bluuebunny/crossref_metadata_2025 huggingface dataset:
Infrared multiphoton absorption and electronic polarizability
Authors: Malvaldi M. , Persico M. , Van Leuven P.
Published: July 2002

The effect of electronic polarizability on the absorption of infrared photons by diatomic molecules in an intense laser field is investigated by numerically simulating the time evolution of the system. The absorption spectrum has a frequency shift proportional to the intensity; its dependence on polarizability and anharmonicity is established. It is shown that for pulsed fields the effect of polarizability is irregularly dependent on the pulse length. Resonances in the half-frequency range are strongly enhanced by the electronic polarizability.
Matrix isolation and spectroscopic characterization of a linear AlOSi radical
Authors: Junker Markus , Friesen Markus , Schnöckel Hansgeorg
Published: July 2002

In the past, matrix isolation technique proved to be a proper method to generate new species by oxidation and reduction of the high-temperature molecule SiO. In each case the variation of the SiO multiple bonding was of central interest. During the reduction of SiO with different metal atoms M, different MSiO intermediates result. The co-condensation of Al atoms with SiO ends up with a linear AlOSi radical, which represents the first example of a metal coordination via the O atom of SiO. The structural data based on IR- and Raman spectra are confirmed by quantum chemical calculations. Bonding of AlOSi is similar to that of the high-temperature molecule AlOAl; however, an additional electron is present in the lowest antibonding Π-orbital.
Vibrational corrections to properties at arbitrary reference geometry
Authors: Ingamells Victoria E. , Papadopoulos Manthos G. , Sadlej Andrzej J.
Published: July 2002

We demonstrate how vibrational contributions to any (static) electric property may be computed with respect to an arbitrary reference geometry which, at a given level of electronic structure theory, need not correspond to the associated minimum energy geometry. Within the harmonic approximation, it is shown that the formulas for the vibrational contributions can be extended to include a second-order corrective term, which is a function of the energy gradient and the (nuclear) first derivatives of the property in question. Taking the BH molecule as a test case, we illustrate that the order of magnitude of the correction increases with order of property (i.e., μ≈10−2→γ≈101−102), and that this value is equivalent to the difference in (pure) electronic contributions evaluated with respect to the optimum and nonoptimum geometries. Furthermore, we show that for a diatomic, vibrational [zero-point vibrational average (ZPVA) and pure] contributions computed at a nonoptimum geometry may be readily corrected to give the optimum geometry values. Thus we provide a route for obtaining total (electronic+vibrational) properties associated with a minimum energy geometry, using information calculated at a nonoptimum geometry.
Theoretical analysis of the influence of stochastic gating on the transient effect in fluorescence quenching by electron transfer
Authors: Bandyopadhyay T. , Seki K. , Tachiya M.
Published: July 2002

For electron transfer (ET) reactions in liquid media, it is not uncommon to find that the stereoselectivity, mutual orientations, conformational fluctuations, spin multiplicity restrictions of the reacting system may kinetically limit its reactivity. We assume that the system in question can stochastically interconvert between reactive (open gate) and nonreactive (closed gate) states at rates competitive with diffusion-influenced ET, and refer to this kind of reaction as stochastically gated diffusion-influenced ET reactions. We utilize the Zhou and Szabo model of stochastically gated diffusion-influenced reactions in order to study the effect of such stochastic fluctuations of reactivity on the transient kinetics of fluorescence quenching in through-solvent photoinduced ET reaction. Different types of transient kinetics, fluorophore gated vis-a-vis quencher gated, are demonstrated in terms of survival probability of the fluorophore, which shows that the analysis of experimental results ignoring such phenomena can be dramatically in error. Approximate analytical solutions of the theory based on projection operator formalism are presented. The exact numerical results including the role of liquid structure and the hydrodynamic hindrance of fluorophore-quencher diffusion rates are found to compare extremely well with the results obtained from a molecular dynamics simulation of the same reaction system. The simulations are based on the rate equations obtained from the first principle. Illustrative calculations and comparisons are presented to demonstrate the competitive interplay between the reaction sink strength, diffusion, and gating rates on the reaction kinetics. A simple method, based on the distribution of ET distance and quantum yield of ET of gateless reactions, is proposed to help delineate the features of such competitive interplay on the asymmetry of the reaction kinetics.
High-resolution rotational coherence spectroscopy of para-cyclohexylaniline
Authors: Riehn Christoph , Weichert Andreas , Lommatzsch Uwe , Zimmermann Marcus , Brutschy Bernhard
Published: July 2002

