Clebsch-Gordan coefficients for symmetric representations of symplectic groups
Method of generating invariants for symplectic groups is formulated. The Clebsch-Gordan coefficients for coupling of symmetric representations D(PO..., O) of groups Sp(2N) were calculated and their symmetry properties were obtained
New information and entropic inequalities for Clebsch-Gordan coefficients
Chernega, V. N.; Manko, O. V.; Manko, V. I.; Seilov, Z.
2016-01-01
The Clebsch-Gordan coefficients of the group SU(2) are shown to satisfy new inequalities. They are obtained using the properties of Shannon and Tsallis entropies. The inequalities associated with the Wigner 3-j symbols are obtained using the relation of Clebsch-Gordan coefficients with probability distributions interpreted either as distributions for composite systems or distributions for noncomposite systems. The new inequalities were found for Hahn polynomials and hypergeometric functions
Clebsch--Gordan Coefficients of the Quaternion Group
Mathar, Richard J.
2010-01-01
The Clebsch--Gordan coefficients of the Kronecker products of the irreducible representations of the Quaternion Group Q8, of the Generalized Quaternion Groups Q16 and Q32, and of the factor group (Q32 X Q32)/{(1,1),(-1,-1)} are computed as eigenvectors of a well-known matrix of triple-products of the irreducible representations.
A simple method for calculating Clebsch-Gordan coefficients
Klink, W H; Wickramasekara, S, E-mail: william-klink@uiowa.ed, E-mail: wickrama@grinnell.ed, E-mail: s-wickram@uiowa.ed [Department of Physics and Astronomy, University of Iowa, Iowa City, IA 52242 (United States)
2010-09-15
This paper presents a simple method for calculating Clebsch-Gordan coefficients for the tensor product of two unitary irreducible representations (UIRs) of the rotation group. The method also works for multiplicity-free irreducible representations appearing in the tensor product of any number of UIRs of the rotation group. The generalization to representations with multiplicity is straightforward and briefly discussed.
Summation free expression for some special Clebsch-Gordan coefficients
The known general formula for the Clebsch-Gordan coefficients of the 3-dimensional rotation group involves one summation which results in explicit summation-free expressions for the coefficients where either one of the angular momenta is the sum of the other two or the magnetic quantum number corresponding to one of the angular momenta takes its maximum value in magnitude. By using very different techniques, explicit expressions for the coefficients 1,0;j2,0|j,0>,2,-1/2|j,0> are also obtained, where the integral or half-integral nature of the j's is indicated by the magnetic quantum number involved. Here the expressions depend upon whether j1+j2+j is an even or an odd integer. For these coefficients, the magnetic quantum numbers involved take their minimum value in magnitude. By using the recursion relation for the coefficients of the form 1,m,j2,-m,|j,0>, we can calculate these coefficients in terms of the above known ones provided we also have the explicit value of the coefficient 1,1;j2,-1|j,0> where j1+j2+j is an odd integer. (The recursion relation for these coefficients in terms of 1,0;j2,0|j,0> becomes a triviality since 1,0;j2,0|j,0> vanishes when j1+j2+j is an odd integer.) Our main purpose in this paper is to give an explicit expression for the coefficients 1,1;j2,-1|j,0> where j1+j2+j is an odd integer. We are able to arrive at our expression by using a complicated transformation between hypergeometric functions which seems to have been neglected so far. For the coefficients where the magnetic quantum numbers have their minimum value in magnitude, this transformed expression becomes summation free and we obtain explicit values of the three already known coefficients and the fourth so far unknown. We believe that further study of this transformation may be useful on its own because it provides a link between very different types of expressions. (author)
Tables of Clebsch-Gordan coefficients adapted to the cubical, tetragonal and digonal double groups
Some basic considerations on the Clebsch-Gordan coefficients adapted to a chain of sub-groups of the universal covering SU2 of the proper rotation group SO3 are reviewed. Extensive tables of Clebsch-Gordan coefficients adapted to a chain isomorphic to SU2 contains O' contains D'4 contains D'2 are presented for consultation. These coefficients are useful in various fields of molecular spectroscopy, particularly in the ligand field theory. The tables listed here constitute an extensive tabulation of coupling coefficients of molecular interest
Structure of the suq(2) quantum algebra and properties of its irreducible representations are considered. Projection operator is constructed as power series of suq(2)-algebra generators. The explicit analytical formula for the q-analogue of Clebsch-Gordan coefficients is derived using this projector. The symmetry properties of these coefficients are discussed. Algebraic tables of coefficients are given. Tensor operators are introduced and Wigner-Eckart theorem is proven
The structure of the quantum algebra suq(2) and the properties of its irreducible representation are considered. The projection operator is constructed as a power series from generators of the suq(2) algebra. The explicit analytical formula for q-analog of Clebsch-Gordan coefficients is derived using this projector. Their symmetry properties are discussed. The algebraic tables of these coefficients are given. The tensor operators are introduced and the Wigner-Eckart theorem is proved. 23 refs.; 4 figs
Schröder, Leif; Schmitz, Christian; Bachert, Peter
2005-05-01
NMR spectra of non-weakly coupled spin systems exhibit asymmetries in line intensities known as "roof effect" in 1D spectroscopy. Due to limited spectral resolution, this effect has not been paid much attention so far in in vivo spectroscopy. But when high-quality spectra are obtained, this effect should be taken into account to explain the quantum-mechanical fine structure of the system. Adenosine 5'-triphosphate (ATP) represents a 31P spin system with multiple line splittings which are caused by J-couplings of medium strength at 1.5 T. We analyzed the ATP roof effect in vivo, especially for the β-ATP multiplet. The intensities of its outer resonances deviate by ca. 12.5% from a symmetrical triplet. As this asymmetry reflects the transition from Paschen-Back to Zeeman effect with total spin that is largely broken up, the Clebsch-Gordan coefficients of the system can be indicated in analogy to the hyperfine structure of hydrogen. Taking the roof effect into account, the χ2 of fitting in vivo ATP resonances is reduced by ca. 9% ( p < 0.005).
Clebsch-Gordan construction of lattice interpolating fields for excited baryons
S. Basak; R. Edwards; G. Fleming; U. Heller; C. Morningstar; D. Richards; I. Sato; S. Wallace
2005-08-01
Large sets of baryon interpolating field operators are developed for use in lattice QCD studies of baryons with zero momentum. Operators are classified according to the double-valued irreducible representations of the octahedral group. At first, three-quark smeared, local operators are constructed for each isospin and strangeness and they are classified according to their symmetry with respect to exchange of Dirac indices. Nonlocal baryon operators are formulated in a second step as direct products of the spinor structures of smeared, local operators together with gauge-covariant lattice displacements of one or more of the smeared quark fields. Linear combinations of direct products of spinorial and spatial irreducible representations are then formed with appropriate Clebsch-Gordan coefficients of the octahedral group. The construction attempts to maintain maximal overlap with the continuum SU(2) group in order to provide a physically interpretable basis. Nonlocal operators provide direct couplings to states that have nonzero orbital angular momentum.
The algebra of dual -1 Hahn polynomials and the Clebsch-Gordan problem of sl_{-1}(2)
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
2012-01-01
The algebra H of the dual -1 Hahn polynomials is derived and shown to arise in the Clebsch-Gordan problem of sl_{-1}(2). The dual -1 Hahn polynomials are the bispectral polynomials of a discrete argument obtained from a q-> -1 limit of the dual q-Hahn polynomials. The Hopf algebra sl_{-1}(2) has four generators including an involution, it is also a q-> -1 limit of the quantum algebra sl_{q}(2) and furthermore, the dynamical algebra of the parabose oscillator. The algebra H, a two-parameter ge...
The new averaged definite parity j/sub z/(ADPj/sub z/) approximation is considered in detail from the standpoint of the exact body frame CC cross section equations. These cross section equations are decomposed into contributions from the various possible orbital angular momenta and projections of the total angular momentum j onto the scattering vector. This decomposition then permits a clearer examination of the quantities actually approximated in j/sub z/-conserving approximations. The previously obtained constant weight version is compared to the present Clebsch--Gordan weight version by applying both to He+H2 collisions. Results for definite parity partial cross sections and integral cross sections are used as the basis of the comparison
Van der Waerden invariant and Wigner coefficients for some compact groups
A simple approach is developed for obtaining the general van der Waerden invariant for SU(n). The solution is symmetric within a phase factor and is expressed in terms of elementary scalars. The results are useful for evaluating the general Wigner coefficient or Clebsch-Gordan coefficient. The internal and the external labelling problems are simultaneously solved by exploiting Speiser's theorem. The SU(5) and O(5) van der Waerden invariants are explicitly worked out; and the general O(5) is contained in SU(2) x SU(2) Wigner coefficient is evaluated as well as certain simple classes of O(5) is contained in SU(2) x U(1) Wigner coefficients. (author)
Bitencourt, Ana Carla P; Littlejohn, Robert G; Anderson, Roger; Aquilanti, Vincenzo
2014-01-01
The Wigner $3j$ symbols of the quantum angular momentum theory are related to the vector coupling or Clebsch-Gordan coefficients and to the Hahn and dual Hahn polynomials of the discrete orthogonal hyperspherical family, of use in discretization approximations. We point out the important role of the Regge symmetries for defining the screen where images of the coefficients are projected, and for discussing their asymptotic properties and semiclassical behavior. Recursion relationships are formulated as eigenvalue equations, and exploited both for computational purposes and for physical interpretations.
Calculations of angular momentum coupling coefficients on a computer code
In this study, Clebsch-Gordan coefficients, 3j symbols, Racah coefficients, Wigner's 6j and 9j symbols were calculated by a prepared computer code of COEFF. The computer program COEFF is described which calculates angular momentum coupling coefficients and expresses them as quotient of two integers multiplied by the square root of the quotient of two integers. The program includes subroutines to encode an integer into its prime factors, to decode of prime factors back into an integer , to perform basic arithmetic operations on prime-coded numbers, as well as subroutines which calculate the coupling coefficients themselves. The computer code COEFF had been prepared to run on a VAX. In this study we rearranged the code to run on PC and tested it successfully. The obtained values in this study, were compared with the values of other computer programmes. A pretty good agreement is obtained between our prepared computer code and other computer programmes
The role of SU(2) 3n-j coefficients in SU(3)
The irreducible representations of the group SU(3) may be given completely in terms of the 3-j, 6-j, and 9-j coefficients of SU(2). More remarkably these same coefficients, and the 12-j coefficients as well, enter into the description of a large class of Clebsch-Gordan (C-G) coefficients for the group SU(3), this occurrence going beyond that in the well-known group-subgroup reduction SU(3)↓U(2). The problem of determining the SU(3) irreducible representations and its C-G coefficients is reviewed, and it is shown how the SU(2) quantities enter into the SU(3) problem in special cases
New algebraic tables of SU(2) quantities
Formulas for Clebsch-Gordan Coefficients, 6-j symbols and 9-j symbols of SU(2) are presented in a ready-to-program way for obtaining algebraic tables. An excerpt of the complete tables are also presented. (Author)
Tables of SU(3) isoscalar factors
The Clebsch-Gordan coefficients of SU(3) are useful in calculations involving baryons and mesons, as well as in calculations involving arbitrary numbers of quarks. For the latter case, one needs the coupling constants between states of nonintegral hypercharges. The existing published tables are insufficient for many such applications, and therefore we have compiled this collection. This report supplies the isoscalar factors required to reconstruct the Clebsch-Gordan coefficients for a large set of products of representations
Some aspects of q- and qp- boson calculus
A set of compatible formulas for the Clebsch-Gordan coefficients of the quantum algebra Uq(su2) is given in this paper. These formulas are q-deformations of known formulas, as for instance: Wigner, van der Waerden, and Racah formulas. They serve as starting points for deriving various realizations of the unit tensor of Uq(su2) in terms of q-boson operators. the passage from the one-parameter quantum algebra Uq(su2) to the two-parameter quantum algebra Uqp(u2) is discussed at the level of Clebsch-Gordan coefficients. (authors)
Gómez-Rocha, María
2012-01-01
In this article we point out that the unitary transformation that relates the chiral basis $\\{R; I J^{PC}\\}$ and the $\\{I; ^{2S+1}L_J \\}$ basis, which was already derived for canonical spin in instant form, is also applicable in light-cone representations. From the most general expression for the Clebsch-Gordan coefficients of the Poincar\\'e group one can see that the chiral limit brings the angular momentum coupling into a simple form that permits a clear relation in terms of SU(2) Clebsch-Gordan coefficients. It provides a tool of measurement of chiral symmetry in relativistic composite systems.
Rotations and angular momentum
This paper is devoted to the analysis of rotational invariance and the properties of angular momentum in quantum mechanics. In particular, the problem of addition of angular momenta is treated in detail, and tables of Clebsch-Gordan coefficients are included
Construction of SU(3) irreps in canonical SO(3)-coupled bases
Rowe, D. J.; Thiamová, Gabriela
2008-01-01
Roč. 41, č. 6 (2008), 065206/1-065206/9. ISSN 1751-8113 Institutional research plan: CEZ:AV0Z10480505 Keywords : CLEBSCH-GORDAN-COEFFICIENT * NUCLEAR SHELL MODEL * SO(3) BASE S Subject RIV: BE - Theoretical Physics Impact factor: 1.540, year: 2008
Generalized Uncertainty Principle and Angular Momentum
Bosso, Pasquale
2016-01-01
Various models of quantum gravity suggest a modification of the Heisenberg's Uncertainty Principle, to the so-called Generalized Uncertainty Principle, between position and momentum. In this work we show how this modification influences the theory of angular momentum in Quantum Mechanics. In particular, we compute Planck scale corrections to angular momentum eigenvalues, the Hydrogen atom spectrum, the Stern-Gerlach experiment and the Clebsch-Gordan coefficients. We also examine effects of the Generalized Uncertainty Principle on multi-particle systems.
Configuration space FADDEEV calculations
805The detailed study of few-body systems provides one of the most precise tools for studying the dynamics of nuclei. We have investigated the physical and mathematical consequences of using different interactions which fit the same two-body data in three-body models. In addition, new methods for coupling multiquark states such that the resulting state has the correct permutation symmetry have been found. Procedures for computing the Clebsch-Gordan coefficients for these states have been developed
Minisuperspace limit of the AdS3 WZNW model
Ribault, Sylvain
2009-01-01
We derive the three-point function of the AdS3 WZNW model in the minisuperspace limit by Wick rotation from the H3+ model. The result is expressed in terms of Clebsch-Gordan coefficients of the Lie algebra sl(2,R). We also introduce a covariant basis of functions on AdS3, which can be interpreted as bulk-boundary propagators.
The Demazure-Tits subgroup of a simple Lie group
Michel, L.; Patera, J.; Sharp, R. T.
1988-04-01
The Demazure-Tits subgroup of a simple Lie group G is the group of invariance of Clebsch-Gordan coefficients tables (assuming an appropriate choice of basis). The structure of the Demazure-Tits subgroups of An, Bn, Cn, Dn, and G2 is described. Orbits of the permutation action of the DT group in any irreducible finite-dimensional representation space of A2, C2, and G2 are decomposed into the sum of irreducible representations of the DT group.
Invariants, Projection Operators and $SU(N)\\times SU(N)$ Irreducible Schwinger Bosons
Mathur, Manu; Raychowdhury, Indrakshi; Sreeraj, T.P.
2011-01-01
We exploit SU(N) Schwinger bosons to construct and analyze the coupled irreducible representations of $SU(N) \\times SU(N)$ in terms of the invariant group. The corresponding projection operators are constructed in terms of the invariant group generators. We also construct $SU(N) \\times SU(N)$ irreducible Schwinger bosons which directly create these coupled irreducible states. The SU(N) Clebsch Gordan coefficients are computed as the matrix elements of the projection operators.
Elasticity tensor and ultrasonic velocities for anisotropic cubic polycrystal
2008-01-01
The orientation distribution of crystallites in a polycrystal can be described by the orientation distribution function(ODF) . The ODF can be expanded under the Wigner D-bases. The expanded coefficients in the ODF are called the texture coefficients. In this paper,we use the Clebsch-Gordan expression to derive an explicit expression of the elasticity tensor for an anisotropic cubic polycrystal. The elasticity tensor contains three material constants and nine texture coefficients. In order to measure the nine texture coefficients by ultrasonic wave,we give relations between the nine texture coefficients and ultrasonic propagation velocities. We also give a numerical example to check the relations.
Self-dual continuous series of representations for Uq(sl(2)) and Uq(osp(1 vertical stroke 2))
We determine the Clebsch-Gordan and Racah-Wigner coefficients for continuous series of representations of the quantum deformed algebras Uq(sl(2)) and Uq(osp(1 vertical stroke 2)). While our results for the former algebra reproduce formulas by Ponsot and Teschner, the expressions for the orthosymplectic algebra are new. Up to some normalization factors, the associated Racah-Wigner coefficients are shown to agree with the fusing matrix in the Neveu-Schwarz sector of N=1 supersymmetric Liouville field theory.
Addition theorems for spin spherical harmonics: I. Preliminaries
Bouzas, Antonio O, E-mail: abouzas@mda.cinvestav.mx [Departamento de Fisica Aplicada, CINVESTAV-IPN, Carretera Antigua a Progreso Km. 6, Apdo. Postal 73 ' Cordemex' , Merida 97310, Yucatan (Mexico)
2011-04-22
We develop a systematic approach to deriving addition theorems for, and some other bilocal sums of, spin spherical harmonics. In this first part we establish some necessary technical results. We discuss the factorization of orbital and spin degrees of freedom in certain products of Clebsch-Gordan coefficients, and obtain general explicit results for the matrix elements in configuration space of tensor products of arbitrary rank of the position and angular-momentum operators. These results are the basis of the addition theorems for spin spherical harmonics obtained in part II (2011 J. Phys. A: Math. Theor. 44 165302).
Strong interactions, Zweig's rule, and weaker interactions
An attempt is made to connect five notions: Strong interaction scattering amplitudes do not involve the action of a Hamiltonian and are only Clebsch-Gordan coefficients. The four momentum vector P is an SU(something) operator. The four momentum of a quark does not change in a strong interaction scattering. Zweig's rule. Gluons should not be drawn in strong interaction scattering diagrams. Finally, a simple explanation will be offered for the weak interaction of leptons amongst themselves and with hadrons. (U.S.)
Small antiferromagnetic spin systems-Sublattice Hamiltonians
A few examples of four-spin Heisenberg systems with dominant antiferromagnetic couplings are considered. All systems can be described by the so-called sublattice Hamiltonian H=SA.SB or its modifications, where SX is the total spin of a sublattice X=A, B. In such a case (eigen)energies are simple functions of the total spin number S, total spins of sublattices SA, SB, and the Hamiltonian parameters (ratios of exchange integrals). Moreover, eigenstates are strictly determined by a coupling scheme assumed and the appropriate Clebsch-Gordan coefficients. In this sense the systems considered are classical ones.
Angular analyses in relativistic quantum mechanics
This work describes the angular analysis of reactions between particles with spin in a fully relativistic fashion. One particle states are introduced, following Wigner's method, as representations of the inhomogeneous Lorentz group. In order to perform the angular analyses, the reduction of the product of two representations of the inhomogeneous Lorentz group is studied. Clebsch-Gordan coefficients are computed for the following couplings: l-s coupling, helicity coupling, multipolar coupling, and symmetric coupling for more than two particles. Massless and massive particles are handled simultaneously. On the way we construct spinorial amplitudes and free fields; we recall how to establish convergence theorems for angular expansions from analyticity hypothesis. Finally we substitute these hypotheses to the idea of 'potential radius', which gives at low energy the usual 'centrifugal barrier' factors. The presence of such factors had never been deduced from hypotheses compatible with relativistic invariance. (author)
Relativistic quantum mechanics
Horwitz, Lawrence P
2015-01-01
This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins and angular momenta can be combined through the usual rotation group Clebsch-Gordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum Lax-Phillips theory of semigroup evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. Th...
Field operators for anyons and plektons
Given its superselection sectors with non-abelian braid group statistics, we extend the algebra A of local observables into an algebra F containing localized intertwiner fields which carry the superselection charges. The construction of the inner degrees of freedom, as well as the study of their transformation properties (quantum symmetry), are entirely in terms of the superselection structure of the observables. As a novel and characteristic feature for braid group statistics, Clebsch-Gordan and commutation 'coefficients' generically take values in the algebra M of symmetry operators, much as it is the case with quasi-Hopf symmetry. A, F, and M are all C* algebras, i.e. represented by bounded operators on a Hilbert space with positive metric. (orig.)
