bluuebunny/crossref_metadata_2025 huggingface dataset:
Quantization: Towards a comparison between methods
Authors: Tuynman G. M.
Published: July 2002

In this paper it is shown that the procedure of geometric quantiztion applied to Kähler manifolds gives the following result: the Hilbert space ℋ consists, roughly speaking, of holomorphic functions on the phase space M and to each classical observable f (i.e., a real function on M) is associated an operator f on ℋ as follows: first multiply by f+ 1/4 ℏΔdRf (ΔdR being the Laplace–de Rham operator on the Kähler manifold M) and then take the holomorphic part [see G. M. Tuynman, J. Math. Phys. 27, 573 (1987)]. This result is correct on compact Kähler manifolds and correct modulo a boundary term ∫Mdα on noncompact Kähler manifolds. In this way these results can be compared with the quantization procedure of Berezin [Math. USSR Izv. 8, 1109 (1974); 9, 341 (1975); Commun. Math. Phys. 40, 153 (1975)], which is strongly related to quantization by *-products [e.g., see C. Moreno and P. Ortega-Navarro; Amn. Inst. H. Poincaré Sec. A: 38, 215 (1983); Lett. Math. Phys. 7, 181 (1983); C. Moreno, Lett. Math. Phys. 11, 361 (1986); 12, 217 (1986)]. It is shown that on irreducible Hermitian spaces [see S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces (Academic, Orlando, FL, 1978] the contravariant symbols (in the sense of Berezin) of the operators f as above are given by the functions f+ 1/4 ℏΔdRf. The difference with the quantization result of Berezin is discussed and a change in the geometric quantization scheme is proposed.
A singular integral equation formulation and solution for transport in semi-infinite ducts
Authors: Malvagi Fausto , Pomraning G. C.
Published: July 2002

An unusual two-group transport equation, associated with particle transport in a duct, and possessing a full ‘‘removal matrix’’ is considered. An approximate solution for the exiting distribution is obtained by an application of the facile (FN) method. An integral transform technique is used to transform the problem into a singular integral equation, which serves as a basis for the FN approximation. The set of basis functions is derived from the singular eigenfunctions of the original problem. Comparisons of the reflection probability with numerical solutions show the accuracy and the remarkable efficiency of the FN method.
An unconventional canonical quantization of local scalar fields over quantum space-time
Authors: Banai Miklós
Published: July 2002

The central issue addressed in this paper is the following: Is the conventional procedure the only one for extending the canonical quantization method for local field theories or does another way exist? Here an unconventional extension of the canonical quantization method is presented for a classical local field theory consisting of N real scalar fields. This approach is essentially a reconsideration of the conventional procedure in an alternative way offered by a recent new approach of classical local field theories. The proposed canonical commutation relations have a solution in the A-valued Hilbert space ℋA =ℋ⊗A, unique up to A-unitary equivalence, where A is the algebra of the bounded operators of the Hilbert space L2(R3). The canonical equations as operator equations are equivalent in form to the classical field equations, and are a priori well-defined for interacting systems, too. This model of quantized fields lacks some of the difficulties of the conventional approach, e.g., the rigorous application of the interaction picture is not stemmed by Haag’s theorem and the ultraviolet catastrophe (there are no ultraviolet divergences in the S matrices of the model). Examples of the model satisfying the asymptotic condition provide examples for the axioms of Haag–Kastler while they satisfy the axioms Wightman only partially. The consistent interpretation of the model requires a new concept of space-time, a quantum space-time. The ‘‘local’’ state space ℋA of the model is constructed over this quantum space-time.
Towards the proof of the cosmic censorship hypothesis in cosmological space-times
Authors: Krȯlak Andrzej
Published: July 2002

A theorem supporting the view that the cosmic censorship hypothesis proved recently by Krȯlak [A. Krȯlak, Gen. Relativ. Gravit. 15, 99 (1983); J. Class. Quantum Grav. 3, 267 (1986)] for asymptotically flat space-times, is true in general, is generalized so that it is applicable to cosmological situations.
Cartan and relativistic spin fluids in a rotating cylinder
Authors: Krisch J. P. , Smalley L. L.
Published: July 2002

Spin-fluid sources and their metric are obtained for an infinite rotating cylinder. The calculation is performed in general relativity and the Cartan theory. The spin fluids are significantly different in the two theories.
Quantum mechanics with higher time derivatives: Some mathematical facts and the inclusion of gravitational self-interaction
Authors: Popova Alla D.
Published: July 2002

The inclusion of self-interaction, in particular, gravitational into the quantum mechanics of a particle (first quantization) implies two necessary features: dealing with quantum mechanics involving the second time derivative and the construction of a variational principle maintaining the rescaling invariance of the wave function. The relevant variational principle is constructed which is not the principle of extremality of any action. Some general mathematical facts lain in the basis of this construction are discussed.
An Sp(2)-covariant version of generalized canonical quantization of dynamical systems with linearly dependent constraints
Authors: Batalin I. A. , Lavrov P. M. , Tyutin I. V.
Published: July 2002

