bluuebunny/crossref_metadata_2025 huggingface dataset:
Ground state benzene–argon intermolecular potential energy surface
Authors: Koch Henrik , Fernández Berta , Makarewicz Jan
Published: July 2002

A highly accurate ab initio intermolecular potential energy surface for the benzene–argon van der Waals complex is evaluated using the coupled cluster singles and doubles model including connected triple excitations [CCSD(T)] model with an augmented correlation consistent polarized valence double zeta basis set extended with midbond functions. The vibrational energy levels obtained by full three-dimensional dynamical calculations are in excellent agreement with the available experimental data.
Molecular dynamics simulation of formamide in water using density functional theory and classical potentials
Authors: Chalmet S. , Ruiz-López M. F.
Published: July 2002

We report the first molecular dynamics simulation of an amide in water in which the solute is fully described through quantum mechanics methods (density functional theory in our case). All solute’s degrees of freedom are allowed to vary. The solvent is described through a classical potential. We have chosen for our study the simple formamide molecule since it allows hybrid simulations to be carried out at a sophisticated quantum level. More precisely, we have considered two computational schemes: in the first one, we use a small double-ζ basis set and a local approximation of the exchange-correlation functional whereas, in the second, an extended triple-ζ+polarization basis set, as well as a gradient-corrected functional, has been employed. The analysis of the results is focused on both structural and energetic aspects. Particular attention is paid to the time variation of dihedral angles in formamide connected to nitrogen pyramidalization and NH2 subunit rotation. The agreement with available experimental and theoretical data is satisfactory. Nevertheless, the limits of the method are pointed out, in particular the need to improve the description of the nonelectrostatic term of the solute-solvent interaction potential. One of the main advantages of the hybrid approach is that polarization effects are included in a rigorous manner. This renders possible a detailed discussion on the role of hydration effects on amides structure, a point of considerable relevance due to the biochemical importance of the peptidic bond.
Electron-lattice dynamics on Jahn–Teller surfaces in Ag:Xe crystals
Authors: Bammel K. , Dietrich P. , Schwentner N.
Published: July 2002

Excitation of the s-p transition of Ag isolated in a Xe crystal leads to a dynamic Jahn–Teller splitting which, in addition to spin-orbit coupling, removes the degeneracy of the excited p orbital. The dynamics on these Jahn–Teller surfaces and the vibrational relaxation leading to strongly Stokes shifted emission bands is studied with 170 fs time resolution. The wave packet dynamics is followed by one-color resonant pump–probe spectroscopy and a recurrence at 1.3 ps after excitation into the upper two states of the triplet is observed. Two-color fluorescence depletion experiments are used to investigate the dynamics during relaxation to the minima of the excited states. Excited state absorption competes with stimulated emission and an energy of the Ag+ state in Xe is deduced to 5.73 eV.
Ab Initio study of dopant insertion into carbon nanotubes
Authors: Farajian Amir A. , Ohno Kaoru , Esfarjani Keivan , Maruyama Yutaka , Kawazoe Yoshiyuki
Published: July 2002

Ab initio total energy calculation and molecular dynamics simulation on the process of dopant insertion into carbon nanotubes are carried out on the basis of the all-electron mixed basis approach within the local density approximation. First, an upper bound for the height of the potential barrier which is seen by typical alkali metals (Na and K) going through the center of a hexagonal ring of the nanotube is estimated to be 40 eV for Na and 90 eV for K. Next, such an insertion process is simulated with a suitable kinetic energy of the dopant (70 eV for Na and 150 eV for K). It is observed that the carbon atoms are pushed to open the hexagonal ring wider and the dopant passes through. After encapsulation, the hexagonal ring restores its initial configuration, while the impact shock propagates along the nanotube and gradually decays.
Screening ionic motion in sodalite cages: A dynamical study
Authors: Filippone F. , Gianturco F. A.
Published: July 2002