Multipole expansions in four-dimensional hyperspherical harmonics
The technique of vector differentiation is applied to the problem of the derivation of multipole expansions in four-dimensional space. Explicit expressions for the multipole expansion of the function rnCj(r-circumflex) with r = r1 + r2 are given in terms of tensor products of two hyperspherical harmonics depending on the unit vectors r-circumflex1 and r-circumflex2. The multipole decomposition of the function (r1 . r2)n is also derived. The proposed method can be easily generalized to the case of the space with dimensionality larger than four. Several explicit expressions for the four-dimensional Clebsch-Gordan coefficients with particular values of parameters are presented in the closed form
Light baryon spectrum using improved interpolating operators
S. Basak, R. G. Edwards, G. T. Fleming, J. Juge, A. Lichtl, C. Morningstar D. G. Richards, I. Sato, S. J. Wallace
2006-06-26
Energies for excited light baryons are computed in quenched QCD with a pion mass of 490 MeV. Operators used in the simulations include local operators and the simplest nonlocal operators that have nontrivial orbital structures. All operators are designed with the use of Clebsch-Gordan coefficients of the octahedral group so that they transform irreducibly under the group rotations. Matrices of correlation functions are computed for each irreducible representation, and then the variational method is applied to separate mass eigenstates. We obtained 17 states for isospin 1/2 and 11 states for isospin 3/2 in various spin-parity channels including J{sup P}=5/2{sup {+-}}. The pattern of the lowest-lying energies from each irrep is discussed. We use anisotropic lattices of volume 24{sup 3} x 64 with temporal lattice spacing a{sub t}{sup -1}=6.05 GeV with renormalized anisotropy xi=3.0.
General utility computer programs for nuclear structure experiments
The Nuclear codes package contains several theory programs which allow the calculation of many quantities needed in nuclear structure experiments. These codes were initially created to be run on Vax Machines. Therefore, many errors result at their compilation on Linux Machines. We fixed these errors and verified the result with input parameters that generate known output quantities. The following programs are available on the Linux network at the Department of Nuclear Physics: 1. BASS -Program to calculate fusion barriers and the limiting angular momentum for complete fusion of heavy ions, using the Bass model; 2. BM1BE2 -Program to calculate the ratio of the reduced transition probabilities: B(M1;I→I-1)/B(E2;I→I-2) = 2/2 and the mixing ratio of ΔI = 1 transitions: δ = 0.799· Eγ(MeV)· /. The Program uses the semi-classical formalism of Doenau and Frauendorf. The extension to multi-quasiparticle structures follows Radford's prescription; 3. CLEBSCH -Program to calculate the Clebsch-Gordan coefficients: ; 4. CLEB - Calculates only the following Clebsch-Gordan coefficients: and ; 5. DEDX - Based on an old Oak Ridge code, this program calculates stopping powers and ranges. It works with all chemical elements, plus the compounds ISOBUTANE and MYLAR; 6. EPSBET - The program makes conversion between Nilsson epsilon deformations and Warsaw betas, i.e. shape defined in terms of epsilons will be expanded in terms of betas. Originally written by W. Nazarewicz; 7. GOSTOP - This program allows the calculation of electronic and nuclear stopping powers. Data for the stopper material density are taken from the American Institute of Physics handbook; 8. QUAD - Program which extracts β2 and ε2 values from a given quadrupole moment Q0; 9. STIME Program to calculate stopping times for ions in materials; 10. WU - Program to calculate the reduced electromagnetic transition rates B(EL), B(ML) and the ratios B(EL)/B(EL)W and B(ML)/B(ML)W (in Weiskopf units). (authors)
Moussa, P. [Commissariat a l' Energie Atomique, 91 - Saclay (France). Centre d' Etudes Nucleaires
1968-06-01
This work describes the angular analysis of reactions between particles with spin in a fully relativistic fashion. One particle states are introduced, following Wigner's method, as representations of the inhomogeneous Lorentz group. In order to perform the angular analyses, the reduction of the product of two representations of the inhomogeneous Lorentz group is studied. Clebsch-Gordan coefficients are computed for the following couplings: l-s coupling, helicity coupling, multipolar coupling, and symmetric coupling for more than two particles. Massless and massive particles are handled simultaneously. On the way we construct spinorial amplitudes and free fields; we recall how to establish convergence theorems for angular expansions from analyticity hypothesis. Finally we substitute these hypotheses to the idea of 'potential radius', which gives at low energy the usual 'centrifugal barrier' factors. The presence of such factors had never been deduced from hypotheses compatible with relativistic invariance. (author) [French] On decrit un formalisme permettant de tenir compte de l'invariance relativiste, dans l'analyse angulaire des amplitudes de reaction entre particules de spin quelconque. Suivant Wigner, les etats a une particule sont introduits a l'aide des representations du groupe de Lorentz inhomogene. Pour effectuer les analyses angulaires, on etudie la reduction du produit de deux representations du groupe de Lorentz inhomogene. Les coefficients de Clebsch-Gordan correspondants sont calcules dans les couplages suivants: couplage l-s couplage d'helicite, couplage multipolaire, couplage symetrique pour plus de deux particules. Les particules de masse nulle et de masse non nulle sont traitees simultanement. Au passage, on introduit les amplitudes spinorielles et on construit les champs libres, on rappelle comment des hypotheses d'analyticite permettent d'etablir des theoremes de convergence pour les
Interacting boson approximation
Lectures notes on the Interacting Boson Approximation are given. Topics include: angular momentum tensors; properties of T/sub i//sup (n)/ matrices; T/sub i//sup (n)/ matrices as Clebsch-Gordan coefficients; construction of higher rank tensors; normalization: trace of products of two s-rank tensors; completeness relation; algebra of U(N); eigenvalue of the quadratic Casimir operator for U(3); general result for U(N); angular momentum content of U(3) representation; p-Boson model; Hamiltonian; quadrupole transitions; S,P Boson model; expectation value of dipole operator; S-D model: U(6); quadratic Casimir operator; an O(5) subgroup; an O(6) subgroup; properties of O(5) representations; quadratic Casimir operator; quadratic Casimir operator for U(6); decomposition via SU(5) chain; a special O(3) decomposition of SU(3); useful identities; a useful property of D/sub αβγ/(α,β,γ = 4-8) as coupling coefficients; explicit construction of T/sub x//sup (2)/ and d/sub αβγ/; D-coefficients; eigenstates of T3; and summary of T = 2 states
Configuration space Faddeev calculations
The detailed study of few-body systems provides one of the most effective means for studying nuclear physics at subnucleon distance scales. For few-body systems the model equations can be solved numerically with errors less than the experimental uncertainties. We have used such systems to investigate the size of relativistic effects, the role of meson-exchange currents, and the importance of quark degrees of freedom in the nucleus. Complete calculations for momentum-dependent potentials have been performed, and the properties of the three-body bound state for these potentials have been studied. Few-body calculations of the electromagnetic form factors of the deuteron and pion have been carried out using a front-form formulation of relativistic quantum mechanics. The decomposition of the operators transforming convariantly under the Poincare group into kinematical and dynamical parts has been studies. New ways for constructing interactions between particles, as well as interactions which lead to the production of particles, have been constructed in the context of a relativistic quantum mechanics. To compute scattering amplitudes in a nonperturbative way, classes of operators have been generated out of which the phase operator may be constructed. Finally, we have worked out procedures for computing Clebsch-Gordan and Racah coefficients on a computer, as well as giving procedures for dealing with the multiplicity problem
Speziale, Simone
2016-01-01
We study the SL(2,C) Clebsch-Gordan coefficients appearing in the lorentzian EPRL spin foam amplitudes for loop quantum gravity. We show how the amplitudes decompose into SU(2) nj-symbols at the vertices and integrals over boosts at the edges. The integrals define edge amplitudes that can be evaluated analytically using and adapting results in the literature, leading to a pure state sum model formulation. This procedure introduces virtual representations which, in a manner reminiscent to virtual momenta in Feynman amplitudes, are off-shell of the simplicity constraints present in the theory, but with the integrands that peak at the on-shell values. We point out some properties of the edge amplitudes which are helpful for numerical and analytical evaluations of spin foam amplitudes, and suggest among other things a simpler model useful for calculations of certain lowest order amplitudes. As an application, we estimate the large spin scaling behaviour of the simpler model, on a closed foam with all 4-valent edg...
Conformal invariant two particle processes
For the conformal group (essentially the SO2(n,2)group) in n-dimensional Minkowsi-space homogeneous spaces are studied which can be interpreted as 2-particle configuration spaces, and 2-particle representations are induced (both participants are spin 0 particles). The eigensolutions of the Casimir-operator in momentum space are Clebsch-Gordan coefficients in momentum basis. The separation of a complete set of comuting operators from the Casimir eigenvalue equations results in all cases in differential equations with 2 variables (a direct consequence of the rank 2 of the homogen spaces), which can be classified as 'generalized hypergeometric differential operators in 2 variables' (this type, as the author supposes, has not been delt with in the literature so far). In the second part the classical conform invariant (relativistic) 2-particle problem, corresponding to the common quantum mechanical (or quantum field theoretical) problem, is presented and solved completely. It is shown for example that for participant momentums (reasonable in the classic sens) on the forward - or on the zero cone only scattering and no bound states are found. (orig./WBU)
Double groups and projective representations
Altmann, S. L.; Herzig, P.
Some problems are discussed in relation to the usual treatment of improper groups through their double groups, in particular the identification (rather than the mere isomorphism) of such groups as C3v and D3. The enhancement of SU(2) by the addition of the inversion is analysed for this purpose. This requires a careful discussion of the behaviour of spinors under inversion and two types of spinors are defined, Cartan and Pauli spinors, that behave differently with respect to inversion, although it is shown that this difference merely entails a choice of gauge in the language of projective representations. A distinction is proposed between the inversion operation and the parity operator: when the former is realized as a binary rotation in 4-space, the latter can be identified with its infinitesimal generator. The passage from SO(3) to O(3) (group of all proper and improper rotations) is studied and a hitherto unknown faithful projective representations of O(3) is given. It is shown how spinor representations can be constructed for improper point groups in either the Cartan or Pauli gauges. A choice of gauge is proposed to ensure agreement with current practice in angular momentum theory and with that in single point groups. As an example, Clebsch-Gordan coefficients are constructed for C3v.
Bytsko, Andrei
2016-01-01
Unitary representations of the Temperley-Lieb algebra $TL_N(Q)$ on the tensor space $({\\mathbb C^n})^{\\otimes N}$ are considered. Two criteria are given for determining when an orthogonal projection matrix $P$ of a rank $r$ gives rise to such a representation. The first of them is the equality of traces of certain matrices and the second is the unitary condition for a certain partitioned matrix. Some estimates are obtained on the lower bound of $Q$ for a given dimension $n$ and rank $r$. It is also shown that if $4r>n^2$, then $Q$ can take only a discrete set of values determined by the value of $n^2/r$. In particular, the only allowed value of $Q$ for $n=r=2$ is $Q=\\sqrt{2}$. Finally, properties of the Clebsch-Gordan coefficients of the quantum Hopf algebra $U_q(su_2)$ are used in order to find all $r=1$ and $r=2$ unitary tensor space representations of $TL_N(Q)$ such that $Q$ depends continuously on $q$ and $P$ is the projection in the tensor square of a simple $U_q(su_2)$ module on the subspace spanned by ...
A SUSY SU(5)xT' Unified Model of Flavour with large \\theta_{13}
Meroni, Aurora; Spinrath, Martin
2012-01-01
We present a SUSY SU(5)xT' unified flavour model with type I see-saw mechanism of neutrino mass generation, which predicts the reactor neutrino angle to be \\theta_{13} = 0.14 close to the recent results from the Daya Bay and RENO experiments. The model predicts also values of the solar and atmospheric neutrino mixing angles, which are compatible with the existing data. The T' breaking leads to tri-bimaximal mixing in the neutrino sector, which is perturbed by sizeable corrections from the charged lepton sector. The model exhibits geometrical CP violation, where all complex phases have their origin from the complex Clebsch-Gordan coefficients of T'. The values of the Dirac and Majorana CP violating phases are predicted. For the Dirac phase in the standard parametrisation of the neutrino mixing matrix we get a value close to 90 degrees \\delta = \\pi/2 - 0.45 \\theta^c = 84.3 degrees, \\theta^c being the Cabibbo angle. The neutrino mass spectrum can be with normal ordering (2 cases) or inverted ordering. In each ca...
A Minimal Model of Neutrino Flavor
Luhn, Christoph; Wingerter, Akın
2012-01-01
Models of neutrino mass which attempt to describe the observed lepton mixing pattern are typically based on discrete family symmetries with a non-Abelian and one or more Abelian factors. The latter so-called shaping symmetries are imposed in order to yield a realistic phenomenology by forbidding unwanted operators. Here we propose a supersymmetric model of neutrino flavor which is based on the group T7 and does not require extra Z_N or U(1) factors, which makes it the smallest realistic family symmetry that has been considered so far. At leading order, the model predicts tribimaximal mixing which arises completely accidentally from a combination of the T7 Clebsch-Gordan coefficients and suitable flavon alignments. Next-to-leading order (NLO) operators break the simple tribimaximal structure and render the model compatible with the recent results of the Daya Bay and Reno collaborations which have measured a reactor angle of around 9 degrees. Problematic NLO deviations of the other two mixing angles can be cont...
This work demonstrates that the quantum mechanical moments of a state described by the density matrix correspond to discrete spherical harmonic moments of the classical multipole expansion of the spatial distribution of the angular momentum vectors. For the diagonal density matrix elements, this work exploits the fact that the quantum mechanical vector coupling (Clebsch-Gordan) coefficients become increasingly accurate discrete representations of spherical harmonics as j increases. A Schwinger-type basis accounts for nonaxially symmetric angular distributions, which result in nonzero off-diagonal elements of the density matrix. The resulting discrete minimum uncertainty picture of the classical moments has a stringent equivalence with the quantum mechanical one for all j and provides an unambiguous connection for the classical and quantum moments in the large j limit. The equivalence is numerically tested for simple models, and there is a satisfying equivalence even for small j. Applications, implications, and extensions are indicated, and the relevance of this work for the interpretation of classical mechanical simulations of inelastic and reactive molecular collisions will be documented elsewhere
Population dynamics in a metastable neon magneto-optical trap
Glover, R. D.; Calvert, J. E.; Sang, R. T.
2013-02-01
We observe the population dynamics within a metastable neon magneto-optical trap (MOT) through the measurement of the average squared Clebsch-Gordan coefficient C2 over a range of laser detunings. The magnitude of C2 is dependent on the internal quantum state of an atom interacting with the light field and is found to show a strong dependence on the applied laser detuning. Previously it has been reported [Townsend , Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.52.1423 52, 1423 (1995)] that trapped atoms in a MOT are pumped towards the states that interact most strongly with the local field and therefore the measured value of C2 is larger than the average over all possible transitions. For the 3P2-to-3D3 cooling transition in metastable neon the average C2 value is equal to 0.46; however, we have measured 0.29±0.03
Configuration space Faddeev calculations: Progress report for period 1 January 1986-31 December 1986
The detailed study of few-body nuclear systems provides a powerful tool to identify the relevant degrees of freedom in the nucleus. For these systems one can perform detailed and accurate numerical calculations which can be used to study the interactions between the various degrees of freedom. We have used these systems to investigate the size of the relativistic effects, the role of meson exchange currents, and the importance of the quark degrees of freedom in the nuclear system. New computational tools have been developed to treat relativistic operators. The effects of the Coulomb polarization potential on the low-energy scattering parameters have been investigated, and the effects of the Coulomb interaction on charge symmetry breaking have been studied. We have continued our project to find representations for multiparticle scattering amplitudes which satisfy certain physical properties. Finally, we have extended our work on the realization of the irreducible representations of compact groups as spaces of polynomials. These realizations can then be used in a symbolic manipulation program to generate Clebsch-Gordan and Racah coefficients for groups important in nuclear physics applications. 37 refs
Coefficients for Interrater Agreement.
Zegers, Frits E.
1991-01-01
The degree of agreement between two raters rating several objects for a single characteristic can be expressed through an association coefficient, such as the Pearson product-moment correlation. How to select an appropriate association coefficient, and the desirable properties and uses of a class of such coefficients--the Euclidean…
On the relation between the modular double of Uq(sl(2,R)) and the quantum Teichmueller theory
We exhibit direct relations between the modular double of Uq(sl(2,R)) and the quantum Teichmueller theory. Explicit representations for the fusion- and braiding operations of the quantum Teichmueller theory are immediate consequences. Our results include a simplified derivation of the Clebsch-Gordan decomposition for the principal series of representation of the modular double of Uq(sl(2,R)).
Constellations and projective classical groups
The constellation concept is recalled (geometrical description of a ray in a vector space). The groups PO(n + 1, C) or PSp(n + 1, C) are shown to preserve 'harmonic conjugation' between two constellations. The action of the Lorentz subgroup and its rotation subgroup is described. Finally, a theorem concerning Clebsch-Gordan product of constellations is proved. (orig.)
The projective Lie algebra of the Lorentz group and homographic transformations
The Lorentz group is used as the group of homographic transformations on the Riemann sphere. Its Lie algebra is shown to have a very simple interpretation with the aid of cross products and constellation formalism. This property is used to give a constellation description of the Clebsch-Gordan series for the product of two states of spin 1
Transport Coefficients of Fluids
Eu, Byung Chan
2006-01-01
Until recently the formal statistical mechanical approach offered no practicable method for computing the transport coefficients of liquids, and so most practitioners had to resort to empirical fitting formulas. This has now changed, as demonstrated in this innovative monograph. The author presents and applies new methods based on statistical mechanics for calculating the transport coefficients of simple and complex liquids over wide ranges of density and temperature. These molecular theories enable the transport coefficients to be calculated in terms of equilibrium thermodynamic properties, and the results are shown to account satisfactorily for experimental observations, including even the non-Newtonian behavior of fluids far from equilibrium.
The Randomized Dependence Coefficient
Lopez-Paz, David; Hennig, Philipp; Schölkopf, Bernhard
2013-01-01
We introduce the Randomized Dependence Coefficient (RDC), a measure of non-linear dependence between random variables of arbitrary dimension based on the Hirschfeld-Gebelein-R\\'enyi Maximum Correlation Coefficient. RDC is defined in terms of correlation of random non-linear copula projections; it is invariant with respect to marginal distribution transformations, has low computational cost and is easy to implement: just five lines of R code, included at the end of the paper.
Do Fresnel coefficients exist?
Felbacq, D; Guizal, B.; F Zolla
2001-01-01
The starting point of the article is the puzzling fact that one cannot recover the Fresnel coefficients by letting tend the width of a slab to infinity. Without using the so-called limiting absorption principle, we show by a convenient limit analysis that it is possible to define rigorously the field diffracted by a semi-infinite periodic medium.
Denominator function for canonical SU(3) tensor operators
The definition of a canonical unit SU(3) tensor operator is given in terms of its characteristic null space as determined by group-theoretic properties of the intertwining number. This definition is shown to imply the canonical splitting conditions used in earlier work for the explicit and unique (up to +- phases) construction of all SU(3) WCG coefficients (Wigner--Clebsch--Gordan). Using this construction, an explicit SU(3)-invariant denominator function characterizing completely the canonically defined WCG coefficients is obtained. It is shown that this denominator function (squared) is a product of linear factors which may be obtained explicitly from the characteristic null space times a ratio of polynomials. These polynomials, denoted G/sup t//sub q/, are defined over three (shift) parameters and three barycentric coordinates. The properties of these polynomials (hence, of the corresponding invariant denominator function) are developed in detail: These include a derivation of their degree, symmetries, and zeros. The symmetries are those induced on the shift parameters and barycentric coordinates by the transformations of a 3 x 3 array under row interchange, column interchange, and transposition (the group of 72 operations leaving a 3 x 3 determinant invariant). Remarkably, the zeros of the general G/sup t//sub q/ polynomial are in position and multiplicity exactly those of the SU(3) weight space associated with irreducible representation [q-1,t-1,0]. The results obtained are an essential step in the derivation of a fully explicit and comprehensible algebraic expression for all SU(3) WCG coefficients
The Truth About Ballistic Coefficients
Courtney, Michael
2007-01-01
The ballistic coefficient of a bullet describes how it slows in flight due to air resistance. This article presents experimental determinations of ballistic coefficients showing that the majority of bullets tested have their previously published ballistic coefficients exaggerated from 5-25% by the bullet manufacturers. These exaggerated ballistic coefficients lead to inaccurate predictions of long range bullet drop, retained energy and wind drift.
