bluuebunny/crossref_metadata_2025 huggingface dataset:
Additive isometries on a quaternionic Hilbert space
Authors: Sharma C. S. , Almeida D. F.
Published: July 2002

A systematic study of additive isometries on a quaternionic Hilbert space is presented. A number of new results describing the properties of such operators are proved. The work culminates in the first mathematical proof of Wigner’s theorem for quaternionic Hilbert spaces of dimension other than 2 which asserts that any operator which preserves the absolute value of the inner product on a quaternionic Hilbert space is equivalent, in the sense of differing pointwise by a mere phase factor, to a linear isometry. A complete and concise description of the exceptional situation in a two-dimensional quaternionic Hilbert space is given.
A simple Lagrangian for integrable systems
Authors: de Almeida da Silva M. A. , Das Ashok
Published: July 2002

A simple Lagrangian for integrable models that can describe the entire hierachy of equations associated with the system is proposed. In addition, the Lax equation, the recursion relation between the conserved quantities, as well as the vanishing of the Nijenhuis torsion tensor can also be derived from the system of equations following from this Lagrangian.
Completeness relations for Maass Laplacians and heat kernels on the super Poincaré upper half-plane
Authors: Oshima Kazuto
Published: July 2002

Simple completeness relations are proposed for Maass Laplacians. With the help of these completeness relations, correct heat kernels of (super) Maass Laplacians are derived on the (super) Poincaré upper half-plane.
Hidden symmetry and potential group of the Maxwell fish-eye
Authors: Frank Alejandro , Leyvraz François , Wolf Kurt Bernardo
Published: July 2002

The Maxwell fish-eye is an exceptional optical system that shares with the Kepler problem and the point rotor (mass point on a sphere) a hidden, higher rotation symmetry. The Hamiltonian is proportional to the Casimir invariant. The well-known stereographic map is extended to canonical transformations between of the phase spaces of the constrained rotor and the fish-eye. Their dynamical group is a pseudoorthogonal one that permits a succint ‘‘4π’’ wavization of the constrained system. The fish-eye exhibits, unavoidably, chromatic dispersion. Further, a larger conformal dynamical group contains the potential group, that relates the closed, inhomogeneous fish-eye system to similar, scaled ones. Asymptotically, it is related to free propagation in homogenous media.
Cohomology theory and deformations of Z2-graded lie algebras
Authors: Tripathy K. C. , Patra M. K.
Published: July 2002

The algebraic cohomology and the spectral sequences for a Z2-graded Lie algebra are briefly reviewed. The reducibility property of a strongly semisimple Lie superalgebra is established. The role of second and third cohomologies in the deformation of a Lie superalgebra is discussed. Using spectral sequences, the second cohomology of the full BRS algebra is shown to be the ground field and the third cohomology being trivial implies that osp(1,2) is the only graded Lie algebra obtained by deformation of the full BRS algebra. A similar analysis yields the superconformal algebra as a deformation of the super Poincaré algebra. The superconformal algebra so derived contains so(4,1) as the even part, ruling out the existence of negative curvature of a de Sitter universe!
Integrable Hamiltonian systems related to the polynomial eigenvalue problem
Authors: Zeng Yunbo , Li Yishen
Published: July 2002

The independent integrals of motion in involution for the Hamiltonian system related to the second-order polynomial eigenvalue problem are constructed by using relevant recursion formula. The hierarchy of Hamiltonian systems obtained from the above problem and the time part of the Lax pair are shown to be completely integrable and they are shown to commute with each other. Furthermore, their solution solves the evolution equation associated with the Lax pair.
Multi-Hamiltonian structure of equations of hydrodynamic type
Authors: Gümral H. , Nutku Y.
Published: July 2002

The discussion of the Hamiltonian structure of two-component equations of hydrodynamic type is completed by presenting the Hamiltonian operators for Euler’s equation governing the motion of plane sound waves of finite amplitude and another quasilinear second-order wave equation. There exists a doubly infinite family of conserved Hamiltonians for the equations of gas dynamics that degenerate into one, namely, the Benney sequence, for shallow-water waves. Infinite sequences of conserved quantities for these equations are also presented. In the case of multicomponent equations of hydrodynamic type, it is shown, that Kodama’s generalization of the shallow-water equations admits bi-Hamiltonian structure.
Exact solutions of Einstein’s equations for space-time with local rotational symmetry in which the Dirac equation separates
Authors: Jing Jiliang
Published: July 2002

The Einstein’s equations for space-time with local rotational symmetry in which the Dirac equation separates are studied. All possible solutions are exhibited for a fluid with negative pressure. Other solutions correspond to radiation and a stiff fluid.
A class of Bäcklund transformations for equations of the type u
x
y=f(u,u
x)
Authors: Sophocleous C. , Kingston J. G.
Published: July 2002

The Bäcklund transformation u=F(u′,u′x,uy) is considered for equations of the form uxy=f(u,ux). The nonlinear forms of f(u,ux) that admit such transformations are completely classified. New Bäcklund transformations for modified sine-Gordon, modified sinh-Gordon, and modified Liouville equations are obtained.
String cosmology in spherically symmetric space-time
Authors: Chakraborty Subenoy , Chakraborty Ashok Kr.
Published: July 2002

