bluuebunny/crossref_metadata_2025 huggingface dataset:
A class of unitary representations of the Lie group Sp(3, R), its coherent states, and its map to a symplectic realization on sp*(3, R)
Authors: Kramer P. , Papadopolos Z. , Schweizer W.
Published: July 2002

Unitary representations from the positive discrete series of Sp(3, R) with lowest weight w={w0w0w0} are considered. By use of new relations on the enveloping algebra, the generators are constructed as differential operators acting on functions of six real variables. Coherent states for these representations are constructed with the help of the Iwasawa decomposition and used to map the representation space to a symplectic realization on the dual sp*(3, R).
G
H
∞ supermanifolds
Authors: Bryant Peter
Published: July 2002

G H ∞ -de Witt supermanifolds were recently introduced by Rogers [Commun. Math. Phys. 105, 375 (1986)]. It is shown that these supermanifolds correspond to objects in a specified category of extended graded manifolds (subject only to the condition L>2q), and some conclusions are drawn about their structure. In particular, it is shown that a GH∞ -de Witt supermanifold is always a vector bundle over its body. Finally it is shown that extended graded manifolds are always trivial extensions of ordinary graded manifolds. This means that all GH∞-de Witt supermanifolds are in fact H∞.
Recursion operator and bi-Hamiltonian structure for integrable multidimensional lattices
Authors: Ragnisco O. , Santini P. M.
Published: July 2002

The recursion operator and the bi-Hamiltonian structure for an integrable two-dimensional version of the Toda chain are algorithmically derived from the corresponding linear problem. The intimate relation between two-dimensional theories and non-Abelian one-dimensional theories is emphasized. The analogies and differences between discrete and continuous integrable two-dimensional systems are pointed out and discussed.
Properties of Leach–Flessas–Gorringe polynomials
Authors: Pursey D. L.
Published: July 2002

A generating function is obtained for the polynomials recently introduced by Leach, Flessas, and Gorringe [J. Math. Phys. 30, 406 (1989)], and is then used to relate the Leach–Flessas–Gorringe (or LFG) polynomials to Hermite polynomials. The generating function is also used to express a number of integrals involving the LFG polynomials as finite sums of parabolic cylinder functions.
Local supersymmetry in nonrelativistic systems
Authors: Urrutia L. F. , Zanelli J.
Published: July 2002

Classical and quantum nonrelativistic interacting systems invariant under local supersymmetry are constructed by the method of taking square roots of the bosonic constraints that generate timelike reparametrization, leaving the action unchanged. In particular, the square root of the Schrödinger constraint is shown to be the nonrelativistic limit of the Dirac constraint. Contact is made with standard models of supersymmetric quantum mechanics through the reformulation of locally invariant systems in terms of their true degrees of freedom. Contrary to the field theory case, it is shown that locally invariant systems are completely equivalent to corresponding globally invariant systems, where the latter are the Heisenberg picture description of the former with respect to some fermionic time.
Squeezing of free Bose fields
Authors: Sl/owikowski Wojtek , Mo/lmer Klaus
Published: July 2002

The relevant structure of a Bose Fock space using the notion of free commutative algebra with unit element and with a scalar product is incorporated. The squeezed states are then the exponentials of quadratic forms and can be written in the normal form of a general squeeze group. The connection of this group to polarization of the initial Hilbert space is established and its infinitesimal generator is computed. In this way, a common denominator for a series of papers is provided in the topic of light squeezing and last but not least a mathematical formalism is provided that may prove convenient in the general treatment of quantum optics.
Uniqueness of the Virasoro algebra
Authors: Uretsky Jack L.
Published: July 2002

It is shown that the structure constants of the Virasoro algebra are uniquely specified, up to rescaling of the generators, by the requirement that they be nonvanishing. Permitting some of the structure constants to vanish leads to other Lie algebras, including the Witt algebras. Given the grading of the Virasoro algebra, nonvanishing of the structure constants is both necessary and sufficient for the algebra to be the Virasoro algebra.
The two-dimensional magnetic field problem revisited
Authors: Anghel N.
Published: July 2002

The Atiyah–Patodi–Singer index theorem is used to relate the analytic and topological indices of a spin 1/2 -charged particle in a two-dimensional magnetic field.
Hosotani breaking of E6 to a subgroup of rank five
Authors: McInnes Brett
Published: July 2002

On multiply connected manifolds, it is possible to construct vacuum gauge configurations with nontrivial holonomy groups. This is the basis of the Hosotani mechanism. This naturally suggests a ‘‘Hosotani inverse problem’’: If we wish to break a gauge group G to a subgroup H, what are the possible finite holonomy groups having this effect, and what can one say about the fundamental groups of the underlying manifolds? Usually, this problem is too difficult to solve, but we show that, for G=E6 and H locally isomorphic to the rank five group SU(3)×SU(2)×U(1)×U(1), a complete solution is possible. It is hoped that the results will aid a search for examples of Calabi–Yau manifolds leading to a low-energy gauge group of rank five.
High-energy, large-momentum-transfer processes: The N-rung ladder diagram of φ3 theory
Authors: Newton Conrad , Wu Tai Tsun
Published: July 2002