Supersymmetry generators of arbitrary spin
The infinitesimal generators of supersymmetry and translation form a solvable invariant subalgebra of the full graded Lie algebra. In O'Raifeartaigh's classification scheme this belongs to Case (iii). In general, the degree-n supersymmetry generators may be defined by requiring their nth derived algebra to be equal to translations. Degree-1 supersymmetries are studied for which S/subi/,S/subj/ = c (α/sup mu/C)/subi//subj/P/sub mu/, where a graded commutator is used. Supposing that ]S/subi/] belongs to some representation of the Lorentz group, the conditions on α/sup mu/ and C which result from Jacobi identities and Hermitian conjugation are studied. For the three-dimensional case the conditions are satisfied if (α/subk/C)/subi//subj/ is chosen to be a Clebsch-Gordan coefficient. This allows S to have any spin not-equal 0 and also gives the correct spin-statistics connection (grading). In the four-dimensional case it is shown how the problem is related to that of finding Lagrangian densities L/subk/ = ipsi-barα/sup mu/partial/sub mu/psi and L/subm/ = psi-barpsi, which are Hermitian scalars. There are an infinite number of possible representations to which S/subi/ can belong, including those of Bhabha type, for which the spin-statistics connection comes naturally from the representation. At the same time there can be supersymmetry generators of several different spins. The Volkov-Akulov nonlinear realization works in all cases and a supersymmetry-invariant Lagrangian can be constructed. Anticommutators seem to be important only in the sense that then finite-dimensional linear realizations can exist
The spin correlations ωrz, r=1,2,3, and the probability pN of finding a system in the Neel state for the antiferromagnetic ring Fe6III (the so-called 'small ferric wheel') are calculated. States with magnetization M=0 and total spin 0≤S≤15, labeled by two (out of four) one-dimensional irreducible representations (irreps) of the point symmetry group D6, are taken into account. This choice follows from importance of these irreps in analyzing low-lying states in each S multiplet. Taking into account the Clebsch-Gordan coefficients for coupling total spins of sublattices (SA=SB=(15/2)) the global Neel probability pN* can be determined. Dependences of these quantities on state energy (per bond and in the units of exchange integral J) and the total spin S are analyzed. Providing we have determined pN(S), etc., for other antiferromagnetic rings (Fe10, for instance) we could try to approximate results for the largest synthesized ferric wheel Fe18. Since thermodynamic properties of Fe6 have been investigated recently, in the present considerations they are not discussed, but only used to verify obtained values of eigenenergies. Numerical results are calculated with high precision using two main tools: (i) thorough analysis of symmetry properties including methods of algebraic combinatorics and (ii) multiple precision arithmetic library GMP. The system considered yields more than 45 000 basic states (the so-called Ising configurations), but application of the method proposed reduces this problem to 20-dimensional eigenproblem for the ground state (S=0). The largest eigenproblem has to be solved for S=4; its dimension is 60. These two facts (high precision and small resultant eigenproblems) confirm the efficiency and usefulness of such an approach, so it is briefly discussed here
Photoelectron angular distribution and photoionization cross sections for H2
Photoionization of H2 from its ground 1μ/sub g/+ state is studied theoretically. The rotational quantization is introduced in addition to the conventional vibrational-electronic transitions during the photoionization process. The photoionization differential cross section of this rotating system is derived and proved to be expressible in the simple form of [sigma(v')/4π][1 + #betta#(v')P2(cos theta)] for H2+ in the vibrational level v' or in the well-known form of (sigma/sub T//4π) [1 + #betta#P2(cos theta)] after summing over all of the vibrational levels of H2+. The angle theta of the ejected electron is measured from the polarization direction of the radiation for the linearly polarized light or measured from the light propagation direction for the unpolarized light. The asymmetry parameters #betta#(v') and #betta#, which are expressed explicitly here in terms of Racah and Clebsch-Gordan coefficients and electronic transition moments, are shown to equal approximately to 2 for the case of linearly polarized light and -1 for the case of unpolarized light. The differential cross section is also proved to be independent of the initial rotational quantum number N'' (of H2) by neglecting vibrational-rotational interactions. Using single-center electronic wave functions for both the molecular system and the outgoing electron and including partial waves l = 1, 3 and 5 in the continuum (Coulomb) wave functions, sigma(v') and #betta#(v') are computed as a function of v' at 584 A. The calculated ratios sigma(v')/sigma(v'=2) agree with the measured vibrational intensity distributions. sigma/sub T/ and #betta# are computed in the incident photon energy range of 600 A to 440 A and the results compare favorably with previous calculations
Schröder, Leif; Bachert, Peter
2003-10-01
Spin systems with residual dipolar couplings such as creatine, taurine, and lactate in skeletal muscle tissue exhibit first-order spectra in in vivo 1H NMR spectroscopy at 1.5 T because the coupled protons are represented by (nearly) symmetrized eigenfunctions. The imidazole ring protons (H2, H4) of carnosine are suspected to form also a coupled system. The ring's stiffness could enable a connectivity between these anisochronous protons with the consequence of second-order spectra at low field strength. Our purpose was to study whether this deviation from the Paschen-Back condition can be used to detect the H2-H4 coupling in localized 1D 1H NMR spectra obtained at 1.5 T (64 MHz) from the human calf in a conventional whole-body scanner. As for the hydrogen hyperfine interaction, a Breit-Rabi equation was derived to describe the transition from Zeeman to Paschen-Back regime for two dipolar-coupled protons. The ratio of the measurable coupling strength ( Sk) and the difference in resonance frequencies of the coupled spins (Δ ω) induces quantum-state mixing of various degree upon definition of an appropriate eigenbase of the coupled spin system. The corresponding Clebsch-Gordan coefficients manifest in characteristic energy corrections in the Breit-Rabi formula. These additional terms were used to define an asymmetry parameter of the line positions as a function of Sk and Δ ω. The observed frequency shifts of the resonances were found to be consistent with this parameter within the accuracy achievable in in vivo NMR spectroscopy. Thus it was possible to identify the origin of satellite peaks of H2, H4 and to describe this so far not investigated type of residual dipolar coupling in vivo.
Converting Sabine absorption coefficients to random incidence absorption coefficients
Jeong, Cheol-Ho
2013-01-01
Absorption coefficients measured by the chamber method are referred to as Sabine absorption coefficients, which sometimes exceed unity due to the finite size of a sample and non-uniform intensity in the reverberation chambers under test. In this study, conversion methods from Sabine absorption...... coefficients to random incidence absorption coefficients are proposed. The overestimations of the Sabine absorption coefficient are investigated theoretically based on Miki's model for porous absorbers backed by a rigid wall or an air cavity, resulting in conversion factors. Additionally, three optimizations...
On the Kendall Correlation Coefficient
Stepanov, Alexei
2015-01-01
In the present paper, we first discuss the Kendall rank correlation coefficient. In continuous case, we define the Kendall rank correlation coefficient in terms of the concomitants of order statistics, find the expected value of the Kendall rank correlation coefficient and show that the later is free of n. We also prove that in continuous case the Kendall correlation coefficient converges in probability to its expected value. We then propose to consider the expected value of the Kendall rank ...
WEIR COEFFICIENT FOR CYLINDRICAL WEIRS
Senayi DÖNMEZ
2002-01-01
Full Text Available In this study, the weir coefficient for cylindrical weirs was experimentally investigated. Experiments were conducted for both free and submerged overflow conditions. Experimental results have indicated that the weir coefficient is about 3.50-3.80 for the free overflow condition. The weir coefficient for the submerged overflow condition varies with the amount of submergence.
Transfer coefficients for terrestrial foodchains
Transfer coefficients to predict the passage of isotopes from the environment to terrestrial foods have been derived for various radionuclides of importance in the nuclear fuel cycle. These data update and extend previously recommended handbook values. We derive transfer coefficients to terrestrial foods and describe the systematics of the derived transfer coefficients. Suggestions are offered for changes in the values of transfer coefficients to terrestrial foods that now appear in federal regulatory guides. Deficiencies in our present knowledge concerning transfer coefficients and limitations in the use of these values to ensure compliance with radiation protection standards are discussed. (orig.) 891 HP/orig. 892 MB
Drag Coefficient of Hexadecane Particles
Nakao, Yoshinobu; Hishida, Makoto; Kajimoto, Sadaaki; Tanaka, Gaku
This paper deals with the drag coefficient of solidified hexadecane particles and their free rising velocity in liquid. The drag coefficient was experimentally investigated in Reynolds number range of about 40-300. The present experimental results are summarized in the following; (1) the drag coefficient of solidified hexadecane particles formed in liquid coolant by direct contact cooling is higher than that of a smooth surface sphere, this high drag coefficient seems to be attributed to the non-smooth surface of the solidified hexadecane particles, (2) experimental correlation for the drag coefficient of the solidified hexadecane particles was proposed, (3 ) the measured rising velocity of the solidified hexadecane particle agrees well with the calculated one, (4) the drag coefficients of hexadecane particles that were made by pouring hexadecane liquid into a solid hollow sphere agreed well with the drag coefficient of smooth surface sphere.
Sabine absorption coefficients to random incidence absorption coefficients
Jeong, Cheol-Ho
2014-01-01
Absorption coefficients measured by the chamber method are referred to as Sabine absorption coefficients, which sometimes exceed unity due to the finite size of a specimen and non-uniform intensity in the test chamber. In this study, several methods that convert Sabine absorption coefficients into...... random incidence absorption coefficients for porous absorbers are investigated. Two optimization-based conversion methods are suggested: the surface impedance estimation for locally reacting absorbers and the flow resistivity estimation for extendedly reacting absorbers. The suggested conversion methods...
Quadrature formulas for Fourier coefficients
Bojanov, Borislav; Petrova, Guergana
2009-09-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives.
Quadrature formulas for Fourier coefficients
Bojanov, Borislav
2009-09-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives. © 2009 Elsevier B.V. All rights reserved.
Measuring of heat transfer coefficient
Henningsen, Poul; Lindegren, Maria
Subtask 3.4 Measuring of heat transfer coefficient Subtask 3.4.1 Design and setting up of tests to measure heat transfer coefficient Objective: Complementary testing methods together with the relevant experimental equipment are to be designed by the two partners involved in order to measure the h...
Standardized Discriminant Coefficients: A Rejoinder.
Mueller, Ralph O.; Cozad, James B.
1993-01-01
Although comments of D.J. Nordlund and R. Nagel are welcomed, their arguments are not sufficient to accept the recommendation of using total variance estimates to standardize canonical discriminant function coefficients. If standardized coefficients are used to help interpret a discriminant analysis, pooled within-group variance estimates should…
Computational Seebeck Coefficient Measurement Simulations
Martin, Joshua
2012-01-01
We have employed finite element analysis to develop computational Seebeck coefficient metrology simulations. This approach enables a unique exploration of multiple probe arrangements and measurement techniques within the same temporal domain. To demonstrate the usefulness of this approach, we have performed these Seebeck coefficient measurement simulations to quantitatively explore perturbations to voltage and temperature correspondence, by comparing simultaneous and staggered data acquisitio...
Determination Permeability Coefficient from Piezocone
Qiang Wang
2014-01-01
Full Text Available The permeability coefficient of soil profile is one of the problems concerned by engineers, and the determination of permeability coefficient method mainly relies on the laboratory permeability test and field pumping test, but these tests are time-consuming and inefficient, and especially the permeability coefficient of soil under the condition of partial drainage was difficult to determine; in this paper, the modern digital CPTU technology was used. Dimensional permeability KT was defined by using the dimensionless normalized cone tip resistance Qt, friction factor Fr, and pore pressure ratio Bq, these parameters enable plots of Bq-Qt, Fr-Qt, Bq-Fr to be contoured KT and hence for permeability coefficient. The relationship has been applied to Nanjing 4th Yangtze river bridge, and compared with laboratory penetration test. The results indicate that the method can accurately determine the permeability coefficient of soil under partial drainage condition and provide the theoretical basis for engineering application.
Operator properties of generalized coherent state systems
N Mukunda
2001-02-01
The main properties of standard quantum mechanical coherent states and the two generalizations of Klauder and of Perelomov are reviewed. For a system of generalized coherent states in the latter sense, necessary and sufﬁcient conditions for existence of a diagonal coherent stable representation for all Hilbert-Schmidt operators are obtained. The main ingredients are Clebsch-Gordan theory and induced representation theory.
On the relation between the modular double of U{sub q}(sl(2,R)) and the quantum Teichmueller theory
Nidaiev, Iurii; Teschner, Joerg
2013-02-15
We exhibit direct relations between the modular double of U{sub q}(sl(2,R)) and the quantum Teichmueller theory. Explicit representations for the fusion- and braiding operations of the quantum Teichmueller theory are immediate consequences. Our results include a simplified derivation of the Clebsch-Gordan decomposition for the principal series of representation of the modular double of U{sub q}(sl(2,R)).
Uq(sl(2)) invariant operators and minimal theories fusion matrices
The existence of Uq(sl(2)) invariant operators for qp=1 leads to relations for the quantum Clebsch-Gordan kernels and for the quantum 6j-symbols (= fusion matrices). These relations effectively reduce some equalities, inherited from the generic q case, and imply, in particular, that the polynomial identities for the quantum 6j-symbols are consistent with the minimal theories chiral fusion rules. (author). 26 refs
8D oscillator as a hidden SU(2) monopole
With help of the generalized version of the Hurwitz transformation, the five-dimensional SU(2)-monopole model is constructed analytically from the eight-dimensional quantum oscillator. The Clebsch-Gordan expansion stimulated by the space-gauge coupling, the hyperangular and the radial parts of the total wave function, the energy spectrum of the charge-monopole bound system, and the corresponding degeneracy are calculated
Predicting Abraham model solvent coefficients
Bradley, Jean-Claude; Abraham, Michael H; Acree, William E; Lang, Andrew SID
2015-01-01
Background The Abraham general solvation model can be used in a broad set of scenarios involving partitioning and solubility, yet is limited to a set of solvents with measured Abraham coefficients. Here we extend the range of applicability of Abraham’s model by creating open models that can be used to predict the solvent coefficients for all organic solvents. Results We created open random forest models for the solvent coefficients e, s, a, b, and v that had out-of-bag R2 values of 0.31, 0.77...
Reactivity coefficients by perturbation theory
The development of the formulae of perturbation theory provides a good opportunity to use one of the principal devices of mathematical heuristics, i.e. proceeding by analogy from something that is simple to something that is more complicated. This paper: (a) Reviews the formulation of perturbation theory as a method of calculating reactivity coefficients; this consists mainly of developing the differential equation for the adjoint flux, as a continuous function of position and lethargy, by proceeding by analogy from the one-group differential equation for adjoint flux. (b) Presents an application of the two-group form of perturbation theory to a boiling-mercury-cooled fast-breeder reactor (MCBR). It is seen that the net Hg density coefficient of reactivity for the first-design-try for the MCBR is negative for some regions and positive for others. However, it is negative for regions of highest statistical weight and where the density change for a power change would be the greatest. The overall Hg density coefficient is thus negative, i.e. the void coefficient is positive-an unsafe condition. It can be easily seen from the two-group formulation what design changes had to be made to obtain a design which would have a negative void coefficient. It developed in subsequent investigations that there were such design changes that could be made and a design of the MCBR with a negative void coefficient was eventually achieved. (author)
Transport coefficients of heavy baryons
Tolos, Laura; Torres-Rincon, Juan M.; Das, Santosh K.
2016-08-01
We compute the transport coefficients (drag and momentum diffusion) of the low-lying heavy baryons Λc and Λb in a medium of light mesons formed at the later stages of high-energy heavy-ion collisions. We employ the Fokker-Planck approach to obtain the transport coefficients from unitarized baryon-meson interactions based on effective field theories that respect chiral and heavy-quark symmetries. We provide the transport coefficients as a function of temperature and heavy-baryon momentum, and analyze the applicability of certain nonrelativistic estimates. Moreover we compare our outcome for the spatial diffusion coefficient to the one coming from the solution of the Boltzmann-Uehling-Uhlenbeck transport equation, and we find a very good agreement between both calculations. The transport coefficients for Λc and Λb in a thermal bath will be used in a subsequent publication as input in a Langevin evolution code for the generation and propagation of heavy particles in heavy-ion collisions at LHC and RHIC energies.
Analysis of internal conversion coefficients
An extensive database has been assembled that contains the three most widely used sets of calculated internal conversion coefficients (ICC): [Hager R.S., Seltzer E.C., 1968. Internal conversion tables. K-, L-, M-shell Conversion coefficients for Z=30 to Z=103, Nucl. Data Tables A4, 1-237; Band I.M., Trzhaskovskaya M.B., 1978. Tables of gamma-ray internal conversion coefficients for the K-, L- and M-shells, 10≤Z≤104, Special Report of Leningrad Nuclear Physics Institute; Roesel F., Fries H.M., Alder K., Pauli H.C., 1978. Internal conversion coefficients for all atomic shells, At. Data Nucl. Data Tables 21, 91-289] and also includes new Dirac-Fock calculations [Band I.M. and Trzhaskovskaya M.B., 1993. Internal conversion coefficients for low-energy nuclear transitions, At. Data Nucl. Data Tables 55, 43-61]. This database is linked to a computer program to plot ICCs and their combinations (sums and ratios) as a function of Z and energy, as well as relative deviations of ICC or their combinations for any pair of tabulated data. Examples of these analyses are presented for the K-shell and total ICCs of the gamma-ray standards [Hansen H.H., 1985. Evaluation of K-shell and total internal conversion coefficients for some selected nuclear transitions, Eur. Appl. Res. Rept. Nucl. Sci. Tech. 11.6 (4) 777-816] and for the K-shell and total ICCs of high multipolarity transitions (total, K-, L-, M-shells of E3 and M3 and K-shell of M4). Experimental data sets are also compared with the theoretical values of these specific calculations
Viscosity coefficient with pairing interaction
In the study of dynamic process (for example, deep-inelastic scattering of heavy ion, nuclear fission), viscosity, which describes the coupling between the intrinsic degrees of freedom and the collective one, is a basic quantity. In this paper, under BCS approximation, we derive a microscopic expression of viscosity coefficient with pairing interaction by means of a linear response theory. Taking the fission process of 236U as an example, we discuss the effect of pairing interaction on the viscosity coefficient. The results show that pairing interaction must be taken into account at lower temperature and can be neglected at a high-temperature region
Estimating the Polyserial Correlation Coefficient.
Bedrick, Edward J.; Breslin, Frederick C.
1996-01-01
Simple noniterative estimators of the polyserial correlation coefficient are developed by exploiting a general relationship between the polyserial correlation and the point polyserial correlation to give extensions of the biserial estimators of K. Pearson (1909), H. E. Brogden (1949), and F. M. Lord (1963) to the multicategory setting. (SLD)
Fresnel coefficients as hyperbolic rotations
Monzon, J. J.; Sanchez-Soto, L. L.
2001-01-01
We describe the action of a plane interface between two semi-infinite media in terms of a transfer matrix. We find a remarkably simple factorization of this matrix, which enables us to express the Fresnel coefficients as a hyperbolic rotation.
Jeong, Cheol-Ho; Chang, Ji-ho
2015-01-01
Absorption coefficients measured in reverberation chambers, Sabine absorption coefficients, suffer from two major problems. Firstly, they sometimes exceed unity. Secondly, the reproducibility of the Sabine absorption coefficients is quite poor, meaning that the Sabine absorption coefficients vary...
Clustering Coefficients in Multiplex Networks
Cozzo, Emanuele; De Domenico, Manlio; Solé, Albert; Arenas, Alex; Gómez, Sergio; Porter, Mason A; Moreno, Yamir
2013-01-01
Recent advances in the study of complex networked systems has highlighted that our interconnected world is made of networks that are coupled together through different layers that each stand for one type of interaction or system. Despite this situation, it is traditional to aggregate multiplex data into a single weighted network in order take advantage of existing tools. This is admittedly convenient, but it is also extremely problematic. In this paper, we generalize the concept of clustering coefficients for multiplex networks. We show how the layered structure of multiplex networks introduces a new degree of freedom that has a fundamental effect on transitivity. We compute our new multiplex clustering coefficients for several real multiplex networks and illustrate why generalizing monoplex concepts to multiplex networks must be done with great care.
