bluuebunny/crossref_metadata_2025 huggingface dataset:
Tunnelling lifetimes of metastable and binding properties of stable covalent BeCn2− (n=4,6) dianions
Authors: Dreuw A. , Cederbaum L. S.
Published: July 2002

Mixed beryllium carbon dianions BeC42− and BeC62− have been examined using ab initio methods. The dianionic systems have been investigated in detail with respect to electron autodetachment as well as with respect to fragmentation. Only linear isomers have been found to represent geometrically stable isomers, i.e., are minima on the corresponding potential energy surfaces. While a linear isomer of the BeC42− dianions lies on the verge of electronic stability, a linear isomer of the BeC62− dianions, better referred to as C2BeC42−, is the smallest free stable Be–C dianion. To estimate the lifetime of the BeC42− system we have calculated the repulsive Coulomb barrier following ab initio approaches introduced in this work and used this potential to compute the tunnel probability with the help of Wentzel–Kramer–Brioullin theory. The tunnel probability makes the lifetime of the system directly accessible, when the electron detachment energy (EDE) is known. All calculated EDEs yield lifetimes markedly longer than 5 μs, which is the lower limit for experimental observation in a mass spectrometer.
Surface of active polarons: A semiexplicit solvation method for biomolecular dynamics
Authors: Kimura S. Roy , Brower Richard C. , Zhang Chao , Sugimori Masamichi
Published: July 2002

We present a strategy for solvating biomolecules in molecular dynamics or Monte Carlo simulations. The method employs a thin layer (often monomolecular) of explicit water with additional external forces representing the electrostatics, pressure, fluctuations, and dissipations caused by the neglected bulk. Long-range electrostatic corrections are supplied through a set of variable surface charges (polarons) that recreates the mean reaction field (or dielectric properties) of an infinite solvent. We refer to this “fictitious” boundary layer as a “surface of active polarons” (or SOAP). Test simulations of the solvation free energies of 15 amino acid analogs and nine ions are in good agreement with experiment (correlation coefficients: 0.995 and 1.000, respectively) despite the use of unaltered published force-fields with only one adjustable parameter. Dynamical capabilities of SOAP are illustrated by application to a six residue peptide with a stable conformation (SYPFDV), as well as a flexible nine residue HIV-1 gp120 peptide (TLTSCNTSV from PDB 1hhg). Future extensions, calibrations, and applications are discussed briefly.
Evidence of Fermi resonance in core-ionized methane
Authors: Karlsen Tor , Bo/rve Knut J.
Published: July 2002

A full quartic potential energy surface is determined for core-ionized methane and used to investigate coupling between vibrational modes. A strong Fermi resonance is found between the first excited state of the symmetric stretching mode ν1′ and a doubly excited bending mode, whereas the corresponding interaction is less pronounced for v1′=2. In terms of the carbon 1s photoelectron spectrum of methane, the net effect of the mode coupling is to reduce the apparent contribution from anharmonicity to peak positions. The contribution from anharmonicity to the intensity of each peak is dominated by cubic and quartic terms in the symmetric stretching coordinate, and remains significant. This resolves a paradox pointed out in a recent experimental work [Carroll et al., Phys. Rev. A 59, 3386 (1999)].
Extraction of interaction potentials between amino acids from native protein structures
Authors: Dima Ruxandra I. , Settanni Giovanni , Micheletti Cristian , Banavar Jayanth R. , Maritan Amos
Published: July 2002

We discuss methods for the determination of the effective pairwise interactions between amino acids in globular proteins in order to be able to easily recognize the native state conformation of any protein sequence among a set of decoy structures. The first method entails the application of a numerical strategy to a training set of proteins that maximizes the native fold stability with respect to alternative structures. The extracted parameters are shown to be very reliable for identifying the native states of proteins (unrelated to those in the training set) among thousands of conformations. Folding transition temperatures are estimated for a few proteins for which reliable alternative structures have recently been generated. The only poor performers are proteins with stabilizing heme groups whose complexity cannot be captured by standard pairwise energy functionals. The key ingredient of this technique is the knowledge of viable decoys for each protein sequence in the training set. We then present a second strategy which circumvents this difficulty. This method relies on the fact that protein sequences are special compared to random heteropolymers and are characterized by high thermodynamic stability in their native conformations. We validate the technique on a lattice model of proteins, we apply it to real proteins and carry out tests of the quality of the extracted interaction parameters. We find that this novel technique leads to good results that are comparable to those obtained with the first method.
Vibrational spectroscopy of a transient species through time-resolved Fourier transform infrared emission spectroscopy: The vinyl radical
Authors: Letendre Laura , Liu Dean-Kuo , Pibel Charles D. , Halpern Joshua B. , Dai Hai-Lung
Published: July 2002

An approach for detecting the vibrational spectrum of transient species is demonstrated on the vinyl radical. Photodissociation of carefully chosen precursors at selected photolysis wavelengths produce highly vibrationally excited radicals. Infrared (IR) emission from these radicals is then measured by time-resolved Fourier transform spectroscopy with nanosecond time resolution. All nine vibrational bands of the vinyl radical, generated from four different precursors, are obtained and reported here for the first time.
Photoionization dynamics probed by angle-resolved photoelectron spectroscopy of NH3(B̃ 1E″)
Authors: Townsend Dave , Reid Katharine L.
Published: July 2002

