bluuebunny/crossref_metadata_2025 huggingface dataset:
Time-dependent rotated Hartree: Formal development
Authors: Meyer H.-D. , Kučar J. , Cederbaum L. S.
Published: July 2002

A new approximation for solving the time-dependent Schrödinger equation is proposed. It improves the time-dependent Hartree approximation by including time-dependent unitary operators acting on the Hartree product. This allows for the approximate description of the correlation between the various degrees of freedom. The mathematical structure of the new approach is analyzed and an alternative Lie algebraic derivation is presented. By adopting two different time-dependent variational principles two different sets of equations are obtained. Differences between the two resulting methods are discussed.
Quantization of conformally invariant Bargmann–Wigner equations with gauge freedom
Authors: Heidenreich W. F. , Lorente M.
Published: July 2002

Massless, conformally invariant Bargmann–Wigner equations with gauge freedom are found. An invariant indefinite metric quantization is described.
Finite energy solutons for (1+1)-dimensional σ models
Authors: Piette Bernard , Zakrzewski Wojciech J.
Published: July 2002

Various properties of finite energy solutions of the (1+1)-dimensional sigma models are studied. It is shown that the energy densities of these solutions exhibit some extended lump-like structures that cross each other without interaction, and that the procedure of adding a soliton to a given solution developed by Harnad, Schnider, and Saint-Aubin [Commun. Math. Phys. 92, 329 (1984); 43, 33 (1984)] mixes the matrix elements of this solution in a complicated way, but it does not modify its energy momentum tensor density. The one parameter family of conserved currents discovered by Eichenherr, Forger, and Pohlmeyer [Nucl. Phys. B 155, 381 (1979); 164, 528 (1980); Commun. Math. Phys. 46, 207 (1976)] must be considered to distinguish between such solutions. Finally the Uhlenbeck method of construction of Euclidean solutions modified to make it applicable to the construction of Minkowskian solutions for some classes of sigma models. It is shown that this method does not modify the energy momentum tensor density either.
On the velocities of the barotropic perfect fluids
Authors: Coll Bartolomé , Ferrando Joan Josep
Published: July 2002

The conditions for a unit vector field to be the velocity of a relativistic barotropic perfect fluid are given. These conditions induce an eightfold classification of such fluids; for every class, the admissible barotropic variables are found. Some special cases, in particular polytropic fluids, are analyzed separately.
The probability operator in quantum theory and quantization of a system of free fields
Authors: Basu Sujit , Kuryshkin V. V.
Published: July 2002

A theoretical framework for quantization, defined by the normalized positive-definite probability operator establishing dynamical correspondence between classical and quantum Poisson brackets, is presented. The resulting quantum theory, unlike the conventional one, admits consistent probabilistic interpretation. It is shown that, in the nonrelativistic case, quantization based on the probability operator leads to the theory known as ‘‘quantum mechanics with a non-negative quantum distribution function.’’ A generalization of the proposed framework to the case of the relativistic theory of fields is attempted. Four auxiliary problems of constructing probability operators of one-dimensional field oscillators in Bose and Fermi algebras are formulated and solved. On the basis of these solutions it is concluded that spinor fields are not quantizable in the Bose algebra with the help of the probability operator (the analog of Pauli’s theorem). An equation for the probability operator of a system of free fields is derived from the principles of dynamical correspondence and translational invariance. The physical meaning of the operators corresponding to classical field amplitudes, such as annihilation and creation operators of field quanta with definite energy-momentum, is shown to emerge as a consequence of this equation. It is shown that the quantization of a system consisting only of tensor fields or only of spinor fields in the formalism of the probability operator leads to difficulties. It is shown further that these difficulties can be removed by considering quantization of a system containing both tensor and spinor fields. As an illustration, quantization of a system consisting of a massive vector field and a massive spinor field is considered and it is found that a noncontradictory quantization requires the mass of the vector particle to be less than that of the spinor particle. The probability operator thus acts as a mechanism of selection of the fields to be quantized already at the level of free fields.
Algorithmic method for deriving Lax pairs from the invariant Painlevé analysis of nonlinear partial differential equations
Authors: Musette M. , Conte R.
Published: July 2002

Given a partial differential equation, its Painlevé analysis will first be performed with a built-in invariance under the homographic group acting on the singular manifold function. Then, assuming an order for the underlying Lax pair, a multicomponent pseudopotential of projective Riccati type, the components of which are homographically invariant, is introduced. If the equation admits a classical Darboux transformation, a very small set of determining equations whose solution yields the Lax pair will be generated in the basis of the pseudopotential. This new method will be applied to find the yet unpublished Lax pair of the scalar Hirota–Satsuma equation.
Evaluation of the propagator for a quadratic Hamiltonian with arbitrary ordering
Authors: Fesseha K.
Published: July 2002

Path integral methods are used to derive an exact expression for the propagator for a quadratic Hamiltonian with arbitrary ordering. The van Vleck–Pauli relation is found to be a special case of our general result.
Quantized Arnold cat maps can be entropic K-systems
Authors: Narnhofer Heide
Published: July 2002

Automorphisms on the irrational rotation algebra with respect to their ergodic properties are studied. Especially it is shown that for a dense set of the rotation parameter θ cat maps are entropic K-systems.
New class solutions of the 3-D Laplace equation
Authors: Martinov N. , Ouroushev D. , Grigorov A.
Published: July 2002