The asymptotic form of the amplitude for the N-rung ladder diagram in φ3 theory is calculated in the limit s≫‖t‖≫m2. The result is proportional to s−1‖t‖−N+1 times a homogeneous polynomial of degree 2N−2 in ln s and ln‖t‖. It is not an analytic function of s and t, although the first N+1 derivatives are continuous in the physical region. Points of nonanalyticity occur when ln‖t‖=γ ln s for γ= (1)/(2) , (1)/(3) ,..., 1/(N−2). The notion of reduced Symanzik functions is introduced. With the aid of these reduced Symanzik functions, a generating function is derived for the leading logarithms of all ladder diagrams.
The Dirac equation in a non-Riemannian manifold III: An analysis using the algebra of quaternions and octonions
Authors: Marques-Bonham Sirley
Published: July 2002

The geometrical properties of a flat tangent space-time local to the manifold of the Einstein–Schrödinger nonsymmetric theory to which an internal octonionic space is attached, is developed here. As an application of the theory, an octonionic Dirac equation for a spin-1/2 particle is also obtained, where is now used an octonionic-like gauge field. It is shown that the (quaternionic) nonsymmetric Yang–Mills theory can be easily recovered and from there, the usual gauge theory on a curved space.
Sugawara-type constructions of the Virasoro algebra based on the twisted affine Kac–Moody superalgebras
Authors: Tsohantjis I. , Cornwell J. F.
Published: July 2002

Explicit realizations of representations of the Virasoro algebra are obtained using highest-weight representations of the twisted affine Kac–Moody superalgebras A(2)(2l−1/0) (for l≥2), A(4)(2l/0) (for l≥1), and C(2)(l+1) (for l≥1) in a generalization of the Sugawara construction. It is also shown that A(2)(2l−1/0) (for l≥2) and A(4)(2l/0) (for l≥1) can be modified to produce ‘‘Neveu–Schwarz’’ type superalgebras, and the corresponding Sugawara construction is given for these. For C(2)(l+1) (for l≥1) it is demonstrated that no such ‘‘Neveu–Schwarz’’ modification is possible.
Four-dimensional conformal and quaternionic structures
Authors: Robinson D. C.
Published: July 2002

The relationship between almost (complex) quaternionic and conformal structures on four-dimensional manifolds is exhibited. Its use in the investigation of the conformal structure of space-time is demonstrated.
New solutions of Braid group representations associated with Yang–Baxter equation
Authors: Ge Mo-Lin , Xue Kang
Published: July 2002

By directly solving quantum Yang–Baxter equations (QYBE) in terms of the extended expansion scheme, besides the known solutions we find new family of solutions of braid group representations associated with the fundamental representations of An, Bn, Cn, and Dn.
Inverse scattering, output kernels, and Jost solutions
Authors: Kirst Th.
Published: July 2002

An operator is derived that projects the Marchenko output kernel onto the Gel’fand–Levitan output kernel in their complete domains of definition. The application of this operator, which can be interpreted as an alternative input kernel, is discussed for generalized Bargmann-type potentials in view of representations that simplify numerical calculations. The relevant quantities, off-shell T matrices included, are expressed analytically and in unified form.
Interaction of null dust clouds fronted by plane impulsive gravitational waves. II
Authors: Taub A. H.
Published: July 2002

This paper extends the earlier discussion of the types of energy-momentum tensors Tμν that can exist in the region of interaction of two colliding plane impulsive gravitational waves, each followed by a null dust cloud. Two additional types of tensors Tμν are discussed. For each of the five types of interaction regions solutions to the Einstein field equations are obtained assuming solution of the vacuum equations are known.
Stable symplectic maps
Authors: Channell Paul J.
Published: July 2002

For a symplectic vector space of arbitrary even dimension it is shown how to construct an infinite class of nonlinear sympletic maps of the space that are absolutely stable, i.e., have invariant closed balls. Explicit examples are presented.
The stability of Maxwell’s equations associated with an initial boundary value problem in quarter space
Authors: Swart J. H.
Published: July 2002

The stability of the solutions of Maxwell’s equations in vacuo is considered for an initial-boundary value problem in quarter space, and the class of linear zero-order boundary conditions that leads to stable solutions is determined.
Unified models from gauged supergroups. II. Exceptional series D(2,1;α), G(3), F(4)
Authors: Jarvis P. D. , McAnally D. S.
Published: July 2002

Previously elaborated principles [J. Math. Phys. 31, 1783 (1990)] for dimensional reduction of models of gauged supergroups over supercoset spaces are applied to the exceptional superalgebras. The superspace is parametrized by a pair of Grassmann coordinates.
On gauge-invariant and phase-invariant spinor analysis. II
Authors: Buchdahl H. A.
Published: July 2002

Granted customary definitions, the operations of juggling indices and covariant differentiation do not commute with one another in a Weyl space. The same noncommutativity obtains in the spinor calculus of Infeld and van der Waerden. Gauge-invariant and phase-invariant calculations therefore tend to be rather cumbersome. Here, a modification of the definition of covariant derivative leads immediately to a manifestly gauge-invariant and phase-invariant version of Weyl–Cartan space and of the two-spinor calculus associated with it in which the metric tensor and the metric spinor are both covariant constant.
The Barut–Girardello coherent states
Authors: Basu Debabrata
Published: July 2002