A high-resolution rotational coherence spectroscopy (RCS) investigation of para-cyclohexylaniline (pCHA) was performed with a solid-state picosecond laser setup, which allowed for the determination of rotational constants with unprecedented precision for a RCS experiment. The technique of time-resolved fluorescence depletion was used for the RCS measurements. The unique structural features of pCHA enabled the determination of both ground and excited state rotational constants. Three different sets of recurrences were observed in the spectrum and assigned to K″-, K′-, and J″-type transients. From a detailed analysis by a grid search procedure based on the numerical simulation of RCS spectra and a nonlinear least-squares fitting routine the following rotational constants for the ground state were obtained: A″=2406.5±0.6 MHz, (B+C)″=714.9±0.4 MHz. For the electronic excited state two different sets of constants were found to fit the experimental data within the reported uncertainties: set (I) A′=2343.6±1.3 MHz, (B+C)′=714.4±1.7 MHz and set (II) A′=2346.3±1.3 MHz, (B+C)′=719.3±2.1 MHz. From additional information set (II) was found preferable for the description of the excited state. Furthermore, the fluorescence lifetime and the alignment of the transition dipole moment in the molecular frame were obtained from the fit procedure. For a structural characterization of pCHA we performed ab initio calculations of the electronic ground and excited state using HF/6-31G(d) and CIS/6-31G(d) levels of theory, respectively. These results were compared with the experiments and used to investigate the dependence of the rotational constants on characteristic intramolecular coordinates.
Computer simulation studies of a square-well fluid in a slit pore. Spreading pressure and vapor–liquid phase equilibria using the virtual-parameter-variation method
Authors: Vörtler Horst L. , Smith William R.
Published: July 2002

We study model square-well fluids with well-width parameter λ=1.5 confined to hard planar slits. We derive a general computer simulation method for numerically calculating an arbitrary first derivative of the canonical ensemble partition function with respect to a simulation parameter, which we call the virtual-parameter-variation method. Two special cases of this approach are the Widom test-particle insertion method for calculating the excess chemical potential, and a method for calculating the pressure due to Eppenga and Frenkel [Mol. Phys. 52, 52, 1303 (1984)]. We use this approach to calculate the volume derivative parallel to the slit walls of the Helmholtz free energy in an (N,V,T) Monte Carlo simulation, and show that this spreading pressure is numerically consistent with the thermodynamic pressure obtained by integration of the Gibbs–Duhem equation using the simulated chemical potentials of the confined fluid as a function of density. We obtain new simulation results for the spreading pressure and the phase equilibrium properties of the confined square-well fluid, and we also estimate its critical point properties, observing a decrease of the critical temperature in comparison to the bulk fluid.
Two-step phase separation of a polymer mixture. I. New scaling analysis for the main scattering peak
Authors: Hashimoto Takeji , Hayashi Masaki , Jinnai Hiroshi
Published: July 2002

Time-resolved light scattering experiments have been performed on the two-step phase separation process for a binary mixture of deuterated polybutadiene and protonated polyisoprene with the critical composition. The first-step phase separation was induced by quenching the system from a temperature T0 in a single-phase state to T1. At various times in the late stage spinodal decomposition (SD) at T1, the mixture was further subjected to the second-step phase separation by temperature jump (T-jump) from T1 to T2 in such a way that the driving force for the phase separation increases and hence phase separation process is accelerated. The comparison between the single-step phase separation behavior from T0 to T1 or to T2 and the two-step phase separation behavior was made in terms of the time evolution of the main scattering peak arising from a dominant mode of the composition fluctuations developed in the phase separation process. To do so, we proposed and applied a new scaling method for the scattering peak position, qm,1, and intensity, Im,1, to explore the time evolution of the fluctuations for the two-step phase separation process. The new scaling method, which takes into account an abrupt change in the spatio-temporal scale of phase-separating system involved by the second-step T-jump clearly elucidates a nonlinear pathway according to which the initial structures developed in the first-step process is relaxed and transformed toward an equilibrium structure at T2 after the second-step process.
Static hyperpolarizability of the water dimer and the interaction hyperpolarizability of two water molecules
Authors: Maroulis George
Published: July 2002

We report an extensive investigation of the electric dipole moment (μα), static polarizability (ααβ), and hyperpolarizability (βαβγ and γαβγδ) of the water dimer. Calculations were performed at both rigid and relaxed monomer geometries. At the rigid monomer geometry (RIMG), a very large [9s6p6d4f/6s5p3d2 f] basis set consisting of 370 Gaussian-type functions is thought to provide self-consistent field (SCF) values very close to the Hartree–Fock limit for all properties: total dipole moment μ=1.0706ea0, mean and anisotropy of the dipole polarizability ᾱ=16.98 and Δα=2.69e2a02Eh−1, first hyperpolarizability (in the direction of the dipole moment vector) β̄=−2.9e3a03Eh−2, and mean second dipole hyperpolarizability γ̄=1906e4a04Eh−3. Very large electron correlation effects are observed for the hyperpolarizability. At the CCSD(T) level, coupled-cluster theory with single, double and perturbatively linked triple excitations, our best values are μ=1.0204ea0, ᾱ=19.54, and Δα=3.06e2a02Eh−1, β̄=−6.5e3a03Eh−2, and γ̄=3669e4a04Eh−3. ᾱ((H2O)2) and γ̄((H2O)2) are not drastically different than twice the size of ᾱ(H2O) and γ̄(H2O). Our efforts to estimate the interaction properties of two water molecules in the dimer lead to the conclusion that ᾱinter and γ̄inter are rather small. Further calculations at a relaxed monomer geometry (REMG) corroborate this conclusion. We have fully explored basis set effects at all levels of theory and for all properties. We rely on a sequence of small-sized but sufficiently flexible basis sets in order to propose reliable computational strategies for the extension of electric property calculations to large water clusters.
Gauge theories, the holonomy operator, and the Riemann–Hilbert problem
Authors: Newman E. T.
Published: July 2002

