bluuebunny/crossref_metadata_2025 huggingface dataset:
The multiconfiguration time-dependent Hartree method generalized to the propagation of density operators
Authors: Raab A. , Burghardt I. , Meyer H.-D.
Published: July 2002

The multiconfiguration time-dependent Hartree (MCTDH) method is formulated for density operators and applied to their numerical propagation. We introduce two types of MCTDH density operators which are expanded in different kinds of so-called single-particle density operators. The latter may either be hermitian, or else represent ket–bra products of so-called single-particle functions. For both types of MCTDH expansions of density operators we derive equations of motion employing the Dirac–Frenkel/MacLachlan variational principle. Further an alternative set of equations of motion for the second type of density operators is proposed, which is not based on a variational principle but derived by taking partial traces. We thus obtain three sensible approaches within the framework of the MCTDH method which differ in their performance and properties. We investigate these approaches and their properties analytically and numerically. Our numerical results refer to a model of vibronic-coupling dynamics in the pyrazine molecule representing coupled electronic states with four vibrational modes and two and three electronic states respectively. We analyze the closed-system dynamics for this model with temperature-dependent initial states. The influence of temperature on state populations, on correlation functions and on absorption spectra is discussed. We assess the numerical performance of two of the three approaches and find that both can be very efficiently applied to investigate the type of systems studied here.
An investigation of density functionals: The first-row transition metal dimer calculations
Authors: Yanagisawa Susumu , Tsuneda Takao , Hirao Kimihiko
Published: July 2002

The performance of different density functional theory (DFT) methods was investigated in the calculations of the bond length and the binding energy of the first-low transition metal dimers. The 4s–3d interconfigurational energies and 4s and 3d ionization potentials were also calculated for the first-row transition metal atoms. In general, the hybrid DFT method, B3LYP, yields the bond lengths that are too short compared to the experimental ones. In contrast, the optimized bond lengths by nonhybrid DFT methods such as BOP or PW91 are in good agreement with the experiment. It was also found that nonhybrid DFT methods overestimate the binding energies, because they have a tendency to overstabilize the electron configurations that contain the atomic and molecular orbitals in a higher angular momentum open shell. The hybrid DFT method yields more accurate binding energies, but it estimates rather poor energy gaps between states whose spin multiplicity is quite different.
Exact and asymptotic solutions of the mixed quantum-classical Liouville equation
Authors: Wan Chun-Cheng , Schofield Jeremy
Published: July 2002

In this article, an exact surface-hopping procedure and an approximate asymptotic method for performing molecular dynamics based on a mixed quantum-classical Liouville equation [J. Chem. Phys. 110, 8919 (1999)] for partially Wigner transformed dynamical variables of a coupled quantum subsystem and classical bath are elaborated. The methods are based upon writing the equations of motion in a basis set in which quantum transitions do not alter the classical trajectory, and therefore avoid ad-hoc momentum jump approximations and are free of singular kernels associated with sampling momenta. Results obtained utilizing the new trajectory methods are presented for a model two-level system bilinearly coupled to a classical harmonic oscillator. These results are compared to results obtained from standard methods of performing mixed quantum-classical dynamics. The new methods perform well for the model system over a wide range of initial kinetic energies.
Probing the electronic structure of redox species and direct determination of intrinsic reorganization energies of electron transfer reactions
Authors: Wang Xue-Bin , Wang Lai-Sheng
Published: July 2002

An experimental technique capable of directly determining the intrinsic reorganization energies of bimolecular electron transfer reactions is described. Appropriate solution phase redox species are prepared in the gas phase using electrospray ionization and probed using photodetachment spectroscopy. Five metal complex anions involved in the Fe2+–Fe3+ redox couple are investigated and the intramolecular reorganization energies are measured directly from spectral features due to removing the most loosely bound 3d electron from the Fe(II)-complexes. The photodetachment spectra also yield electronic structure information about the Fe2+–Fe3+ redox couple and provide a common electronic structure origin for the reducing capability of the Fe(II)-complexes, the most common redox reagents.
Desorption of CO from Ru(001) induced by near-infrared femtosecond laser pulses
Authors: Funk S. , Bonn M. , Denzler D. N. , Hess Ch. , Wolf M. , Ertl G.
Published: July 2002

Irradiation of a Ru(001) surface covered with CO using intense femtosecond laser pulses (800 nm, 130 fs) leads to desorption of CO with a nonlinear dependence of the yield on the absorbed fluence (100–380 J/m2). Two-pulse correlation measurements reveal a response time of 20 ps (FWHM). The lack of an isotope effect together with the strong rise of the phonon temperature (2500 K) and the specific electronic structure of the adsorbate–substrate system strongly indicate that coupling to phonons is dominant. The experimental findings can be well reproduced within a friction-coupled heat bath model. Yet, pronounced dynamical cooling in desorption, found in the fluence-dependence of the translational energy, and in a non-Arrhenius behavior of the desorption probability reflect pronounced deviations from thermal equilibrium during desorption taking place on such a short time scale.
Classical and quantum symmetry groups of a free-fall particle
Authors: Iwai Toshihiro , Rew See-Gew
Published: July 2002