Cosmological solutions for the string model are done in a spherically symmetric Kantowski–Sachs metric ansatz. Solutions are evaluated for three equations of states for string density. Also, an analytic relation between the metric coefficients is assumed. A first-order autonomous system is developed from the field equations and a line singularity is found.
Evaluation of the spherical Bessel transform of a Whittaker function: An application of a difference equation method
Authors: Maximon Leonard C.
Published: July 2002

A simple analytic expression for the spherical Bessel transform of the zero-range bound state wave function with the Coulomb interaction present, for the lth partial wave, expressed as a Whittaker function, is obtained. The result is given in terms of polynomials of degree l, the exponential function, and a simple hypergeometric function which is independent of l. Transformations of this latter function are derived in terms of more rapidly convergent series. The method presented has much wider application, since it relies essentially only on the existence of differential-difference equations for the functions involved, and the solution of the inhomogeneous difference and differential equations satisfied by the transform.
Real wave equations for positive-frequency electromagnetic fields and their Green’s function solutions
Authors: Cardoso J. G.
Published: July 2002

A method is provided whereby solutions of the inhomogeneous wave equations that describe the propagation of positive-frequency photons in the forward tube of complex Minkowski space may be formally expressed in terms of integrals involving the tensor product of appropriate Green’s functions. It is pointed out that this method can be used also for treating problems involving wave operators defined on arbitrary product spaces.
Exact partition functions of interacting lattice fermions
Authors: Grandati Y. , Bérard A. , Grangé P.
Published: July 2002

Exact expressions are obtained for Grassmann integrals of exponentials corresponding to the partition functions of systems of lattice fermions with nearest-neighbor interactions. It is achieved by relating to the dimer problem and use of its combinatorial techniques.
R-matrix approach to quantum superalgebras suq(m‖n)
Authors: Chang D. , Phillips I. , Rozansky L.
Published: July 2002

Quantum superalgebras suq(m‖n) are studied in the framework of R-matrix formalism. Explicit parametrization of L(+) and L(−) matrices in terms of suq(m‖n) generators are presented. We also show that quantum deformation of nonsimple superalgebra su(n‖n) requires its extension to u(n‖n).
Reductions by isometries of the self-dual Yang–Mills equations in four-dimensional Euclidean space
Authors: Kovalyov M. , Légaré M. , Gagnon L.
Published: July 2002

A classification of the subgroups of the four-dimensional Euclidean group is given. The (anti-) self-dual Yang–Mills equations in four-dimensional Euclidean space are then reduced for each class representative and for any gauge group when a strict invariance of the gauge fields is required, or for the gauge group SO(3) if the gauge fields remain invariant up to gauge transformations. Amongst the residual systems, many constitute sets of first order ordinary differential equations sharing the Painlevé property.
Quasi-exactly-solvable system and sphaleron stability
Authors: Braibant S. , Brihaye Y.
Published: July 2002

We show explicitly that the eigenvalue equation describing the normal modes of the sphalerons in the 1+1 Abelian Higgs model is a quasi-exactly-solvable system.
Frequency expansion method for the one-dimensional Fokker–Planck equation
Authors: Miyazawa Toru
Published: July 2002

A frequency expansion method is formulated for the one-variable Fokker–Planck equation. It is shown that this method is valid for potentials U(x) which diverge faster than log‖x‖ or converge to a limit faster than any powers of x as x→±∞. The analysis is based on the study of the reflection coefficients for the Fokker–Planck equation. Expressions for the expansion coefficients of the reflection coefficients are also derived.
The functional integral for fields in a cavity
Authors: Vanzo Luciano
Published: July 2002

The functional integral for a scalar field confined in a cavity and subjected to linear boundary conditions is discussed herein. It is shown how the functional measure can be conveniently dealt with by modifying the classical action with boundary corrections. The nonuniqueness of the boundary actions is described with a three-parameter family of them giving identical boundary conditions. In some cases, the corresponding Green’s function will define a kind of generalized Gaussian measure on function space. The vacuum energy is discussed, paying due attention to its anomalous scale dependence, and the physical issues involved are considered.
Solvable (nonrelativistic, classical) n-body problems on the line. I
Authors: Calogero F. , Xiaoda Ji
Published: July 2002

Several solvable n-body problems on the line are exhibited. They are characterized by equations of motion of Newtonian type, mjẍj=Fj, j=1,...,n, with the ‘‘forces’’ Fj given as explicit functions of the ‘‘particle coordinates’’ xk and their velocities ẋk, k=1,...,n; the forces Fj generally also depend on some free parameters, so that in each case there is actually a class of solvable models. In this paper the emphasis is on translation-invariant models, and on values of n sufficiently small (‘‘few-body problems’’) to allow the display of the solution of the initial-value problem in completely explicit form.
Complex symplectic geometry and compact locally hyper-Kählerian manifolds
Authors: McInnes Brett
Published: July 2002