Portable vapor diffusion coefficient meter
Ho, Clifford K.
2007-06-12
An apparatus for measuring the effective vapor diffusion coefficient of a test vapor diffusing through a sample of porous media contained within a test chamber. A chemical sensor measures the time-varying concentration of vapor that has diffused a known distance through the porous media. A data processor contained within the apparatus compares the measured sensor data with analytical predictions of the response curve based on the transient diffusion equation using Fick's Law, iterating on the choice of an effective vapor diffusion coefficient until the difference between the predicted and measured curves is minimized. Optionally, a purge fluid can forced through the porous media, permitting the apparatus to also measure a gas-phase permeability. The apparatus can be made lightweight, self-powered, and portable for use in the field.
SPATIAL DEPENDENCE OF REACTIVITY COEFFICIENTS
Salah, Sideeg
2011-01-01
The objective of this thesis is to study and understand the behavior of the reactivity coefficients (RCs) in a boiling water reactor (BWR) partially within 25 different segments with different void fractions, with enriched oxide fuel (UOX) core, as well as to evaluate the methodologies exposed in [10]. These two normalization methods (described in chapter 3) are used to analyse the contribution of each segment of the core having different regions (fuel, clad, coolant, moderator and channel b...
Matrix Fourier transform with discontinuous coefficients
Yaremko, O.; Zhuravleva, E.
2013-01-01
The explicit construction of direct and inverse Fourier's vector transform with discontinuous coefficients is presented. The technique of applying Fourier's vector transform with discontinuous coefficients for solving problems of mathematical physics.Multidimensional integral transformations with non-separated variables for problems with discontinuous coefficients are constructed in this work. The coefficient discontinuities focused on the of parallel hyperplanes. In this work explicit formul...
Investigating bias in squared regression structure coefficients
Nimon, Kim F.; Zientek, Linda R.; Thompson, Bruce
2015-01-01
The importance of structure coefficients and analogs of regression weights for analysis within the general linear model (GLM) has been well-documented. The purpose of this study was to investigate bias in squared structure coefficients in the context of multiple regression and to determine if a formula that had been shown to correct for bias in squared Pearson correlation coefficients and coefficients of determination could be used to correct for bias in squared regression structure coefficie...
Diffusion coefficients for absorbing materials
A method to improve the diffusion results for systems containing strong absorbers is described. Each absorbing material is transformed into an equivalent rectangle. Transport and diffusion calculations in slab geometry are performed for both directions of the rectangle, and group-dependent diffusion coefficients are determined by matching the outgoing currents. Test problems comprise a critical slab, a compact PWR fuel element storage pool and two BWR fuel elements with a control rod and a poison cell. The multiplication factors of these systems are calculated with an accuracy of 1 to 2%. (Auth.)
Higher Order Macro Coefficients in Periodic Homogenization
Conca, Carlos; San Martin, Jorge; Smaranda, Loredana; Vanninathan, Muthusamy
2011-09-01
A first set of macro coefficients known as the homogenized coefficients appear in the homogenization of PDE on periodic structures. If energy is increased or scale is decreased, these coefficients do not provide adequate approximation. Using Bloch decomposition, it is first realized that the above coefficients correspond to the lowest energy and the largest scale. This naturally paves the way to introduce other sets of macro coefficients corresponding to higher energies and lower scales which yield better approximation. The next task is to compare their properties with those of the homogenized coefficients. This article reviews these developments along with some new results yet to be published.
Higher Order Macro Coefficients in Periodic Homogenization
Conca, Carlos; San Martin, Jorge [Departamento de IngenierIa Matematica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile and Centro de Modelamiento Matematico, UMR 2071 CNRS-UChile, Casilla 170/3 - Correo 3, Santiago (Chile); Smaranda, Loredana [Department of Mathematics, Faculty of Mathematics and Computer Science, University of Pitesti, 110040 Pitesti, Str. Targu din Vale Nr.1, Arges (Romania); Vanninathan, Muthusamy, E-mail: cconca@dim.uchile.cl, E-mail: jorge@dim.uchile.cl, E-mail: smaranda@dim.uchile.cl, E-mail: vanni@math.tifrbng.res.in [TIFR-CAM, Post Bag 6503, GKVK Post, Bangalore - 560065 (India)
2011-09-15
A first set of macro coefficients known as the homogenized coefficients appear in the homogenization of PDE on periodic structures. If energy is increased or scale is decreased, these coefficients do not provide adequate approximation. Using Bloch decomposition, it is first realized that the above coefficients correspond to the lowest energy and the largest scale. This naturally paves the way to introduce other sets of macro coefficients corresponding to higher energies and lower scales which yield better approximation. The next task is to compare their properties with those of the homogenized coefficients. This article reviews these developments along with some new results yet to be published.
VHTRC temperature coefficient benchmark problem
As an activity of IAEA Coordinated Research Programme, a benchmark problem is proposed for verifications of neutronic calculation codes for a low enriched uranium fuel high temperature gas-cooled reactor. Two problems are given on the base of heating experiments at the VHTRC which is a pin-in-block type core critical assembly loaded mainly with 4% enriched uranium coated particle fuel. One problem, VH1-HP, asks to calculate temperature coefficient of reactivity from the subcritical reactivity values at five temperature steps between an room temperature where the assembly is nearly at critical state and 200degC. The other problem, VH1-HC, asks to calculate the effective multiplication factor of nearly critical loading cores at the room temperature and 200degC. Both problems further ask to calculate cell parameters such as migration area and spectral indices. Experimental results corresponding to main calculation items are also listed for comparison. (author)
Index-free Heat Kernel Coefficients
De van Ven, A E M
1998-01-01
Using index-free notation, we present the diagonal values of the first five heat kernel coefficients associated with a general Laplace-type operator on a compact Riemannian space without boundary. The fifth coefficient appears here for the first time. For a flat space with a gauge connection, the sixth coefficient is given too. Also provided are the leading terms for any coefficient, both in ascending and descending powers of the Yang-Mills and Riemann curvatures, to the same order as required for the fourth coefficient. These results are obtained by directly solving the relevant recursion relations, working in Fock-Schwinger gauge and Riemann normal coordinates. Our procedure is thus noncovariant, but we show that for any coefficient the `gauged' respectively `curved' version is found from the corresponding `non-gauged' respectively `flat' coefficient by making some simple covariant substitutions. These substitutions being understood, the coefficients retain their `flat' form and size. In this sense the fift...
Innovative Correlation Coefficient Measurement with Fuzzy Data
Berlin Wu; Chin Feng Hung
2016-01-01
Correlation coefficients are commonly found with crisp data. In this paper, we use Pearson’s correlation coefficient and propose a method for evaluating correlation coefficients for fuzzy interval data. Our empirical studies involve the relationship between mathematics achievement and other projects.
Diffusion coefficient in photon diffusion theory
Graaff, R; Ten Bosch, JJ
2000-01-01
The choice of the diffusion coefficient to be used in photon diffusion theory has been a subject of discussion in recent publications on tissue optics. We compared several diffusion coefficients with the apparent diffusion coefficient from the more fundamental transport theory, D-app. Application to
Coefficient of Partial Correlation and Its Calculation
段全才; 张保法
1992-01-01
This thesis offers the general concept of coefficient of partial correlation.Starting with regres-sion analysis,the paper,by using samples,infers the general formula of expressing coefficient of partial correlation by way of simple correlation coefficient.
Standards for Standardized Logistic Regression Coefficients
Menard, Scott
2011-01-01
Standardized coefficients in logistic regression analysis have the same utility as standardized coefficients in linear regression analysis. Although there has been no consensus on the best way to construct standardized logistic regression coefficients, there is now sufficient evidence to suggest a single best approach to the construction of a…
Soccer Ball Lift Coefficients via Trajectory Analysis
Goff, John Eric; Carre, Matt J.
2010-01-01
We performed experiments in which a soccer ball was launched from a machine while two high-speed cameras recorded portions of the trajectory. Using the trajectory data and published drag coefficients, we extracted lift coefficients for a soccer ball. We determined lift coefficients for a wide range of spin parameters, including several spin…
Transport coefficients of relativistic systems
It becomes increasingly important to know the strength of dissipative effects in relativistic hydrodynamics. Recently, scientists have strongly focused on shear viscosity. Nevertheless, heat flow, being proportional to spatial gradients of e.g. chemical potential over temperature, can also be an important effect in studies of relativistic fluid dynamics. We investigated the heat conductivity coefficient for an ultrarelativistic Boltzmann-gas, using our partonic transport model BAMPS. BAMPS solves the relativistic Boltzmann-equation numerically for arbitrary different particle species. We use pQCD scattering cross-sections. Furthermore, the response of a charged, relativistic gas onto an external electric field determines the electric conductivity. We investigated the electric conductivity of different model systems using three different methods: analytic transport theory, linear response via Green-Kubo formulae in equilibrium BAMPS-setups, and applying the textbook-picture of linear response to BAMPS. We plan to investigate the electric conductivity with the recently improved 2<->3 processes from BAMPS and compare the results with lattice QCD.
Energy coefficients for a propeller series
Olsen, Anders Smærup
2004-01-01
The efficiency for a propeller is calculated by energy coefficients. These coefficients are related to four types of losses, i.e. the axial, the rotational, the frictional, and the finite blade number loss, and one gain, i.e. the axial gain. The energy coefficients are derived by use of the...... potential theory with the propeller modelled as an actuator disk. The efficiency based on the energy coefficients is calculated for a propeller series. The results show a good agreement between the efficiency based on the energy coefficients and the efficiency obtained by a vortex-lattice method....
Justification for change in AXAIR dispersion coefficients
AXAIR is the primary dose assessment code used at the Savannah River Site (SRS) to predict doses following hypothetical releases of relatively short durations. The atmospheric dispersion coefficients currently used in AXAIR are analytical expressions developed to fit the curves in the Turner Workbook as referred to in USNRC Regulatory Guide 1.145. This report explores the ramifications and benefits of changing the dispersion coefficients to a combination of Pasquill's lateral dispersion coefficients and Briggs' vertical dispersion coefficients. The differences in the dispersion coefficients have a minor effect on the relative air concentrations for stability classes A--D, but a significant difference is seen for classes E, F, and G
Rotational raman lidar for aerosol scattering coefficients
Two channel lidar signals which are composed of the total rotational scattering and elastic signals provide good information for the aerosol scattering coefficients. We can calculate the aerosol backscattering coefficient and extinction coefficient directly without any assumption and calibration process. Generally, a high spectral resolution lidar is used for an aerosol monitoring. But we have designed a new normal spectral receiving lidar system which contains the scattering information simultaneously, and we have retrieved the aerosol scattering coefficient. The results show that there is no need to assume any relation between the aerosol backscattering and extinction and to consider any wavelength calibration process for the aerosol scattering coefficient
Continuous quantum mechanics of single particles in closed and quasi-closed systems: Pt. III and IV
Brieger, M. [DLR Deutsches Zentrum fuer Luft- und Raumfahrt e.V., Stuttgart (Germany). Inst. fuer Technische Physik
2005-07-01
The rigorous solution to Schroedinger's nonrelativistic time-dependent equation of a single electron's spin-orbit or magnetic hyperfine interaction reveals the full dynamics of angular momentum coupling especially in the presence of an external, arbitrarily oriented magnetic field. Besides of making a description of major dynamical properties possible in simple classical terms, it also sheds new light on the seeming quantization of states: They turn out to be exceptional states of dynamical balance, which in the field-free case are only made possible by the respective pairs of Clebsch-Gordan coefficients. Moreover, the results not only show that integer and half-integer quantum numbers of the total angular momentum only apply to this special case but that in the general case they are also able to obtain the well-known splitting pattern of the stationary energy levels in the field as produced by separately identifiable, field-dependent contributions from the spin-orbit or the magnetic hyperfine interactions on the one hand, and the magnetic dipole interaction with external magnetic fields on the other in a way not accessible to the Breit-Rabi formula. The results further demonstrate that the total magnetic moment responds quite sensitively to even weak field strengths, i.e., with substantial changes although the linear Zeeman effect suggests their seeming constancy in low fields also for levels with vertical stroke M{sub J} vertical stroke < l+1/2. Although Schroedinger's equation is equivalent to an energy representation this detailed description of the behavior of the total magnetic moment is made possible by the fortunate fact that the coupling magnetic moments enter the Hamiltonian linearly. This circumstance can be exploited to describe in full detail how the total magnetic moment behaves in an arbitrarily oriented magnetic field. It is found that its motion in this environment consists of a basic Larmor precession about the field direction
Enlarged symmetry algebras of spin chains, loop models, and S-matrices
The symmetry algebras of certain families of quantum spin chains are considered in detail. The simplest examples possess m states per site (m>=2), with nearest-neighbor interactions with U(m) symmetry, under which the sites transform alternately along the chain in the fundamental m and its conjugate representation m-bar. We find that these spin chains, even with arbitrary coefficients of these interactions, have a symmetry algebra Am much larger than U(m), which implies that the energy eigenstates fall into sectors that for open chains (i.e., free boundary conditions) can be labeled by j=0,1,...,L, for the 2L-site chain such that the degeneracies of all eigenvalues in the jth sector are generically the same and increase rapidly with j. For large j, these degeneracies are much larger than those that would be expected from the U(m) symmetry alone. The enlarged symmetry algebra Am(2L) consists of operators that commute in this space of states with the Temperley-Lieb algebra that is generated by the set of nearest-neighbor interaction terms; Am(2L) is not a Yangian. There are similar results for supersymmetric chains with gl(m+n|n) symmetry of nearest-neighbor interactions, and a richer representation structure for closed chains (i.e., periodic boundary conditions). The symmetries also apply to the loop models that can be obtained from the spin chains in a spacetime or transfer matrix picture. In the loop language, the symmetries arise because the loops cannot cross. We further define tensor products of representations (for the open chains) by joining chains end to end. The fusion rules for decomposing the tensor product of representations labeled j1 and j2 take the same form as the Clebsch-Gordan series for SU(2). This and other structures turn the symmetry algebra Am into a ribbon Hopf algebra, and we show that this is 'Morita equivalent' to the quantum group Uq(sl2) for m=q+q-1. The open-chain results are extended to the cases vertical bar m vertical barm or Uq(sl2
Continuous quantum mechanics of single particles in closed and quasi-closed systems: Pt. III and IV
The rigorous solution to Schroedinger's nonrelativistic time-dependent equation of a single electron's spin-orbit or magnetic hyperfine interaction reveals the full dynamics of angular momentum coupling especially in the presence of an external, arbitrarily oriented magnetic field. Besides of making a description of major dynamical properties possible in simple classical terms, it also sheds new light on the seeming quantization of states: They turn out to be exceptional states of dynamical balance, which in the field-free case are only made possible by the respective pairs of Clebsch-Gordan coefficients. Moreover, the results not only show that integer and half-integer quantum numbers of the total angular momentum only apply to this special case but that in the general case they are also able to obtain the well-known splitting pattern of the stationary energy levels in the field as produced by separately identifiable, field-dependent contributions from the spin-orbit or the magnetic hyperfine interactions on the one hand, and the magnetic dipole interaction with external magnetic fields on the other in a way not accessible to the Breit-Rabi formula. The results further demonstrate that the total magnetic moment responds quite sensitively to even weak field strengths, i.e., with substantial changes although the linear Zeeman effect suggests their seeming constancy in low fields also for levels with vertical stroke MJ vertical stroke < l+1/2. Although Schroedinger's equation is equivalent to an energy representation this detailed description of the behavior of the total magnetic moment is made possible by the fortunate fact that the coupling magnetic moments enter the Hamiltonian linearly. This circumstance can be exploited to describe in full detail how the total magnetic moment behaves in an arbitrarily oriented magnetic field. It is found that its motion in this environment consists of a basic Larmor precession about the field direction superimposed on which is
Barbier, R.
1995-09-22
This thesis concerns some aspects of new symmetries in Nuclear Physics. It comprises three parts. The first one is devoted to the study of the quantum algebra U{sub qp}(u{sub 2}). More precisely, we develop its Hopf algebraic structure and we study its co-product structure. The bases of the representation theory of U{sub qp}(u{sub 2}) are introduced. On one hand, we construct the finite-dimensional irreducible representations of U{sub qp}(u{sub 2}). On the other hand, we calculate the Clebsch-Gordan coefficients with the projection operator method. To complete our study, we construct some deformed boson mappings of the quantum algebras U{sub qp}(u{sub 2}), U{sub q{sup 2}}(su{sub 2}) and U{sub qp}(u{sub 1,1}). The second part deals with the construction of a new phenomenological model of the non rigid rotator. This model is based on the quantum algebra U{sub qp}(u{sub 2}). The rotational energy and the E2 reduced transition probabilities are obtained. They depend on the two deformation parameters q and p of the quantum algebra. We show how the use of the two-parameter deformation of the algebra U{sub qp}(u{sub 2}) leads to a generalization of the U{sub q}(su{sub 2})-rotator model. We also introduce a new model of the anharmonic oscillator on the basis of the quantum algebra U{sub qp}(u{sub 2}). We show that the system of the U{sub q}(su{sub 2})-rotator and of the anharmonic oscillator can be coupled with the use of the deformation parameters of U{sub qp}(u{sub 2}). A ro-vibration energy formula and expansion `a la` Dunham are obtained. The aim of the last part is to apply our non rigid rotator model to the rotational collective dynamics of the superdeformed nuclei of the A{approx}130 - 150 and A{approx}190 mass regions and deformed nuclei of the actinide and rare earth series. We adjust the free parameters of our model and compare our results with those from four other models of the non rigid rotator. A comparative analysis is given in terms of transition energies.
Quantum algebra Uqp(u2) and application to the rotational collective dynamics of the nuclei
This thesis concerns some aspects of new symmetries in Nuclear Physics. It comprises three parts. The first one is devoted to the study of the quantum algebra Uqp(u2). More precisely, we develop its Hopf algebraic structure and we study its co-product structure. The bases of the representation theory of Uqp(u2) are introduced. On one hand, we construct the finite-dimensional irreducible representations of Uqp(u2). On the other hand, we calculate the Clebsch-Gordan coefficients with the projection operator method. To complete our study, we construct some deformed boson mappings of the quantum algebras Uqp(u2), Uq2(su2) and Uqp(u1,1). The second part deals with the construction of a new phenomenological model of the non rigid rotator. This model is based on the quantum algebra Uqp(u2). The rotational energy and the E2 reduced transition probabilities are obtained. They depend on the two deformation parameters q and p of the quantum algebra. We show how the use of the two-parameter deformation of the algebra Uqp(u2) leads to a generalization of the Uq(su2)-rotator model. We also introduce a new model of the anharmonic oscillator on the basis of the quantum algebra Uqp(u2). We show that the system of the Uq(su2)-rotator and of the anharmonic oscillator can be coupled with the use of the deformation parameters of Uqp(u2). A ro-vibration energy formula and expansion 'a la' Dunham are obtained. The aim of the lest part is to apply our non rigid rotator model to the rotational collective dynamics of the superdeformed nuclei of the A∼130 - 150 and A∼190 mass regions and deformed nuclei of the actinide and rare earth series. We adjust the free parameters of our model and compare our results with those arising from four other models of the non rigid rotator. A comparative analysis is given in terms of transition energies. We calculate the dynamical moments of inertia with the fitted parameters. A comparison between the results of different models shows the role played by
Full text: The behavior of an atom in the magnetic field can be studied numerically based on the parameters of the fine structure (the radial integrals in the energy operator matrix). A set of the fine structure parameters ensuring the correlation with experimentally observed energies was obtained in the previous works of the authors. The authors provide the results of the numerical study of magnetic sublevels behavior for NeI and ArI (of specified configurations) in the magnetic fields up to 150 kOe. Using the free momentums representation and the Clebsch-Gordan coefficients the authors succeeded to obtain the expressions for the diagonal and non-diagonal elements of the atom-field interaction matrices in LSJM-representation as well as to refine the signs of the non-diagonal elements. (γψi|W|γψi) = (((J(J + 1) + L(L + 1) - S (S +1)/2J(J + 1))gl + ((J(J + 1) - L(L + 1) + S (S +1)/2J(J + 1))gs)) μ0H M (ΔJ 0 ΔL = ΔS = 0 ; (γψi|W|γ'ψj) √[((J - L + S + 1)(J + L - S + 1)(J + L + S + 2)(L + S - J))/4(J + 1)2(2J + 1)(2J + 3) x ((J + 1)2 - M2 x (gl - gs)μ0H] (ΔJ 0 ±1, ΔL ΔS = 0, Jmin). The energies of Zeeman's sublevels were calculated by means of the diagonalization of the complete energy operator matrix, which was expressed in LS-representation with additional elements accounting for the atom-field interaction. The diagonalization was carried out for all the values of the magnetic quantum number M. The distinctive details of Zeemann's structure especially points of crossing and anticrossing areas of magnetic sublevels were obtained for 2p55g configuration of NeI and 3p55g configuration of ArI. (author)
Determination of the surface drag coefficient
Mahrt, L.; Vickers, D.; Sun, J.L.;
2001-01-01
This study examines the dependence of the surface drag coefficient on stability, wind speed, mesoscale modulation of the turbulent flux and method of calculation of the drag coefficient. Data sets over grassland, sparse grass, heather and two forest sites are analyzed. For significantly unstable ...... of calculation, partly due to meandering of the stress vector.......This study examines the dependence of the surface drag coefficient on stability, wind speed, mesoscale modulation of the turbulent flux and method of calculation of the drag coefficient. Data sets over grassland, sparse grass, heather and two forest sites are analyzed. For significantly unstable...... conditions, the drag coefficient does not depend systematically on z/L but decreases with wind speed for fixed intervals of z/L, where L is the Obukhov length. Even though the drag coefficient for weak wind conditions is sensitive to the exact method of calculation and choice of averaging time, the decrease...