It is shown that the completeness problem of the SL(2, R) coherent states proposed by Barut and Girardello leads to a moment problem, not a Mellin transform. This moment problem, which also appears in the theory of para-Bose oscillators, has been solved following the Sharma–Mehta–Mukunda–Sudarshan solution of the problem. The matrix element of finite transformation in the coherent state basis is shown to satisfy a ‘‘quasiorthogonality’’ condition analogous to the orthogonality condition of the matrix element in the canonical basis. Finally, the Barut–Girardello ‘‘Hilbert space of entire analytic functions of growth (1,1)’’ turns out to be only a subspace of Bargmann’s well-known Hilbert space of analytic functions. This subspace, which has been called ‘‘the reduced Bargmann space’’ in a previous paper, is an invariant subspace of SL(2,R). With this identification the generators of the group in this realization turn out to be the well-known boson operators of Holman and Biedenharn.
Groups of equivariant loops in SL(n+1,C) and soliton equations
Authors: McIntosh Ian
Published: July 2002

This article studies a generalization of the Drinfel’d and Sokolov hierarchies for sln+1 and shows how the dressing transformation [as interpreted by Segal and Wilson, Publ. Math. IHES 61, 5 (1985)] produces a large class of almost globally analytic solutions. Many of these solutions are ‘‘of finite type,’’ i.e., related to the Jacobian of a complete algebraic curve.
Racah sum rule and Biedenharn–Elliott identity for the super-rotation 6−j symbols
Authors: Minnaert Pierre , Toshev Stoyan
Published: July 2002

It is shown that the well-known Racah sum rule and Biedenharn–Elliott identity satisfied by the recoupling coefficients or by the 6−j symbols of the usual rotation SO(3) algebra can be extended to the corresponding features of the super-rotation osp(1‖2) superalgebra. The structure of the sum rules is completely similar in both cases, the only difference concerns the signs which are more involved in the super-rotation case.
Deformation methods for single paraoscillator systems
Authors: Dunne Robert S.
Published: July 2002

The origin of and distinction between the two deformation techniques currently in use for single particle paraoscillators is made clear. For paraoscillators deformed using the more familiar method, algebra deformation, (i) a single deformation function unifying parabosons and parafermions is provided and (ii) Fock space representations of all single paraoscillator systems as bilinear combinations of deformed oscillators are obtained. For the (distinct) Fock space deformation method, the deformed paraoscillator algebras are worked out in detail and their Casimir operators are given. Difficulties concerning the relationship between the single particle Calogero–Vasiliev oscillator and the single particle parabose system are resolved.
Painlevé analysis and integrability properties of a 2+1 nonrelativistic field theory
Authors: Knecht M. , Pasquier R. , Pasquier J. Y.
Published: July 2002

A model for planar phenomena introduced by Jackiw and Pi and described by a Lagrangian including a Chern–Simons term is considered. The associated equations of motion, among which there is a 2+1 gauged nonlinear Schrödinger equation, are rewritten into a gauge independent form involving the modulus of the matter field. Application of a Painlevé analysis, as adapted to partial differential equations by Weiss, Tabor, and Carnevale, shows up resonance values that are all integer. However, compatibility conditions need be considered which cannot be satisfied consistently in general. Such a result suggests that the examined equations are not integrable, but provides tools for the investigation of the integrability of different reductions. This in particular puts forward the familiar integrable Liouville and 1+1 nonlinear Schrödinger equations.
Derivative and higher-order extensions of Davey–Stewartson equation from matrix Kadomtsev–Petviashvili hierarchy
Authors: Kundu Anjan , Strampp Walter
Published: July 2002

It is shown that by considering the more general dressing operators, the matrix Kadomtsev–Petviashvili (KP) hierarchy can yield new integrable equations in (2+1) dimensions along with the corresponding Lax pair. In particular integrable extensions of the Davey–Stewartson (DS) equation with variable dependent coefficients, with derivative terms and with higher-order nonlinear terms, are obtained. One of such extended DS equations is found to be a higher-dimensional generalization of the Kundu–Eckhaus equation. Exact localized solutions of these DS equations are presented. The effect of such transformations on the constrained matrix KP system is analyzed.
Fundamental solutions for partial differential equations with reflection group invariance
Authors: Berest Yuri , Molchanov Yuri
Published: July 2002

The Dunkl differential-difference operator associated with a finite reflection group is used to extend the Weyl–Heisenberg algebra. The subalgebra of mastersymmetries graded by the characters of the Coxeter group W is constructed. It provides us with a new class of intertwining operators for appropriate W-invariant differential equations. These intertwining operators turn out to be suitable for constructing fundamental solutions. The remarkable example is given by the iterated wave operator with a Calogero-type potential for which the fundamental solution can be derived through the relevant intertwining operator in an explicit form. It is found that under appropriate conditions such an equation satisfies Huygens’s principle in the sense that its fundamental solution possesses a nontrivial (inner) lacuna.
The Itzykson–Zuber integral for U(m‖n)
Authors: Alfaro Jorge , Medina Ricardo , Urrutia Luis F.
Published: July 2002