Symmetry of a free-fall particle is studied in quantum as well as classical mechanics. The quantum symmetry group is shown to be a central extension of the classical one. In the case of two degrees of freedom, the action of the quantum symmetry group is expressed in the form of integral transform as a unitary operator on the space of wave functions.
The Dirac Coulomb Green’s function and its application to relativistic Rayleigh scattering
Authors: Wong M. K. F. , Yeh E. H. Y.
Published: July 2002

The Dirac Coulomb Green’s function is obtained in both coordinate and momentum space. The Green’s function in coordinate space is obtained by the eigenfunction expansion method in terms of the wave functions obtained by Wong and Yeh. The result is simpler than those obtained previously by other authors, in that the radial part for each component contains one term only instead of four terms. Our Green’s function reduces to the Schrödinger Green’s function upon some simple conditions, chiefly by neglecting the spin and replacing λ by l. The Green’s function in momentum space is obtained as the Fourier transform of the coordinate space Green’s function, and is expressed in terms of basically three types of functions: (1) FA (α; β1 β2 β3; γ1 γ2 γ3; z1 z2 z3), (2) the hypergeometric function, and (3) spherical harmonics. The matrix element for Rayleigh scattering, or elastic Compton scattering, from relativistically bound electrons is then obtained in analytically closed form. The matrix element is written basically in terms of the coordinate space Dirac Coulomb Green’s function. The technique used in the evaluation of the matrix element is based on the calculation of the momentum space Dirac Coulomb Green’s function. Finally the relativistic result is compared with the nonrelativistic result.
Soliton structure of the Drinfel’d–Sokolov–Wilson equation
Authors: Hirota R. , Grammaticos B. , Ramani A.
Published: July 2002

An integrable equation due to Drinfel’d and Sokolov [Sov. Math. Dokl. 23, 457 (1981)] and Wilson [Phys. Lett. A 89, 332 (1982)] (DSW) is studied in detail. It is shown how this system can be obtained as a six-reduction of the Kadomtsev–Petviashvili hierarchy. This equation presents a novel type of solutions called static solitons: they are static solutions that interact with moving solitons without deformations. Examples of such solutions are given, together with a general procedure for their construction. Finally the Painlevé analysis of the DSW equation is performed directly on the bilinear form, which constitutes a new application of the singularity analysis method.
Classification of ten-dimensional kinematical groups with space isotropy
Authors: Bacry H. , Nuyts J.
Published: July 2002

All the abstract ten-dimensional real Lie algebras that contain as a subalgebra the algebra of the three-dimensional rotation group (generators J) and decompose under the rotation group into three three-vector representation spaces (J itself, K, and P) and a scalar (generator H) are classified. In all cases, the existence of a homogeneous space of dimension 4 is shown.
A class of solutions for self-gravitating dust in Newtonian gravity
Authors: Buchert Thomas , Götz Günter
Published: July 2002

The Lagrange method is used to obtain a class of solutions of the three-dimensional hydrodynamical equations governing the motion of matter with vanishing pressure in its own Newtonian gravitational field. The class is characterized by the property that each fluid particle has constant acceleration. The class contains rotational and irrotational flows. For rotational flows the expansion tensor has one zero eigenvalue, while for irrotational flows it has two zero eigenvalues, which implies that every fluid element contracts or expands in two or one spatial directions, respectively; nevertheless, the density depends on all three coordinates. The general one-dimensional solution is included as a subclass.
Noether’s theorem in symmetric stochastic calculus of variations
Authors: Misawa Tetsuya
Published: July 2002

Quite recently, a symmetric stochastic calculus of variations was proposed to formulate canonical stochastic dynamics, which is an extension of Nelson’s stochastic mechanics. In this article a ‘‘Noether’s theorem’’ is formulated within this calculus of variations. Conservation laws of momentum, angular momentum, and energy are proved, which are related with the same laws in quantum mechanics.
The Jordan–Schwinger representations of Cayley–Klein groups. I. The orthogonal groups
Authors: Gromov N. A. , Man’ko V. I.
Published: July 2002

The Cayley–Klein groups are defined as the groups that are obtained by the contractions and analytical continuations of the orthogonal groups. The Jordan–Schwinger representations of Cayley–Klein groups are discussed based on the mixed sets of creation and annihilation operators of boson or fermion type. The matrix elements of finite group transformations are obtained in the bases of coherent and Fock states.
Symmetries, conserved quantities, and hierarchies for some lattice systems with soliton structure
Authors: Zhang Hongwei , Tu Gui-zhang , Oevel Walter , Fuchssteiner Benno
Published: July 2002

Basic invariants, such as conserved quantities, symmetries, mastersymmetries, and recursion operators are explicitly constructed for the following nonlinear lattice systems: The modified Korteweg–de Vries lattice, the Ablowitz–Ladik lattice, the Brusci–Ragnisco lattice, the Ragnisco–Tu lattice and some cases of the class of integrable systems introduced by Bogoyavlensky. The algorithmic basis for obtaining these quantities is described and the interrelation between the underlying mastersymmetry approach and the Lax pair analysis is discussed. By explicit presentation of the higher-order members of the corresponding hierarchies new completely integrable lattice flows are found. For all systems, multi-Hamiltonian formulations are given.
Series solutions for the Dirac equation in Kerr–Newman space-time
Authors: Kalnins E. G. , Miller W.
Published: July 2002