Complex symplectic geometry is the study of complex manifolds admitting a global closed nondegenerate holomorphic two-form. Compact, simply connected complex symplectic manifolds are of interest for various reasons; for example, they always admit a Ricci-flat metric. In this work, the close relationship between the complex geometry of such manifolds and their Riemannian structures is exploited in order to obtain results in both directions: Riemannian techniques are used to obtain results on the complex automorphism group, and the problem of constructing examples of compact locally hyper-Kählerian manifolds with prescribed holonomy groups is discussed.
On the equivalence of two super Korteweg–deVries theories: A bi-Hamiltonian viewpoint
Authors: Morosi Carlo , Pizzocchero Livio
Published: July 2002

From a bi-Hamiltonian viewpoint the equivalence of two supersymmetric Korteweg–deVries theories, introduced by Manin–Radul and Laberge–Mathieu, is discussed herein. It is shown that the transformation connecting the two theories (proposed recently in the literature) preserves the bi-Hamiltonian structures; moreover, another derivation of this transformation, stemming from bi-Hamiltonian reduction theory and strongly emphasizing the geometrical meaning of the above equivalence is presented.
Soliton solutions and gauge equivalence for the quadratic bundle
Authors: Vaklev Y.
Published: July 2002

A more simple form than the one given by Vaklev [J. Math. Phys. 33, 4111 (1992)] for the soliton solutions related to the quadratic bundle [E. A. Kuznetzov and A. V. Mikhailov, Teor. Mat. Fiz. 30, 303 (1977); D. J. Kaup and A. C. Newell, J. Math. Phys. 19, 798 (1978); V. S. Gerdjikov, M. I. Ivanov, and P. P. Kulish, Teor. Mat. Fiz. 44, 342 (1980); V. S. Gerdjikov and M. I. Ivanov, Bulg. J. Phys. 10, 13 (1983); 10, 2, 129 (1983)] is obtained. The corresponding solutions for the gauge equivalent case are obtained as well. Among them one can find the N-soliton solutions for the derivative nonlinear Schrödinger equation, their gauge equivalents, etc. The method used in the article allows one to express some integrals by means of appropriate determinants and thus the result is obtained without integration.
Dirac’s equation on the quantum net
Authors: Selesnick S. A.
Published: July 2002

The quantum net model differs from other quantizations and discretizations of space-time in being founded upon quantum-logical principles. Fermions are envisaged as arising from defects in the net. Such defects are investigated and it is found that the attempt to vary them infinitesimally gives rise to a reticular version of the Dirac operator, which now has a simple interpretation in terms of quantum mechanical infinitesimal parallel transport. The analog of the usual massless Weyl equations are found to hold on the net, and algebraic solutions are deduced by exploiting its inherent logical structure. A correspondence principle then applies to show that these equations and their solutions correspond precisely to the ones expected in the continuum. (In the course of this, new basis-independent expressions for the complex Minkowski-space Dirac matrices are found.) Finally, an attempt is made to introduce gravity into the net, and the flat space Dirac Lagrangian is modified accordingly.
Isotropic classical spin chains showing nearest neighbor correlated cationic distributions
Authors: Curély Jacques , Georges Roland
Published: July 2002

A model is proposed for calculating the magnetic susceptibility of isotropic classical spin chains showing nearest neighbor correlated cationic distributions. It allows one to obtain a general closed-form expression: This expression formally looks like previous ones obtained in the case of random chains for which the neighboring cationic species are not correlated; but here the previous intervening scalar parameters are replaced by vectorial and matricial expressions.
Gravitational mass anomaly
Authors: Glass E. N. , Naber M. G.
Published: July 2002

The mass of gravitational sources differs by a factor of 2 when computed by the Komar superpotential and when computed in the gravitational weak field limit. The difference has been recognized for some time since both the linearized theory and the Einstein pseudotensor yield the same value, different by a factor of 2 from the Komar mass. The great advantage of the Komar superpotential over other methods is its tensorial formulation, however it fails to produce a Noether quantity. A different tensorial method is suggested that is free of the mass anomaly, namely, the zero and first Taub numbers [Phys. Rev. D 47, 474 (1993)] which are indeed Noether quantities. The zeroth Taub number is obtained from the Penrose–Goldberg superpotential [Phys. Rev. D 41, 410 (1990)].
Maximum entropy algorithm for spectral estimation problem with aipriori information
Authors: Ugrinovsky Roman
Published: July 2002

The power density estimation problem with a priori information about spectrum is considered. The problem is reduced to a power density estimation problem with spectral gaps. The solution of the problem is studied in the context of the trigonometric moment problem with gaps. The necessary and sufficient conditions are established for the existence of solution and all solutions are described in indeterminate cases. A new definition of the entropy functional is given. The effective algorithm to construct maximum entropy solution is proposed. A number of explicit illustrations are presented.
Comment on the solutions of the graded Yang–Baxter equation
Authors: Chung Won-Sang
Published: July 2002

In this comment we obtain two types of solutions of the graded Yang–Baxter equation whose symmetry group is GLqs(1‖1).
Clebsch–Gordan coefficients and related identities obtained by an integration over the group space of SUq(2)
Authors: Cadavid A. C. , Finkelstein R. J.
Published: July 2002