We show that the photoionization dynamics of a small excited polyatomic molecule can be partially elucidated from the measurement of photoelectron angular distributions (PADs) at an energy resolution of only around 20 meV following excitation of various selected rotational levels in an excited electronic state. To illustrate this we present PADs corresponding to the formation of vibrationally resolved NH3+ following the excitation of NH3 to selected rotational levels in its B̃ 1E″ electronic state. We also present a preliminary time-of-flight photoelectron spectrum showing peaks corresponding to resolved rotational levels of the NH3+ ion.
Combination of small angle scattering and three-dimensional stochastic reconstruction for the study of adsorption–desorption processes in Vycor porous glass
Authors: Kikkinides E. S. , Kainourgiakis M. E. , Stefanopoulos K. L. , Mitropoulos A. Ch. , Stubos A. K. , Kanellopoulos N. K.
Published: July 2002

We study sorption and transport processes in dry and wet (preadsorbed with CH2Br2) Vycor glass by combining small angle scattering and three-dimensional (3D) stochastic reconstruction methods. Three-phase systems of solid, condensate, and void space, are generated for the first time, by the combination of the above methods. The resulting 3D images can visualize the evolution of the adsorption process and show how sorption alters the pore space characteristics of the material. Desorption is modeled in this system with the additional employment of an invasion percolation algorithm to account for the hysteresis effect caused by the inaccessible regions of the porous matrix. It is found that desorption is simulated very well provided that the main mechanism for hysteresis depends only on the topology of the pore space and not on thermodynamic effects. Based on a random-walk procedure, Knudsen transport properties of the reconstructed images are also determined for different degrees of saturation, providing very good agreement with experimental relative permeability data. Thus, relative permeability reflects purely the pore accessibility properties of the material and may assist in discerning their exact contribution to the equilibrium sorption hysteresis loop.
Rotational energy transfer within CH A 2Δ(v=0) and B 2Σ−(v=0) states by collisions with He, Ar, N2, CO, N2O, and CHBr3 using a time-resolved Fourier transform spectrometer
Authors: Wang Chaung-Chi , Chen Yu-Pern , Chin Thou-Long , Huang Hong-Yi , Lin King-Chuen
Published: July 2002

By using a step-scan Fourier transform spectrometer, we have studied collisionally-induced rotational energy transfer (RET) of the CH A(2Δ) (N⩽16,v=0) and B(2Σ−) (N⩽16,v=0) states. The collision partners used for the B state are He, Ar, N2, CO, N2O, and CHBr3, while He and Ar are for the A state. The time-resolved spectra obtained in the nanosecond regime may yield the RET information straightforward under a single pressure of the collider. The resultant RET rate constants for both states range from 10−12 to 10−10 cm3 molecule−1 s−1, comparable to the gas kinetic. The trend follows the order of He∼Ar<N2∼CO<N2O<CHBr3 for the B state, and He<Ar for the A state. For the B state, the findings of multi-quantum changing collisions up to ΔN=±3 and markedly large rate constants imply that the RET collisions are dominated by long-range attractive force. The collision complexes possibly formed between the CH(B) and the colliders are long-lived enough to allow for effective removal of the rotational energy more than a quantum level in a single collision. In contrast, a single quantum change in the RET collision found in the A state suggests dominance of a repulsive interaction between the colliding species, which has been verified previously in the measurements of temperature dependence of the electronic quenching.
Fourier transform emission spectrum of the HCSi radical, Ã 2Σ+–X̃ 2Πi transition
Authors: Cireasa R. , Cossart D. , Vervloet M. , Robbe J. M.
Published: July 2002

A Fourier transform emission spectrum of the HCSi, Ã 2Σ+–X̃ 2Πi transition was observed by means of a Schüler-type discharge tube in the 9000–14 000 cm−1 spectral region. Three bands whose origins appeared at 12 934.406, 11 766.721, and 10 752.430 cm−1 were rotationally analyzed and assigned, respectively, to the (100)–(000), (000)–(000), and (000)–(100) bands. The new ab initio calculated A(X̃ 2Π) spin–orbit constant agrees well with the experimental value. Weak rotational perturbations in the (100) level of the upper electronic state are likely due to highly excited vibrational levels of the ground state, whereas the “anomalous” increase of the spin–rotation constant in the (100) level of the ground state relative to the (000) level was shown to result of a Fermi interaction with the (020) Π2 Renner–Teller components. A comparison was made between the rotational constants of the (000) ground state level with those obtained in concomitant works.
Resonant ion-dip infrared spectroscopy of benzene–(water)9: Expanding the cube
Authors: Gruenloh Christopher J. , Carney Joel R. , Hagemeister Fredrick C. , Zwier Timothy S. , Wood John T. , Jordan Kenneth D.
Published: July 2002