The Dirac equation is solved for an electron in a Kerr–Newman geometry using an adaptation of the procedure of Chandrasekhar. The corresponding eigenfunctions obtained can be represented as series of Jacobi polynomials. The spectrum of eigenvalues can be calculated using continued fraction techniques. Representations for the eigenvalues and eigenfunctions are obtained for various ranges of the parameters appearing in the Kerr–Newman metric. Some comments concerning the bag model of nucleons are made.
Models of q-algebra representations: q-integral transforms and ‘‘addition theorems’’
Authors: Kalnins E. G. , Miller Willard
Published: July 2002

In his classic book on group representations and special functions Vilenkin studied the matrix elements of irreducible representations of the Euclidean and oscillator Lie algebras with respect to countable bases of eigenfunctions of the Cartan subalgebras, and he computed the summation identities for Bessel functions and Laguerre polynomials associated with the addition theorems for these matrix elements. He also studied matrix elements of the pseudo-Euclidean and pseudo-oscillator algebras with respect to the continuum bases of generalized eigenfunctions of the Cartan subalgebras of these Lie algebras and this resulted in realizations of the addition theorems for the matrix elements as integral transform identities for Bessel functions and for confluent hypergeometric functions. Here we work out q analogs of these results in which the usual exponential function mapping from the Lie algebra to the Lie group is replaced by the q-exponential mappings Eq and eq. This study of representations of the Euclidean quantum algebra and the q-oscillator algebra (not a quantum algebra) leads to summation, integral transform, and q-integral transform identities for q analogs of the Bessel and confluent hypergeometric functions, extending the results of Vilenkin for the q=1 case.
Vertex operators for physical states of bosonic string
Authors: Nergiz Serdar
Published: July 2002

The commutator of the Virasoro operator Lm and general vertex operator V for the mass level L is explicitly calculated. By demanding that a physical vertex operator must be of conformal dimension J=1, a set of algebraic equations for determining the vertex operators corresponding to all physical states of bosonic strings is obtained. Explicit expressions for the first three mass levels are given.
Symmetries and constants of the motion for higher-order Lagrangian systems
Authors: de León Manuel , de Diego David Martín
Published: July 2002

We obtain a classification of infinitesimal symmetries of an autonomous higher-order Lagrangian system by using the theory of lifts of vector fields to tangent bundles. Also, a classification of infinitesimal symmetries of a time-dependent higher-order Lagrangian system is obtained. The relationship between infinitesimal symmetries and constants of the motion is investigated.
Relativistic and Newtonian κ -space–times
Authors: de Azcárraga J. A. , Pérez Bueno J. C.
Published: July 2002

The deformations of the Galilei algebra and their associated noncommutative Newtonian space–times are investigated. This is done by analyzing the possible nonrelativistic limits of an eleven generator (pseudo)extended κ-Poincaré algebra 𝒫̃κ and their implications for the existence of a first-order differential calculus. The additional one-form needed to achieve a consistent calculus on κ-Minkowski space is shown to be related to the additional central generator entering in the 𝒫̃κ Hopf algebra. In the process, deformations of the extended Galilei and Galilei algebras are introduced which have, respectively, a cocycle and a bicrossproduct structure.
Comments on Hamiltonian structures for the n-dimensional Lotka–Volterra equations [J. Math. Phys. 36, 3520–3534 (1995)]
Authors: Cairó Laurent , Feix Marc R.
Published: July 2002

In a recent paper, Plank presents results on first integrals for the Lotka–Volterra system (LVS) and their use as possible Hamiltonians. Since he was not acquainted with already published results, we feel that an embedding of his results in those of previous papers can clarify some of his statements. We concentrate our comments on the results presented in his paragraphs III and IV.
The spherical curl transform of a linear force-free magnetic field
Authors: MacLeod Malcolm A.
Published: July 2002

The description of linear force-free magnetic fields in terms of the Moses eigenfunctions of the curl operator begun previously is here completed by the derivation of a general expression for the field’s spherical curl transform. This enables the transform space representation of a given field to be determined and compared with that of other fields, assisting the analysis and classification of this type of magnetic field as well as providing a basis for generalization. The result obtained gives the spherical curl transform as a weighted projection of the vector Radon transform of the field on the appropriate curl eigenvector. The process is exemplified by the determination of the transforms of three fields: the simplest force-free magnetic field, and the Lundquist and classical spheromak fields. The latter two are both of interest as models of the magnetic fields of solar magnetic clouds, while the classical spheromak field is relevant to the design of nuclear fusion reactors as well. The use of the transform in generalizing the Lundquist field is briefly discussed. As before, all results apply equally well to the description of the Trkalian subset of Beltrami fields in fluid dynamics.
The geometrical theory of constraints applied to the dynamics of vakonomic mechanical systems: The vakonomic bracket
Authors: Martı́nez Sonia , Cortés Jorge , de León Manuel
Published: July 2002

