a slight modification of the Rosen HMS metric will yield the corresponding metric on the space of all four-dimensional metrics of Lorentz signature. Finally, interesting avenues of further research are indicated, particularly with respect to the structure and comparison of Lagrangian-based gravitational theories which are similar to Einstein's general relativity

Atto second high harmonic sources

International Nuclear Information System (INIS)

Nam, Chang Hee

2008-01-01

High harmonic generation is a powerful method to produce attosecond pulses. The high harmonics, emitted from atoms driven by intense femtosecond laser pulses, can from an attosecond pulse train with equally spaced harmonic spectrum or an isolated single attosecond pulse with broad continuum spectrum. Using high power femtosecond laser technology developed at CXRC, we have investigated the spectral and temporal characteristics of high harmonics obtained from gaseous atoms. The spectral structure of harmonics could be manipulated by controlling laser chirp, and continuous tuning of harmonic wavelengths was achieved. For rigorous temporal characterization of attosecond harmonic pulses a cross correlation technique was applied to the photoionization process by harmonic and IR femtosecond pulses and achieved the complete temporal reconstruction of attosecond pulse trains, revealing the detailed temporal structure of the attosecond chirp by material dispersion. The duration of attosecond high harmonic pulses is usually much longer than that of transform limited pulses due to the inherent chirp originating from the harmonic generation process. The attosecond chirp compensation in the harmonic generation medium itself was demonstrated, thereby realizing the generation of near transform limited attosecond pulses. The interference of attosecond electron wave packets, generated from an atom by attosecond harmonic pulses, will be also presented

Experimental and numerical research on cavitating flows around axisymmetric bodies

International Nuclear Information System (INIS)

Haipeng, Wei; Song, Fu; Qin, Wu; Biao, Huang; Guoyu, Wang

2014-01-01

We investigated the cavitating flows around different axisymmetric bodies based on experiments and numerical simulation. In the numerical simulation, the multiphase Reynolds averaged Navier Stokes equations (RANS) were solved via the commercial computational fluid dynamics code CFX. The modified k-wSST turbulence model was used along with the transport equation-based cavitation model. In the experiments, a high-speed video technique was used to observe the unsteady cavitating flow patterns, and the dynamic force measurement system was used to measure the hydrodynamics of the axisymmetric bodies under different cavitation conditions. Results are shown for the hemisphere bodies, conical bodies and blunt bodies. Reasonable agreements were obtained between the computational and experimental results. The results show that for the hemispherical body, the cavity consists of quasi-steady transparent region and unsteady foggy water-vapor mixture region, which contains small-scale vortices and is dominated by bubble clusters, causing irregular disturbances at the cavity interfaces. The curvature at the front of the conical body is larger, resulting in that the flow separates at the shoulder of the axisymmetric body. The cavity stretches downstream and reaches to a fixed cavity length and shape. For blunt bodies, the incipient cavitation number is larger than that for the hemispherical body. A large cloud cavity is formed at the shoulder of the blunt body in the cores of vortices in high shear separation regions and the re-entrant jet does not significantly interact with the cavity interface when it moves upstream. As to the dynamic characteristics of unsteady cavitating flows around the axisymmetric bodies, the pulsation frequency for the hemispherical body is larger than that for the blunt body. For the hemispherical body, the pulsation is mainly caused by the high-frequency, small-scale shedding at the rear end of the cavity, while for the blunt body, the main factor for

High-harmonic spectroscopy of oriented OCS molecules: emission of even and odd harmonics.

Science.gov (United States)

Kraus, P M; Rupenyan, A; Wörner, H J

2012-12-07

We study the emission of even and odd high-harmonic orders from oriented OCS molecules. We use an intense, nonresonant femtosecond laser pulse superimposed with its phase-controlled second harmonic field to impulsively align and orient a dense sample of molecules from which we subsequently generate high-order harmonics. The even harmonics appear around the full revivals of the rotational dynamics. We demonstrate perfect coherent control over their intensity through the subcycle delay of the two-color fields. The odd harmonics are insensitive to the degree of orientation, but modulate with the degree of axis alignment, in agreement with calculated photorecombination dipole moments. We further compare the shape of the even and odd harmonic spectra with our calculations and determine the degree of orientation.

Axisymmetric tokamak scapeoff transport

International Nuclear Information System (INIS)

Singer, C.E.; Langer, W.D.

1982-08-01

We present the first self-consistent estimate of the magnitude of each term in a fluid treatment of plasma transport for a plasma lying in regions of open field lines in an axisymmetric tokamak. The fluid consists of a pure hydrogen plasma with sources which arise from its interaction with neutral hydrogen atoms. The analysis and results are limited to the high collisionality regime, which is optimal for a gaseous neutralizer divertor, or to a cold plasma mantle in a tokamak reactor. In this regime, both classical and neoclassical transport processes are important, and loss of particles and energy by diamagnetic flow are also significant. The prospect of extending the analysis to the lower collisionality regimes encountered in many existing experiments is discussed

Axisymmetric free convection boundary-layer flow past slender bodies

NARCIS (Netherlands)

Kuiken, H.K.

1968-01-01

Radial curvature effects on axisymmetric free convection boundary-layer flow are investigated for vertical cylinders and cones for some special non-uniform temperature differences between the surface and the ambient fluid. The solution is given as a power series expansion, the first term being equal

Gaps, Rings, and Non-Axisymmetric Structures in Protoplanetary Disks - From Simulations to ALMA Observations

OpenAIRE

Flock, M.; Ruge, J. P.; Dzyurkevich, N.; Henning, Th.; Klahr, H.; Wolf, S.

2014-01-01

International audience; Aims. Recent observations by the Atacama Large Millimeter/submillimeter Array (ALMA) of disks around young stars revealed distinct asymmetries in the dust continuum emission. In this work we wish to study axisymmetric and non-axisymmetric structures that are generated by the magneto-rotational instability in the outer regions of protoplanetary disks. We combine the results of state-of-the-art numerical simulations with post-processing radiative transfer (RT) to generat...

Thermodynamic properties of ideal Fermi gases in a harmonic potential in an n-dimensional space under the generalized uncertainty principle

Science.gov (United States)

Li, Heling; Ren, Jinxiu; Wang, Wenwei; Yang, Bin; Shen, Hongjun

2018-02-01

Using the semi-classical (Thomas-Fermi) approximation, the thermodynamic properties of ideal Fermi gases in a harmonic potential in an n-dimensional space are studied under the generalized uncertainty principle (GUP). The mean particle number, internal energy, heat capacity and other thermodynamic variables of the Fermi system are calculated analytically. Then, analytical expressions of the mean particle number, internal energy, heat capacity, chemical potential, Fermi energy, ground state energy and amendments of the GUP are obtained at low temperatures. The influence of both the GUP and the harmonic potential on the thermodynamic properties of a copper-electron gas and other systems with higher electron densities are studied numerically at low temperatures. We find: (1) When the GUP is considered, the influence of the harmonic potential is very much larger, and the amendments produced by the GUP increase by eight to nine orders of magnitude compared to when no external potential is applied to the electron gas. (2) The larger the particle density, or the smaller the particle masses, the bigger the influence of the GUP. (3) The effect of the GUP increases with the increase in the spatial dimensions. (4) The amendments of the chemical potential, Fermi energy and ground state energy increase with an increase in temperature, while the heat capacity decreases. T F0 is the Fermi temperature of the ideal Fermi system in a harmonic potential. When the temperature is lower than a certain value (0.22 times T F0 for the copper-electron gas, and this value decreases with increasing electron density), the amendment to the internal energy is positive, however, the amendment decreases with increasing temperature. When the temperature increases to the value, the amendment is zero, and when the temperature is higher than the value, the amendment to the internal energy is negative and the absolute value of the amendment increases with increasing temperature. (5) When electron

Two dimensional (4,0) supergravity in harmonic superspace. The action and the matter couplings

International Nuclear Information System (INIS)

Lhallabi, T.; Saidi, E.H.

1988-08-01

The superfield formulation of the two dimensional (4,0) supergravity is developed using the harmonic superspace techniques. The different sets of constraints are given and their solutions are expressed in terms of a SU(2) self dual torsion superfield and harmonic prepotentials. The pure auxiliary (4,0) Einstein action generalizing the (2,0) one is written down and the most general (4,0) matter couplings are given. (author). 24 refs

Decay of passive scalar fluctuations in axisymmetric turbulence

Science.gov (United States)

Yoshimatsu, Katsunori; Davidson, Peter A.; Kaneda, Yukio

2016-11-01

Passive scalar fluctuations in axisymmetric Saffman turbulence are examined theoretically and numerically. Theoretical predictions are verified by direct numerical simulation (DNS). According to the DNS, self-similar decay of the turbulence and the persistency of the large-scale anisotropy are found for its fully developed turbulence. The DNS confirms the time-independence of the Corrsin integral.

Static axisymmetric discs and gravitational collapse

Energy Technology Data Exchange (ETDEWEB)

Chamorro, A.; Gregory, R.; Stewart, J.M.

1987-09-08

Regular static axisymmetric vacuum solutions of Einstein's field equations representing the exterior field of a finite thin disc are found. These are used to describe the slow collapse of a disc-like object. If no conditions are placed on the matter, a naked singularity is formed and the cosmic censorship hypothesis would be violated. Imposition of the weak energy condition, however, prevents slow collapse to a singularity and preserves the validity of this hypothesis. The validity of the hoop conjecture is also discussed.

Stability and instability of axisymmetric droplets in thermocapillary-driven thin films

Science.gov (United States)

Nicolaou, Zachary G.

2018-03-01

The stability of compactly supported, axisymmetric droplet states is considered for driven thin viscous films evolving on two-dimensional surfaces. Stability is assessed using Lyapunov energy methods afforded by the Cahn-Hilliard variational form of the governing equation. For general driving forces, a criterion on the gradient of profiles at the boundary of their support (their contact slope) is shown to be a necessary condition for stability. Additional necessary and sufficient conditions for stability are established for a specific driving force corresponding to a thermocapillary-driven film. It is found that only droplets of sufficiently short height that satisfy the contact slope criterion are stable. This destabilization of droplets with increasing height is characterized as a saddle-node bifurcation between a branch of tall, unstable droplets and a branch of short, stable droplets.

A Family of Vortices to Study Axisymmetric Vortex Breakdown and Reconnection

Science.gov (United States)

Young, Larry A.

2007-01-01

A new analytic model describing a family of vortices has been developed to study some of the axisymmetric vortex breakdown and reconnection fluid dynamic processes underlying body-vortex interactions that are frequently manifested in rotorcraft and propeller-driven fixed-wing aircraft wakes. The family of vortices incorporates a wide range of prescribed initial vorticity distributions -- including single or dual-core vorticity distributions. The result is analytical solutions for the vorticity and velocities for each member of the family of vortices. This model is of sufficient generality to further illustrate the dependence of vortex reconnection and breakdown on initial vorticity distribution as was suggested by earlier analytical work. This family of vortices, though laminar in nature, is anticipated to provide valuable insight into the vortical evolution of large-scale rotor and propeller wakes.

Axisymmetric toroidal equilibrium with flow and anisotropic pressure

International Nuclear Information System (INIS)

Iacono, R.; Bondeson, A.; Troyon, F.; Gruber, R.

1989-10-01

Axisymmetric toroidal plasma equilibria with mass flows and anisotropic pressure are investigated. The equilibrium system is derived for a general functional form of the pressures, which includes both fluid models, such as the magnetohydrodynamic (MHD) and the double-adiabatic models, and Grad's guiding centre model. This allows for detailed comparisons between the models and clarifies how the 'first hyperbolic region', occurring in the fluid theory when the poloidal flow is of the order of the poloidal sound speed, can be eliminated in guiding centre theory. In the case of a pure toroidal rotation, macroscopic equations of state are derived from the guiding centre model, characterized by a parallel temperature that is constant on each magnetic surface and a perpendicular temperature that varies with the magnetic field. The outward centrifugal shifts of the magnetic axis and of the mass density profile, due to toroidal rotation, are increased by anisotropy. The guiding centre model shows that poloidal flow produces an inward shift of the density profile, in contrast with the MHD result. (author) 1 fig., 1 tab., 17 refs

CLASSIFICATION OF STELLAR ORBITS IN AXISYMMETRIC GALAXIES

Energy Technology Data Exchange (ETDEWEB)

Li, Baile; Holley-Bockelmann, Kelly [Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235 (United States); Khan, Fazeel Mahmood, E-mail: baile.li@vanderbilt.edu, E-mail: k.holley@vanderbilt.edu, E-mail: khanfazeel.ist@gmail.com [Department of Space Science, Institute of Space Technology, P.O. Box 2750 Islamabad (Pakistan)

2015-09-20

It is known that two supermassive black holes (SMBHs) cannot merge in a spherical galaxy within a Hubble time; an emerging picture is that galaxy geometry, rotation, and large potential perturbations may usher the SMBH binary through the critical three-body scattering phase and ultimately drive the SMBH to coalesce. We explore the orbital content within an N-body model of a mildly flattened, non-rotating, SMBH-embedded elliptical galaxy. When used as the foundation for a study on the SMBH binary coalescence, the black holes bypassed the binary stalling often seen within spherical galaxies and merged on gigayear timescales. Using both frequency-mapping and angular momentum criteria, we identify a wealth of resonant orbits in the axisymmetric model, including saucers, that are absent from an otherwise identical spherical system and that can potentially interact with the binary. We quantified the set of orbits that could be scattered by the SMBH binary, and found that the axisymmetric model contained nearly six times the number of these potential loss cone orbits compared to our equivalent spherical model. In this flattened model, the mass of these orbits is more than three times that of the SMBH, which is consistent with what the SMBH binary needs to scatter to transition into the gravitational wave regime.

Axisymmetric vibrations of thick shells of revolution

International Nuclear Information System (INIS)

Suzuki, Katsuyoshi; Kosawada, Tadashi; Takahashi, Shin

1983-01-01

Axisymmetric shells of revolution are used for chemical plants, nuclear power plants, aircrafts, structures and so on, and the elucidation of their free vibration is important for the design. In this study, the axisymmetric vibration of a barrel-shaped shell was analyzed by the modified thick shell theory. The Lagrangian during one period of the vibration of a shell of revolution was determined, and from its stopping condition, the vibration equations and the boundary conditions were derived. The vibration equations were analyzed strictly by using the series solution. Moreover, the basic equations for the strain of a shell and others were based on those of Love. As the examples of numerical calculation, the natural frequency and vibration mode of the symmetrical shells of revolution fixed at both ends and supported at both ends were determined, and their characteristics were clarified. By comparing the results of this study with the results by thin shell theory, the effects of shearing deformation and rotary inertia on the natural frequency and vibration mode were clarified. The theoretical analysis and the numerical calculation are described. The effects of shearing deformation and rotary inertia on the natural frequency became larger in the higher order vibration. The vibration mode did not much change in both theories. (Kako, I.)

Investigation of Three-Dimensional Axisymmetric Unsteady Stagnation-Point Flow and Heat Transfer Impinging on an Accelerated Flat Plate

OpenAIRE

ali shokrgozar abbasi; Asghar Baradaran Rahimi; Hamidreza Mozayeni

2016-01-01

General formulation and solution of Navier-Stokes and energy equations are sought in the study of threedimensional axisymmetric unsteady stagnation-point flow and heat transfer impinging on a flat plate when the plate is moving with variable velocity and acceleration towards the main stream or away from it. As an application, among others, this accelerated plate can be assumed as a solidification front which is being formed with variable velocity. An external fluid, along z - directi...

Harmonic operation of high gain harmonic generation free electron laser

International Nuclear Information System (INIS)

Deng Haixiao; Chinese Academy of Sciences, Beijing; Dai Zhimin

2008-01-01

In high gain harmonic generation (HGHG) free electron laser (FEL), with the right choice of parameters of the modulator undulator, the dispersive section and the seed laser, one may make the spatial bunching of the electron beam density distribution correspond to one of the harmonic frequencies of the radiator radiation, instead of the fundamental frequency of the radiator radiation in conventional HGHG, thus the radiator undulator is in harmonic operation (HO) mode. In this paper, we investigate HO of HGHG FEL. Theoretical analyses with universal method are derived and numerical simulations in ultraviolet and deep ultraviolet spectral regions are given. It shows that the power of the 3rd harmonic radiation in the HO of HGHG may be as high as 18.5% of the fundamental power level. Thus HO of HGHG FEL may obtain short wavelength by using lower beam energy. (authors)

Reversed straining in axisymmetric compression test

DEFF Research Database (Denmark)

Arentoft, Mogens; Wanheim, Tarras; Lindegren, Maria

2005-01-01

A large group of the cold forging processes is carried out in a thick – walled container with the deformation force transmitted through a punch moving axially in the container. The work piece, being entrapped between punch and container will expand and exert a radial pressure resulting in an expa...... to simulate these conditions a reversed axisymmetrical material tester is designed and constructed. Three different materials were tested, aluminum alloy AA6082, technically pure copper (99.5%) and cold forging steel Ma8, at different temperatures found during cold forging....

Secular instability of axisymmetric rotating stars to gravitational radiation reaction

International Nuclear Information System (INIS)

Managan, R.A.

1985-01-01

A generalization of the Eulerian variational principle derived by Ipser and Managan, for nonaxisymmetric neutral modes of axisymmetric fluid configurations, is developed. The principle provides a variational basis for calculating the frequencies of nonaxisymmetric normal modes proportional to e/sup i/(sigmat + mphi). A modified form of this principle, valid for sigma near 0, is also developed. The latter principle is used to locate the points where the frequency of a nonaxisymmetric normal mode of an axisymmetric rotating fluid configuration passes through zero. lt is at these points that the configuration becomes secularly unstable to gravitational radiation reaction (GRR). This is demonstrated directly by including the GRR potential and showing that the imaginary part of sigma passes through zero and becomes negative at these points. The imaginary part of the frequency is used to estimate the e-folding time of the mode. This variational principle is applied to sequences of rotating polytropes. The sequences are constructed using four rotation laws at each value of the polytropic index n = 0.5, 1.0, 1.5, 2.0, and 3.0. The values of (T/W)/sub m/, the ratio of the rotational kinetic energy to the magnitude of the gravitational potential energy at the onset of instability, and timescales for the modes with m = 2, 3, and 4 are estimated for each sequence. The value of (T/W) 2 is largely independent of the equation of state and rotation law. For m > 2, (T/W)/sub m/ decreases as the equation of state becomes softer, i.e., as the polytropic index n increases, and increases as the amount of differential rotation increases. The most striking result of this behavior occurs for uniform rotation

A non-conforming generalization of Raviart-Thomas elements to the spherical harmonic form of the even-parity neutron transport equation

Energy Technology Data Exchange (ETDEWEB)

Van Criekingen, S. [Commissariat a l' energie atomique (CEA-Saclay), DEN/DM2S/SERMA/LENR (Bat 470), 91191 Gif-sur-Yvette Cedex (France)]. E-mail: serge.van-criekingen@cea.fr

2006-05-15

The Raviart-Thomas finite elements provide an appropriate spatial discretization of the mixed-dual form of the diffusion equation. This discretization can then be coupled to an efficient solution method. The high performances achieved by such an approach triggered research on its possible generalization to the transport equation using a spherical harmonic (or P {sub N}) angular approximation. In view of the difficulty of developing a straightforward generalization within the mixed-dual framework, we here consider 2D non-conforming (i.e., allowing interface discontinuities) finite elements coupled to the second-order form of the transport equation. This non-conforming approach keeps the mixed-dual property of the relaxation of the flux interface continuity constraint. We investigate different non-conforming elements and compare them to the well-known Lagrangian conforming elements.

A non-conforming generalization of Raviart-Thomas elements to the spherical harmonic form of the even-parity neutron transport equation

International Nuclear Information System (INIS)

Van Criekingen, S.

2006-01-01

The Raviart-Thomas finite elements provide an appropriate spatial discretization of the mixed-dual form of the diffusion equation. This discretization can then be coupled to an efficient solution method. The high performances achieved by such an approach triggered research on its possible generalization to the transport equation using a spherical harmonic (or P N ) angular approximation. In view of the difficulty of developing a straightforward generalization within the mixed-dual framework, we here consider 2D non-conforming (i.e., allowing interface discontinuities) finite elements coupled to the second-order form of the transport equation. This non-conforming approach keeps the mixed-dual property of the relaxation of the flux interface continuity constraint. We investigate different non-conforming elements and compare them to the well-known Lagrangian conforming elements

Quantify Plasma Response to Non-Axisymmetric (3D) Magnetic Fields in Tokamaks, Final Report for FES (Fusion Energy Sciences) FY2014 Joint Research Target

International Nuclear Information System (INIS)

Strait, E. J.; Park, J. K.; Marmar, E. S.; Ahn, J. W.; Berkery, J. W.; Burrell, K. H.; Canik, J. M.; Delgado-Aparicio, L.; Ferraro, N. M.; Garofalo, A. M.; Gates, D. A.; Greenwald, M.; Kim, K.; King, J. D.; Lanctot, M. J.; Lazerson, S. A.; Liu, Y. Q.; Lore, J. D.; Menard, J. E.; Nazikian, R.; Shafer, M. W.; Paz-Soldan, C.; Reiman, A. H.; Rice, J. E.; Sabbagh, S. A.; Sugiyama, L.; Turnbull, A. D.; Volpe, F.; Wang, Z. R.; Wolfe, S. M.

2014-01-01

The goal of the 2014 Joint Research Target (JRT) has been to conduct experiments and analysis to investigate and quantify the response of tokamak plasmas to non-axisymmetric (3D) magnetic fields. Although tokamaks are conceptually axisymmetric devices, small asymmetries often result from inaccuracies in the manufacture and assembly of the magnet coils, or from nearby magnetized objects. In addition, non-axisymmetric fields may be deliberately applied for various purposes. Even at small amplitudes of order 10 -4 of the main axisymmetric field, such ''3D'' fields can have profound impacts on the plasma performance. The effects are often detrimental (reduction of stabilizing plasma rotation, degradation of energy confinement, localized heat flux to the divertor, or excitation of instabilities) but may in some case be beneficial (maintenance of rotation, or suppression of instabilities). In general, the magnetic response of the plasma alters the 3D field, so that the magnetic field configuration within the plasma is not simply the sum of the external 3D field and the original axisymmetric field. Typically the plasma response consists of a mixture of local screening of the external field by currents induced at resonant surfaces in the plasma, and amplification of the external field by stable kink modes. Thus, validated magnetohydrodynamic (MHD) models of the plasma response to 3D fields are crucial to the interpretation of existing experiments and the prediction of plasma performance in future devices. The non-axisymmetric coil sets available at each facility allow well-controlled studies of the response to external 3D fields. The work performed in support of the 2014 Joint Research Target has included joint modeling and analysis of existing experimental data, and collaboration on new experiments designed to address the goals of the JRT. A major focus of the work was validation of numerical models through quantitative comparison to experimental data

Quantify Plasma Response to Non-Axisymmetric (3D) Magnetic Fields in Tokamaks, Final Report for FES (Fusion Energy Sciences) FY2014 Joint Research Target

Energy Technology Data Exchange (ETDEWEB)

Strait, E. J. [General Atomics, San Diego, CA (United States); Park, J. -K. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Marmar, E. S. [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Ahn, J. -W. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Berkery, J. W. [Columbia Univ., New York, NY (United States); Burrell, K. H. [General Atomics, San Diego, CA (United States); Canik, J. M. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Delgado-Aparicio, L. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Ferraro, N. M. [General Atomics, San Diego, CA (United States); Garofalo, A. M. [General Atomics, San Diego, CA (United States); Gates, D. A. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Greenwald, M. [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Kim, K. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); King, J. D. [General Atomics, San Diego, CA (United States); Lanctot, M. J. [General Atomics, San Diego, CA (United States); Lazerson, S. A. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Liu, Y. Q. [Culham Science Centre, Abingdon (United Kingdom). Euratom/CCFE Association; Logan, N. C. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Lore, J. D. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Menard, J. E. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Nazikian, R. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Shafer, M. W. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Paz-Soldan, C. [General Atomics, San Diego, CA (United States); Reiman, A. H. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Rice, J. E. [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Sabbagh, S. A. [Columbia Univ., New York, NY (United States); Sugiyama, L. [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Turnbull, A. D. [General Atomics, San Diego, CA (United States); Volpe, F. [Columbia Univ., New York, NY (United States); Wang, Z. R. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Wolfe, S. M. [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

2014-09-30

The goal of the 2014 Joint Research Target (JRT) has been to conduct experiments and analysis to investigate and quantify the response of tokamak plasmas to non-axisymmetric (3D) magnetic fields. Although tokamaks are conceptually axisymmetric devices, small asymmetries often result from inaccuracies in the manufacture and assembly of the magnet coils, or from nearby magnetized objects. In addition, non-axisymmetric fields may be deliberately applied for various purposes. Even at small amplitudes of order 10^-4 of the main axisymmetric field, such “3D” fields can have profound impacts on the plasma performance. The effects are often detrimental (reduction of stabilizing plasma rotation, degradation of energy confinement, localized heat flux to the divertor, or excitation of instabilities) but may in some case be beneficial (maintenance of rotation, or suppression of instabilities). In general, the magnetic response of the plasma alters the 3D field, so that the magnetic field configuration within the plasma is not simply the sum of the external 3D field and the original axisymmetric field. Typically the plasma response consists of a mixture of local screening of the external field by currents induced at resonant surfaces in the plasma, and amplification of the external field by stable kink modes. Thus, validated magnetohydrodynamic (MHD) models of the plasma response to 3D fields are crucial to the interpretation of existing experiments and the prediction of plasma performance in future devices. The non-axisymmetric coil sets available at each facility allow well-controlled studies of the response to external 3D fields. The work performed in support of the 2014 Joint Research Target has included joint modeling and analysis of existing experimental data, and collaboration on new experiments designed to address the goals of the JRT. A major focus of the work was validation of numerical models through quantitative comparison to experimental data, in

Numerical description of cavitation on axisymmetric bodies

Energy Technology Data Exchange (ETDEWEB)

Hickox, C.E.; Hailey, C.E.; Wolfe, W.P.; Watts, H.A.; Gross, R.J.; Ingber, M.S.

1988-01-01

This paper reports on ongoing studies which are directed toward the development of predictive techniques for the modeling of steady cavitation on axisymmetric bodies. The primary goal of the modeling effort is the prediction of cavity shape and pressure distribution from which forces and moments can be calculated. Here we present an overview of the modeling techniques developed and compare predictions with experimental data obtained from water tunnel tests for both limited and supercavitation. 14 refs., 4 figs.

Floquet-Green function formalism for harmonically driven Hamiltonians

International Nuclear Information System (INIS)

Martinez, D F

2003-01-01

A method is proposed for the calculation of the Floquet-Green function of a general Hamiltonian with harmonic time dependence. We use matrix continued fractions to derive an expression for the 'dynamical effective potential' that can be used to calculate the Floquet-Green function of the system. We demonstrate the formalism for the simple case of a space-periodic (in the tight-binding approximation) Hamiltonian with a defect whose on-site energy changes harmonically with time. We study the local density of states for this system and the behaviour of the localized states as a function of the different parameters that characterize the system

The shape of an axisymmetric bubble in uniform motion

Indian Academy of Sciences (India)

Axisymmetric bubble shapes; non-linear free boundary problems; surface singularity methods in potential flows. PACS Nos 47.55.Dz; 47.11.+j; 47.15.Hg. 1. .... should be fast and reasonably accurate, (c) the iterative procedure for determining .... curve while K2 is the other associated principal curvature; K2 can be deduced.

Modelling axisymmetric cod-ends made of different mesh types

DEFF Research Database (Denmark)

Priour, D.; Herrmann, Bent; O'Neill, F.G.

2009-01-01

the selectivity process has become more important. This paper presents a model of the deformation of an axisymmetric cod-end. The twine tension and the catch pressure acting on the knots of each mesh along the cod-end profile are calculated, and a Newton-Raphson scheme is used to estimate the equilibrium position...

Emergency Entry with One Control Torque: Non-Axisymmetric Diagonal Inertia Matrix

Science.gov (United States)

Llama, Eduardo Garcia

2011-01-01

In another work, a method was presented, primarily conceived as an emergency backup system, that addressed the problem of a space capsule that needed to execute a safe atmospheric entry from an arbitrary initial attitude and angular rate in the absence of nominal control capability. The proposed concept permits the arrest of a tumbling motion, orientation to the heat shield forward position and the attainment of a ballistic roll rate of a rigid spacecraft with the use of control in one axis only. To show the feasibility of such concept, the technique of single input single output (SISO) feedback linearization using the Lie derivative method was employed and the problem was solved for different number of jets and for different configurations of the inertia matrix: the axisymmetric inertia matrix (I(sub xx) > I(sub yy) = I(sub zz)), a partially complete inertia matrix with I(sub xx) > I(sub yy) > I(sub zz), I(sub xz) not = 0 and a realistic complete inertia matrix with I(sub xx) > I(sub yy) > I)sub zz), I(sub ij) not= 0. The closed loop stability of the proposed non-linear control on the total angle of attack, Theta, was analyzed through the zero dynamics of the internal dynamics for the case where the inertia matrix is axisymmetric (I(sub xx) > I(sub yy) = I(sub zz)). This note focuses on the problem of the diagonal non-axisymmetric inertia matrix (I(sub xx) > I(sub yy) > I(sub zz)), which is half way between the axisymmetric and the partially complete inertia matrices. In this note, the control law for this type of inertia matrix will be determined and its closed-loop stability will be analyzed using the same methods that were used in the other work. In particular, it will be proven that the control system is stable in closed-loop when the actuators only provide a roll torque.

Elastoplastic buckling of quasi axisymmetric shells of revolution

International Nuclear Information System (INIS)

Combescure, A.

1987-01-01

This paper gives the formulation of a finite element which allows the computation of quasi axisymmetric shells of revolution. This element has two nodes and the displacement field is developped in Fourier series. In this paper, an emphasis is put on the elastic and plastic buckling formulation. Two examples are developped in details showing the applicability and the interest of such a finite element. (orig.)

An axisymmetric gravitational collapse code

Energy Technology Data Exchange (ETDEWEB)

Choptuik, Matthew W [CIAR Cosmology and Gravity Program, Department of Physics and Astronomy, University of British Columbia, Vancouver BC, V6T 1Z1 (Canada); Hirschmann, Eric W [Department of Physics and Astronomy, Brigham Young University, Provo, UT 84604 (United States); Liebling, Steven L [Southampton College, Long Island University, Southampton, NY 11968 (United States); Pretorius, Frans [Theoretical Astrophysics, California Institute of Technology, Pasadena, CA 91125 (United States)

2003-05-07

We present a new numerical code designed to solve the Einstein field equations for axisymmetric spacetimes. The long-term goal of this project is to construct a code that will be capable of studying many problems of interest in axisymmetry, including gravitational collapse, critical phenomena, investigations of cosmic censorship and head-on black-hole collisions. Our objective here is to detail the (2+1)+1 formalism we use to arrive at the corresponding system of equations and the numerical methods we use to solve them. We are able to obtain stable evolution, despite the singular nature of the coordinate system on the axis, by enforcing appropriate regularity conditions on all variables and by adding numerical dissipation to hyperbolic equations.