Remarks on the maximum correlation coefficient
Dembo, Amir; Kagan, Abram; Shepp, Lawrence A.
2001-01-01
The maximum correlation coefficient between partial sums of independent and identically distributed random variables with finite second moment equals the classical (Pearson) correlation coefficient between the sums, and thus does not depend on the distribution of the random variables. This result is proved, and relations between the linearity of regression of each of two random variables on the other and the maximum correlation coefficient are discussed.
The Intuitionistic Fuzzy Normed Space of Coefficients
Bilalov, B. T.; S. M. Farahani; Guliyeva, F. A.
2012-01-01
Intuitionistic fuzzy normed space is defined using concepts of $t$ -norm and $t$ -conorm. The concepts of fuzzy completeness, fuzzy minimality, fuzzy biorthogonality, fuzzy basicity, and fuzzy space of coefficients are introduced. Strong completeness of fuzzy space of coefficients with regard to fuzzy norm and strong basicity of canonical system in this space are proved. Strong basicity criterion in fuzzy Banach space is presented in terms of coefficient operator.
NEW CORRELATION COEFFICIENT FOR DATA ANALYSIS
Falie, Dragos; Livia DAVID
2012-01-01
The proposed correlation coefficient better characterize the statistical independence of two random variables that are a linear mixture of two independent sources. This correlation coefficient can be calculated with analytical relations or with the known algorithms of independent components analysis (ICA). The value of the correlation coefficient is zero when the random variables are a statistically independent and it is one when these are fully dependent.
Index-free Heat Kernel Coefficients
van de Ven, Anton E. M.
1997-01-01
Using index-free notation, we present the diagonal values of the first five heat kernel coefficients associated with a general Laplace-type operator on a compact Riemannian space without boundary. The fifth coefficient appears here for the first time. For a flat space with a gauge connection, the sixth coefficient is given too. Also provided are the leading terms for any coefficient, both in ascending and descending powers of the Yang-Mills and Riemann curvatures, to the same order as require...
Magnetoelectric voltage coefficients of magnetoelectric composites
WAN Yong-ping; ZHONG Zheng; QIU Jin-hao
2006-01-01
The magnetoelectric(ME) effect of the particulate magnetostrictive/piezoelectric composite was theoretically studied. The dependence of the ME voltage coefficients on the material properties of the magnetostrictive phase was discussed. The permittivity,permeability and the elastic modulus of the magnetostrictive phase generally have obvious influences on the ME voltage coefficients. The magnetostrictive phase with a large permittivity,large permeability or stiffer modulus will respectively contribute to the higher ME voltage coefficients. For a certain kind of piezoelectric matrix,the ME voltage coefficients can be improved to some extent by choosing those magnetostrictive materials with large permittivity,permeability or high elastic modulus.
Alternatives to Pearson's and Spearman's Correlation Coefficients
Smarandache, Florentin
2008-01-01
This article presents several alternatives to Pearson's correlation coefficient and many examples. In the samples where the rank in a discrete variable counts more than the variable values, the mixtures that we propose of Pearson's and Spearman's correlation coefficients give better results.
Factorization of Transport Coefficients in Macroporous Media
Shapiro, Alexander; Stenby, Erling Halfdan
2000-01-01
We prove the fundamental theorem about factorization of the phenomenological coefficients for transport in macroporous media. By factorization we mean the representation of the transport coefficients as products of geometric parameters of the porous medium and the parameters characteristic of the...
A gain-coefficient switched Alexandrite laser
Lee, Chris J.; van der Slot, Peter J. M.; Boller, Klaus-J.
2012-01-01
We report on a gain-coefficient switched Alexandrite laser. An electro-optic modulator is used to switch between high and low gain states by making use of the polarization dependent gain of Alexandrite. In gain-coefficient switched mode, the laser produces 85 ns pulses with a pulse energy of 240 mJ at a repetition rate of 5 Hz.
Problems with Discontinuous Diffusion/Dispersion Coefficients
Stefano Ferraris
2012-01-01
accurate on smooth solutions and based on a special numerical treatment of the diffusion/dispersion coefficients that makes its application possible also when such coefficients are discontinuous. Numerical experiments confirm the convergence of the numerical approximation and show a good behavior on a set of benchmark problems in two space dimensions.
Rare earth compounds have potential applications in thermoelectric devices due to their large value conductivity and Seebeck coefficient. CePd3 has the highest reported Seebeck coefficient (S ∼ 125 μV/K), when doped appropriately, among all rare-earth compounds. This high value is explained as a result of the placement of the cerium f1 level. (author)
Coefficient Alpha Bootstrap Confidence Interval under Nonnormality
Padilla, Miguel A.; Divers, Jasmin; Newton, Matthew
2012-01-01
Three different bootstrap methods for estimating confidence intervals (CIs) for coefficient alpha were investigated. In addition, the bootstrap methods were compared with the most promising coefficient alpha CI estimation methods reported in the literature. The CI methods were assessed through a Monte Carlo simulation utilizing conditions…
On Burnett coefficients in periodic media
Conca, Carlos; Orive, Rafael; Vanninathan, Muthusamy
2006-03-01
The aim of this work is to demonstrate a curious property of general periodic structures. It is well known that the corresponding homogenized matrix is positive definite. We calculate here the next order Burnett coefficients associated with such structures. We prove that these coefficients form a tensor which is negative semidefinite. We also provide some examples showing degeneracy in multidimension.
A gain-coefficient switched Alexandrite laser
Lee, C. J.; van der Slot, P. J. M.; Boller, K. J.
2013-01-01
We report on a gain-coefficient switched Alexandrite laser. An electro-optic modulator is used to switch between high and low gain states by making use of the polarization dependent gain of Alexandrite. In gain-coefficient switched mode, the laser produces 85 ns pulses with a pulse energy of 240 mJ
Heat transfer coefficient for boiling carbon dioxide
Knudsen, Hans Jørgen Høgaard; Jensen, Per Henrik
1998-01-01
Heat transfer coefficient and pressure drop for boiling carbon dioxide (R744) flowing in a horizontal pipe has been measured. The calculated heat transfer coeeficient has been compared with the Chart correlation of Shah. The Chart Correlation predits too low heat transfer coefficient but the ratio...
Effective stress coefficient for uniaxial strain condition
Alam, Mohammad Monzurul; Fabricius, Ida Lykke
2012-01-01
coefficient from one dimensional rock mechanical deformation. We further investigated the effect of boundary condition on the stress dependency of effective stress coefficient and discussed its application in reservoir study. As stress field in the reservoirs are most unlikely to be hydrostatic, effective...... stress determined under uniaxial strain condition will be more relevant in reservoir studies....
Coefficients of heat transfer in condensation
The authors analyze the problem of determining the coefficients of heat transfer in the condensation of steam on vertical walls in terms of the Prandtl hypothesis and the Reynolds analogy for distribution of the turbulent thermal conductivity across the condensate film. From the assumed model the authors derived expressions for the heat transfer coefficients
Graphite friction coefficient for various conditions
2001-01-01
The friction coefficient the graphite used in the Tsinghua University 10MW High Tem-perature Gas-Cooled Reactor was analyzed for various conditions. The variation of the graphitefriction coefficient was measured for various sliding velocities, sliding distances, normal loads, en-vironments and temperatures. A scanning elector microscope (SEM) was used to analyze the fric-tion surfaces.
Effective stress coefficient for uniaxial strain condition
Alam, M.M.; Fabricius, I.L.
2012-01-01
coefficient from one dimensional rock mechanical deformation. We further investigated the effect of boundary condition on the stress dependency of effective stress coefficient and discussed its application in reservoir study. As stress field in the reservoirs are most unlikely to be hydrostatic, effective...... stress determined under uniaxial strain condition will be more relevant in reservoir studies. Copyright 2012 ARMA, American Rock Mechanics Association....
Effective stress coefficient for uniaxial strain condition
Alam, Mohammad Monzurul; Fabricius, Ida Lykke
2012-01-01
coefficient from one dimensional rock mechanical deformation. We further investigated the effect of boundary condition on the stress dependency of effective stress coefficient and discussed its application in reservoir study. As stress field in the reservoirs are most unlikely to be hydrostatic, effective...
Helioseismic Solar Cycle Changes and Splitting Coefficients
S. C. Tripathy; Kiran Jain; A. Bhatnagar
2000-09-01
Using the GONG data for a period over four years, we have studied the variation of frequencies and splitting coefficients with solar cycle. Frequencies and even-order coefficients are found to change significantly with rising phase of the solar cycle. We also find temporal variations in the rotation rate near the solar surface.
Friction Coefficient for Quarks in Supergravity Duals
Antonyan, E.
2006-01-01
We study quarks moving in strongly-coupled plasmas that have supergravity duals. We compute the friction coefficient of strings dual to such quarks for general static supergravity backgrounds near the horizon. Our results also show that a previous conjecture on the bound has to be modified and higher friction coefficients can be achieved.
On diffusion approximation with discontinuous coefficients
Krylov, N. V.; Liptser, R.
2002-01-01
Convergence of stochastic processes with jumps to diffusion processes is investigated in the case when the limit process has discontinuous coefficients. An example is given in which the diffusion approximation of a queueing model yields a diffusion process with discontinuous diffusion and drift coefficients.
Tracking time-varying coefficient-functions
Nielsen, Henrik Aalborg; Nielsen, Torben Skov; Joensen, Alfred K.;
2000-01-01
otherwise unknown, functions of a low-dimensional input process. These coefficient functions are estimated adaptively and recursively without specifying a global parametric, form, i.e. the method allows for online tracking of the coefficient functions. Essentially, in its most simple form, the method is a...
Estimating Runoff Coefficients Using Weather Radars
Ahm, Malte; Thorndahl, Søren Liedtke; Rasmussen, Michael R.;
2012-01-01
This paper presents a method for estimating runoff coefficients of urban drainage catchments based on a combination of high resolution weather radar data and insewer flow measurements. By utilising the spatial variability of the precipitation it is possible to estimate the runoff coefficients...
Gini coefficient as a life table function
2003-06-01
Full Text Available This paper presents a toolkit for measuring and analyzing inter-individual inequality in length of life by Gini coefficient. Gini coefficient and four other inequality measures are defined on the length-of-life distribution. Properties of these measures and their empirical testing on mortality data suggest a possibility for different judgements about the direction of changes in the degree of inequality by using different measures. A new computational procedure for the estimation of Gini coefficient from life tables is developed and tested on about four hundred real life tables. The estimates of Gini coefficient are precise enough even for abridged life tables with the final age group of 85+. New formulae have been developed for the decomposition of differences between Gini coefficients by age and cause of death. A new method for decomposition of age-components into effects of mortality and composition of population by group is developed. Temporal changes in the effects of elimination of causes of death on Gini coefficient are analyzed. Numerous empirical examples show: Lorenz curves for Sweden, Russia and Bangladesh in 1995, proportional changes in Gini coefficient and four other measures of inequality for the USA in 1950-1995 and for Russia in 1959-2000. Further shown are errors of estimates of Gini coefficient when computed from various types of mortality data of France, Japan, Sweden and the USA in 1900-95, decompositions of the USA-UK difference in life expectancies and Gini coefficients by age and cause of death in 1997. As well, effects of elimination of major causes of death in the UK in 1951-96 on Gini coefficient, age-specific effects of mortality and educational composition of the Russian population on changes in life expectancy and Gini coefficient between 1979 and 1989. Illustrated as well are variations in life expectancy and Gini coefficient across 32 countries in 1996-1999 and associated changes in life expectancy and Gini
Diffusion coefficients of paracetamol in aqueous solutions
Highlights: ► Mutual diffusion coefficients of paracetamol in aqueous dilute solutions. ► Influence of the thermodynamic factors on the variation of their mutual diffusion coefficients. ► Estimation of the mutual limiting diffusion coefficients of the molecular, Dm0, and ionized forms, D±0, of this drug. - Abstract: Binary mutual diffusion coefficients measured by the Taylor dispersion method, for aqueous solutions of paracetamol (PA) at concentrations from (0.001 to 0.050) mol·dm−3 at T = 298.15 K, are reported. From the Nernst–Hartley equation and our experimental results, the limiting diffusion coefficient of this drug and its thermodynamic factors are estimated, thereby contributing in this way to a better understanding of the structure of such systems and of their thermodynamic behaviour in aqueous solution at different concentrations.
Takebe, Shinichi; Abe, Masayoshi [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
2001-03-01
The distribution coefficient is very important parameter for environmental impact assessment on the disposal of radioactive waste arising from research institutes. The literature survey in the country was mainly carried out for the purpose of selecting the reasonable distribution coefficient value on the utilization of this value in the safety evaluation. This report was arranged much informations on the distribution coefficient for inputting to the database for each literature, and was summarized as a literature information data on the distribution coefficient. (author)
The distribution coefficient is very important parameter for environmental impact assessment on the disposal of radioactive waste arising from research institutes. The literature survey in the country was mainly carried out for the purpose of selecting the reasonable distribution coefficient value on the utilization of this value in the safety evaluation. This report was arranged much informations on the distribution coefficient for inputting to the database for each literature, and was summarized as a literature information data on the distribution coefficient. (author)
FRICTION COEFFICIENT OF DIAMOND WIRE SAW
Siniša Dunda
1998-12-01
Full Text Available In order to estimate the diamond wire saw upon quarrying of dimension stone, it is necessary to know the value of a friction coefficient on the driving pulley of the saw. Therefore the numerical value of the friction coefficient between diamond wire and coating of a driving pulley was determined in experimental way. The experiments were conducted under different working conditions. The resulting average value of the friction coefficient upon working in wet and muddy conditions amounted to µ = 0,32.
Soccer ball lift coefficients via trajectory analysis
Goff, John Eric [Department of Physics, Lynchburg College, Lynchburg, VA 24501 (United States); Carre, Matt J, E-mail: goff@lynchburg.ed [Department of Mechanical Engineering, University of Sheffield, Sheffield S1 3JD (United Kingdom)
2010-07-15
We performed experiments in which a soccer ball was launched from a machine while two high-speed cameras recorded portions of the trajectory. Using the trajectory data and published drag coefficients, we extracted lift coefficients for a soccer ball. We determined lift coefficients for a wide range of spin parameters, including several spin parameters that have not been obtained by today's wind tunnels. Our trajectory analysis technique is not only a valuable tool for professional sports scientists, it is also accessible to students with a background in undergraduate-level classical mechanics.
Measuring optical temperature coefficients of Intralipid (registered)
The temperature sensitivities of absorption and reduced scattering coefficients in the range 700-1000 nm are determined for the liquid phantom Intralipid (registered) using spatially resolved continuous wave measurements. The measurements were conducted on a 10 L heated volume of 1% Intralipid (registered) subjected to a 40-30 deg. C cooling regime. The temperature sensitivities of the absorbance coefficients are similar to that expected for pure water. However, the reduced scattering coefficients are more sensitive than can be explained by temperature related density changes, and show an unexpected relationship with wavelength. We have also found that temperature perturbations provide a useful means to evaluate instrument model performance
Generalized Coefficients for Hopf Cyclic Cohomology
Hassanzadeh, Mohammad; Kucerovsky, Dan; Rangipour, Bahram
2014-09-01
A category of coefficients for Hopf cyclic cohomology is defined. It is shown that this category has two proper subcategories of which the smallest one is the known category of stable anti Yetter-Drinfeld modules. The middle subcategory is comprised of those coefficients which satisfy a generalized SAYD condition depending on both the Hopf algebra and the (co)algebra in question. Some examples are introduced to show that these three categories are different. It is shown that all components of Hopf cyclic cohomology work well with the new coefficients we have defined.
Cohomology with Coefficients for Operadic Coalgebras
Anita Majumdar; Donald Yau
2009-09-01
Corepresentations of a coalgebra over a quadratic operad are defined, and various characterizations of them are given. Cohomology of such an operadic coalgebra with coefficients in a corepresentation is then studied.
Combinatorics of 3n-j coefficients
The purpose of this paper is to outline the general theory of recouping coefficients in the theory of angular momentum form the viewpoint of generating functions along the lines initiated by Schwinger, but with special emphasis on the combinatorial aspects
Transonic Blunt Body Aerodynamic Coefficients Computation
Sancho, Jorge; Vargas, M.; Gonzalez, Ezequiel; Rodriguez, Manuel
2011-05-01
In the framework of EXPERT (European Experimental Re-entry Test-bed) accurate transonic aerodynamic coefficients are of paramount importance for the correct trajectory assessment and parachute deployment. A combined CFD (Computational Fluid Dynamics) modelling and experimental campaign strategy was selected to obtain accurate coefficients. A preliminary set of coefficients were obtained by CFD Euler inviscid computation. Then experimental campaign was performed at DNW facilities at NLR. A profound review of the CFD modelling was done lighten up by WTT results, aimed to obtain reliable values of the coefficients in the future (specially the pitching moment). Study includes different turbulence modelling and mesh sensitivity analysis. Comparison with the WTT results is explored, and lessons learnt are collected.
Thermal Expansion Coefficients of Thin Crystal Films
无
2005-01-01
The formulas for atomic displacements and Hamiltonian of a thin crystal film in phonon occupation number representation are obtained with the aid of Green's function theory. On the basis of these results, the formulas for thermal expansion coefficients of the thin crystal film are derived with the perturbation theory, and the numerical calculations are carried out. The results show that the thinner films have larger thermal expansion coefficients.
Photon diffusion coefficient in an absorbing medium
Aronson, Raphael; Corngold, Noel
1999-01-01
A number of investigators have recently claimed, based on both analysis from transport theory and transport theory-based Monte Carlo calculations, that the diffusion coefficient for photon migration should be taken to be independent of absorption. We show that these analyses are flawed and that the correct way of extracting diffusion theory from transport theory gives an absorption-dependent diffusion coefficient. Experiments by two different sets of investigators give conflicting results con...
Experimental determination of bagasse stiffness coefficient
Nelson Arzola de la Peña
2010-01-01
The experimentally determined stiffness coefficient of bagasse is described in this paper. This property defines the behaviour of the reaction forces exerted upon the bagasse layer when being compressed during juice-extraction in a sugar-cane mill. This information is important for correctly analysing sugar-cane mill operation and design. An experimental device was used for obtaining the stiffness coefficient; it consisted of a piston, a piston-skirt, a hydraulic press and instrumentation for...
A Kendall correlation coefficient for functional dependence
Valencia García, Dalia Jazmín; Romo, Juan; Lillo, Rosa E.
2013-01-01
Measuring dependence is a basic question when dealing with functional observations. The usual correlation for curves is not robust. Kendall's coefficient is a natural description of dependence between finite dimensional random variables. We extend this concept to functional observations. Given a bivariate sample of functions, a robust analysis of dependence can be carried out through the functional version of a Kendall correlation coefficient introduced in this paper. We also study its statis...
Clustering coefficient without degree correlations biases
Soffer, Sara Nadiv; Vazquez, Alexei
2004-01-01
The clustering coefficient quantifies how well connected are the neighbors of a vertex in a graph. In real networks it decreases with the vertex degree, which has been taken as a signature of the network hierarchical structure. Here we show that this signature of hierarchical structure is a consequence of degree correlation biases in the clustering coefficient definition. We introduce a new definition in which the degree correlation biases are filtered out, and provide evidence that in real n...