A vakonomic mechanical system can be alternatively described by an extended Lagrangian using the Lagrange multipliers as new variables. Since this extended Lagrangian is singular, the constraint algorithm can be applied and a Dirac bracket giving the evolution of the observables can be constructed.
Stochastic estimation of coherent structures in turbulent boundary layers
Authors: Guezennec Y. G.
Published: July 2002

The stochastic estimation provides a means of estimating conditional averages from unconditional statistics, namely, the two-point correlation tensor. This technique is applied to three-dimensional data obtained in a fully turbulent boundary layer. The results of linear and nonlinear estimates are compared to the corresponding conditional averages and the agreement is found to be excellent, with little improvement for nonlinear estimates. Extensions of the technique to space-time estimates of one- and two-point conditional averages are also presented, the latter providing a means to examine structures associated with a given length scale.
Viscous flows down an inclined plane: Instability and finger formation
Authors: Schwartz Leonard W.
Published: July 2002

The free-surface lubrication equations, including the effects of both gravity and surface tension, are solved numerically for the evolution of thin liquid films on an inclined plane. The advancing contact angle is taken to be zero, equivalent to the assumption of perfect wetting. The shape of a flowing drop compares well, in detail, with a recently published interferometric study. A mound of liquid whose cross section is intially invariant in the horizontal direction is allowed to flow down a vertical plane with no slip imposed on the confining side walls. Fingers, or rivulets, form that are similar to those observed experimentally. The instability that leads to fingering is lateral flow driven by surface tension with larger curvature at the finger troughs. A scaling law for the prediction of finger width is derived.
On the shock enhancement of confined supersonic mixing flows
Authors: Lu P. J. , Wu K. C.
Published: July 2002

Direct numerical simulations using high-resolution total variation diminishing (TVD) scheme are performed for studying the shock enhancement of two-dimensional confined (spatially growing) supersonic mixing flows. Several specially designed mixing enhancement schemes are examined with emphasis placed on the study of the fundamental aspects involved in the shock-induced mixing enhancement process. The merits associated with these mixing enhancement schemes are evaluated based on a cost/effectiveness criterion, in which the cost paid for the total pressure loss encountered and the improvement in mixing gained are considered together. The results suggest that mixing enhancement using shock waves can only be effective if the stimulation is spatially persistent, and begins from the very upstream. Being motivated by this observation, an idea of using wavy-wall configuration to generate the desirable periodic shock stimulation is proposed and investigated. The computed results show that, by an appropriate manipulation of the parameters including wall wavelength, relative phase shift between the top and bottom walls, as well as the amplitude of the waviness, considerable improvement in mixing efficiency can be achieved.
A simple demonstration of a rarefied gas flow induced over a plane wall with a temperature gradient
Authors: Sone Yoshio
Published: July 2002

A simple experiment to demonstrate a rarefied gas flow induced along an unequally heated wall is proposed. A flow along a vertical wall with a downward temperature gradient is detected by a small windmill. Transition from upward natural convection under atmospheric pressure to a downward flow in a rarefied gas is observed.
Transverse flow over a wavy cylinder
Authors: Ahmed Anwar , Bays-Muchmore Byram
Published: July 2002

Transverse flow over a wavy cylinder was investigated experimentally; surface-pressure distributions and flow visualizations were obtained for a set of wavy cylinders with different axial wavelengths. Significant spanwise pressure gradients were present, resulting in three-dimensional separation lines and the formation of streamwise trailing vortex structures near the geometric nodes. Despite the symmetry of the geometries, the separated flow structures near the geometric nodes were distinctly asymmetric a large fraction of time. Integration of the pressure data revealed greater sectional drag coefficients at the geometric nodes than at the geometric saddles.
Instabilities in two-dimensional spatially periodic flows. Part I: Kolmogorov flow
Authors: Thess André
Published: July 2002

The linear stability of the parallel flow ψ0=sin(y) (Kolmogorov flow) is considered, taking into account viscosity, linear friction, and confinement (lateral walls). The computations provide neutral stability curves in the parameter space, wave numbers, and wave speeds, as well as the spatial structure of first unstable modes. Evidence is presented that stability parameters depend nonuniformly on the confinement. It is shown that already weak transverse confinement significantly decreases the longitudinal wavelength of perturbations at instability onset. Strong confinement changes the character of the instability into an oscillatory one instead of a purely exponential growing mode, which is obtained for weakly confined systems. Theoretical predictions of critical parameters are in reasonable agreement with experimental results in electromagnetically driven flows of conducting fluids.
Polarized vorticity dynamics on a vortex column
Authors: Melander Mogens V. , Hussain Fazle
Published: July 2002