The techniques of resonant two-photon ionization (R2PI), UV-UV hole-burning, and resonant ion-dip infrared (RIDIR) spectroscopy have been employed along with density functional theory (DFT) calculations to characterize the hydrogen-bonding topologies of three isomers of benzene–(water)9. Isomers I and II, with R2PI transitions shifted, respectively, by +77 and +63 cm−1 from the benzene monomer, have similar intensities in the R2PI spectrum. The signal from the third isomer (isomer III, shifted +60 cm−1) is present at about one-fourth the intensity of the other two. The experimental RIDIR spectrum of isomer I bears a strong resemblance to the spectrum of the benzene–(water)8 D2d-symmetry cubic structure identified in earlier work, but possessing an extra single-donor transition associated with the ninth water molecule. Using the S4 and D2d symmetry forms of the water octamer as base structures to which the ninth water molecule can be added, a total of nine “expanded-cube” structures are identified for W9 arising from two distinct insertion points in the W8(D2d) cube (D1,D2) and three such points in the W8(S4) cube (S1-S3). DFT calculations predict these to be spread over an energy range of less than 1 kcal/mol. Given that each of the nine “expanded-cube” (water)9 structures contains five symmetry-inequivalent free OH groups, a total of 45 “expanded-cube” benzene–(water)9 conformational isomers are predicted. Structural and vibrational frequency calculations have been performed on seven of these to determine how the (water)9 structural type and the attachment point of benzene to the structure affect the total energy and vibrational frequencies of the cluster. Based on a comparison of the experimental RIDIR spectrum with the calculated vibrational frequencies and infrared intensities, isomer I is attributed to the BW9(D1) structure in which benzene attaches to W9(D1) at the free OH of the water molecule which donates a H-bond to the ninth water. This structure has a calculated binding energy that is about 0.13 kcal/mol greater in magnitude than any other benzene–(water)9 isomer studied. The experimental spectra of isomers II and III are of insufficient quality to assign them to specific BW9 structures with confidence. However, isomer II is most consistent with an S4-derived expanded cube structure (either S1 or S2), while isomer III shows characteristics consistent with a second D1-derived BW9 structure in which benzene is attached at a position on the expanded cube remote from the ninth water.
Character table for the 1080-element point-group-like subgroup of SU(3)
Authors: Flyvbjerg Henrik
Published: July 2002

The character table for S(1080), the largest point-group-like subgroup of SU(3), is presented. So is the reduction of the first 28 SU(3) characters to S(1080) characters. These tables are needed in a recently proposed systematic description of SU(3)-invariant lattice gauge theories by effective S(1080)-invariant theories. Problems encountered in an alternative systematics, using only local S(1080)-invariant theories, are discussed.
Soliton solutions for self-dual SU(3) gauge field theory
Authors: Papadopoulos Demetrios
Published: July 2002

The Belinskii–Zakharov technique is applied to find a soliton solution for self-dual SU(3) gauge fields with axial symmetry on a Euclidean four-dimensional flat space. We find that for the special case of solutions generated from a special class of diagonal seed solutions the obtained soliton solutions reduce to quadratures.
Statistical mechanics in a conformally static setting. II
Authors: Kandrup Henry E.
Published: July 2002

This paper examines the statistical mechanics of a collection of N identical, classical point masses, which interact relativistically via a simple scalar field in a conformally static background geometry. The model system considered here should be representative of any system in which the particle and field equations are both linear. Attention focuses first upon the formulation of exact equations for the evolution of appropriately defined reduced distribution functions and the interpretation of these relations. In particular, a projection operator formalism is used to derive exact coupled equations for the evolution of the irreducible one-particle and one-oscillator distributions, which contain no explicit reference to more complicated particle–oscillator correlation functions. Attention focuses also upon the issue of how the analysis would be further complicated by allowing for nonlinear effects, e.g., in the particle equations of motion. The subtleties that arise in this case serve to indicate the limitations of the kinetic theory of self-gravitating systems developed by Israel and Kandrup, which entails the consideration of particle and field equations linearized about some (possibly highly nontrivial!) background solution.
Bianchi type-VI solutions in modified Brans–Dicke cosmology
Authors: Ram Shri
Published: July 2002

The spatially homogeneous and anisotropic Bianchi type-VI0 cosmological dust solution for the modified Brans–Dicke theory is presented. Some properties of the model are discussed.
Global existence and asymptotic behavior for the discrete velocity models of the Boltzmann equation
Authors: Toscani G.
Published: July 2002

By using fixed point techniques, some theorems which supply local and global existence, uniqueness, and asymptotic behavior of the solution of a general discrete velocity model of the Boltzmann equation in three dimensions are given.
On a class of differential equations derived from plasma statistics
Authors: Liboff Richard L.
Published: July 2002

A class of second-order differential equations stemming from an equation of motion for the two-particle spatial correlation function in one-component plasmas is studied. These equations contain an irregular singularity of varying order at the origin. The general form of solution is obtained which, together with the construction of asymptotic series, demonstrates that both solutions to all equations in the class are singular at the origin. Behavior removed from the origin is shown to be oscillatory or exponential depending on specifics of the equations.
Rotation in cosmology: Comments on ‘‘Imparting rotation to a Bianchi type II space-time,’’ by M. J. Rebouças and J. B. S. d’Olival [J. Math. Phys. 2
7, 417 (1986)] and similar papers
Authors: Jantzen Robert T.
Published: July 2002