The Itzykson–Zuber (IZ) integral is computed for the superunitary group U(m‖n). As a consequence, the nonzero correlations of superunitary matrices can be found.
Quantization of diffeomorphism-invariant theories with fermions
Authors: Baez John C. , Krasnov Kirill V.
Published: July 2002

We extend ideas developed for the loop representation of quantum gravity to diffeomorphism-invariant gauge theories coupled to fermions. Let P→Σ be a principal G-bundle over space and let F be a vector bundle associated to P whose fiber is a sum of continuous unitary irreducible representations of the compact connected gauge group G, each representation appearing together with its dual. We consider theories whose classical configuration space is A×F, where A is the space of connections on P and F is the space of sections of F, regarded as a collection of Grassmann-valued fermionic fields. We construct the “quantum configuration space” Ā×F̄ as a completion of A×F. Using this, we construct a Hilbert space L2(Ā×F̄) for the quantum theory on which all automorphisms of P act as unitary operators, and determine an explicit “spin network basis” of the subspace L2((Ā×F̄)/Ḡ) consisting of gauge-invariant states. We represent observables constructed from holonomies of the connection along paths together with fermionic fields and their conjugate momenta as operators on L2((Ā×F̄)/Ḡ). We also construct a Hilbert space Hdiff of diffeomorphism-invariant states using the group averaging procedure of Ashtekar, Lewandowski, Marolf, Mourão and Thiemann.
Generalized Knizhnik–Zamolodchikov equations and isomonodromy quantization of the equations integrable via the Inverse Scattering Transform: Maxwell–Bloch system with pumping
Authors: Babujian H. M. , Kitaev A. V.
Published: July 2002

Canonical quantization of the isomonodromy solutions of equations integrable via the Inverse Scattering Transform leads to generalized Knizhnik–Zamolodchikov equations. One can solve these equations by the off-shell Bethe ansatz method provided the Knizhnik–Zamolodchikov equations are related with the highest weight representations of the corresponding Lie algebras: These solutions can be written in terms of multi-variable generalizations of special functions of the hypergeometric type. In this work, we consider a realization of the above scheme for the Maxwell–Bloch system with pumping: quantum states for this system are found in terms of the multi-variable confluent hypergeometric function.
A uniqueness theorem for distributions and its application to nonlocal quantum field theory
Authors: Soloviev M. A.
Published: July 2002

It is shown that if a distribution u∈D′(Rn) has support in a convex cone not containing a straight line and its Fourier transform is carried by a closed cone K different from the whole space, i.e., ũ∈D̃′(K), K≠Rn, then u is zero. This result leads to a new and most general proof of the PCT theorem which covers nonlocal quantum fields with arbitrary high-energy behavior.
A stochastic method for Brownian-like optical transport calculations in anisotropic biosuspensions and blood
Authors: Miller Steven
Published: July 2002

A generic stochastic method is presented that rapidly evaluates numerical bulk flux solutions to the one-dimensional integrodifferential radiative transport equation, for coherent irradiance of optically anisotropic suspensions of nonspheroidal bioparticles, such as blood. As Fermat rays or geodesics enter the suspension, they evolve into a bundle of random paths or trajectories due to scattering by the suspended bioparticles. Overall, this can be interpreted as a bundle of Markov trajectories traced out by a “gas” of Brownian-like point photons being scattered and absorbed by the homogeneous distribution of uncorrelated cells in suspension. By considering the cumulative vectorial intersections of a statistical bundle of random trajectories through sets of interior data planes in the space containing the medium, the effective equivalent information content and behavior of the (generally unknown) analytical flux solutions of the radiative transfer equation rapidly emerges. The fluxes match the analytical diffuse flux solutions in the diffusion limit, which verifies the accuracy of the algorithm. The method is not constrained by the diffusion limit and gives correct solutions for conditions where diffuse solutions are not viable. Unlike conventional Monte Carlo and numerical techniques adapted from neutron transport or nuclear reactor problems that compute scalar quantities, this vectorial technique is fast, easily implemented, adaptable, and viable for a wide class of biophotonic scenarios. By comparison, other analytical or numerical techniques generally become unwieldy, lack viability, or are more difficult to utilize and adapt. Illustrative calculations are presented for blood medias at monochromatic wavelengths in the visible spectrum.
Deformations of surfaces associated with integrable Gauss–Mainardi–Codazzi equations
Authors: Ceyhan Ö. , Fokas A. S. , Gürses M.
Published: July 2002

Using the formulation of the immersion of a two-dimensional surface into the three-dimensional Euclidean space proposed recently, a mapping from each symmetry of integrable equations to surfaces in R3 can be established. We show that among these surfaces the sphere plays a unique role. Indeed, under the rigid SU(2) rotations all integrable equations are mapped to a sphere. Furthermore we prove that all compact surfaces generated by the infinitely many generalized symmetries of the sine-Gordon equation are homeomorphic to a sphere. We also find some new Weingarten surfaces arising from the deformations of the modified Kurteweg–de Vries and of the nonlinear Schrödinger equations. Surfaces can also be associated with the motion of curves. We study curve motions on a sphere and we identify a new integrable equation characterizing such a motion for a particular choice of the curve velocity.
Wavelet approximate inertial manifold in nonlinear solitary wave equation
Authors: Tian Lixin
Published: July 2002