An axisymmetric gravitational collapse code

International Nuclear Information System (INIS)

Choptuik, Matthew W; Hirschmann, Eric W; Liebling, Steven L; Pretorius, Frans

2003-01-01

We present a new numerical code designed to solve the Einstein field equations for axisymmetric spacetimes. The long-term goal of this project is to construct a code that will be capable of studying many problems of interest in axisymmetry, including gravitational collapse, critical phenomena, investigations of cosmic censorship and head-on black-hole collisions. Our objective here is to detail the (2+1)+1 formalism we use to arrive at the corresponding system of equations and the numerical methods we use to solve them. We are able to obtain stable evolution, despite the singular nature of the coordinate system on the axis, by enforcing appropriate regularity conditions on all variables and by adding numerical dissipation to hyperbolic equations

New chemical-DSMC method in numerical simulation of axisymmetric rarefied reactive flow

Science.gov (United States)

Zakeri, Ramin; Kamali Moghadam, Ramin; Mani, Mahmoud

2017-04-01

The modified quantum kinetic (MQK) chemical reaction model introduced by Zakeri et al. is developed for applicable cases in axisymmetric reactive rarefied gas flows using the direct simulation Monte Carlo (DSMC) method. Although, the MQK chemical model uses some modifications in the quantum kinetic (QK) method, it also employs the general soft sphere collision model and Stockmayer potential function to properly select the collision pairs in the DSMC algorithm and capture both the attraction and repulsion intermolecular forces in rarefied gas flows. For assessment of the presented model in the simulation of more complex and applicable reacting flows, first, the air dissociation is studied in a single cell for equilibrium and non-equilibrium conditions. The MQK results agree well with the analytical and experimental data and they accurately predict the characteristics of the rarefied flowfield with chemical reaction. To investigate accuracy of the MQK chemical model in the simulation of the axisymmetric flow, air dissociation is also assessed in an axial hypersonic flow around two geometries, the sphere as a benchmark case and the blunt body (STS-2) as an applicable test case. The computed results including the transient, rotational and vibrational temperatures, species concentration in the stagnation line, and also the heat flux and pressure coefficient on the surface are compared with those of the other chemical methods like the QK and total collision energy (TCE) models and available analytical and experimental data. Generally, the MQK chemical model properly simulates the chemical reactions and predicts flowfield characteristics more accurate rather than the typical QK model. Although in some cases, results of the MQK approaches match with those of the TCE method, the main point is that the MQK does not need any experimental data or unrealistic assumption of specular boundary condition as used in the TCE method. Another advantage of the MQK model is the

Application of Quasi-Newton methods to the analysis of axisymmetric pressure vessels

International Nuclear Information System (INIS)

Parisi, D.A.C.

1987-01-01

This work studies the application of Quasi-Newton techniques to material nonlinear analysis of axisymmetrical pressure vessels by the finite element method. In the formulation the material bahavior is described by an isotropic elastoplastic model with strain hardening. The continum is discretized through triangular finite elements of axisymmetrical solids with linear interpolation of the displacement field. The incremental governing equations are derived by the virtual work. The solution of the system of simultaneous nonlinear equations is solved iteratively by the Quasi-Newton method employing the BFGS update. The numerical performance of the proposed method is compared with the Newton-Raphson method and some of its variants through some selected examples. (author) [pt

Generating transverse response explicitly from harmonic oscillators

Science.gov (United States)

Yao, Yuan; Tang, Ying; Ao, Ping

2017-10-01

We obtain stochastic dynamics from a system-plus-bath mechanism as an extension of the Caldeira-Leggett (CL) model in the classical regime. An effective magnetic field and response functions with both longitudinal and transverse parts are exactly generated from the bath of harmonic oscillators. The effective magnetic field and transverse response are antisymmetric matrices: the former is explicitly time-independent corresponding to the geometric magnetism, while the latter can have memory. The present model can be reduced to previous representative examples of stochastic dynamics describing nonequilibrium processes. Our results demonstrate that a system coupled with a bath of harmonic oscillators is a general approach to studying stochastic dynamics, and provides a method to experimentally implement an effective magnetic field from coupling to the environment.

Fast axisymmetric stability calculations using variational techniques

International Nuclear Information System (INIS)

Haney, S.W., Pearlstein, L.D.; Bulmer, R.H.

1991-01-01

A procedure for treating the axisymmetric (n = 0) stability of diverted plasmas in the presence of arbitrary, but toroidally symmetric, structures and active feedback circuits has been developed and implemented as a module in the TEQ free-boundary equilibrium code. This procedure is based on a variational solution of the ideal MHD normal mode equations. Inertia is ordered small but provides a constraint to allow the calculation of the poloidal and toroidal components of the plasma displacement. Feedback based on flux loop measurements is handled by introducing an adjoint system into the variational principle. Approximately 200 trial functions for the radial component of the plasma displacement and 200 magnetic surfaces are employed to obtain highly accurate estimates of the passive growth rate and the non-rigid eigenfunction. Nevertheless, the method is extremely fast: typically 10-20 sec of Cray 2 CPU time are required to analyze a realistic tokamak configuration. This speed, along with the direct coupling to the MHD equilibrium solver, allows interactive investigations of tokamak axisymmetric stability. Benchmarks with TSC and GATO are presented along with parameter scans for ITER and BPX. The results emphasize the importance of considering non-rigid mode effects which for ITER, yield higher nominal growth rates (non-rigid: 45 Hz, rigid: 25 Hz) and atypical internal inductance dependence (smaller l i more unstable)

Second-harmonic generation in second-harmonic fiber Bragg gratings.

Science.gov (United States)

Steel, M J; de Sterke, C M

1996-06-20

We consider the production of second-harmonic light in gratings resonant with the generated field, through a Green's function approach. We recover some standard results and obtain new limits for the uniform grating case. With the extension to nonuniform gratings, we find the Green's function for the second harmonic in a grating with an arbitrary phase shift at some point. We then obtain closed form approximate expressions for the generated light for phase shifts close to π/2 and at the center of the grating. Finally, comparing the uniform and phase-shifted gratings with homogeneous materials, we discuss the enhancement in generated light and the bandwidth over which it occurs, and the consequences for second-harmonic generation in optical fiber Bragg gratings.

Coherence properties of the harmonic generation in intense laser field

International Nuclear Information System (INIS)

Salieres, P.

1995-01-01

In this thesis is presented an experimental and theoretical study of the harmonic generation in intense field and coherence properties of this radiation. The first part reminds the main harmonic specter characteristics. Follow then experimental studies of the tray extension with the laser lighting, the harmonic generation by ions, and the influence of the laser field on the efficiency of generation. The second part presents the quantum model of the harmonic generation in tunnel regime that we have used for the calculation of the dipoles. We compare dependence in lighting of some harmonic, by insisting on the characteristic behavior of the atomic phase. The theory of the propagation is presented in third part. After the reminder of the case of a perturbative polarization, we develop the case of the polarization in tunnel regime. With the help of numerical simulations, we show the influence of the atomic phase on the agreement of phase, and therefore on the efficiency of conversion and profiles of generation in the medium. The importance of the geometry of the interaction is underlined. The part IV presents the study of the spatial coherence of the harmonic radiation. We develop first consequences of the theory of the agreement of phase for profiles of emission. Then the comparison with experimental profiles is detailed in function of the different parameters( order of non linearity, laser lighting, position of the focus by report in the gaseous medium). The study of the spectral and temporal coherence of the part V begins with the experimental effect investigation of the ionization on specters of the harmonic of weak order. We present then theoretical predictions of the preceding model for spectral and temporal profiles of the harmonic of highest order, generated in tunnel regime. The part VI is devoted to the UVX source aspect of the harmonic radiation. General characteristics (number of photons, agreement) are first detailed, then we present the first experiences

Harmonic Interaction Analysis in Grid Connected Converter using Harmonic State Space (HSS) Modeling

DEFF Research Database (Denmark)

Kwon, Jun Bum; Wang, Xiongfei; Bak, Claus Leth

2015-01-01

-model, are introduced to analyze these problems. However, it is found that Linear Time Invariant (LTI) base model analysis makes it difficult to analyze these phenomenon because of time varying system operation trajectories, varying output impedance seen by grid connected systems and neglected switching component......An increasing number of power electronics based Distributed Generation (DG) systems and loads generate coupled harmonic as well as non-characteristic harmonic with each other. Several methods like impedance based analysis, which is derived from conventional small signal- and average...... during the modeling process. This paper investigates grid connected converter by means of Harmonic State Space (HSS) small signal model, which is modeled from Linear Time varying Periodically (LTP) system. Further, a grid connected converter harmonic matrix is investigated to analyze the harmonic...

Harmonic ratcheting for fast acceleration

Science.gov (United States)

Cook, N.; Brennan, J. M.; Peggs, S.

2014-04-01

A major challenge in the design of rf cavities for the acceleration of medium-energy charged ions is the need to rapidly sweep the radio frequency over a large range. From low-power medical synchrotrons to high-power accelerator driven subcritical reactor systems, and from fixed focus alternating gradient accelerators to rapid cycling synchrotrons, there is a strong need for more efficient, and faster, acceleration of protons and light ions in the semirelativistic range of hundreds of MeV/u. A conventional way to achieve a large, rapid frequency sweep (perhaps over a range of a factor of 6) is to use custom-designed ferrite-loaded cavities. Ferrite rings enable the precise tuning of the resonant frequency of a cavity, through the control of the incremental permeability that is possible by introducing a pseudoconstant azimuthal magnetic field. However, rapid changes over large permeability ranges incur anomalous behavior such as the "Q-loss" and "f-dot" loss phenomena that limit performance while requiring high bias currents. Notwithstanding the incomplete understanding of these phenomena, they can be ameliorated by introducing a "harmonic ratcheting" acceleration scheme in which two or more rf cavities take turns accelerating the beam—one turns on when the other turns off, at different harmonics—so that the radio frequency can be constrained to remain in a smaller range. Harmonic ratcheting also has straightforward performance advantages, depending on the particular parameter set at hand. In some typical cases it is possible to halve the length of the cavities, or to double the effective gap voltage, or to double the repetition rate. This paper discusses and quantifies the advantages of harmonic ratcheting in general. Simulation results for the particular case of a rapid cycling medical synchrotron ratcheting from harmonic number 9 to 2 show that stability and performance criteria are met even when realistic engineering details are taken into consideration.

New SU(1,1) position-dependent effective mass coherent states for a generalized shifted harmonic oscillator

International Nuclear Information System (INIS)

Yahiaoui, Sid-Ahmed; Bentaiba, Mustapha

2014-01-01

A new SU(1,1) position-dependent effective mass coherent states (PDEM CS) related to the shifted harmonic oscillator (SHO) are deduced. This is accomplished by applying a similarity transformation to the generally deformed oscillator algebra (GDOA) generators for PDEM systems and a new set of operators that close the su(1,1) Lie algebra are constructed, being the PDEM CS of the basis for its unitary irreducible representation. From the Lie algebra generators, we evaluate the uncertainty relationship for a position and momentum-like operators in the PDEM CS and show that it is minimized in the sense of Barut–Girardello CS. We prove that the deduced PDEM CS preserve the same analytical form than those of Glauber states. As an illustration of our procedure, we depicted the 2D-probability density in the PDEM CS for SHO with the explicit form of the mass distribution with no singularities. (paper)

Vortical motion in the head of an axisymmetric gravity current

NARCIS (Netherlands)

Patterson, M.D.; Simpson, J.E.; Dalziel, S.B.; Heijst, van G.J.F.

2006-01-01

A series of experiments that examine the initial development of an axisymmetric gravity current have been carried out. The experiments highlight the growth of a ring vortex that dominates the dynamics of the gravity current's early time propagation. In particular, the experiments show three distinct

An axisymmetric inertia-gravity wave generator

Science.gov (United States)

Maurer, P.; Ghaemsaidi, S. J.; Joubaud, S.; Peacock, T.; Odier, P.

2017-10-01

There has been a rich interplay between laboratory experimental studies of internal waves and advancing understanding of their role in the ocean and atmosphere. In this study, we present and demonstrate the concept for a new form of laboratory internal wave generator that can excite axisymmetric wave fields of arbitrary radial structure. The construction and operation of the generator are detailed, and its capabilities are demonstrated through a pair of experiments using a Bessel function and a bourrelet (i.e., ring-shaped) configuration. The results of the experiments are compared with the predictions of an accompanying analytical model.

Standard superfields in the harmonic formalism of supergauge theories

International Nuclear Information System (INIS)

Zupnik, B.M.; Tolstonog, L.V.

1989-01-01

Connection between the standard superfield formalism and the harmonic superspace method is studied in the 6-dimensional and extended 4-dimensional supergauge theories. The action of the abelian theory is expressed in terms of the real prepotential V ik . A generalization for the non-abelian case can be performed with the help of the iterative method. Analysing the supergauge theory with the gauge group SU(2) the authors exploit the exact solution of the equations for the harmonic superfield connections which can be expressed in terms of the real prepotential V iklm in a special gauge

Input Harmonic Analysis on the Slim DC-Link Drive Using Harmonic State Space Model

DEFF Research Database (Denmark)

Yang, Feng; Kwon, Jun Bum; Wang, Xiongfei

2017-01-01

The harmonic performance of the slim dc-link adjustable speed drives has shown good performance in some studies but poor in some others. The contradiction indicates that a feasible theoretical analysis is still lacking to characterize the harmonic distortion for the slim dc-link drive. Considerin...... results of the slim dc-link drive, loaded up to 2.0 kW, are presented to validate the theoretical analysis....... variation according to the switching instant, the harmonics at the steady-state condition, as well as the coupling between the multiple harmonic impedances. By using this model, the impaction on the harmonics performance by the film capacitor and the grid inductance is derived. Simulation and experimental...

Physics of tissue harmonic imaging by ultrasound

Science.gov (United States)

Jing, Yuan

Tissue Harmonic Imaging (THI) is an imaging modality that is currently deployed on diagnostic ultrasound scanners. In THI the amplitude of the ultrasonic pulse that is used to probe the tissue is large enough that the pulse undergoes nonlinear distortion as it propagates into the tissue. One result of the distortion is that as the pulse propagates energy is shifted from the fundamental frequency of the source pulse into its higher harmonics. These harmonics will scatter off objects in the tissue and images formed from the scattered higher harmonics are considered to have superior quality to the images formed from the fundamental frequency. Processes that have been suggested as possibly responsible for the improved imaging in THI include: (1) reduced sensitivity to reverberation, (2) reduced sensitivity to aberration, and (3) reduction in side lobes. By using a combination of controlled experiments and numerical simulations, these three reasons have been investigated. A single element transducer and a clinical ultrasound scanner with a phased array transducer were used to image a commercial tissue-mimicking phantom with calibrated targets. The higher image quality achieved with THI was quantified in terms of spatial resolution and "clutter" signals. A three-dimensional model of the forward propagation of nonlinear sound beams in media with arbitrary spatial properties (a generalized KZK equation) was developed. A time-domain code for solving the KZK equation was validated with measurements of the acoustic field generated by the single element transducer and the phased array transducer. The code was used to investigate the impact of aberration using tissue-like media with three-dimensional variations in all acoustic properties. The three-dimensional maps of tissue properties were derived from the datasets available through the Visible Female project. The experiments and simulations demonstrated that second harmonic imaging (1) suffers less clutter associated with

Analysis of axisymmetric and non-axisymmetric wave propagation in a homogeneous piezoelectric solid circular cylinder of transversely isotropic material

CSIR Research Space (South Africa)

Shatalov, MY

2010-01-01

Full Text Available artefacts. An elaborate discussion of these artefacts is given by Yenwong-Fai, (Yenwong-Fai, 2008). These artefacts could be simply detected and eliminated from the dispersion plots by program tools.Our algorithm, as it has been implemented, does.... Arthur G. Every and our student Alfred S. Yenwong-Fai participating in the investigation of the non-axisymmetric case of the piezoelectric cylinder vibrations (Shatalov, et al. 2009). I also want to thank Mr. Yuri M. Shatalov who investigated...

Excitation of nonaxisymmetric perturbations by the axisymmetric explosive magnetorotational instability in Keplerian discs

Science.gov (United States)

Shtemler, Yu.; Mond, M.; Liverts, E.

2018-02-01

The excitation of nonaxisymmetric quasi-resonant triads by clustering around a dominant axisymmetric explosively unstable magnetorotational instability (MRI) in Keplerian discs is investigated. Clustering, namely, the mutual interactions of a large number of quasi-resonant triads that are connected by a single dominant explosively unstable axisymmetric triad, is invoked in order to provide a viable mechanism for the stabilization of the explosive nature of the latter. The results, however, are of wider scope as the proposed clustering scenario also provides a strong mechanism for the excitation of high-amplitude nonaxisymmetric perturbations. The latter play a major role in the nonlinear evolution of the MRI on the route to fully developed turbulence.

Non-axisymmetric SOL-transport study for tokamaks and stellarators

International Nuclear Information System (INIS)

Sardei, F.; Feng, Y.; Kisslinger, J.; Grigull, P.; Kobayashi, M.; Harting, D.; Reiter, D.; Federici, G.; Loarte, A.

2007-01-01

The paper addresses basic features of non-axisymmetric edge transport induced in tokamaks by local limiters or external magnetic perturbations and in low-shear stellarators by the presence of edge magnetic islands. 3D simulations and, if available for comparison, experimental results are presented and discussed for three devices, ITER during start-up operation, TEXTOR-DED and W7-AS, having edge topologies totally different from each other. The modeling is performed with the EMC3/EIRENE code, which treats self-consistently plasma, neutral and impurity transport in a general 3D scrape-off layer (SOL) with arbitrarily complex geometry of magnetic configuration and plasma-facing components. Shown are code predictions of the power load on the ITER start-up limiters as well as modeling results on the transport in the TEXTOR-DED stochastic edge and on the physics of stable detachment in W7-AS. Experimental observations confirming the code simulations are referenced for both TEXTOR-DED and W7-AS, a direct comparison between modeling and experimental results is shown for W7-AS

Vector model for polarized second-harmonic generation microscopy under high numerical aperture

International Nuclear Information System (INIS)

Wang, Xiang-Hui; Chang, Sheng-Jiang; Lin, Lie; Wang, Lin-Rui; Huo, Bing-Zhong; Hao, Shu-Jian

2010-01-01

Based on the vector diffraction theory and the generalized Jones matrix formalism, a vector model for polarized second-harmonic generation (SHG) microscopy is developed, which includes the roles of the axial component P z , the weight factor and the cross-effect between the lateral components. The numerical results show that as the relative magnitude of P z increases, the polarization response of the second-harmonic signal will vary from linear polarization to elliptical polarization and the polarization orientation of the second-harmonic signal is different from that under the paraxial approximation. In addition, it is interesting that the polarization response of the detected second-harmonic signal can change with the value of the collimator lens NA. Therefore, it is more advantageous to adopt the vector model to investigate the property of polarized SHG microscopy for a variety of cases

Comparison study among conventional, tissue harmonic and pulse inversion harmonic images to evaluate pleural effusion and ascites

International Nuclear Information System (INIS)

Chung, Hwan Hoon; Kim, Yun Hwan; Kang, Chang Ho; Park, Bum Jin; Chung, Kyoo Byung; Suh, Won Hyuck

2000-01-01

To determine the most useful sonographic technique to evaluate pleural effusion and ascites by comparing conventional, tissue harmonic and pulse inversion harmonic images. 12 patients having pleural effusion and 14 patients having ascites were included in this study. 18 patients were male and 8 patients were female. Average age was 54.8 yrs (25-77). We compared images which had been taken at the same section with 3 above mentioned sonographic techniques. Evaluation was done by 3 radiologists in consensus and grades were given to 3 techniques from 1 to 3. Evaluating points were 1) normal structures that border the fluid such as liver, peritoneal lining, pleura, 2) septation in fluid, 3) debris floating in fluid, and 4) artifacts. Pulse inversion harmonic image was the best in image quality for normal structures, followed by tissue harmonic and conventional image (p<0.05). Pulse inversion harmonic image was better than conventional image to evaluate septation in fluid (p<0.05), but there were no statistically significant difference between pulse inversion and tissue harmonic images, and tissue harmonic and conventional images. Tissue harmonic image was better than pulse inversion harmonic and conventional images to evaluate debris floating in fluid (p<0.05) but there was no statistically significant difference between these two latter techniques. Artifacts were most prominent on conventional image followed by tissue harmonic and pulse inversion harmonic image (p<0.05). Pulse inversion harmonic image was the best sonographic technique to evaluate pleural effusion or ascites, However, Tissue harmonic image was the best for evaluation of debris.

Comparison study among conventional, tissue harmonic and pulse inversion harmonic images to evaluate pleural effusion and ascites

Energy Technology Data Exchange (ETDEWEB)

Chung, Hwan Hoon; Kim, Yun Hwan; Kang, Chang Ho; Park, Bum Jin; Chung, Kyoo Byung; Suh, Won Hyuck [Korea University College of Medicine, Seoul (Korea, Republic of)

2000-12-15

To determine the most useful sonographic technique to evaluate pleural effusion and ascites by comparing conventional, tissue harmonic and pulse inversion harmonic images. 12 patients having pleural effusion and 14 patients having ascites were included in this study. 18 patients were male and 8 patients were female. Average age was 54.8 yrs (25-77). We compared images which had been taken at the same section with 3 above mentioned sonographic techniques. Evaluation was done by 3 radiologists in consensus and grades were given to 3 techniques from 1 to 3. Evaluating points were 1) normal structures that border the fluid such as liver, peritoneal lining, pleura, 2) septation in fluid, 3) debris floating in fluid, and 4) artifacts. Pulse inversion harmonic image was the best in image quality for normal structures, followed by tissue harmonic and conventional image (p<0.05). Pulse inversion harmonic image was better than conventional image to evaluate septation in fluid (p<0.05), but there were no statistically significant difference between pulse inversion and tissue harmonic images, and tissue harmonic and conventional images. Tissue harmonic image was better than pulse inversion harmonic and conventional images to evaluate debris floating in fluid (p<0.05) but there was no statistically significant difference between these two latter techniques. Artifacts were most prominent on conventional image followed by tissue harmonic and pulse inversion harmonic image (p<0.05). Pulse inversion harmonic image was the best sonographic technique to evaluate pleural effusion or ascites, However, Tissue harmonic image was the best for evaluation of debris.

Effect of Axisymmetric Aft Wall Angle Cavity in Supersonic Flow Field

Science.gov (United States)

Jeyakumar, S.; Assis, Shan M.; Jayaraman, K.

2018-03-01

Cavity plays a significant role in scramjet combustors to enhance mixing and flame holding of supersonic streams. In this study, the characteristics of axisymmetric cavity with varying aft wall angles in a non-reacting supersonic flow field are experimentally investigated. The experiments are conducted in a blow-down type supersonic flow facility. The facility consists of a supersonic nozzle followed by a circular cross sectional duct. The axisymmetric cavity is incorporated inside the duct. Cavity aft wall is inclined with two consecutive angles. The performance of the aft wall cavities are compared with rectangular cavity. Decreasing aft wall angle reduces the cavity drag due to the stable flow field which is vital for flame holding in supersonic combustor. Uniform mixing and gradual decrease in stagnation pressure loss can be achieved by decreasing the cavity aft wall angle.

CRUCIB: an axisymmetric convection code

International Nuclear Information System (INIS)

Bertram, L.A.

1975-03-01

The CRUCIB code was written in support of an experimental program aimed at measurement of thermal diffusivities of refractory liquids. Precise values of diffusivity are necessary to realistic analysis of reactor safety problems, nuclear waste disposal procedures, and fundamental metal forming processes. The code calculates the axisymmetric transient convective motions produced in a right circular cylindrical crucible, which is surface heated by an annular heat pulse. Emphasis of this report is placed on the input-output options of the CRUCIB code, which are tailored to assess the importance of the convective heat transfer in determining the surface temperature distribution. Use is limited to Prandtl numbers less than unity; larger values can be accommodated by replacement of a single block of the code, if desired. (U.S.)

Representation Discovery using Harmonic Analysis

CERN Document Server

Mahadevan, Sridhar

2008-01-01

Representations are at the heart of artificial intelligence (AI). This book is devoted to the problem of representation discovery: how can an intelligent system construct representations from its experience? Representation discovery re-parameterizes the state space - prior to the application of information retrieval, machine learning, or optimization techniques - facilitating later inference processes by constructing new task-specific bases adapted to the state space geometry. This book presents a general approach to representation discovery using the framework of harmonic analysis, in particu

Cumulative second-harmonic generation of Lamb waves propagating in a two-layered solid plate

International Nuclear Information System (INIS)

Xiang Yanxun; Deng Mingxi

2008-01-01

The physical process of cumulative second-harmonic generation of Lamb waves propagating in a two-layered solid plate is presented by using the second-order perturbation and the technique of nonlinear reflection of acoustic waves at an interface. In general, the cumulative second-harmonic generation of a dispersive guided wave propagation does not occur. However, the present paper shows that the second-harmonic of Lamb wave propagation arising from the nonlinear interaction of the partial bulk acoustic waves and the restriction of the three boundaries of the solid plates does have a cumulative growth effect if some conditions are satisfied. Through boundary condition and initial condition of excitation, the analytical expression of cumulative second-harmonic of Lamb waves propagation is determined. Numerical results show the cumulative effect of Lamb waves on second-harmonic field patterns. (classical areas of phenomenology)

A novel harmonic current sharing control strategy for parallel-connected inverters

DEFF Research Database (Denmark)

Guan, Yajuan; Guerrero, Josep M.; Savaghebi, Mehdi

2017-01-01

A novel control strategy which enables proportional linear and nonlinear loads sharing among paralleled inverters and voltage harmonic suppression is proposed in this paper. The proposed method is based on the autonomous currents sharing controller (ACSC) instead of conventional power droop control...... to provide fast transient response, decoupling control and large stability margin. The current components at different sequences and orders are decomposed by a multi-second-order generalized integrator-based frequency locked loop (MSOGI-FLL). A harmonic-orthogonal-virtual-resistances controller (HOVR......) is used to proportionally share current components at different sequences and orders independently among the paralleled inverters. Proportional resonance controllers tuned at selected frequencies are used to suppress voltage harmonics. Simulations based on two 2.2 kW paralleled three-phase inverters...

Maximal Regularity of the Discrete Harmonic Oscillator Equation

Directory of Open Access Journals (Sweden)

Airton Castro

2009-01-01

Full Text Available We give a representation of the solution for the best approximation of the harmonic oscillator equation formulated in a general Banach space setting, and a characterization of lp-maximal regularity—or well posedness—solely in terms of R-boundedness properties of the resolvent operator involved in the equation.

Kinetic extensions of magnetohydrodynamic models for axisymmetric toroidal plasmas

International Nuclear Information System (INIS)

Cheng, C.Z.

1989-04-01

A nonvariational kinetic-MHD stability code (NOVA-K) has been developed to integrate a set of non-Hermitian integro-differential eigenmode equations due to energetic particles for axisymmetric toroidal plasmas in a general flux coordinate system with an arbitrary Jacobian. The NOVA-K code employs the Galerkin method involving Fourier expansions in the generalized poloidal angle θ and generalized toroidal angle /zeta/ directions, and cubic-B spline finite elements in the radial /Psi/ direction. Extensive comparisons with the existing variational ideal MHD codes show that the ideal MHD version of the NOVA-K code converges faster and gives more accurate results. The NOVA-K code is employed to study the effects of energetic particles on MHD-type modes: the stabilization of ideal MHD internal kink modes and the excitation of ''fishbone'' internal kink modes; and the alpha particle destabilization of toroidicity-induced Alfven eigenmodes (TAE) via transit resonances. Analytical theories are also presented to help explain the NOVA-K results. For energetic trapped particles generated by neutral beam injection (NBI) or ion cyclotron resonant heating (ICRH), a stability window for the n = 1 internal kink mode in the hot particle beta space exists even in the absence of the core ion finite Larmor radius effect. On the other hand, the trapped alpha particles are found to have negligible effects on the stability of the n = 1 internal kink mode, but the circulating alpha particles can strongly destabilize TAE modes via inverse Landau damping associated with the spatial gradient of the alpha particle pressure. 60 refs., 24 figs., 1 tab

SEAWAT-based simulation of axisymmetric heat transport.

Science.gov (United States)

Vandenbohede, Alexander; Louwyck, Andy; Vlamynck, Nele

2014-01-01

Simulation of heat transport has its applications in geothermal exploitation of aquifers and the analysis of temperature dependent chemical reactions. Under homogeneous conditions and in the absence of a regional hydraulic gradient, groundwater flow and heat transport from or to a well exhibit radial symmetry, and governing equations are reduced by one dimension (1D) which increases computational efficiency importantly. Solute transport codes can simulate heat transport and input parameters may be modified such that the Cartesian geometry can handle radial flow. In this article, SEAWAT is evaluated as simulator for heat transport under radial flow conditions. The 1971, 1D analytical solution of Gelhar and Collins is used to compare axisymmetric transport with retardation (i.e., as a result of thermal equilibrium between fluid and solid) and a large diffusion (conduction). It is shown that an axisymmetric simulation compares well with a fully three dimensional (3D) simulation of an aquifer thermal energy storage systems. The influence of grid discretization, solver parameters, and advection solution is illustrated. Because of the high diffusion to simulate conduction, convergence criterion for heat transport must be set much smaller (10(-10) ) than for solute transport (10(-6) ). Grid discretization should be considered carefully, in particular the subdivision of the screen interval. On the other hand, different methods to calculate the pumping or injection rate distribution over different nodes of a multilayer well lead to small differences only. © 2013, National Ground Water Association.

Harmonic Patterns in Forex Trading

OpenAIRE

Nemček, Sebastian

2013-01-01

This diploma thesis is committed to examination of validity of Harmonic Patterns in Forex trading. Scott Carney described existing and introduced new Harmonic Patterns in 1999 in his book Harmonic Trader. These patterns use the Fibonacci principle to analyze price action and to provide both bullish and bearish trading signals. The goal of this thesis is to find out whether harmonic trading strategy on selected pairs is profitable in FX market, which patterns are the most profitable and what i...

Eddy currents in a nonperiodic vacuum vessel induced by axisymmetric plasma motion

International Nuclear Information System (INIS)

DeLucia, J.

1985-12-01

A method is described for calculating the two-dimensional trajectory of a vertically or horizontally unstable axisymmetric tokamak plasma in the presence of a resistive vacuum vessel. The vessel is not assumed to have toroidal symmetry. The plasma is represented by a current-filament loop that is free to move vertically and to change its major radius. Its position is evolved in time self-consistently with the vacuum vessel eddy currents. The plasma current, internal inductance, and poloidal beta can be specified functions of time so that eddy currents resulting from a disruption can be modeled. The vacuum vessel is represented by a set of current-filaments whose positions and orientations are chosen to model the dominant eddy current paths. Although the specific application is to TFTR, the present model is of general applicability. 7 refs., 4 figs., 2 tabs

Calculation of rf fields in axisymmetric cavities

International Nuclear Information System (INIS)

Iwashita, Y.

1985-01-01

A new code, PISCES, has been developed for calculating a complete set of rf electromagnetic modes in an axisymmetric cavity. The finite-element method is used with up to third-order shape functions. Although two components are enough to express these modes, three components are used as unknown variables to take advantage of the symmetry of the element matrix. The unknowns are taken to be either the electric field components or the magnetic field components. The zero-divergence condition will be satisfied by the shape function within each element

Sensitivity of echo enabled harmonic generation to sinusoidal electron beam energy structure

Directory of Open Access Journals (Sweden)

E. Hemsing

2017-06-01

Full Text Available We analytically examine the bunching factor spectrum of a relativistic electron beam with sinusoidal energy structure that then undergoes an echo-enabled harmonic generation (EEHG transformation to produce high harmonics. The performance is found to be described primarily by a simple scaling parameter. The dependence of the bunching amplitude on fluctuations of critical parameters is derived analytically, and compared with simulations. Where applicable, EEHG is also compared with high gain harmonic generation (HGHG and we find that EEHG is generally less sensitive to several types of energy structure. In the presence of intermediate frequency modulations like those produced by the microbunching instability, EEHG has a substantially narrower intrinsic bunching pedestal.

Global regularity for a family of 3D models of the axi-symmetric Navier–Stokes equations

Science.gov (United States)

Hou, Thomas Y.; Liu, Pengfei; Wang, Fei

2018-05-01

We consider a family of three-dimensional models for the axi-symmetric incompressible Navier–Stokes equations. The models are derived by changing the strength of the convection terms in the axisymmetric Navier–Stokes equations written using a set of transformed variables. We prove the global regularity of the family of models in the case that the strength of convection is slightly stronger than that of the original Navier–Stokes equations, which demonstrates the potential stabilizing effect of convection.