The Clebsch–Gordan coefficients of SUq(2) are here calculated by an integration over the group manifold following the Woronowicz prescription. A representation is obtained that is different from the one derived from the q-group algebra. The equivalency of the two results implies a q-identity and establishes a relation between q-hypergeometric functions. In the limit q=1, our result gives a different expression for the Clebsch–Gordan coefficients of SU(2), and the q-identity relation reduces to an identity between binomial coefficients. The Woronowicz technique is extended to calculate the integral of the product of many irreducible representations. A summary of the main results has already been presented elsewhere.
Some remarks on metric and Weyl connections
Authors: Hall G. S. , Haddow Barry M.
Published: July 2002

A discussion is given regarding those Lie subgroups of GL(n, R) which contain SO(n) or SO(n−1,1) as Lie subgroups. The result is applied to the theory of holonomy groups and in particular to metric and Weyl connections. Some general remarks regarding the relationship between metric connections and curvature tensors are given.
Integrable pseudo-Euclidean Toda-like systems in multidimensional cosmology with multicomponent perfect fluid
Authors: Gavrilov V. R. , Ivashchuk V. D. , Melnikov V. N.
Published: July 2002

The multidimensional cosmological model describing the evolution of n Einstein spaces in the presence of multicomponent perfect fluid is considered. When the vectors corresponding to the equations of state of the components are orthogonal with respect to the minisuperspace metric, the Einstein equations are integrated and a Kasner-like form of the solutions is presented. For special sets of parameters the cosmological model is reduced to the Euclidean Toda-like system connected with some Lie algebra G. For G=A2 exact solutions are explicitly written. A certain family of wormhole solutions is also obtained.
Vertex normal ordering as a consequence of nonsymmetric bilinear forms in Clifford algebras
Authors: Fauser Bertfried
Published: July 2002

We consider Clifford algebras with nonsymmetric bilinear forms. They parametrize the chosen ideal in the isomorphism class of the standard symmetric ones. Since the content of physical theories depends on the injection ⊕nΛn𝒱→CL(𝒱,Q), one has to transform to the standard construction. The injection is described by the antisymmetric part of the bilinear form. This process results in the appropriate vertex normal ordering terms, which are now obtained from the theory itself and not added ad hoc via a regularization argument.
Hamiltonian structure for degenerate AKNS systems
Authors: Corona-Corona Gulmaro
Published: July 2002

There is a family of degenerate AKNS systems for which the full theory of generic AKNS systems does not directly extend. The linear space of potentials still has a natural Poisson structure, but the scattering method used by Beals and Sattinger to show complete integrability for the generic AKNS systems fails for the degenerate case. A Poisson structure is not induced on the scattering side as in the generic case. As a consequence, the problem of complete integrability for degenerate AKNS systems still is an open question. In addition, contrary to the generic case, the Lax pair gives flows for degenerate integrable systems that are nonlocal. In general, they do not exist, and they are no longer linear on the scattering side. Necessary conditions for their existence and for linear evolution in the scattering side are found.
Towards a Coulomb gas of instantons of the S0(4)×U(1) Higgs model on R4
Authors: Arthur K. , O’Brien G. M. , Tchrakian D. H.
Published: July 2002

The SO(4)×U(1) Higgs model on R4 is extended by a F3 term so that the action receives a non-vanishing contribution from the interactions of two-instantons and three-instantons, and can be expressed as the inverse of the Laplacian on R4 in terms of the mutual distances of the instantons. The one-instanton solutions of both the basic and the extended models have been studied in detail numerically.
Deforming maps for Lie group covariant creation and annihilation operators
Authors: Fiore Gaetano
Published: July 2002

Any deformation of a Weyl or Clifford algebra 𝒜 can be realized through a “deforming map,” i.e., a formal change of generators in 𝒜. This is true in particular if 𝒜 is covariant under a Lie algebra g and its deformation is induced by some triangular deformation Uhg of the Hopf algebra Ug. We propose a systematic method to construct all the corresponding deforming maps, together with the corresponding realizations of the action of Uhg. The method is then generalized and explicitly applied to the case that Uhg is the quantum group Uhsl(2). A preliminary study of the status of deforming maps at the representation level shows in particular that “deformed” Fock representations induced by a compact Uhg can be interpreted as standard “undeformed” Fock representations describing particles with ordinary Bose or Fermi statistics.
Symmetries of Hamiltonian systems with two degrees of freedom
Authors: Damianou P. A. , Sophocleous C.
Published: July 2002

We classify the Lie point symmetry groups for an autonomous Hamiltonian system with two degrees of freedom. With the exception of the harmonic oscillator or a free particle where the dimension is 15, we obtain all dimensions between 1 and 7. For each system in the classification we examine integrability.
Solutions of Penrose’s equation
Authors: Glass E. N. , Kress Jonathan
Published: July 2002

The computational use of Killing potentials which satisfy Penrose’s equation is discussed. Penrose’s equation is presented as a conformal Killing–Yano equation and the class of possible solutions is analyzed. It is shown that solutions exist in space–times of Petrov type O, D, or N. In the particular case of the Kerr background, it is shown that there can be no Killing potential for the axial Killing vector.
Black hole interacting with matter as a simple dynamical system
Authors: Hájı́ček Petr
Published: July 2002