Measuring Resource Inequality: The Gini Coefficient
Michael T. Catalano
2009-07-01
Full Text Available This paper stems from work done by the authors at the Mathematics for Social Justice Workshop held in June of 2007 at Middlebury College. We provide a description of the Gini coefficient and some discussion of how it can be used to promote quantitative literacy skills in mathematics courses. The Gini Coefficient was introduced in 1921 by Italian statistician Corrado Gini as a measure of inequality. It is defined as twice the area between two curves. One, the Lorenz curve for a given population with respect to a given resource, represents the cumulative percentage of the resource as a function of the cumulative percentage of the population that shares that percentage of the resource. The second curve is the line y = x which is the Lorenz curve for a population which shares the resource equally. The Gini coefficient can be interpreted as the percentage of inequality represented in the population with respect to the given resource. We propose that the Gini coefficient can be used to enhance students’ understanding of calculus concepts and provide practice for students in using both calculus and quantitative literacy skills. Our examples are based mainly on distribution of energy resources using publicly available data from the Energy Information Agency of the United States Government. For energy resources within the United States, we find that by household, the Gini coefficient is 0.346, while using the 51 data points represented by the states and Washington D.C., the Gini coefficient is 0.158. When we consider the countries of the world as a population of 210, the Gini coefficient is 0.670. We close with ideas for questions which can be posed to students and discussion of the experiences two other mathematics instructors have had incorporating the Gini coefficient into pre-calculus-level mathematics classes.
Onsager coefficients of a Brownian Carnot cycle
Izumida, Yuki; Okuda, Koji
2010-01-01
We study a Brownian Carnot cycle introduced by T. Schmiedl and U. Seifert [Europhys. Lett. \\textbf{81}, 20003 (2008)] from a viewpoint of the linear irreversible thermodynamics. By considering the entropy production rate of this cycle, we can determine thermodynamic forces and fluxes of the cycle and calculate the Onsager coefficients for general protocols, that is, arbitrary schedules to change the potential confining the Brownian particle. We show that these Onsager coefficients contain the...
Diffusion Coefficients of Fluorinated Surfactants in Water:
Pereira, Luís A.M.; Martins, Luís F. G.; Ascenso, José R.; Morgado, Pedro; Ramalho, João P. P.; Filipe, Eduardo J. M.
2014-01-01
Intradiffusion coefficients of 2,2,2-trifluoroethanol in water have been measured by the pulsed field gradient (PFG)-NMR spin−echo technique as a function of temperature and composition on the dilute alcohol region. The measurements extend the range of compositions already studied in the literature and, for the first time, include the study of the temperature dependence. At the same time, intradiffusion coefficients of 2,2,2-trifluoroethanol, 2,2,3,3,3-pentafluoropropan-1-ol, ...
Investigation of photon attenuation coefficients for marble
The total linear attenuation coefficients μ (cm-1) have been obtained using the XCOM program at photon energies of 1 keV to 1 GeV for six different natural marbles produced in different places in Turkey. The individual contribution of photon interaction processes to the total linear attenuation coefficients for marble has been investigated. The calculated results were also compared with the measurements. The results obtained for marble were also compared with concrete. (note)
Fractal fractal dimensions of deterministic transport coefficients
Klages, R.; Klauss, T.
2003-01-01
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze the structure of the associated irregular diffusion coefficient and current by numerically computing dimensions from box-counting and from the autocorrelation function of these graphs. We find that both dimensions are fractal for large parameter intervals a...
Decomposition of the Gini coefficient using Stata
Alejandro López Feldman
2009-01-01
The Gini coefficient is widely used to measure inequality in the distribution of income, consumption, and other welfare proxies. Decomposing this measure can help you understand the determinants of inequality. In this presentation, I will use income data from Mexico to illustrate a user-written command, descogini, that implements the Gini decomposition proposed by Lerman and Yitzhaki (1985, Review of Economics and Statistics 67: 151–156). Using this command, the Gini coefficient for total inc...
Transport coefficients for inelastic Maxwell mixtures
Garzo, Vicente; Astillero, Antonio
2004-01-01
The Boltzmann equation for inelastic Maxwell models is used to determine the Navier-Stokes transport coefficients of a granular binary mixture in $d$ dimensions. The Chapman-Enskog method is applied to solve the Boltzmann equation for states near the (local) homogeneous cooling state. The mass, heat, and momentum fluxes are obtained to first order in the spatial gradients of the hydrodynamic fields, and the corresponding transport coefficients are identified. There are seven relevant transpor...
Multiple poes and other features of affine Toda field theory
Some perturbative features of affine Toda field theory are explored, in particular the mechanisms responsible for the first-, second- and third-order poles in the conjectured exact factorisable S-matrices in the ADE series of models. It is found that generic collections of Feynman diagrams are responsible for the leading order poles in any of the theories. However, the complexity is such that it has not yet proved possible to analyse all the singularities that occur up to order twelve. Some comments are made on an associated tiling problem and on an interesting connection between the affine Toda couplings and the Clebsch-Gordan decomposition of tensor products. (orig.)
Experimental Mg IX photo recombination rate coefficient
The rate coefficient for radiative and dielectronic recombination of beryllium-like magnesium ions was measured with high resolution at the Heidelberg heavy-ion storage ring TSR. In the electron-ion collision energy range 0-207 eV resonances due to 2s → 2p (ΔN = 0) and 2s → 3l (ΔN = 1) core excitations were detected. At low energies below 0.15 eV the recombination rate coefficient is dominated by strong 1s2(2s2p 3P)7l resonances with the strongest one occurring at an energy of only 21 meV. These resonances decisively influence the Mg IX recombination rate coefficient in a low temperature plasma. The experimentally derived Mg IX dielectronic recombination rate coefficient (±15% systematical uncertainty) is compared with the recommendation by Mazzotta et al. (1998, AandAS, 133, 403) and the recent calculations by Gu (2003, ApJ, 590, 1131) and by Colgan et al. (2003, AandA, 412, 597). These results deviate from the experimental rate coefficient by 130%, 82% and 25%, respectively, at the temperature where the fractional abundance of Mg IX is expected to peak in a photoionized plasma. At this temperature a theoretical uncertainty in the 1s2(2s2p 3P)7l resonance positions of only 100 meV would translate into an uncertainty of the plasma rate coefficient of almost a factor 3. This finding emphasizes that an accurate theoretical calculation of the Mg IX recombination rate coefficient from first principles is challenging. (authors)
Experimental Mg IX photorecombination rate coefficient
Schippers, S.; Schnell, M.; Brandau, C.; Kieslich, S.; Müller, A.; Wolf, A.
2004-07-01
The rate coefficient for radiative and dielectronic recombination of beryllium-like magnesium ions was measured with high resolution at the Heidelberg heavy-ion storage ring TSR. In the electron-ion collision energy range 0-207 eV resonances due to 2s -> 2p (Δ N = 0) and 2s -> 3l (Δ N=1) core excitations were detected. At low energies below 0.15 eV the recombination rate coefficient is dominated by strong 1s2 (2s 2p 3P) 7l resonances with the strongest one occuring at an energy of only 21 meV. These resonances decisively influence the Mg IX recombination rate coefficient in a low temperature plasma. The experimentally derived Mg IX dielectronic recombination rate coefficient (±15% systematical uncertainty) is compared with the recommendation by Mazzotta et al. (1998, A&AS, 133, 403) and the recent calculations by Gu (2003, ApJ, 590, 1131) and by Colgan et al. (2003, A&A, 412, 597). These results deviate from the experimental rate coefficient by 130%, 82% and 25%, respectively, at the temperature where the fractional abundance of Mg IX is expected to peak in a photoionized plasma. At this temperature a theoretical uncertainty in the 1s2 (2s 2p 3P) 7l resonance positions of only 100 meV would translate into an uncertainty of the plasma rate coefficient of almost a factor 3. This finding emphasizes that an accurate theoretical calculation of the Mg IX recombination rate coefficient from first principles is challenging.
Inverse determination of local heat transfer coefficient
The naphtalene sublimation and transient methods are widely used techniques which are particularly useful in complex flows and solid shapes. Both techniques have been widely used with considerable success but they are not appropriate for high temperatures. An alternative method to obtain the local convective heat transfer coefficient, that does not have any disadvantages noted above, is the inverse procedure. Determination of the space-variable heat transfer coefficient on a complex shape surface requires the solution of the nonlinear inverse heat conduction problem. The distribution of the heat transfer coefficient is calculated from temperature measurements at interior points of the solid and measured fluid temperature. The unknown parameters associated with the solution are selected to achieve the closest agreement in a least squares sense between the computed and measured temperatures using the Levenberg - Marquardt method. The nonlinear least - squares problem is parameterized by assuming the staircase changes of heat transfer coefficient on the boundary or expressing the space variations of the heat transfer coefficient in the functional form. The uncertainties in the estimated components of the heat transfer coefficient or in the estimated parameters are determined for the temperature measurements with known and unknown standard deviations. The determination of the circumferential heat transfer coefficient distribution on the heated tube with two longitudinal fins in cross flow demonstrates the accuracy of the developed method. The actual experimental data were used. Experiments were performed with an array of vertical tubes arranged in staggered pattern. The experimental results reported herein are among the first that show the variation of the local heat transfer coefficients over the circumference of the finned tube. Most data reported previously were acquired for smooth tubes at low temperatures. The main advantage of the method is that it does not
Experimental Mg IX photorecombination rate coefficient
Schippers, S; Brandau, C; Kieslich, S; Müller, A; Wolf, A
2004-01-01
The rate coefficient for radiative and dielectronic recombination of berylliumlike magnesium ions was measured with high resolution at the Heidelberg heavy-ion storage ring TSR. In the electron-ion collision energy range 0-207 eV resonances due to 2s -> 2p (Delta N = 0) and 2s -> 3l (Delta N=1) core excitations were detected. At low energies below 0.15 eV the recombination rate coefficient is dominated by strong 1s2 (2s 2p 3P) 7l resonances with the strongest one occuring at an energy of only 21 meV. These resonances decisively influence the Mg IX recombination rate coefficient in a low temperature plasma. The experimentally derived Mg IX dielectronic recombination rate coefficient (+-15% systematical uncertainty) is compared with the recommendation by Mazzotta et al. (1998, A&AS, 133, 403) and the recent calculations by Gu (2003, ApJ, 590, 1131) and by Colgan et al. (2003, A&A, 412, 597). These results deviate from the experimental rate coefficient by 130%, 82% and 25%, respectively, at the temperatu...
Experimental methodology for obtaining sound absorption coefficients
Carlos A. Macía M
2011-07-01
Full Text Available Objective: the authors propose a new methodology for estimating sound absorption coefficients using genetic algorithms. Methodology: sound waves are generated and conducted along a rectangular silencer. The waves are then attenuated by the absorbing material covering the silencer’s walls. The attenuated sound pressure level is used in a genetic algorithm-based search to find the parameters of the proposed attenuation expressions that include geometric factors, the wavelength and the absorption coefficient. Results: a variety of adjusted mathematical models were found that make it possible to estimate the absorption coefficients based on the characteristics of a rectangular silencer used for measuring the attenuation of the noise that passes through it. Conclusions: this methodology makes it possible to obtain the absorption coefficients of new materials in a cheap and simple manner. Although these coefficients might be slightly different from those obtained through other methodologies, they provide solutions within the engineering accuracy ranges that are used for designing noise control systems.
Ekström, Joakim
2011-01-01
Spearman’s rank correlation coefficient is shown to be a deterministic transformation of the empirical polychoric correlation coefficient. The transformation is a homeomorphism under given marginal probabilities, and has a fixed point at zero. Moreover, the two measures of association for ordinal variables are asymptotically equivalent, in a certain sense. If the ordinal variables arise from discretizations, such as groupings of values into categories, Spearman’s rank correlation coefficient ...
Improved Diffusion Coefficients for Stellar Plasmas
Brassard, P.; Fontaine, G.
2014-04-01
We are currently working on the fourth generation of our codes for building evolutionary and static models of hot subdwarf and white dwarf stars. One of the improvements of these codes consists in an update of all the microphysics involved in the computations. As part of our efforts, we have taken a look at possible improvements for the diffusion coefficients. Since the publication of the widely used diffusion coefficients of Paquette et al. (1986), the number-crunching power of computers has immensely increased, allowing more accurate computations of the triple collision integrals. We have thus produced new tables of diffusion coefficients with higher accuracy and higher resolution than before, of general use in stellar astrophysics.
Curvature of Indoor Sensor Network: Clustering Coefficient
2009-03-01
Full Text Available We investigate the geometric properties of the communication graph in realistic low-power wireless networks. In particular, we explore the concept of the curvature of a wireless network via the clustering coefficient. Clustering coefficient analysis is a computationally simplified, semilocal approach, which nevertheless captures such a large-scale feature as congestion in the underlying network. The clustering coefficient concept is applied to three cases of indoor sensor networks, under varying thresholds on the link packet reception rate (PRR. A transition from positive curvature (“meshed” network to negative curvature (“core concentric” network is observed by increasing the threshold. Even though this paper deals with network curvature per se, we nevertheless expand on the underlying congestion motivation, propose several new concepts (network inertia and centroid, and finally we argue that greedy routing on a virtual positively curved network achieves load balancing on the physical network.
A drying coefficient for building materials
Scheffler, Gregor Albrecht; Plagge, Rudolf
2009-01-01
The drying experiment is an important element of the hygrothermal characterisation of building materials. Contrary to other moisture transport experiments as the vapour diffusion and the water absorption test, it is until now not possible to derive a simple coefficient for the drying. However, in...... many cases such a coefficient would be highly appreciated, e.g. in interaction of industry and research or for the distinction and selection of suitable building materials throughout design and practise. This article first highlights the importance of drying experiments for hygrothermal...... characterisation of building materials on which the attempt is based to standardize the drying experiment as well as to derive a single number material coefficient. The drying itself is briefly reviewed and existing approaches are discussed. On this basis, possible definitions are evaluated. Finally, a drying...
Understanding correlation coefficients in treaty verification
DeVolpi, A.
1991-11-01
When a pair of images are compared on a point-by-point basis, the linear-correlation coefficient is usually used as a measure of similarity or dissimilarity. This paper evaluates the theoretical underpinnings and limitation of the linear-correlation coefficient, as well as other related statistics, particularly for cases where inherent white noise is present. As a result of the limitations in linear-correlation, an additional step has been derived -- local-sum clustering -- in order to improve recognition of small dissimilarities in a pair images. Results show that three-stage procedure, consisting of first establishing congruence of the two images, than using the linear-correlation coefficient as a test of true negatives, and finally qualifying a true positive by using the cluster (local-sum) method. These algorithmic stages would be especially useful in arms control treaty verification.
The axial distribution of reactivity coefficients
The purpose of the present work is to investigate the correlation of the axial distributions of the different reactivity coefficients with the neutron flux and the neutron flux squared. Calculations were carried out for the Zion Unit 2 PWR. Reactivity coefficients, forward fluxes and adjoint fluxes were all computed and correlations obtained. The core length was divided into 7 axial regions in order to obtain the effect on reactivity in the reactor as a whole of changing the cross sections in each axial region in turn. The parameters chosen for change were coolant density, coolant temperature and fuel temperature. The results appear to bear out our original hypothesis that the reactivity coefficient profiles have a higher positive correlation with the total flux squared profile than with the linear flux profile. (authors). 5 refs., 2 figs
Oxygen atom loss coefficient of carbon nanowalls
Mozetic, Miran, E-mail: miran.mozetic@guest.arnes.si [Jozef Stefan Institute, Jamova cesta 39, 1000 Ljubljana (Slovenia); Vesel, Alenka [Jozef Stefan Institute, Jamova cesta 39, 1000 Ljubljana (Slovenia); Stoica, Silviu Daniel; Vizireanu, Sorin; Dinescu, Gheorghe [National Institute for Laser, Plasma and Radiation Physics, 409 Atomistilo Street, PO Box MG-36, Magurele, Bucharest 077125 (Romania); Zaplotnik, Rok [Jozef Stefan Institute, Jamova cesta 39, 1000 Ljubljana (Slovenia)
2015-04-01
Highlights: • Atomic oxygen loss coefficient on carbon nanowalls (CNWs) was evaluated. • Atomic oxygen loss coefficient of CNW is the largest among any known materials. • Surface atom loss is a major loss mechanism at room temperatures. - Abstract: Extremely high values of atomic oxygen loss coefficient on carbon nanowall (CNW) surface are reported. CNW layers consisting of interconnected individual nanostructures with average length of 1.1 μm, average thickness of 66 nm and surface density of 3 CNW/μm{sup 2} were prepared by plasma jet enhanced chemical-vapor deposition using C{sub 2}H{sub 2}/H{sub 2}/Ar gas mixtures. The samples were characterized by scanning electron microscopy (SEM), atomic force microscopy (AFM), transmission electron microscopy (TEM), Raman spectrometry (RS) as well as X-ray photoelectron spectroscopy (XPS). The surface loss coefficient was measured at room temperature in a flowing afterglow at different densities of oxygen atoms supplied from inductively coupled radiofrequency O{sub 2} plasma. The RF generator operated at 13.56 MHz and different nominal powers up to 900 W corresponding to different O-atom density in the afterglow up to 1.3 × 10{sup 21} m{sup −3}. CNW and several different samples of known coefficients for heterogeneous surface recombination of neutral oxygen atoms have been placed separately in the afterglow chamber and the O-atom density in their vicinity was measured with calibrated catalytic probes. Comparison of measured results allowed for determination of the loss coefficient for CNWs and the obtained value of 0.59 ± 0.03 makes this material an extremely effective sink for O-atoms.
Super-b4 coefficients in supergravity
For covariantly chiral superfields coupled to background Yang-Mills superfields and defined on a curved superspace background, the superfield analogue of the heat kernel associated with the differential operator appearing in the quadratic part of the action is defined. The super-b4 coefficient in the asymptotic expansion of the kernel is computed using a system of superspace normal coordinates. These coefficients are shown to determine the one-loop trace supermultiplet and the one-loop logarithmic divergence for pure supergravity. (author)
Criterions for fixing regulatory seismic acceleration coefficients
Acceleration coeffficients to be taken into account in seismic areas for calculation of structures are defined in national seismic regulations. Joined to the described qualitative requirements, these coefficients represent a balance between precaution costs and avoided damages, both in terms of material repairing costs and damage to human life. Persons in charge of fixing these coefficients must be informed of corresponding quantitative aspects. Data on seismic motions occurrencies and consequences are gathered here and convoluted to mean damage evaluations. Indications on precaution costs are joined, which shows that currently recommended levels of seismic motions are high relatively to financial profitability, and represent in fact an aethical choice about human life value
Bayes estimation of the multiple correlation coefficient
Tiwari, RC
1989-01-01
Let R denote the population multiple correlation coefficient of one variable on the other (m-1), in a m-variate normal —2 distribution. Bayes estimator of R, given only the sample 2 multiple correlation coefficient R, is derived with respect to the squared error loss function and a Beta prior distribution.-2 These results are then related to the Bayes estimates of R /(1-_o R), a parameter considered recently by Muirhead (1985). The ideas are illustrated and the effect of various parameters st...
ANL results for LMFR reactivity coefficients benchmark
The fast reactor analysis methods developed at ANL were extensively tested in ZPR and ZPPR experiments, applied to EBR-2 and FFTF test reactors. The basic nuclear data library used was ENDF/B-V.2 with the ETOE-2 data processing code and the ENDF/B-VI. Multigroup constants were generated by Monte Carlo code MCNP2-2. Neutron flux calculation were done by DIF3D code applying neutron diffusion theory and finite difference method. The results obtained include basic parameters; fuel and structure regional Doppler coefficients; geometry expansion fuel coefficients; kinetics parameters. In general, agreement between phase 1 and 2 results were excellent
Viscous Coefficients of a Hot Pion Gas
Sourav Sarkar
2013-01-01
Full Text Available The steps essentially involved in the evaluation of transport coefficients in linear response theory using Kubo formulas are to relate the defining retarded correlation function to the corresponding time-ordered one and to evaluate the latter in the conventional perturbation expansion. Here we evaluate the viscosities of a pion gas carrying out both the steps in the real-time formulation. We also obtain the viscous coefficients by solving the relativistic transport equation in the Chapman-Enskog approximation to leading order. An in-medium π π cross-section is used in which spectral modifications are introduced in the propagator of the exchanged ρ .