The aim of this paper is to clarify confusing notions of the word ‘‘rotation’’ as applied to cosmological solutions of metric theories of gravity, both in general and in the specific case addressed by the article in which these confusing notions have recently reappeared.
Green’s functions for nonlinear Klein–Gordon kink perturbation theory
Authors: Flesch R. J. , Trullinger S. E.
Published: July 2002

A Green’s function is defined for nonlinear Klein–Gordon theories in terms of the solutions to the eigenvalue equation obtained by linearizing the nonlinear wave equation about a static kink waveform. Analytic forms in terms of ‘‘modified’’ Lommel functions of two variables are derived for the sine–Gordon, phi-4, and double quadratic potentials. Asymptotic forms for the Green’s functions are obtained by investigating the asymptotic behavior of the modified Lommel functions. Methods for calculating the Lommel functions are also outlined.
Differential-difference AKNS equations and homogeneous Heisenberg algebras
Authors: Bergvelt M. J. , ten Kroode A. P. E.
Published: July 2002

The well-known evolution equations associated to the homogeneous Heisenberg algebras of Kac–Moody algebras g(1) (AKNS systems) are extended by differential-difference equations that can be written in zero curvature form.
Canonical stochastic dynamical systems
Authors: Misawa Tetsuya , Yasue Kunio
Published: July 2002

A canonical stochastic dynamical system for time-symmetric semimartingales is formulated by the stochastic least action principle in a new stochastic calculus of variations. A certain class of stochastic dynamical systems gives a Hamiltonian formalism of Nelson’s stochastic mechanics. In a manner analogous to classical mechanics, the notions of a stochastic Poisson bracket and canonical transformation are introduced to the stochastic dynamical systems. It is shown that the phase factor of the wave function plays the role of a generating function of the canonical transformation.
On a new class of completely integrable nonlinear wave equations. II. Multi-Hamiltonian structure
Authors: Nutku Y.
Published: July 2002

The multi-Hamiltonian structure of a class of nonlinear wave equations governing the propagation of finite amplitude waves is discussed. Infinitely many conservation laws had earlier been obtained for these equations. Starting from a (primary) Hamiltonian formulation of these equations the necessary and sufficient conditions for the existence of bi-Hamiltonian structure are obtained and it is shown that the second Hamiltonian operator can be constructed solely through a knowledge of the first Hamiltonian function. The recursion operator which first appears at the level of bi-Hamiltonian structure gives rise to an infinite sequence of conserved Hamiltonians. It is found that in general there exist two different infinite sequences of conserved quantities for these equations. The recursion relation defining higher Hamiltonian structures enables one to obtain the necessary and sufficient conditions for the existence of the (k+1)st Hamiltonian operator which depends on the kth Hamiltonian function. The infinite sequence of conserved Hamiltonians are common to all the higher Hamiltonian structures. The equations of gas dynamics are discussed as an illustration of this formalism and it is shown that in general they admit tri-Hamiltonian structure with two distinct infinite sets of conserved quantities. The isothermal case of γ=1 is an exceptional one that requires separate treatment. This corresponds to a specialization of the equations governing the expansion of plasma into vacuum which will be shown to be equivalent to Poisson’s equation in nonlinear acoustics.
Interference in the radiation of two relativistic charges
Authors: Hojman R. , Palma G. , Peña L. , Tabensky R.
Published: July 2002

The radiation produced by two interacting relativistic point charges is considered. Under an appropriate approximation the radiation of the system as a whole (interference effects included) is expressed as a function of the relative velocity.
Collapse and exponentiation of infinite symmetry algebras of Euclidean projective and Grassmannian σ models
Authors: Arsenault Guy , Jacques Michel , Saint-Aubin Yvan
Published: July 2002

Various two-dimensional σ models enjoy an infinite set of infinitesimal transformations acting on their solution space. The action of these symmetries is investigated for the Euclidean projective and Grassmannian σ models. On the (anti-) self-dual sector of the latter, the algebra of symmetries is shown to collapse to a finite-dimensional algebra isomorphic to sl(n+1,C) for the models with fields in the Grassmannians Gn+1,p. The finite action obtained by exponentiation is given in a closed form. For CPn models, this result is extended to the whole space of finite action solutions and the structure of the algebra remains sl(n+1,C). Hence the action is not transitive on the solution space.
On modeling discontinuous media. One-dimensional approximations
Authors: Sabatier P. C. , Dolveck-Guilpard B.
Published: July 2002

Distorted wave Born series are derived for the impedance equation [A−1(d/dx)A(d/dx)+k2]p=0, where A is a piecewise differentiable function. The first and second orders are given explicitly. They hold for impedances A, which include discontinuities, before and/or after perturbation, so that the problem could not be reduced to the Schrödinger one. The results are used for discussing homogenizations currently practiced in modeling discontinuous media.
Finitely many δ interactions with supports on concentric spheres
Authors: Shabani J.
Published: July 2002

Using the theory of self-adjoint extensions of symmetric operators the precise mathematical definition of the quantum Hamiltonian describing a finite number of δ interactions with supports on concentric spheres is given. Its resolvent is also derived, its spectral properties are described, and it is shown how this Hamiltonian can be obtained as a norm resolvent limit of a family of local scaled short-range Hamiltonians.
Application of spectral deformation to the Vlasov–Poisson system. II. Mathematical results
Authors: Hislop Peter D. , Crawford John David
Published: July 2002