This paper studies the dynamical behavior of a weakly damped forced Korteweg–de Vries (KdV) equation in a wavelet basis and introduces the wavelet approximate inertial manifold and wavelet Galerkin solution of weakly damped forced KdV equation. The results includes theorems that for the KdV equation the wavelet approximate inertial manifold (WAIM) exists and sets up the wavelet Galerkin method of the equation. Error estimates are given by using the WAIM.
Attenuation of phonon–ripplon oscillations in an electron crystal over superfluid He3–4He solutions
Authors: Dotsenko V. V. , Sivokon’ V. E. , Kovdrya Yu. Z. , Grigor’ev V. N.
Published: July 2002

The phonon–ripplon oscillation spectrum of a Wigner crystal with a surface density 1.3⋅109 cm−2 of electrons over superfluid He4 and He3–4He solutions is studied in the temperature range 70–600 mK. Measurements were made in the frequency range 1–20 MHz. It is shown that resonance frequencies are in good agreement with the theoretical estimates. An analysis of the data shows that the attenuation of capillary waves is not the main mechanism determining the energy losses in a Wigner crystal. A new technique employing the width of the coupled phonon–ripplon resonances is used to determine the mobility of Wigner crystals.
Current–voltage characteristic of a two-dimensional Corbino disk under the QHE conditions of quantum Hall effect
Authors: Shikin V. B. , Shikina Yu. V.
Published: July 2002

A theory of current–voltage characteristic (IVC) is proposed for a gated Corbino disk with a 2D spinless electron system and magnetic filling factors close to an integral value. The described results systematically include the features of the electrochemical potential of the 2D electron system in a magnetic field, which are responsible for sharp magnetocapacitance “dips” for integral values of the magnetic filling factor. The theory is used for qualitative interpretation of the observed weakly nonlinear peculiarities of IVC as well as for prediction of local details in the distribution of electron density and electric potential in a current-carrying Corbino disc. Corresponding measurements can be made, for instance, by using the linear electrooptical effect.
Surface magnetic-plasma waves at the ferrodielectric–semiconductor boundary
Authors: Fal’ko V. L. , Khankina S. I. , Yakovenko V. M.
Published: July 2002

The electromagnetic properties of the ferrodielectric–conducting medium system are investigated in a constant magnetic field at low temperatures. It is shown that new vibrational branches, viz. pseudosurface waves characterized by collisionless damping, emerge in a strong magnetic field at sufficiently high concentrations of charge carriers. The mechanism of collisionless (radiative) damping is connected with the existence of additional electromagnetic fields propagating into the bulk of the conducting medium. The range of such waves is determined, and the functional dependences of their frequency and damping on the magnitude and direction of the external magnetic field are derived.
Quantum size effect and interlayer electron tunneling in metal-semiconductor superlattices
Authors: Fogel’ N. Ya. , Slutskin A. A. , Kovtun H. A. , Shekhter R. I.
Published: July 2002

A new type of quantum size effect in metal-semiconductor superlattices is predicted. Giant oscillations of the transverse tunnel conductivity arise if size quantization of the electron spectrum in the metal layers takes place. This effect is due to the fact that the probability of metal electron tunneling through a semiconductor layer depends sharply on the electron incidence angle. The oscillations have been found to exist even in disordered systems, provided the electrons in metal layers undergo low-angle scattering on imperfections.
The role of normal processes in the thermal conductivity of solid deuterium
Authors: Korolyuk O. A. , Gorodilov B. Ya. , Krivchikov A. I. , Dudkin V. V.
Published: July 2002

The thermal conductivity of orthodeuterium crystals containing a neon impurity is investigated in the temperature interval 1.8–17 K. The results of the measurements are described in the framework of the relaxation-time model with allowance for phonon–phonon scattering processes. The intensity of the normal scattering processes for deuterium are determined. The existing theoretical models are used to estimate the intensity of the phonon scattering processes for a number of cryocrystals. The calculated intensity of the normal processes is compared to the experimental result.
Instantaneous dissipations of turbulent energy and temperature in a wake
Authors: Antonia R. A. , Browne L. W. B. , Shah D. A.
Published: July 2002

Approximations to the instantaneous dissipation of temperature variance and to an instantaneous pseudodissipation of kinetic energy in the turbulent far wake of a cylinder have been measured, using either four hot wires or four cold wires arranged in the form of a square. Results, including probability density functions and spectra as well as joint probability density functions and cospectra between individual components of the dissipations, suggest a close similarity between the two dissipations. The influence of the organized motion on the flow structure is briefly discussed in the context of cospectra and correlation coefficients for the components of the two dissipations. One implication of the similarity between the spectra of the two dissipations is the constancy of the time scale ratio, defined on a spectral basis, of the velocity and temperature fields.
Gallery of Fluid Motion
Authors: Reed Helen L.
Published: July 2002

This article displays winning photographs from the sixth Annual Fluid Mechanics Photo Contest held at the November 1988 meeting of the American Physical Society, Division of Fluid Dynamics, Buffalo, New York.
Amplitude-modulated excitation of a turbulent mixing layer
Authors: Glezer A. , Wygnanski I. , Gu X.
Published: July 2002