Shear viscosity coefficient of liquid lanthanides
Present paper deals with the computation of shear viscosity coefficient (η) of liquid lanthanides. The effective pair potential v(r) is calculated through our newly constructed model potential. The Pair distribution function g(r) is calculated from PYHS reference system. To see the influence of local field correction function, Hartree (H), Tailor (T) and Sarkar et al (S) local field correction function are used. Present results are compared with available experimental as well as theoretical data. Lastly, we found that our newly constructed model potential successfully explains the shear viscosity coefficient (η) of liquid lanthanides
Study on the Friction Coefficient in Grinding
无
2002-01-01
The friction between the abrasive grains and workpi ec e is a crutial factor determining the main grinding output. Few studies have bee n carried out investigating the values of the friction coefficient in grinding, due to the difficulty of direct measurement. In this paper, a mathematical model of the friction coefficient in grinding has been established with the aid of a new grinding parameter C ge, which has close relations to wheel wear rate Z s, metal removal rate Z w, specific energy u and gr...
Coefficient of Restitution of Wet Tennis Balls
Eugene Jang; Tony Kim
2014-01-01
The coefficient of restitution of a damp tennis ball is of interest to tennis players. Using a spray bottle, water was added to a tennis ball and the mass of water on the wet ball was determined. The ball was then dropped from a fixed height of 0.86 m. The motion was recorded with a video camera and the bounce height was measured. Using the bounce height and the original height, the coefficient of restitution for that mass of added water was determined. The research found the mass of wa...
Estimating inbreeding coefficients from NGS data
Vieira, Filipe Garrett; Fumagalli, Matteo; Albrechtsen, Anders;
2013-01-01
Most methods for Next-Generation Sequencing (NGS) data analyses incorporate information regarding allele frequencies using the assumption of Hardy-Weinberg Equilibrium (HWE) as a prior. However, many organisms including domesticated, partially selfing or with asexual life cycles show strong...... deviations from HWE. For such species, and specially for low coverage data, it is necessary to obtain estimates of inbreeding coefficients (F) for each individual beforecalling genotypes. Here, we present two methods for estimating inbreeding coefficients from NGS data based on an Expectation...
Mohammed, Ahmed; Zeleke, Aklilu
2015-01-01
We introduce a class of second-order ordinary differential equations (ODEs) with variable coefficients whose closed-form solutions can be obtained by the same method used to solve ODEs with constant coefficients. General solutions for the homogeneous case are discussed.
Pressure-viscosity coefficient of biobased lubricants
Film thickness is an important tribological property that is dependent on the combined effect of lubricant properties, material property of friction surfaces, and the operating conditions of the tribological process. Pressure-viscosity coefficient (PVC) is one of the lubricant properties that influe...
Regularity of the Interband Light Absorption Coefficient
M Krishna
2010-06-01
In this paper we consider the interband light absorption coefficient (ILAC), in a symmetric form, in the case of random operators on the -dimensional lattice. We show that the symmetrized version of ILAC is either continuous or has a component which has the same modulus of continuity as the density of states.
Infinite matrices, wavelet coefficients and frames
N. A. Sheikh
2004-01-01
Full Text Available We study the action of A on f∈L2(ℝ and on its wavelet coefficients, where A=(almjklmjk is a double infinite matrix. We find the frame condition for A-transform of f∈L2(ℝ whose wavelet series expansion is known.
Combinatorics of 3n-j coefficients
The binary coupling theory of the addition of n+1 angular momenta, or, equivalently, of the reduction of n+1 multiple Kronecker products of the unitary irreducible representations of the unitary group SU(2), is reviewed with emphasis on the combinatorial structure. Using labeled binary trees, we give the generating function for the coupled angular-momentum function corresponding to every binary coupling scheme. From this result, we obtain the generating function for the coefficients for all recoupling coefficients. We generalize the methods of Schwinger, but formulated in the ring of polynomials. A key concept for recoupling coefficients is the double Pfaffian, which is closely related to MacMahon's master theorem. Work in progress includes the classification of 3n-j coefficients, the investigation of representations of U(n+1) that arise from its right action on the 2x(n+1) matrix Z of indeterminates whose columns are the two-component spinors associated with the (n+1)-angular-momentum basis function, and related problems
Calculation of aberration coefficients by ray tracing
Oral, Martin; Lencová, Bohumila
2009-01-01
Roč. 109, č. 11 (2009), s. 1365-1373. ISSN 0304-3991 R&D Projects: GA AV ČR IAA100650805 Institutional research plan: CEZ:AV0Z20650511 Keywords : Aberrations * Aberration coefficients * Ray tracing * Regression * Fitting Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 2.067, year: 2009
The Evolution of Pearson's Correlation Coefficient
Kader, Gary D.; Franklin, Christine A.
2008-01-01
This article describes an activity for developing the notion of association between two quantitative variables. By exploring a collection of scatter plots, the authors propose a nonstandard "intuitive" measure of association; and by examining properties of this measure, they develop the more standard measure, Pearson's Correlation Coefficient. The…
Confidence Intervals for Cronbach's Coefficient Alpha Values
A.J. Koning (Alex); Ph.H.B.F. Franses (Philip Hans)
2003-01-01
textabstractCoefficient Alpha, which is widely used in empirical research, estimates the reliability of a test consisting of parallel items. In practice it is difficult to compare values of alpha across studies as it depends on the number of items used. In this paper we provide a simple solution, wh
Pressure viscosity coefficient of vegetable oils
The elastohydrodynamic (EHD) pressure viscosity coefficient (PVC) of ten vegetable oils from commodity and new crops, and two petroleum-based oils, polyalphaolefin (PAO) and hexadecane, were investigated. PVC was measured using three different methods: the So and Klaus (S-K) procedure from oil visco...
Coefficient Quantization for Frames in Banach Spaces
Casazza, P. G.; Dilworth, S. J.; Odell, E.; Schlumprecht, Th.; Zsak, Andras
2007-01-01
Let $(e_i)$ be a fundamental system of a Banach space. We consider the problem of approximating linear combinations of elements of this system by linear combinations using quantized coefficients. We will concentrate on systems which are possibly redundant. Our model for this situation will be frames in Banach spaces.
Diffusion Coefficient Measurements: Sulphuric Acid – Air
Brus, David; Neitola, K.; Petäjä, T.; Lihavainen, H.
Helsinki : -, 2010, P2L7. ISBN N. [International Aerosol Conference IAC 2010. Helsinki (FI), 29.08.2010-03.09.2010] Institutional research plan: CEZ:AV0Z40720504 Keywords : diffusion coefficient * sulphuric acid * flow tube Subject RIV: CF - Physical ; Theoretical Chemistry www.iac2010.fi
Coefficient Omega Bootstrap Confidence Intervals: Nonnormal Distributions
Padilla, Miguel A.; Divers, Jasmin
2013-01-01
The performance of the normal theory bootstrap (NTB), the percentile bootstrap (PB), and the bias-corrected and accelerated (BCa) bootstrap confidence intervals (CIs) for coefficient omega was assessed through a Monte Carlo simulation under conditions not previously investigated. Of particular interests were nonnormal Likert-type and binary items.…
Uses and Misuses of the Correlation Coefficient.
Onwuegbuzie, Anthony J.; Daniel, Larry G.
The purpose of this paper is to provide an in-depth critical analysis of the use and misuse of correlation coefficients. Various analytical and interpretational misconceptions are reviewed, beginning with the egregious assumption that correlational statistics may be useful in inferring causality. Additional misconceptions, stemming from…
Experimental determination of bagasse stiffness coefficient
Nelson Arzola de la Peña
2010-04-01
Full Text Available The experimentally determined stiffness coefficient of bagasse is described in this paper. This property defines the behaviour of the reaction forces exerted upon the bagasse layer when being compressed during juice-extraction in a sugar-cane mill. This information is important for correctly analysing sugar-cane mill operation and design. An experimental device was used for obtaining the stiffness coefficient; it consisted of a piston, a piston-skirt, a hydraulic press and instrumentation for measuring the pressures so produced and piston position at different times. Compression rate, humidity level and degree of bagasse fragmentation were the experimental factors taken into account in the experimental design. The investigation was carried out with 40%-80% humidity level and up to 0.06 compression rates. All experimental factors proved statistically significant in the bagasse stiffness coefficient experimental model so obtained. Bagasse was seen to behave as a very rigid elastic material under normal sugar-mill pressure operating conditions, having 50 MPa to 20,000 MPa stiffness coefficient values.
Molar extinction coefficients of some fatty acids
Sandhu, G.K.; Singh, K.; Lark, B.S.; Gerward, Leif
2002-01-01
) and stearic acid (C18H36O2), has been measured at the photon energies 81, 356, 511, 662, 1173 and 1332 keV. Experimental values for the molar extinction coefficient, the effective atomic number and the electron density have been derived and compared with theoretical calculations. There is good...
Power coefficient anomaly in Joyo, (2)
In this report, the presumption about the mechanism having caused the power coefficient anomaly in Joyo during the 75 MW power-raising test in 1979 is described. After the previous report, the new information about the results of the post-irradiation examination and the analysis of the power coefficient of Joyo were able to be obtained. From these information, the mechanism of causing the anomaly was presumed as follows. In 50 MW operation, the fuel burnup reached about 10,000 MWD/ton at the end of second cycle, and produced fission gas was almost retained in fuel pellets. When the power was raised from 50 MW to 75 MW for the first time, the fission gas began to be released when 50 MW was somewhat exceeded. The fission gas release caused the temperature rise and cracking of fuel pellets, and elongated fuel stack length abruptly. These phenomena induced to enlarge the fuel expansion reactivity effect and Doppler reactivity effect, and caused the anomalous behavior of power coefficient. After reaching 75 MW, the fuel stack length did not respond normally to reactor power change, and the magnitude of power coefficient became smaller. The reactivity was lost considerably from the core after the anomaly. (Kako, I.)
Second virial coefficients of dipolar hard spheres
Philipse, A.P.; Kuipers, B.W.M.
2010-01-01
An asymptotic formula is reported for the second virial coefficient B2 of a dipolar hard-sphere (DHS) fluid, in zero external field, for strongly coupled dipolar interactions. This simple formula, together with the one for the weak-coupling B2, provides an accurate prediction of the second virial co
Detailed Investigations of Load Coefficients on Grates
Andersen, Thomas Lykke; Rasmussen, Michael R.; Frigaard, Peter
In this report is presented the results of model tests carried out at Dept. of Civil Engineering, aalborg University (AAU) on behalf of DONG Energy A/S and Vattenfall A/S, Denmark. The objective of the tests was to investigate the load coefficient on different grates and a solid plate for designing...
Coefficient of Restitution of a Tennis Ball
Andre Roux
2007-06-01
Full Text Available The coefficient of restitution (COR of a tennis ball was investigated over a range of impact velocities. It was found that the COR of the ball was lower than ATP regulations specify, and that the COR decreased with increasing impact velocity.
Coefficient of Restitution of a Tennis Ball
Andre Roux; Jennifer Dickerson
2007-01-01
The coefficient of restitution (COR) of a tennis ball was investigated over a range of impact velocities. It was found that the COR of the ball was lower than ATP regulations specify, and that the COR decreased with increasing impact velocity.
Bitplane Image Coding With Parallel Coefficient Processing.
Auli-Llinas, Francesc; Enfedaque, Pablo; Moure, Juan C; Sanchez, Victor
2016-01-01
Image coding systems have been traditionally tailored for multiple instruction, multiple data (MIMD) computing. In general, they partition the (transformed) image in codeblocks that can be coded in the cores of MIMD-based processors. Each core executes a sequential flow of instructions to process the coefficients in the codeblock, independently and asynchronously from the others cores. Bitplane coding is a common strategy to code such data. Most of its mechanisms require sequential processing of the coefficients. The last years have seen the upraising of processing accelerators with enhanced computational performance and power efficiency whose architecture is mainly based on the single instruction, multiple data (SIMD) principle. SIMD computing refers to the execution of the same instruction to multiple data in a lockstep synchronous way. Unfortunately, current bitplane coding strategies cannot fully profit from such processors due to inherently sequential coding task. This paper presents bitplane image coding with parallel coefficient (BPC-PaCo) processing, a coding method that can process many coefficients within a codeblock in parallel and synchronously. To this end, the scanning order, the context formation, the probability model, and the arithmetic coder of the coding engine have been re-formulated. The experimental results suggest that the penalization in coding performance of BPC-PaCo with respect to the traditional strategies is almost negligible. PMID:26441420
Tracking Time-Varying Coefficient-Functions
Nielsen, Henrik Aalborg; Nielsen, Torben Skov; Joensen, Alfred K.; Madsen, Henrik; Holst, Jan
1999-01-01
A conditional parametric ARX-model is an ARX-model in which the parameters re replaced by smooth functions of an, possibly multivariate, externalinput signal. These functions are called coefficient functions is suggested. Essentially, in its most simple form, this method is a combination of recur...
Measuring correlations between non-stationary series with DCCA coefficient
Kristoufek, Ladislav
2014-05-01
In this short report, we investigate the ability of the DCCA coefficient to measure correlation level between non-stationary series. Based on a wide Monte Carlo simulation study, we show that the DCCA coefficient can estimate the correlation coefficient accurately regardless the strength of non-stationarity (measured by the fractional differencing parameter d). For a comparison, we also report the results for the standard Pearson correlation coefficient. The DCCA coefficient dominates the Pearson coefficient for non-stationary series.
Coefficient convexity of divisors of x^n-1
Decker, Andreas
2010-01-01
We say a polynomial f having integer coefficients is strongly coefficient convex if the set of coefficients of f consists of consecutive integers only. We establish various results suggesting that the divisors of x^n-1 with integer coefficients have the tendency to be strongly coefficient convex and have small coefficients. The case where n=p^2*q with p and q primes is studied in detail.
A novel parameterization of x-ray interaction cross-sections is developed, and employed to describe the x-ray linear attenuation coefficient and mass energy absorption coefficient for both elements and mixtures. The new parameterization scheme addresses the Z-dependence of elemental cross-sections (per electron) using a simple function of atomic number, Z. This obviates the need for a complicated mathematical formalism. Energy dependent coefficients describe the Z-direction curvature of the cross-sections. The composition dependent quantities are the electron density and statistical moments describing the elemental distribution. We show that it is possible to describe elemental cross-sections for the entire periodic table and at energies above the K-edge (from 6 keV to 125 MeV), with an accuracy of better than 2% using a parameterization containing not more than five coefficients. For the biologically important elements and the energy range 30- keV, the parameterization utilizes four coefficients. At higher energies, the parameterization uses fewer coefficients with only two coefficients needed at megavoltage energies
Minior Actinide Doppler Coefficient Measurement Assessment
Nolan E. Hertel; Dwayne Blaylock
2008-04-10
The "Minor Actinide Doppler Coefficient Measurement Assessment" was a Department of Energy (DOE) U-NERI funded project intended to assess the viability of using either the FLATTOP or the COMET critical assembly to measure high temperature Doppler coefficients. The goal of the project was to calculate using the MCNP5 code the gram amounts of Np-237, Pu-238, Pu-239, Pu-241, AM-241, AM-242m, Am-243, and CM-244 needed to produce a 1E-5 in reactivity for a change in operating temperature 800C to 1000C. After determining the viability of using the assemblies and calculating the amounts of each actinide an experiment will be designed to verify the calculated results. The calculations and any doncuted experiments are designed to support the Advanced Fuel Cycle Initiative in conducting safety analysis of advanced fast reactor or acceoerator-driven transmutation systems with fuel containing high minor actinide content.
Relations between coefficients of fractional parentage
For each of the (9/2) (11/2), and (13/2) single j shells we have only one state with J=j v=3 for a five particle system. For four identical particles there can be more than one state of seniority four. We note some 'ratio' relations for the coefficients of fractional parentage for the four and five identical particle systems, which are found in the works of de Shalit and Talmi [Nuclear Shell Theory (Academic Press, New York, 1963)] and Talmi [Simple Models of Complex Nuclei (Harwood Academic, Reading, UK, 1993)] to be useful for explaining the vanishing of a five particle coefficients of fractional parentage (cfp). These relations are used to show that there is a special (g9/2)4 I=4 v=4 wave function that cannot be admixed with an I=4 v=2 wave function, even with seniority violating interactions
Electrochemical determination of partition coefficients of drugs.
Kontturi, K; Murtomäki, L
1992-10-01
An electrochemical method for the determination of partition coefficients of drugs that can exist as ions in aqueous solutions is presented. The method involves cyclic voltammetry at the polarizable interface between two immiscible electrolyte solutions. Because n-octanol is an unsuitable solvent for electrochemical purposes, 1,2-dichloroethane, which has electronic properties similar to those of n-octanol, was used in the measurements. The values obtained could be correlated with the values for n-octanol-water partition taken from the literature by an approach based on the linear solvation relationship: log P1 = a log P2 + b; in this relationship, a and b are constants and P1 and P2 correspond to the two different organic and aqueous phase partition equilibria. Furthermore, aqueous diffusion coefficients of drugs were determined from voltammograms. PMID:1432622
Rotational dissipation and the Miesowicz coefficients.
Simões, M; Yamaguti, K; Palangana, A J
2009-12-01
In this work, we will study the relative contribution of each of the two dissipative channels of the Eriksen, Leslie, and Parodi (ELP) approach to the observed values of the Miesowicz viscosity coefficients of the nematic liquid crystals. According to the fundamental equation of the liquid crystal's viscosity dissipative process, TS=-integral d3r(sigma)ijA(ij)+hxN , there are two channels by which the nematic viscous dissipation can occur: or it occurs by means of a shear flow configuration, where A(ij) is the characterizing term, or it occurs by means of a rotational configuration, where N is the characterizing term (these parameters will be defined in the paper). It will be also shown that this relative contribution can be measured by a simple relationship connecting the Miesowicz coefficients, which exhibits a quasitemperature independent behavior, suggesting that it is nearly constant through the entire domain of the nematic phase. PMID:20365179
Doppler coefficient measurements in Zebra Core 5
Measurements using a central hot loop in Zebra Core 5 are described. Results are given for the Doppler coefficients found in a number of assemblies with PuO2 and 16% PuO2/84% depleted UO2 pins, loaded with different combinations of steel, sodium or void pins. The mixed oxide results are in general about 20% more negative than was calculated using the FD2 data set, but agreement is good if the plutonium contributions in the calculations are omitted. The small positive Doppler coefficient calculated for Pu239 was not observed, and two measurements indicated instead a small negative effect. The Doppler effect in the mixed oxide systems was found to vary approximately as 1/T. The results from the empty loop and non-fissile assemblies indicate either a small negative Doppler effect in steel or alternatively the presence of an unexplained expansion effect. (author)
Testing the correlated random coefficient model
Heckman, James J.; Schmierer, Daniel; Urzua, Sergio
2010-01-01
The recent literature on instrumental variables (IV) features models in which agents sort into treatment status on the basis of gains from treatment as well as on baseline-pretreatment levels. Components of the gains known to the agents and acted on by them may not be known by the observing economist. Such models are called correlated random coefficient models. Sorting on unobserved components of gains complicates the interpretation of what IV estimates. This paper examines testable implicati...
LOSS COEFFICIENT DEPENDENCE OF TURBINE BLADE CASCADE
Matějka, M.; Šafařík, P.; Luxa, Martin; Šimurda, David; Synáč, J.
Glasgow: ASME, 2010, s. 1-9. ISBN 978-0-7918-4402-1. [ASME Turbo Expo 2010. Glasgow (GB), 14.06.2010-18.06.2010] R&D Projects: GA MŠk(CZ) 1M06031; GA AV ČR(CZ) IAA200760801 Institutional research plan: CEZ:AV0Z20760514 Keywords : loss coefficient * turbine cascade * pneumatic measurement Subject RIV: BK - Fluid Dynamics http://www.asmeconferences.org/TE10/ConfSpecInfo.cfm
Basketball Surfaces and Coefficient of Restitution
Kristyn Peacock; Faith Pearson
2015-01-01
A basketball was released from varying drop heights to simulate the impact speeds of a typical soft, medium, and hard dribble. This was repeated across four different surfaces that students typically play on–exposed aggregate concrete, maple wood flooring, EPI Outdoor Sport flooring, and playground rubber mesh. From the measured drop and bounce heights, the coefficient of restitution(COR)was calculated. It was concluded that only playground rubber mesh had COR’s below the regula...