FLEXURAL STRESS ANALYSIS OF RIGID PAVEMENTS USING AXI-SYMMETRIC AND PLANE STRAIN FEM

Directory of Open Access Journals (Sweden)

V.A. Sawant

2017-11-01

Full Text Available The design of pavement involves a study of soils and paving materials, their response under load for different climatic conditions. In the present study, an attempt has been made to compare stresses predicted using two finite element analyses. First analysis is based on the twodimensional plane strain assumption where as in second approach axi-symmetric condition is assumed to consider three-dimensional behavior of rigid pavement. The results are compared with flexural stresses obtained from conventional Portland Cement Association method. The computed flexural stresses obtained from axi-symmetric condition are found to be in close agreement with PCA method. Results of plane strain analysis show a fair agreement after application of an appropriate multiplication factor

Non-Axisymmetric Oscillation of Acoustically Levitated Water Drops at Specific Frequencies

International Nuclear Information System (INIS)

Chang-Le, Shen; Wen-Jun, Xie; Bing-Bo, Wei

2010-01-01

A category of non-axisymmetric oscillations of acoustically levitated water drops was observed. These oscillations can be qualitatively described by superposing a sectorial oscillating term upon the initial oblate shape resulting from the effect of acoustic radiation pressure. The oscillation frequencies are around 25 Hz for the 2-lobed mode and exactly 50 Hz for the 3- and 4-lobed modes. These oscillations were excited by the disturbance from the power supply. For the same water drop, higher mode oscillations were observed with more oblate initial shape, indicating that the eigenfrequencies of these non-axisymmetric oscillations decrease with increasing initial distortion. The maximum velocity and acceleration within the oscillating drop can attain 0.3m·s −1 and 98.7m·s −2 respectively, resulting in strong fluid convection and enhanced heat and mass transfer. (condensed matter: structure, mechanical and thermal properties)

Synthesis of Variable Harmonic Impedance in Inverter-Interfaced Distributed Generation Unit for Harmonic Damping Throughout a Distribution Network

DEFF Research Database (Denmark)

Wang, Xiongfei; Blaabjerg, Frede; Chen, Zhe

2012-01-01

This paper proposes a harmonic impedance synthesis technique for voltage-controlled distributed generation inverters in order to damp harmonic voltage distortion on a distribution network. The approach employs a multiloop control scheme, where a selective harmonic load current feedforward loop...... at the dominant harmonic frequencies. Thus, the harmonic voltage drop on the grid-side inductance and the harmonic resonances throughout a distribution feeder with multiple shunt-connected capacitors can be effectively attenuated. Simulation and laboratory test results validate the performance of the proposed...

Tuvan throat singing and harmonics

Science.gov (United States)

Ruiz, Michael J.; Wilken, David

2018-05-01

Tuvan throat singing, also called overtone singing, provides for an exotic demonstration of the physics of harmonics as well as introducing an Asian musical aesthetic. A low fundamental is sung and the singer skillfully alters the resonances of the vocal system to enhance an overtone (harmonic above the fundamental). The result is that the listener hears two pitches simultaneously. Harmonics such as H8, H9, H10, and H12 form part of a pentatonic scale and are commonly selected for melody tones by Tuvan singers. A real-time spectrogram is provided in a video (Ruiz M J 2018 Video: Tuvan Throat Singing and Harmonics http://mjtruiz.com/ped/tuva/) so that Tuvan harmonics can be visualized as they are heard.

Current Harmonics Compensation in Microgrids Exploiting the Power Electronics Interfaces of Renewable Energy Sources

Directory of Open Access Journals (Sweden)

Ioannis Bouloumpasis

2015-03-01

Full Text Available This work presents a method of current harmonic reduction in a distorted distribution system. In order to evaluate the proposed method a grid with high-order current harmonics is assumed. The reduction of current distortion is feasible due to the pulse modulation of an active filter, which consists of a buck-boost converter connected back-to-back to a polarity swapping inverter. For a practical application, this system would be the power electronic interface of a Renewable Energy Source (RES and therefore it changes a source of harmonics to a damping harmonics system. Using the proposed method, the current Total Harmonic Distortion (THD of the grid is reduced below the acceptable limits and thus the general power quality of the system is improved. Simulations in the MATLAB/SIMULINK platform and experiments have been performed in order to verify the effectiveness of the proposed method.

Axisymmetric MHD equilibrium solver with bicubic Hermite elements

International Nuclear Information System (INIS)

Luetjens, H.; Bondeson, A.; Roy, A.

1990-05-01

A numerical code solving axisymmetric magnetohydrodynamic equilibria with rectangular bicubic Hermite elements has been developed. Two test cases are used for checking the convergence rate of the solution. The mapping of the equilibrium quantities into flux coordinates for magnetohydrodynamic stability calculation is performed by a method which preserves the convergence properties of the cubic Hermite elements. Convergence studies show the behaviour of the stability results when the equilibrium mesh is varied. (author) 13 refs., 3 tabs

Wave function for harmonically confined electrons in time-dependent electric and magnetostatic fields.

Science.gov (United States)

Zhu, Hong-Ming; Chen, Jin-Wang; Pan, Xiao-Yin; Sahni, Viraht

2014-01-14

We derive via the interaction "representation" the many-body wave function for harmonically confined electrons in the presence of a magnetostatic field and perturbed by a spatially homogeneous time-dependent electric field-the Generalized Kohn Theorem (GKT) wave function. In the absence of the harmonic confinement - the uniform electron gas - the GKT wave function reduces to the Kohn Theorem wave function. Without the magnetostatic field, the GKT wave function is the Harmonic Potential Theorem wave function. We further prove the validity of the connection between the GKT wave function derived and the system in an accelerated frame of reference. Finally, we provide examples of the application of the GKT wave function.

Tissue Harmonic Synthetic Aperture Imaging

DEFF Research Database (Denmark)

Rasmussen, Joachim

The main purpose of this PhD project is to develop an ultrasonic method for tissue harmonic synthetic aperture imaging. The motivation is to advance the field of synthetic aperture imaging in ultrasound, which has shown great potentials in the clinic. Suggestions for synthetic aperture tissue...... system complexity compared to conventional synthetic aperture techniques. In this project, SASB is sought combined with a pulse inversion technique for 2nd harmonic tissue harmonic imaging. The advantages in tissue harmonic imaging (THI) are expected to further improve the image quality of SASB...

Using "Tracker" to Prove the Simple Harmonic Motion Equation

Science.gov (United States)

Kinchin, John

2016-01-01

Simple harmonic motion (SHM) is a common topic for many students to study. Using the free, though versatile, motion tracking software; "Tracker", we can extend the students experience and show that the general equation for SHM does lead to the correct period of a simple pendulum.

MHD stability calculations of high-β quasi-axisymmetric stellarators

International Nuclear Information System (INIS)

Fu, G.Y.; Ku, L.P.; Pomphrey, N.; Redi, M.; Kessel, C.; Monticello, D.; Reiman, A.; Hughes, M.; Cooper, W.A.; Nuehrenberg, C.

2001-01-01

The MHD stability of quasi-axisymmetric compact stellarators is investigated. It is shown that bootstrap current driven external kink modes can be stabilized by a combination of edge magnetic shear and appropriate 3D plasma boundary shaping while maintaining good quasi-axisymmetry. The results demonstrate that there exists a new class of stellarators with quasi-axisymmetry, large bootstrap current, high MHD beta limit, and compact size. (author)

MHD stability calculations of high-β quasi-axisymmetric stellarators

International Nuclear Information System (INIS)

Fu, G.Y.; Ku, L.P.; Pomphrey, N.; Redi, M.H.; Kessel, C.; Monticello, D.A.; Reiman, A.; Hughes, M.; Cooper, W.A.; Nuehrenberg, C.

1999-01-01

The MHD stability of quasi-axisymmetric compact stellarators is investigated. It is shown that bootstrap current driven external kink modes can be stabilized by a combination of edge magnetic shear and appropriate 3D plasma boundary shaping while maintaining good quasi-axisymmetry. The results demonstrate that there exists a new class of stellarators with quasi-axisymmetry, large bootstrap current, high MHD beta limit, and compact size. (author)

MHD Stability Calculations of High-Beta Quasi-Axisymmetric Stellarators

International Nuclear Information System (INIS)

Kessel, C.; Fu, G.Y.; Ku, L.P.; Redi, M.H.; Pomphrey, N.

1999-01-01

The MHD stability of quasi-axisymmetric compact stellarators is investigated. It is shown that bootstrap current driven external kink modes can be stabilized by a combination of edge magnetic shear and appropriate 3D plasma boundary shaping while maintaining good quasi-axisymmetry. The results demonstrate that there exists a new class of stellarators with quasi-axisymmetry, large bootstrap current, high MHD beta limit, and compact size

Nonlinear coupling of flow harmonics: Hexagonal flow and beyond

Science.gov (United States)

Giacalone, Giuliano; Yan, Li; Ollitrault, Jean-Yves

2018-05-01

Higher Fourier harmonics of anisotropic flow (v4 and beyond) get large contributions induced by elliptic and triangular flow through nonlinear response. We present a general framework of nonlinear hydrodynamic response which encompasses the existing one and allows us to take into account the mutual correlation between the nonlinear couplings affecting Fourier harmonics of any order. Using Large Hadron Collider data on Pb+Pb collisions at s =2.76 TeV, we perform an application of our formalism to hexagonal flow, v6, a coefficient affected by several nonlinear contributions which are of the same order of magnitude. We obtain the first experimental measure of the coefficient χ624, which couples v6 to v2 and v4. This is achieved by putting together the information from several analyses: event-plane correlations, symmetric cumulants, and higher order moments recently analyzed by the ALICE Collaboration. The value of χ624 extracted from data is in fair agreement with hydrodynamic calculations, although with large error bars, which would be dramatically reduced by a dedicated analysis. We argue that within our formalism the nonlinear structure of a given higher order harmonic can be determined more accurately than the harmonic itself, and we emphasize potential applications to future measurements of v7 and v8.

Entanglement in the harmonic chain and quantum fields

International Nuclear Information System (INIS)

Kofler, J.; Vedral, V.; Brukner, C.

2005-01-01

Full text: Relativistic field theory is a natural basis for the theoretical investigation of quantum entanglement, since the concept of locality and causality is inherently included. Vacuum entanglement of relativistic fields manifests itself in Hawking radiation and the Unruh effect. But it also is encountered in the linear harmonic chain, which - in the continuum limit and if generalized to three spatial dimensions - becomes the real scalar Klein-Gordon field. One can define average position and momentum operators for two separated blocks of oscillators in the harmonic chain and investigate the entanglement - by means of a separability criterion - between these blocks as a function of their distance and the coupling between the oscillators. This motivated us to rewrite the general separability conditions for continuous variables into the language of quantum field theory, where the position and momentum operator become integrals of the Klein-Gordon field and the conjugate momentum field, respectively. The role of the modes (or particles) is then merely played by the space(-time) regions over which the integration takes (author)

Sigma models in (4,4) harmonic superspace

International Nuclear Information System (INIS)

Ivanov, E.; Joint Inst. for Nuclear Research, Dubna; Sutulin, A.

1994-04-01

We define basics of (4,4) 2D harmonic superspace with two independent sets of SU(2) harmonic variables and apply it to construct new superfield actions of (4,4) supersymmetric two-dimensional sigma models with torsion and mutually commuting left and right complex structures, as well as of their massive deformations. We show that the generic off-shell sigma model action is the general action of constrained analytic superfields q (1,1) representing twisted N=4 multiplets in (4,4) harmonic superspace. The massive term of q (1,1) is shown to be unique; it generates a scalar potential the form of which is determined by the metric on the target bosonic manifold. We discuss in detail (4,4) supersymmetric group manifold SU(2)xU(1) WZNW sigma model and its Liouville deformation. A deep analogy of the relevant superconformally invariant analytic superfield action to that of the improved tensor N=2 4D multiplet is found. We define (4,4) duality transformation and find new off-shell dual representations of the previously constructed actions via unconstrained analytic (4,4) superfields. The main peculiarities of the (4,4) duality transformation are: (i) It preserves manifest (4,4) supersymmetry; (ii) dual actions reveal a gauge invariance needed for the onshell equivalence to the original description; (iii) in the actions dual to the massive ones 2D supersymmetry is modified off shell by SU(2) tensor central charges. The dual representation suggests some hints of how to describe (4,4) models with non-commuting complex structures in the harmonic superspace. (orig.)

On the conformal equivalence of harmonic maps and exponentially harmonic maps

International Nuclear Information System (INIS)

Hong Minchun.

1991-06-01

Suppose that (M,g) and (N,h) are compact smooth Riemannian manifolds without boundaries. For m = dim M ≥3, and Φ: (M,g) → (N,h) is exponentially harmonic, there exists a smooth metric g-tilde conformally equivalent to g such that Φ: (M,g-tilde) → (N,h) is harmonic. (author). 7 refs

Determination of averaged axisymmetric flow surfaces according to results obtained by numerical simulation of flow in turbomachinery

Directory of Open Access Journals (Sweden)

Bogdanović-Jovanović Jasmina B.

2012-01-01

Full Text Available In the increasing need for energy saving worldwide, the designing process of turbomachinery, as an essential part of thermal and hydroenergy systems, goes in the direction of enlarging efficiency. Therefore, the optimization of turbomachinery designing strongly affects the energy efficiency of the entire system. In the designing process of turbomachinery blade profiling, the model of axisymmetric fluid flows is commonly used in technical practice, even though this model suits only the profile cascades with infinite number of infinitely thin blades. The actual flow in turbomachinery profile cascades is not axisymmetric, and it can be fictively derived into the axisymmetric flow by averaging flow parameters in the blade passages according to the circular coordinate. Using numerical simulations of flow in turbomachinery runners, its operating parameters can be preliminarily determined. Furthermore, using the numerically obtained flow parameters in the blade passages, averaged axisymmetric flow surfaces in blade profile cascades can also be determined. The method of determination of averaged flow parameters and averaged meridian streamlines is presented in this paper, using the integral continuity equation for averaged flow parameters. With thus obtained results, every designer can be able to compare the obtained averaged flow surfaces with axisymmetric flow surfaces, as well as the specific work of elementary stages, which are used in the procedure of blade designing. Numerical simulations of flow in an exemplary axial flow pump, used as a part of the thermal power plant cooling system, were performed using Ansys CFX. [Projekat Ministarstva nauke Republike Srbije, br. TR33040: Revitalization of existing and designing new micro and mini hydropower plants (from 100 kW to 1000 kW in the territory of South and Southeast Serbia

Waveguide harmonic damper for klystron amplifier

International Nuclear Information System (INIS)

Kang, Y.

1998-01-01

A waveguide harmonic damper was designed for removing the harmonic frequency power from the klystron amplifiers of the APS linac. Straight coaxial probe antennas are used in a rectangular waveguide to form a damper. A linear array of the probe antennas is used on a narrow wall of the rectangular waveguide for damping klystron harmonics while decoupling the fundamental frequency in dominent TE 01 mode. The klystron harmonics can exist in the waveguide as waveguide higher-order modes above cutoff. Computer simulations are made to investigate the waveguide harmonic damping characteristics of the damper

Application of the Least Squares Method in Axisymmetric Biharmonic Problems

Directory of Open Access Journals (Sweden)

Vasyl Chekurin

2016-01-01

Full Text Available An approach for solving of the axisymmetric biharmonic boundary value problems for semi-infinite cylindrical domain was developed in the paper. On the lateral surface of the domain homogeneous Neumann boundary conditions are prescribed. On the remaining part of the domain’s boundary four different biharmonic boundary pieces of data are considered. To solve the formulated biharmonic problems the method of least squares on the boundary combined with the method of homogeneous solutions was used. That enabled reducing the problems to infinite systems of linear algebraic equations which can be solved with the use of reduction method. Convergence of the solution obtained with developed approach was studied numerically on some characteristic examples. The developed approach can be used particularly to solve axisymmetric elasticity problems for cylindrical bodies, the heights of which are equal to or exceed their diameters, when on their lateral surface normal and tangential tractions are prescribed and on the cylinder’s end faces various types of boundary conditions in stresses in displacements or mixed ones are given.

A Fast Algorithm for Maximum Likelihood Estimation of Harmonic Chirp Parameters

DEFF Research Database (Denmark)

Jensen, Tobias Lindstrøm; Nielsen, Jesper Kjær; Jensen, Jesper Rindom

2017-01-01

. A statistically efficient estimator for extracting the parameters of the harmonic chirp model in additive white Gaussian noise is the maximum likelihood (ML) estimator which recently has been demonstrated to be robust to noise and accurate --- even when the model order is unknown. The main drawback of the ML......The analysis of (approximately) periodic signals is an important element in numerous applications. One generalization of standard periodic signals often occurring in practice are harmonic chirp signals where the instantaneous frequency increases/decreases linearly as a function of time...

Studying the universality of field induced tunnel ionization times via high-order harmonic spectroscopy

International Nuclear Information System (INIS)

Soifer, H; Bruner, B D; Dudovich, N; Negro, M; Devetta, M; Vozzi, C; Faccialà, D; Silvestri, S de; Stagira, S

2014-01-01

High-harmonic generation spectroscopy is a promising tool for resolving electron dynamics and structure in atomic and molecular systems. This scheme, commonly described by the strong field approximation, requires a deep insight into the basic mechanism that leads to the harmonic generation. Recently, we have demonstrated the ability to resolve the first stage of the process—field induced tunnel ionization—by adding a weak perturbation to the strong fundamental field. Here we generalize this approach and show that the assumptions behind the strong field approximation are valid over a wide range of tunnel ionization conditions. Performing a systematic study—modifying the fundamental wavelength, intensity and atomic system—we observed a good agreement with quantum path analysis over a range of Keldysh parameters. The generality of this scheme opens new perspectives in high harmonics spectroscopy, holding the potential of probing large, complex molecular systems. (paper)

Precise Model Analysis for 3-phase High Power Converter using the Harmonic State Space Modeling

DEFF Research Database (Denmark)

Kwon, Jun Bum; Wang, Xiongfei; Blaabjerg, Frede

2015-01-01

This paper presents about the generalized multi-frequency modeling and analysis methodology, which can be used in control loop design and stability analysis. In terms of the switching frequency of high power converter, there can be harmonics interruption if the voltage source converter has a low...... switching frequency ratio or multi-sampling frequency. The range of the control bandwidth can include the switching component. Thus, the systems become unstable. This paper applies the Harmonic State Space (HSS) Modeling method in order to find out the transfer function for each harmonics terms...

Control and metrology of high harmonic generation on plasma mirrors

International Nuclear Information System (INIS)

Monchoce, Sylvain

2014-01-01

When an ultra intense femtosecond laser with high contrast is focused on a solid target, the laser field at focus is sufficient enough to completely ionize the target surface during the rising edge of the laser pulse and form a plasma. This dense plasma entirely reflects the incident beam in the specular direction: this is a so-called plasma mirror. As the interaction between the laser and the plasma mirror is highly non-linear, it thus leads to the high harmonic generation (HHG) in the reflected beam. In the temporal domain, this harmonic spectrum is associated to a train of atto-second pulses. The aim of my PhD were to experimentally control this HHG and to measure the properties of the harmonics. We first studied the optimization of the harmonic signal, and then the spatial characterization of the harmonic beam in the far-field (harmonic divergence). These characterizations are not only important to develop an intense XUV/atto-second light source, but also to get a better understanding of the laser-matter interaction at very high intensity. We have thus been able to get crucial information of the electrons and ions dynamics of the plasma, showing that the harmonics can also be used as a diagnostic of the laser-plasma interaction. We then developed a new general approach for optically-controlled spatial structuring of overdense plasmas generated at the surface of initially plain solid targets. We demonstrate it experimentally by creating sinusoidal plasma gratings of adjustable spatial periodicity and depth, and study the interaction of these transient structures with an ultra-intense laser pulse to establish their usability at relativistically high intensities. We then show how these gratings can be used as a 'spatial ruler' to determine the source size of the high-order harmonic beams produced at the surface of an overdense plasma. These results open new directions both for the metrology of laser-plasma interactions and the emerging field of ultrahigh

Boundary singularity of Poisson and harmonic Bergman kernels

Czech Academy of Sciences Publication Activity Database

Engliš, Miroslav

2015-01-01

Roč. 429, č. 1 (2015), s. 233-272 ISSN 0022-247X R&D Projects: GA AV ČR IAA100190802 Institutional support: RVO:67985840 Keywords : harmonic Bergman kernel * Poisson kernel * pseudodifferential boundary operators Subject RIV: BA - General Mathematics Impact factor: 1.014, year: 2015 http://www.sciencedirect.com/science/article/pii/S0022247X15003170

The resonating group method in an harmonic oscillator basis

International Nuclear Information System (INIS)

Silvestre-Brac, B.; Gignoux, C.; Ayant, Y.

1987-05-01

The scattering states for a general many body system is formulated within the resonating group method. The resulting Lippman-Schwinger equation is solved in an harmonic oscillator basis for which a number of advantages are emphasized. The analytical formula giving the free propagator in that basis is fully derived

Harmonic Damping in DG-Penetrated Distribution Network

DEFF Research Database (Denmark)

Lu, Jinghang; Savaghebi, Mehdi; Guerrero, Josep M.

2016-01-01

Grid background harmonics may be amplified, propagate through a long distribution feeder and even lead to power system instability. In this paper, harmonic propagation issue is investigated and mitigation of the harmonics is analyzed by using transmission line theory which has already been applied...... in power systems. It is demonstrated that a specific harmonic will not be amplified if the feeder’s length is less than one quarter of the harmonic wavelength meanwhile the terminal impedance is less than characteristic impedance. Besides, three scenarios will be considered in accordance...... with the relationship between the feeder’s length and harmonic wavelength. Harmonic suppression control strategies will be respectively designed considering 5th and 7th harmonics coexisting in the distribution line. Finally, a simulation study has been performed to verify the theoretical analysis and demonstrate...

Equilibrium and ballooning mode stability of an axisymmetric tensor pressure tokamak

International Nuclear Information System (INIS)

Cooper, W.A.; Bateman, G.; Nelson, D.B.; Kammash, T.

1980-08-01

A force balance relation, a representation for the poloidal beta (β/sub p/), and expressions for the current densities are derived from the MHD equilibrium relations for an axisymmetric tensor pressure tokamak. Perpendicular and parallel beam pressure components are evaluated from a distribution function that models high energy neutral particle injection. A double adiabatic energy principle is derived from that of Kruskal and Oberman, with correction terms added. The energy principle is then applied to an arbitrary cross-section axisymmetric tokamak to examine ballooning instabilities of large toroidal mode number. The resulting Euler equation is remarkably similar to that of ideal MHD. Although the field-bending term is virtually unaltered, the driving term is modified because the pressures are no longer constant on a flux surface. Either a necessary or a sufficient marginal stability criterion for a guiding center plasma can be derived from this equation whenever an additional stabilizing element unique to the double adiabatic theory is either kept or neglected, respectively

Spherical harmonic expansion of short-range screened Coulomb interactions

Energy Technology Data Exchange (ETDEWEB)

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

2006-07-07

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

Elimination of harmonics in multilevel inverters with non-equal dc sources using PSO

International Nuclear Information System (INIS)

Al-Othman, A.K.; Abdelhamid, Tamer H.

2009-01-01

Multilevel inverters supplied from equal and constant dc sources almost do not exist in practical applications. The variation of the dc sources affects the values of the switching angles required for each specific harmonic profile, as well as increases the difficulty of the harmonic elimination's equations. This paper presents an extremely fast optimal solution of harmonic elimination of multilevel inverters with non-equal dc sources using a novel Particle Swarm Optimization (PSO) algorithm. The overall system is suitable for large variable speed drives, UPS systems, and on-line utility applications such as static var compensation. A set of mathematical equations describing the general output waveform of the multilevel inverter with non-equal dc sources is formulated. PSO is then employed to compute the optimal solution set of switching angles, if it exists, for each required harmonic profile. Theoretical studies for different case studies regarding the number of levels and harmonic profile are carried out to show the effectiveness and robustness of the proposed technique, and validated through both simulations and laboratory experimentation

Harmonic supergraphs. Green functions

International Nuclear Information System (INIS)

Galperin, A.; Ivanov, E.; Gievetsky, V.; Sokatchev, E.

1985-01-01

The quantization procedure in the harmonic superspace approach is worked out. Harmonic distributions are introduced and are used to construct the analytic superspace delta-functions and the Green functions for the hypermultiplet and the N=2 Yang-Mills superfields. The gauge fixing is described and the relevant Faddeev-Popov ghosts are defined. The corresponding BRST transformations are found. The harmonic superspace quantization of the N=2 gauge theory turns out to be rather simple and has many parallels with that for the standard (N=0) Yang-Mills theory. In particular, no ghosts-forghosts are needed

A pretandem harmonic buncher

International Nuclear Information System (INIS)

Lin, Qui-xun; Van Wechel, T.D.

1987-01-01

A single gap harmonic buncher has been constructed as a pretandem buncher. Over 85% of a proton dc beam has been bunched into pulses. The width (fwhm) of the pulses is 0.7 ns. The buncher is based on that built at Argonne. Changes were made to the buncher's configuration so that the buncher could be tuned to the desired four harmonic frequencies. A method of calibrating and setting the relative phases and amplitudes of the four harmonic frequencies has been used to obtain an optimum sawtooth-like bunching waveform

Harmonic Interaction Analysis in Grid-connected Converter using Harmonic State Space (HSS) Modeling

DEFF Research Database (Denmark)

Kwon, Jun Bum; Wang, Xiongfei; Blaabjerg, Frede

2017-01-01

research about the harmonic interaction. However, it is found that the Linear Time Invariant (LTI) based model analysis makes it difficult to analyze these phenomena because of the time-varying properties of the power electronic based systems. This paper investigates grid-connected converter by using......An increasing number of power electronic based Distributed Generation (DG) systems and loads generate not only characteristic harmonics but also unexpected harmonics. Several methods like impedance based analysis, which are derived from the conventional average model, are introduced to perform...

Structural relations of harmonic sums and Mellin transforms up to weight w=5

Energy Technology Data Exchange (ETDEWEB)

Bluemlein, Johannes

2009-01-15

We derive the structural relations between the Mellin transforms of weighted Nielsen integrals emerging in the calculation of massless or massive single-scale quantities in QED and QCD, such as anomalous dimensions and Wilson coefficients, and other hard scattering cross sections depending on a single scale. The set of all multiple harmonic sums up to weight five cover the sums needed in the calculation of the 3-loop anomalous dimensions. The relations extend the set resulting from the quasi-shuffle product between harmonic sums studied earlier. Unlike the shuffle relations, they depend on the value of the quantities considered. Up to weight w=5, 242 nested harmonic sums contribute. In the present physical applications it is sufficient to consider the sub-set of harmonic sums not containing an index i=-1, which consists out of 69 sums. The algebraic relations reduce this set to 30 sums. Due to the structural relations a final reduction of the number of harmonic sums to 15 basic functions is obtained. These functions can be represented in terms of factorial series, supplemented by harmonic sums which are algebraically reducible. Complete analytic representations are given for these 15 meromorphic functions in the complex plane deriving their asymptotic- and recursion relations. A general outline is presented on the way nested harmonic sums and multiple zeta values emerge in higher order calculations of zero- and single scale quantities. (orig.)

Equations of motion according to the asymptotic post-Newtonian scheme for general relativity in the harmonic gauge

Science.gov (United States)

Arminjon, Mayeul

2005-10-01

The asymptotic scheme of post-Newtonian approximation defined for general relativity in the harmonic gauge by Futamase & Schutz (1983) is based on a family of initial data for the matter fields of a perfect fluid and for the initial metric, defining a family of weakly self-gravitating systems. We show that Weinberg’s (1972) expansion of the metric and his general expansion of the energy-momentum tensor T, as well as his expanded equations for the gravitational field and his general form of the expanded dynamical equations, apply naturally to this family. Then, following the asymptotic scheme, we derive the explicit form of the expansion of T for a perfect fluid, and the expanded fluid-dynamical equations. (These differ from those written by Weinberg.) By integrating these equations in the domain occupied by a body, we obtain a general form of the translational equations of motion for a 1PN perfect-fluid system in general relativity. To put them into a tractable form, we use an asymptotic framework for the separation parameter η, by defining a family of well-separated 1PN systems. We calculate all terms in the equations of motion up to the order η3 included. To calculate the 1PN correction part, we assume that the Newtonian motion of each body is a rigid one, and that the family is quasispherical, in the sense that in all bodies the inertia tensor comes close to being spherical as η→0. Apart from corrections that cancel for exact spherical symmetry, there is in the final equations of motion one additional term, as compared with the Lorentz-Droste (Einstein-Infeld-Hoffmann) acceleration. This term depends on the spin of the body and on its internal structure.

Axisymmetric core collapse simulations using characteristic numerical relativity

International Nuclear Information System (INIS)

Siebel, Florian; Mueller, Ewald; Font, Jose A.; Papadopoulos, Philippos

2003-01-01

We present results from nonrotating axisymmetric stellar core collapse simulations in general relativity. Our hydrodynamics code has proved robust and accurate enough to allow for a detailed analysis of the global dynamics of the collapse. Contrary to traditional approaches based on the 3+1 formulation of the gravitational field equations, our framework uses a foliation based on a family of outgoing light cones, emanating from a regular center, and terminating at future null infinity. Such a coordinate system is well adapted to the study of interesting dynamical spacetimes in relativistic astrophysics such as stellar core collapse and neutron star formation. Perhaps most importantly this procedure allows for the extraction of gravitational waves at future null infinity, along with the commonly used quadrupole formalism for the gravitational wave extraction. Our results concerning the gravitational wave signals show noticeable disagreement when those are extracted by computing the Bondi news at future null infinity on the one hand and by using the quadrupole formula on the other hand. We have a strong indication that for our setup the quadrupole formula on the null cone does not lead to physical gravitational wave signals. The Bondi gravitational wave signals extracted at infinity show typical oscillation frequencies of about 0.5 kHz

Linear theory of the tearing instability in axisymmetric toroidal devices

International Nuclear Information System (INIS)

Rogister, A.; Singh, R.

1988-08-01

We derive a very general kinetic equation describing the linear evolution of low m/l modes in axisymmetric toroidal plasmas with arbitrary cross sections. Included are: Ion sound, inertia, diamagnetic drifts, finite poloidal beta, and finite ion Larmor radius effects. Assuming the magnetic surfaces to form a set of nested tori with circular cross sections of shifted centers, and introducing adequate simplifications justified by our knowledge of experimental tokamak plasmas, we then obtain explicitely the sets of equations describing the coupling of the quasimodes 0/1, 1/1, 2/1, and, for m≥2, m/1, (m+1)/1. By keeping finite aspect ratio effects into account when calculating the jump of the derivative of the eigenfunction, it is shown that the theory can explain the rapid evolution, within one sawtooth period, of the growth rate of the sawteeth precursors from resistive values to magnetohydrodynamic ones. The characteristics thus theoretically required from current profiles in sawtoothing discharges have clearly been observed. Other aspects of the full theory could be relevant to the phenomenon of major disruptions. (orig.)

On the equivalence between the discrete ordinates and the spherical harmonics methods in radiative transfer

International Nuclear Information System (INIS)

Barichello, L.B.; Siewert, C.E.

1998-01-01

In this work concerning steady-state radiative-transfer calculations in plane-parallel media, the equivalence between the discrete ordinates method and the spherical harmonics method is proved. More specifically, it is shown that for standard radiative-transfer problems without the imposed restriction of azimuthal symmetry the two methods yield identical results for the radiation intensity when the quadrature scheme for the discrete ordinates method is defined by the zeros of the associated Legendre functions and when generalized Mark boundary conditions are used to define the spherical harmonics solution. It is also shown that, with these choices for a quadrature scheme and for the boundary conditions, the two methods can be formulated so as to require the same computational effort. Finally a justification for using the generalized Mark boundary conditions in the spherical harmonics solution is given

A simulation study of harmonics regeneration in noise reduction for electric and acoustic stimulation.