The so-called Riemann–Hilbert problem has arisen and plays a major role in the study of many nonlinear integrable systems, such as the sine–Gordon equation, stationary axial symmetric Einstein equations, etc. Here it is shown how the Riemann–Hilbert problem arises naturally in the study of self-dual Yang–Mills fields in Minkowski space via a simple geometric construction of the holonomy operator on anti-self-dual planes. This Riemann–Hilbert problem is then converted to a linear homogeneous differential equation that is considerably simpler to study than the original problem. Finally it is shown that the nonlinear equation of Yang for self-dual fields is easily understood from the holonomy point of view.
Bell’s inequalities and quantum field theory. II. Bell’s inequalities are maximally violated in the vacuum
Authors: Summers Stephen J. , Werner Reinhard
Published: July 2002

In the context of the study of Bell’s inequalities carried out in Paper I [J. Math. Phys. 28, 2440 (1987)], it is proven that Bell’s inequalities are maximally violated in the vacuum state by suitable spacelike separated observables for both Bose and Fermi free quantum field theories.
Highly excited stable bound states in strongly coupled lattice gauge theories
Authors: Ferreira Sabino José , Schor Ricardo S. , O’Carroll Michael L.
Published: July 2002

The mass spectrum of pure three-dimensional SU(2) lattice gauge theory in the adjoint representation is studied. An exact analysis in an approximate model predicts the existence of highly excited bound states. The existence of this bound state in a high-spin state is proved and a convergent expansion for its mass is obtained.
Field theory of geometric p-branes
Authors: Ho Choon-Lin
Published: July 2002

In this paper, p-brane field theory is constructed in terms of functions of geometric p-surfaces. Nambu–Goto p-brane dynamics is incorporated in the Dirac form. The field equation for toroidal p-branes in p+2 dimensions is exactly solved for, and is shown to admit an equally spaced mass-squared spectrum containing massless states.
A simple proof of the result that the Wigner transformation is of finite order
Authors: Rashid M. A.
Published: July 2002

Using a set of functions with linear span that is dense in L2(R2N), a simple proof is constructed of the result (discovered and proved by Várilly and Gracia-Bondia recently [J. Math. Phys. 28, 2390 (1987)]) that the Wigner transformation is of order 24 and that its sixth power is the inverse Fourier transform (or Fourier cotransform).
A classical particle in heat bath under the influence of external noise
Authors: Mencia Bravo J. , Velasco R. M. , Sancho J. M.
Published: July 2002

A very simple model of a classical particle in a heat bath under the influence of external noise is studied. By means of a suitable hypothesis, the heat bath is reduced to an internal colored noise (Ornstein–Uhlenbeck noise). In a second step, an external noise is coupled to the bath. The steady state probability distributions are obtained.
Characteristic functional structure of infinitesimal symmetry mappings of classical dynamical systems. IV. Classical (velocity-independent) mappings of second-order differential equations
Authors: Katzin Gerald H. , Levine Jack
Published: July 2002

In a recent paper [J. Math. Phys. 26, 3080 (1985)], the first of this series, it was shown that velocity-dependent symmetry mappings of second-order dynamical systems have a characteristic functional structure which is the same for all dynamical systems. The present paper continues the investigation of this characteristic functional structure. A shortened, improved, conceptionally simpler proof of the existence of the characteristic structure is given. It is shown how this characteristic functional structure may be formally incorporated into a new procedure for the determination of classical (velocity-independent) symmetries of dynamical systems. In addition to providing insight into symmetry analysis this new procedure is also a practical alternative to existing symmetry methods for those dynamical systems for which there exist sufficient knowledge of the form of the dynamical solution, so that it is feasible to determine constants of motion by inversion (or the converse). Application of the procedure to time-dependent linear systems readily gives the complete classical symmetry group for the one-dimensional case (with generators in a somewhat simpler form than those obtained by Leach, Research Report AM-79:05, La Trobe Univ., Bundoora, Australia, (1979)) and the n-dimensional isotropic case [with generators the same as those obtained by Lopez, J. Math. Phys. 29, 1097 (1988)]. By inspection the formalism shows all n-dimensional time-dependent linear systems admit at least a 2n-parameter classical symmetry group and all decoupled n-dimensional time-dependent linear systems admit at least a 3n-parameter classical symmetry group. Other applications to linear and nonlinear systems are given.
Extensions of representations of Lie superalgebras
Authors: Ben Amor Hedi , Pinczon Georges
Published: July 2002

The notion of extensions of representations of a Lie superalgebra is defined and related to associated cohomology. Sufficient conditions for triviality of an extension are given, such as: extensions of representations, having different infinitesimal characters, always split. Irreducible Harish–Chandra modules of osp(1,2), and their extensions, are constructed and classified.
Operator representations of the real twisted canonical commutation relations
Authors: Schmüdgen Konrad
Published: July 2002