An Sp(2)-covariant version of the method of generalized canonical quantization of dynamical systems with linearly dependent first-class constraints is proposed. The existence theorem for solutions of generating equations of a gauge algebra is proved and the natural arbitrariness in these solutions is described. The scheme proposed is shown to be equivalent to the standard version of generalized canonical quantization.
S-matrix and Jost functions of Schrödinger Hamiltonian related to the Stark effect
Authors: Kvitsinsky Andrei A. , Kostrykin Vadim V.
Published: July 2002

The scattering theory for the Hamiltonian of the Stark effect is considered. A partial decomposition of the S-matrix is derived corresponding to separation of variables in the parabolic coordinates, and the analytic structure of the partial Jost functions and S-matrices are studied.
Symmetry reduction of the Wess–Zumino model and supersymmetric reduced systems
Authors: Légaré M.
Published: July 2002

An investigation of the supersymmetric reduction of the Wess–Zumino model is carried out for the subgroups of the Poincaré group. The necessary conditions for residual supersymmetry derived from super Poincaré transformations and a classification of the subalgebras of the Poincaré algebra, which might give rise to supersymmetric residual systems, are obtained. Two supersymmetric reductions of the off-shell model (with interactions) by bidimensional subgroups are presented.
The one-speed albedo and the slab albedo problems for the FBIS kernel
Authors: Tezcan C.
Published: July 2002

The one-speed albedo and the slab albedo problems are studied for the forward–backward–isotropic scattering (FBIS) kernel. The method of elementary solutions is used and the expansion coefficients are obtained by solving the resulting Fredholm integral equations. The zeroth-order results for the FBIS kernel are reduced to BIS, FIS models, and also to the well-known IS model. In the limit as the slab thickness becomes infinite, the special cases for the albedo problem for the same models are also obtained.
On the classification of Lie subalgebras and Lie subgroups
Authors: Grigore D. R. , Popp O. T.
Published: July 2002

Starting from a paper of Patera et al. [J. Math. Phys. 16, 1597 (1975)], the classification of Lie subalgebras is analyzed, up to conjugation, for a Lie algebra having a solvable ideal. Here, the hypothesis of semidirect product structure is not made; this leads to some natural affine structure. Next, a complete classification is made of closed Lie subgroups of a given Lie group, up to conjugation (supposing the corresponding classification for Lie subalgebras is known). This is illustrated in the case of the group SE(3).
Integrability conditions and the integration of the Bianchi identities in Petrov type-I vacuum space-times
Authors: Bonanos S.
Published: July 2002

The three-dimensional matrix formulation of the vacuum Einstein equations is used to derive the general form of the integrability conditions arising under an arbitrary choice of frame in Petrov type-I space-times. When these integrability conditions are satisfied, the Bianchi identities can be integrated, giving simple analytic expressions for the components of the Weyl tensor in terms of its invariants and the parameters determining the frame.
Pertinent statistics for describing a system of particles
Authors: Zinoun A. , Cortois J.
Published: July 2002

Algebraical structures that characterize different statistics for describing a system of particles are represented by equivalence classes of bilinear maps. Theorems that connect these structures are presented.
Canonical transformation method for static-source meson Hamiltonians
Authors: Bolsterli M.
Published: July 2002

A new canonical-transformation method is used to treat static-source meson Hamiltonians.
On the characters of solvable finite groups
Authors: Caride A. O. , Zanette S. I. , Nogueira S. R. A.
Published: July 2002

A method to calculate the characters of a finite group in terms of the characters of a normal subgroup is proposed with the only condition that the factor group may be a cyclic group of prime order. The method can also be used recursively to calculate the characters of any solvable finite group.
Right-invariant metrics on the Lie group SU(3) and the Gell-Mann–Okubo formula
Authors: Coquereaux Robert , Esposito-Farese Gilles
Published: July 2002

The classification of right-invariant Riemannian metrics (and Riemannian structures) on SU(3) is studied and a parametrization for all of them will be given. It will be indicated how to discuss flavor symmetry breaking in hadronic physics using this language long with a geometrical interpretation for the Gell-Mann–Okubo formula.
Functional measure for gauge fields on periodic lattices
Authors: Reisz T.
Published: July 2002

The effective action for non-Abelian gauge theories on a finite, periodic lattice is derived by imposing the static, time averaged Landau gauge. This gauge appears to be very convenient for problems in which there is one preferred direction, as in the finite temperature case.
Non-Abelian singletons
Authors: Flato M. , Fronsdal C.
Published: July 2002

Non-Abelian vector gauge theories, with gauge groups of the type U(1)×SU(n)×SU(n′)×⋅⋅⋅, have been formulated in terms of scalar singleton fields. Massless vector mesons appear as two-singleton states. The theory is a gauge theory already at the singleton level, and singleton brst transformations induce BRST transformations of the ordinary kind.
U
q
covariant oscillators and vertex operators
Authors: Hadjiivanov L. K. , Paunov R. R. , Todorov I. T.
Published: July 2002