It is shown that vortex core dynamics results from the interaction of two slowly deforming, but overlapping, helical vortex structures. These are the left- and right-handed components of the vortex, and are obtained by a generalized Helmholtz decomposition (the complex helical wave decomposition) of the vorticity field. This decomposition is based on a Fourier expansion in eigenfunctions of the curl operator, which has only real eigenvalues λ. The sum of eigenmodes with λ≳0 (λ<0) constitutes the right (left) polarized component, and the vector lines of the field (e.g., vortex lines) are locally right (left) handed helixes. It is found that for a localized vortex the polarized structures are also localized, a crucial result for physical space applications. The polarized vortex structures deform slowly (compared to unpolarized structures) and behave almost like solitary waves when isolated. It is shown that this is because the nonlinearity in the Navier–Stokes equations is largely suppressed between eigenmodes of the same polarity. Moreover, the helicity of polarized structures is very high. The interaction between overlapping polarized structures however gives each structure a different propagation velocity and also results in some additional deformation. The latter is shown to occur mainly in two places: at the front of the structure where a low enstrophy bubble forms (which is a permanent feature in each of the polarized packets), and at the back where a tail develops. Otherwise, the deformation occurs on a much slower time scale compared to that for unpolarized vortices. Thus the rapid changes in the total vorticity field result from the superposition of two slowly deforming structures moving in opposite directions, as is the case for the one-dimensional (1-D) wave equation. The decomposition can also be applied to turbulent flows. In fact, it offers new insight into the structure of turbulent shear flows. The organization of small-scale vortical threads forming in the neighborhood of a coherent structure and their polarization serve as a prime example.
Statistical analysis of the effects of helicity in inhomogeneous turbulence
Authors: Yokoi Nobumitsu , Yoshizawa Akira
Published: July 2002

Effects of helicity in three-dimensional incompressible inhomogeneous turbulence are examined with the aid of a two-scale direct-interaction approximation (DIA). The turbulent helicity gives a measure of the reflectional asymmetry in a turbulent flow and its inhomogeneity contributes to the sustainment of large-scale vorticity field in a three-dimensional mean flow. The importance of helicity effects is discussed in the context of flows in a rotating system and swirling flows in a pipe. A three-equation model with the turbulent helicity incorporated is proposed using the theoretical results. The validity of the model is confirmed quantitatively through the application to a decaying swirling flow in a pipe.
A comparison of the dielectric and plasma wakefield accelerators
Authors: Keinigs Rhon , Peter William , Jones Michael E.
Published: July 2002

A comparison of two advanced accelerator concepts, the plasma wakefield accelerator (PWA) and the dielectric wakefield accelerator (DWA), is presented. Emphasis focuses on the peak accelerating gradients and transformer ratios that can be achieved in these two devices. The effect of finite plasma size on the PWA is also analyzed. For the same cavity geometry and drive beam current, it is found that the dielectric wakefield accelerator can generate a peak field that is comparable to the field that can be generated in the plasma wakefield accelerator. Provided that ideal beam pulse shaping can be achieved, the transformer ratio for the PWA is ten times larger than that for the DWA. A change in this ideal pulse shape results in closer agreement for the transformer ratios. Given these encouraging preliminary results for the DWA it is concluded that the simplicity of employing a passive structure as an accelerating medium warrants further experimental testing of the dielectric wakefield accelerator.
Cyclotron resonance masers with inhomogeneous external magnetic fields
Authors: Nusinovich G. S.
Published: July 2002

A theory has been developed that describes relativistic cyclotron resonance masers with axially inhomogeneous external magnetic fields. The axial profiling of the magnetic field permits one to maintain the cyclotron resonance between the electromagnetic wave and decelerating electrons that is especially important for relativistic gyrotraveling wave tubes, gyroklystrons, and gyrotwystrons. Some general features of particle trapping by the wave are considered and the possibility of achieving a high electron efficiency is analyzed in a simple model of such an interaction.
Reconnection of vorticity lines and magnetic lines*
Authors: Greene John M.
Published: July 2002

Magnetic field and fluid vorticity share many features. First, as divergence-free vector fields they are conveniently visualized in terms of their field lines, curves that are everywhere tangent to the field. The lines indicate direction and their density indicates field strength. The question arises of the extent to which the evolution of the fields can be treated in terms of the evolution of their field lines. The essential answer has been given by Newcomb [Ann. Phys. (NY) 3, 347 (1958)]. He derived the general conditions on the evolution of vector fields that permit the identification of field lines from one instant to the next. The equations of evolution of the vorticity field and the magnetic field fall within Newcomb’s analysis. The dynamics of the flows differs between these two systems, so that geometrically similar phenomena happen in different ways in the two systems. This provides opportunity for comparison and contrast. In this paper the geometrical similarities are emphasized. Reconnection will be defined here as evolution in which it is not possible to preserve the global identification of some field lines. There is a close relation between reconnection and the topology of the vector field lines. Nontrivial topology occurs where the field has null points or there are field lines that are closed loops.
Shock formation in fluids having embedded regions of negative nonlinearity
Authors: Cramer M. S. , Sen R.
Published: July 2002