Science.gov (United States)

Hu, Yi

2010-05-01

Recent research results show that combined electric and acoustic stimulation (EAS) significantly improves speech recognition in noise, and it is generally established that access to the improved F0 representation of target speech, along with the glimpse cues, provide the EAS benefits. Under noisy listening conditions, noise signals degrade these important cues by introducing undesired temporal-frequency components and corrupting harmonics structure. In this study, the potential of combining noise reduction and harmonics regeneration techniques was investigated to further improve speech intelligibility in noise by providing improved beneficial cues for EAS. Three hypotheses were tested: (1) noise reduction methods can improve speech intelligibility in noise for EAS; (2) harmonics regeneration after noise reduction can further improve speech intelligibility in noise for EAS; and (3) harmonics sideband constraints in frequency domain (or equivalently, amplitude modulation in temporal domain), even deterministic ones, can provide additional benefits. Test results demonstrate that combining noise reduction and harmonics regeneration can significantly improve speech recognition in noise for EAS, and it is also beneficial to preserve the harmonics sidebands under adverse listening conditions. This finding warrants further work into the development of algorithms that regenerate harmonics and the related sidebands for EAS processing under noisy conditions.

Harmonics in transmission power systems

DEFF Research Database (Denmark)

Wiechowski, Wojciech Tomasz

. The comparison shows that results obtained used both types of the cores are the same, so it is concluded that both cores can be used for harmonic measurements. Low-inductance resistors are introduced in the secondary circuits, in series with the metering and protective relaying. On those resistors, the harmonic......Some time ago, Energinet.dk, the Transmission System Operator of the 150 kV and 400 kV transmission network in Denmark, had experienced operational malfunctions of some of the measuring and protection equipment. Also an overloading of a harmonic filter has been reported, and therefore, a need...... end only so the ground is not used as a return path. A way to reduce the capacitive coupling is to provide shielding. Harmonic currents are measured using the conventional inductive voltage transformers. Both protective and metering cores were compared if they could be used for harmonic measurements...

Exact Time-Dependent Wave Functions of a Confined Time-Dependent Harmonic Oscillator with Two Moving Boundaries

International Nuclear Information System (INIS)

Lo, C.F.

2009-01-01

By applying the standard analytical techniques of solving partial differential equations, we have obtained the exact solution in terms of the Fourier sine series to the time-dependent Schroedinger equation describing a quantum one-dimensional harmonic oscillator of time-dependent frequency confined in an infinite square well with the two walls moving along some parametric trajectories. Based upon the orthonormal basis of quasi-stationary wave functions, the exact propagator of the system has also been analytically derived. Special cases like (i) a confined free particle, (ii) a confined time-independent harmonic oscillator, and (iii) an aging oscillator are examined, and the corresponding time-dependent wave functions are explicitly determined. Besides, the approach has been extended to solve the case of a confined generalized time-dependent harmonic oscillator for some parametric moving boundaries as well. (general)

Study on A Control Method of PAPF for Resonance Damping and Harmonics Compensation in Power System

DEFF Research Database (Denmark)

Zhou, Fang; Wu, Longhui; Chen, Zhe

2009-01-01

In power system, capacitors are widely used to compensate reactive power, which generally cause resonance problems in harmonic distorted network. In this paper, A method of using a parallel active power filter (PAPF) to damp the resonances is proposed. The proposed method is compound with traditi......In power system, capacitors are widely used to compensate reactive power, which generally cause resonance problems in harmonic distorted network. In this paper, A method of using a parallel active power filter (PAPF) to damp the resonances is proposed. The proposed method is compound...... with traditional method, it shows that whether the capacitor current is included in the detecting current of PAPF or not. Also the PAPF with proposed method has strong ability in harmonic compensation. Finally, the experiment results are presented to verify the analysis....

Effects of shape and stroke parameters on the propulsion performance of an axisymmetric swimmer.

Science.gov (United States)

Peng, Jifeng; Alben, Silas

2012-03-01

In nature, there exists a special group of aquatic animals which have an axisymmetric body and whose primary swimming mechanism is to use periodic body contractions to generate vortex rings in the surrounding fluid. Using jellyfish medusae as an example, this study develops a mathematical model of body kinematics of an axisymmetric swimmer and uses a computational approach to investigate the induced vortex wakes. Wake characteristics are identified for swimmers using jet propulsion and rowing, two mechanisms identified in previous studies of medusan propulsion. The parameter space of body kinematics is explored through four quantities: a measure of body shape, stroke amplitude, the ratio between body contraction duration and extension duration, and the pulsing frequency. The effects of these parameters on thrust, input power requirement and circulation production are quantified. Two metrics, cruising speed and energy cost of locomotion, are used to evaluate the propulsion performance. The study finds that a more prolate-shaped swimmer with larger stroke amplitudes is able to swim faster, but its cost of locomotion is also higher. In contrast, a more oblate-shaped swimmer with smaller stroke amplitudes uses less energy for its locomotion, but swims more slowly. Compared with symmetric strokes with equal durations of contraction and extension, faster bell contractions increase the swimming speed whereas faster bell extensions decrease it, but both require a larger energy input. This study shows that besides the well-studied correlations between medusan body shape and locomotion, stroke variables also affect the propulsion performance. It provides a framework for comparing the propulsion performance of axisymmetric swimmers based on their body kinematics when it is difficult to measure and analyze their wakes empirically. The knowledge from this study is also useful for the design of robotic swimmers that use axisymmetric body contractions for propulsion.

Effects of shape and stroke parameters on the propulsion performance of an axisymmetric swimmer

International Nuclear Information System (INIS)

Peng Jifeng; Alben, Silas

2012-01-01

In nature, there exists a special group of aquatic animals which have an axisymmetric body and whose primary swimming mechanism is to use periodic body contractions to generate vortex rings in the surrounding fluid. Using jellyfish medusae as an example, this study develops a mathematical model of body kinematics of an axisymmetric swimmer and uses a computational approach to investigate the induced vortex wakes. Wake characteristics are identified for swimmers using jet propulsion and rowing, two mechanisms identified in previous studies of medusan propulsion. The parameter space of body kinematics is explored through four quantities: a measure of body shape, stroke amplitude, the ratio between body contraction duration and extension duration, and the pulsing frequency. The effects of these parameters on thrust, input power requirement and circulation production are quantified. Two metrics, cruising speed and energy cost of locomotion, are used to evaluate the propulsion performance. The study finds that a more prolate-shaped swimmer with larger stroke amplitudes is able to swim faster, but its cost of locomotion is also higher. In contrast, a more oblate-shaped swimmer with smaller stroke amplitudes uses less energy for its locomotion, but swims more slowly. Compared with symmetric strokes with equal durations of contraction and extension, faster bell contractions increase the swimming speed whereas faster bell extensions decrease it, but both require a larger energy input. This study shows that besides the well-studied correlations between medusan body shape and locomotion, stroke variables also affect the propulsion performance. It provides a framework for comparing the propulsion performance of axisymmetric swimmers based on their body kinematics when it is difficult to measure and analyze their wakes empirically. The knowledge from this study is also useful for the design of robotic swimmers that use axisymmetric body contractions for propulsion. (paper)

The harmonic oscillator and the position dependent mass Schroedinger equation: isospectral partners and factorization operators

International Nuclear Information System (INIS)

Morales, J.; Ovando, G.; Pena, J. J.

2010-01-01

One of the most important scientific contributions of Professor Marcos Moshinsky has been his study on the harmonic oscillator in quantum theory vis a vis the standard Schroedinger equation with constant mass [1]. However, a simple description of the motion of a particle interacting with an external environment such as happen in compositionally graded alloys consist of replacing the mass by the so-called effective mass that is in general variable and dependent on position. Therefore, honoring in memoriam Marcos Moshinsky, in this work we consider the position-dependent mass Schrodinger equations (PDMSE) for the harmonic oscillator potential model as former potential as well as with equi-spaced spectrum solutions, i.e. harmonic oscillator isospectral partners. To that purpose, the point canonical transformation method to convert a general second order differential equation (DE), of Sturm-Liouville type, into a Schroedinger-like standard equation is applied to the PDMSE. In that case, the former potential associated to the PDMSE and the potential involved in the Schroedinger-like standard equation are related through a Riccati-type relationship that includes the equivalent of the Witten superpotential to determine the exactly solvable positions-dependent mass distribution (PDMD)m(x). Even though the proposed approach is exemplified with the harmonic oscillator potential, the procedure is general and can be straightforwardly applied to other DEs.

Multidimensional high harmonic spectroscopy

International Nuclear Information System (INIS)

Bruner, Barry D; Soifer, Hadas; Shafir, Dror; Dudovich, Nirit; Serbinenko, Valeria; Smirnova, Olga

2015-01-01

High harmonic generation (HHG) has opened up a new frontier in ultrafast science where attosecond time resolution and Angstrom spatial resolution are accessible in a single measurement. However, reconstructing the dynamics under study is limited by the multiple degrees of freedom involved in strong field interactions. In this paper we describe a new class of measurement schemes for resolving attosecond dynamics, integrating perturbative nonlinear optics with strong-field physics. These approaches serve as a basis for multidimensional high harmonic spectroscopy. Specifically, we show that multidimensional high harmonic spectroscopy can measure tunnel ionization dynamics with high precision, and resolves the interference between multiple ionization channels. In addition, we show how multidimensional HHG can function as a type of lock-in amplifier measurement. Similar to multi-dimensional approaches in nonlinear optical spectroscopy that have resolved correlated femtosecond dynamics, multi-dimensional high harmonic spectroscopy reveals the underlying complex dynamics behind attosecond scale phenomena. (paper)

Below-threshold harmonic generation from strong non-uniform fields

Science.gov (United States)

Yavuz, I.

2017-10-01

Strong-field photoemission below the ionization threshold is a rich/complex region where atomic emission and harmonic generation may coexist. We studied the mechanism of below-threshold harmonics (BTH) from spatially non-uniform local fields near the metallic nanostructures. Discrete harmonics are generated due to the broken inversion symmetry, suggesting enriched coherent emission in the vuv frequency range. Through the numerical solution of the time-dependent Schrödinger equation, we investigate wavelength and intensity dependence of BTH. Wavelength dependence identifies counter-regular resonances; individual contributions from the multi-photon emission and channel-closing effects due to quantum path interferences. In order to understand the underlying mechanism of BTH, we devised a generalized semi-classical model, including the influence of Coulomb and non-uniform field interactions. As in uniform fields, Coulomb potential in non-uniform fields is the determinant of BTH; we observed that the generation of BTH are due to returning trajectories with negative energies. Due to large distance effectiveness of the non-uniformity, only long trajectories are noticeably affected.

On solution of Maxwell's equations in axisymmetric domains with edges. Part II: Numerical aspects

International Nuclear Information System (INIS)

Nkemzi, Boniface

2003-10-01

In this paper we consider the Fourier-finite-element method for treating the Maxwell's equations in three-dimensional axisymmetric domains with reentrant edges. By means of partial Fourier analysis, the 3D BVP is decomposed into an infinite sequence of 2D variational equations in the plane meridian domain of the axisymmetric domain, a finite number of which is considered and treated using nodal H 1 -conforming finite elements. For domains with reentrant edges, the singular field method is employed to compensate the singular behavior of the solutions. Emphases are given to estimates of the Fourier-finite-element approximation error and convergence analysis in the H 1 -norm under different regularity assumptions. (author)

Audibility of harmonics in 'periodic white noise'

NARCIS (Netherlands)

Duifhuis, H.; Tomesen, H.H.

1970-01-01

In a previous article (Duifhuis, 1970) results' concerning the audibility of harmonics in a periodic pulse have been presented. Each of the lower harmonics could be perceived separately, whereas the high harmonics were heard together as one complex signal. High harmonics, however, appeared to be

Absorption of acoustic waves by sunspots. II - Resonance absorption in axisymmetric fibril models

Science.gov (United States)

Rosenthal, C. S.

1992-01-01

Analytical calculations of acoustic waves scattered by sunspots which concentrate on the absorption at the magnetohydrodynamic Alfven resonance are extended to the case of a flux-tube embedded in a uniform atmosphere. The model is based on a flux-tubes of varying radius that are highly structured, translationally invariant, and axisymmetric. The absorbed fractional energy is determined for different flux-densities and subphotospheric locations with attention given to the effects of twist. When the flux is highly concentrated into annuli efficient absorption is possible even when the mean magnetic flux density is low. The model demonstrates low absorption at low azimuthal orders even in the presence of twist which generally increases the range of wave numbers over which efficient absorption can occur. Resonance absorption is concluded to be an efficient mechanism in monolithic sunspots, fibril sunspots, and plage fields.

Probabilistic Harmonic Modeling of Wind Power Plants

DEFF Research Database (Denmark)

Guest, Emerson; Jensen, Kim H.; Rasmussen, Tonny Wederberg

2017-01-01

A probabilistic sequence domain (SD) harmonic model of a grid-connected voltage-source converter is used to estimate harmonic emissions in a wind power plant (WPP) comprised of Type-IV wind turbines. The SD representation naturally partitioned converter generated voltage harmonics into those...... with deterministic phase and those with probabilistic phase. A case study performed on a string of ten 3MW, Type-IV wind turbines implemented in PSCAD was used to verify the probabilistic SD harmonic model. The probabilistic SD harmonic model can be employed in the planning phase of WPP projects to assess harmonic...

SIGMARZ, Stress Analysis of Axisymmetric or Plane Structures

International Nuclear Information System (INIS)

1978-01-01

1 - Nature of the physical problem solved: Classic stress analysis program for axisymmetric or plane geometric structures. 2 - Method of solution: The finite element method is used. Input are the finite element nodes, the imposed displacements, the applied forces at the nodes and the volumetric distributed forces. The linear equation system is solved by the Cholesky method. 3 - Restrictions on the complexity of the problem: Maximum number of nodes: 800; Maximum number of elements: 1300; Maximum number of displacements: 300; Maximum band width: 72

Harmonics in power systems of ships with electrical propulsion drives. Comparison between different converters

Energy Technology Data Exchange (ETDEWEB)

Lehtonen, M [VTT Energy, Espoo (Finland). Energy Systems

1996-11-01

In this report the effects of harmonics in marine power systems is discussed and a comparison is given between the most typical converter types, including pulse width modulated drives, load commutated inverters and cycloconverters. The effect of harmonic distortion on the power system equipment and loads is first briefly discussed. Special attention is given to the circumstances in the low voltage distribution system, where general load equipment is connected. In addition to the total harmonic distortion the effect of voltage deviation to the supply quality is also considered. The origin of harmonics in the load currents of the three converter types is then considered. The differences between the converters are outlined, and the most typical spectra are presented. The possible means for reducing the harmonic distortion are also studied. The solutions considered are the increasing of the short circuit level, the use of harmonic filters and the increasing of the pulse number. In the case of cycloconverters, the optimization of the phase shift between the parallel operating bridges is also presented. Finally the effects of different converter types on the voltage quality are compared using calculations made for a typical marine power system. (author)

Stationary axisymmetric four dimensional space-time endowed with Einstein metric

International Nuclear Information System (INIS)

Hasanuddin; Azwar, A.; Gunara, B. E.

2015-01-01

In this paper, we construct Ernst equation from vacuum Einstein field equation for both zero and non-zero cosmological constant. In particular, we consider the case where the space-time admits axisymmetric using Boyer-Lindquist coordinates. This is called Kerr-Einstein solution describing a spinning black hole. Finally, we give a short discussion about the dynamics of photons on Kerr-Einstein space-time

Efficiency of the generation of impulsion by cyclotron waves currents of the electrons in an Axisymmetric Tokamak; Eficiencia de la generacion de corrientes de impulsion por ondas ciclotronicas de los electrones en un Tokamak axisimetrico

Energy Technology Data Exchange (ETDEWEB)

Gutierrez T, C.; Beltran P, M. [ININ, 52045 Ocoyoacac, Estado de Mexico (Mexico)

2004-07-01

The neoclassical theory of transport is used to calculate the current efficiency of electronic cyclotron impulsion (ECCD) in an axisymmetric tokamak in the few collisions regime. The standard parameter of the tokamak is used to obtain a system of equations that describe the hydrodynamic of the plasma, where the ponderomotive force (PM) due to high power radio frequency waves is taken in account. The PM force is produced in the proximity of electron cyclotron resonance surface in a specific poloidal localization. The efficiency ECCD is analyzed in the cases of first and second harmonic (for different angles of injection of radio frequency waves) and it is validated using the experimental values of the TCV and T-10 tokamaks. The results are according to those obtained by means of the techniques of the Green functions. (Author)

Adaptive Virtual Impedance Scheme for Selective Compensation of Voltage Unbalance and Harmonics in Microgrids

DEFF Research Database (Denmark)

Savaghebi, Mehdi; Shafiee, Qobad; Vasquez, Juan Carlos

2015-01-01

and current inner control loops in order to fix the filter capacitor voltage and a virtual impedance loop mainly for voltage harmonics and unbalance compensation. The virtual impedance is set by the central secondary controller to mitigate the voltage distortion at sensitive load bus (SLB). Secondary...... controller is connected to a measurement unit to obtain the data of voltage harmonics and unbalance at microgrid SLB and broadcasts the commands for adjusting the virtual impedance of each unit. A general case with a combined voltage harmonic and unbalance distortion is considered. In such a case, voltage...... distortion is mitigated by selective insertion of capacitive virtual impedances for negative sequence of fundamental component as well as positive and negative sequences of main harmonics. The values of virtual capacitances are determined based on the required voltage quality at the load bus; thus...

Complex harmonic modal analysis of rotor systems

International Nuclear Information System (INIS)

Han, Dong Ju

2015-01-01

Complex harmonic analysis for rotor systems has been proposed from the strict complex modal analysis based upon Floquet theory. In this process the harmonic balance method is adopted, effectively associated with conventional eigenvalue analysis. Also, the harmonic coefficients equivalent to dFRFs in harmonic mode has been derived in practice. The modes are classified from identifying the modal characteristics, and the adaptation of harmonic balance method has been proven by comparing the results of the stability analyses from Floque theory and the eigen analysis. The modal features of each critical speed are depicted in quantitatively and qualitatively by showing that the strengths of each component of the harmonic coefficients are estimated from the order of magnitude analysis according to their harmonic patterns. This effectiveness has been verified by comparing with the numerical solutions

Harmonic uniflow engine

Science.gov (United States)

Bennett, Charles L.

2016-03-22

A reciprocating-piston uniflow engine includes a harmonic oscillator inlet valve capable of oscillating at a resonant frequency for controlling the flow of working fluid into the engine. In particular, the inlet valve includes an inlet valve head and a spring arranged together as a harmonic oscillator so that the inlet valve head is moveable from an unbiased equilibrium position to a biased closed position occluding an inlet. When released, the inlet valve head undergoes a single oscillation past the equilibrium position to a maximum open position and returns to a biased return position close to the closed position to choke the flow and produce a pressure drop across the inlet valve causing the inlet valve to close. In other embodiments, the harmonic oscillator arrangement of the inlet valve enables the uniflow engine to be reversibly operated as a uniflow compressor.

Synchrotron radiation and absorption at electron cyclotron harmonics in inhomogeneous plasmas

International Nuclear Information System (INIS)

Hu, Jian-Long.

1993-01-01

In order to understand fully the absorption, emission and conversion phenomena for any electron cyclotron harmonic, one must include all relevant mode conversion processes and a finite parallel wave number k parallel . Relativistic plasma mode conversion and tunneling equations at the second and third electron cyclotron harmonics have been derived analytically. A finite k parallel has been introduced which keeps the coupling between the O-mode, the X-mode and the Bernstein wave in the mode conversion problems without absorption have been obtained, and the connection formulas between different wave branches have been established. The corresponding transmission, reflection and conversion coefficients have also been given. Mode conversion problem at any harmonic has been generalized to either a three branch or a five branch problem. A comparison between the coupled equation and the uncoupled equation has been made. The effort has been directed at the third harmonic since the adsorption at ω = 2ω ce is known to be very strong in virtually every fusion case. Both the low density limit and the high density limit cases have been studied separately. The relativistic effects on the mode conversion and absorption problem has been analyzed. The mode conversion equation with absorption has been solved by using the Green function method. The electron cyclotron emission experiments have already begun at 3ω ce , and the third harmonic is the first nontrivial case of importance

Scramjet test flow reconstruction for a large-scale expansion tube, Part 2: axisymmetric CFD analysis

Science.gov (United States)

Gildfind, D. E.; Jacobs, P. A.; Morgan, R. G.; Chan, W. Y. K.; Gollan, R. J.

2017-11-01

This paper presents the second part of a study aiming to accurately characterise a Mach 10 scramjet test flow generated using a large free-piston-driven expansion tube. Part 1 described the experimental set-up, the quasi-one-dimensional simulation of the full facility, and the hybrid analysis technique used to compute the nozzle exit test flow properties. The second stage of the hybrid analysis applies the computed 1-D shock tube flow history as an inflow to a high-fidelity two-dimensional-axisymmetric analysis of the acceleration tube. The acceleration tube exit flow history is then applied as an inflow to a further refined axisymmetric nozzle model, providing the final nozzle exit test flow properties and thereby completing the analysis. This paper presents the results of the axisymmetric analyses. These simulations are shown to closely reproduce experimentally measured shock speeds and acceleration tube static pressure histories, as well as nozzle centreline static and impact pressure histories. The hybrid scheme less successfully predicts the diameter of the core test flow; however, this property is readily measured through experimental pitot surveys. In combination, the full test flow history can be accurately determined.

Pascu-Type Harmonic Functions with Positive Coefficients Involving Salagean Operator

Directory of Open Access Journals (Sweden)

K. Vijaya

2014-01-01

harmonic functions which are orientation preserving and univalent in the open unit disc. Among the results presented in this paper including the coeffcient bounds, distortion inequality, and covering property, extreme points, certain inclusion results, convolution properties, and partial sums for this generalized class of functions are discussed.

A Compact Quasi-axisymmetric Stellarator Reactor

International Nuclear Information System (INIS)

Ku, L.P.

2003-01-01

We report the progress made in assessing the potential of compact, quasi-axisymmetric stellarators as power-producing reactors. Using an aspect ratio A=4.5 configuration derived from NCSX and optimized with respect to the quasi-axisymmetry and MHD stability in the linear regime as an example, we show that a reactor of 1 GW(e) maybe realizable with a major radius *8 m. This is significantly smaller than the designs of stellarator reactors attempted before. We further show the design of modular coils and discuss the optimization of coil aspect ratios in order to accommodate the blanket for tritium breeding and radiation shielding for coil protection. In addition, we discuss the effects of coil aspect ratio on the peak magnetic field in the coils

Hot Wire Measurements in a Axisymmetric Shear Layer with Swirl

Science.gov (United States)

Ewing, D.; Pollard, A.

1996-11-01

It is well known that the introduction of swirl in an axisymmetric jet can influence the development of and mixing in the near field of the jet. Recent efforts to compute this flow have demonstrated that the development of the near field is dependent on parameters at the jet outlet other than distribution of the swirl component, such as the distribution the mean radial velocity (Xai, J.L., Smith, B.L., Benim, A. C., Schmidli, J., and Yadigaroglu, G. (1996) Influence of Boundary Conditions on Swirling Flow in Combustors, Proc. ASME Fluid. Eng. Div. Summer Meeting), San Diego, Ca., July 7-11.. An experimental rig has been designed to produce co-axial round and annular swirling jets with uniform outlet conditions in each flow. The flow rate and swirl component from each of these jets can be controlled independently and the rig can be configured to produce both co- and counter-swirling flows. Thus, the rig can be used to carry out an extensive investigation of the effect of swirl on the development of axisymmetric flows. The key design features of the rig and the first sets of hot-wire measurements in the shear layer will be reported here.

Waveforms for optimal sub-keV high-order harmonics with synthesized two- or three-colour laser fields.

Science.gov (United States)

Jin, Cheng; Wang, Guoli; Wei, Hui; Le, Anh-Thu; Lin, C D

2014-05-30

High-order harmonics extending to the X-ray region generated in a gas medium by intense lasers offer the potential for providing tabletop broadband light sources but so far are limited by their low conversion efficiency. Here we show that harmonics can be enhanced by one to two orders of magnitude without an increase in the total laser power if the laser's waveform is optimized by synthesizing two- or three-colour fields. The harmonics thus generated are also favourably phase-matched so that radiation is efficiently built up in the gas medium. Our results, combined with the emerging intense high-repetition MHz lasers, promise to increase harmonic yields by several orders to make harmonics feasible in the near future as general bright tabletop light sources, including intense attosecond pulses.

Analysis of Harmonic Coupling and Stability in Back-to-Back Converter Systems for Wind Turbines using Harmonic State Space (HSS)

DEFF Research Database (Denmark)

Kwon, Jun Bum; Wang, Xiongfei; Bak, Claus Leth

2015-01-01

Understanding about harmonic propagation in wind turbine converter is fundamental to research the influence of these on a large network harmonic distortion. Therefore, the analysis of wind turbine converter harmonic spectrum as well as the influence of converter operating point into the network i...... connected into the large wind farm model to analyze the overall steady-state harmonic as well as harmonic stability. All theoretical modeling and analysis is verified by means of simulation and experimental results.......Understanding about harmonic propagation in wind turbine converter is fundamental to research the influence of these on a large network harmonic distortion. Therefore, the analysis of wind turbine converter harmonic spectrum as well as the influence of converter operating point into the network...... is urgently important issues in harmonic studies on wind farm. However, the conventional modeling procedure and simplified model for controller design are not enough to analyze such complicated systems. Besides, they have many limitations in terms of including a non-linear component, different operating...

Comparison of mechanisms involved in image enhancement of Tissue Harmonic Imaging

Science.gov (United States)

Cleveland, Robin O.; Jing, Yuan

2006-05-01

Processes that have been suggested as responsible for the improved imaging in Tissue Harmonic Imaging (THI) include: 1) reduced sensitivity to reverberation, 2) reduced sensitivity to aberration, and 3) reduction in the amplitude of diffraction side lobes. A three-dimensional model of the forward propagation of nonlinear sound beams in media with arbitrary spatial properties (a generalized KZK equation) was developed and solved using a time-domain code. The numerical simulations were validated through experiments with tissue mimicking phantoms. The impact of aberration from tissue-like media was determined through simulations using three-dimensional maps of tissue properties derived from datasets available through the Visible Female Project. The experiments and simulations demonstrated that second harmonic imaging suffers less clutter from reverberation and side-lobes but is not immune to aberration effects. The results indicate that side lobe suppression is the most significant reason for the improvement of second harmonic imaging.

High-frequency harmonic imaging of the eye

Science.gov (United States)

Silverman, Ronald H.; Coleman, D. Jackson; Ketterling, Jeffrey A.; Lizzi, Frederic L.

2005-04-01

Purpose: Harmonic imaging has become a well-established technique for ultrasonic imaging at fundamental frequencies of 10 MHz or less. Ophthalmology has benefited from the use of fundamentals of 20 MHz to 50 MHz. Our aim was to explore the ability to generate harmonics for this frequency range, and to generate harmonic images of the eye. Methods: The presence of harmonics was determined in both water and bovine vitreous propagation media by pulse/echo and hydrophone at a series of increasing excitation pulse intensities and frequencies. Hydrophone measurements were made at the focal point and in the near- and far-fields of 20 MHz and 40 MHz transducers. Harmonic images of the anterior segment of the rabbit eye were obtained by a combination of analog filtering and digital post-processing. Results: Harmonics were generated nearly identically in both water and vitreous. Hydrophone measurements showed the maximum second harmonic to be -5 dB relative to the 35 MHz fundamental at the focus, while in pulse/echo the maximum harmonic amplitude was -15dB relative to the fundamental. Harmonics were absent in the near-field, but present in the far-field. Harmonic images of the eye showed improved resolution. Conclusion: Harmonics can be readily generated at very high frequencies, and at power levels compliant with FDA guidelines for ophthalmology. This technique may yield further improvements to the already impressive resolutions obtainable in this frequency range. Improved imaging of the macular region, in particular, may provide significant improvements in diagnosis of retinal disease.

Axisymmetric tandem mirror stabilized by a magnetic limiter

International Nuclear Information System (INIS)

Kesner, J.; Post, R.S.; Lane, B.

1985-06-01

In order to stabilize MHD-like, fast growing m = 1 fluctuations in the central cell of a tandem mirror we propose the introduction of a magnetic limiter. The magnetic limiter would create a ring null in the magnetic field. Electrons which enter the null can stream azimuthally and thereby ''short-circuit'' m = 1 fluctuations. Some pressure could be maintained on the separatrix flux surface by locating the null on a local magnetic maxima or by axial plugging. This scheme introduces the possibility of a fully axisymmetric tandem mirror

Flow in axisymmetric expansion in a catalytic converter

DEFF Research Database (Denmark)

Gotfredsen, Erik; Meyer, Knud Erik

The flow in an axisymmetric expansion (circular diffusor) is used in many different engineering applications, such as heat exchangers, catalytic converters and filters. These applications require a relatively uniform flow at the inlet. To minimise the pressure loss, an ideal solution would...... Velocimetry (PIV) is a unique method that resolve the entire cross flow. This type of flow is expected to have a fluctuating ‘jet’-like structure from the smaller inlet pipe into the larger converter. The fluctuations of the jet are difficult, if not impossible, to capture with standard time averaged models...

Harmonics Monitoring Survey on LED Lamps

Directory of Open Access Journals (Sweden)

Abdelrahman Ahmed Akila

2017-03-01

Full Text Available Light Emitting Diode (LED lamps are being increasingly used in many applications. These LED lamps operate using a driver, which is a switching device. Hence, LED lamps will be a source of harmonics in the power system. These harmonics if not well treated, may cause severe performance and operational problems. In this paper, harmonics (amplitude and phase angles generated by both LED lamps and conventional fluorescent lamps will be studied practically. Then they will be analyzed and evaluated. Compared to each other harmonics generated by both LED and conventional florescent lamps, self mitigation may occur based on the phase angle of these harmonics. All data will be measured using power analyzer and will be done on a sample of actual lamps.

Computer model for harmonic ultrasound imaging.

Science.gov (United States)

Li, Y; Zagzebski, J A

2000-01-01

Harmonic ultrasound imaging has received great attention from ultrasound scanner manufacturers and researchers. In this paper, we present a computer model that can generate realistic harmonic images. In this model, the incident ultrasound is modeled after the "KZK" equation, and the echo signal is modeled using linear propagation theory because the echo signal is much weaker than the incident pulse. Both time domain and frequency domain numerical solutions to the "KZK" equation were studied. Realistic harmonic images of spherical lesion phantoms were generated for scans by a circular transducer. This model can be a very useful tool for studying the harmonic buildup and dissipation processes in a nonlinear medium, and it can be used to investigate a wide variety of topics related to B-mode harmonic imaging.

A high-precision algorithm for axisymmetric flow

Directory of Open Access Journals (Sweden)

A. Gokhman

1995-01-01

Full Text Available We present a new algorithm for highly accurate computation of axisymmetric potential flow. The principal feature of the algorithm is the use of orthogonal curvilinear coordinates. These coordinates are used to write down the equations and to specify quadrilateral elements following the boundary. In particular, boundary conditions for the Stokes' stream-function are satisfied exactly. The velocity field is determined by differentiating the stream-function. We avoid the use of quadratures in the evaluation of Galerkin integrals, and instead use splining of the boundaries of elements to take the double integrals of the shape functions in closed form. This is very accurate and not time consuming.

Numerical determination of axisymmetric toroidal magnetohydrodynamic equilibria

International Nuclear Information System (INIS)

Johnson, J.L.; Dalhed, H.E.; Greene, J.M.

1978-07-01

Numerical schemes for the determination of stationary axisymmetric toroidal equilibria appropriate for modeling real experimental devices are given. Iterative schemes are used to solve the elliptic nonlinear partial differential equation for the poloidal flux function psi. The principal emphasis is on solving the free boundary (plasma-vacuum interface) equilibrium problem where external current-carrying toroidal coils support the plasma column, but fixed boundary (e.g., conducting shell) cases are also included. The toroidal current distribution is given by specifying the pressure and either the poloidal current or the safety factor profiles as functions of psi. Examples of the application of the codes to tokamak design at PPPL are given

High-order harmonics generation from overdense plasmas

International Nuclear Information System (INIS)

Quere, F.; Thaury, C.; Monot, P.; Martin, Ph.; Geindre, J.P.; Audebert, P.; Marjoribanks, R.