Recently, a variational principle has been derived from Einstein–Hilbert and a matter Lagrangian for the spherically symmetric system of a dust shell and a black hole. The so-called physical region of the phase space, which contains all physically meaningful states of the system defined by the variational principle, is specified; it has a complicated boundary. The principle is then transformed to new variables that remove some problems of the original formalism: the whole phase space is covered (in particular, the variables are regular at all horizons), the constraint has a polynomial form, and the constraint equation is uniquely solvable for two of the three conserved momenta. The solutions for the momenta are written down explicitly. The symmetry group of the system is studied. The equations of motion are derived from the transformed principle and are shown to be equivalent to the previous ones. Some lower-dimensional systems are constructed by exclusion of cyclic variables, and some of their properties are found.
The kinematical role of automorphisms in the orthonormal frame approach to Bianchi cosmology
Authors: Jantzen R. T. , Uggla C.
Published: July 2002

The automorphism group and frame commutator relations in the orthonormal frame approach to Bianchi cosmology are used to construct an explicit coordinate representation of the orthonormal frame itself (and hence of the spacetime metric) which depends algebraically on the connection coefficients. This is not possible in general inhomogeneous models where differential equations must instead be solved. The shift vector field required for this procedure is intimately related to the true Smarr–York minimal strain and minimal distortion shifts.
Lifetimes of impurity states in crossed magnetic and electric fields
Authors: Gyger Sébastien , Martin Philippe A.
Published: July 2002

We study the quantum dynamics of localized impurity states created by a point interaction for an electron moving in two dimensions under the influence of a perpendicular magnetic field and an in-plane weak electric field. All impurity states are unstable in presence of the electric field. Their lifetimes are computed and shown to grow in a Gaussian way as the electric field tends to zero.
Instanton correction of prepotential in Ruijsenaars model associated with N=2 SU(2) Seiberg–Witten theory
Authors: Ohta Yűji
Published: July 2002

Instanton correction of prepotential of the one-dimensional SL(2) Ruijsenaars model is presented with the help of the Picard–Fuchs equation of Pakuliak–Perelomov type. It is shown that the instanton-induced prepotential reduces to that of the SU(2) gauge theory coupled with a massive adjoint hypermultiplet.
Rayleigh–Taylor instability in a finite thickness layer of a viscous fluid
Authors: Brown Hugh R.
Published: July 2002

The Rayleigh–Taylor instability in a finite thickness layer of viscous fluid has been studied in the creeping flow limit. The wavelength of fastest growth was found to be controlled by the larger of the layer thickness or a parameter that was a function of the ratio of the surface tension to the pressure gradient.
Colored stochastic noises in the renormalization group approach of turbulence
Authors: Carati D.
Published: July 2002

The large scale properties of the forced Navier–Stokes equation are investigated by using the renormalization group theory of turbulence. The assumptions made on the stochastic forcing are as weak as possible. Particularly, the white noise hypothesis is abandoned. This provides a new expansion parameter that is not related to the usual ε expansion. Numerical values for the Kolmogorov constant and other typical constants of the fully developed turbulence are obtained and are in good agreement with experimental data.
Sensitivity of liquid bridges subject to axial residual acceleration
Authors: Zhang Yiqiang , Alexander J. Iwan D.
Published: July 2002

It has become evident that the float zone crystal growth method and isothermal liquid bridges may be very sensitive to the residual acceleration environment of a spacelab. Indeed, the shape equilibria show a high degree of sensitivity and, thus, even the small steady acceleration associated with the effective low gravity environment of a spacecraft cannot be ignored. Using a slender-body approximation, the problem of determining the axisymmetric response of the shape of the free surface of a cylindrical liquid column bounded by two solid regions is modeled by a 1-D system of nonlinear equations. It is found that the sensitivity of the zone shape depends on the static Bond number, B0, aspect ratio, and viscosity, as well as the amplitude and frequency of the disturbance. The general trend is an increase in tolerable residual gravity with increasing frequency. At the eigenfrequencies of the zone, however, there are dramatic deviations from this trend. At these frequencies the tolerable residual gravity level can be two orders of magnitude lower at this frequency. For the cases considered the values of B0 were taken to be 0.002 and 0.02 and the dimensionless viscosities, C=ν(ρ/γR0)1/2, used were in the range 0.001–0.01. Aspect ratios ranging from 96.3% to 82.7% of the Rayleigh limit were examined. For these cases, the frequencies associated with the lowest tolerable acceleration have been found in the 10−2–10−1 Hz range. In terms of previously recorded and predicted residual accelerations, the sensitive frequency ranges for the cases examined are 10−2–10−1 Hz and 1–10 Hz. Maximum tolerable residual gravity levels as low as 10−6 g have been calculated. The effect of viscosity is seen to increase the tolerable acceleration level for all frequencies. The equilibrium shape, as determined by the steady background acceleration, has a pronounced effect at low frequencies. A change in slenderness of the bridge markedly changes the sensitivity to residual acceleration as the Rayleigh limit is approached.
Turbulence in a reacting contact surface
Authors: Johnson J. A. , Johnson L. E. , Lu X. N.
Published: July 2002