This paper presents a mathematical description of the linearized Vlasov–Poisson operator Lk acting on a family of Banach spaces Xp, related to L p (R), and the application of the method of spectral deformation to this model. It is shown that a type-A analytic family of operators Lk(θ), θ∈C, Lk(0) =Lk can be associated with Lk. By means of this family, the Landau damped modes of the plasma are identified as the spectral resonances of Lk. Existence and uniqueness of solutions to the initial-value problem for the evolution equation ∂ν g =Lk(θ)g is proven. An expansion of any solution to the initial-value problem (with sufficiently smooth initial data) is obtained in terms of the eigenfunctions of Lk(θ) and a spectral integral over the essential spectrum. This is applied to derive an expansion for solutions to the Vlasov equation in which the Landau damped portions of the distribution function are manifestly exhibited. A self-contained discussion of the spectral deformation method and an extension of it to certain closed operators on Banach spaces is also given.
On modeling discontinuous media. Three-dimensional scattering
Authors: Sabatier P. C.
Published: July 2002

A realistic model for the propagation of scalar waves in a medium must take into account discontinuities of the medium parameters, which may act as ‘‘hard’’ reflectors; discontinuities of their gradient, which may act as ‘‘soft’’ reflectors; and continuous variations of parameters. The direct scattering problem is presented here. The ‘‘mixed potential–impedance’’ equation that characterizes the model depends on two arbitrary parameters: one of them would be the potential if the equation reduces to the Schrödinger equation; the other one would be related to the impedance if the equation describes more ‘‘classical’’ waves. After the mathematical tools are constructed (Green’s functions, etc.), a rigorous three-dimensional scattering theory is described. It encompasses the quantum three-dimensional scattering theory and the theory of acoustical scattering (for instance) by systems of regular surfaces of arbitrary shape. The main integral equations of the quantum scattering theory are generalized. Scattering amplitudes due to reflectors and scattering amplitudes due to diffuse scattering after reflectors have been taken into account are defined and constructed. Born and quadratic approximations are discussed: the explicit formulas corresponding to the scattering by discontinuities and those corresponding to diffuse scattering are not reducible to each other exactly (i.e., unless filtering and errors are allowed). The results can also be used to described rigorously the three-dimensional scattering by the ‘‘wave-equation’’ in the frequency domain—and in particular the response to an impulsive localized source. Further generalizations are in progress.
On Clebsch–Gordan coefficients and matrix elements of representations of the quantum algebra U
q(su2)
Authors: Groza V. A. , Kachurik I. I. , Klimyk A. U.
Published: July 2002

Clebsch–Gordan coefficients and matrix elements of irreducible representations of the quantum algebra Uq(su2) were considered in several papers. In particular, a few expressions for them were derived. An approach to Clebsch–Gordan coefficients and to matrix elements of representations of Uq(su2) on the base of the theory of basic hypergeometric functions is given. This approach allows one to obtain q-analogs of all well-known classical expressions for Clebsch–Gordan coefficients (most of them were absent). New symmetry relations, generating functions, and recurrence formulas for Clebsch–Gordan coefficients of Uq(su2) are obtained. Unlike other papers, Clebsch–Gordan coefficients and matrix elements are considered on the base of minimal theoretical constructions (in fact, without using the notion of a C* algebra and of a Hopf algebra).
Dilation currents
Authors: Benn I. M. , Wood W. P.
Published: July 2002

The conserved currents related to conformal Killing vectors are analyzed. By considering the dilation generator of Minkowski space-time, with the assumption that fields are static, arrived at is what is often known as the relativistic virial theorem. The application of this result to force-free electromagnetic fields is discussed, and the result is shown how it can rule out particlelike solutions to certain field theories.
Energy levels of a three-dimensional anharmonic oscillator with sextic perturbation
Authors: Witwit M. R. M.
Published: July 2002

Renormalized series version of inner product and renormalized series techniques with Hill determinant approach are used to calculate the energy eigenvalues for a three-dimensional oscillator for several sets of parameters. Our techniques were modified to treat higher power of perturbation for two eigenstates E0,0,1 and E1,1,0 with odd parity.
Self-dual connections, torsion and Ashtekar’s variables
Authors: Maluf José W.
Published: July 2002

Two identities are derived in terms of an arbitrary self-dual connection and the associated spin connection which show that torsion contributes to the simple complex-valued structure of the Hamiltonian and vector constraints in Ashtekar’s formulation of canonical gravity. A comparison is established between the Hamiltonian formulations of the Einstein–Cartan–Sciama–Kibble (ECSK) theory and the one in terms of Ashtekar’s variables, both in the matter-free case, in order to emphasize that in the latter the torsion tensor restricted to three-dimensional spacelike hypersurface does not vanish prior to the imposition of the reality conditions.
Realization of a class of affine Lie superalgebras
Authors: Su Yucai
Published: July 2002

In this paper, a class of affine Lie superalgebras is presented, whose Dynkin diagrams are constructed by, as usual, extending a Dynkin diagram D of Lie algebra (or superalgebra) by adding a node ψ that corresponds to the lowest root ψ0 of D. However, this added node ψ does not have the same degree as ψ0 in Z2 gradation (Z2=Z/2Z), i.e., ψ corresponds to an odd or even root as ψ0 corresponds to even or odd root. As far as we know, these Lie superalgebras did not appear in literature, and therefore we believe these are a new class of affine Lie superalgebras.
One-dimensional nonautonomous dynamical systems with exact transcendental invariants
Authors: Pereira L. G. , Goedert J.
Published: July 2002