The problem of finding a solution of the three-dimensional Laplace equation is reduced to the problem of solving a system of nonlinear algebraic equations by a new ansatz. The obtained solutions are expressed in real Jacobi elliptic functions and are periodic in three dimensions. They depend on four free parameters. The space behavior and the periodicity of the solutions with respect to the values of the free parameters are investigated.
Primary operators of coset conformal field theories
Authors: Shin H. J.
Published: July 2002

The nature of primary operators of coset conformal field theories is discussed. Some primary states of typical coset conformal field theory are explicitly calculated that have correct conformal dimensions and dynamics. The nature of modular invariant partition functions from the diagonal sum of absolute squares of characters of coset primary states is studied.
On the representation of operator algebras of the quantum conformal field theory
Authors: Juriev D. V.
Published: July 2002

It is established in this paper that an arbitrary operator algebra of the quantum conformal field theory admits the strict representation by matrices, whose elements belong to the special operator algebra−the algebra of the vertex operators in the model of the Verma modules over the Virasoro algebra.
A relation between two perturbation methods generating Padé upper and lower bounds to ground state eigenvalues
Authors: Khalil A. B.
Published: July 2002

A reciprocal relation is established between the mean values of the resolvent of the Hamiltonian of a quantum mechanical system and an operator, the zeros of which give rise to the Brillouin–Wigner perturbation series. Also discussed are the consequences of this relation to the Rayleigh–Schrödinger and Brillouin–Wigner approaches for getting Padé approximants upper and lower bounds for the ground state eigenvalue.
Dust metrics with comoving constant curvature slices
Authors: Bona C. , Palou P.
Published: July 2002

Irrotational dust metrics are considered by requiring the hypersurfaces orthogonal to the matter wordlines to be of constant curvature. The resulting line elements are either contained in the well-known Szekeres dust solutions or they are homogeneous metrics of Bianchi class I or V.
Singularities inside matter: The static case
Authors: de Felice F. , Usseglio-Tomasset S. , Bradley M.
Published: July 2002

A classification of the curvature singularities inside matter is proposed for studying the properties of the nearby space-time regions. Only the Schwarszchild interior solution, with the coordinate radius of the boundary rb=9/8rg, and the Tolman V and the Tolman VI solutions are considered. First a criterion is established for comparison between any two different space-times. Then the above solutions are compared, establishing that (i) curvature singularities inside matter appear to evolve in their strength together with the relative increase of the hydrostatic pressure over the energy density; (ii) the strength of a singularity can be monitored by the occurrence of physical effects like the trapping of the null geodesics, and (iii) these effects appear intrinsically related to the singularity strength rather than to the type of solution being considered here.
Spin-weighted cylindrical harmonics and the Euclidean group of the plane
Authors: Torres del Castillo G. F.
Published: July 2002

It is shown that the spin-weighted cylindrical harmonics s Jαm(ρ,φ), which are functions defined on the plane, are related to representation matrices of the group of rigid motions on the plane. It is also shown that the raising and lowering operators of the spin weight and of the z component of the angular momentum are related to two copies of the Lie algebra of the Euclidean group of the plane.
Witten complex and supersymmetric quantum mechanics on SO(3)
Authors: Hirokane Tohru , Miyajima Mitsuharu , Yasui Yukinori
Published: July 2002

A supersymmetric quantum mechanics on SO(3) is examined. It was found that instanton solutions and the normal coordinate expansions around them allow the explicit path integration. The Witten complex is obtained by calculating the matrix elements of the generalized exterior derivative.
Eigenstates of bilinears in paraboson operators and their inverses
Authors: Saxena G. M. , Mehta C. L. , Mathur B. S.
Published: July 2002

The inverse of paraboson annihilation and creation operators is introduced. The properties of these operators, their number state representation and commutation relations are discussed. Also introduced are the family of eigenstates of bilinears in paraboson operators and their inverses; and study the nonclassical properties, namely, squeezing and fluctuations in number of parabosons in these eigenstates. It is observed that a family of the eigenstates of a+−1a is the parasqueezed vacuum, S(σ)‖0,α〉. Similarly, a family of the eigenstates of aa+−1 is the parasqueezed first state, S(σ)‖n=1,α〉.
The universal propagator for spin [or SU (2)] coherent states
Authors: Tomé Wolfgang A. , Klauder John R.
Published: July 2002

Following constructions in the case of canonical and affine coherent states, a universal propagator for a general Hamiltonian appropriate to a single spin degree of freedom is introduced. The universal propagator is a single function, independent of any particular choice of fiducial vector, which, nonetheless, propagates all coherent state Hilbert space representatives correctly. Furthermore, we explicitly construct the universal propagator for several examples.
Fisher information, prior probabilities, and the state determination of spin-1/2 and spin-1 systems
Authors: Slater Paul B.
Published: July 2002