U q (sl(2)) covariant Bose and Fermi oscillators are studied systematically and applied to constructing vertex operators and Uq invariant blocks. For qp=−1 (p=2,3,...) a p2-dimensional unitary Fock space representation of the Bose oscillator algebra 𝒜−(q) is constructed. This representation does not allow, however, for the construction of all Uq invariant blocks associated with an indecomposable representation of Uq. An extension of 𝒜− is needed in this case, which involves operators creating states of q spin projection ±p/2 from the Fock vacuum. The extended algebra only has infinite-dimensional indefinite metric space representations. An algebraic notion of trace is introduced (provided q2≠1 in the Bose case). This allows the introduction of a family of (in general, mixed) Uq invariant ‘‘temperature’’ states, such that the vacuum expectation value appears in the zero temperature limit.
The functional integral for a free particle on a half-plane
Authors: Carreau Michel
Published: July 2002

A free nonrelativistic particle moving in two dimensions on a half-plane can be described by self-adjoint Hamiltonians characterized by boundary conditions imposed on the systems. The most general boundary condition is parameterized in terms of the elements of an infinite-dimensional matrix. We construct the Brownian functional integral for each of these self-adjoint Hamiltonians. Nonlocal boundary conditions are implemented by allowing the paths striking the boundary to jump to other locations on the boundary. Analytic continuation in time results in the Green’s functions of the Schrödinger equation satisfying the boundary condition characterizing the self-adjoint Hamiltonian.
The C*-algebra obtained by completing the quantum group Funq
(SU(2))
Authors: Meister Andreas
Published: July 2002

For positive q, the scalar product defined by the integral on Funq(SU(2)) is used to complete Funq(SU(2)) to a Hilbert space ℋq. The dual map to the coproduct on Funq(SU(2)) makes ℋq into a Banach algebra without unit. Multiplication from the left defines a *-representation of Funq(SU(2)) on ℋq and thus Funq(SU(2)) can be completed to a C*-algebra ℱq. This C*-algebra is shown to coincide with the C*-algebra SUν(2) considered by Woronowicz [Publ. RIMS, Kyoto Univ. 23, 117 (1987)]. General representations of ℱq are discussed and the spectrum of ℱq and its Jacobson topology are calculated.
Multiparameter deformations of the universal enveloping algebras of the simple Lie algebras A
l for all l≥2 and the Yang–Baxter equation
Authors: Cornwell J. F.
Published: July 2002

A {1+1/2l(l−1)}-parameter deformation of the universal enveloping algebra of the simple Lie algebra Al(=sl(l+1, C)) is derived for all l≥2, starting from a certain multiparameter matrix that satisfies the quantum Yang–Baxter equation. It is shown that this Hopf algebra has the same product relations and antipode as the standard one-parameter deformation Uq(sl(l+1,C)), but has a different coproduct. It is also shown that for all l≥2 there exists a 1/2l(l−1)-parameter Hopf algebra whose product relations are merely the commutation relations of Al itself, but whose coproduct is different from the usual one for the universal enveloping algebra of Al.
Comment on: Hamiltonian formulation of a theory with constraints [U. Kulshreshta, J. Math. Phys. 33, 633 (1992)]
Authors: Corichi Alejandro
Published: July 2002

The Hamiltonian formulation of a constrained dynamical system, analyzed by Kulshreshta [J. Math. Phys. 33, 633 (1992)] is discussed. The theory possesses four coordinates and four primary second class constraints and thus two physical degrees of freedom. The correct equations of motion for the system are given. The reduced theory (q4=k) is shown to have three primary and one secondary second class constraints instead of three primary first class ones as claimed by Kulshreshta. The equations of motion are derived using the Dirac bracket.
Deformation map and Hermitian representations of k-Poincaré algebra
Authors: Maślanka Pawel/
Published: July 2002

A deformation map from the classical to the deformed Poincaré algebra is given. The Hermitian representations of deformed algebra corresponding to all orbits in p space are explicitly constructed.
Some remarks on sectional curvature and tidal accelerations
Authors: Hall G. S. , Hossack A. D.
Published: July 2002

Some recent results of Beem and Parker regarding tidal accelerations and the algebraic structure of the Riemann tensor are generalized.
Some properties of the inertia tensor in Dixon’s theory
Authors: San Miguel A. , Vicente F.
Published: July 2002

On the assumption that the Riemannian curvature and its variation over space–time are small enough and using an explicit expression for the inertia tensor defined by Dixon in his approach to describe the dynamics of extended bodies in general relativity, a proof of the semidefinite negative signature of the inertia tensor is given. Also, a coordinate evolution equation for the inertia tensor of an isolated extended body moving on a reference three-manifold is obtained.
Representations of quantum SU(3)
Authors: Capps Richard H.
Published: July 2002

The problem of constructing representations of the quantum group SU(3)q is considered. This algebra may be constructed from two sets of SU(2)q generators, oriented at an angle of 120° from each other. If one makes use of known results for SU(2)q, the problem reduces to finding the transformation matrices between two sets of basis vectors, in each of which the Casimir operator for one of the SU(2)q’s is diagonal. Two simple prescriptions are given for finding these matrices in a general case, using a convenient set of variables. An exact solution is given for all irreducible representations in which the maximum weight multiplicity is 2.
Exact solution of evolution equation for randomly interrupted diffusion
Authors: L/uczka Jerzy , Niemiec Mariusz , Piotrowski Edward
Published: July 2002