The covariant differential calculus on the quantum vector space CNq leads to q deformations of the canonical commutation relations and of the Weyl algebra. If the deformation parameter q is of modulus one, integrable (‘‘well-behaved’’) representations of this twisted canonical commutation relations by self-adjoint operators on a Hilbert space are defined and studied. All faithful irreducible integrable representations of the real q-Weyl algebra are classified up to unitary equivalence.
W gravity, N=2 strings, and 2+2 SU*(∞) Yang–Mills instantons
Authors: Castro Carlos
Published: July 2002

It is conjectured that W gravity can be interpreted as the gauge theory of φ diffeomorphisms in the space of dimensionally reduced D=2+2 SU*(∞) Yang–Mills instantons. These φ diffeomorphisms preserve a volume-three form and are those that furnish the correspondence between the dimensionally reduced Plebanski equation and the KP equation in (1+2) dimensions. A supersymmetric extension furnishes super-W gravity. The super-Plebanski equation generates self-dual complexified super gravitational backgrounds (SDSG) in terms of the super-Plebanski second heavenly form. Since the latter equation yields N=1, D=4 SDSG complexified backgrounds associated with the complexified-cotangent space of the Riemannian surface, (T*Σ)c, required in the formulation of SU*(∞) complexified Self-Dual Yang-Mills theory, (SDYM); it naturally follows that the recently constructed D=2+2 N=4 SDSYM theory, as the consistent background of the open N=2 superstring, can be embedded into the N=1 SU*(∞) complexified self-dual-super-Yang–Mills (SDSYM) in D=3+3 dimensions. This is achieved after using a generalization of self-duality for D≳4. Finally, the plausible relationship between the geometry of N=2 strings and the moduli of SU*(∞) complexified SDSYM in 3+3 dimensions is indicated.
Harish–Chandra modules of the intermediate series over the high rank Virasoro algebras and high rank super-Virasoro algebras
Authors: Su Yucai
Published: July 2002

Indecomposable modules with weight multiplicities ≤1 over the high rank Virasoro algebras are constructed and classified. A notion of the high rank super-Virasoro algebras is introduced. The classification of all indecomposable modules with weight multiplicities ≤1 over the high rank super-Virasoro algebras is obtained.
Long time behavior of ‘‘X-led’’ reactions
Authors: Rondoni Lamberto
Published: July 2002

Single chemical reactions with a finite, but arbitrary, number of chemicals are considered, and the properties of the dynamical systems which arise in modeling the time evolution of the corresponding concentrations are studied. No space variables are included in the models, as it is assumed that the reactions take place in well stirred reactor tanks. The time variable is assumed to take discrete values which are multiples of a finite interval Δt. The links between such dynamical systems and the nonlinear stochastic processes derived from statistical dynamics are presented. Also, the concept of X-led reactions is introduced, as a generalization of the dynamics associated with density- and activity-led reactions. In all cases, maps of the interval whose convergence properties are investigated are obtained. The fact that taking Δt → 0 reproduces better and better the solution of the associated differential equations is briefly discussed.
Why fundamental structures are first or second ordera)
Authors: Coleman Robert Alan , Korté Herbert
Published: July 2002

The fundamental result is proven that no G-structures that are properly of higher order k≥3 can exist; that is, if a differentiable manifold has a geometric structure at all there must exist geometric structure at first or second order. Because this theorem limits the cases to be considered, it is relevant for the classification of G-structures. Also proven are several results that underscore the special role of second-order equation-of-motion structures for material bodies. In particular, it is proven that geodesic equation-of-motion structures of order k≥3 necessarily admit solutions that break the light barrier.
The equivalence between the Mandelstam and the Cayley–Hamilton identities
Authors: Berenstein D. E. , Urrutia L. F.
Published: July 2002

Starting from the Cayley–Hamilton identities for n×n ordinary matrices which result from the application of the corresponding Cayley–Hamilton theorem, the generic Mandelstam identities are derived. The converse of the above statement is also proven. The method is extended to supermatrices and a definition of the generic Mandelstam identities in that case is proposed.
A calculation with a biorthogonal wavelet transformation
Authors: Falomir H. , Muschietti M. A. , Santangelo E. M. , Solomin J.
Published: July 2002

The use of a biorthogonal basis for continuous wavelet transformations is explored, thus relaxing the so-called admissibility condition on the analyzing wavelet. As an application, the eigenvalues and corresponding radial eigenfunctions of the Hamiltonian of relativistic hydrogen-like atoms are determined.
New properties and examples of incomplete Lorentzian tori
Authors: Romero Alfonso , Sánchez Miguel
Published: July 2002

A new procedure to construct incomplete metrics on a two-torus is introduced. Relations between curvature and completeness are explored, and examples showing a wide independence among them are given. Incompleteness appears as a usual property of the Lorentzian tori, and the density of the incomplete metrics in the set of all the Lorentzian ones is discussed. This article can be seen as a partial study of compact space-times and the conformal Lorentzian moduli space Mod(T2), as claimed by Yurtsever [J. Math. Phys. 31, 3064 (1990)], and as a continuation of the authors’ previous article [J. Math. Phys. 34, 3768 (1993)].
Uncertainty relation in quantum mechanics with quantum group symmetry
Authors: Kempf Achim
Published: July 2002