The steepening of one-dimensional finite-amplitude waves in inviscid Van der Waals gases is described. The undisturbed medium is taken to be unbounded, at rest and uniform. The specific heat is taken to be large enough to generate an embedded region of negative nonlinearity in the general neighborhood of the saturated vapor line and thermodynamic critical point. Under these conditions the shock formation process may differ significantly from that predicted by the perfect gas theory. The present study illustrates these differences for both isolated pulses and periodic wave trains. It is further shown that as many as three shocks, two compression and one expansion, may be formed in a single pulse or, in the case of wave trains, repeated element. It is also shown that the convected sound speed may become identical to the thermodynamic sound speed of the undisturbed medium at three distinct values of the density; the first of these corresponds to the density of the undisturbed medium while the other two are related to an integral of the fundamental derivative along an isentrope. The results obtained are expected to hold for any fluid which possesses such an embedded region of negative nonlinearity.
Stress transport in the rotational and irrotational zones of turbulent shear flows
Authors: Byggstoyl S. , Kollmann W.
Published: July 2002

The transport equations for intermittency factor and conditioned moments are analyzed for turbulent shear flows with free boundaries. Conditions are established for molecular diffusion to dominate the progression of the turbulent zone. The terms related to the dynamics of the interface for mean velocity and apparent stresses in turbulent and nonturbulent zones are shown to be linked by a local relation, and the limit of large distance from the turbulent region for the nonturbulent zone stress equation is given.
Direct numerical simulations of round jets: Vortex induction and side jets
Authors: Brancher P. , Chomaz J. M. , Huerre P.
Published: July 2002

In this paper, a numerical investigation of three-dimensional round jets subjected to streamwise and azimuthal perturbations is reported. The main objective of the study is to give a consistent scenario for the breaking of rotational symmetry in such flows which may ultimately lead to the production of intense side jets. In particular it is shown that the development of the Widnall instability on the primary vortex rings and the evolution of the Bernal and Roshko [J. Fluid Mech. 170, 499 (1986)] streamwise vortices generated by the instability of the braid could be deeply intertwined. A comprehensive discussion of the vortex induction mechanisms leading to the reorientation of the initial vorticity both in the ring and braid regions and to the deformation of the rings is presented. The recent analysis by Monkewitz and Pfizenmaier [Phys. Fluids A 3, 1356 (1991)] is confirmed in the sense that strong radial ejection of fluid is not directly linked to the deformation of the vortex rings but rather to the occurrence of coherent streamwise vortex pairs. However, the final relative position of the streamwise vortex pairs with respect to the deformations of the vortex rings differs slightly from Monkewitz and Pfizenmaier’s proposition.
Finite amplitude perturbation and spots growth mechanism in plane Couette flow
Authors: Dauchot O. , Daviaud F.
Published: July 2002

The plane Couette flow, a shear flow linearly stable for all values of the Reynolds number, R, is experimentally studied. A finite amplitude perturbation, local in both time and space, is created in order to destabilize the flow. A critical amplitude, Ac(R), below which disturbances are not sustained is measured. Above this amplitude, a turbulent spot grows to a spatially-bounded turbulent state, persistent over times long compared to its typical growth time. The critical amplitude, Ac(R), is seen to diverge when R approaches the nonlinear critical Reynolds number RNL=325±5 from above. Below this value of the Reynolds number, no destabilization occurs with this kind of perturbation, whatever its amplitude. The divergent behavior on approaching RNL is characterized in terms of a power law. This result sheds light on the discrepancies previously observed between critical Reynolds number measurements. The spot is then analyzed in terms of its inside structure, spreading rates, as well as waves and velocity profiles close to the spot, in order to compare it to plane Poiseuille and boundary layer spots. The spot evolution appears to be very similar to that observed for the plane Poiseuille spot. It is shown that the growth of the plane Couette spot can be described by the mechanism of ‘‘growth by destabilization.’’
Asymptotic analysis and symmetry in MHD convection
Authors: Alboussière T. , Garandet J. P. , Moreau R.
Published: July 2002

The motion of an electrically conducting fluid in the presence of a steady magnetic field is analyzed. For any non-uniform magnetic field and any non-electromagnetic driving force, a high Hartmann number asymptotic analysis is developed using curvilinear coordinates based on the magnetic field. This analysis yields the structure of the electric current density and velocity fields. In a second step, orthogonal planar symmetries lead to a significant simplification of the asymptotic structure, depending on the nature of the symmetry. The asymptotic solution is applied to some configurations, some of them corresponding to crystal growth from a melt. In the case of electrically insulating boundaries, the nature of the symmetry is found to govern the magnitude and structure of the damped velocity.
Asymptotic solutions of miscible displacements in geometries of large aspect ratio
Authors: Yang Zhengming , Yortsos Yanis C.
Published: July 2002

Asymptotic solutions are developed for miscible displacements at Stokes flow conditions between parallel plates or in a cylindrical capillary, at large values of the geometric aspect ratio. The single integro-differential equation obtained is solved numerically for different values of the Péclet number and the viscosity ratio. At large values of the latter, the solution consists of a symmetric finger propagating in the middle of the gap or the capillary. Constraints on conventional convection-dispersion-equation approach for studying miscible instabilities in planar Hele–Shaw cells are obtained. The asymptotic formalism is next used to derive—in the limit of zero diffusion— a hyperbolic equation for the cross-sectionally averaged concentration, the solution of which is obtained by analytical means. This solution is valid as long as sharp shock fronts do not form. The results are compared with recent numerical simulations of the full problem and experiments of miscible displacement in a narrow capillary.
Reduced dynamical models of nonisothermal transitional grooved-channel flow
Authors: Sahan R. A. , Liakopoulos A. , Gunes H.
Published: July 2002