2006-01-01

Complete test of publication follows. When an intense laser beam reflects on an overdense plasma generated on a solid target, high-order harmonics of the incident laser frequency are observed in the reflected beam. This process provides a way to produce XUV femtosecond and attosecond pulses in the μJ range from ultrafast ultraintense lasers. Studying the mechanisms responsible for this harmonic emission is also of strong fundamental interest: just as HHG in gases has been instrumental in providing a comprehensive understanding of basic intense laser-atom interactions, HHG from solid-density plasmas is likely to become a unique tool to investigate many key features of laser-plasma interactions at high intensities. We will present both experimental and theoretical evidence that two mechanisms contribute to this harmonic emission: - Coherent Wake Emission: in this process, harmonics are emitted by plasma oscillations in te overdense plasma, triggered in the wake of jets of Brunel electrons generated by the laser field. - The relativistic oscillating mirror: in this process, the intense laser field drives a relativistic oscillation of the plasma surface, which in turn gives rise to a periodic phase modulation of the reflected beam, and hence to the generation of harmonics of the incident frequency. Left graph: experimental harmonic spectrum from a polypropylene target, obtained with 60 fs laser pulses at 10 19 W/cm 2 , with a very high temporal contrast (10 10 ). The plasma frequency of this target corresponds to harmonics 15-16, thus excluding the CWE mechanism for the generation of harmonics of higher orders. Images on the right: harmonic spectra from orders 13 et 18, for different distances z between the target and the best focus. At the highest intensity (z=0), harmonics emitted by the ROM mechanism are observed above the 15th order. These harmonics have a much smaller spectral width then those due to CWE (below the 15th order). These ROM harmonics vanish as soon

MMS Observations of Harmonic Electromagnetic Cyclotron Waves

Science.gov (United States)

Usanova, M.; Ahmadi, N.; Ergun, R.; Trattner, K. J.; Fuselier, S. A.; Torbert, R. B.; Mauk, B.; Le Contel, O.; Giles, B. L.; Russell, C. T.; Burch, J.; Strangeway, R. J.

2017-12-01

Harmonically related electromagnetic ion cyclotron waves with the fundamental frequency near the O+ cyclotron frequency were observed by the four MMS spacecraft on May 20, 2016. The wave activity was detected by the spacecraft on their inbound passage through the Earth's morning magnetosphere during generally quiet geomagnetic conditions but enhanced solar wind dynamic pressure. It was also associated with an enhancement of energetic H+ and O+ ions. The waves are seen in both magnetic and electric fields, formed by over ten higher order harmonics, most pronounced in the electric field. The wave activity lasted for about an hour with some wave packets giving rise to short-lived structures extending from Hz to kHz range. These observations are particularly interesting since they suggest cross-frequency coupling between the lower and higher frequency modes. Further work will focus on examining the nature and role of these waves in the energetic particle dynamics from a theoretical perspective.

Axisymmetric force-free states and relaxation of a spheroidal spheromak

International Nuclear Information System (INIS)

Throumoulopoulos, G.N.; Pantis, G.

1990-01-01

Axisymmetric force-free equilibrium eigenstates for a prolate as well as an oblate spheroidal Spheromak with arbitrary elongation are obtained. In the framework of the Woltjer-Taylor relaxation theory the relaxed states are also identified. A simple hypothesis for the relaxation process is introduced, which implies that the plasma relaxes from multitoroidal formations to a singly toroidal configuration, in qualitative agreement with experimental results. (author)

Axisymmetric force-free states and relaxation of a spheroidal spheromak

International Nuclear Information System (INIS)

Throumoulopoulos, G.N.; Pantis, G.

1990-01-01

Axisymmetric force-free equilibrium eigenstates for a prolate as well as an oblate spheroidal spheromak with arbitrary elongation are obtained. In the framework of the Woltjer-Taylor relaxation theory the relaxed states are also identified. A simple hypothesis for the relaxation process is introduced which implies that the plasma relaxes from multitoroidal formations to a singly toroidal configuration in qualitative agreement with experimental results. (Author)

Harmonic Detection at Initialization With Kalman Filter

DEFF Research Database (Denmark)

Hussain, Dil Muhammad Akbar; Imran, Raja Muhammad; Shoro, Ghulam Mustafa

2014-01-01

Most power electronic equipment these days generate harmonic disturbances, these devices hold nonlinear voltage/current characteristic. The harmonics generated can potentially be harmful to the consumer supply. Typically, filters are integrated at the power source or utility location to filter out...... the affect of harmonics on the supply. For the detection of these harmonics various techniques are available and one of that technique is the Kalman filter. In this paper we investigate that what are the consequences when harmonic detection system based on Kalman Filtering is initialized...

Comment on 'Generalization of the Darboux transformation and generalized harmonic oscillators'

International Nuclear Information System (INIS)

Schulze-Halberg, Axel

2005-01-01

The authors Song and Klauder (2003 J. Phys. A: Math. Gen. 36 8673-84) present a generalized Darboux transformation, applicable to Hamiltonians with linear terms in the momentum. We show here that this generalized Darboux transformation is just the standard Darboux transformation in different coordinates. (comment)

Harmonic response of coupled and uncoupled granular YBCO

International Nuclear Information System (INIS)

Torralba, Maria Veronica S; Sarmago, Roland V

2004-01-01

The harmonic responses of granular YBCO were obtained via mutual inductance measurements. Two samples, one with and another without intergranular coupling, were investigated in terms of the harmonic components of magnetization at various field amplitudes and frequencies. By comparing the behaviour of the features in the harmonics to that of the peaks in the fundamental response, we explicitly identified which features in the harmonics originate from intragranular harmonic generation and which arise due to a contribution of intergranular coupling. Harmonic responses were obtained despite the absence of vortices and even harmonics were detected in a purely AC magnetic field

Jordan-Schwinger map, 3D harmonic oscillator constants of motion, and classical and quantum parameters characterizing electromagnetic wave polarization

International Nuclear Information System (INIS)

Mota, R D; Xicotencatl, M A; Granados, V D

2004-01-01

In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse

Jordan Schwinger map, 3D harmonic oscillator constants of motion, and classical and quantum parameters characterizing electromagnetic wave polarization

Science.gov (United States)

Mota, R. D.; Xicoténcatl, M. A.; Granados, V. D.

2004-02-01

In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse.

Jordan-Schwinger map, 3D harmonic oscillator constants of motion, and classical and quantum parameters characterizing electromagnetic wave polarization

Energy Technology Data Exchange (ETDEWEB)

Mota, R D [Unidad Profesional Interdisciplinaria de IngenierIa y TecnologIas Avanzadas, IPN. Av. Instituto Politecnico Nacional 2580, Col. La Laguna Ticoman, 07340 Mexico DF (Mexico); Xicotencatl, M A [Departamento de Matematicas del Centro de Investigacion y Estudios Avanzados del IPN, Mexico DF, 07000 (Mexico); Granados, V D [Escuela Superior de FIsica y Matematicas, Instituto Politecnico Nacional, Ed. 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico DF (Mexico)

2004-02-20

In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse.

Numerical methods for axisymmetric and 3D nonlinear beams

Science.gov (United States)

Pinton, Gianmarco F.; Trahey, Gregg E.

2005-04-01

Time domain algorithms that solve the Khokhlov--Zabolotzskaya--Kuznetsov (KZK) equation are described and implemented. This equation represents the propagation of finite amplitude sound beams in a homogenous thermoviscous fluid for axisymmetric and fully three dimensional geometries. In the numerical solution each of the terms is considered separately and the numerical methods are compared with known solutions. First and second order operator splitting are used to combine the separate terms in the KZK equation and their convergence is examined.

Nonlinear to Linear Elastic Code Coupling in 2-D Axisymmetric Media.

Energy Technology Data Exchange (ETDEWEB)

Preston, Leiph [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2017-08-01

Explosions within the earth nonlinearly deform the local media, but at typical seismological observation distances, the seismic waves can be considered linear. Although nonlinear algorithms can simulate explosions in the very near field well, these codes are computationally expensive and inaccurate at propagating these signals to great distances. A linearized wave propagation code, coupled to a nonlinear code, provides an efficient mechanism to both accurately simulate the explosion itself and to propagate these signals to distant receivers. To this end we have coupled Sandia's nonlinear simulation algorithm CTH to a linearized elastic wave propagation code for 2-D axisymmetric media (axiElasti) by passing information from the nonlinear to the linear code via time-varying boundary conditions. In this report, we first develop the 2-D axisymmetric elastic wave equations in cylindrical coordinates. Next we show how we design the time-varying boundary conditions passing information from CTH to axiElasti, and finally we demonstrate the coupling code via a simple study of the elastic radius.

Characterization of a medium-sized washer-gun for an axisymmetric mirror

Science.gov (United States)

Yi, Hongshen; Liu, Ming; Shi, Peiyun; Yang, Zhida; Zhu, Guanghui; Lu, Quanming; Sun, Xuan

2018-04-01

A new medium-sized washer gun is developed for a plasma start-up in a fully axisymmetric mirror. The gun is positioned at the east end of the Keda Mirror with AXisymmetricity facility and operated in the pulsed mode with an arc discharging time of 1.2 ms and a typical arc current of 8.5 kA with 1.5 kV discharge voltage. To optimize the operation, a systematic scan of the neutral pressure, the arc voltage, the bias voltage on a mesh grid 6 cm in front of the gun and an end electrode located on the west end of mirror, and the mirror ratio was performed. The streaming plasma was measured with triple probes in the three mirror cells and a diamagnetic loop in the central cell. Floating potential measurements suggest that the plasma could be divided into streaming and mirror-confined plasmas. The floating potential for the streaming plasma is negative, with an electric field pointing inwards. The mirror-confined plasma has a typical lifetime of 0.5 ms.

Electromagnetic cyclotron harmonic waves

International Nuclear Information System (INIS)

Ohnuma, T.; Watanabe, T.; Hamamatsu, K.

1981-09-01

Electromagnetic electron cyclotron harmonic waves just below the electron cyclotron harmonics are investigated numerically and experimentally. Backward waves which are observed to propagate nearly perpendicular to the magnetic field just below the electron cyclotron frequency in a high density magnetoplasma are confirmed to be in accord with the theoretical electromagnetic cyclotron waves. (author)

Second harmonic generation in a bounded magnetoplasma

International Nuclear Information System (INIS)

Thomas, D.G.

1975-01-01

An experimental study of second harmonic generation in a magnetized plasma contained in a cylindrical cavity resonator shows how the harmonic power varies with fundamental power, background gas pressure, and magnetization. Two cavities were designed. For each the TM010 resonance was in the S-band and the TM011 resonance in the C-band. Both frequencies were harmonically related when the d.c. discharge sustaining the plasma was adjusted to give plasma frequencies of approximately 0.7 GHz and 1.53 GHz. The experimental results show the harmonic power approximately proportional to the square of the fundamental power from 5 to 100 mw, and a decreasing function of pressure from 10 to 150 millitorr. Experiments at constant plasma frequency and varying magnetic field from 0 to 3000 Gauss show a sharp drop in harmonic power to undetectable levels when the electron cyclotron frequency approximates either the fundamental or second harmonic frequencies. These effects are attributed, respectively, to the coupling of fundamental power to other modes and to cavity detuning away from the harmonic. With the plasma frequency adjusted to maintain simultaneous resonance of fundamental and harmonic, a harmonic signal maximum occurred when the upper hybrid frequency approximated the harmonic frequency. Several anomalies, apparently related to the magnetization, background gas, and electron density distribution were observed. Otherwise, the results are qualitatively consistent with the first order theory for a cold, collisional plasma

Analysis of Harmonics Suppression by Active Damping Control on Multi Slim DC-link Drives

DEFF Research Database (Denmark)

Yang, Feng; Máthé, Lászlo; Lu, Kaiyuan

2016-01-01

Compared with conventional dc-link drive, slim dc-link drive is expected to achieve lower cost and longer life time. However, harmonics distortion problem may occur in such drive systems. This paper proposes to use an active damping control method to suppress the harmonic distortion...... with the benefit of low cost and also low loss. A new analysis method, based on the frequency domain impedance model, is presented to explore the mechanism of harmonics suppression. Also, a general method is presented to build the impedance model of a PMSM drive system using Field Oriented Control (FOC) method....... Some design issues, including power levels, current control bandwidth and harmonic interaction, are discussed when the drive system is fed by a weak grid. Case studies on a two-drive system composed by two slim dc-link drive units are provided to verify the proposed analysis method....

Intense harmonic generation from various ablation media

International Nuclear Information System (INIS)

Ozaki, T.; Elouga, L.; Suzuki, M.; Kuroda, H.; Ganeev, R.A.

2006-01-01

Complete test of publication follows. High-order harmonic generation (HHG) is a unique source of coherent extreme ultraviolet (XUV) radiation, which can produce soft x-rays within the spectral 'water-window' (between 2.3 and 4.4 nm), and ultimately short pulses with attosecond duration. However, the intensity of present-day harmonics is still low, and serious applications will need an increase of the conversion efficiency. Instead of using gas media, one can also use ablation material, produced on solid targets using a low-intensity prepulse, as the nonlinear medium to generate high-order harmonics. Recently, we have successfully demonstrated the generation of up to the 63 rd harmonic (λ = 12.6 nm) of a Ti:sapphire laser radiation using boron ablation, and a strong enhancement in the intensity of the 13 th harmonic from indium ablation. These harmonics were generated with a modest laser (10 mJ, 150 fs) and with the pre-pulse to main pulse energy ratio constant. In this paper, we perform systematic investigations of ablation harmonics, using the 200 mJ, 30 fs Ti:sapphire beam line of the Canadian Advanced Laser Light Source (ALLS) facility. ALLS allows studying ablation harmonics over wider experimental parameters, and with independent control over the pre-pulse and main pulse energies. The 10 Hz, 200 mJ Ti:sapphire beam line of ALLS is divided into two beams. Each beam has its own energy control system, which allows independent control over the energy of each beam. One of the beams is used as a pre-pulse for creating ablation, which is focused onto the solid target without pulse compression, with pulse duration of 200 ps. The second beam is used as the main pulse for harmonic generation. The main pulse is delayed in time relative to the pre-pulse by propagating through an optical delay line, and then sent through a pulse compressor. The compressed pulse duration have typical pulse duration of 30 fs FWHM, which is then focused onto the ablation medium using MgF 2

Harmonic balance approach to the periodic solutions of the (an)harmonic relativistic oscillator

International Nuclear Information System (INIS)

Belendez, Augusto; Pascual, Carolina

2007-01-01

The first-order harmonic balance method via the first Fourier coefficient is used to construct two approximate frequency-amplitude relations for the relativistic oscillator for which the nonlinearity (anharmonicity) is a relativistic effect due to the time line dilation along the world line. Making a change of variable, a new nonlinear differential equation is obtained and two procedures are used to approximately solve this differential equation. In the first the differential equation is rewritten in a form that does not contain a square-root expression, while in the second the differential equation is solved directly. The approximate frequency obtained using the second procedure is more accurate than the frequency obtained with the first due to the fact that, in the second procedure, application of the harmonic balance method produces an infinite set of harmonics, while in the first procedure only two harmonics are produced. Both approximate frequencies are valid for the complete range of oscillation amplitudes, and excellent agreement of the approximate frequencies with the exact one are demonstrated and discussed. The discrepancy between the first-order approximate frequency obtained by means of the second procedure and the exact frequency never exceeds 1.6%. We also obtained the approximate frequency by applying the second-order harmonic balance method and in this case the relative error is as low 0.31% for all the range of values of amplitude of oscillation A

Expansion into lattice harmonics in cubic symmetries

Science.gov (United States)

Kontrym-Sznajd, G.

2018-05-01

On the example of a few sets of sampling directions in the Brillouin zone, this work shows how important the choice of the cubic harmonics is on the quality of approximation of some quantities by a series of such harmonics. These studies led to the following questions: (1) In the case that for a given l there are several independent harmonics, can one use in the expansion only one harmonic with a given l?; (2) How should harmonics be ordered: according to l or, after writing them in terms of (x4 + y4 + z4)n (x2y2z2)m, according to their degree q = n + m? To enable practical applications of such harmonics, they are constructed in terms of the associated Legendre polynomials up to l = 26. It is shown that electron momentum densities, reconstructed from experimental data for ErGa3 and InGa3, are described much better by harmonics ordered with q.

Balancing Vibrations at Harmonic Frequencies by Injecting Harmonic Balancing Signals into the Armature of a Linear Motor/Alternator Coupled to a Stirling Machine

Science.gov (United States)

Holliday, Ezekiel S. (Inventor)

2014-01-01

Vibrations at harmonic frequencies are reduced by injecting harmonic balancing signals into the armature of a linear motor/alternator coupled to a Stirling machine. The vibrations are sensed to provide a signal representing the mechanical vibrations. A harmonic balancing signal is generated for selected harmonics of the operating frequency by processing the sensed vibration signal with adaptive filter algorithms of adaptive filters for each harmonic. Reference inputs for each harmonic are applied to the adaptive filter algorithms at the frequency of the selected harmonic. The harmonic balancing signals for all of the harmonics are summed with a principal control signal. The harmonic balancing signals modify the principal electrical drive voltage and drive the motor/alternator with a drive voltage component in opposition to the vibration at each harmonic.

Synthesis of variable harmonic impedance in inverter-interfaced distributed generation unit for harmonic damping throughout a distribution network

DEFF Research Database (Denmark)

Wang, Xiongfei; Blaabjerg, Frede; Chen, Zhe

2012-01-01

This paper proposes a harmonic impedance synthesis technique for voltage-controlled distributed generation inverter in order to damp harmonic voltage distortion on a distribution network. The approach employs a multiloop control scheme, where a selective load harmonic current feedforward loop bas...

Harmonic d-tensors

Energy Technology Data Exchange (ETDEWEB)

Hohmann, Manuel [Physikalisches Institut, Universitaet Tartu (Estonia)

2016-07-01

Tensor harmonics are a useful mathematical tool for finding solutions to differential equations which transform under a particular representation of the rotation group SO(3). In order to make use of this tool also in the setting of Finsler geometry, where the objects of relevance are d-tensors instead of tensors, we construct a set of d-tensor harmonics for both SO(3) and SO(4) symmetries and show how these can be used for calculations in Finsler geometry and gravity.

Power quality issues current harmonics

CERN Document Server

Mikkili, Suresh

2015-01-01

Power Quality Issues: Current Harmonics provides solutions for the mitigation of power quality problems related to harmonics. Focusing on active power filters (APFs) due to their excellent harmonic and reactive power compensation in two-wire (single phase), three-wire (three-phase without neutral), and four-wire (three-phase with neutral) AC power networks with nonlinear loads, the text:Introduces the APF technology, describing various APF configurations and offering guidelines for the selection of APFs for specific application considerationsCompares shunt active filter (SHAF) control strategi

Three-Phase Harmonic Analysis Method for Unbalanced Distribution Systems

Directory of Open Access Journals (Sweden)

Jen-Hao Teng

2014-01-01

Full Text Available Due to the unbalanced features of distribution systems, a three-phase harmonic analysis method is essential to accurately analyze the harmonic impact on distribution systems. Moreover, harmonic analysis is the basic tool for harmonic filter design and harmonic resonance mitigation; therefore, the computational performance should also be efficient. An accurate and efficient three-phase harmonic analysis method for unbalanced distribution systems is proposed in this paper. The variations of bus voltages, bus current injections and branch currents affected by harmonic current injections can be analyzed by two relationship matrices developed from the topological characteristics of distribution systems. Some useful formulas are then derived to solve the three-phase harmonic propagation problem. After the harmonic propagation for each harmonic order is calculated, the total harmonic distortion (THD for bus voltages can be calculated accordingly. The proposed method has better computational performance, since the time-consuming full admittance matrix inverse employed by the commonly-used harmonic analysis methods is not necessary in the solution procedure. In addition, the proposed method can provide novel viewpoints in calculating the branch currents and bus voltages under harmonic pollution which are vital for harmonic filter design. Test results demonstrate the effectiveness and efficiency of the proposed method.

Bunching phase and constraints on echo enabled harmonic generation

Science.gov (United States)

Hemsing, E.

2018-05-01

A simple mathematical description is developed for the bunching spectrum in echo enabled harmonic generation (EEHG) that incorporates the effect of additional electron beam energy modulations. Under common assumptions, they are shown to contribute purely through the phase of the longitudinal bunching factor, which allows the spectral moments of the bunching to be calculated directly from the known energy modulations. In particular, the second moment (spectral bandwidth) serves as simple constraint on the amplitude of the energy modulations to maintain a transform-limited seed. We show that, in general, the impact on the spectrum of energy distortions that develop between the EEHG chicanes scales like the harmonic number compared to distortions that occur upstream. This may limit the parameters that will allow EEHG to reach short wavelengths in high brightness FELs.

Harmonic engine

Science.gov (United States)

Bennett, Charles L [Livermore, CA

2009-10-20

A high efficiency harmonic engine based on a resonantly reciprocating piston expander that extracts work from heat and pressurizes working fluid in a reciprocating piston compressor. The engine preferably includes harmonic oscillator valves capable of oscillating at a resonant frequency for controlling the flow of working fluid into and out of the expander, and also preferably includes a shunt line connecting an expansion chamber of the expander to a buffer chamber of the expander for minimizing pressure variations in the fluidic circuit of the engine. The engine is especially designed to operate with very high temperature input to the expander and very low temperature input to the compressor, to produce very high thermal conversion efficiency.

Nonconforming axisymmetric elements for the analysis of containment structures

International Nuclear Information System (INIS)

Choi, C.K.; Kim, S.Y.

1989-01-01

In this study, the behaviors of the conforming isoparametric quadrilateral 4-node and triangular 3-nod axisymmetric solid elements are improved by adding nonconforming displacement modes. The convergence tests and the irregular mesh tests have been established through the analyses of a primary shield wall typed structure. For example study, a containment wall with internal pressure of 60 ksi has been analyzed. It shows that the nonconforming elements behave better than the conforming elements, especially, in the structurally discontinuous regions

Coherent harmonics generated by a super-short electron pulse

International Nuclear Information System (INIS)

Ding Wu

1996-01-01

A novel mechanism generating superradiance harmonics is found. In this superradiance harmonics, the temporal width of harmonics is extremely short, the ratio of high harmonic fundamental wave is much higher than the known superradiance harmonics

Motions in a Bose condensate: X. New results on stability of axisymmetric solitary waves of the Gross-Pitaevskii equation

OpenAIRE

Berloff, Natalia G.; Roberts, Paul H.

2004-01-01

The stability of the axisymmetric solitary waves of the Gross-Pitaevskii (GP) equation is investigated. The Implicitly Restarted Arnoldi Method for banded matrices with shift-invert was used to solve the linearised spectral stability problem. The rarefaction solitary waves on the upper branch of the Jones-Roberts dispersion curve are shown to be unstable to axisymmetric infinitesimal perturbations, whereas the solitary waves on the lower branch and all two-dimensional solitary waves are linea...

Harmonic lasing in X-ray FELs

Energy Technology Data Exchange (ETDEWEB)

Schneidmiller, E.A.; Yurkov, M.V.

2012-05-15

Harmonic lasing in a free electron laser with a planar undulator (under the condition that the fundamental frequency is suppressed) might be a cheap and efficient way of extension of wavelength ranges of existing and planned X-ray FEL facilities. Contrary to nonlinear harmonic generation, harmonic lasing can provide much more intense, stable, and narrow-band FEL beam which is easier to handle due to the suppressed fundamental frequency. In this paper we perform a parametrization of the solution of the eigenvalue equation for lasing at odd harmonics, and present an explicit expression for FEL gain length, taking into account all essential effects. We propose and discuss methods for suppression of the fundamental harmonic. We also suggest a combined use of harmonic lasing and lasing at the retuned fundamental wavelength in order to reduce bandwidth and to increase brilliance of X-ray beam at saturation. Considering 3rd harmonic lasing as a practical example, we come to the conclusion that it is much more robust than usually thought, and can be widely used in the existing or planned X-ray FEL facilities. In particular, LCLS after a minor modification can lase to saturation at the 3rd harmonic up to the photon energy of 25-30 keV providing multi-gigawatt power level and narrow bandwidth. As for the European XFEL, harmonic lasing would allow to extend operating range (ultimately up to 100 keV), to reduce FEL bandwidth and to increase brilliance, to enable two-color operation for pump-probe experiments, and to provide more flexible operation at different electron energies. Similar improvements can be realized in other X-ray FEL facilities with gap-tunable undulators like FLASH II, SACLA, LCLS II, etc. Harmonic lasing can be an attractive option for compact X-ray FELs (driven by electron beams with a relatively low energy), allowing the use of the standard undulator technology instead of small-gap in-vacuum devices. Finally, in this paper we discover that in a part of the

Symmetries in physics and harmonics

International Nuclear Information System (INIS)

Kolk, D.

2006-01-01

In this book the symmetries of elementary particles are described in relation to the rules of harmonics in music. The selection rules are described in connections with harmonic intervals. Also symmetry breaking is considered in this framework. (HSI)

ASSESSMENT OF BACTERIAL BIOSURFACTANT PRODUCTION THROUGH AXISYMMETRICAL DROP SHAPE-ANALYSIS BY PROFILE

NARCIS (Netherlands)

VANDERVEGT, W; VANDERMEI, HC; BUSSCHER, HJ

Axisymmetric drop shape analysis by profile (ADSA-P) is a technique developed in colloid and surface science to simultaneously determine the contact angle and liquid surface tension from the profile of a droplet resting on a solid surface. In this paper is described how ADSA-P can be employed to

Harmonic generation effect in high-Tc films

International Nuclear Information System (INIS)

Khare, Neeraj; Shrivastava, S.K.; Padmanabhan, V.P.N.; Khare, Sangeeta; Gupta, A.K.

1997-01-01

Harmonic generation in thick BPSCCO and thin YBCO films are reported. The application of an ac field (H ac > H c1 ) of frequency f causes the generation of odd harmonics of frequency (2n+1)f. The application of dc field in addition to the ac field causes the appearance of even harmonics also in the BPSCCO film. However, the appearance of even harmonics is not observed in YBCO film with high J c ∼ 1.6x10 6 A/cm 2 and appearance of second harmonic with small magnitude is observed in YBCO film with low J c ∼ 2x10 3 A/cm 2 . The variation of amplitudes of these harmonics are studied as a function of magnitude of ac and dc field and the results are explained in the framework of critical state model. A high-T c film magnetometer based on the measurement of the amplitude of second harmonic has been developed whose field sensitivity is ∼ 1.5x10 -8 T. (author)

High-harmonic generation in a dense medium

International Nuclear Information System (INIS)

Strelkov, V.V.; Platonenko, V.T.; Becker, A.

2005-01-01

The high-harmonic generation in a plasma or gas under conditions when the single-atom response is affected by neighboring ions or atoms of the medium is studied theoretically. We solve numerically the three-dimensional Schroedinger equation for a single-electron atom in the combined fields of the neighboring particles and the laser, and average the results over different random positions of the particles using the Monte Carlo method. Harmonic spectra are calculated for different medium densities and laser intensities. We observe a change of the harmonic properties due to a random variation of the harmonic phase induced by the field of the medium, when the medium density exceeds a certain transition density. The transition density is found to depend on the harmonic order, but it is almost independent of the fundamental intensity. It also differs for the two (shorter and longer) quantum paths. The latter effect leads for ionic densities in the transition regime to a narrowing of the harmonic lines and a shortening of the attosecond pulses generated using a group of harmonics

An axisymmetric PFEM formulation for bottle forming simulation

Science.gov (United States)

Ryzhakov, Pavel B.

2017-01-01

A numerical model for bottle forming simulation is proposed. It is based upon the Particle Finite Element Method (PFEM) and is developed for the simulation of bottles characterized by rotational symmetry. The PFEM strategy is adapted to suit the problem of interest. Axisymmetric version of the formulation is developed and a modified contact algorithm is applied. This results in a method characterized by excellent computational efficiency and volume conservation characteristics. The model is validated. An example modelling the final blow process is solved. Bottle wall thickness is estimated and the mass conservation of the method is analysed.

Frequency locking of a field-widened Michelson interferometer based on optimal multi-harmonics heterodyning.

Science.gov (United States)

Cheng, Zhongtao; Liu, Dong; Zhou, Yudi; Yang, Yongying; Luo, Jing; Zhang, Yupeng; Shen, Yibing; Liu, Chong; Bai, Jian; Wang, Kaiwei; Su, Lin; Yang, Liming

2016-09-01

A general resonant frequency locking scheme for a field-widened Michelson interferometer (FWMI), which is intended as a spectral discriminator in a high-spectral-resolution lidar, is proposed based on optimal multi-harmonics heterodyning. By transferring the energy of a reference laser to multi-harmonics of different orders generated by optimal electro-optic phase modulation, the heterodyne signal of these multi-harmonics through the FWMI can reveal the resonant frequency drift of the interferometer very sensitively within a large frequency range. This approach can overcome the locking difficulty induced by the low finesse of the FWMI, thus contributing to excellent locking accuracy and lock acquisition range without any constraint on the interferometer itself. The theoretical and experimental results are presented to verify the performance of this scheme.

Renormalizable N=2 supersymmetric and gauge invariant interactions from the N=2 harmonic superspace with central charges

International Nuclear Information System (INIS)

Saidi, E.H.

1986-04-01

The N=2 harmonic-superspace in the presence of central charges is developed. Renormalizable interactions unusual in N=2 supersymmetric theories, are derived in a consistent way. Symmetries generated by the central charges are discussed. A certain equivalence between N=2 harmonic superspace with and without central charges is established. A non-abelian generalization of the model is given. (author)

Harmonic currents circulation in electrical networks simulation and analysis

Energy Technology Data Exchange (ETDEWEB)

Em-Mamlouk, W.M. [MEP, Cairo (Egypt); El-Sharkawy, M.A. [Shams Univ., Cairo (Egypt). Dept. of Electrical Power and Machines; Mostafa, H.E. [Jazan Univ., Jazan (Saudi Arabia). Electrical Dept.

2009-07-01

A detailed harmonic flow analysis for a 13-bus balanced industrial distribution system was presented. The aim of the study was to determine the influence of harmonic sources in various branches of the system on voltage and current waveforms before disruptions to the utility supply system occurred. The current harmonic contents of an adjustable speed drive (ASD) were studied under various loading conditions. The test system was simulated using a standard study test system. Harmonic effects from multiple sources were investigated, and voltage distortion on the different buses was monitored. The study demonstrated that while the harmonic loads circulated harmonic currents in all system branches, no harmonic source was directly connected to the system buses. Many of the investigated cases exceeded allowable voltage total harmonic distortion and or current total harmonic distortion standards set by the Institute of Electrical and Electronic Engineers (IEEE). It was concluded that active harmonic filters should be used to prevent the effects of harmonic current circulation at different buses on neighbouring loads within a system. 8 refs., 11 tabs., 15 figs.

Exact solution of the time-dependent harmonic plus an inverse harmonic potential with a time-dependent electromagnetic field

International Nuclear Information System (INIS)

Yuece, Cem

2003-01-01

In this paper, the problem of the charged harmonic plus an inverse harmonic oscillator with time-dependent mass and frequency in a time-dependent electromagnetic field is investigated. It is reduced to the problem of the inverse harmonic oscillator with time-independent parameters and the exact wave function is obtained

Preserving spherical symmetry in axisymmetric coordinates for diffusion problems

International Nuclear Information System (INIS)

Brunner, T. A.; Kolev, T. V.; Bailey, T. S.; Till, A. T.

2013-01-01

Persevering symmetric solutions, even in the under-converged limit, is important to the robustness of production simulation codes. We explore the symmetry preservation in both a continuous nodal and a mixed finite element method. In their standard formulation, neither method preserves spherical solution symmetry in axisymmetric (RZ) coordinates. We propose two methods, one for each family of finite elements, that recover spherical symmetry for low-order finite elements on linear or curvilinear meshes. This is a first step toward understanding achieving symmetry for higher-order elements. (authors)

Young children's harmonic perception.