Confidence Intervals for Cronbach's Coefficient Alpha Values
Koning, Alex; Franses, Philip Hans
2003-01-01
textabstractCoefficient Alpha, which is widely used in empirical research, estimates the reliability of a test consisting of parallel items. In practice it is difficult to compare values of alpha across studies as it depends on the number of items used. In this paper we provide a simple solution, which amounts to computing the confidence intervals of an alpha, as these intervals automatically account for differences across the numbers of items. We also give appropriate statistics to test for ...
Confidence Intervals for Cronbach's Coefficient Alpha Values
Koning, A. J.; Franses, Ph.H.B.F.
2003-01-01
Coefficient Alpha, which is widely used in empirical research, estimates the reliability of a test consisting of parallel items. In practice it is difficult to compare values of alpha across studies as it depends on the number of items used. In this paper we provide a simple solution, which amounts to computing the confidence intervals of an alpha, as these intervals automatically account for differences across the numbers of items. We also give appropriate statistics to test for significant ...
Significane levels of linear correlation coefficients
The determination of the significance (confidence) levels of linear correlation coefficients is discussed. Several methods which have been used in the analysis of channel correlations in nuclear physics are compared. A relatively new method, the bootstrap, is described and applied to a number of examples. Significance levels obtained with the different methods are usually comparable, but there are cases for which large differences exist. Reasons for these differences and the advantages of the bootstrap over previous methods are discussed. (orig.)
Recursive algorithms, branching coefficients and applications
Lyakhovsky, Vladimir
2010-01-01
Recurrent relations for branching coefficients in affine Lie algebras integrable highest weight modules are studied. The decomposition algorithm based on the injection fan technique is adopted to the situation where the Weyl denominator becomes singular with respect to a reductive subalgebra. We study some modifications of the injection fan technique and demonstrate that it is possible to define the "subtracted fans" that play the role similar to the original ones. Possible applications of subtracted fans in CFT models are considered.
Sensitivity of the Heat Transfer Coefficient Calculation
Singer, Sasa
2014-01-01
The purpose of the Liscic/Petrofer probe is to determine the cooling intensity during liquid quenching in laboratory and workshop environments. The surface heat transfer coefficient is calculated by the one-dimensional finite volume method from the smoothed temperature curve, measured at a near-surface point in the probe. Smoothed reference temperature curves for oil and water, based on measurements made by the probe, are used in a series of numerical experiments to investigate the sensitivit...
Efficient estimation of price adjustment coefficients
Lyhagen, Johan
1999-01-01
The price adjustment coefficient model of Amihud and Mendelson (1987) is shown to be suitable for estimation by the Kalman filter. A techique that, under some commonly used conditions, is asymptotically efficient. By Monte Carlo simulations it is shown that both bias and mean squared error are much smaler compared to the estimator proposed by Damodaran and Lim (1991) and Damodaran (1993). A test for the adeqacy of the model is also proposed. Using data from four minor, the nordic countries ex...
Testing local versions of correlation coefficients
Kalogirou, Stamatis
2011-01-01
The aim of this paper is to define and test local versions of standard correlation coefficients in statistical analysis. This research is motivated by the increasing number of applications using local versions of exploratory and explanatory spatial data analysis methods. A common example of the latter is local regression. Methods such as the Geographically Weighted Regression argue that it is necessary to check spatial non-stationarity in the relationships between a geographic phenomenon and ...
Correlation and prediction of gaseous diffusion coefficients.
Marrero, T. R.; Mason, E. A.
1973-01-01
A new correlation method for binary gaseous diffusion coefficients from very low temperatures to 10,000 K is proposed based on an extended principle of corresponding states, and having greater range and accuracy than previous correlations. There are two correlation parameters that are related to other physical quantities and that are predictable in the absence of diffusion measurements. Quantum effects and composition dependence are included, but high-pressure effects are not. The results are directly applicable to multicomponent mixtures.
On the Central Coefficients of Riordan Matrices
Barry, Paul
2013-01-01
We use the Lagrange-Bürmann inversion theorem to characterize the generating function of the central coefficients of the elements of the Riordan group of matrices. We apply this result to calculate the generating function of the central elements of a number of explicit Riordan arrays, defined by rational expressions, and in two cases we use the generating functions thus found to calculate the Hankel transforms of the central elements, which are themselves expressible as combinatorial polynomi...
Coefficients of symmetric square L-functions
LAU; Yuk-Kam
2010-01-01
Let λsym2f(n) be the n-th coefficient in the Dirichlet series of the symmetric square L-function associated with a holomorphic primitive cusp form f.We prove Ω± results for λsym2f(n) and evaluate the number of positive(resp.,negative) λsym2f(n) in some intervals.
AN EXHAUSTIVE COEFFICIENT OF RANK CORRELATION
Agostino Tarsitano; Rosetta Lombardo
2011-01-01
Rank association is a fundamental tool for expressing dependence in cases in which data are arranged in order. Measures of rank correlation have been accumulated in several contexts for more than a century and we were able to cite more than thirty of these coefficients, from simple ones to relatively complicated definitions invoking one or more systems of weights. However, only a few of these can actually be considered to be admissible substitutes for Pearson’s correlation. The main drawback ...
Fresnel coefficients for a layer of NIM
Reflection and transmission of traveling and evanescent waves by a layer of material with a negative index of refraction (NIM) is studied by means of the Fresnel coefficients. We derive their values in the “NIM limit”, and we show that this limit is consistent with the exact solution. It is also indicated that simply substituting the negative values of the relative permittivity and permeability of the NIM material into the exact solution leads to incorrect results for evanescent waves.
Seebeck coefficients of half-metallic ferromagnets
Balke, Benjamin; OUARDI, SIHAM; Graf, Tanja; Barth, Joachim; Blum, Christian G. F.; FECHER, GERHARD H.; Shkabko, Andrey; Weidenkaff, Anke; Felser, Claudia
2009-01-01
In this report the Co2 based Heusler compounds are discussed as potential materials for spin voltage generation. The compounds were synthesized by arcmelting and consequent annealing. Band structure calculations were performed and revealed the compounds to be half-metallic ferromagnets. Magnetometry was performed on the samples and the Curie temperatures and the magnetic moments were determined. The Seebeck coefficients were measured from low to ambient temperatures for all compounds. For sel...
ON DAMPING COEFFICIENT DUE TO PHASE TRANSFORMATION
Din-YuHSIEH
2003-01-01
The damping coefficient of capillary waves due to the evaporation-condensation process at the interface of the two phases of a fluid is evaluated. To highlight the mechanism of the effect of heat and mass transfer across the interface between regions of liquid and vapor, potential flow of incompressible fluids are assumed. Thus other mechanisms of damping are neglected. To fascilitate the analysis, the method of multiple-scale is employed in the analysis, even though the problem is linear.
Thin film description by wavelet coefficients statistics
Boldyš, Jiří; Hrach, R.
2005-01-01
Roč. 55, č. 1 (2005), s. 55-64. ISSN 0011-4626 Grant ostatní: GA UK(CZ) 173/2003 Institutional research plan: CEZ:AV0Z10750506 Keywords : thin films * wavelet transform * descriptors * histogram model Subject RIV: BD - Theory of Information Impact factor: 0.360, year: 2005 http://library.utia.cas.cz/separaty/2009/ZOI/boldys-thin film description by wavelet coefficients statistics .pdf
The attenuation coefficients in CT: Didactic review
The review article refers details about the derivation of the Attenuation coefficient of the CT-Number, the electron density and physical density, the effective atomic number, dual KV scanning, the performance of different scanners, furtheron the CT-numbers of intracranial structures, the attempts of characterization of tissue by CT, measurements of effective atomic number and electron density, distribution and probability of occurance of CT-numbers, and distribution of CT-numbers in space. (AJ)
Uranium GI absorption coefficients for young children
Uranium is ubiquitously found in drinking water and food. The absorption fraction (f1) is an important parameter in risk assessment of uranium burdens from ingestion. Although absorption of uranium from the gastrointestinal tract (GI) has been studied extensively in both animals and humans in the past, human data among young children are rare. In a previous study based on measurements of uranium concentration in only 11 bone-ash samples collected by Health Canada, the GI absorption coefficient for uranium ingestion by infants, about 3 months of age were determined. The result was 0.256 which was much higher than the ICRP recommended f1 values of 0.04 for infants and 0.02 for anyone more than 1 year of age. To extend the study, a total of 73 bone-ash samples were selected for children ranging in age from 0 to 7 years. The estimated absorption coefficients were 0.093±0.113 for infants, and 0.050±0.032 for 1 - 7 years of age. This study provides human absorption coefficients of ingested uranium for young children of two age groups. (author)
Feedback reactivity coefficients and their coupling
Coupled reactivity feedback coefficients which accounts for variation in fuel temperature and moderator void simultaneously, have been determined for swimming pool type research reactor namely Pakistan Research Reactor PARR-1. The state of art is core criticality calculations, employing lattice cell code WIMS-D/4 and application of Taylor series expansion for core reactivity up to third order, involving two variables, i.e. fuel temperature and coolant void. The spectral effects in one region due to change of parameter in other region have also been studied. When spectral changes in moderator region due to 20 K change in fuel temperature have been incorporated in the calculation of fuel temperature coefficient, the results seems to be improved by 4.12%. Further, the results of void coefficient of reactivity show the improvement of 0.1% when the spectral effect in fuel region due to 5% change in void in moderator region is taken into account. These differences seem to be an improvement in the results, as physically any change in one region is accompanied by change in the other region
Feedback reactivity coefficients and their coupling
Khan, Rustam [Pakistan Institute of Engineering and Applied Sciences, P.O. Nilore, Islamabad (Pakistan)]. E-mail: rustamzia@yahoo.com; Hamid, Tehsin [Directorate of Safety, P.O. Box 1114, Islamabad (Pakistan); Bakhtyar, Sabiha [Pakistan Institute of Nuclear Science and Technology, P.O. Nilore, Islamabad (Pakistan)
2007-05-15
Coupled reactivity feedback coefficients which accounts for variation in fuel temperature and moderator void simultaneously, have been determined for swimming pool type research reactor namely Pakistan Research Reactor PARR-1. The state of art is core criticality calculations, employing lattice cell code WIMS-D/4 and application of Taylor series expansion for core reactivity up to third order, involving two variables, i.e. fuel temperature and coolant void. The spectral effects in one region due to change of parameter in other region have also been studied. When spectral changes in moderator region due to 20 K change in fuel temperature have been incorporated in the calculation of fuel temperature coefficient, the results seems to be improved by 4.12%. Further, the results of void coefficient of reactivity show the improvement of 0.1% when the spectral effect in fuel region due to 5% change in void in moderator region is taken into account. These differences seem to be an improvement in the results, as physically any change in one region is accompanied by change in the other region.
Analysis of flow coefficient in chair manufacture
Ivković Dragoljub
2005-01-01
Full Text Available The delivery on time is not possible without the good-quality planning of deadlines, i.e. planning of the manufacturing process duration. The study of flow coefficient enables the realistic forecasting of the manufacturing process duration. This paper points to the significance of the study of flow coefficient on scientific basis so as to determine the terms of the end of the manufacture of chairs made of sawn timber. Chairs are the products of complex construction, often almost completely made of sawn timber as the basic material. They belong to the group of export products, so it is especially significant to analyze the duration of the production cycle, and the type and the degree of stoppages in this type of production. Parallel method of production is applied in chair manufacture. The study shows that the value of flow coefficient is close to one or higher, in most cases. The results indicate that the percentage of interoperational stoppage is unjustifiably high, so it is proposed how to decrease the percentage of stoppages in the manufacturing process.
The Phi-coefficient, the Tetrachoric Correlation Coefficient, and the Pearson-Yule Debate
Ekström, Joakim
2011-01-01
Two measures of association for dichotomous variables, the phi-coefficient and the tetrachoric correlation coefficient, are reviewed and differences between the two are discussed in the context of the famous so-called Pearson-Yule debate, that took place in the early 20th century. The two measures of association are given mathematically rigorous definitions, their underlying assumptions are formalized, and some key properties are derived. Furthermore, existence of a continuous bijection betwe...
Tests of Hypotheses Arising in the Correlated Random Coefficient Model
Heckman, James J.; Schmierer, Daniel
2010-01-01
This paper examines the correlated random coefficient model. It extends the analysis of Swamy (1971, 1974), who pioneered the uncorrelated random coefficient model in economics. We develop the properties of the correlated random coefficient model and derive a new representation of the variance of the instrumental variable estimator for that model. We develop tests of the validity of the correlated random coefficient model against the null hypothesis of the uncorrelated random coefficient model.
Measuring correlations between non-stationary series with DCCA coefficient
Ladislav Kristoufek
2013-01-01
In this short report, we investigate the ability of the DCCA coefficient to measure correlation level between non-stationary series. Based on a wide Monte Carlo simulation study, we show that the DCCA coefficient can estimate the correlation coefficient accurately regardless the strength of non-stationarity (measured by the fractional differencing parameter $d$). For a comparison, we also report the results for the standard Pearson's correlation coefficient. The DCCA coefficient dominates the...
Hydrodynamic Coefficients of Ships with Forward Speed in Shallow Waters
M.HASANADIL; DUANWen-yang; WANGYu
2004-01-01
Effects of depth and forward speed on hydrodynamic coefficients of ships are presented in this paper. A modified simple Green function technique was used to calculate 2D coefficients while strip theory was used to calculate 3D coefficients. Numerical results are provided for hydrodynamic coefficients of parabolic hull ship. It is found out that both depth and forward speed have considerable effects on hydrodynamic coefficients of ship.
Transport coefficients of He(+) ions in helium.
Viehland, Larry A; Johnsen, Rainer; Gray, Benjamin R; Wright, Timothy G
2016-02-21
This paper demonstrates that the transport coefficients of (4)He(+) in (4)He can be calculated over wide ranges of E/N, the ratio of the electrostatic field strength to the gas number density, with the same level of precision as can be obtained experimentally if sufficiently accurate potential energy curves are available for the X(2)Σu (+) and A(2)Σg (+) states and one takes into account resonant charge transfer. We start by computing new potential energy curves for these states and testing their accuracy by calculating spectroscopic values for the separate states. It is established that the potentials obtained by extrapolation of results from d-aug-cc-pVXZ (X = 6, 7) basis sets using the CASSCF+MRCISD approach are each in exceptionally close agreement with the best potentials available and with experiment. The potentials are then used in a new computer program to determine the semi-classical phase shifts and the transport cross sections, and from these the gaseous ion transport coefficients are determined. In addition, new experimental values are reported for the mobilities of (4)He(+) in (4)He at 298.7 K, as a function of E/N, where careful consideration is given to minimizing various sources of uncertainty. Comparison with previously measured values establishes that only one set of previous data is reliable. Finally, the experimental and theoretical ion transport coefficients are shown to be in very good to excellent agreement, once corrections are applied to account for quantum-mechanical effects. PMID:26896985
Control in the coefficients with variational crimes
Evgrafov, Anton; Marhadi, Kun Saptohartyadi
2012-01-01
fourth order. Methods which do not require approximation subspaces to conform to the smoothness requirements dictated by the PDE are very attractive for such problems. However, variational formulations of such methods normally contain boundary integrals whose dependence on the small, with respect to...... “volumetric” Lebesgue norm, changes of the coefficients is generally speaking not continuous. We utilize the lifting formulation of the discontinuous Galerkin method to deal with this issue.Our main result is that limit points of sequences of designs verifying discrete versions of stationarity can also be...
Measuring subdiffusion parameter and subdiffusion coefficient
We derive theoretical formulas which allow one to extract the subdiffusion parameter α and subdiffusion coefficient Dα form measured concentration profiles of transported substance in a subdiffusive medium. The parameters occur in the relation defining the subdiffusion 2> = 2Dαtα/[Γ(1+α)] with α 2> denotes the mean-square displacement of a Brownian particle. The analysis is performed separately for the medium, where optical measurements of concentrations are possible (the medium is transparent for a laser beam), as well as for the non-transparent medium. (author)
Determination of coefficient matrices for ARMA model
A new recursive algorithm for determining coefficient matrices of ARMA model from measured data is presented. The Yule-Walker equations for the case of ARMA model are derived from the ARMA innovation equation. The recursive algorithm is based on choosing appropriate form of the operator functions and suitable representation of the (n+1)-th order operator functions according to ones with the lower order. Two cases, when the order of the AR part is equal to one of the MA part, and the optimal case, were considered. (author) 5 refs
Semiclassical OPE coefficients from 3D gravity
Chang, Chi-Ming
2016-01-01
We present a closed form expression for the semiclassical OPE coefficients that are universal for all 2D CFTs with a "weak" light spectrum, by taking the semiclassical limit of the fusion kernel. We match this with a properly regularized and normalized bulk action evaluated on a geometry with three conical defects, analytically continued in the deficit angles beyond the range for which a metric with positive signature exists. The analytically continued geometry has a codimension-one coordinate singularity surrounding the heaviest conical defect. This singularity becomes a horizon after Wick rotating to Lorentzian signature, suggesting a connection between universality and the existence of a horizon.
Energy reflection coefficient of backscattered heavy ions
An energy-dependent albedo problem, i.e., the energy-dependent leakage spectrum for a half-space of material irradiated by a monoenergetic beam of ions is investigated in this paper. For this purpose the flux decomposition procedure is applied. It is based on separation of the ion flux into terms that are exactly analytically solved and those calculated by the ordinary DPN approximation. Slowing down of particles is described by elastic scattering and various models for dealing with the anisotropy of ion scattering. The ion energy reflection coefficient is computed and compared to the values obtained by the exact and variational methods as well as DPN flux approximation
Kinetic coefficients for quark-antiquark plasma
The quark-antiquark plasma near equilibrium is studied. The results are based on the Heinz kinetic equations with the Boltzmann collision operator approximated by a relaxation term with the relaxation time, τ, treated as a small parameter. Linear in τ solutions of these equations are used to calculate the transport coefficients: the non-abelian version of Ohm's law, and the shear and volume viscosities. We introduce new chemical potentials which determine the color density matrix of quarks (antiquarks). Gradients of these potentials generate color currents. 12 refs. (author)
Effective Diffusion Coefficients in Coal Chars
Johnsson, Jan Erik; Jensen, Anker
2001-01-01
Knowledge of effective diffusion coefficients in char particles is important when interpreting experimental reactivity measurements and modeling char combustion or NO and N2O reduction. In this work, NO and N2O reaction with a bituminous coal char was studied in a fixed-bed quartz glass reactor....... In the case of strong pore diffusion limitations, the error in the interpretation of experimental results using the mean pore radius could be a factor of 5 on the intrinsic rate constant. For an average coal char reacting with oxygen at 1300 K, this would be the case for particle sizes larger than...
ON DAMPING COEFFICIENT DUE TO PHASE TRANSFORMATION
Din-Yu HSIEH
2003-01-01
The damping coefficient of capillary waves due to the evaporation-condensation process at the interface of the two phases of a fluid is evaluated.To highlight the mechanism of the effect of heat and mass transfer across the interface between regions of liquid and vapor,potential flow of incompressible fluids are assumed.Thus other mechanisms of damping are neglected.To fascilitate the analysis,the method of multiple-scale is employed in the analysis,even though the problem is linear.
Studies of Gaseous Multiplication Coefficient in Isobutane
Lima, Iara B.; Vivaldini, Túlio C.; Gonçalves, Josemary A. C.; Botelho, Suzana; Ridenti, Marco A.; Fonte, Paulo; Mangiarotti, Alessio; Pascholati, Paulo R.; Bueno Tobias, Carmen C.
2010-05-01
This work presents the studies of gaseous multiplication coefficient behavior for isobutane, as function of the reduced electric field, by means of signal amplitude analysis. The experimental method used is based on the Pulsed Townsend technique, which follows from Townsend equation solution for a uniform electric field. In our configuration, the anode is made of a high resistivity (2.1012 Ω.cm) glass, while the cathode is of aluminium. In order to validate the technique and to analyze effects of non-uniformity, results for nitrogen, which has well-established data available in literature, are also presented.
Studies of Gaseous Multiplication Coefficient in Isobutane
This work presents the studies of gaseous multiplication coefficient behavior for isobutane, as function of the reduced electric field, by means of signal amplitude analysis. The experimental method used is based on the Pulsed Townsend technique, which follows from Townsend equation solution for a uniform electric field. In our configuration, the anode is made of a high resistivity (2.1012 Ω.cm) glass, while the cathode is of aluminium. In order to validate the technique and to analyze effects of non-uniformity, results for nitrogen, which has well-established data available in literature, are also presented.