Reduced dynamical models are derived for transitional flow and heat transfer in a periodically grooved channel. The full governing partial differential equations are solved by a spectral element method. Spontaneously oscillatory solutions are computed for Reynolds number Re⩾300 and proper orthogonal decomposition is used to extract the empirical eigenfunctions at Re=430, 750, 1050, and Pr=0.71. In each case, the organized spatio-temporal structures of the thermofluid system are identified, and their dependence on Reynolds number is discussed. Low-dimensional models are obtained for Re=430, 750, and 1050 using the computed empirical eigenfunctions as basis functions and applying Galerkin’s method. At least four eigenmodes for each field variable are required to predict stable, self-sustained oscillations of correct amplitude at “design” conditions. Retaining more than six eigenmodes may reduce the accuracy of the low-order models due to noise introduced by the low-energy high order eigenmodes. The low-order models successfully describe the dynamical characteristics of the flow for Re close to the design conditions. Far from the design conditions, the reduced models predict quasi-periodic or period-doubling routes to chaos as Re is increased. The case Pr=7.1 is briefly discussed.
Breakdown of scaling in droplet fission at high Reynolds number
Authors: Brenner Michael P. , Eggers Jens , Joseph Kathy , Nagel Sidney R. , Shi X. D.
Published: July 2002

In this paper we address the shape of a low-viscosity fluid interface near the breaking point. Experiments show that the shape varies dramatically as a function of fluid viscosity. At low viscosities, the interface develops a region with an extremely sharp slope, with the steepness of the slope diverging with vanishing viscosity. Numerical simulations demonstrate that this tip forms as a result of a convective instability in the fluid; in the absence of viscosity this instability results in a finite time singularity of the interface far before rupture (in which the interfacial curvature diverges). The dynamics before the instability roughly follow the scaling laws consistent with predictions based on dimensional analysis, though these scaling laws are violated at the instability. Since the dynamics after rupture is completely determined by the shape at the breaking point, the time dependences of recoiling do not follow a simple scaling law. In the process of demonstrating these results, we present detailed comparisons between numerical simulations and experimental drop shapes with excellent agreement.
The role of capillary waves in two-fluid atomization
Authors: Tsai Shirley C. , Luu Patrick , Childs Paul , Teshome Asseged , Tsai Chen S.
Published: July 2002

A mechanistic study of two-fluid atomization has been carried out using a new spray technique called ultrasound-modulated two-fluid (UMTF) atomization. This technique is based on resonance between the liquid capillary waves generated by ultrasound and those generated by high-velocity air. Specifically, capillary waves are established on the surface of a liquid jet as it issues from a coaxial two-fluid atomizer, the nozzle tip of which vibrates at the same frequency as the ultrasound while the frequency of the capillary waves is only half of the ultrasound frequency. As these capillary waves travel downstream in the direction of air flow, their amplitude is further amplified by the air flowing around them. Atomization occurs when the wave amplitude becomes too great to maintain wave stability; the resulting drop sizes are proportional to the wavelength of the resonant capillary waves which is determined by the harmonic frequency of the ultrasound in accordance with the Kelvin equation. Theoretical calculations of the amplitude growth rate are based on two models of temporal instability of wind-generated capillary waves: Taylor’s dispersion relation and Jeffreys’ one-parameter (sheltering factor) model. Good agreements between the theoretical predictions by these models and the experimental results of how drop-size and size distributions are influenced by air velocity and surface tension led to the conclusion that Taylor-mode breakup of capillary waves plays a very important role in two-fluid atomization. Furthermore, all peak drop diameters can be accounted for by the harmonic frequencies of the ultrasound. Hence, it is further concluded that secondary atomization is negligible in co-flow two-fluid atomization of a water jet at air velocities up to 170 m/s and air-to-water mass ratio up to 5.6. In addition, uniform drops with diameters predetermined by the ultrasound frequency can be accomplished by adjusting the air velocity.
Steady incompressible magnetohydrodynamic flow near a point of reattachment
Authors: Dorrepaal J. M. , Moosavizadeh S.
Published: July 2002

The oblique stagnation-point flow of an electrically conducting fluid in the presence of a magnetic field is a highly nonlinear problem whose solution is of interest even in the simplest of geometries. The problem models the flow of a viscous conducting fluid near a point where a separation vortex reattaches itself to a rigid boundary. A similarity solution exists which reduces the problem to a coupled system of four ordinary differential equations which can be integrated numerically. The problem has two independent parameters, the conductivity of the fluid and the strength of the magnetic field. Solutions are tabulated for a variety of cases involving the two parameters. The geometry of the flow as well as that of the induced magnetic field is determined near the point of reattachment.
Similarity of gravity current fronts
Authors: Parsons Jeffrey D. , Garcı́a Marcelo H.
Published: July 2002