Turbulent features in a shock tube’s contact surface with 2NO2〈=〉N2O4 are explored. Turbulent densities and velocities show an overall power-law dependence in the fluctuation spectra. At fixed reactant percentages, turbulence increases with increasing Reynolds number. At fixed Reynolds numbers, increasing the reactant percentages cause a reduction in turbulence and an increase in the relative strength of discrete high-frequency components in the density fluctuation spectra. The reliability of conventional chemical modeling for this system apparently decreases with increasing turbulence in a manner suggestive of reaction rate distortion, consistent with theoretical speculation.
The Jeffery paradox as the limit of a three-dimensional Stokes flow
Authors: Smith S. H.
Published: July 2002

The solution of the biharmonic equation for the slow viscous flow resulting from a line rotlet in front of a circular cylinder indicates the physically unrealistic behavior of a uniform stream at infinity—an example of the Jeffery paradox. It is shown here, when the three-dimensional motion resulting from a finite line rotlet parallel to the (infinite) circular cylinder is investigated, that the length h of the cylinder has to be so large that O[(ln h)−1] terms are negligible before this two-dimensional result is correct.
A global study of enhanced stretching and diffusion in chaotic tangles
Authors: Beigie Darin , Leonard Anthony , Wiggins Stephen
Published: July 2002

A global, finite-time study is made of stretching and diffusion in a class of chaotic tangles associated with fluids described by periodically forced two-dimensional dynamical systems. Invariant lobe structures formed by intersecting global stable and unstable manifolds of persisting invariant hyperbolic sets provide the geometrical framework for studying stretching of interfaces and diffusion of passive scalars across these interfaces. In particular, the present study focuses on the material curve that initially lies on the unstable manifold segment of the boundary of the entraining turnstile lobe.

A knowledge of the stretch profile of a corresponding curve that evolves according to the unperturbed flow, coupled with an appreciation of a symbolic dynamics that applies to the entire original material curve in the perturbed flow, provides the framework for understanding the mechanism for, and topology of, enhanced stretching in chaotic tangles. Secondary intersection points (SIP’s) of the stable and unstable manifolds are particularly relevant to the topology, and the perturbed stretch profile is understood in terms of the unperturbed stretch profile approximately repeating itself on smaller and smaller scales. For sufficiently thin diffusion zones, diffusion of passive scalars across interfaces can be treated as a one-dimensional process, and diffusion rates across interfaces are directly related to the stretch history of the interface.

An understanding of interface stretching thus directly translates to an understanding of diffusion across interfaces. However, a notable exception to the thin diffusion zone approximation occurs when an interface folds on top of itself so that neighboring diffusion zones overlap. An analysis which takes into account the overlap of nearest neighbor diffusion zones is presented, which is sufficient to capture new phenomena relevant to efficiency of mixing. The analysis adds to the concentration profile a saturation term that depends on the distance between neighboring segments of the interface. Efficiency of diffusion thus depends not only on efficiency of stretching along the interface, but on how this stretching is distributed relative to the distance between neighboring segments of the interface.
Effective equations and the inverse cascade theory for Kolmogorov flows
Authors: E Weinan , Shu Chi-Wang
Published: July 2002

A detailed study is presented of the inverse cascade process in the Kolmogorov flows in the limit as the forcing wave number goes to infinity. Extensive numerical results reveal that energy is transferred from high wave numbers to low ones through two distinctive stages. At the early stage, the low wave-number spectrum evolves to a universal k−4 decay law. At the same time, enough scales are generated between the forcing scale (small) and the size of the system (large scale) so that there is no longer separation of scales in the system. In the next stage the flow undergoes a transition to a continuum of scales. This transition proceeds through the formation of a hierarchy of layers of elongated vortices at increasingly larger scales with alternating orientation. To explain these phenomena, effective equations governing the evolution of the large-scale quantities are derived. Strong numerical evidence is presented that even with smooth initial data, the solution to the effective equation develops a k−4 type singularity at a finite time. The effective equation also exhibits a weak instability which suggest that gradients in the direction of the forcing will grow much quicker than gradients in other directions.
Statistical mechanics and correlation properties of a rotating two-dimensional flow of like-sign vortices
Authors: Viecelli J. A.
Published: July 2002

The Hamiltonian flow of a set of point vortices of like sign and strength has a low-temperature phase consisting of a rotating triangular lattice of vortices, and a normal temperature turbulent phase consisting of random clusters of vorticity that orbit about a common center along random tracks. The mean-field flow in the normal temperature phase has similarities with turbulent quasi-two-dimensional rotating laboratory and geophysical flows, whereas the low-temperature phase displays effects associated with quantum fluids. In the normal temperature phase the vortices follow power-law clustering distributions, while in the time domain random interval modulation of the vortex orbit radii fluctuations produces singular fractional exponent power-law low-frequency spectra corresponding to time autocorrelation functions with fractional exponent power-law tails. Enhanced diffusion is present in the turbulent state, whereas in the solid-body rotation state vortices thermally diffuse across the lattice. Over the entire temperature range the interaction energy of a single vortex in the field of the rest of the vortices follows positive temperature Fermi–Dirac statistics, with the zero temperature limit corresponding to the rotating crystal phase, and the infinite temperature limit corresponding to a Maxwellian distribution. Analyses of weather records dependent on the large-scale quasi-two-dimensional atmospheric circulation suggest the presence of singular fractional exponent power-law spectra and fractional exponent power-law autocorrelation tails, consistent with the theory.
Computation of the Loitsianski integral in decaying isotropic turbulence
Authors: Chasnov J. R.
Published: July 2002