New classes of dynamical systems for nonautonomous particle motion in one dimension are exactly solved in terms of arbitrary functions of both space and time. Besides extending considerably the class of mechanical systems with known exact solutions, the explicit dependence on space represents an improvement on previous results, such as those obtained by Lewis and Leach. This might be helpful for extending the Lewis and Symon technique of constructing the BGKY type of solutions for the Vlasov–Poisson equations.
Inverse scattering in 1-D nonhomogeneous media and recovery of the wave speed
Authors: Aktosun Tuncay , Klaus Martin , van der Mee Cornelis
Published: July 2002

The inverse scattering problem for the 1-D Schrödinger equation d2ψ/dx2 + k2ψ= k2P(x)ψ + Q(x)ψ is studied. This equation is equivalent to the 1-D wave equation with speed 1/√1−P(x) in a nonhomogeneous medium where Q(x) acts as a restoring force. When Q(x) is integrable with a finite first moment, P(x)<1 and bounded below and satisfies two integrability conditions, P(x) is recovered uniquely when the scattering data and Q(x) are known. Some explicitly solved examples are provided.
Fundamental algebra for quantum mechanics on S
D and gauge potentials
Authors: Ohnuki Y. , Kitakado S.
Published: July 2002

Quantum mechanics on SD is formulated. The algebra of (D+1)-dimensional Euclidean group is set up as fundamental commutation relation, which plays the role of the ordinary canonical algebra on the flat space. Compared to the standard procedure of using Dirac’s formalism for quantization of the constrained system, our method leads to more general results. Monopolelike structure appears inside the SD, which becomes visible when the space is cut by 3-dimensional hyperplane. Gauge potential for this structure is obtained. We also show, that no higher dimensional singularity can appear inside the SD.
Integrals of motion for the Lorenz system
Authors: Gupta Neelam
Published: July 2002

A direct method is proposed for determining the conditions under which the Lorenz system is integrable. This method uses only leading singular behavior to recover all known integrals of motion together with a few new ones.
A superalgebra U
q[osp(3/2)] generated by deformed paraoperators and its morphism onto a W
q(1/1) Clifford–Weyl algebra
Authors: Palev Tchavdar D.
Published: July 2002

A deformed universal enveloping superalgebra Uq of the Lie superalgebra osp(3/2), which is a Hopf algebra, is defined as freely generated by deformed para-Bose operators B± and deformed para-Fermi operators F±. The q analog of the Cartan–Weyl basis and all deformed supercommutation relations between the generators are written down. A morphism of Uq onto a deformed Clifford–Weyl superalgebra Wq(1/1)a is constructed, where Wq(1/1)a is generated by q bosons b± and q fermions f± under the condition that the q bosons anticommute with the q fermions. The corresponding oscillator representation is studied.
Classification of scalar fields in general relativity
Authors: Santos J. , Rebouças M. J. , Teixeira A. F. F.
Published: July 2002

Canonical forms for the energy–momentum tensor of the scalar field in the framework of general relativity are derived and algebraically classified. Four different types arise depending on the vectorial character of the gradient of the scalar field. For each canonical form a solution of the Einstein-massless scalar field equations is presented. There emerges from our investigation alternative physical interpretation for two known space–times.
Cylindrically symmetric thin walls in general relativity
Authors: Khorrami M. , Mansouri R.
Published: July 2002

Assuming a continuous ansatz for the metric the Einstein equations for a thin wall with cylindrical symmetry are solved herein. The solution can correspond to a collapsing matter shell leading to a naked, without horizon, singularity.
Nonuniqueness in inverse acoustic scattering on the line
Authors: Aktosun Tuncay , van der Mee Cornelis
Published: July 2002

The generalized one-dimensional Schrödinger equation d2φ/dx2+k2H(x)2φ =P(x)φ is considered. The nonuniqueness is studied in the recovery of the function P(x) when the scattering matrix, H(x), and the bound state energies and norming constants are known. It is shown that when the reflection coefficient is unity at zero energy, there is a one-parameter family of functions P(x) corresponding to the same scattering data. An explicitly solved example is provided. The construction of H(x) from the scattering data is also discussed when H(x) is piecewise continuous, and two explicitly solved examples are given with H(x) containing a jump discontinuity.
Nonsingular gravity without black holes
Authors: Cornish Neil J. , Moffat John W.
Published: July 2002

A nonsingular static spherically symmetric solution of the nonsymmetric gravitational and electromagnetic theory (NGET) field equations is derived, which depends on the four parameters m,l2,Q and s, where m is the mass, Q is the electric charge, l2 is the NGT charge of a body and s is a dimensionless constant. The electromagnetic field invariant is also singularity-free, so that it is possible to construct regular particlelike solutions in the theory. All the curvature invariants are finite, there are no null surfaces in the spacetime and there are no black holes. A new stable, superdense object (SDO) replaces black holes.
Classical extended conformal algebras associated with constrained KP hierarchy
Authors: Huang Wen-Jui , Shaw J. C. , Yen H. C.
Published: July 2002