An evolution equation of integro-differential type for a one-dimensional probability distribution of a linear process driven by additive randomly interrupted Gaussian white noise is exactly solved. A family of propagators for a probability distribution of the process is obtained. Selected examples of a time-dependent distribution are presented.
Spectral properties of observables and convex mappings in quantum mechanics
Authors: Cassinelli Gianni , Lahti Pekka J.
Published: July 2002

Observables of a physical system can be identified with convex mappings sending states into probability measures. The properties of these mappings determine the spectral properties of the observables. The mutually exclusive cases of injective and surjective mappings are characterized, and the convex structure of their ranges are investigated. In particular, the validity of the Krein–Milman property for these convex sets is studied.
On the spinor structure of the proton wave function
Authors: Carimalo C.
Published: July 2002

In the framework of a relativistic extension of the three-constituent–quark model of the proton, spinors of third rank in Dirac indices are used to express covariantly the spin structure of S-state baryons of spin 1/2 or 3/2. These spinors are defined directly in terms of 4-spinors of the Dirac space D, and classified according to the irreducible representations of both the (internal) Lorentz spin group acting on E=D×D×D, and the permutation group S3. All possible combinations of spin, flavor, and momentum distributions of quarks in S-state baryons are considered from the point of view of S3. We also suggest the possibility of defining Dirac matrices acting on E, which may prove important in view of studying three-quark confinement forces through an effective relativistic wave equation for the proton.
Convergence of Nelson diffusions with time-dependent electromagnetic potentials
Authors: Posilicano Andrea , Ugolini Stefania
Published: July 2002

Some recent results on the convergence of Nelson diffusions are extended to the case of Schrödinger operators with time-dependent electromagnetic potentials. It is proven that the sequence {P n}n≥1 of measures on the canonical space of physical trajectories associated to the solutions of Schrödinger equations in Nelson’s scheme, corresponding to the sequence {(Vn,An)}n≥1 ⊆C1(R;ℛ×L2(R3)), converges in the total variation norm under the assumptions that for every fixed t the scalar potentials Vn(t) converge in ℛ, the space of Rollnik class potentials, and the vector potentials An(t) converge in Lloc∞(R;L2(R3)). In order to prove these results conditions are given under which solutions of Schrödinger equations are continuous in the (time-dependent electromagnetic) potentials in the norm of the Sobolev space H1(R3).
A quantum mechanical point of view to perturbative problems in classical mechanics
Authors: Dattoli G. , Torre A.
Published: July 2002

In this article it is shown that perturbative methods currently exploited in quantum mechanics can be used to treat a classical Liouville problem describing the evolution of an ensemble of noncollisional particles. The method discussed is based on the concepts of an evolution operator and interaction picture, which can be introduced for a classical Hamiltonian in full analogy with quantum mechanics. The usefulness of the developed method to treat the quantum extension of the Liouville equation is also stressed.
Asymptotics for the Kummer function of Bose plasmas
Authors: Kowalenko Victor , Frankel N. E.
Published: July 2002

The asymptotic expansions for the Kummer function obtained in the study of the linear response of magnetized Bose plasmas at T=0 K are presented for large and small values of its parameter, thereby displaying the function’s asymptotic nonuniformity. The large parameter expansion plays a determining role in the behavior of these Bose systems in the limit that the external magnetic field B→0. This particular expansion is generalized herein and its validity tested by determining the asymptotic expansion for the Hurwitz zeta function.
How to solve path integrals in quantum mechanics
Authors: Grosche Christian , Steiner Frank
Published: July 2002

A systematic classification of Feynman path integrals in quantum mechanics is presented and a table of solvable path integrals is given which reflects the progress made during the last 15 years, including, of course, the main contributions since the invention of the path integral by Feynman in 1942. An outline of the general theory is given which will serve as a quick reference for solving path integrals. Explicit formulas for the so-called basic path integrals are presented on which the general scheme to classify and calculate path integrals in quantum mechanics is based.
Path integrals on homogeneous manifolds
Authors: Marinov M. S.
Published: July 2002

Quantum kinematics are considered for two classes of systems: (i) the coordinate space is a homogeneous Riemannian manifold and the kinetic energy is the Laplace–Beltrami operator, (ii) the phase-space is a homogeneous Kählerian manifold where the algebra of observables is the universal enveloping algebra of the symmetry group. In both the cases, the path integrals are derived from more fundamental principles. The derivation enables a definite description of the classes of trajectories which constitute the domain of integration in the path integrals. The specification of the classes of functions is important for consistency of the approach. The standard action functional and the variational principle appear in the steepest descent method corresponding to the semiclassical approximation.
Kazakov–Migdal model with logarithmic potential and the double Penner matrix model
Authors: Paniak Lori , Weiss Nathan
Published: July 2002