Science.gov (United States)

Costa-Giomi, Eugenia

2003-11-01

Harmony and tonality are two of the most difficult elements for young children to perceive and manipulate and are seldom taught in the schools until the end of early childhood. Children's gradual harmonic and tonal development has been attributed to their cumulative exposure to Western tonal music and their increasing experiential knowledge of its rules and principles. Two questions that are relevant to this problem are: (1) Can focused and systematic teaching accelerate the learning of the harmonic/tonal principles that seem to occur in an implicit way throughout childhood? (2) Are there cognitive constraints that make it difficult for young children to perceive and/or manipulate certain harmonic and tonal principles? A series of studies specifically addressed the first question and suggested some possible answers to the second one. Results showed that harmonic instruction has limited effects on children's perception of harmony and indicated that the drastic improvement in the perception of implied harmony noted approximately at age 9 is due to development rather than instruction. I propose that young children's difficulty in perceiving implied harmony stems from their attention behaviors. Older children have less memory constraints and more strategies to direct their attention to the relevant cues of the stimulus. Younger children focus their attention on the melody, if present in the stimulus, and specifically on its concrete elements such as rhythm, pitch, and contour rather than its abstract elements such as harmony and key. The inference of the abstract harmonic organization of a melody required in the perception of implied harmony is thus an elusive task for the young child.

Second-harmonic generation in shear wave beams with different polarizations

Science.gov (United States)

Spratt, Kyle S.; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.; Hamilton, Mark F.

2015-10-01

A coupled pair of nonlinear parabolic equations was derived by Zabolotskaya [1] that model the transverse components of the particle motion in a collimated shear wave beam propagating in an isotropic elastic solid. Like the KZK equation, the parabolic equation for shear wave beams accounts consistently for the leading order effects of diffraction, viscosity and nonlinearity. The nonlinearity includes a cubic nonlinear term that is equivalent to that present in plane shear waves, as well as a quadratic nonlinear term that is unique to diffracting beams. The work by Wochner et al. [2] considered shear wave beams with translational polarizations (linear, circular and elliptical), wherein second-order nonlinear effects vanish and the leading order nonlinear effect is third-harmonic generation by the cubic nonlinearity. The purpose of the current work is to investigate the quadratic nonlinear term present in the parabolic equation for shear wave beams by considering second-harmonic generation in Gaussian beams as a second-order nonlinear effect using standard perturbation theory. In order for second-order nonlinear effects to be present, a broader class of source polarizations must be considered that includes not only the familiar translational polarizations, but also polarizations accounting for stretching, shearing and rotation of the source plane. It is found that the polarization of the second harmonic generated by the quadratic nonlinearity is not necessarily the same as the polarization of the source-frequency beam, and we are able to derive a general analytic solution for second-harmonic generation from a Gaussian source condition that gives explicitly the relationship between the polarization of the source-frequency beam and the polarization of the second harmonic.

Second-harmonic generation in shear wave beams with different polarizations

Energy Technology Data Exchange (ETDEWEB)

Spratt, Kyle S., E-mail: sprattkyle@gmail.com; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.; Hamilton, Mark F. [Applied Research Laboratories, The University of Texas at Austin, P. O. Box 8029, Austin, Texas 78713–8029, US (United States)

2015-10-28

A coupled pair of nonlinear parabolic equations was derived by Zabolotskaya [1] that model the transverse components of the particle motion in a collimated shear wave beam propagating in an isotropic elastic solid. Like the KZK equation, the parabolic equation for shear wave beams accounts consistently for the leading order effects of diffraction, viscosity and nonlinearity. The nonlinearity includes a cubic nonlinear term that is equivalent to that present in plane shear waves, as well as a quadratic nonlinear term that is unique to diffracting beams. The work by Wochner et al. [2] considered shear wave beams with translational polarizations (linear, circular and elliptical), wherein second-order nonlinear effects vanish and the leading order nonlinear effect is third-harmonic generation by the cubic nonlinearity. The purpose of the current work is to investigate the quadratic nonlinear term present in the parabolic equation for shear wave beams by considering second-harmonic generation in Gaussian beams as a second-order nonlinear effect using standard perturbation theory. In order for second-order nonlinear effects to be present, a broader class of source polarizations must be considered that includes not only the familiar translational polarizations, but also polarizations accounting for stretching, shearing and rotation of the source plane. It is found that the polarization of the second harmonic generated by the quadratic nonlinearity is not necessarily the same as the polarization of the source-frequency beam, and we are able to derive a general analytic solution for second-harmonic generation from a Gaussian source condition that gives explicitly the relationship between the polarization of the source-frequency beam and the polarization of the second harmonic.

Second-harmonic generation in shear wave beams with different polarizations

International Nuclear Information System (INIS)

Spratt, Kyle S.; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.; Hamilton, Mark F.

2015-01-01

A coupled pair of nonlinear parabolic equations was derived by Zabolotskaya [1] that model the transverse components of the particle motion in a collimated shear wave beam propagating in an isotropic elastic solid. Like the KZK equation, the parabolic equation for shear wave beams accounts consistently for the leading order effects of diffraction, viscosity and nonlinearity. The nonlinearity includes a cubic nonlinear term that is equivalent to that present in plane shear waves, as well as a quadratic nonlinear term that is unique to diffracting beams. The work by Wochner et al. [2] considered shear wave beams with translational polarizations (linear, circular and elliptical), wherein second-order nonlinear effects vanish and the leading order nonlinear effect is third-harmonic generation by the cubic nonlinearity. The purpose of the current work is to investigate the quadratic nonlinear term present in the parabolic equation for shear wave beams by considering second-harmonic generation in Gaussian beams as a second-order nonlinear effect using standard perturbation theory. In order for second-order nonlinear effects to be present, a broader class of source polarizations must be considered that includes not only the familiar translational polarizations, but also polarizations accounting for stretching, shearing and rotation of the source plane. It is found that the polarization of the second harmonic generated by the quadratic nonlinearity is not necessarily the same as the polarization of the source-frequency beam, and we are able to derive a general analytic solution for second-harmonic generation from a Gaussian source condition that gives explicitly the relationship between the polarization of the source-frequency beam and the polarization of the second harmonic

WKB theory for high-n modes in axisymmetric toroidal plasmas

International Nuclear Information System (INIS)

Dewar, R.L.; Chance, M.S.; Glasser, A.H.; Greene, J.M.; Frieman, E.A.

1979-09-01

It is demonstrated that the low-frequency, k/sub parallel//k/sub perpendicular/ approx. = 0 normal modes of an axisymmetric plasma, at large but finite toroidal mode number n, can be obtained by solving a novel WKB problem involving an infinite number of branches. Formulae for the frequencies of periodic normal modes are derived. The analysis is performed in the context of an ideal MHD model, and comparison is made with numerical ballooning mode results

Classical and multilinear harmonic analysis

CERN Document Server

Muscalu, Camil

2013-01-01

This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and useful to graduates and researchers in pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. The first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón-Zygmund and Littlewood-Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman-Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. The material in this vo...

Higher order harmonics of reactor neutron equation

International Nuclear Information System (INIS)

Li Fu; Hu Yongming; Luo Zhengpei

1996-01-01

The flux mapping method using the higher order harmonics of the neutron equation is proposed. Based on the bi-orthogonality of the higher order harmonics, the process and formulas for higher order harmonics calculation are derived via the source iteration method with source correction. For the first time, not only any order harmonics for up-to-3-dimensional geometry are achieved, but also the preliminary verification to the capability for flux mapping have been carried out

VARIABILITY FROM NON-AXISYMMETRIC FLUCTUATIONS INTERACTING WITH STANDING SHOCKS IN TILTED BLACK HOLE ACCRETION DISKS

Energy Technology Data Exchange (ETDEWEB)

Henisey, Ken B. [Natural Science Division, Pepperdine University, Malibu, CA 90263 (United States); Blaes, Omer M. [Department of Physics, University of California, Santa Barbara, CA 93106 (United States); Fragile, P. Chris [Department of Physics and Astronomy, College of Charleston, Charleston, SC 29424 (United States)

2012-12-10

We study the spatial and temporal behavior of fluid in fully three-dimensional, general relativistic, magnetohydrodynamical simulations of both tilted and untilted black hole accretion flows. We uncover characteristically greater variability in tilted simulations at frequencies similar to those predicted by the formalism of trapped modes, but ultimately conclude that its spatial structure is inconsistent with a modal interpretation. We find instead that previously identified, transient, overdense clumps orbiting on roughly Keplerian trajectories appear generically in our global simulations, independent of tilt. Associated with these fluctuations are acoustic spiral waves interior to the orbits of the clumps. We show that the two non-axisymmetric standing shock structures that exist in the inner regions of these tilted flows effectively amplify the variability caused by these spiral waves to markedly higher levels than in untilted flows, which lack standing shocks. Our identification of clumps, spirals, and spiral-shock interactions in these fully general relativistic, magnetohydrodynamical simulations suggests that these features may be important dynamical elements in models that incorporate tilt as a way to explain the observed variability in black hole accretion flows.

Bounce-harmonic Landau Damping of Plasma Waves

Science.gov (United States)

Anderegg, Francois

2015-11-01

We present measurement of plasma wave damping, spanning the temperature regimes of direct Landau damping, bounce-harmonic Landau damping, inter-species drag damping, and viscous damping. Direct Landau damping is dominant at high temperatures, but becomes negligible as v vph / 5 . The measurements are conducted in trapped pure ion plasmas contained in Penning-Malmberg trap, with wave-coherent LIF diagnostics of particle velocities. Our focus is on bounce harmonics damping, controlled by an applied ``squeeze'' potential, which generates harmonics in the wave potential and in the particle dynamics. A particle moving in z experiences a non-sinusoidal mode potential caused by the squeeze, producing high spatial harmonics with lower phase velocity. These harmonics are Landau damped even when the mode phase velocity vph is large compared to the thermal velocity v , since the nth harmonic is resonant with a particle bouncing at velocity vb =vph / n . Here we increase the bounce harmonics through applied squeeze potential; but some harmonics are always present in finite length systems. For our centered squeeze geometry, theory shows that only odd harmonics are generated, and predicts the Landau damping rate from vph / n . Experimentally, the squeeze potential increases the wave damping and reduces its frequency. The frequency shift occurs because the squeeze potential reduces the number of particle where the mode velocity is the largest, therefore reducing the mode frequency. We observe an increase in the damping proportional to Vs2,and a frequency reduction proportional to Vs , in quantitative agreement with theory. Wave-coherent laser induced fluorescence allows direct observation of bounce resonances on the particle distribution, here predominantly at vph / 3 . A clear increase of the bounce harmonics is visible on the particle distribution when the squeeze potential is applied. Supported by NSF Grant PHY-1414570, and DOE Grants DE-SC0002451 and DE-SC0008693.

Understanding fifth-harmonic generation in CLBO

Science.gov (United States)

Patankar, S.; Yang, S. T.; Moody, J. D.; Bayramian, A. J.; Swadling, G. F.; Barker, D.; Datte, P.; Mennerat, G.; Norton, M.; Carr, C. W.; Begishev, I. A.; Bromage, J.; Ross, J. S.

2018-02-01

We report on results of fifth harmonic generation in Cesium Lithium Borate (CLBO) using a three-crystal cascaded frequency conversion scheme designed to study the energy balance of the final sum frequency generation stage. The experimental setup independently combines the first and fourth harmonic of a Nd:Glass laser in a 5mm thick CLBO crystal. Energy balance between the incoming and output energy is close to unity when the CLBO is out of phase matching and approximately 80% when the crystal is in phase matching. A detailed analysis of the residual fundamental and fourth harmonic energy indicates 5th harmonic light is being generated but only 26% is unaccounted for. We attribute the missing light to linear transmission loss in the CLBO oven. The ratio of the output to input energy is unity when the missing 5th harmonic is incorporated into the calculations. Two-dimensional plane wave mixing simulations show agreement with the results at lower intensities.

MODFLOW equipped with a new method for the accurate simulation of axisymmetric flow

Science.gov (United States)

Samani, N.; Kompani-Zare, M.; Barry, D. A.

2004-01-01

Axisymmetric flow to a well is an important topic of groundwater hydraulics, the simulation of which depends on accurate computation of head gradients. Groundwater numerical models with conventional rectilinear grid geometry such as MODFLOW (in contrast to analytical models) generally have not been used to simulate aquifer test results at a pumping well because they are not designed or expected to closely simulate the head gradient near the well. A scaling method is proposed based on mapping the governing flow equation from cylindrical to Cartesian coordinates, and vice versa. A set of relationships and scales is derived to implement the conversion. The proposed scaling method is then embedded in MODFLOW 2000. To verify the accuracy of the method steady and unsteady flows in confined and unconfined aquifers with fully or partially penetrating pumping wells are simulated and compared with the corresponding analytical solutions. In all cases a high degree of accuracy is achieved.

Efficient second harmonic generation by para-nitroaniline embedded in electro-spun polymeric nanofibres

Science.gov (United States)

Gonçalves, Hugo; Saavedra, Inês; Ferreira, Rute AS; Lopes, PE; de Matos Gomes, Etelvina; Belsley, Michael

2018-03-01

Intense well polarized second harmonic light was generated by poly(methyl methacrylate) nanofibres with embedded para-nitroaniline nanocrystals. Subwavelength diameter fibres were electro-spun using a 1:2 weight ratio of chromophore to polymer. Analysis of the generated second harmonic light indicates that the para-nitroaniline molecules, which nominally crystalize in the centrosymmetric space group, were organized into noncentrosymmetric structures leading to a second order susceptibility dominated by a single tensor element. Under the best deposition conditions, the nanofibrers display an effective nonlinear optical susceptibility approximately two orders of magnitude greater than that of potassium dihydrogen phosphate. Generalizing this approach to a broad range of organic molecules with strong individual molecular second order nonlinear responses, but which nominally form centrosymmetric organic crystals, could open a new pathway for the fabrication of efficient sub-micron sized second harmonic light generators.

Third Harmonic Imaging using a Pulse Inversion

DEFF Research Database (Denmark)

Rasmussen, Joachim; Du, Yigang; Jensen, Jørgen Arendt

2011-01-01

The pulse inversion (PI) technique can be utilized to separate and enhance harmonic components of a waveform for tissue harmonic imaging. While most ultrasound systems can perform pulse inversion, only few image the 3rd harmonic component. PI pulse subtraction can isolate and enhance the 3rd...

Elastic layer under axisymmetric indentation and surface energy effects

Science.gov (United States)

Intarit, Pong-in; Senjuntichai, Teerapong; Rungamornrat, Jaroon

2018-04-01

In this paper, a continuum-based approach is adopted to investigate the contact problem of an elastic layer with finite thickness and rigid base subjected to axisymmetric indentation with the consideration of surface energy effects. A complete Gurtin-Murdoch surface elasticity is employed to consider the influence of surface stresses. The indentation problem of a rigid frictionless punch with arbitrary axisymmetric profiles is formulated by employing the displacement Green's functions, derived with the aid of Hankel integral transform technique. The problem is solved by assuming the contact pressure distribution in terms of a linear combination of admissible functions and undetermined coefficients. Those coefficients are then obtained by employing a collocation technique and an efficient numerical quadrature scheme. The accuracy of proposed solution technique is verified by comparing with existing solutions for rigid indentation on an elastic half-space. Selected numerical results for the indenters with flat-ended cylindrical and paraboloidal punch profiles are presented to portray the influence of surface energy effects on elastic fields of the finite layer. It is found that the presence of surface stresses renders the layer stiffer, and the size-dependent behavior of elastic fields is observed in the present solutions. In addition, the surface energy effects become more pronounced with smaller contact area; thus, the influence of surface energy cannot be ignored in the analysis of indentation problem especially when the indenter size is very small such as in the case of nanoindentation.

Aerodynamics characteristic of axisymmetric surface protuberance in supersonic regime

KAUST Repository

Qamar, Adnan; Sanghi, Sanjeev

2012-01-01

The present work deals with the problem of an axi-symmetric surface protuberance mounted on a spherical nosed body of revolution. The numerical computations are carried out for laminar supersonic viscous flow for trapezoidal shape axi-symmetric protuberances. A free stream Mach number ranging from 3 to 8 in steps of 1 at a fixed free stream Reynolds number of 1.8x10(4) has been used in the present study. The steady solutions are obtained using a time marching approach. A newly developed Particle Velocity Upwinding (PVU) scheme has been used for the computation. The spatial flow pattern exhibits a strong bow shock in front of the hemispherical nose, which engulfs the entire base body. Near the protuberance, the fluid particle decelerates due to the adverse pressure created by the protuberance and thus the flow separates in front of the protuberance. This point of separation is found to be a function of Mach number and the protuberance shape. A low-pressure expansion region dominates the base region of the obstacle. The reattachment point for the base separation is also a function of Mach number. As the Mach number is increased the reattachment point shifts toward the protuberances base. A weak recompression shock is also seen in the base, which affects the separated zone behind the protuberance. The important design parameters such as skin friction, heat transfer, drag, and surface pressure coefficients are reported extensively.

On propagation of axisymmetric waves in pressurized functionally graded elastomeric hollow cylinders

Science.gov (United States)

Wu, Bin; Su, Yipin; Liu, Dongying; Chen, Weiqiu; Zhang, Chuanzeng

2018-05-01

Soft materials can be designed with a functionally graded (FG) property for specific applications. Such material inhomogeneity can also be found in many soft biological tissues whose functionality is only partly understood to date. In this paper, we analyze the axisymmetric guided wave propagation in a pressurized FG elastomeric hollow cylinder. The cylinder is subjected to a combined action of axial pre-stretch and pressure difference applied to the inner and outer cylindrical surfaces. We consider both torsional waves and longitudinal waves propagating in the FG cylinder made of incompressible isotropic elastomer, which is characterized by the Mooney-Rivlin strain energy function but with the material parameters varying with the radial coordinate in an affine way. The pressure difference generates an inhomogeneous deformation field in the FG cylinder, which dramatically complicates the superimposed wave problem described by the small-on-large theory. A particularly efficient approach is hence employed which combines the state-space formalism for the incremental wave motion with the approximate laminate or multi-layer technique. Dispersion relations for the two types of axisymmetric guided waves are then derived analytically. The accuracy and convergence of the proposed approach is validated numerically. The effects of the pressure difference, material gradient, and axial pre-stretch on both the torsional and the longitudinal wave propagation characteristics are discussed in detail through numerical examples. It is found that the frequency of axisymmetric waves depends nonlinearly on the pressure difference and the material gradient, and an increase in the material gradient enhances the capability of the pressure difference to adjust the wave behavior in the FG cylinder. This work provides a theoretical guidance for characterizing FG soft materials by in-situ ultrasonic nondestructive evaluation and for designing tunable waveguides via material tailoring along

Validation Techniques of network harmonic models based on switching of a series linear component and measuring resultant harmonic increments

DEFF Research Database (Denmark)

Wiechowski, Wojciech Tomasz; Lykkegaard, Jan; Bak, Claus Leth

2007-01-01

In this paper two methods of validation of transmission network harmonic models are introduced. The methods were developed as a result of the work presented in [1]. The first method allows calculating the transfer harmonic impedance between two nodes of a network. Switching a linear, series network......, as for example a transmission line. Both methods require that harmonic measurements performed at two ends of the disconnected element are precisely synchronized....... are used for calculation of the transfer harmonic impedance between the nodes. The determined transfer harmonic impedance can be used to validate a computer model of the network. The second method is an extension of the fist one. It allows switching a series element that contains a shunt branch...

Material density measurements from dynamic flash x-ray radiographs using axisymmetric tomography

International Nuclear Information System (INIS)

Fugelso, E.

1981-03-01

The axisymmetric version of the tomographic x-ray reconstruction procedures has been utilized to determine the material density for the impact of a cylinder on a steel plate. Derivations of the reconstruction algorithms relating x-ray radiographic intensities to the material densities are presented. Effects of noise, point spread functions, and motion blur are minimized

Relationship between harmonic analysis on SU(2) and on SL(2,C)/SU(2)

International Nuclear Information System (INIS)

Healy, D.M. Jr.

1986-01-01

A topic of interest in harmonic analysis is the comparison of Fourier transforms on compact and noncompact spaces. The Poisson summation formula provides a classical example of this idea by providing an explicit relationship between harmonic analysis on the real line R and on the circle S 1 . This dissertation provides a new geometric proof of this formula, and then generalizes this approach to obtain a relationship between Fourier transforms on Upsilon, the space of positive matrices in SL(2,C), and Fourier transforms on SU(2)

Benefits from the BESSY FEL Higher Harmonic Radiation

CERN Document Server

Goldammer, K

2005-01-01

In the FEL process, bunching and coherent radiation is produced at the fundamental frequency as well as its higher harmonics. BESSY proposes a linac-based cascaded High-Gain Harmonic-Generation (HGHG) free electron laser (FEL) multi-user facility. The BESSY soft X-ray FEL will be seeded by three lasers spanning the spectral range of 230nm to 460nm. Two to four HGHG stages downconvert the seed wavelength to the desired radiation range of 1.24nm to 51nm using higher harmonic bunching. As a surplus, higher harmonic radiation is intrinsically produced in each FEL stage. Radiation on a higher harmonic of the FEL frequency is of high interest because it yields the possibility to reduce the number of FEL stages. This paper details extensive studies of the higher harmonic content of the BESSY FEL radiation. Important aspects of FEL interaction on higher harmonics as resulting from theory and from numerical simulations are discussed. For the case of the BESSY FEL, methods for improving the harmonic content are present...

SAFE-AXISYM, Stress Analysis of Axisymmetric Composite Structure by Finite Elements Method

International Nuclear Information System (INIS)

Cornell, D.C.

1967-01-01

1 - Nature of physical problem solved: SAFE-AXISYM is a program for the analysis of multi-material axisymmetric composite structures. It is designed for the analysis of heterogeneous structures such as reinforced and/or prestressed concrete vessels. The structure is assumed to be linearly elastic, and only bodies of revolution subjected to axisymmetric loading can be treated. 2 - Method of solution: SAFE-AXISYM uses a finite element method with a modified Gauss-Seidel iteration scheme. A reference grid subdivides the structure into ring-like small, finite elements, the vertices of which are called nodes. The grid may be generated by hand, by the computer or by a combination of the two methods. Each node has two degrees of freedom, translation in the and in the axial direction. Both zero and non-zero fixed displacement constraints may be assumed, and the loading condition may be mechanical and/or thermal. 3 - Restrictions on the complexity of the problem: Multi-material structures with varying rigidities converge very slowly. Not valid for incompressible materials. Maximum number of nodes = 475. Maximum number of elements = 1100

Axisymmetric modeling of ultrashort-pulse laser interactions with thin metal film

Directory of Open Access Journals (Sweden)

E. Majchrzak

2011-10-01

Full Text Available The hyperbolic two-temperature model is used in order to describe the heat propagation in metal film subjected to an ultrashort-pulse laser heating. An axisymmetric heat soureceewith Gaussian temporeal and spatial distributions has been taken into account. At the stage of numerical computations the finite difference method is used. In the final part of the paper the examples of computations are shown.

Second harmonic electromagnetic emission via Langmuir wave coalescence

International Nuclear Information System (INIS)

Willes, A.J.; Robinson, P.A.; Melrose, D.B.

1996-01-01

The coalescence of Langmuir waves to produce electromagnetic waves at twice the plasma frequency is considered. A simplified expression for the rate of production of second harmonic electromagnetic waves is obtained for a broad class of Langmuir spectra. In addition, two different analytic approximations are considered. The validity of the commonly used head-on approximation is explored, in which the two coalescing Langmuir waves are assumed to approach from opposite directions. This approximation breaks down at low Langmuir wavenumbers, and for narrow Langmuir wave spectra. A second, more general, approximation is introduced, called the narrow-spectrum approximation, which requires narrow spectral widths of the Langmuir spectra. The advantages of this approximation are that it does not break down at low Langmuir wavenumbers, and that it remains valid for relatively broad Langmuir wave spectra. Finally, the applicability of these approximations in treating harmonic radiation in type III solar radio bursts is discussed. copyright 1996 American Institute of Physics

A review of findings of a study of rocket based combined cycle engines applied to extensively axisymmetric single stage to orbit vehicles

Science.gov (United States)

Foster, Richard W.

1992-01-01

Extensively axisymmetric and non-axisymmetric Single Stage To Orbit (SSTO) vehicles are considered. The information is presented in viewgraph form and the following topics are presented: payload comparisons; payload as a percent of dry weight - a system hardware cost indicator; life cycle cost estimations; operations and support costs estimation; selected engine type; and rocket engine specific impulse calculation.

Hermitian harmonic maps into convex balls

International Nuclear Information System (INIS)

Li Zhenyang; Xi Zhang

2004-07-01

In this paper, we consider Hermitian harmonic maps from Hermitian manifolds into convex balls. We prove that there exist no non-trivial Hermitian harmonic maps from closed Hermitian manifolds into convex balls, and we use the heat flow method to solve the Dirichlet problem for Hermitian harmonic maps when the domain is compact Hermitian manifold with non-empty boundary. The case where the domain manifold is complete(noncompact) is also studied. (author)

A study of parametric instability in a harmonic gyrotron: Designs of third harmonic gyrotrons at 94 GHz and 210 GHz

International Nuclear Information System (INIS)

Saraph, G.P.; Antonsen, T.M. Jr.; Nusinovich, G.S.; Levush, B.

1995-01-01

Mode competition can present a major hurdle in achieving stable, efficient operation of a gyrotron at the cyclotron harmonics. A type of mode interaction in which three modes at different cyclotron harmonics are parametrically coupled together is analyzed here. This coupling can lead to parametric excitation or suppression of a mode; cyclic mode hopping; or the coexistence of three modes. Simulation results are presented for the parametric instability involving modes at the fundamental, second harmonic, and third harmonic of the cyclotron frequency. It is shown that the parametric excitation can lead to stable, efficient operation of a high-power gyrotron at the third harmonic. Based on this phenomenon, two practical designs are presented here for the third harmonic operation at 94 and 210 GHz. copyright 1995 American Institute of Physics

Harmonic disturbance location by applying Bayesian inference

NARCIS (Netherlands)

Ye, G.; Xiang, Y.; Cuk, V.; Cobben, J.F.G.

2016-01-01

Harmonic pollution is one of the most important power quality issues in electric power systems. Correct location of the main harmonic disturbance source is a key step to solve the problem. This paper presents a method to detect the location of harmonic disturbance source in low voltage network

Introduction to classical and quantum harmonic oscillators

CERN Document Server

Bloch, Sylvan C

2013-01-01

From conch shells to lasers . harmonic oscillators, the timeless scientific phenomenon As intriguing to Galileo as they are to scientists today, harmonic oscillators have provided a simple and compelling paradigm for understanding the complexities that underlie some of nature's and mankind's most fascinating creations. From early string and wind instruments fashioned from bows and seashells to the intense precision of lasers, harmonic oscillators have existed in various forms, as objects of beauty and scientific use. And harmonic oscillation has endured as one of science's most fascinating con

Dual aperture dipole magnet with second harmonic component

Science.gov (United States)

Praeg, Walter F.

1985-01-01

An improved dual aperture dipole electromagnet includes a second-harmonic frequency magnetic guide field winding which surrounds first harmonic frequency magnetic guide field windings associated with each aperture. The second harmonic winding and the first harmonic windings cooperate to produce resultant magnetic waveforms in the apertures which have extended acceleration and shortened reset portions of electromagnet operation.

Evaluation of Harmonics Impact on Digital Relays

Directory of Open Access Journals (Sweden)

Kinan Wannous

2018-04-01

Full Text Available This paper presents the concept of the impact of harmonic distortion on a digital protection relay. The aim is to verify and determine the reasons of a mal-trip or failure to trip the protection relays; the suggested solution of the harmonic distortion is explained by a mathematical model in the Matlab Simulink programming environment. The digital relays have been tested under harmonic distortions in order to verify the function of the relays algorithm under abnormal conditions. The comparison between the protection relay algorithm under abnormal conditions and a mathematical model in the Matlab Simulink programming environment based on injected harmonics of high values is provided. The test is separated into different levels; the first level is based on the harmonic effect of an individual harmonic and mixed harmonics. The test includes the effect of the harmonics in the location of the fault point into distance protection zones. This paper is a new proposal in the signal processing of power quality disturbances using Matlab Simulink and the power quality impact on the measurements of the power system quantities; the test simulates the function of protection in power systems in terms of calculating the current and voltage values of short circuits and their faults. The paper includes several tests: frequency variations and decomposition of voltage waveforms with Fourier transforms (model and commercial relay, the effect of the power factor on the location of fault points, the relation between the tripping time and the total harmonic distortion (THD levels in a commercial relay, and a comparison of the THD capture between the commercial relay and the model.

Fusion-product transport in axisymmetric tokamaks: losses and thermalization

International Nuclear Information System (INIS)

Hively, L.M.

1980-01-01

High-energy fusion-product losses from an axisymmetric tokamak plasma are studied. Prompt-escape loss fluxes (i.e. prior to slowing down) are calculated including the non-separable dependence of flux as a function of poloidal angle and local angle-of-incidence at the first wall. Fusion-product (fp) thermalization and heating are calculated assuming classical slowing down. The present analytical model describes fast ion orbits and their distribution function in realistic, high-β, non-circular tokamak equilibria. First-orbit losses, trapping effects, and slowing-down drifts are also treated

Modelling Acoustic Wave Propagation in Axisymmetric Varying-Radius Waveguides

DEFF Research Database (Denmark)

Bæk, David; Willatzen, Morten

2008-01-01

A computationally fast and accurate model (a set of coupled ordinary differential equations) for fluid sound-wave propagation in infinite axisymmetric waveguides of varying radius is proposed. The model accounts for fluid heat conduction and fluid irrotational viscosity. The model problem is solved...... by expanding solutions in terms of cross-sectional eigenfunctions following Stevenson’s method. A transfer matrix can be easily constructed from simple model responses of a given waveguide and later used in computing the response to any complex wave input. Energy losses due to heat conduction and viscous...

Fast harmonic field mapper

International Nuclear Information System (INIS)

Au, R.; Fowler, M.; Hanawa, H.; Riedel, J.; Qua, Z.G.

1984-01-01

In early 1983 it was decided to mount coils on arms separated by 120 degrees and buck them out so that the third harmonic dphi/dt component would be cancelled and thus the first and second field harmonics could be very accurately measured. The original intention was to do as others had done, namely, use fast ADC's to read the voltages, and computer process the result to get the Fourier components. However, because of the 100 to 1 dynamic range of the fast ADC's and the likelihood that noise would be a problem, the authors decided to do things differently. Using a fast Fourier transform analyzer was considered, but this instrument is very expensive, so they decided to use a completely electronic analog approach: The authors decided to use active bandpass filters to render the harmonic components

Stability and nonlinear dynamics of gyrotrons at cyclotron harmonics

International Nuclear Information System (INIS)

Saraph, G.P.; Nusinovich, G.S.; Antonsen, T.M. Jr.; Levush, B.

1992-01-01

Gyrotrons operating at higher harmonics of the cyclotron frequency can overcome the frequency limitations caused by achievable strength of the magnetic field. However, the excitation of modes at the fundamental frequency exhibit a major problem for stable operation of harmonic gyrotron at high power with high efficiency. Therefore the issues of stability of gyrotron operation at the cyclotron harmonics and nonlinear dynamics of mode interaction are of great importance. The results of the authors stability analysis and multimode simulation are presented here. A detailed nonlinear theory of steady state single mode operation at cyclotron harmonics has been presented previously, taking into account beam-wave coupling and nonlinear gain function at cyclotron harmonics. A set of equations describing low gain regime interaction of modes resonant at different cyclotron harmonics was studied before. The multifrequency time-dependent nonlinear analysis presented here is based on previous gyrotron studies and beam-wave interaction at cyclotron harmonics. The authors have determined the parameter space for stable single mode operation at the second harmonic. The nonlinear dynamics of mode evolution and mode interaction for a harmonic gyrotron is presented. A new nonlinear effect in which the parasite at the fundamental harmonic helps excite the operating mode at the second harmonic has been demonstrated

Detection of Harmonic Occurring using Kalman Filtering

DEFF Research Database (Denmark)

Hussain, Dil Muhammad Akbar; Shoro, Ghulam Mustafa; Imran, Raja Muhammed

2014-01-01

/current characteristic. These harmonics are not to be allowed to grow beyond a certain limit to avoid any grave consequence to the customer’s main supply. Filters can be implemented at the power source or utility location to eliminate these harmonics. In this paper we detect the instance at which these harmonics occur...