The commutation relations, uncertainty relations, and spectra of position and momentum operators were studied within the framework of quantum group symmetric Heisenberg algebras and their (Bargmann) Fock representations. As an effect of the underlying noncommutative geometry, a length and a momentum scale appear, leading to the existence of nonzero minimal uncertainties in the positions and momenta. The usual quantum mechanical behavior is recovered as a limiting case for not too small and not too large distances and momenta.
Dissipation in Wigner–Poisson systems
Authors: Lange Horst , Zweifel P. F.
Published: July 2002

The Wigner–Poisson (WP) system (or quantum Vlasov–Poisson system) is modified to include dissipative terms in the Hamiltonian. By utilizing the equivalence of the WP system to the Schrödinger–Poisson system, global existence and uniqueness are proved and regularity properties are deduced. The proof differs somewhat from that for the nondissipative case treated previously by Brezzi–Markowich and Illner et al.; in particular the Hille–Yosida Theorem is used since the linear evolution is not unitary, and a Liapunov function is introduced to replace the energy, which is not conserved.
Charge transfer model and three body-scattering
Authors: Ito Hiroshi T.
Published: July 2002

The asymptotics of total scattering cross sections for a three-body quantum system with two heavy particles are studied when the masses tend to infinity. It is assumed that the initial channel is a two-cluster channel such that a light particle and a heavy one form a bound state and the relative velocity of another heavy particle to the pair is fixed. It is shown that the limits exist and they can be expressed in terms of transition probabilities which appear in the scattering theory for the charge transfer models.
Riemannian three-metrics with degenerate Ricci tensors
Authors: McManus Des J.
Published: July 2002

A complete classification of Riemannian three-metrics whose Ricci tensor possesses exactly two distinct constant eigenvalues is given: those metrics that admit a G4 as the maximal isometry group belong to either Petrov case IIIq=0, or VII, or VIII; those metrics that admit a G3 as the maximal isometry group belong to either Bianchi class VI0, or VIII, or IX. An explicit coordinate representation is given for all the homogeneous and inhomogeneous solutions.
Generalizations of the Wess–Zumino–Witten model and Ferretti–Rajeev model to any dimensions: CP-invariance and geometry
Authors: Fujii Kazuyuki
Published: July 2002

The Wess–Zumino–Witten model in two dimensions is generalized to one in any even dimensions and the Ferretti–Rajeev model in three dimensions to one in any odd dimensions. In this connection some properties of fermion number (topological) currents in odd dimensions are also discussed.
A q-superdimension formula for irreps of type I quantum superalgebras
Authors: Links J. R. , Gould M. D.
Published: July 2002

We derive a closed formula for the q-superdimensions of a wide class of irreps, including all unitary irreps, of the type I quantum superalgebras.
Separation of the massless field equations for arbitrary spin in the Robertson–Walker space–time
Authors: Zecca Antonio
Published: July 2002

The massless spin 2 free-field equation is studied in the Robertson–Walker space–time via the Newman–Penrose formalism and separated by using a Chandrasekhar–Teukolski method. The resulting temporal and angular equations are explicitly integrated. The radial equations are solved in the flat universe case. The closed universe case shows, in principle, the existence of a discrete spectrum of the energy of the massless particles. In the general case of spin greater than 2 the massless field equations are shown to be separable by induction. The separated equations admit the same recurrence structure and analog interpretation properties of the spin 2 and less than 2 cases.
Inclusion of gauge bosons in the tensor formulation of the Dirac theory
Authors: Reifler Frank , Morris Randall
Published: July 2002

A recent article characterized all classical tensor systems which admit Fermi quantization as those having unitary Lie–Poisson brackets. Examples include Euler’s tensor equation for a rigid body and Dirac’s bispinor equation in tensor form. It was further shown that the tensor form of Dirac’s bispinor Lagrangian can be derived from a tetrad formulation of a Kaluza–Klein model, which unifies the Dirac and Einstein Lagrangians. Thus, fermions, like bosons, are represented as gauge fields in the tensor formulation of the Dirac theory. In this article boson gauge fields are added to the unified Dirac–Einstein Lagrangian by defining the gauge group of the Kaluza–Klein model to be a semi-direct product. It is shown that the semi-direct product structure uniquely prescribes the usual ‘‘minimal coupling’’ between bosons and fermions.
Phase-space representation of quantum state vectors
Authors: Ban Masashi
Published: July 2002

Phase-space representation of quantum state vectors is obtained within the framework of the relative-state formulation. For this purpose, the Hilbert space of a quantum system is enlarged by introducing an auxiliary quantum system. Relative-position state and relative-momentum state are defined in the extended Hilbert space of the composite quantum system and expressions of basic operators such as canonical position and momentum operators, acting on these states, are obtained. Phase-space functions which represent a state vector of the relevant quantum system are obtained in terms of the relative-position states and the relative-momentum states. The absolute-square of the phase-space function represents the probability distribution of the phase-space variables. Time-evolution of a quantum system is investigated in terms of the phase-space functions. The relations to the phase-space representations formulated by the other methods are obtained.
Some remarks on the Navier–Stokes equations in R3
Authors: Lemarié-Rieusset Pierre Gilles
Published: July 2002