The Kazakov–Migdal (KM) model is a U(N) lattice gauge theory with a scalar field in the adjoint representation but with no kinetic term for the gauge field. This model is formally soluble in the limit N→∞ though explicit solutions are available for a very limited number of scalar potentials. A ‘‘double Penner’’ model in which the potential has two logarithmic singularities provides an example of an explicitly soluble model. The formal solution to this double Penner KM Model is reviewed first. Special attention is paid to the relationship of this model to an ordinary (one) matrix model whose potential has two logarithmic singularities (the double Penner model). A detailed analysis is presented of the large N behavior of this double Penner model. The various one cut and two cut solutions are described and cases in which ‘‘eigenvalue condensation’’ occurs at the singular points of the potential are discussed. Then the consequences of our study for the KM model described above are discussed. The phase diagram of the model is presented and its critical regions are described.
Classification of the local extensions of the SU(2)×SU(2) chiral current algebras
Authors: Stanev Yassen S.
Published: July 2002

All local extensions of the chiral algebra of observables in the SU(2)⊗r conformal current algebra models are classified for r≤4 and all levels ki. This method is based on analyzing the polynomial solutions of the corresponding Knizhnik–Zamolodchikov equations and can be applied also for explicit construction of all local extensions corresponding to conformal embeddings of SU(2)⊗r for any r.
Casorati determinant solutions for the discrete Painlevé III equation
Authors: Kajiwara Kenji , Ohta Yasuhiro , Satsuma Junkichi
Published: July 2002

The discrete Painlevé III equation is investigated based on the bilinear formalism. It is shown that it admits the solutions expressed by the Casorati determinant whose entries are given by the discrete Bessel functions. Moreover, based on the observation that these discrete Bessel functions are transformed to the q-Bessel functions by a simple variable transformation, we present a q-difference analog of the Painlevé III equation.
Relativistic quantum mechanics on the SL(2,R) space–time
Authors: Fülöp T.
Published: July 2002

The Schrödinger-type formalism of the Klein–Gordon quantum mechanics is adapted for the case of the SL(2,R) space–time. The free particle case is solved, the results of a recent work are reproduced while all the other, topologically nontrivial solutions and the antiparticle modes are also found, and a deeper insight into the physical content of the theory is given.
The von Karman equations, the stress function, and elastic ridges in high dimensions
Authors: Kramer Eric M.
Published: July 2002

The elastic energy functional of a thin elastic rod or sheet is generalized to the case of an M-dimensional manifold in N-dimensional space. We derive potentials for the stress field and curvatures and find the generalized von Karman equations for a manifold in elastic equilibrium. We perform a scaling analysis of an M−1-dimensional ridge in an M=N−1-dimensional manifold. A ridge of linear size X in a manifold with thickness h≪X has a width w∼h1/3X2/3 and a total energy E∼μhM(X/h)M−5/3, where μ is a stretching modulus. We also prove that the total bending energy of the ridge is exactly five times the total stretching energy. These results match those of A. Lobkovsky [Phys. Rev. E 53, 3750 (1996)] for the case of a bent plate in three dimensions.
Massive spin-2 propagators on de Sitter space
Authors: Gabriel Cl. , Spindel Ph.
Published: July 2002

We compute the Pauli–Jordan, Hadamard, and Feynman propagators for the massive metrical perturbations on de Sitter space. They are expressed both in terms of mode sums and in invariant forms.
Diffeomorphism invariant integrable field theories and hypersurface motions in Riemannian manifolds
Authors: Bordemann Martin , Hoppe Jens
Published: July 2002

We discuss hypersurface motions in Riemannian manifolds whose normal velocity is a function of the induced hypersurface volume element and derive a second-order partial differential equation for the corresponding time function τ(x) at which the hypersurface passes the point x. Equivalently, these motions may be described in a Hamiltonian formulation as the singlet sector of certain diffeomorphism-invariant field theories. At least in some (infinite class of) cases, which could be viewed as a large-volume limit of Euclidean M-branes moving in an arbitrary M+1-dimensional Riemannian manifold, the models are integrable: In the time-function formulation the equation becomes linear [with τ(x) a harmonic function on the embedding Riemannian manifold]. We explicitly compute solutions to the large volume limit of Euclidean membrane dynamics in R3 by methods used in electrostatics and point out an additional gradient flow structure in Rn. In the Hamiltonian formulation we discover infinitely many hierarchies of integrable, multidimensional, N-component theories possessing infinitely many diffeomorphism invariant, Poisson commuting, conserved charges.
The reduced self-dual Yang–Mills equation, binary and infinitesimal Darboux transformations
Authors: Ustinov N. V.
Published: July 2002

The self-dual Yang–Mills equation in the (2+1)-dimensional space–time is considered. Binary Darboux transformation of a new kind is applied to obtain the infinite hierarchy of solutions expressed through ones of corresponding Lax pairs on an initial solution of the equation studied. Sufficient conditions are given for the solutions built to take values in the class of unimodular positive-definite matrices. A new infinitesimal Darboux transformation is introduced and a particular solution of the linearization of the self-dual Yang–Mills equation is given. Two hierarchies of infinitesimal symmetries depending on a solution of the nonlinear equation are extracted.
Microscopic SUπ(3)⊗SUν(3) interpretation of a two triaxial rotor model
Authors: Filippov G. F. , Lisetskyi A. F. , Draayer J. P.
Published: July 2002