The (Fisher) information matrix (I2p) for a p×p density matrix (ρ) is taken to be the (2p2+p)-dimensional information matrix of a 2p-variate real normal distribution with an a priori zero mean vector and a covariance matrix (Σ2p), the two diagonal blocks of which are formed from the symmetric (real) component of ρ, and the two off-diagonal blocks from the skew-symmetric (imaginary) part of ρ. The inverse square root ‖nI2p‖−1/2 (where n is the number of observations) serves as a unitary invariant prior distribution over (the precision matrices) Σ2p−1 and ‖nI2p‖1/2 over Σ2p—and consequently over the p×p (mixed and pure) density matrices. The availability of these priors should facilitate the process of state determination. An uncertainty principle for the estimation of ρ is formulated. The determinant of Σ2p proves for integral p≥1 to equal (2−p‖ρ‖)2.
Euclidean Majorana fermions, fermionic integrals, and relative Pfaffians
Authors: Borthwick David
Published: July 2002

The construction of Euclidean Majorana fermions on a two-dimensional cylindrical space–time is discussed, based on a given real-time theory. After a review of the basics of defining Euclidean fermions in the free theory, a functional integral formulation for the Euclidean theory is introduced. This functional integral connects the expectation values of the Euclidean fields with the theory of relative Pfaffians. A proof, which draws on these ideas, is given for the Feynman–Kac formula of a general interacting theory.
Local classification of constraints
Authors: Chmielowski Piotr
Published: July 2002

We give a new proof of a theorem locally classifying classical dynamical systems with constraints, and discuss possible applications of the result to quantization of such systems, in particular of General Relativity.
The Kaup–Broer system and trilinear odes of Painlevé type
Authors: Strampp Walter
Published: July 2002

The Kaup–Broer hierarchy can be considered as a certain reduction of the KP hierarchy. Upon introducing the τ-function the Kaup–Broer system can be formulated in trilinear form giving rise to Wronskian solutions. In this paper several odes of the Painlevé type obtained through reductions of the Kaup–Broer system are considered. Those odes take a trilinear form which allows a linearization.
On crossing dust shells
Authors: Frauendiener J. , Klein C.
Published: July 2002

The crossing of two dust shells is considered as a simplified model for shell crossing during the spherically symmetric collapse of dust. It is shown that one encounters the same problems as in the latter case if one wants to continue the space-time dynamically through the region of intersection. To get a unique solution of the equations of motion, detailed information on the interaction between the shells has to be given. A corresponding Newtonian model is discussed and compared with the relativistic case. Furthermore it is shown that dust shells cannot be obtained as limiting cases of extended dust regions.
Colored quantum universal enveloping algebras
Authors: Quesne C.
Published: July 2002

We define some new algebraic structures, termed colored Hopf algebras, by combining the coalgebra structures and antipodes of a standard Hopf algebra set ℋ, corresponding to some parameter set 𝒬, with the transformations of an algebra isomorphism group 𝒢, herein called color group. Such transformations are labeled by some color parameters, taking values in a color set 𝒞. We show that various classes of Hopf algebras, such as almost cocommutative, coboundary, quasitriangular, and triangular ones, can be extended into corresponding colored algebraic structures, and that colored quasitriangular Hopf algebras, in particular, are characterized by the existence of a colored universal ℛ-matrix, satisfying the colored Yang–Baxter equation. The present definitions extend those previously introduced by Ohtsuki, which correspond to some substructures in those cases where the color group is Abelian. We apply the new concepts to construct colored quantum universal enveloping algebras of both semisimple and nonsemisimple Lie algebras, considering several examples with fixed or varying parameters. As a by-product, some of the matrix representations of colored universal ℛ-matrices, derived in the present paper, provide new solutions of the colored Yang–Baxter equation, which might be of interest in the context of integrable models.
The Einstein–Hilbert–Yang–Mills–Higgs action and the Dirac–Yukawa operator
Authors: Tolksdorf Jürgen
Published: July 2002

In this article we show in some detail how the full action functional of the standard model of elementary particle physics can be described within the geometrical setting of generalized Dirac operators. We thereby introduce a new model building kit for (a certain class of) gauge invariant theories which provides a unified geometrical description of Einstein’s theory of gravity and Yang–Mills gauge theories on the “classical” level. Moreover, when the gauge symmetry is spontaneously broken, the Higgs sector as well has a natural geometrical interpretation. It turns out that the Higgs field is related to the gravitational potential. Since the full action functional of the standard model is derived in one stroke, the appropriate parameters of the model have to satisfy certain relations similar to those in the Connes–Lott approach. Likewise, this may yield some phenomenological consequences, which is illustrated by using the gauge group of the standard model in the case of N generations of leptons and quarks.
Unobstructedness of Calabi–Yau orbi-Kleinfolds
Authors: Ran Z.
Published: July 2002

We show that Calabi–Yau spaces with certain types of hypersurface-quotient singularities have unobstructed deformations. This applies in particular to all Calabi–Yau orbifolds nonsingular in codimension 2.
Information-theoretical derivation of an extended thermodynamical description of radiative systems
Authors: Fort J. , Llebot J. E.
Published: July 2002

A radiative equation of the Cattaneo–Vernotte type is derived from information theory and the radiative transfer equation. The equation thus derived is a radiative analog of the equation that is used for the description of hyperbolic heat conduction. It is shown, without recourse to any phenomenological assumption, that radiative transfer may be included in a natural way in the framework of extended irreversible thermodynamics (EIT).
Demazure characters and WZW fusion rules
Authors: Walton Mark A.
Published: July 2002