We study various existence and uniqueness results for solutions of the Navier–Stokes equations in connection with function spaces related to real harmonic analysis.
Covariant spin structure
Authors: Sardanashvily Gennadi A.
Published: July 2002

Dirac fermion fields associated with different tetrad gravitational fields and under general covariant transformations are described by sections of the composite bundle S→Σ→X4, which is both the Dirac spinor bundle over the tetrad bundle Σ and the natural one over X4. As a natural bundle, S→X4 admits general covariant transformations which are those of Dirac spin structures. A different way is to consider a background spin structure. We find gauge transformations which preserve this spin structure, but act on effective tetrad fields as general covariant transformations.
Possibly degenerate tetrad gravity and Maxwell–Dirac fields
Authors: Canarutto Daniel
Published: July 2002

I present an integrated approach to tetrad gravity and Maxwell–Dirac fields, which is not singular in the case when the tetrad is degenerate. All field equations are linear. The geometric data consist only of a complex vector bundle S→M with two-dimensional fibers, where M is a real 4-manifold. All needed structures are functorially derived from S. Any considered object which is not a functorial construction is assumed to be a dynamical field.
A new look at the Schouten–Nijenhuis, Frölicher–Nijenhuis, and Nijenhuis–Richardson brackets
Authors: Gozzi E. , Mauro D.
Published: July 2002

In this paper we re-express the Schouten–Nijenhuis, the Frölicher–Nijenhuis, and the Nijenhuis–Richardson brackets on a symplectic space using the extended Poisson brackets structure present in the path-integral formulation of classical mechanics.
Initial turbulence effect on jet evolution with and without tonal excitation
Authors: Raman G. , Zaman K. B. M. Q. , Rice E. J.
Published: July 2002

The effect of the initial turbulence level on the development of an axisymmetric jet was experimentally investigated. The turbulence intensity at the jet exit was varied, over the range 0.15%–5%, by using screens and grids placed upstream of an 8.8 cm diam nozzle. Top-hat initial mean velocity profiles with approximately identical boundary layer states were ensured in all cases; the turbulence was homogeneous and the spectra were broadband. It was found, contrary to earlier reports, that the natural jet evolution remained essentially unchanged for varying initial turbulence intensities. The response of the jet to single frequency, plane wave excitation was then studied over the full range of initial turbulence intensities. It was found that for even the highest turbulence (5%), the jet was quite excitable and could be influenced measurably by a tone of small amplitude. However, the jet ‘‘excitability,’’ as assessed from the variations of the mean velocity as well as the total and fundamental rms amplitudes on the axis, diminished with increasing initial turbulence. As the initial turbulence was increased, the amplitude of the discrete tone had to be increased in order to achieve the same excited state of the jet. It was also found that there existed a limit to the jet excitability, beyond which no additional effect could be achieved, as the amplitude of the discrete tone was increased. Results are also shown for a case having no grid or boundary layer trip, yielding a nominally laminar boundary layer at the jet exit. This case illustrates the profound effect of the initial boundary layer state on the jet evolution and excitability. This jet decayed the fastest naturally, and consequently, it was the least excitable, in spite of very low initial turbulence intensity (0.15%).
The onset of chaotic oscillations and rapid growth of a spherical bubble at subcritical conditions in an incompressible liquid
Authors: Szeri Andrew J. , Leal L. Gary
Published: July 2002

Recently developed techniques of Wiggins [SIAM J. Appl. Math. 48, 262 (1988)] are used to study the onset of chaotic oscillations and explosive growth of a spherical bubble in an otherwise quiescent, incompressible fluid. It is shown that bubbles forced with a quasiperiodic background pressure can respond chaotically and grow explosively at lower amplitudes of the primary component of the forcing than bubbles forced with a single frequency. The means of extension of these results to an arbitrary, but finite, number of forcing frequencies is presented.
On the growth of mushroomlike structures in nonlinear spatially developing Goertler vortex flow
Authors: Lee Kiseok , Liu Joseph T. C.
Published: July 2002

Spatially developing longitudinal vortices, originating from upstream Goertler vortices, are studied by a finite-difference algorithm. Three-dimensional parabolized Navier–Stokes equations for a ‘‘slightly’’ concave wall and a thin boundary layer are used, in conjunction with the total (mean plus perturbation) flow quantities as dependent variables. The behavior of Goertler vortex development from the linear region to the fully nonlinear region was obtained just prior to the development of secondary instabilities and turbulence. Comparisons with the experiments are discussed, showing the development of mushroomlike features in the streamwise velocity component.
On shock polar analysis and analytical expressions for vorticity deposition in shock-accelerated density-stratified interfaces
Authors: Samtaney Ravi , Zabusky Norman J.
Published: July 2002

Vorticity is deposited due to baroclinic effects on the surface of a density-stratified interface accelerated by a shock. An analytical expression is presented, derived from shock polar analysis, for circulation per unit length on a fast–slow planar density interface inclined at an angle to the incident shock. The analytical expression is integrated to yield total circulation on nonplanar interfaces (sinusoidal and semicircular interfaces) accelerated by shocks. The analytical results agree well with diagnostics from numerical experiments using a second-order Godunov code for the Euler equations.
The configurations of a FENE bead-spring chain in transient rheological flows and in a turbulent flow
Authors: Massah Heshmat , Kontomaris Kostas , Schowalter William R. , Hanratty Thomas J.
Published: July 2002