A description of the relative motion of neutrons and protons in strongly deformed even-even nuclei is reduced to that of two coupled triaxial rotors, one representing the neutrons and the other the protons, by using generating function methods. The two rotor theory is interpreted as a generalization of the Elliott SU(3) model with a neutron–proton direct product SUν(3)×SUπ(3) substructure. The second order Casimir operator for this system is constructed and some of its eigenfunctions are found in explicit form in the Fock–Bargmann space representation. Analytical results for isovector M1 transitions probabilities are obtained and the results compared with experimental data and pseudo-SU(3) calculations. Graphs picturing the relative orientation of neutron-proton rotors in Ne22 are presented.
Fast and slow solutions in General Relativity: The initialization procedure
Authors: Iriondo Mirta S. , Leguizamón Enzo O. , Reula Oscar A.
Published: July 2002

We apply recent results in the theory of PDE, specifically in problems with two different time scales, to Einstein’s equations near their Newtonian limit. The results imply a justification to post-Newtonian approximations when initialization procedures to different orders are made on the initial data. We determine up to what order initialization is needed in order to detect the contribution to the quadrupole moment due to the slow motion of a massive body as distinct from initial data contributions to fast solutions and prove that such initialization is compatible with the constraint equations. Using the results mentioned, the first post-Newtonian equations and their solutions in terms of Green’s functions are presented in order to indicate how to proceed in calculations with this approach.
Multilinear representations of rotation groups within geometric algebra
Authors: Ashdown M. A. J. , Somaroo S. S. , Gull S. F. , Doran C. J. L. , Lasenby A. N.
Published: July 2002

It is shown that higher-weighted representations of rotation groups can be constructed using multilinear functions in geometric algebra. Methods for obtaining the irreducible representations are found, and applied to the spatial rotation group, SO(3), and the proper Lorentz group, SO+(1,3). It is also shown that the representations can be generalized to non-linear functions, with applications to relativistic wave equations describing higher-spin particles, such as the Rarita–Schwinger equations. The internal spin degrees of freedom and the external space–time degrees of freedom are handled within the same mathematical structure.
Anomalous dimension in the solution of the Barenblatt’s equation
Authors: Chen Cheng , Cheng G.
Published: July 2002

A new method is presented to obtain the anomalous dimension in the solution of the Barenblatt’s equation. The result is the same as that in the renormalization group (RG) approach. It gives us insight on the perturbative solution of the Barenblatt’s equation in the RG approach. Based on this discussion, an improvement is made to take into account, in a more complete way, the nonlinear effect, which is included in the Heaviside function in higher orders. This improved result is better than that in the RG approach.
Twisting cocycles in fundamental representation and triangular bi-crossproduct Hopf algebras
Authors: Mudrov A. I.
Published: July 2002

We find the general solution to the twisting equation in the tensor bialgebra T(R) of an associative unital ring R viewed as that of fundamental representation for a universal enveloping Lie algebra and its quantum deformations. We suggest a procedure of constructing twisting cocycles belonging to a given quasitriangular sub-bialgebra H⊂T(R). This algorithm generalizes Reshetikhin’s approach, which involves cocycles fulfilling the Yang–Baxter equation. Within this framework we study a class of quantized inhomogeneous Lie algebras related to associative rings in a certain way, for which we build twisting cocycles and universal R-matrices. Our approach is a generalization of the methods developed for the case of commutative rings in our recent work including such well-known examples as Jordanian quantization of the Borel subalgebra of sl(2) and the null-plane quantized Poincaré algebra by Ballesteros et al. We reveal the role of special group 1-cocycles in this process and establish the bi-crossproduct structure of the examples studied.
Universality of the future chronological boundary
Authors: Harris Steven G.
Published: July 2002

The purpose of this note is to establish, in a categorical manner, the universality of the Geroch-Kronheimer-Penrose (GKP) causal boundary when considering the types of causal structures that may profitably be put on any sort of boundary for a space–time. Actually, this can only be done for the future causal boundary (or the past causal boundary) separately; furthermore, only the chronology relation, not the causality relation, is considered, and the GKP topology is eschewed. The final result is that there is a unique map, with the proper causal properties, from the future causal boundary of a space–time onto any “reasonable” boundary which supports some sort of chronological structure and which purports to consist of a future completion of the space–time. Furthermore, the future causal boundary construction is categorically unique in this regard.
Application of geometric probability techniques to the evaluation of interaction energies arising from a general radial potential
Authors: Schleef David , Parry Michelle , Tu Shu-Ju , Woodahl Brian , Fischbach Ephraim
Published: July 2002

A formalism is developed for using geometric probability techniques to evaluate interaction energies arising from a general radial potential V(r12), where r12=|r2−r1|. The integrals that arise in calculating these energies can be separated into a radial piece that depends on r12 and a nonradial piece that describes the geometry of the system, including the density distribution. We show that all geometric information can be encoded into a “radial density function” G(r12;ρ1,ρ2), which depends on r12 and the densities ρ1 and ρ2 of two interacting regions. G(r12;ρ1,ρ2) is calculated explicitly for several geometries and is then used to evaluate interaction energies for several cases of interest. Our results find application in elementary particle, nuclear, and atomic physics.
Momentum and spin of a particle with spin unity
Authors: van Wyk C. B.
Published: July 2002