The Demazure character formula is applied to the Verlinde formula for the fusion rules of Wess–Zumino–Witten (WZW) models. We follow Littelmann’s derivation of a generalized Littlewood–Richardson rule that computes tensor products for simple Lie algebras. A combinatorial rule for WZW fusions does not result, however. Only a modified version of the Littlewood–Richardson rule is obtained that computes an (old) upper bound on the fusion coefficients of Ar WZW models. We argue that this is because the characters of simple Lie algebras appear in this treatment, instead of the corresponding affine characters. The Bruhat order on the affine Weyl group must be implicated in any combinatorial rule for WZW fusions; the Bruhat order on subgroups of this group (such as the finite Weyl group) does not suffice.
Superconnections and the Higgs field
Authors: Roepstorff G.
Published: July 2002

Within the mathematical framework of Quillen, one interprets the Higgs field as part of the superconnection 𝔻 on a superbundle. We propose to take as superbundle the exterior algebra ∧V obtained from a Hermitian vector bundle V of rank n with structure group U(n) and study the curvature F=D2. The Euclidean action, at most quadratic in 𝔽 and invariant under gauge transformations, depends on n+1 central charges. Spontaneous symmetry breaking is related to a nonvanishing constant scalar curvature in the ground state, F=Lc2, where Lc is the Higgs condensate. The U(1) Higgs model is nothing but the familiar Ginzburg–Landau theory, whereas the U(2) Higgs model relates to the electro-weak theory (without matter fields). The present formulation leads to the relation g2=3g′2 for the coupling constants, the formula sin2 θ=1/4 for the Weinberg mixing angle, and the ratio mW2:mZ2:mH2=3:4:12 for the masses of W±, Z0, and the Higgs boson. Experimentally observed deviations are attributed to loop corrections.
Analyzing Glauber dynamics by comparison of Markov chains
Authors: Randall Dana , Tetali Prasad
Published: July 2002

A popular technique for studying random properties of a combinatorial set is to design a Markov chain Monte Carlo algorithm. For many problems there are natural Markov chains connecting the set of allowable configurations which are based on local moves, or “Glauber dynamics.” Typically these single-site update algorithms are difficult to analyze, so often the Markov chain is modified to update several sites simultaneously. Recently there has been progress in analyzing these more complicated algorithms for several important combinatorial problems. In this work we use the comparison technique of Diaconis and Saloff-Coste to show that several of the natural single-point update algorithms are efficient. The strategy is to relate the mixing rate of these algorithms to the corresponding nonlocal algorithms which have already been analyzed. This allows us to give polynomial time bounds for single-point update algorithms for problems such as generating planar tilings and random triangulations of convex polygons. We also survey several other comparison techniques, along with specific applications, which have been used in the context of estimating mixing rates of Markov chains.
Dual Lagrangian field theories
Authors: Ferraris M. , Francaviglia M. , Raiteri M.
Published: July 2002

We investigate how, under suitable regularity conditions, first-order Lagrangian field theories can be recasted in terms of a second-order Lagrangian, called the dual Lagrangian of the theory, depending on canonical conjugate momenta together with their derivatives. The necessary and sufficient conditions which allow such a (local) reformulation, obtained through a suitable generalization of the Legendre transformation, are analyzed. The global geometric framework is also investigated in detail. As an example, we apply the dual Lagrangian formulation to the Hilbert Lagrangian and to Euclidean self-dual gravity.
On the mathematical structure of thermodynamics
Authors: Matolcsi T.
Published: July 2002

A mathematically exact dynamical theory of classical thermodynamics of homogeneous bodies is presented in which processes are time-dependent functions, governed by an ordinary differential equation. The fundamental objects of the mathematical structure of a thermodynamical system are the dynamical law, the thermodynamical force, and the constraints; all the other usual notions, too, such as substances, bodies, linear approximation by Onsager, etc. have got a mathematical definition. Equilibria are the constant processes; their stability is investigated by Lyapunov’s method.
The motion of surfaces in geodesic coordinates and 2+1-dimensional breaking soliton equation
Authors: Li Yishen , Chen Chunli
Published: July 2002

The system of evolution equations for general motion of surfaces in geodesic coordinates is analyzed to reduce the number of variables as well as equations. A special choice for some variants deduces that the surface and the motion of surface correspond to a nonlinear Schrödinger equation and a 2+1-dimensional breaking soliton equation; respectively. We also study some geometric properties corresponding to the integrals of the motion of surface and the motion of the curve on the surface. The spectral parameter is introduced.
Classical r-matrices for the osp(2/2) Lie superalgebra
Authors: Juszczak Cezary
Published: July 2002

The co-Lie structures compatible with the osp(2/2) Lie superalgebra structure are investigated and found to be all of the coboundary type. The corresponding classical r-matrices are classified into several disjoint families. The osp(1/2)⊕u(1) Lie superbialgebras are also classified.
Generalized binomial distributions
Authors: Kowalski Kenneth L.
Published: July 2002