The time evolution of the Loitsianski integral at high-Reynolds numbers is determined by computing an ensemble average of a large number of independent large-eddy simulations of decaying isotropic turbulence. It is found that the Loitsianski integral becomes proportional to tγ at large times and that γ ≊0.25. The present simulations illustrate the efficient use of massively parallel computers for simulating large ensembles of turbulent flows.
A low-dimensional model for chaos in open fluid flows
Authors: Olinger D. J.
Published: July 2002

A forced Landau–Stuart equation is studied in order to derive a low-dimensional model describing the temporal behavior of a paradigm open flow, the two-dimensional forced cylinder wake. Numerical results from the model exhibit several characteristics of circle maps, and compare qualitatively to previous experimental results for an oscillating cylinder wake. The low-dimensional model is also shown to reduce to a circle map in the limit of small forcing amplitudes. Observation of circle map dynamics in the forced Landau–Stuart equation strengthens the conjecture that globally unstable fluid flows are amenable to a dynamical systems approach focusing on the study of low-dimensional iterative maps. The established connection between the Landau–Stuart equation and the circle map unifies certain aspects of spatiotemporal stability and low-dimensional chaos theory.
Nonlinear magnetohydrodynamic studies of the tilt mode in field-reversed configurations
Authors: Milroy R. D. , Barnes D. C. , Bishop R. C. , Webster R. B.
Published: July 2002

A three-dimensional magnetohydrodynamic code has been used to study the nonlinear evolution of the tilt instability in a field-reversed configuration. The evolution of the mode has been followed through magnetic field reconnection to complete the loss of confinement, with no evidence of any nonlinear stabilizing effects. The influence of plasma rotation has also been investigated. It was found that while the mode remains unstable, its character changed at high rotation rates. It evolves from an internal mode with a very small displacement velocity at the separatrix, to an external mode with almost no radial component to the displacement velocity. Hall term effects were found to be capable of reducing the growth rate for small and elongated configurations, but again, a change in mode character was found to prevent the stabilization predicted in a previous analysis. Kinetic effects remain the most promising mechanism to explain the observed stability of current experiments.
The effects of collisions on the plasma presheath
Authors: Koch D. J. , Hitchon W. N. G.
Published: July 2002

A numerical study of the plasma presheath has been performed, extending earlier work to include the effects of general source functions, and allowing for collisions in the presheath. Analytic results for a collisionless presheath with particular source functions have been confirmed, and comparisons with a numerical study of a weakly collisional presheath have been made. The extrapolation of these calculations to high collision frequency, where they are compared to a simple analytic model, and the effects of the choice of source functions are presented.
Quasiperiodic behavior in beam-driven strong Langmuir turbulence
Authors: Robinson P. A. , Newman D. L.
Published: July 2002

The evolution of unmagnetized beam-driven strong Langmuir turbulence is studied in two dimensions by numerically integrating the Zakharov equations for systems pumped by monochromatic and broadband negative-damping drivers with nonzero central wavenumber. Long-time statistically steady states are reached for which the dependence of the evolution on the driver wavenumber, growth rate, and bandwidth is examined in detail. For monochromatic drivers, a quasiperiodic cycle is found to develop if the driver wavenumber is sufficiently large. In this cycle, energy from the driven mode undergoes a sequence of weak-turbulence backscatter decays, which transfer energy to an approximately isotropic long-wavelength condensate. During this phase, beam-aligned chains of propagating beat waves develop and perpendicular density waves are also excited. Subsequently, nucleation of waves in density cavities causes a series of wave collapses (involving coherent wave–wave interactions) to occur, during which short-wavelength damping reduces the system energy in discrete steps. Finally, the cycle restarts. The characteristic frequency of the quasiperiodic cycle and the average system energy are both approximately proportional to the growth rate. Broadening of the driver in wavenumber tends to degrade the system-wide coherence of the cycle, but its main features appear to survive on the scale of the coherence length of the driver.
Upper-hybrid vortex solitons
Authors: Jovanović D. , Shukla P. K. , de Angelis U.
Published: July 2002

A Zakharov-type set of two differential equations is derived, describing the interaction of upper-hybrid waves with low-frequency density perturbations in the case of Boltzmann distributed electrons. It is shown that low-frequency self-interaction terms lead to the formation of a traveling solution in the form of a solitary double vortex. This solution can be identified as a new nonlinear mode, related to the driven Hasegawa–Mima modon.
Improved analytic equilibrium for a field-reversed configuration
Authors: Steinhauer Loren C.
Published: July 2002