High order harmonic generation in rare gases

Energy Technology Data Exchange (ETDEWEB)

Budil, Kimberly Susan [Univ. of California, Davis, CA (United States)

1994-05-01

The process of high order harmonic generation in atomic gases has shown great promise as a method of generating extremely short wavelength radiation, extending far into the extreme ultraviolet (XUV). The process is conceptually simple. A very intense laser pulse (I ~10¹³-10¹⁴ W/cm²) is focused into a dense (~10¹⁷ particles/cm³) atomic medium, causing the atoms to become polarized. These atomic dipoles are then coherently driven by the laser field and begin to radiate at odd harmonics of the laser field. This dissertation is a study of both the physical mechanism of harmonic generation as well as its development as a source of coherent XUV radiation. Recently, a semiclassical theory has been proposed which provides a simple, intuitive description of harmonic generation. In this picture the process is treated in two steps. The atom ionizes via tunneling after which its classical motion in the laser field is studied. Electron trajectories which return to the vicinity of the nucleus may recombine and emit a harmonic photon, while those which do not return will ionize. An experiment was performed to test the validity of this model wherein the trajectory of the electron as it orbits the nucleus or ion core is perturbed by driving the process with elliptically, rather than linearly, polarized laser radiation. The semiclassical theory predicts a rapid turn-off of harmonic production as the ellipticity of the driving field is increased. This decrease in harmonic production is observed experimentally and a simple quantum mechanical theory is used to model the data. The second major focus of this work was on development of the harmonic "source". A series of experiments were performed examining the spatial profiles of the harmonics. The quality of the spatial profile is crucial if the harmonics are to be used as the source for experiments, particularly if they must be refocused.

Stimulated Brillouin scattering during electron gyro-harmonic heating at EISCAT

Directory of Open Access Journals (Sweden)

H. Y. Fu

2015-08-01

Full Text Available Observations of secondary radiation, stimulated electromagnetic emission (SEE, produced during ionospheric modification experiments using ground-based, high-power, high-frequency (HF radio waves are considered. The High Frequency Active Auroral Research Program (HAARP facility is capable of generating narrowband SEE in the form of stimulated Brillouin scatter (SBS and stimulated ion Bernstein scatter (SIBS in the SEE spectrum. Such narrowband SEE spectral lines have not been reported using the European Incoherent Scatter (EISCAT heater facility before. This work reports the first EISCAT results of narrowband SEE spectra and compares them to SEE previously observed at HAARP during electron gyro-harmonic heating. An analysis of experimental SEE data shows observations of emission lines within 100 Hz of the pump frequency, interpreted as SBS, during the 2012 July EISCAT campaign. Experimental results indicate that SBS strengthens as the pump frequency approaches the third electron gyro-harmonic. Also, for different heater antenna beam angles, the CUTLASS radar backscatter induced by HF radio pumping is suppressed near electron gyro-harmonics, whereas electron temperature enhancement weakens as measured by EISCAT/UHF radar. The main features of these new narrowband EISCAT observations are generally consistent with previous SBS measurements at HAARP.

Numerical exploration of non-axisymmetric divertor closure in the small angle slot (SAS) divertor at DIII-D

Science.gov (United States)

Frerichs, Heinke; Schmitz, Oliver; Covele, Brent; Guo, Houyang; Hill, David; Feng, Yuhe

2017-10-01

In the Small Angle Slot (SAS) divertor in DIII-D, the combination of misaligned slot structure and non-axisymmetric perturbations to the magnetic field causes the strike point to vary radially along the divertor slot and even leave it at some toroidal locations. This effect essentially introduces an opening in the divertor slot from where recycling neutrals can easily escape, and thereby degrade performance of the slot divertor. This effect has been approximated by a finite gap in the divertor baffle. Simulations with EMC3-EIRENE show that a toroidally localized loss of divertor closure can result in non-axisymmetric divertor densities and temperatures. This introduces a density window of 10-15% on top of the nominal threshold separatrix density during which a non-axisymmetric onset of local detachment occurs, initially leaving the gap and up to 60 deg beyond that still attached. Conversely, the impact of such toroidally localized divertor perturbations on the toroidal symmetry of midplane separatrix conditions is small. This work has been funded by the U.S. Department of Energy under Early Career Award Grant DE-SC0013911, and Grant DE-FC02-04ER54698.

Harmonic Instability Analysis of Single-Phase Grid Connected Converter using Harmonic State Space (HSS) modeling method

DEFF Research Database (Denmark)

Kwon, Jun Bum; Wang, Xiongfei; Bak, Claus Leth

2015-01-01

The increasing number of renewable energy sources at the distribution grid is becoming a major issue for utility companies, since the grid connected converters are operating at different operating points due to the probabilistic characteristics of renewable energy. Besides, typically, the harmonics...... proposes a new model of a single phase grid connected renewable energy source using the Harmonic State Space modeling approach, which is able to identify such problems and the model can be extended to be applied in the multiple connected converter analysis. The modeling results show the different harmonic...... and impedance from other renewable energy sources are not taken carefully into account in the installation and design. However, this may bring an unknown harmonic instability into the multiple power sourced system and also make the analysis difficult due to the complexity of the grid network. This paper...

Contribution in the area of harmonics in electric power systems; Contribuicoes na area de harmonicos em sistemas eletricos de potencia

Energy Technology Data Exchange (ETDEWEB)

Oliveira, Aloisio de

1989-07-01

A general approach of the state of art of the harmonic generation, its sources, its limits, its measurement methods and its effects on the electric system components is presented. This thesis shows that this is an open field to research, modelling and solutions. It also helps towards the investigation of the effects caused by harmonics on the conventional KWh energy meters and on potential and current transformers. It presents the basis for the development and construction of prototypes to be utilized in the generation and measurement of harmonics. Finally a practical approach has been given to calculate the equivalent harmonic impedance as seen by a giving consumer. (author)

Integration of Transients in Axisymmetrical Cavities for Accelerators: Formulation and applications to BNL Photocathode Gun

International Nuclear Information System (INIS)

Parsa, Z.; Serafini, L.

1992-04-01

This note provides a sketch of the formalism used for the Integration of Transients in Axisymmetrical Cavities for Accelerators, (ITACA). Application to study the BNL Photocathode Gun via the code ITACA is also included

Axisymmetric Magnetic Mirror Fusion-Fission Hybrid

Energy Technology Data Exchange (ETDEWEB)

Moir, R. W. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Martovetsky, N. N. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Molvik, A. W. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Ryutov, D. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Simonen, T. C. [Univ. of California, Berkeley, CA (United States)

2011-05-13

The achieved performance of the gas dynamic trap version of magnetic mirrors and today’s technology we believe are sufficient with modest further efforts for a neutron source for material testing (Q=P_fusion/P_input~0.1). The performance needed for commercial power production requires considerable further advances to achieve the necessary high Q>>10. An early application of the mirror, requiring intermediate performance and intermediate values of Q~1 are the hybrid applications. The Axisymmetric Mirror has a number of attractive features as a driver for a fusion-fission hybrid system: geometrical simplicity, inherently steady-state operation, and the presence of the natural divertors in the form of end tanks. This level of physics performance has the virtue of low risk and only modest R&D needed and its simplicity promises economy advantages. Operation at Q~1 allows for relatively low electron temperatures, in the range of 4 keV, for the DT injection energy ~ 80 keV. A simple mirror with the plasma diameter of 1 m and mirror-to-mirror length of 35 m is discussed. Simple circular superconducting coils are based on today’s technology. The positive ion neutral beams are similar to existing units but designed for steady state. A brief qualitative discussion of three groups of physics issues is presented: axial heat loss, MHD stability in the axisymmetric geometry, microstability of sloshing ions. Burning fission reactor wastes by fissioning actinides (transuranics: Pu, Np, Am, Cm, .. or just minor actinides: Np, Am, Cm, …) in the hybrid will multiply fusion’s energy by a factor of ~10 or more and diminish the Q needed to less than 1 to overcome the cost of recirculating power for good economics. The economic value of destroying actinides by fissioning is rather low based on either the cost of long-term storage or even deep geologic disposal so most of the revenues of hybrids will come from electrical power. Hybrids that obtain revenues from

Confluent hypergeometric orthogonal polynomials related to the rational quantum Calogero system with harmonic confinement

International Nuclear Information System (INIS)

van Diejen, J.F.

1997-01-01

Two families (type A and type B) of confluent hypergeometric polynomials in several variables are studied. We describe the orthogonality properties, differential equations, and Pieri-type recurrence formulas for these families. In the one-variable case, the polynomials in question reduce to the Hermite polynomials (type A) and the Laguerre polynomials (type B), respectively. The multivariable confluent hypergeometric families considered here may be used to diagonalize the rational quantum Calogero models with harmonic confinement (for the classical root systems) and are closely connected to the (symmetric) generalized spherical harmonics investigated by Dunkl. (orig.)

Jet flow issuing from an axisymmetric pipe-cavity-orifice nozzle

Directory of Open Access Journals (Sweden)

Broučková Zuzana

2016-01-01

Full Text Available An axisymmetric air jet flow is experimentally investigated under passive flow control. The jet issues from a pipe of the inner diameter and length of 10 mm and 150 mm which is equipped with an axisymmetric cavity at the pipe end. The cavity operates as a resonator creating self-sustained acoustic excitations of the jet flow. A mechanism of excitations is rather complex – in comparison with a common Helmholtz resonator. The experiments were performed using flow visualization, microphone measurements and time-mean velocity measurements by the Pitot probe. The power spectral density (PSD and the sound pressure level (SPL were evaluated from microphone measurements. The jet Reynolds number ranged Re = 1600–18 000. Distinguishable peaks in PSD indicated a function of the resonator. Because the most effective acoustic response was found at higher Re, a majority of experiments focused on higher Re regime. The results demonstrate effects of the passive control on the jet behavior. Fluid mixing and velocity decay along the axis is intensified. It causes shortening of the jet transition region. On the other hand, an inverse proportionality of the velocity decay (u ~ 1/x in the fully developed region is not changed. The momentum and kinetic energy fluxes decrease more intensively in the controlled jets in comparison with common jets.

Axisymmetric magnetic mirrors for plasma confinement. Recent development and perspectives

International Nuclear Information System (INIS)

Kruglyakov, E.P.; Dimov, G.I.; Ivanov, A.A.; Koidan, V.S.

2003-01-01

Mirrors are the only one class of fusion systems which completely differs topologically from the systems with closed magnetic configurations. At present, three modern types of different mirror machines for plasma confinement and heating exist in Novosibirsk (Gas Dynamic Trap,- GDT, Multi-mirror,- GOL-3, and Tandem Mirror,- AMBAL-M). All these systems are attractive from the engineering point of view because of very simple axisymmetric geometry of magnetic configurations. In the present paper, the status of different confinement systems is presented. The experiments most crucial for the mirror concept are described such as a demonstration of different principles of suppression of electron heat conductivity (GDT, GOL-3), finding of MHD stable regimes of plasma confinement in axisymmetric geometry of magnetic field (GDT, AMBAL-M), an effective heating of a dense plasma by relativistic electron beam (GOL-3), observation of radial diffusion of quiescent plasma with practically classical diffusion coefficient (AMBAL-M), etc. It should be mentioned that on the basis of the GDT it is possible to make a very important intermediate step. Using 'warm' plasma and oblique injection of fast atoms of D and T one can create a powerful 14 MeV neutron source with a moderate irradiation area (about 1 square meter) and, accordingly, with low tritium consumption. The main plasma parameters achieved are presented and the future perspectives of different mirror machines are outlined. (author)

Magnetohydrodynamic helical structures in nominally axisymmetric low-shear tokamak plasmas

International Nuclear Information System (INIS)

Graves, J P; Brunetti, D; Cooper, W A; Reimerdes, H; Halpern, F; Pochelon, A; Sauter, O; Chapman, I T

2013-01-01

The primary goal of hybrid scenarios in tokamaks is to enable high performance operation with large plasma currents whilst avoiding MHD instabilities. However, if a local minimum in the safety factor is allowed to approach unity, the energy required to overcome stabilizing magnetic field line bending is very small, and as a consequence, large MHD structures can be created, with typically dominant m = n = 1 helical component. If there is no exact q = 1 rational surface the essential character of these modes can be modelled assuming ideal nested magnetic flux surfaces. The methods used to characterize these structures include linear and non-linear ideal MHD stability calculations which evaluate the departure from an axisymmetric plasma state, and also equilibrium calculations using a 3D equilibrium code. While these approaches agree favourably for simulations of ITER relevant hybrid regimes in this paper, the relevance of the ideal MHD model itself is tested through empirical examination of helical states in MAST and TCV. While long lived modes in MAST do not have island structures, some of the continuous mode oscillations exhibited in high elongation experiments in TCV indicate that resistivity may play a role in further weakening the ability of the tokamak core to remain axisymmetric. The simulations and experiments consistently highlight the need to control the safety factor in hybrid scenarios planned for future fusion grade tokamaks such as ITER. (paper)

Principal component analysis of the nonlinear coupling of harmonic modes in heavy-ion collisions

Science.gov (United States)

BoŻek, Piotr

2018-03-01

The principal component analysis of flow correlations in heavy-ion collisions is studied. The correlation matrix of harmonic flow is generalized to correlations involving several different flow vectors. The method can be applied to study the nonlinear coupling between different harmonic modes in a double differential way in transverse momentum or pseudorapidity. The procedure is illustrated with results from the hydrodynamic model applied to Pb + Pb collisions at √{sN N}=2760 GeV. Three examples of generalized correlations matrices in transverse momentum are constructed corresponding to the coupling of v22 and v4, of v2v3 and v5, or of v23,v33 , and v6. The principal component decomposition is applied to the correlation matrices and the dominant modes are calculated.

Utilization of axisymmetrical models in the description of the fluctuating temperature field and in the calculation of turbulent thermal diffusivity

International Nuclear Information System (INIS)

Cintra Filho, J. de S.

1981-01-01

The fluctuating temperature field structure is studied for the case of turbulent circular pipe flow. Experimentally determined integral length scales are used in modeling this structure in terms of axisymmetric forms. It is found that the appropriate angle of axisymmetry is larger than the one for modeling the large scale velocity structure. The axisymmetric model is then used to examine the validity and the prediction capability of the Tyldesley and Silver's non-spherical eddy diffusivity theory. (Author) [pt

Double Harmonic Transmission (D.H.T.

Directory of Open Access Journals (Sweden)

Sava Ianici

2006-10-01

Full Text Available The paper presents the construction and functioning of a new type of harmonic drive named double harmonic transmission (D.H.T.. In the second part of this paper is presented the dynamic analysis of the double harmonic transmission, which is based on the results of the experimental researches on the D.H.T. This study of the stress status and the forces distribution is necessary for to determine the durability on the portant elements of the D.H.T.

Pseudo harmonic morphisms on Riemannian polyhedra

International Nuclear Information System (INIS)

Aprodu, M.A.; Bouziane, T.

2004-10-01

The aim of this paper is to extend the notion of pseudo harmonic morphism (introduced by Loubeau) to the case when the source manifold is an admissible Riemannian polyhedron. We define these maps to be harmonic in the sense of Eells-Fuglede and pseudo-horizontally weakly conformal in our sense. We characterize them by means of germs of harmonic functions on the source polyhedron, in the sense of Korevaar-Schoen, and germs of holomorphic functions on the Kaehler target manifold. (author)

Coherent harmonic production using a two-section undulator FEL

Energy Technology Data Exchange (ETDEWEB)

Jaroszynski, D.A. [Commissariat a l`Energie, Bruyeres-le-Chatel (France); Prazeres, R.; Glotin, F. [Centre Universitaire Paris-Sud (France)] [and others

1995-12-31

We present measurements and a theoretical analysis of a new method of generating harmonic radiation in a free-electron laser oscillator with a two section undulator in a single optical cavity. To produce coherent harmonic radiation the undulator is arranged so that the downstream undulator section resonance frequency matches a harmonic of the upstream undulator. Both the fundamental and the harmonic optical fields evolve in the same optical cavity and are coupled out with different extraction fractions using a hole in one of the cavity mirrors. We present measurements that show that the optical power at the second and third harmonic can be enhanced by more than an order of magnitude in this fundamental/harmonic configuration. We compare the production of harmonic radiation of a two sectioned fundamental/harmonic undulator with that produced from a FEL operating at its highest efficiency with a step-tapered undulator, where the bunching at the end of the first section is very large. We examine, the dependence of the harmonic power on the intracavity power by adjusting the optical cavity desynchronism, {delta}L. We also examine the evolution of the fundamental and harmonic powers as a function of cavity roundtrip number to evaluate the importance of the small signal gain at the harmonic. We compare our measurements with predictions of a multi-electron numerical model that follows the evolution of fundamental and harmonic power to saturation. This fundamental/harmonic mode, of operation of the FEL may have useful applications in the production of coherent X-ray and VUV radiation, a spectral range where high reflectivity optical cavity mirrors are difficult or impossible to manufacture.

The computation of multiple MHD equilibria in axisymmetric and straight geometry

International Nuclear Information System (INIS)

Thomas, C.Ll.

1979-01-01

The details of the numerical methods used in codes for computing MHD equilibria in discrete conductor configurations are described with both code users and code writers in mind. Results produced by the codes have been successfully verified against analytic results and independent computations. The axisymmetric code has proved to be a valuable diagnostic aid for the TOSCA experiment. The user images of the codes are described in the appendices. (author)

An Axisymmetric View of Concentric Eyewall Evolution in Hurricane Rita (2005)

Science.gov (United States)

2012-08-01

of Hurricane Hugo (1989). Mon. Wea. Rev., 136, 1237–1259. Martinez, Y., G. Brunet, and M. K. Yau, 2010: On the dynamics of two-dimensional hurricane ...An Axisymmetric View of Concentric Eyewall Evolution in Hurricane Rita (2005) MICHAEL M. BELL Naval Postgraduate School, Monterey, California, and... Hurricane Research Division, Miami, Florida WEN-CHAU LEE National Center for Atmospheric Research,* Boulder, Colorado (Manuscript received 23 June 2011, in

Internal-Model-Principle-Based Specific Harmonics Repetitive Controller for Grid-Connected PWM Inverters

Directory of Open Access Journals (Sweden)

Wenzhou Lu

2016-01-01

Full Text Available This paper analyzes the general properties of IMP-based controller and presents an internal-model-principle-based (IMP-based specific harmonics repetitive control (SHRC scheme. The proposed SHRC is effective for specific nk±m order harmonics, with n>m≥0 and k=0,1,2,…. Using the properties of exponential function, SHRC can also be rewritten into the format of multiple resonant controllers in parallel, where the control gain of SHRC is n/2 multiple of that of conventional RC (CRC. Therefore, including SHRC in a stable closed-loop feedback control system, asymptotic disturbance eliminating, or reference tracking for any periodic signal only including these specific harmonic components at n/2 times faster error convergence rate compared with CRC can be achieved. Application examples of SHRC controlled three-phase/single-phase grid-connected PWM inverters demonstrate the effectiveness and advantages of the proposed SHRC scheme.

A Case Study of Harmonic Impact on a Motor-Generator Set System

Energy Technology Data Exchange (ETDEWEB)

Joung, Pil-Bum [KHNP CRI, Daejeon (Korea, Republic of)

2016-10-15

Motor-Generator Sets are usually used to supply power to a Control Element Drive Mechanism Control System (CEDMCS) at nuclear power plants with pressurized water reactors. Two Motor-Generator Sets, which have 100% capacity, are operated in parallel to improve the reliability of the power supply to the CEDMCS. Fig. 1 presents a diagram of a Motor- Generator Set system. The system of a Motor-Generator Set is composed of electrical equipment, such as a motor, a fly-wheel, and a generator, an exciter and protection-control device, such as a protective relay, synchro check relay, and an auto voltage regulator. In general, the harmonic impact of electrical equipment increases the deterioration of the equipment, the motor, and the generator’s lifetime, which can also be caused by vibration and over-heating and maloperation of the protection-control device. In this paper, we came to understand the harmonic impact on the Motor-Generator Set system through a study of delaying parallel operation by non-operation of the synchro check relay and the fault of under voltage protective relay. Thus, KHNP has established and applied the measures of harmonic reduction by the CEDMCS, such as limiting the voltage harmonic distortion to less than 10%, which is described in IEEE Std 519.

Second harmonic generation imaging

CERN Document Server

2013-01-01

Second-harmonic generation (SHG) microscopy has shown great promise for imaging live cells and tissues, with applications in basic science, medical research, and tissue engineering. Second Harmonic Generation Imaging offers a complete guide to this optical modality, from basic principles, instrumentation, methods, and image analysis to biomedical applications. The book features contributions by experts in second-harmonic imaging, including many pioneering researchers in the field. Written for researchers at all levels, it takes an in-depth look at the current state of the art and possibilities of SHG microscopy. Organized into three sections, the book: Provides an introduction to the physics of the process, step-by-step instructions on how to build an SHG microscope, and comparisons with related imaging techniques Gives an overview of the capabilities of SHG microscopy for imaging tissues and cells—including cell membranes, muscle, collagen in tissues, and microtubules in live cells—by summarizing experi...

Harmonization: A Need for EU Action on Consumer Credit?

DEFF Research Database (Denmark)

Jørgensen, Tanja

2015-01-01

seem small, there is still a need for EU action, but with a different approach that considers the nature of consumer credit. This means a focus on preventing overindebtedness and ensuring financial stability as well as a high level of consumer protection in a financialized and thereby more complex......As in the consumer area in general, the objective of the internal market has been applied as a reason why there is a EU need for action regarding consumer credit. Even though it is more than 25 years ago since the first Consumer Credit Directive harmonized aspects of the legislation in the Member...... States, cross-border activities are still extremely low. The achievement of the internal market depends on the consumers’ and the creditors’ overall incentives to cross-border activities, where harmonized aspects of the legislation are only an insignificant motivation. Despite a need for EU action may...

Second-harmonic imaging of semiconductor quantum dots

DEFF Research Database (Denmark)

Østergaard, John Erland; Bozhevolnyi, Sergey I.; Pedersen, Kjeld

2000-01-01

Resonant second-harmonic generation is observed at room temperature in reflection from self-assembled InAlGaAs quantum dots grown on a GaAs (001) substrate. The detected second-harmonic signal peaks at a pump wavelength of similar to 885 nm corresponding to the quantum-dot photoluminescence maximum....... In addition, the second-harmonic spectrum exhibits another smaller but well-pronounced peak at 765 nm not found in the linear experiments. We attribute this peak to the generation of second-harmonic radiation in the AlGaAs spacer layer enhanced by the local symmetry at the quantum-dot interface. We further...

Harmonic Series Meets Fibonacci Sequence

Science.gov (United States)

Chen, Hongwei; Kennedy, Chris

2012-01-01

The terms of a conditionally convergent series may be rearranged to converge to any prescribed real value. What if the harmonic series is grouped into Fibonacci length blocks? Or the harmonic series is arranged in alternating Fibonacci length blocks? Or rearranged and alternated into separate blocks of even and odd terms of Fibonacci length?

Tuvan Throat Singing and Harmonics

Science.gov (United States)

Ruiz, Michael J.; Wilken, David

2018-01-01

Tuvan throat singing, also called overtone singing, provides for an exotic demonstration of the physics of harmonics as well as introducing an Asian musical aesthetic. A low fundamental is sung and the singer skillfully alters the resonances of the vocal system to enhance an overtone (harmonic above the fundamental). The result is that the…

Transition from gas to plasma kinetic equilibria in gravitating axisymmetric structures

International Nuclear Information System (INIS)

Cremaschini, Claudio; Stuchlík, Zdeněk

2014-01-01

The problem of the transition from gas to plasma in gravitating axisymmetric structures is addressed under the assumption of having initial and final states realized by kinetic Maxwellian-like equilibria. In astrophysics, the theory applies to accretion-disc scenarios around compact objects. A formulation based on non-relativistic kinetic theory for collisionless systems is adopted. Equilibrium solutions for the kinetic distribution functions describing the initial neutral matter and the resulting plasma state are constructed in terms of single-particle invariants and expressed by generalized Maxwellian distributions. The final plasma configuration is related to the initial gas distribution by the introduction of appropriate functional constraints. Qualitative aspects of the solution are investigated and physical properties of the system are pointed out. In particular, the admitted functional dependences of the fluid fields carried by the corresponding equilibrium distributions are determined. Then, the plasma is proved to violate the condition of quasi-neutrality, implying a net charge separation between ions and electrons. This result is shown to be independent of the precise realization of the plasma distribution function, while a physical mechanism able to support a non-neutral equilibrium state is proposed

Transition from gas to plasma kinetic equilibria in gravitating axisymmetric structures

Energy Technology Data Exchange (ETDEWEB)

Cremaschini, Claudio; Stuchlík, Zdeněk [Institute of Physics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám.13, CZ-74601 Opava (Czech Republic)

2014-04-15

The problem of the transition from gas to plasma in gravitating axisymmetric structures is addressed under the assumption of having initial and final states realized by kinetic Maxwellian-like equilibria. In astrophysics, the theory applies to accretion-disc scenarios around compact objects. A formulation based on non-relativistic kinetic theory for collisionless systems is adopted. Equilibrium solutions for the kinetic distribution functions describing the initial neutral matter and the resulting plasma state are constructed in terms of single-particle invariants and expressed by generalized Maxwellian distributions. The final plasma configuration is related to the initial gas distribution by the introduction of appropriate functional constraints. Qualitative aspects of the solution are investigated and physical properties of the system are pointed out. In particular, the admitted functional dependences of the fluid fields carried by the corresponding equilibrium distributions are determined. Then, the plasma is proved to violate the condition of quasi-neutrality, implying a net charge separation between ions and electrons. This result is shown to be independent of the precise realization of the plasma distribution function, while a physical mechanism able to support a non-neutral equilibrium state is proposed.

Acoustic scattering on spheroidal shapes near boundaries

Science.gov (United States)

Miloh, Touvia

2016-11-01

A new expression for the Lamé product of prolate spheroidal wave functions is presented in terms of a distribution of multipoles along the axis of the spheroid between its foci (generalizing a corresponding theorem for spheroidal harmonics). Such an "ultimate" singularity system can be effectively used for solving various linear boundary-value problems governed by the Helmholtz equation involving prolate spheroidal bodies near planar or other boundaries. The general methodology is formally demonstrated for the axisymmetric acoustic scattering problem of a rigid (hard) spheroid placed near a hard/soft wall or inside a cylindrical duct under an axial incidence of a plane acoustic wave.

Importance of Plasma Response to Non-axisymmetric Perturbations in Tokamaks

International Nuclear Information System (INIS)

Park, Jong-kyu; Boozer, Allen H.; Menard, Jonathan E.; Garofalo, Andrea M.; Schaffer, Michael J.; Hawryluk, Richard J.; Kaye, Stanley M.; Gerhardt, Stefan P.; Sabbagh, Steve A. and the NSTX Team

2009-01-01

Tokamaks are sensitive to deviations from axisymmetry as small as (delta)B/B 0 ∼ 10 -4 . These non-axisymmetric perturbations greatly modify plasma confinement and performance by either destroying magnetic surfaces with subsequent locking or deforming magnetic surfaces with associated non-ambipolar transport. The Ideal Perturbed Equilibrium Code (IPEC) calculates ideal perturbed equilibria and provides important basis for understanding the sensitivity of tokamak plasmas to perturbations. IPEC calculations indicate that the ideal plasma response, or equivalently the effect by ideally perturbed plasma currents, is essential to explain locking experiments on National Spherical Torus eXperiment (NSTX) and DIII-D. The ideal plasma response is also important for Neoclassical Toroidal Viscosity (NTV) in non-ambipolar transport. The consistency between NTV theory and magnetic braking experiments on NSTX and DIII-D can be improved when the variation in the field strength in IPEC is coupled with generalized NTV theory. These plasma response effects will be compared with the previous vacuum superpositions to illustrate the importance. However, plasma response based on ideal perturbed equilibria is still not sufficiently accurate to predict the details of NTV transport, and can be inconsistent when currents associated with a toroidal torque become comparable to ideal perturbed currents

New Evidence That Nonlinear Source-Filter Coupling Affects Harmonic Intensity and fo Stability During Instances of Harmonics Crossing Formants.

Science.gov (United States)

Maxfield, Lynn; Palaparthi, Anil; Titze, Ingo

2017-03-01

The traditional source-filter theory of voice production describes a linear relationship between the source (glottal flow pulse) and the filter (vocal tract). Such a linear relationship does not allow for nor explain how changes in the filter may impact the stability and regularity of the source. The objective of this experiment was to examine what effect unpredictable changes to vocal tract dimensions could have on fo stability and individual harmonic intensities in situations in which low frequency harmonics cross formants in a fundamental frequency glide. To determine these effects, eight human subjects (five male, three female) were recorded producing fo glides while their vocal tracts were artificially lengthened by a section of vinyl tubing inserted into the mouth. It was hypothesized that if the source and filter operated as a purely linear system, harmonic intensities would increase and decrease at nearly the same rates as they passed through a formant bandwidth, resulting in a relatively symmetric peak on an intensity-time contour. Additionally, fo stability should not be predictably perturbed by formant/harmonic crossings in a linear system. Acoustic analysis of these recordings, however, revealed that harmonic intensity peaks were asymmetric in 76% of cases, and that 85% of fo instabilities aligned with a crossing of one of the first four harmonics with the first three formants. These results provide further evidence that nonlinear dynamics in the source-filter relationship can impact fo stability as well as harmonic intensities as harmonics cross through formant bandwidths. Copyright © 2017 The Voice Foundation. Published by Elsevier Inc. All rights reserved.

Theoretical description of high-order harmonic generation in solids

International Nuclear Information System (INIS)

Kemper, A F; Moritz, B; Devereaux, T P; Freericks, J K

2013-01-01

We consider several aspects of high-order harmonic generation in solids: the effects of elastic and inelastic scattering, varying pulse characteristics and inclusion of material-specific parameters through a realistic band structure. We reproduce many observed characteristics of high harmonic generation experiments in solids including the formation of only odd harmonics in inversion-symmetric materials, and the nonlinear formation of high harmonics with increasing field. We find that the harmonic spectra are fairly robust against elastic and inelastic scattering. Furthermore, we find that the pulse characteristics can play an important role in determining the harmonic spectra. (paper)

The Virasoro algebra from harmonic superspace

International Nuclear Information System (INIS)

Saidi, E.H.; Zakkari, M.

1990-08-01

Using harmonic superspace techniques, we construct a new field realization of the Virasoro algebra. The main conformal objects are U(1) Cartan tensors instead of the U(1) Lorentz ones. The new conformal model, which admits moreover a d=2 (4,0) global supersymmetry is constructed out of the infinitely relaxed HST and FS hypermultiplets. The conformal current T 4+ together with the harmonic superspace OPE rules are given. The Virasoro algebra and the harmonic superspace Schwarzian derivative S 4+ are also derived. (author). 14 refs

RAXBOD- INVISCID TRANSONIC FLOW OVER AXISYMMETRIC BODIES

Science.gov (United States)

Keller, J. D.

1994-01-01

The problem of axisymmetric transonic flow is of interest not only because of the practical application to missile and launch vehicle aerodynamics, but also because of its relation to fully three-dimensional flow in terms of the area rule. The RAXBOD computer program was developed for the analysis of steady, inviscid, irrotational, transonic flow over axisymmetric bodies in free air. RAXBOD uses a finite-difference relaxation method to numerically solve the exact formulation of the disturbance velocity potential with exact surface boundary conditions. Agreement with available experimental results has been good in cases where viscous effects and wind-tunnel wall interference are not important. The governing second-order partial differential equation describing the flow potential is replaced by a system of finite difference equations, including Jameson's "rotated" difference scheme at supersonic points. A stretching is applied to both the normal and tangential coordinates such that the infinite physical space is mapped onto a finite computational space. The boundary condition at infinity can be applied directly and there is no need for an asymptotic far-field solution. The system of finite difference equations is solved by a column relaxation method. In order to obtain both rapid convergence and any desired resolution, the relaxation is performed iteratively on successively refined grids. Input to RAXBOD consists of a description of the body geometry, the free stream conditions, and the desired resolution control parameters. Output from RAXBOD includes computed geometric parameters in the normal and tangential directions, iteration history information, drag coefficients, flow field data in the computational plane, and coordinates of the sonic line. This program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6600 computer with an overlayed central memory requirement of approximately 40K (octal) of 60 bit words. Optional plotted output

Voltage harmonic elimination with RLC based interface smoothing filter

International Nuclear Information System (INIS)

Chandrasekaran, K; Ramachandaramurthy, V K

2015-01-01

A method is proposed for designing a Dynamic Voltage Restorer (DVR) with RLC interface smoothing filter. The RLC filter connected between the IGBT based Voltage Source Inverter (VSI) is attempted to eliminate voltage harmonics in the busbar voltage and switching harmonics from VSI by producing a PWM controlled harmonic voltage. In this method, the DVR or series active filter produces PWM voltage that cancels the existing harmonic voltage due to any harmonic voltage source. The proposed method is valid for any distorted busbar voltage. The operating VSI handles no active power but only harmonic power. The DVR is able to suppress the lower order switching harmonics generated by the IGBT based VSI. Good dynamic and transient results obtained. The Total Harmonic Distortion (THD) is minimized to zero at the sensitive load end. Digital simulations are carried out using PSCAD/EMTDC to validate the performance of RLC filter. Simulated results are presented. (paper)

Three-dimensional harmonic control of a nuclear reactor

International Nuclear Information System (INIS)

Potapenko, P.T.