The definition, properties, and calculational advantages of the binomial transform representation of a class of finitely enumerated discrete probability distributions that generalize the standard binomial distribution are investigated. Discrete distributions of this type appear in various models of hadron multiparticle production among other physical applications. The compact representations of the generating functions for factorial moments of these discrete distributions obtained using the binomial transform are used to relate the behavior of the complex zeros of the generating functions to different models for the distribution of charged and neutral particles in multihadron production.
Pulsed differential calorimetry of Zn-doped LSCO cuprates
Authors: Basilia G. G. , Kharadze G. A. , Kvavadze K. A. , Nadareishvili M. M. , Brewer D. F. , Ekosipedidis G. , Thomson A. L.
Published: July 2002

The low temperature heat capacity measurements on LSCO samples containing Zn impurities have been performed by means of pulsed differential calorimetry technique. The interpretation of the Zn-concentration dependence of the residual γ-coefficient in the linear temperature part of Cel(T) at T≪Tc is consistent with a model based on the assumption of the d-wave symmetry of the order parameter of these superconducting copper oxides.
Development of an extended proper orthogonal decomposition and its application to a time periodically forced plane mixing layer
Authors: Glezer Ari , Kadioglu Zafer , Pearlstein Arne J.
Published: July 2002

Two extensions of the classical proper orthogonal decomposition (POD) methodology exposited by Lumley for turbulent flows are presented. First, the extended POD (EPOD) can deal with flows lacking statistical stationarity by summing the velocity correlations of an ensemble of time series. Thus it reduces to the classical POD for a statistically stationary flow, and to the ‘‘snapshot’’ of Sirovich for data from a single instant in each realization of an ensemble. Second, the EPOD can deal with flows having one or more length scales exceeding the spatial range over which simultaneous measurements can be made, by generating composite modes using nonsimultaneous, spatially overlapping data. Both new capabilities have been exercised by applying the EPOD to the streamwise velocity component measured by a cross-stream hot-wire rake in an anharmonically forced turbulent plane mixing layer that is not statistically stationary, and is statistically homogeneous in only one direction. It is discovered that as few as three one-dimensional modes are capable of capturing as much as 78% of the ‘‘action’’ in data from ten wires in a cross-stream rake.
Non-Boussinesq effects on transitions in Hele–Shaw convection
Authors: Hwang Shyh-Hong , Chang Hsueh-Chia
Published: July 2002

Mode jumping between buoyancy-induced convection patterns in a slender Hele–Shaw cell (height>width) is studied with a center manifold projection technique at a critical aspect ratio, where both the single-roll and double-roll convection patterns destabilize simultaneously. In contradiction to some experimental observations, the Boussinesq model with insulated or isothermal side wall conditions indicates that the single-roll mode never surrenders its stability and yields to the double-roll mode as the Rayleigh number is increased. By adding the temperature dependence of fluid density and conductivity to the heat equation, it is shown that the single-roll mode can now undergo secondary bifurcations. Hysteretic jumps to the double-roll mode and smooth transitions to a mixed mode, and even to a time-periodic convection pattern, are then possible.
Coherent structure formation and magnetic field line reconnection in magnetohydrodynamic turbulence
Authors: Carbone V. , Veltri P. , Mangeney A.
Published: July 2002

The effects produced by the occurrence of both ideal and resistive instabilities in magnetohydrodynamic (MHD) turbulence are discussed, from the point of view of the formation of coherent structures. It is shown that MHD equations spontaneously develop spatially flat or elongated structures, a fact that might be related with the intermittency of the magnetic field observed in some numerical simulations. It is suggested that these flat structures are perhaps unstable with respect to reconnecting (tearing mode type) perturbations. Such instabilities give rise to a nonlocal energy transfer in the wave number space, which modifies the usual inertial spectrum of MHD turbulence, and increases the rate of energy and correlation dissipation. An explicit nonlinear cascade model that qualitatively takes into account such a nonlocal energy transfer is built up, in order to study dynamically the balance between nonlinear energy cascade and linear tearing mode instability. Finally, an attempt is made to interpret some of the peculiar behavior of published MHD simulations on the basis of the results obtained using the present model.
An experimental investigation into the role of simultaneous amplitude and phase modulation in the transition of a planar jet
Authors: Thomas F. O.
Published: July 2002

An experimental investigation into the role of simultaneous amplitude and phase modulation of velocity fluctuations characterizing the near-field transition of an initially laminar planar jet at moderate Reynolds number is presented. Very low level periodic acoustic excitation at selected frequencies is applied upstream of the nozzle exit in order to introduce an organized carrier wave into the flow. Instantaneous amplitude and phase modulates are computed directly from hot-wire velocity fluctuation data which allows their respective role in the jet transition process to be quantified. It is found that amplitude modulation serves to provide energy to amplifying sideband fluctuations which multitone phase modulation effectively redistributes to neighboring spectral modes in the nonlinear stages of transition. The phase modulation is found to result from an experimentally verified amplitude dependence in the dispersion relation. The phase angle between amplitude and phase modulation is found to be an important parameter in governing the spectral development of the shear layer by its effect on sideband asymmetry. While the essential physics associated with the modulation phenomenon is found to be quite similar to that previously reported in plane wakes, the presence of the subharmonic resonant interaction in the planar jet shear layer adds an additional dimension to the modulation phenomenon.
Chaos and mixing in a geostrophic flow
Authors: Behringer Robert P. , Meyers Steven D. , Swinney Harry L.
Published: July 2002