The first part of this paper deals with the problem of expressing a given boost as the product of an operator which leaves the momentum of a given particle, massive or massless, invariant and a helicity conserving operator. This is done by multiplying boosts and rotations only. In this way more information is obtained than by applying the operators to the relevant vectors. An operator with the property of conserving spin while perhaps changing momentum is developed. The second part of the paper defines a spin angular momentum operator leaving two four-vectors invariant. These vectors are interpreted as the momentum and spin vectors of a massive particle and the theory is extended to accommodate a massless particle. This theory emphasizes the close association of spin and momentum in a relativistic theory. The spin angular momentum operator of a massless particle has invariance properties which resemble some of those of the gauge invariant electromagnetic theory.
Linear stability analysis of multilayer plane Poiseuille flow
Authors: Anturkar Nitin R. , Papanastasiou Tasos C. , Wilkes James O.
Published: July 2002

A linear stability analysis of n-layer plane Poiseuille flow is performed. Asymptotic solutions are constructed at very small and very large wavenumbers. A numerical analysis is carried out by means of a compound matrix method to identify linearly unstable conditions for wavenumbers of O(1). The governing equations and the boundary conditions are conveniently formulated for n-layer flow. Neutral stability curves are plotted over a broad range of parameters for three-layer flows. The investigated parameters include the viscosity ratios, the flow rate ratios, the density ratios, the interfacial tensions, and the Stokes and Reynolds numbers.
On the interaction of a submerged turbulent jet with a clean or contaminated free surface
Authors: Anthony Douglas G. , Hirsa Amir , Willmarth William W.
Published: July 2002

The effect of a free surface on the structure of a submerged turbulent jet is investigated experimentally. Three-component LDV measurements beneath a clean free surface show that the mean flow spreads laterally outward in a shallow surface layer much wider than the mean flow well below the surface. As the free surface is approached, velocity fluctuations normal to the surface are diminished while those parallel to the surface are enhanced. Laser-induced fluorescence is used to show that the surface layer contains fluid ejected from the jet. With the addition of surface-active agents, the surface layer is suppressed.
Near-wall streaky structure in a turbulent boundary layer on a cylinder
Authors: Lueptow Richard M. , Jackson C. Patrick
Published: July 2002

A near-wall streaky structure has been identified in a turbulent boundary layer on a cylinder in axial flow. A platinum wire looped around a cylinder moving in a tank of quiescent water was used to generate hydrogen bubbles near the wall of the cylinder. The streaks that were visualized correspond to high-speed streaks identified by Kline et al. [J. Fluid Mech. 30, 741 (1967)]. The appearance, motion, and spacing of the streaks appear similar to the streaky structure in a planar boundary layer, suggesting a similarity in the mechanism for the generation of turbulence in the boundary layers on a flat plate and on a cylinder.
Oscillating flows over periodic ripples of finite slope
Authors: Hara Tetsu , Mei Chiang C. , Shum K. T.
Published: July 2002

The analysis of a laminar oscillating flow over a wavy surface is an important first step toward understanding the complicated dynamics over sand ripples along sea coasts. In a previous paper, two separate asymptotic theories for modestly large Reynolds numbers were presented, one for finite ripple slope but small Keulegan–Carpenter number, the other for finite Keulegan–Carpenter number but small ripple slope, where the Reynolds number is defined with the ambient oscillation velocity and the ripple amplitude, and the Keulegan–Carpenter number is the ratio of the oscillation amplitude to the ripple wavelength. Different types of vortex motion were found above the ripples. Here, a seminumerical solution of the Navier–Stokes equations in power series of the ripple slope, with emphasis on the intermediate regime where both parameters are finite and the Reynolds number is from order unity to moderately large is presented. For moderately large Reynolds number, the present results are similar to the second asymptotic theory in which there are two boudary layers with an oscillating vortex high above the rippled bed. For relatively small Reynolds numbers of order unity, the Stokes and the outer layers merge. In addition, the presence of bed ripples is found to increase the rate of energy dissipation by as much as 40%.
Comparison between theory and experiment for turbulence in opposed streams
Authors: Kostiuk L. W. , Libby Paul A.
Published: July 2002

Experimental data on the mean axial velocity and the intensity of the radial and axial velocity components on the axis of counterflowing turbulent streams are compared with a previously published Reynolds stress theory. Agreement is found to be satisfactory.
Interaction of disturbances with an oblique detonation wave attached to a wedge
Authors: Lasseigne D. Glenn , Hussaini M. Y.
Published: July 2002

The linear response of an oblique overdriven detonation to imposed free-stream disturbances or to periodic movements of the wedge is examined. The free-stream disturbances are assumed to be steady vorticity waves and the wedge motions are considered to be time periodic oscillations either about a fixed pivot point or along the plane of symmetry of the wedge aligned with the incoming stream. All disturbances are assumed to have wavelengths large compared to the thickness of the detonation so that the detonation is considered to be a region of infinitesimal thickness in which a finite amount of heat is released. The response to the imposed disturbances is a function of the Mach number of the incoming flow, the wedge angle, and the exothermicity of the reaction within the detonation. It is shown that, as the degree of overdrive increases, the amplitude of the response increases significantly; furthermore, a fundamental difference in the dependence of the response on the parameters of the problem is found between the response to a free-stream disturbance and to a disturbance emanating from the wedge surface.
Steady laminar flow of liquid–liquid jets at high Reynolds numbers*
Authors: Richards John R. , Beris Antony N. , Lenhoff Abraham M.
Published: July 2002