The conformal property of the second Hamiltonian structure of constrained KP hierarchy derived by Oevel and Strampp is examined. It is found that it naturally gives a family of nonlocal extended conformal algebras. Two examples of such algebras are given and it is found that they are similar to Bilal’s V algebra. By taking a gauge transformation one can map the constrained KP hierarchy to Kupershmidt’s nonstandard Lax hierarchy. The second Hamiltonian structure in this representation is considered. It is shown that after mapping the Lax operator to a pure differential operator the second structure becomes the sum of the second and the third Gelfand–Dickey brackets defined by this differential operator. The corresponding conformally covariant form of this differential operator is also given.
Black holes and nonlinear scalar fields: A dynamical system approach
Authors: de Oliveira H. P.
Published: July 2002

All the solutions of a three-dimensional dynamical system describing the static and spherically symmetric solutions for a nonlinear scalar field of the Born–Infeld type are studied qualitatively. It is shown that a horizon exists for a large class of solutions in which the scalar field is finite. However, this horizon is singular. In another class of solutions, naked singularities with an everywhere well-behaved scalar field have been found.
Space–time defects: Open and closed shells
Authors: Letelier Patricio S.
Published: July 2002

A class of space–times with zero curvature tensor except on a hypersurface is derived; in particular, metrics that represent parabolic and cylindrical plates, and parabolic, spherical, spheroidal, and toroidal shells are studied. The motion of particles around and inside the defects is considered. The interpretation of some of these space–times as wormholes is briefly considered.
Classification of second order symmetric tensors in five-dimensional Kaluza–Klein-type theories
Authors: Santos J. , Rebouças M. J. , Teixeira A. F. F.
Published: July 2002

An algebraic classification of second order symmetric tensors in five-dimensional Kaluza–Klein-type Lorentzian spaces is presented by using Jordan matrices. It is shown that the possible Segre types are [1,1111], [2111], [311], [zz̄111], and the degeneracies thereof. A set of canonical forms for each Segre type is found. The possible continuous groups of symmetry for each canonical form are also studied.
Eigenvalue integrodifferential equations for orthogonal polynomials on the real line
Authors: Bender Carl M. , Feinberg Joshua
Published: July 2002

The one-dimensional harmonic oscillator wave functions are solutions to a Sturm–Liouville problem posed on the whole real line. This problem generates the Hermite polynomials. However, no other set of orthogonal polynomials can be obtained from a Sturm–Liouville problem on the whole real line. In this paper it is shown how to characterize an arbitrary set of polynomials orthogonal on (−∞,∞) in terms of a system of integrodifferential equations of the Hartree–Fock type. This system replaces and generalizes the linear differential equation associated with a Sturm–Liouville problem. Our results are demonstrated for the special case of continuous Hahn polynomials.
Realizing 3-cocycles as obstructions
Authors: Carey A. L. , Grundling H. , Hurst C. A. , Langmann E.
Published: July 2002

The occurrence of a 3-cocycle in quantum mechanics or quantum field theory has been interpreted somewhat paradoxically as a breakdown of the Jacobi identity. The main result of this paper is that the 3-cocycle in chiral QCD arises as an obstruction which prevents the existence of a certain extension of one Lie algebra by another. This obstruction may be avoided by constructing a modified Lie algebra extension consisting of derivations on the algebra generated by the fields. However the 3-cocycle then appears when an attempt is made to implement these derivations by commutation with unbounded operators in the canonical equal-time formalism. Assuming the existence of these unbounded operators is what leads to the violation of the Jacobi identity.
Dirac monopoles and the Seiberg–Witten monopole equations
Authors: Freund Peter G. O.
Published: July 2002

A simple solution of the Seiberg–Witten monopole equations is given.
Induced QCD from the noncommutative geometry of a supermanifold
Authors: Kalkkinen Jussi
Published: July 2002

The noncommutative geometry of a two-leaf Parisi–Sourlas supermanifold in Connes’ formalism using different K cycles over the Grassmann algebra-valued functions on the supermanifold is studied. We find that the curvature of the trivial noncommutative vector bundle defines in the simplest case the super Yang–Mills action coupled to a scalar field. By considering a modified Dirac operator and a suitable limit of its parameters we then obtain an action that turns out to be the continuum limit of the induced QCD in the Kazakov–Migdal model.
A new integrable symplectic map associated with lattice soliton equations
Authors: Wu Yongtang , Geng Xianguo
Published: July 2002

A method is developed that extends the nonlinearization technique to the hierarchy of lattice soliton equations associated with a discrete 3×3 matrix spectral problem. A new integrable symplectic map and its involutive system of conserved integrals are obtained by the nonlinearization of spatial parts and the time parts of Lax pairs and their adjoint Lax pairs of the hierarchy. Moreover, the solutions of the typical system of lattice equations in the hierarchy are reduced to the solutions of a system of ordinary differential equations and a simple iterative process of the symplectic map.
Multiplane gravitational lensing. III. Upper bound on number of images
Authors: Petters A. O.
Published: July 2002