Experiments on Rossby waves on an azimuthal jet in a rapidly rotating annular tank reveal a striking barrier to mixing across the jet. A model based on the experiments assumes a two-dimensional incompressible flow described by a time-dependent streamfunction consisting of azimuthally propagating waves on a narrow jet. When there is only one wave, all Lagrangian particle trajectories are closed in the appropriate reference frame. When two independent waves are present, some trajectories are chaotic, and the size of the chaotic sea grows as the amplitude of the second wave is increased; however, at least one barrier to global transport—an invariant surface—prohibits trajectories from crossing the jet. The addition of a third wave is found to break the barrier only if the wave amplitudes exceed the width of the jet. In the experiment, the wave amplitude is typically about one-half the jet width, and the barrier to mixing persists even at the highest accessible Reynolds numbers.
The renormalization group dynamics of chaotic mixing of unstable interfaces
Authors: Glimm J. , Zhang Q. , Sharp D. H.
Published: July 2002

The authors’ determination of Rayleigh–Taylor fluid mixing rates is surveyed and placed in a broader scientific context. The significance of universality for this mixing rate is discussed.
Effects of suction and wall shaping on the fundamental parametric resonance in boundary layers
Authors: Masad J. A. , Nayfeh A. H.
Published: July 2002

The effects of self-similar as well as uniform-suction distributions on the primary and fundamental parametric spatial and temporal instabilities of incompressible flows over a flat plate are studied. The Floquet model is used to analyze the fundamental instability. This model is also used to analyze the effect of wall shaping on such instabilities. The mean-flow problems as well as the stability problems are solved using finite differences. The effects of suction and wall shaping are evaluated and discussed in relation to previous works. The relation between spatial and temporal fundamental instabilities is also considered.
On negative eddy viscosity under conditions of isotropy
Authors: Sivashinsky Gregory I. , Frenkel Alexander L.
Published: July 2002

This study considers a large-scale flow freely evolving through a periodic array of oscillating triangular eddies. The effective eddy viscosity induced by the system appears to be isotropic, i.e., insensitive to the spatial orientation of the underlying periodic flow field. In contrast to the previously studied situation with time-independent periodic flow, the eddy viscosity generated by rapidly oscillating eddies may be negative, thereby reducing the total (molecular and eddy) viscosity of the system. At sufficiently high Reynolds numbers, the total viscosity might even become negative promoting spontaneous formation of large-scale structures.
Nonaxisymmetric waves in core-annular flow with a small viscosity ratio
Authors: Boomkamp P. A. M. , Miesen R. H. M.
Published: July 2002

The ‘‘core-annular’’ mode of two-fluid pipeline flow can be an attractive method for the transportation of viscous crude oil. In core-annular flow a thin water film surrounds the oil core and acts as a lubricant. Waves on the oil/water interface play an essential role in the balance of forces on the lighter oil core. The theoretical description of these interfacial waves is the subject of this paper. To predict whether or not a transition of a flat to a wavy interface will occur, the stability of the undisturbed interface is analyzed. The differential equations governing the growth of interfacial disturbances are solved by using matched asymptotic expansions, with the ratio of the viscosities of water and oil (μwater≊10−4μoil) as a small parameter. The stability analysis shows that nonaxisymmetric modes are important, because the growth rates of nonaxisymmetric and axisymmetric modes are approximately the same. This supplements the current picture on the formation of interfacial waves in core-annular flow.
Neoclassical transport of isotropic fast ions
Authors: Hsu C. T. , Catto P. J. , Sigmar D. J.
Published: July 2002

A study of radial gradient-driven neoclassical transport of fast ions, produced by an isotropic source in an axisymmetric toroidal system, is presented. The governing equation is a flux surface averaged Fokker–Planck equation that retains both the effects of the pitch angle scattering and drag. It is solved by utilizing an eigenfunction technique in conjunction with a rigorous numerical treatment. The results, which are valid for finite inverse-aspect-ratio ε, are found to fall between the previous limiting calculations [Nucl. Fusion 15, 359 (1975); Phys. Rev. Lett. 60, 1954 (1988)] for most of the relevant parameter regimes.
Turbulent relaxation in magnetohydrodynamic plasma
Authors: Tetreault D. J.
Published: July 2002

Magnetohydrodynamic (MHD) clump instability is considered as a turbulent relaxation mechanism for current carrying plasma. Predictions of the instability are compared with results from laboratory fusion experiments as well as computer simulations. For the tokamak, the predictions include safety factor [q(a)≤3] and Lundquist number [S≥104] thresholds, a magnetic helicity conserving radial electric field profile, and a voltage spike time of 0.1τRS−1/3, where τR is the resistive time. It is argued that the voltage spike that signals a tokamak disruption is due to the global conservation of magnetic helicity during the instability. In the reversed field pinch (RFP), clump steady states corresponding to B0z field reversed Taylor states at pinch parameters θ≥1.2, for S≥102, and magnetic fluctuation levels δB scaling as S−3/8 and θ3 are predicted. Reasonable agreement is obtained. The MHD clump instability appears to provide a unified picture of tokamak disruptions, where it occurs intermittently in its growth phase, and RFP ‘‘quiescent’’ states, where it is continuously present in its steady state turbulence phase.
Radial electric field effect on resistive interchange modes
Authors: Sugama H. , Wakatani M.
Published: July 2002