The changes in the configuration of a FENE bead-spring chain in a direct numerical simulation of turbulent channel flow and in some simple rheological flows are examined. Unraveling occurs both in uniaxial and shear flows, but the uniaxial flow is more effective. A vortex with a large rotation rate perpendicular to the principal strain of a uniaxial flow has only a minor retarding effect while a small rotation rate delays the unraveling substantially. In a turbulent flow, the chain unravels the most in the viscous sublayer, to about 90% of its fully extended length. It aligns at a 7° angle with the direction of mean flow. In the buffer zone, it unravels and coils up and takes different orientations at different times. Outside the wall region, the chain assumes a coiled configuration. The unraveling of the chain strongly depends on the relaxation time of the chain normalized with the wall shear rate, λ+. A value of λ+=10 exhibits strong unraveling while very weak unraveling is observed below λ+=1.
Experimental measurement of three-wave coupling and energy cascading
Authors: Ritz Ch. P. , Powers E. J. , Bengtson R. D.
Published: July 2002

The nonlinear coupling coefficient and the energy transfer associated with three-wave interactions are computed from measured data of the turbulent edge plasma of the Texas Experimental Tokamak(TEXT) [Nucl. Technol. Fusion 1, 479 (1981)]. The results show the presence of three-wave interactions. The interactions cause energy to cascade away from the dominant waves of the spectrum primarily toward lower, but also toward higher frequencies. The results are obtained with a new digital spectral analysis technique based on the estimation of higher-order cumulants. The method is discussed and tested on a simulation experiment. The same technique is useful for neutral fluids as well.
Canonical Hamiltonian guiding center variables
Authors: White Roscoe B.
Published: July 2002

A simplification of the canonical Hamiltonian variables for the guiding center motion of a charged particle in a general toroidal field is obtained using the Lagrangian formalism.
Collector and source sheaths of a finite ion temperature plasma
Authors: Schwager L. A. , Birdsall C. K.
Published: July 2002

The region between a Maxwellian plasma source and an absorbing surface is described theoretically with a static, kinetic plasma–sheath model and modeled numerically with a dynamic, electrostatic particle simulation. In the kinetic theory, Poisson’s equation and Vlasov equations govern the non-Maxwellian velocity distribution of the ions and electrons. The results in this paper for collector potential and plasma transport agree with the bounded model of Emmert et al. [Phys. Fluids 23, 803 (1980)]. However, this approach differs from those using traditional Bohm sheath analysis by ±0.25 (in units of electron temperature) for potential drop through the collector sheath of a hydrogen plasma. In both the theory and simulation, the plasma source injects equal fluxes of ions and electrons with half-Maxwellian velocities and various mass and temperature ratios and is assumed to have a zero electric field. The potential change within a spatially distributed, full Maxwellian source region is represented with the source sheath potential drop that depends primarily on temperature ratio. This source sheath evolves over a few Debye lengths from the source to neutralize the injected plasma. The plasma flows to an electrically floating collector where the more familiar electron-repelling collector sheath appears. The collector potential ψC and source sheath potential drop ψP (in units of electron temperature) are evaluated as a function of mass and temperature ratio. The velocity moments of density, drift velocity, temperature, kinetic energy flux, and heat flux are also derived as a function of ψC and ψP. Comparisons with electrostatic particle simulations are shown for the ion/electron mass ratios of 40 and 100 and temperature ratios of 0.1, 1, and 10. For a deuterium–tritium plasma (single-ion species with a mass of 2.5 amu) with equal ion and electron temperatures, then, ψC=−3.3 and ψP=−0.3. At the collector, the ions dominate the kinetic energy flux whereas the electrons dominate the heat flux. Ions reach the Bohm minimum energy well within the source sheath, obviating the need for a presheath acceleration.
Effects of higher-order dispersion on envelope solitons
Authors: Kuehl H. H. , Zhang C. Y.
Published: July 2002

The soliton modifications resulting from the addition of a small third derivative term, due to higher-order dispersion, to the nonlinear Schrödinger equation are investigated. Based on direct perturbation theory, it is shown that through first order, the soliton phase and velocity are modified, but the shape, amplitude, and width are unchanged. The radiation stimulated by the third derivative term, which is not predicted by the perturbation theory, is also derived. The expression obtained confirms the result of Wai (Ph.D. thesis, University of Maryland, 1988), which was obtained by a different method. The rate of change of the soliton amplitude due to this radiation, which emerges in front of the soliton, is calculated. The nonlinear term that drives the radiation is shown to grow to a value that is much larger than the unperturbed value.
Toroidal microinstability studies of high-temperature tokamaks
Authors: Rewoldt G. , Tang W. M.
Published: July 2002