1989-01-01

Algorithms for neutron flux control based on harmonic three-dimensional core are considered. The essence of the considered approach includes determination of harmonics amplitudes by signals self-powered detectors placed in reactor channels and reconstruction of neutron field distribution over the reactor core volume using the data obtained. Neutron field harmonic control is shown to be reduced to independent measurement and calculation of height harmonics in channels using techniques developed for channel power control

On the impact of a concave nosed axisymmetric body on a free surface

NARCIS (Netherlands)

Mathai, Varghese; Govardhan, R.N.; Arakeri, V.H.

2015-01-01

We report on an experimental study of the vertical impact of a concave nosed axisymmetric body on a free surface. Previous studies have shown that bodies with a convex nose, like a sphere, produce a well defined splash with a relatively large cavity behind the model. In contrast, we find that with a

Self-driven particles in linear flows and trapped in a harmonic potential

Science.gov (United States)

Sandoval, Mario; Hidalgo-Gonzalez, Julio C.; Jimenez-Aquino, Jose I.

2018-03-01

We present analytical expressions for the mean-square displacement of self-driven particles in general linear flows and trapped in a harmonic potential. The general expressions are applied to three types of linear flows, namely, shear flow, solid-body rotation flow, and extensional flow. By using Brownian dynamics simulations, the effect of trapping and external linear flows on the particles' distribution is also elucidated. These simulations also enabled us to validate our theoretical results.

Seeding High Gain Harmonic Generation with Laser Harmonics produced in Gases

CERN Document Server

Lambert, Guillaume; Couprie, Marie Emmanuelle; Garzella, David; Doria, Andrea; Giannessi, Luca; Hara, Toru; Kitamura, Hideo; Shintake, Tsumoru

2004-01-01

Free electron Lasers employing High Gain Harmonic generation (HGHG) schemes are very promising coherent ligth sources for the soft X-ray regime. They offer both transverse and longitudinal coherence, while Self Amplified Spontaneous Emission schemes have a longitudinal coherence limited. We propose here to seed HGHG with high harmonics produced by a Ti:Sa femtosecond laser focused on a gas jet, tuneable in the 100-10 nm spectral region. Specifities concerning the implementation of this particular laser source as a seed for HGHG are investigated. Semi analytical , numerical 1D and 3D calculations are given, for the cases of the SCSS, SPARC and ARC-EN-CIEL projects.

Recent progress of below-threshold harmonic generation

International Nuclear Information System (INIS)

Xiong, Wei-Hao; Peng, Liang-You; Gong, Qihuang

2017-01-01

The harmonics generated from the interaction of a strong laser field with atoms and molecules in the gas phase can be applied as coherent light sources and detecting techniques for structures and dynamics in matter. In the last three decades, the most prevailing experimental and theoretical studies have been focused on the high-order harmonic generation due to its applications in attosecond science. However, low-order harmonics near the ionization threshold of the target have been less explored, partially because the spectrum in this region is more complicated from both the theoretical and experimental point of view. After several pioneering investigations in the mid 1990s, near threshold harmonics (NTHs) begun to draw a great attention again because of the development of high repetition rate cavity enhanced harmonics about 10 years ago. Very recently, NTHs have attracted a lot of experimental and theoretical studies due to their potential applications as light sources and complicated mechanisms. In this topical review, we will summarize the progress of NTHs, including the early and recent experimental measurements in atoms and molecules, as well as the relevant theoretical explorations of these harmonics. (topical review)

Harmonic generation with a dual frequency pulse.

Science.gov (United States)

Keravnou, Christina P; Averkiou, Michalakis A

2014-05-01

Nonlinear imaging was implemented in commercial ultrasound systems over the last 15 years offering major advantages in many clinical applications. In this work, pulsing schemes coupled with a dual frequency pulse are presented. The pulsing schemes considered were pulse inversion, power modulation, and power modulated pulse inversion. The pulse contains a fundamental frequency f and a specified amount of its second harmonic 2f. The advantages and limitations of this method were evaluated with both acoustic measurements of harmonic generation and theoretical simulations based on the KZK equation. The use of two frequencies in a pulse results in the generation of the sum and difference frequency components in addition to the other harmonic components. While with single frequency pulses, only power modulation and power modulated pulse inversion contained odd harmonic components, with the dual frequency pulse, pulse inversion now also contains odd harmonic components.

Whether diffusion in axisymmetric confinement systems is intrinsically ambipolar

International Nuclear Information System (INIS)

Kovrizhnykh, L.M.

1997-01-01

The problem of diffusion ambipolarity in axisymmetric magnetic systems is analyzed. The question is discussed of whether diffusion is intrinsically ambipolar (and if so, then in which particular cases) or the ambipolarity constraint is an additional independent condition, which does not follow from the equations of motion and, hence, contains new information. It is shown that the second assertion is correct: strictly speaking, diffusion can never be intrinsically ambipolar, and, in the presence of several different mechanisms causing electron and ion losses across the magnetic field, only the total fluxes, but not the partial ones, should satisfy the ambipolarity constraint. (UK)

Harmonic and geometric analysis

CERN Document Server

Citti, Giovanna; Pérez, Carlos; Sarti, Alessandro; Zhong, Xiao

2015-01-01

This book presents an expanded version of four series of lectures delivered by the authors at the CRM. Harmonic analysis, understood in a broad sense, has a very wide interplay with partial differential equations and in particular with the theory of quasiconformal mappings and its applications. Some areas in which real analysis has been extremely influential are PDE's and geometric analysis. Their foundations and subsequent developments made extensive use of the Calderón–Zygmund theory, especially the Lp inequalities for Calderón–Zygmund operators (Beurling transform and Riesz transform, among others) and the theory of Muckenhoupt weights.  The first chapter is an application of harmonic analysis and the Heisenberg group to understanding human vision, while the second and third chapters cover some of the main topics on linear and multilinear harmonic analysis. The last serves as a comprehensive introduction to a deep result from De Giorgi, Moser and Nash on the regularity of elliptic partial differen...

Harmonization versus Mutual Recognition

DEFF Research Database (Denmark)

Jørgensen, Jan Guldager; Schröder, Philipp

The present paper examines trade liberalization driven by the coordination of product standards. For oligopolistic firms situated in separate markets that are initially sheltered by national standards, mutual recognition of standards implies entry and reduced profits at home paired with the oppor......The present paper examines trade liberalization driven by the coordination of product standards. For oligopolistic firms situated in separate markets that are initially sheltered by national standards, mutual recognition of standards implies entry and reduced profits at home paired...... countries and three firms, where firms first lobby for the policy coordination regime (harmonization versus mutual recognition), and subsequently, in case of harmonization, the global standard is auctioned among the firms. We discuss welfare effects and conclude with policy implications. In particular......, harmonized standards may fail to harvest the full pro-competitive effects from trade liberalization compared to mutual recognition; moreover, the issue is most pronounced in markets featuring price competition....

[Harmonization of TSH Measurements.

Science.gov (United States)

Takeoka, Keiko; Hidaka, Yoh; Hishinuma, Akira; Ikeda, Katsuyoshi; Okubo, Shigeo; Tsuchiya, Tatsuyuki; Hashiguchi, Teruto; Furuta, Koh; Hotta, Taeko; Matsushita, Kazuyuki; Matsumoto, Hiroyuki; Murakami, Masami; Maekawa, Masato

2016-05-01

The measured concentration of thyroid stimulating hormone (TSH) differs depending on the reagents used. Harmonization of TSH is crucial because the decision limits are described in current clinical practice guide- lines as absolute values, e.g. 2.5 mIU/L in early pregnancy. In this study, we tried to harmonize the report- ed concentrations of TSH using the all-procedure trimmed mean. TSH was measured in 146 serum samples, with values ranging from 0.01 to 18.8 mIU/L, using 4 immunoassays. The concentration of TSH was highest with E test TOSOH and lowest with LUMIPULSE. The concentrations with each reagent were recalculated with the following formulas: E test TOSOH 0.855x-0.014; ECLusys 0.993x+0.079; ARCHITECT 1.041x- 0.010; and LUMIPULSE 1.096x-0.015. Recalculation eliminated the between-assay discrepancy. These formulas may be used until harmonization of TSH is achieved by the International Federation of Clinical Chemistry and Laboratory Medicine (IFCC).

Two-color phase control of high-order harmonic generation in intense laser fields

International Nuclear Information System (INIS)

Telnov, D.A.; Wang, J.; Chu, S.

1995-01-01

We present a time-independent generalized Floquet approach for nonperturbative treatment of high-order harmonic generation (HG) in intense onea (i) determination of the complex quasienergy eigenvalue and eigenfunction by means of the non-Hermitian Floquet formalism, wherein the Floquet Hamiltonian is discretized by the complex-scaling generalized pseudospectral technique [Wang, Chu, and Laughlin, Phys. Rev. A 50, 3208 (1994)], and (ii) calculation of the HG rates based on the approach that implies the classical treatment of the electromagnetic field and quantal treatment of the atom. The method is applied to the nonperturbative study of HG by the hydrogen atom in strong laser fields with the fundamental frequencies 532 and 775 nm and their third harmonics. The results show a strong dependence on the relative phase δ between the fundamental frequency field and its harmonic. For the intensities used in calculations (1x10 13 and 5x10 13 W/cm 2 for the fundamental frequency 532 nm and 1x10 13 and 3x10 13 W/cm 2 for the fundamental frequency 775 nm, the harmonic intensity being 10 and 100 times weaker), the total photon emission rate has its maximum at δ=0 and minimum at δ=π. However, this tendency, while valid for the first several HG peaks, is reversed for the higher HG peaks. The HG spectrum for δ=π is broader and the peak heights decrease more slowly compared to the case of δ=0. These results have their analog in the multiphoton above-threshold detachment study performed recently for H - ions [Telnov, Wang, and Chu, Phys. Rev. A 51, 4797 (1995)

Characteristics of premixed flames stabilized in an axisymmetric curved-wall jet burner with tip modification

KAUST Repository

Kim, Daejoong; Gil, Y. S.; Chung, TaeWon; Chung, Suk-Ho

2009-01-01

The stabilization characteristics of premixed flames in an axisymmetric curved-wall jet burner have been experimentally investigated. This burner utilized the Coanda effect on top of a burner tip. The initially spherical burner tip was modified to a

On Harmonizing the External Economic Policy among the Countries of the Common Economic Space: Problems and Prospects

OpenAIRE

Elena S. Ratushnyak

2014-01-01

The article provides the tax systems of the countries of the customs union of Belarus, Kazakhstan and Russia, reveals the differences and identifies the need for harmonization and convergence of the structures and principles of taxation, the general tax reforms and harmonization of fiscal policies of member countries in order to increase the investment attractiveness and competitiveness of the national economies in the process of development and integration. The comparison of the existing tax...

From x-ray telescopes to neutron scattering: Using axisymmetric mirrors to focus a neutron beam

International Nuclear Information System (INIS)

Khaykovich, B.; Gubarev, M.V.; Bagdasarova, Y.; Ramsey, B.D.; Moncton, D.E.

2011-01-01

We demonstrate neutron beam focusing by axisymmetric mirror systems based on a pair of mirrors consisting of a confocal ellipsoid and hyperboloid. Such a system, known as a Wolter mirror configuration, is commonly used in X-ray telescopes. The axisymmetric Wolter geometry allows nesting of several mirror pairs to increase collection efficiency. We implemented a system containing four nested Ni mirror pairs, which was tested by the focusing of a polychromatic neutron beam at the MIT Reactor. In addition, we have carried out extensive ray-tracing simulations of the mirrors and their performance in different situations. The major advantages of the Wolter mirrors are nesting for large angular collection and aberration-free performance. We discuss how these advantages can be utilized to benefit various neutron scattering methods, such as imaging, SANS, and time-of-flight spectroscopy.

Axisymmetric Tornado Simulations with a Semi-Slip Boundary

Directory of Open Access Journals (Sweden)

Brian H. Fiedler

2017-12-01

Full Text Available The structure of natural tornadoes and simulated analogs are sensitive to the lower boundary condition for friction. Three-dimensional numerical simulations of storms require a choice for turbulence parameterizations and resolution of wind near the lower boundary. This article explores some of the consequences of choices of a surface drag coefficient on the structure of a mature simulated tornado, using a conventional axisymmetric model. The surface drag parameterization is explored over the range of the semi-slip condition, including the extremes of no-slip and free-slip. A moderate semi-slip condition allows for an extreme pressure deficit, but without the unrealistic vortex breakdown of the no-slip condition.

Harmonic Mitigation Methods in Large Offshore Wind Power Plants

DEFF Research Database (Denmark)

Kocewiak, Łukasz Hubert; Chaudhary, Sanjay; Hesselbæk, Bo

2013-01-01

Various sources of harmonic problems in large wind power plants (WPPs) and optimized harmonic mitigation methods are presented in this paper. The harmonic problems such as sources of harmonic emission and amplification as well as harmonic stability are identified. Also modern preventive...... and remedial harmonic mitigation methods in terms of passive and active filtering are described. It is shown that WPP components such as long HVAC cables and park transformers can introduce significant low-frequency resonances which can affect wind turbine control system operation and overall WPP stability...... as well as amplification of harmonic distortion. It is underlined that there is a potential in terms of active filtering in modern grid-side converters in e.g. wind turbines, STATCOMs or HVDC stations utilized in modern large WPPs. It is also emphasized that the grid-side converter controller should...

Generalized dielectric permittivity tensor

International Nuclear Information System (INIS)

Borzdov, G.N.; Barkovskii, L.M.; Fedorov, F.I.

1986-01-01

The authors deal with the question of what is to be done with the formalism of the electrodynamics of dispersive media based on the introduction of dielectric-permittivity tensors for purely harmonic fields when Voigt waves and waves of more general form exist. An attempt is made to broaden and generalize the formalism to take into account dispersion of waves of the given type. In dispersive media, the polarization, magnetization, and conduction current-density vectors of point and time are determined by the values of the electromagnetic field vectors in the vicinity of this point (spatial dispersion) in the preceding instants of time (time dispersion). The dielectric-permittivity tensor and other tensors of electrodynamic parameters of the medium are introduced in terms of a set of evolution operators and not the set of harmonic function. It is noted that a magnetic-permeability tensor and an elastic-modulus tensor may be introduced for an acoustic field in dispersive anisotropic media with coupling equations of general form

MHD stability analysis of axisymmetric surface current model tokamaks close to the spheromak regime

International Nuclear Information System (INIS)

Honma, Toshihisa; Kaji, Ikuo; Fukai, Ichiro; Kito, Masafumi.

1984-01-01

In the toroidal coordinates, a stability analysis is presented for very low-aspect-ratio tokamaks with circular cross section which is described by a surface current model (SCM) of axisymmetric equilibria. The energy principle determining the stability of plasma is treated without any expansion of aspect ratio. Numerical results show that, owing to the occurrence of the non-axisymmetric (n=1) unstable modes, there exists no MHD-stable ideal SCM spheromak characterized by zero external toroidal vacuum field. Instead, a stable spheromak-type plasma which comes to the ideal SCM spheromak is provided by the configuration with a very weak external toroidal field. Close to the spheromak regime (1.0 1 aspect ratio< = 1.1), the minimum safety factor and the critical β-values increase mo notonically with aspect ratio decreasing from a large value, and curves of βsub(p) versus β in the marginal stability approach to an ideal SCM spheromak line βsub(p)=β. (author)

High-order harmonic conversion efficiency in helium

International Nuclear Information System (INIS)

Crane, J.K.

1992-01-01

Calculated results are presented for the energy, number of photons, and conversion efficiency for high-order harmonic generation in helium. The results show the maximum values that we should expect to achieve experimentally with our current apparatus and the important parameters for scaling this source to higher output. In the desired operating regime where the coherence length, given by L coh =πb/(q-1), is greater than the gas column length, l, the harmonic output can be summarized by a single equation: N q =[(π z n z b 3 τ q |d q | z )/4h]{(p/q)(2l/b) z }. N q - numbers of photons of q-th harmonic; n - atom density; b - laser confocal parameter; τ q - pulse width of harmonic radiation; q - harmonic order; p - effective order of nonlinearity. (Note the term in brackets, the phase-matching function, has been separated from the rest of the expression in order to be consistent with the relevant literature)

Harmonic calculation software for industrial applications with ASDs

DEFF Research Database (Denmark)

Blaabjerg, Frede; Asiminoaei, Lucian; Hansen, Steffan

2007-01-01

This article describes the evaluation of new harmonic calculation software. By using a combination of a prestored database and new interpolation techniques the software can provide the harmonic data on real applications of a very fast speed. The harmonic results obtained with this software have a...

Audibility of high harmonics in a periodic pulse

NARCIS (Netherlands)

Duifhuis, H.

1970-01-01

A periodic pulse consisting of sufficiently narrow pulses has a frequency spectrum which contains all harmonics with equal amplitude. Owing to the limited resolving power of the hearing organ, only the low harmonics can be perceived separately. The high harmonics are heard together as one complex

Non-unique monopole oscillations of harmonically confined Yukawa systems

Science.gov (United States)

Ducatman, Samuel; Henning, Christian; Kaehlert, Hanno; Bonitz, Michael

2008-11-01

Recently it was shown that the Breathing Mode (BM), the mode of uniform radial expansion and contraction, which is well known from harmonically confined Coulomb systems [1], does not exist in general for other systems [2]. As a consequence the monopole oscillation (MO), the radial collective excitation, is not unique, but there are several MO with different frequencies. Within this work we show simulation results of those monopole oscillations of 2-dimensional harmonically confined Yukawa systems, which are known from, e.g., dusty plasma crystals [3,4]. We present the corresponding spectrum of the particle motion, including analysis of the frequencies found, and compare with theoretical investigations.[1] D.H.E. Dubin and J.P. Schiffer, Phys. Rev. E 53, 5249 (1996)[2] C. Henning at al., accepted for publication in Phys. Rev. Lett. (2008)[3] A. Melzer et al., Phys. Rev. Lett. 87, 115002 (2001)[4] M. Bonitz et al., Phys. Rev. Lett. 96, 075001 (2006)

Enhancement of harmonic generation using a two section undulator

International Nuclear Information System (INIS)

Prazeres, R.; Glotin, F.; Jaroszynski, D.A.; Ortega, J.M.; Rippon, C.

1999-01-01

Enhancement of the 2nd and 3rd harmonic of the wavelength of a Free-Electron Laser (FEL) has been measured when a single electron beam is crossing a two-section undulator. To produce the harmonic radiation enhancement, the undulator is arranged so that the resonance wavelength of the 2nd undulator (downstream) matches a harmonic of the 1st undulator (upstream). Both the fundamental and the harmonic optical fields evolve in the same optical cavity and are coupled out with different extraction efficiency, through a hole in one of the cavity mirrors. We present measurements that show that the optical power at the 2nd and 3rd harmonic can be enhanced, by about one order of magnitude, in two configurations: when the resonance wavelength of the 2nd undulator matches the harmonic of 1st one (harmonic configuration), or when the gap of the 2nd undulator is slightly larger than first one (step-tapered configuration). We examine the dependence of the harmonic power on the gap of the 2nd undulator. This fundamental/harmonic mode of operation of the FEL may have useful applications in the production of coherent X-ray and VUV radiation, a spectral range where high reflectivity optical cavity mirrors are difficult or impossible to manufacture

Effects of harmonic roving on pitch discrimination

DEFF Research Database (Denmark)

Santurette, Sébastien; de Kérangal, Mathilde le Gal; Joshi, Suyash Narendra

2015-01-01

Performance in pitch discrimination tasks is limited by variability intrinsic to listeners which may arise from peripheral auditory coding limitations or more central noise sources. The present study aimed at quantifying such “internal noise” by estimating the amount of harmonic roving required...... to impair pitch discrimination performance. Fundamental-frequency difference limens (F0DLs) were obtained in normal-hearing listeners with and without musical training for complex tones filtered between 1.5 and 3.5 kHz with F0s of 300 Hz (resolved harmonics) and 75 Hz (unresolved harmonics). The harmonicity...... that could be used to quantify the internal noise and provide strong constraints for physiologically inspired models of pitch perception....

Studies of harmonic generation in free electron lasers

International Nuclear Information System (INIS)

Goldammer, K.

2007-01-01

Nonlinear harmonic generation is one of the most interesting aspects of Free Electron Lasers under study today. It provides for coherent, high intensity radiation at higher harmonics of the FEL resonant frequency. The sources, numerical simulation and applications of harmonic radiation in cascaded High Gain Harmonic Generation FELs were the subject of this thesis. Harmonic emission in FELs originates from harmonic microbunching of the particles and the particular electron trajectory during FEL interaction. Numerical FEL simulation codes model these analytical equations and predict the performance of Free Electron Lasers with good accuracy. This thesis has relied heavily upon the FEL simulation code Genesis 1.3 which has been upgraded in the framework of this thesis to compute harmonic generation in a self-consistent manner. Tests against analytical predictions suggest that the harmonic power levels as well as harmonic gain lengths are simulated correctly. A benchmark with the FEL simulation code GINGER yields excellent agreement of the harmonic saturation length and saturation power. The new version of the simulation code Genesis was also tested against measurements from the VUV-FEL FLASH at DESY. The spectral power distributions of fundamental and third harmonic radiation were recorded at 25.9 nm and 8.6 nm, respectively. The relative bandwidths (FWHM) were in the range of 2 % for both the fundamental as well as the third harmonic, which was accurately reproduced by time-dependent simulations with Genesis. The new code was also used to propose and evaluate a new design for the BESSY Soft X-Ray FEL, a cascaded High Gain Harmonic Generation FEL proposed by BESSY in Berlin. The original design for the BESSY High Energy FEL line requires four HGHG stages to convert the initial seed laser wavelength of 297.5 nm down to 1.24 nm. A new scheme is proposed that makes use of fifth harmonic radiation from the first stage and reduces the number of HGHG stages to three. It

Studies of harmonic generation in free electron lasers

Energy Technology Data Exchange (ETDEWEB)

Goldammer, K.

2007-11-12

Nonlinear harmonic generation is one of the most interesting aspects of Free Electron Lasers under study today. It provides for coherent, high intensity radiation at higher harmonics of the FEL resonant frequency. The sources, numerical simulation and applications of harmonic radiation in cascaded High Gain Harmonic Generation FELs were the subject of this thesis. Harmonic emission in FELs originates from harmonic microbunching of the particles and the particular electron trajectory during FEL interaction. Numerical FEL simulation codes model these analytical equations and predict the performance of Free Electron Lasers with good accuracy. This thesis has relied heavily upon the FEL simulation code Genesis 1.3 which has been upgraded in the framework of this thesis to compute harmonic generation in a self-consistent manner. Tests against analytical predictions suggest that the harmonic power levels as well as harmonic gain lengths are simulated correctly. A benchmark with the FEL simulation code GINGER yields excellent agreement of the harmonic saturation length and saturation power. The new version of the simulation code Genesis was also tested against measurements from the VUV-FEL FLASH at DESY. The spectral power distributions of fundamental and third harmonic radiation were recorded at 25.9 nm and 8.6 nm, respectively. The relative bandwidths (FWHM) were in the range of 2 % for both the fundamental as well as the third harmonic, which was accurately reproduced by time-dependent simulations with Genesis. The new code was also used to propose and evaluate a new design for the BESSY Soft X-Ray FEL, a cascaded High Gain Harmonic Generation FEL proposed by BESSY in Berlin. The original design for the BESSY High Energy FEL line requires four HGHG stages to convert the initial seed laser wavelength of 297.5 nm down to 1.24 nm. A new scheme is proposed that makes use of fifth harmonic radiation from the first stage and reduces the number of HGHG stages to three. It

Analyzing correlation functions with tesseral and Cartesian spherical harmonics

International Nuclear Information System (INIS)

Danielewicz, Pawel; Pratt, Scott

2007-01-01

The dependence of interparticle correlations on the orientation of particle relative momentum can yield unique information on the space-time features of emission in reactions with multiparticle final states. In the present paper, the benefits of a representation and analysis of the three-dimensional correlation information in terms of surface spherical harmonics is presented. The harmonics include the standard complex tesseral harmonics and the real Cartesian harmonics. Mathematical properties of the lesser known Cartesian harmonics are illuminated. The physical content of different angular harmonic components in a correlation is described. The resolving power of different final-state effects with regard to determining angular features of emission regions is investigated. The considered final-state effects include identity interference, strong interactions, and Coulomb interactions. The correlation analysis in terms of spherical harmonics is illustrated with the cases of Gaussian and blast-wave sources for proton-charged meson and baryon-baryon pairs

Optimal Selective Harmonic Control for Power Harmonics Mitigation

DEFF Research Database (Denmark)

Zhou, Keliang; Yang, Yongheng; Blaabjerg, Frede

2015-01-01

of power harmonics. The proposed optimal SHC is of hybrid structure: all recursive SHC modules with weighted gains are connected in parallel. It bridges the real “nk+-m order RC” and the complex “parallel structure RC”. Compared to other IMP based control solutions, it offers an optimal trade-off among...

Azimuthal anisotropy: The higher harmonics

International Nuclear Information System (INIS)

Poskanzer, Arthur M.; STAR Collaboration

2004-01-01

We report the first observations of the fourth harmonic (v 4 ) in the azimuthal distribution of particles at RHIC. The measurement was done taking advantage of the large elliptic flow generated at RHIC. The integrated v 4 is about a factor of 10 smaller than v 2 . For the sixth (v 6 ) and eighth (v 8 ) harmonics upper limits on the magnitudes are reported

Accurate calculation of high harmonics generated by relativistic Thomson scattering

International Nuclear Information System (INIS)

Popa, Alexandru

2008-01-01

The recent emergence of the field of ultraintense laser pulses, corresponding to beam intensities higher than 10 18 W cm -2 , brings about the problem of the high harmonic generation (HHG) by the relativistic Thomson scattering of the electromagnetic radiation by free electrons. Starting from the equations of the relativistic motion of the electron in the electromagnetic field, we give an exact solution of this problem. Taking into account the Lienard-Wiechert equations, we obtain a periodic scattered electromagnetic field. Without loss of generality, the solution is strongly simplified by observing that the electromagnetic field is always normal to the direction electron-detector. The Fourier series expansion of this field leads to accurate expressions of the high harmonics generated by the Thomson scattering. Our calculations lead to a discrete HHG spectrum, whose shape and angular distribution are in agreement with the experimental data from the literature. Since no approximations were made, our approach is also valid in the ultrarelativistic regime, corresponding to intensities higher than 10 23 W cm -2 , where it predicts a strong increase of the HHG intensities and of the order of harmonics. In this domain, the nonlinear Thomson scattering could be an efficient source of hard x-rays

An Improved Second-Order Generalized Integrator Based Quadrature Signal Generator

DEFF Research Database (Denmark)

Xin, Zhen; Wang, Xiongfei; Qin, Zian

2016-01-01

The second-order generalized integrator based quadrature signal generator (SOGI-QSG) is able to produce in-quadrature signals for many applications, such as frequency estimation, grid synchronization, and harmonic extraction. However, the SOGI-QSG is sensitive to input dc and harmonic components...

Cold-Fluid Equilibrium of a Large-Aspect-Ratio Ellipse-Shaped Charged-Particle Beam in a Non-Axisymmetric Periodic Permanent Magnet Focusing Field

CERN Document Server

Zhou, Jing; Chen Chi Ping

2005-01-01

A new class of equilibrium is discovered for a large-aspect-ratio ellipse-shaped charged-particle beam in a non-axisymmetric periodic permanent magnet focusing field. A paraxial cold-fluid model is employed to derive the equilibrium flow properties and generalized envelope equations with negligibly small emittance. A periodic beam equilibrium solution is obtained numerically from the generalized envelope equations. It is shown that the beam edges are well confined in both transverse directions, and that the equilibrium beam exhibits a small-angle periodic wobble as it propagates. A two-dimensional particle-in-cell (PIC) code, PFB2D, is used to verify the theoretical predictions in the paraxial limit, and to establish validity under non-paraxial situations and the influence of the conductor walls of the beam tunnel.

Optical klystron and harmonic generation free electron laser

Directory of Open Access Journals (Sweden)

Qika Jia

2005-06-01

Full Text Available The optical field evolution of an optical klystron free electron laser is analytically described for both low gain and high gain cases. The harmonic optical klystron (HOK in which the second undulator is resonant on the higher harmonic of the first undulator is analyzed as a harmonic amplifier. The optical field evolution equation of the HOK is derived analytically for both the CHG mode (coherent harmonic generation, the quadratic gain regime and the HGHG mode (high gain harmonic generation, the exponential gain regime, the effects of energy spread, energy modulation, and dispersion in the whole process are taken into account. The linear theory is given and discussed for the HGHG mode. The analytical formula is given for the CHG mode.

Isogeometric analysis and harmonic stator-rotor coupling for simulating electric machines

Science.gov (United States)

Bontinck, Zeger; Corno, Jacopo; Schöps, Sebastian; De Gersem, Herbert

2018-06-01

This work proposes Isogeometric Analysis as an alternative to classical finite elements for simulating electric machines. Through the spline-based Isogeometric discretization it is possible to parametrize the circular arcs exactly, thereby avoiding any geometrical error in the representation of the air gap where a high accuracy is mandatory. To increase the generality of the method, and to allow rotation, the rotor and the stator computational domains are constructed independently as multipatch entities. The two subdomains are then coupled using harmonic basis functions at the interface which gives rise to a saddle-point problem. The properties of Isogeometric Analysis combined with harmonic stator-rotor coupling are presented. The results and performance of the new approach are compared to the ones for a classical finite element method using a permanent magnet synchronous machine as an example.

Numerical analysis of laser ablation using the axisymmetric two-temperature model

Science.gov (United States)

Dziatkiewicz, Jolanta; Majchrzak, Ewa

2018-01-01

Laser ablation of the axisymmetric micro-domain is analyzed. To describe the thermal processes occurring in the micro-domain the two-temperature hyperbolic model supplemented by the boundary and initial conditions is used. This model takes into account the phase changes of material (solid-liquid and liquid-vapour) and the ablation process. At the stage of numerical computations the finite difference method with staggered grid is used. In the final part the results of computations are shown.

Harmonic superspaces of extended supersymmetry

International Nuclear Information System (INIS)

Ivanov, E.; Kalitzin, S.; Nguyen Ai Viet; Ogievetsky, V.

1984-01-01

The main technical apparatus of the harmonic superspace approach to extended SUSY, the calculus of harmonic variables on homogeneous spaces of the SUSY automorphism groups, is presented in detail for N=2, 3, 4. The basic harmonics for the coset manifolds G/H with G=SU(2), H=U(1); G=SU(3), H=SU(2)xU(1) and H=U(1)xU(1); G=SU(4), H=SU(3)xU(1), H=SU(2)xSU(2)xU(1), H=SU(2)xU(1)xU(1) and H=U(1)xU(1)xU(1); G=USp(2), H=SU(2)xSU(2), H=SU(2)xU(1) and H=U(1)xU(1) are tabulated a number of useful relations among them