Shear flow, driven by the radial electric field, has a stabilizing effect on the resistive interchange (or g) mode destabilized by the unfavorable curvature in a heliotron/torsatron. The following conditions are required: (i) kyv0>γgLE/Δ and (ii) Δ<LE, where the flow velocity profile is assumed to be v0 tanh(x/LE), ky is a wave number in the poloidal direction, γg is a growth rate at v0=0, and Δ is a radial mode width at v0=0. The origin x=0 corresponds to a mode resonant surface. When v0 is sufficiently large, the usual Kelvin–Helmholtz instability appears.
Characteristics of edge plasma turbulence on the ATF torsatron
Authors: Uckan T. , Hidalgo C. , Bell J. D. , Harris J. H. , Dunlap J. L. , Wilgen J. B. , Ritz Ch. P. , Rhodes T. L. , Wootton A. J.
Published: July 2002

Measurements of electrostatic fluctuations on the edge of the Advanced Toroidal Facility (ATF) torsatron [Fusion Technol. 10, 179 (1986)] are used to study the role of the edge turbulence in the particle transport in this current-free magnetic configuration. Spatial profiles of the plasma electron density ne, temperature Te, and fluctuations in density (ñe) and in the plasma floating potential (φ̃f ) are measured at the edge in electron cyclotron heated plasmas using a Langmuir probe array. At the last closed flux surface (LCFS), r/a≊1, Te≊20–40 eV, and ne≊1012 cm−3 for a line-averaged electron density n̄e=(3–6)×1012 cm−3. The relative fluctuation levels decrease as the probe is moved into the core plasma. For Te≳20 eV, ñe/ne≊5%, and eφ̃f /Te≊2ñe/ne at r/a=0.95. The measured fluctuation spectra are broadband (40–300 kHz) with k̄ρs≊(0.05–0.1), where k̄ is the average wave number of the fluctuations and ρs is the ion Larmor radius at the sound speed. Near the LCFS, the density fluctuations can be approximated by ñe/ne ≊0.4/k̄Ln, where Ln is the gradient scale length of ne. The propagation direction of the fluctuations reverses to the electron diamagnetic direction at r/a<1. The phase velocity of the fluctuations and the electron drift velocity are comparable. The particle flux estimated from the fluctuations is consistent with fluxes obtained from the particle balance using the Hα spectroscopic measurements. Many of the features seen in the ATF edge fluctuations resemble those of Ohmically heated plasmas in the Texas Experimental Tokamak (TEXT) [Phys. Rev. Lett. 62, 1844 (1989)].
Theory of wave activity occurring in the AMPTE artificial comet
Authors: Bingham R. , Shapiro V. D. , Tsytovich V. N. , de Angelis U. , Gilman M. , Shevchenko V. I.
Published: July 2002

One of the main experiments of the Active Magnetospheric Particle Tracer Explorers (AMPTE) [J. Geophys. Res. 91, 10013 (1986)] satellite mission was the release of neutral barium atoms in the solar wind. The barium atoms ionized by photoionization extremely rapidly forming a dense, expanding, plasma cloud that interrupted the solar wind flow creating diamagnetic cavities. On the upstream side of the cavity a region of compressed plasma and enhanced magnetic field was created as the result of being produced by the slowing down and deflection of the solar wind, and magnetic field line draping. Intense electrostatic and magnetic turbulence was observed by both the IRM [J. Geophys. Res. 91, 10 013 (1986)] and UKS [J. Geophys. Res. 91, 1320 (1986)] satellites at the boundary of the diamagnetic cavity, with the most intense waves being detected near the outer boundary of the compressed region. This paper examines how the newly created expanding plasma couples to the solar wind by means of plasma–beam and current-driven instabilities. In particular, it is shown how lower-hybrid and lower-hybrid drift waves are generated by cross-field proton–barium streaming instabilities and cross-field electron currents. The saturation mechanism for these waves is considered to be the modulational instability, this instability can also lead to filamentation and coupling to magnetosonic modes, which are also observed. As the result of modulational instability the k∥ component increases, which allows the heating and acceleration of electrons that is consistent with the observations.
A theoretical model for intense microwave pulse propagation in an air breakdown environment
Authors: Kuo S. P. , Zhang Y. S.
Published: July 2002

A theoretical model based on two coupled partial differential equations is established to describe the propagation of an intense microwave pulse in air breakdown environment. One is derived from the Poynting theorem, and the other one is the rate equation of electron density. A semiempirical formula of the ionization frequency is adopted for this model. A transformation of these two equations to local time frame of reference is introduced so that they can be solved numerically with considerably reduced computation time. This model is tested by using it to perform the computer simulation of the chamber experiments [S. P. Kuo, Y. S. Zhang, and P. Kossey, J. Appl. Phys. 67, 2762 (1990)]. The numerical results are shown to agree well with the experimental results.
Production and observation of the ion-temperature-gradient instability
Authors: Chen J. , Sen A. K. , Migliuolo S.
Published: July 2002