A family of analytical equilibria for field-reversed configurations has been constructed. Unlike the familiar Hill’s vortex, these equilibria are consistent, in an approximate sense, with the external magnetic field produced by a straight magnetic coil. These equilibria span the range from ‘‘elliptical’’ to ‘‘racetrack’’-like separatrix shape. The properties of the new equilibria are described along with the stability consequences.
The free energy of Maxwell–Vlasov equilibria
Authors: Morrison P. J. , Pfirsch D.
Published: July 2002

A previously derived expression [Phys. Rev. A 40, 3898 (1989)] for the energy of arbitrary perturbations about arbitrary Vlasov–Maxwell equilibria is transformed into a very compact form. The new form is also obtained by a canonical transformation method for solving Vlasov’s equation, which is based on Lie group theory. This method is simpler than the one used before and provides better physical insight. Finally, a procedure is presented for determining the existence of negative-energy modes. In this context the question of why there is an accessibility constraint for the particles, but not for the fields, is discussed.
Hydrodynamic stability and the direct drive approach to laser fusion
Authors: Tabak M. , Munro D. H. , Lindl J. D.
Published: July 2002

In order for inertial confinement fusion (ICF) capsules to achieve high gain, they must not break up because of hydrodynamic instability, the fuel should be maintained on a low adiabat, and the peak laser intensities should be below thresholds of various plasma instabilities. In this paper the results of two-dimensional computer calculations modeling the growth of hydrodynamic instabilities of slabs directly driven with a laser are reported. In order for direct drive capsules to succeed with capsule finishes of 100–300 Å, the capsules must be imploded on an adiabat a factor of 3– 4 in pressure above a Fermi-degenerate adiabat or techniques must be developed for producing density gradient scale lengths of about half the shell thickness. These conclusions depend only weakly on the laser intensity.
Non-neutral plasma shapes and edge profiles
Authors: Peurrung A. J. , Fajans J.
Published: July 2002

Non-neutral plasma shapes and edge profiles are investigated for various plasma and trap parameters. The equilibrium plasma shape is found numerically and compared to the analytically predicted shape. Special attention is given to the profile at the plasma end.
Two-component model of strong Langmuir turbulence: Scalings, spectra, and statistics of Langmuir waves
Authors: Robinson P. A. , Newman D. L.
Published: July 2002

A two-component model of strong Langmuir turbulence is developed, in which intense coherent Langmuir wave packets nucleate from and collapse amid a sea of low-level background waves. Power balance between these two components determines the overall scalings of energy density and power dissipation in the turbulence, and of the rate of formation, number density, volume fraction, and characteristic nucleation time of collapsing wave packets. Recent insights into the structure and evolution of collapsing wave packets are employed to estimate the spectra and field statistics of the turbulence. Extensive calculations using the Zakharov equations in two and three dimensions demonstrate that the predictions of the model are in excellent agreement with numerical results for scalings, spectra, and the distribution of fields in the turbulence in isotropic systems; strong support is thus found for the nucleation model. The scaling behavior proves to be insensitive to the form of the damping of the waves at large wave numbers. Wave collapse is approximately inertial between the nucleation and dissipation scales, yielding power-law energy spectra and field distributions in this range. The existence of a fixed arrest scale manifests itself in exponentially decreasing energy and dissipation spectra at high wave numbers and exponentially decreasing field distributions at high field strengths. It is suggested that such an exponential decrease may explain the field distributions seen in recent beam–plasma experiments. Generalizations to turbulence driven anisotropically by beams or governed by equations other than the Zakharov equations are outlined. It is shown that a previously unrecognized scaling observed in beam-driven systems is correctly predicted by the generalized model.
Representation of magnetic fields with toroidal topology in terms of field-line invariants
Authors: Lewis H. Ralph
Published: July 2002

Beginning with Boozer’s representation of magnetic fields with toroidal topology [Phys. Fluids 26, 1288 (1983)], a general formalism is presented for the representation of any magnetic field with toroidal topology in terms of field-line invariants. The formalism is an application to the magnetic field case of results developed recently by Lewis et al. (submitted for publication to J. Phys. A) for arbitrary time-dependent Hamiltonian systems with one degree of freedom. Every magnetic field with toroidal topology can be associated with time-dependent Hamiltonian systems with one degree of freedom and every time-dependent Hamiltonian system with one degree of freedom can be associated with magnetic fields with toroidal topology. In the Hamiltonian context, given any particular function I(q,p,t), Lewis et al. derived those Hamiltonians for which I(q,p,t) is an invariant. In addition, for each of those Hamiltonians, they derived a function canonically conjugate to I(q,p,t) that is also an invariant. They applied this result to the case where I(q,p,t) is expressed as a function of two canonically conjugate functions. This general Hamiltonian formalism provides a basis for representing magnetic fields with toroidal topology in terms of field-line invariants. The magnetic fields usually contain plasma with flow and anisotropic pressure. A class of fields with or without rotational symmetry is identified for which there are magnetic surfaces. The formalism is developed for application to the case of vacuum magnetic fields.