The evolution of a momentary, spanwise-uniform disturbance in a plane mixing layer was studied experimentally. Since interaction between the disturbance and the two-dimensional (primary) instability of the mean flow is unavoidable, excitation by a low-level, two-dimensional, time-harmonic carrier wave train provided a clear phase reference. The disturbance was generated by a lower frequency pulsed amplitude modulation of the excitation waveform. The duration of the modulating pulse was equal to the carrier wave period, and the degree of modulation was either 2 or 4. A demodulation technique was used to discriminate between the response to the modulating pulse and the harmonic excitation. This technique decomposes the response into a family of modal two-dimensional wave packets, allowing detailed study of the disturbance, and, in particular, the propagation, amplification, and some of the nonlinear aspects of the behavior of its leading modal components. The fundamental packet is advected with the mean velocity of the two streams. Its streamwise extent and dominant frequencies remain virtually unchanged with downstream distance. The passage of the disturbance is accompanied by a spatial and temporal change in the momentum thickness of the harmonically excited flow. Cross-stream distributions of the streamwise velocity perturbation within the disturbance are similar to those of the harmonically excited flow at streamwise stations having the same momentum thickness. High turbulence levels, not prevalent in the harmonically excited shear layer, are detected within the disturbance and suggest the possibility of transient mixing enhancement.
Solitons induced by boundary conditions from the Boussinesq equation
Authors: Chou Ru Ling , Chu C. K.
Published: July 2002

Solitons induced by boundary excitation were first investigated numerically by Bona et al. [Philos. Trans. R. Soc. London, Ser. A 302, 457 (1981)] and by Chu et al. [Commun. Pure Appl. Math. 36, 495 (1983)] using the Korteweg–de Vries (KdV) equation. In this paper, their work is extended by considering various time-dependent boundary conditions and different unperturbed water depths. Then solitons induced from Boussinesq equations under similar conditions are studied, in order to remove the restriction in the KdV equation of propagation in only one direction. Thus soliton head-on collisions (as well as overtaking collisions) and reflections can be treated. The results from these two fully nonlinear equations are compared and they agree extremely well. The results of solitons induced by random boundary values are unexpected and particularly interesting.
Axisymmetric wakes behind a slender body including zero-momentum configurations
Authors: Higuchi Hiroshi , Kubota Toshi
Published: July 2002

An experimental investigation of turbulent axisymmetric wakes including the zero-momentum case was carried out. Mean and fluctuation velocity profiles were measured and self-similar profiles were observed that decayed very rapidly when the momentum was adjusted to be zero. The wake behavior was found to be sensitive to any small mismatch of momentum and the relaxation zone strongly depended on the intensity and scale of the turbulence in the initial wake.
A generalized sideband stability theory via center manifold projection
Authors: Cheng Minquan , Chang Hsueh-Chia
Published: July 2002

A center manifold theory is used to determine all modes that contribute significantly to the leading-order sideband stability of finite-amplitude monochromatic waves. The classical multiscale theories based on the Ginzburg–Landau equation are extended away from near-critical conditions and are shown to have omitted an important contribution from nonlinear interactions with low wave-number modes. Stability bounds on stable monochromatic waves are reported for dispersive systems that extend the classical Eckhaus bound for nondispersive systems and the Lange–Newell and Benjamin–Feir stability conditions for monochromatic waves with critical wave numbers. These new stability bounds are verified numerically by computing the evolving spectrum of a model equation.
Flame length measurements of the turbulent plume
Authors: Johari H.
Published: July 2002

The minimum molecular scale mixing rate of the turbulent plume was found by measurements of the plume ‘‘flame length’’ under various initial conditions. A simple derivation based on the self-similar properties of plumes provides power law relations for the mixing rate, which agree well with the experiments.
Stability of equilibrium solutions reached by ‘‘modified dynamics’’
Authors: Ripa P.
Published: July 2002

A method has been proposed for finding steady solutions of hydrodynamics problems, which represent extrema of energy on isovortical sheets. Here the method is generalized in the form of an algorithm to search for uniformly translating or rotating solutions. It is argued that asymmetric solutions of symmetric systems are not necessarily stable: The energy-momentum extremum has the topology of a curve on the sheet, and therefore a perturbed state might drift away along neighboring curves. If that were the case, and if the drift would just be a displacement with uniform velocity, in physical space, then it might be able to prove stability in a metric that shifts position and compares shapes (as it has been done with the Korteweg–de Vries soliton). These concepts are exemplified using very simple, finite dimension, cases.
The hydrodynamic forces on a cylinder touching a permeable wellbore
Authors: Sherwood J. D.
Published: July 2002

A wellbore (radius b) filled with Newtonian fluid (viscosity η), contains a cylindrical drill string [radius a=b(1−ε)] that touches the wall of the wellbore. Lubrication theory is applied to the fluid-filled annular gap between cylinder and wall, while Darcy’s law is assumed valid within the rock surrounding the wellbore. The force required to lift the cylinder away from the wall with velocity U is F=bBπA−3/5, where B=12ηU/bε3 and A=12k/b2ε3≪1. The couple required to rotate the cylinder (in a rolling motion) with angular velocity ω is T=0.75Db2πA−1/5, where D=12ηωε−3. The effect of a filter cake of permeability kc and thickness g≪b is also considered. Setting K=gk/bkc, the force required to lift the cylinder becomes F=0.72bBπ(K/A)3/4, and the couple is T=0.8Db2π(K/A)1/4.
Spin-up from rest of a mixture
Authors: Ungarish M.
Published: July 2002