The axisymmetric steady-state laminar flow of a Newtonian liquid jet injected vertically into another immiscible Newtonian liquid is investigated for various Reynolds numbers. The steady-state solution was calculated by solving the axisymmetric transient equations of motion and continuity using a numerical scheme based on the volume of fluid (VOF) method combined with the new continuum surface force (CSF) algorithm. The analysis takes into account pressure, viscous, inertial, gravitational, and surface tension forces. Comparison with previous experimental measurements, performed on a xylene/water system, under conditions where all of these forces are important, shows good agreement over the entire range of conditions studied. Comparisons of the present numerical method with the numerical results of previous boundary-layer methods help establish their range of validity.
Finite Larmor radius effects on Alfvén radiative thermal instability
Authors: Shukla P. K. , Murtaza G. , Yu M. Y.
Published: July 2002

It is shown that finite gyroradius effects can couple the shear Alfvén waves to the radiative thermal mode to produce an Alfvén condensation instability.
Buildup of the radiation power spectrum in hot plasma x-ray lasers
Authors: Strauss M.
Published: July 2002

A three-dimensional quantum theory of hot plasma x-ray lasers, which takes into account general transverse profiles of electron density and gain, is presented. Maxwell–Bloch equations, including a fluctuation source term, are used to obtain the buildup of stimulated gain from spontaneous emission. Radiation propagation and amplification equations, which depend only on the average fluctuation fields, are obtained. These equations are appropriate to describe diffraction effects for Fresnel numbers ℱ∼1 and refraction effects for ℱ≫1. In the refraction case a multiple-mode treatment is presented and analytical solutions for the steady-state power spectrum and time-dependent intensity are obtained. The steady-state power spectrum under low-gain (spontaneous) and high-gain (stimulated) conditions is compared and found to be in good agreement with the predictions of the phenomenological photon rate equation.
Parabolic approximation method for the mode conversion-tunneling equation
Authors: Phillips C. K. , Colestock P. L. , Hwang D. Q. , Swanson D. G.
Published: July 2002

The derivation of the wave equation that governs ion cyclotron range of frequencies (ICRF) wave propagation, absorption, and mode conversion within the kinetic layer in tokamaks has been extended to include diffraction and focusing effects associated with the finite transverse dimensions of the incident wave fronts. The kinetic layer considered consists of a uniform density, uniform temperature slab model in which the equilibrium magnetic field is oriented in the ẑ direction and varies linearly in the x̂ direction. An equivalent dielectric tensor, as well as a two-dimensional energy conservation equation, are derived from the linearized Vlasov–Maxwell system of equations. A generalized, but approximate form of the mode conversion-tunneling equation is then extracted from the Maxwell equations, using the parabolic approximation method in which transverse variations of the wave fields are assumed to be weak in comparison to the variations in the primary direction of propagation. Numerical solutions of this approximate wave equation agree well with solutions to the exact wave equation within the kinetic layer.
Ballooning Δ′ in the second stable region
Authors: Bishop C. M. , Hastie R. J. , Sykes A. , Wilson H. R.
Published: July 2002

The stability of resistive ballooning modes in the second ideal stability region is an important issue that has recently received much attention. In this paper it is shown that the ballooning Δ′ is negative, and therefore that the Δ′-driven modes are stable, throughout most of the second region. These results are compared with those of Kim and Choi [Phys. Fluids B 1, 1444 (1989)].
Efficiency dependence on beam current and input power in a cyclotron autoresonance maser amplifier
Authors: Kho T. H. , Lin A. T.
Published: July 2002

The efficiency dependence of a cyclotron autoresonance maser (CARM) amplifier on electron beam current and input power is investigated using computer simulations and a theoretical model is presented to explain the findings. For a resonantly tuned CARM, the efficiency is found to initially increase and then decrease with beam current while for an optimally detuned CARM, the efficiency drops with any increase in beam current. If the current is kept constant, the efficiency is also found to drop as the input wave power is increased. Force bunching is found to play an important role in reducing the efficiency at high-beam current, which may make extension to high power through increasing beam current more difficult to achieve.
Comments on ‘‘Finite Larmor radius effects on thermosolutal instability of a plasma’’ [Phys. Fluids 2
4, 2242 (1981)]
Authors: Saini J. C.
Published: July 2002

The effects of the finite Larmor radius on the thermosolutal instability of an incompressible plasma layer of finite thickness are discussed in the presence of a uniform vertical magnetic field. A sufficient condition for the principle of exchange of stabilities is established.
Nonlinear effects and chaotic behavior at plasma resonance
Authors: Cros B. , Godiot J. , Matthieussent G. , Heron A.
Published: July 2002

Resonant absorption of an electromagnetic wave (f=3.5 GHz) in a multipolar discharge (ne0≂1011 cm−3) with an adjustable density gradient is studied. The transition from a nonlinear steady-state regime toward a chaotic one, occurring when the pump field or the gradient length is increased, is investigated experimentally and numerically.