The Columbia Linear Machine has been modified to produce and study the slab branch of the ion-temperature-gradient instability [Phys. Rev. Lett. 66, 429 (1991)]. A unique heating scheme with biased meshes has been installed to yield a peaked ion temperature and flattish density profiles. Under these conditions, the parameter ηi (=d ln Ti/d ln N) exceeds the critical value and a strong instability has been observed. Based on observations of the azimuthal and axial wavelengths, the real frequency, and increasing mode amplitude with increasing inverse-ion-temperature-gradient scale length, it is identified as the ηi mode. Finally, computational results from a nonlocal theory of the ηi mode corroborate the existence of an instability with the observed azimuthal mode number, axial wavelength, real frequency, and radial structure.
Measurements of the radial structure and poloidal spectra of toroidal Alfvén eigenmodes in the Tokamak Fusion Test Reactor
Authors: Durst R. D. , Fonck R. J. , Wong K. L. , Cheng C. Z. , Fredrickson E. D. , Paul S. F.
Published: July 2002

Toroidal Alfvén eigenmodes (TAE) have been excited by tangential neutral beam injection in the Tokamak Fusion Test Reactor (TFTR) [Proceedings of the Thirteenth International Conference on Plasma Physics and Controlled Nuclear Fusion Research, 1990, Washington, D.C. (International Atomic Energy Agency, Vienna, 1990), Vol. I, p. 9]. Beam emission spectroscopy (BES) has been used to study the radial structure and the poloidal power spectra of these modes. Radial profiles show a global, standing wave structure with a node near r/a=0.6 and a maximum displacement of about 5–10 mm. The cross-phase profiles and the power spectra both imply that the mode is composed of a mixture of components with various poloidal and toroidal mode numbers, as expected for the TAE. Measurements of the poloidal mode spectrum via BES show good agreement with theoretical simulations performed by a nonvariational, kinetic magnetohydrodynamics stability code (nova−k [Cheng, Phys. Rep. 211, 1 (1992)]). In particular, the dominant harmonics in the poloidal spectrum obey the expected relation m+1/2≊q(r)n.
Structure of field-aligned plasma jets associated with magnetic reconnection
Authors: Lee L. C. , Yan M.
Published: July 2002

The structure of field-aligned plasma jets associated with magnetic reconnection is examined. It is found that the plasma jets are located slightly downstream of the magnetic separatrices and each plasma jet consists of two parts: (a) a slow-mode shock and (b) a fast-mode compressional structure. The slow shock accelerates the plasma and converts magnetic energy into flow energy and thermal energy. The fast-mode compressional wave, located immediately downstream of the slow shock, decelerates the plasma and converts part of the flow energy back into magnetic energy and thermal energy. The combined structure of slow shock and fast compressional wave leads to the formation of the narrow field-aligned plasma jet.
Three-dimensional neoclassical nonlinear kinetic equation for low collisionality axisymmetric tokamak plasmas
Authors: Zaitsev F. S. , O’Brien M. R. , Cox M.
Published: July 2002

The three-dimensional nonlinear kinetic equation for low collisionality tokamak plasmas with consistent consideration of neoclassical effects is obtained using an approach differing from the standard neoclassical theory technique. This allows treatment of large banana widths and large inverse aspect ratios. The equation is suitable for computer modeling of bootstrap currents and other phenomena arising from non-Maxwellian distributions. The formalism described in this paper, which is for noncanonical variables, might also be of use for the consistent derivation of three-dimensional kinetic equations that treat other effects, for example, additional heating.
Model study of H-mode behavior induced by radial currents
Authors: Ramachandran H. , Morales G. J. , Fried B. D.
Published: July 2002

A simple model is developed that isolates the essential features of a magnetically confined plasma undergoing anomalous transport and whose properties are manipulated by externally injected radial currents. The model exhibits the following intrinsic properties (not built-in a priori): Ohmic confinement improves with density; L-mode scaling depends on heating power as P−0.6; a transition to H-mode behavior is induced by radial currents on the order of 10 A. The model is benchmarked against the experiments performed in the Continuous Current Tokamak (CCT) [R. J. Taylor et al., Phys. Rev. Lett. 63, 2365 (1989)]; excellent quantitative and qualitative agreement is obtained with most of the observations. Some discrepancies are identified and their significance is elucidated. The new effects explored with the model are H-modes induced by multiple electrodes, auxiliary heating in the presence of radial currents, and the concept of H mode as a ‘‘phase transition.’’
The departure from Darcy flow in natural convection in a vertical porous layer
Authors: Poulikakos Dimos , Bejan Adrian
Published: July 2002

An analytical and numerical study is reported of steady-state natural convection in a two-dimensional porous layer heated from the side. Contrary to previous investigations of the phenomenon, which were all based on the Darcy flow model, a vector generalization of Forchheimer’s one-dimensional model is used in the present study, which is valid for all values of local Reynolds number based on pore size. A matched boundary layer solution of the type developed by Weber for Darcy flow is developed for the limit of large-pore Reynolds numbers (the ‘‘non-Darcy’’ limit). It is shown that the natural convection phenomenon in the non-Darcy limit is governed by a new dimensionless group, the Rayleigh number for the higher Reynolds number limit, Ra∞. Numerical experiments are reported in the range 1.6×105≤Ra∞≤1.6×109, in a porous layer with height/thickness ratio equal to 2, and with a high value of Darcy modified Rayleigh number (Ra=4000). The numerical experiments confirm the flow features and scales anticipated by the matched boundary layer solution for the non-Darcy limit. The experiments also document the transition from the well-known Darcy flow to the large-pore Reynolds-number limit treated in this paper.