Mixing processes in gravity current fronts have only recently been quantified due to their complex, unsteady nature. The similarity of the mixing processes in these pioneer works, however, has not been explored adequately. Experiments that explore a wide range of fronts have been performed. These experiments have used techniques that exhaustively sample the temporal (using a high-speed conductivity probe) and spatial (using planar laser-induced fluorescence) density field more thoroughly than any previous work. Both types of experiments have confirmed earlier research suggesting that low Reynolds number fronts mix differently and less than higher Reynolds number flows. Similarity appeared to be achieved for Req>1000, where Req is a Reynolds number based upon the cube root of the buoyancy flux into the front and the height of current. It appears that certain secondary mixing processes, seen by other researchers studying stratified mixed layers, are responsible for the earlier changes seen with Reynolds number and cause significant mixing at the front.
Imaging of particle shear migration with electrical impedance tomography
Authors: Butler Jason E. , Bonnecaze Roger T.
Published: July 2002

Electrical impedance tomography (EIT) is used to investigate the net migration of particles in a suspension undergoing pressure-driven flow through a tube at low Reynolds number. A low frequency electrical current is applied to the flowing suspension by two flush-mounted electrodes on the pipe wall to create a potential field which is sampled by other pairs of flush-mounted electrodes. A numerical inversion of the data, which takes into account the geometry and symmetry of the problem, gives the conductivity variation within the flow. An image of the suspension particle volume fraction in the tube is then formed using a relationship between the local conductivity and local suspension concentration. Consistent with particle shear migration of a concentrated suspension at low Reynolds number, the images from experimental data show a net migration of particles toward the centerline of the tube. The images of a 0.25 volume fraction suspension at the lowest Reynolds number examined compare favorably to an existing continuum theory of particle shear migration. Other images from experiments at higher, but still small Reynolds numbers, and at volume fractions of 0.25 and 0.40 are also presented. The particle migration measured with the relatively inexpensive EIT at the latter condition is in very good agreement with the particle distribution measured with magnetic resonance imaging by Hampton et al. [J. Rheol. 41, 621 (1997)].
Vortex interaction and mixing in a driven gaseous axisymmetric jet
Authors: Meyer T. R. , Dutton J. C. , Lucht R. P.
Published: July 2002

Vortex formation and merging are investigated in the near field of a driven axisymmetric jet. Acoustic forcing is used to obtain repeatable vortex pairing events, and simultaneous passive scalar and cold-chemistry planar laser-induced flourescence are used to obtain instantaneous images of molecularly mixed jet fluid fraction. The time-varying scalar dissipation field and area-averaged stirredness of the vortex core region are measured at various stages of vortex interaction. These mixing properties are analyzed in conjunction with the observed vortex dynamics, such as the time-dependent vortex convection velocity. The results indicate that there are several phases of the pairing event with distinct mixing characteristics, including vortex roll-up, interaction, coalescence, and reentrainment. Vortex roll-up is nearly laminar with molecular diffusion between the layers of jet and co-flow fluid. The most dramatic change in the mixing state of the leading vortex, which includes the appearance of a uniformly mixed core region, occurs as the trailing vortex approaches and interferes with co-flow fluid entrainment. Vortex coalescence is marked by gross deformation and stretching of the trailing vortex, and rapid homogenization of the diffusion layers. Finally, re-entrainment of pure fluid after the pairing event results in an elongated, nonrotating structure. These stages of vortex pairing correspond to the temporal evolution of vorticity observed in previous studies.
Effects of trailing jet instability on vortex ring formation
Authors: Zhao Wei , Frankel Steven H. , Mongeau Luc G.
Published: July 2002

Numerical simulations of an impulsively started jet were performed in order to investigate the effects of trailing jet instability on axisymmetric vortex ring formation. The predictions were compared to experimental results reported in the literature and to recently published numerical results. The total and vortex ring circulations were found to be in good agreement with both the experimental and the numerical results. The presence of a universal formation time scale was confirmed. The results also highlighted an important interaction between an instability which develops in the trailing jet for large discharge times and the dynamics of the head vortex ring. This interaction accelerates the process by which the vortex ring detaches from the trailing jet and has a significant effect on the vortex ring circulation.
Folded waveguide gyrotron traveling-wave-tube amplifier
Authors: Choi J. J. , Armstrong C. M. , Ganguly A. K. , Calise F.
Published: July 2002

A compact, low cost gyrotron traveling-wave-tube (gyro-TWT) amplifier capable of producing high-power, broadband, millimeter wave radiation is reported. The interaction circuit is a periodic, magnetic field plane (H plane) bend, transverse folded waveguide employed with a high-power axis-encircling electron beam. Transverse beam modulation and wave amplification in the folded waveguide gyro-TWT are observed in both linear theory and large signal simulations. Calculations from an equivalent circuit model and a three-dimensional electromagnetic code predict a mode coalescing of the first stop-band in a periodic structure. The mode coalescing is verified from experimental measurements.