A cylindrical container, filled with a homogeneous suspension of heavy particles in a fluid, is instantaneously set into rapid rotation around its axis of symmetry. The subsequent mixture motion is investigated within the framework of an averaged continuum approach, by asymptotic and numerical solutions of the ‘‘mixture’’ and ‘‘two-fluid’’ models, respectively. The resulting velocity field is similar to that of a homogeneous fluid [J. Fluid Mech. 20, 383 (1964)], where three regions can be distinguished: a nonrotating, shrinking, core (I); the embedding, spinning but still undeveloped domain (III); and the Ekman layers (II), which transport fluid from region I into region III. This flow field induces a novel and peculiar solution for the volume fraction α, whose details are governed by λ (=ratio of separation to spin-up time intervals). The results indicate that the initial α(0) prevails in regions I and II, but considerable separation takes place in domain III—provided that λ is not large. Therefore, during the spin-up process, [α/α(0)] decays substantially not only with time, but also with the axial distance from the endplates (Ekman layers) and with radial distance from region I. Moreover, if λ≪1, [α/α(0)]≪1 is expected in region III.
Space-dependent solutions for the generalized Boltzmann equation
Authors: Zanette Damián H.
Published: July 2002

The Boltzmann equation for a spatially inhomogeneous system, when annihilation and regeneration processes are allowed, is studied in the hydrodynamical approach. The density and mean velocity equations are exactly solved in the limit of zero temperature, displaying remarkable differences with the homogeneous case. The influence of advective processes is discussed.
Statistics of optimal particle streak photography
Authors: Altman Donald B.
Published: July 2002

A number of statistical problems pertinent to the optimal use of particle streak photography are examined with the goal of deriving error bars and practical rules of thumb. The seeding density of particles is analyzed with the goal of maximizing the number of isolated streaks from randomly distributed particles. The number of overlapped streaks, the main source of ‘‘noise’’ in reading streak photographs, is also derived. Results are presented for the two limiting cases of nearly parallel streaks and random streak orientation. Estimation of the mean of an arbitrary velocity field with randomly placed noise-free measurements is discussed. Closed-form solutions are derived for the special case of a sinusoidal velocity field, where bias and variance of the estimate about the true value are obtained. The derivation is repeated with the addition of random noise and the trade-off between randomly placed (streak) measurements and a smaller number of optimally placed (probe) measurements is examined. Although the closed-form solutions are for simple flows, a recipe is given for application of the same techniques to arbitrary quasistationary flows. Errors in the measurement of average quadratic quantities such as wavelength-averaged Reynolds stresses are examined. The results are shown to be identical to those of estimating wavelength-averaged velocity. The statistical techniques used in this work are applicable to other types of randomly located flow measurements.
Stability criteria for flow along a convex wall
Authors: Herron Isom H.
Published: July 2002

Flow along a curved wall is susceptible to centrifugal instability. The criterion of Synge [Proc. R. Soc. London Ser. A 167, 250 (1938)] for the stability of flow between rotating cylinders is generalized to the case of an arbitrary flow along a convex wall. Sufficient conditions for the linear stability of the flow are given, based on the behavior of a function similar to the Rayleigh discriminant.
Finite conductivity effects on the MHD instabilities in uniformly elongating plastic jets
Authors: Littlefield David L.
Published: July 2002

The effect of finite electrical conductivity on the stability of perfectly plastic jets is considered. Application of the analysis to shaped-charge jets is of primary interest. The jet is assumed to be uniformly elongating and axisymmetric. An axial electric current is introduced in the jet at time t=0 and permitted to diffuse over time. After base solutions to the relevant governing equations are calculated, the stability characteristics of the jet are determined using linear perturbation theory. Solutions to the first-order equations indicate that disturbances in the magnetic field and pressure distributions vary significantly depending on the conductivity. The growth rate in the boundary perturbation, however, demonstrates that jets of finite conductivity are only slightly more stable than equivalent jets of infinite conductivity. The behavior of these instabilities is discussed in terms of the applicable physical mechanisms.
The role of turbulent fluid dynamics in water/oil emulsion formation
Authors: Oliver R. , Smith J. G. B.
Published: July 2002