The total number of lensed images of a light source undergoing gravitational lensing varies as the source traverses a caustic network. It is rigorously shown that for a pointlike light source not on any caustic, a three-dimensional distribution of g point masses on g lens planes creates at most 2(22(g−1)−1) lensed images of the source (g⩾2). This complements previous work [Paper I, J. Math. Phys. 36, 4263 (1995)] that showed at least 2g lensed images occur. Application of the upper bound to the global geometry of caustics is also presented. Our methods are based on a complex formulation of point-mass gravitational lensing and techniques from the theory of resultants. The latter yields a new approach to studying upper bounds on number of lensed images due to point-mass gravitational lens systems.
Microscopic dynamics from a coarsely defined solution to the protein folding problem
Authors: Fernández Ariel , Colubri Andrés
Published: July 2002

In this work we introduce a least-action formulation of the protein folding problem casted within a coarse description of the soft mode dynamics of the peptide chain. Ultimately, we show that this coarse variational approach can be lifted to yield the microscopic long-time torsional dynamics responsible for the actual folding process. As a first step, a binary coding of local topological constraints associated to each structural motif is introduced to coarsely mimic the long-time dynamics. Folding pathways are initially resolved as transitions between patterns of locally encoded structural signals. Our variational approach is aimed at identifying the most economic pathway with respect to the stepwise cost in conformational freedom. Our treatment allows us to account for the expediency of the process in proteins effectively capable of in vitro renaturation. We identify the dominant pathway by introducing a coarse version of Lagrangian microscopic dynamics. The coarse folding pathways are generated by a parallel search for structural patterns in a matrix of local topological constraints (LTM) of the chain. Each local topological constraint represents a coarse description of a local torsional state and each pattern is evaluated, translated, and finally recorded as a contact matrix (CM), an operation that is subject to a renormalization feedback loop. The renormalization operation periodically introduces long-range correlations on the LTM according to the latest CM generated by translation. Local topological constraints may form consensus regions in portions of the chain that translate as secondary structure motifs or tertiary interactions. Nucleation steps and cooperative effects are accounted for by means of the renormalization operation, which warrants the persistence of seeding patterns upon successive LTM evaluations. Relevant folding time scales beyond the realm of molecular dynamics simulations become accessible through the coarsely codified representation of local torsional constraints. The validity of our approach is tested vis à vis experimentally probed folding pathways generating tertiary interactions in proteins that may recover their active structure under in vitro renaturation conditions. We focus on determining significant folding intermediates and the late kinetic bottlenecks that occur within the first 1100 s of the renaturation process. After the computational accessibility of this coarse solution of the folding problem becomes apparent, we show how to lift our variational problem to microscopic dynamics of the peptide chain. The consistency of our approach is revealed by an actual generation of Newton’s laws at the microscopic level through an inverse projection of the coarse dynamics originally generated through the pattern recognition computation.
Quantum sources and a quantum coding theorem
Authors: King Christopher , Leśniewski Andrezj
Published: July 2002

We define a large class of quantum sources and prove a quantum analog of the asymptotic equipartition property. Our proof relies on using local measurements on the quantum source to obtain an associated classical source. The classical source provides an upper bound for the dimension of the relevant subspace of the quantum source, via the Shannon–McMillan noiseless coding theorem. Along the way we derive a bound for the von Neumann entropy of the quantum source in terms of the Shannon entropy of the classical source, and we provide a definition of ergodicity of the quantum source. Several explicit models of quantum sources are also presented.
Ekman number dependence of the size of secondary flow regions generated by torsionally oscillating disks in stratified fluids
Authors: Folse R. F. , Wu Xueming
Published: July 2002

Measurements have been made of the size of the region of secondary flow in linearly stratified fluids (Brunt–Väisälä frequencies in the range 1.07–2.69 rad/sec that has been caused by torsionally oscillating disks, with radii of 3.0 cm≤r≤4.5 cm. Amplitudes of oscillation were held constant at approximately 1 rad and the frequency of oscillation varied from 0.69 rad/sec≤ω≤4.78 rad/sec. The fluid was bounded in a cylindrical container with a radius of 7.05 cm and the kinematic viscosity in the vicinity of the disk ν=1.08 cS, was approximately constant. Experiments were performed to extend the work of Folse et al. [Phys. Fluids 29, 667 (1986)] to include variations in the Ekman number, Ek=ν/ωr2. The size of the secondary flow region was measured from shadowgraphs and the flow field was mapped using a two-component laser-Doppler velocimeter. An empirical correlation of the data with the results of Folse et al. is presented.
Effect of suction on the subharmonic instability of compressible boundary layers
Authors: Masad J. A. , Nayfeh A. H.
Published: July 2002

The effect of self-similar suction distributions on the subharmonic instability of a two-dimensional (2-D) compressible boundary layer over an insulated flat plate is analyzed using the Floquet model. The resulting problem is solved numerically by using finite differences. Results are presented for different Mach numbers. For supersonic flows results for first- and second-mode primary waves are presented. It is found that when the primary wave is a first mode, suction stabilizes the subharmonic wave at low and moderate Mach numbers. However, at high Mach numbers suction loses its effectiveness. When the primary wave is a second mode, suction is also found to stabilize the subharmonic mode. When the primary wave is a first mode merging with a second mode, the subharmonic wave is strongly destabilized by suction.