Results from comprehensive kinetic microinstability calculations are presented, showing the effects of toroidicity on the ion temperature gradient mode and its relationship to the trapped-electron mode in high-temperature tokamak plasmas. The corresponding particle and energy fluxes have also been computed. It is found that, although drift-type microinstabilities persist over a wide range of values of the ion temperature gradient parameter ηi≡(d ln Ti/dr)/ (d ln ni/dr), the characteristic features of the dominant mode are those of the ηi-type instability when ηi>ηic∼1.2–1.4 and of the trapped-electron mode when ηi<ηic.
Plasma evolution from laser-driven gold disks. II. Computational design and analysis
Authors: Ress D. , Suter L. J. , Gabl E. F. , Failor B. H.
Published: July 2002

The lasnex computer code [Comments Plasma Phys. Controlled Fusion 2, 51 (1975)] was used in the design and analysis of an experimental study of laser-driven plasma blowoff from gold disks. In the study, several temporal profiles of 0.53 mm laser illumination were used, including square pulses, picket pulse trains, and pulses with graduated leading edges. Preliminary modeling suggested diagnostic techniques [time- and space-resolved imaging of M-band x-ray emission and time- and space-averaged measurements of high-energy (3.5–20 keV) x-ray spectra] that complemented diagnostics already used in such experiments (four-frame holographic imaging to determine the electron-density profile in the underdense corona plasma). In this article, the lasnex results are analyzed and are compared with the measured plasma electron-density profiles and with time- and space-averaged measurements of the corona temperature. The simulation tracks the observed electron-density profiles fairly well during the early portions of the laser drive, during which the spatial profiles are approximately self-similar, but overestimates the electron density in the later, steady-state segment of the profile. For the corona electron temperature, simulation and experiment agree to within the experimental accuracy of ±20%.
Relaxation for one-dimensional plasma: Test particles versus global distribution behavior
Authors: Rouet J. L. , Feix M. R.
Published: July 2002

The behavior of a one-dimensional weakly correlated plasma is studied using an exact algorithm. The simulations deal with a crucial point of the kinetic linearized theory (Lenard–Balescu equation). This equation describes the evolution of different subpopulations, introduced by a ‘‘gedanken experiment’’ easily performed on the computer, which exhibits the different scalings of the relaxation times of ‘‘distinguished’’ particles and overall population.
Linear studies of m=1 modes in high-temperature plasmas with a four-field model
Authors: Aydemir A. Y.
Published: July 2002

The m=1 mode in high temperature plasmas is examined using a simple four-field model of tokamak dynamics derived by Hazeltine et al. [Phys. Fluids 30, 3204 (1987)]. It is shown that, despite its simplicity, the model reproduces with remarkable accuracy results obtained with more sophisticated kinetic treatments in various collisionality regimes. The effects of parallel compressibility on the m=1 mode in the collisional, semicollisional, and collisionless regimes are also discussed. Coupling to the ion sound waves is found to be weakly destabilizing in the collisional regime, and stabilizing in the semicollisional and collisionless regimes.
Inclusion of poloidal potential variation in neoclassical transport
Authors: Stringer T. E.
Published: July 2002

Inclusion of the electrostatic potential is found to increase the electron neoclassical heat flux by an order of magnitude, while producing only a modest increase in the ion heat flux. The analysis is done for the plateau regime, though a similar behavior is expected in the banana regime. The poloidally varying potential, determined by quasineutrality, is predominantly due to ion Landau damping. The resulting E×B drift introduces terms into the electron heat flux that are comparable to those previously derived for the ion heat flux. Similar terms enter the particle flux, but here they cancel due to momentum balance.
Evidence of stimulated Raman scattering occurring in laser filaments in long-scale-length plasmas
Authors: Afshar-rad T. , Coe S. E. , Willi O. , Desselberger M.
Published: July 2002

A time-resolved study is presented of stimulated Raman backscatter (B-SRS) produced in a large-scale-length preformed plasma in an intense laser pulse. The first direct experimental results are presented to (i) show that the B-SRS is generated predominantly in laser filaments and (ii) provide a direct correlation between the spectral and spatial emission profiles of the B-SRS as a function of interaction irradiance. The ‘‘anomalous’’ B-SRS spectral features so commonly reported in time-resolved studies are shown to be the characteristic emission of B-SRS from filaments. The B-SRS fraction was also measured as a function of interaction irradiance. The B-SRS intensity ‘‘threshold’’ and ‘‘saturating’’ behavior recorded can be well described for the present interaction conditions. The onset of B-SRS is shown to be strongly correlated with the intensity threshold of the filamentation instability. The effect of laser beam ‘‘smoothing’’ techniques on the B-SRS emission have also been investigated, using either a random phase plate (RPP) or induced spatial incoherence (ISI). The results suggest that their effectiveness in suppressing B-SRS is strongly associated with their ability to reduce the level of filamentation while still producing a high level of plasma perturbation which can effectively destroy the phase-matching conditions necessary for B-SRS.
Sheath evolution in a negative ion plasma
Authors: Amin Ali , Aossey David , Nguyen Binh Ton , Kim Hyun-Soo , Cooney Jamie L. , Lonngren Karl E.
Published: July 2002

The spatial and temporal evolution of a sheath surrounding a planar electrode whose potential is suddenly decreased in a quasineutral plasma consisting of positive ions, negative ions, and electrons is numerically investigated. The model predicts several features observed in recent laboratory experiments directed toward the excitation and subsequent propagation of solitons in such a plasma.