This paper is principally concerned with the production of emulsion droplets (water in oil) by a continuous process that exploits hydrodynamic instability phenomena. This is done by utilizing the characteristic isotropic turbulence, which can be set up in a tube, duct, or nozzle. Studies completed have focused on the prediction and experimental verification of the creation of water-in-oil emulsion droplets, of diameter D in the range 0.5≤D≤10 μm, whereby an aqueous phase-oil phase system is formed into a stabilized emulsion. This is achieved using a novel mixing technique that hydrodynamic instabilities in the form of ‘‘Kolmogorov’’ isotropic, turbulent fluid eddies whose size scale λK, frequency of occurrence fK, and fluctuating velocity ũ′ are readily defined in both numerical and physical terms. Results from this work will be discussed, including the generation of scale-up rules for such systems in terms of geometry and fluid flow velocities that yield continuous emulsions. In particular, the effect of the fluid–fluid and interface variables interfacial tension γi, and dispersed phase viscosity ηd, will be highlighted in relation to the prediction of emulsion droplet size dd, and distribution n[dd], σSD. A major conclusion from our work is that the role of fluid dynamics in interfacial phenomena, such as the creation of stable dispersions, is much more important than chemists would have us believe!
Effect of rotation on turbulent mixing across a density interface
Authors: Fleury M. , Mory M.
Published: July 2002

The effect of rotation on mixing across a density interface is studied experimentally in a two-layer stratified fluid. Mixing is caused by turbulence produced in one of the layers by an oscillating grid. The flow depends on the Richardson number Ri=g′l/u2 and the Rossby number Ro=u/2Ωl, where u, l, g′=gΔp/p, and Ω are, respectively, the local rms, velocity and integral length scale of the turbulence, the reduced gravity, and the background rotation rate. The entrainment rate E of the interface is measured as a function of Ri and Ro in two different regions of the tank, namely, in the region closest to the grid, where turbulence is weakly affected by rotation, and far from the grid, where turbulence become quasi-2D under the effect of rotation. The most important result is the observed decrease of the entrainment rate E in the presence of rotation, when compared with nonrotating experiments. A general entrainment law in the form of E=0.5 Ro Ri is established in contrast with the measured entertainment law under nonrotating conditions E=1.6 Ri−3/2. The ranges of Ri and Ro covered are 7<Ri<50 and 0.1<Ro<1.0. At low values of Ri (Ri<10) and as a function of Ro, significant deviations from the law Ro Ri−1 are observed. At high values of Ri, the comparison between the results obtained under rotating and nonrotating conditions show that rotation has no effect on turbulent mixing when Ri>(3.2)2Ro−2.

Interface displacement spectra provide additional information on the dynamics of the interface and the mixing process. These spectra were computed from the records of the interface position obtained using a new device based on the measurements of the traveling time of ultrasonic waves. This method gives information similar to the LIF technique used by Hannoun and List,1 except that the thickness of the interface is not determined. For nonrotating conditions, the spectra show maximum oscillations of the interface at the frequency (g′/l)1/2/2π of internal waves, in agreement with Hannoun and List.1 For higher frequencies, the spectrum decreases with increasing frequency like ω−n with 3<n< (11)/(3) . The results are discussed in relation to the model of Phillips2 (n=3) and the model recently proposed by Mory3 (n= (11)/(3) ). Under rotating conditions, the spectra are not modified for frequencies larger than the Coriolis frequency. Significant fluctuations are observed below the Coriolis frequency, which are related to the radiation of energy by inertial waves in the nonstirred layer.
Chaotic sedimentation of spheroidal particles in a cellular flow field
Authors: Shin H. , Maxey M.
Published: July 2002

Chaotic mixing of Lagrangian fluid elements has been shown to be a feature of several unsteady two-dimensional flows or steady three-dimensional flows. There is also an interesting group of problems relating to the sedimentation of discrete particles, and for nonspherical particles which respond to the local flow conditions we have found the particle motion to be chaotic even in simple, steady two-dimensional flows. Specifically, we have studied the motion of rigid spheroidal particles settling under gravity in a spatially periodic, cellular flow field. The particles are small compared to the cell size and sufficiently small that their motion relative to the fluid satisfies conditions for Stokes flow. The position of the particle X(t) and the symmetry axis m are determined by (dX/dt)=u[X(t),t]+W1 (ĝ⋅m)m+W2 (ĝ−ĝ⋅mm), (dm/dt)=( (1)/(2) ω+Dm×E⋅m)×m. The flow field considered is u=(sin πx cos πy, −cos πx sin πy, 0) and ω and E are the corresponding local vorticity and rate of strain; W1 and W2 are the terminal fall speeds parallel and normal to the symmetry axis m, while ĝ is (0, 1, 0).

The ratio W2/W1, and the parameter D are set by the aspect ratio of the particle, but for the purpose of analysis may be varied separately. Previous work1 has dealt with the restricted problem of planar motion, where m3=0, and given general numerical results on settling rates and particle suspension by the flow. Clear evidence was found from the trajectories of selected particles of chaotic motion in certain parts of the flow. More recently we have investigated in more detail the transition from regular to chaotic motion in this restricted problem. Based on perturbation analysis of periodic solutions, Poincaré sections, and determination of Lyapunov exponents we conclude that regions of regular motion where particles are suspended by the flow persist but the extent of these regions is greatly reduced for increasingly nonspherical shapes. Chaotic tumbling motion occurs outside these regions, as the particle turns in response to the local vorticity and rate of strain. Interestingly, chaotic motion is found even if the particle turns only in response to the local vorticity. Besides summarizing these results for the restricted problem, we present results for the unrestricted problem of three-dimensional motion which could be used for comparison with experiments.

We find that the motion is qualitatively similar with both regular and chaotic regions.