The dynamical evolution of protonated helium clusters inside sodalite cages (silica-sodalite and acidic sodalite) is followed via a Car–Parrinello approach. The static simulations give framework structural and electronic features that agree with previous experimental and theoretical data. The protonated helium clusters are used to screen the positive charge borne by a “naked” proton, and are intended as simplified models of the solvation sphere of H+. The action of the framework on the solvation shell of the proton is shown to be mainly due to induction-polarization or Coulombic forces, with a minor contribution of resonant energy exchange between the framework modes and the cluster oscillators. The covalent nature of the zeolitic O–H bond is determined with the aid of the bond order conservation principle.
Infrared spectrum of the CH2 out-of-plane fundamental of C2H5
Authors: Sears Trevor J. , Johnson Philip M. , BeeBe-Wang Joanne
Published: July 2002

Measurements of the ethyl radical -CH2 out-of-plane rocking vibrational fundamental by transient diode laser absorption spectroscopy are reported. The new data provide information on the structure of, and the barrier to internal rotation in, the radical, and how these quantities change on vibrational excitation. We find that the effective barrier decreases from approximately 17 cm−1 in the zero point level to 10 cm−1 in the excited vibrational level. The assigned data set now contains approximately 450 rotation-torsional transitions and has been fit to a model effective Hamiltonian. The derived molecular parameters generally reproduce the measured line positions to better than 0.01 cm−1, but this does not approach the estimated measurement accuracy of 0.001–0.002 cm−1.
Photodissociation dynamics of N4+ in the 300–670 nm range
Authors: Williams Skip , Dressler Rainer A. , Chiu Yu-Hui
Published: July 2002

The photodissociation of N4+ produced in a supersonic jet ion source is studied in an octopole ion guide at selected wavelengths in the 300–670 nm range. The N2+ photofragment recoil velocity distributions are measured using the guided-ion beam time-of-flight (GIB-TOF) technique. The derived kinetic energy release distributions are structureless at all photon energies. The average anisotropy parameter, 〈β〉, ranges between 0.7 and 1.2. The absolute magnitude and photon energy dependence of both average kinetic energy release, 〈ET′〉, and 〈β(ET′)〉 are inconsistent with a previously assumed impulsive mechanism. Experiments are also conducted with N4+ produced with ∼0.6 eV internal excitation. This results in a reduction of the observed kinetic energy release and anisotropy parameter, implying that different regions of the excited state surfaces are accessed when ion vibrational modes are excited. The observations can be rationalized by invoking excited states with bent equilibrium geometries, consistent with valence-bond calculations of Langenberg et al. [Langenberg et al., Chem. Phys. 221, 225 (1997)].
Near-critical dynamical behavior of an ionic micellar solution
Authors: Isojima T. , Fujii S. , Kubota K. , Hamano K.
Published: July 2002

A series of experiments, static light scattering, dynamic light scattering, and shear viscosity, have been performed to study the critical properties of micellar solution of sodium dodecyl sulfate (SDS) and butanol in an aqueous solution of sodium chloride in terms of the modified dynamical droplet model. The exponents ν and γ for the long range correlation length and the osmotic compressibility were obtained as 0.736 and 1.374, respectively, in agreement with Fisher’s renormalized Ising model. The experimental investigation on the dynamic critical behavior suggests that the modified dynamical droplet model, which assumes that the local fluctuations activated thermally behave as the physical clusters with a fractal dimension of df=2.49 and a polydispersity exponent of τ=2.21, describes well the dynamical behavior of the SDS ionic micellar mixture together with an evaluation of the effective micellar size of 7–8 nm.
On the deconvolution of the temporal width of laser pulses from pump–probe signals
Authors: Henriksen Niels E. , Engel Volker
Published: July 2002

We consider pump–probe frequency integrated fluorescence signals. These transients, in general, arise from wave packets where the intrinsic dynamics and the response to the pump pulse is entangled in a complicated way. The signal from an infinitely short δ-pump pulse is the only exception. However, if the pump–probe signal is integrated over the frequencies of the pump laser, the signal can be expressed as a convolution of the pulse envelope with the signal obtained from a δ-pulse excitation. We consider the deconvolution of the pulse envelope and demonstrate that the signal corresponding to a δ-pump pulse can be recovered exactly from signals using pump pulses of finite temporal width. Numerical examples are presented for asymptotic fragment detection in the reaction, ICN→I+CN.
High-pressure Brillouin study of solid HBr at pressures up to 7 GPa
Authors: Shimizu H. , Kanazawa M. , Kume T. , Sasaki S.
Published: July 2002

High-pressure Brillouin scattering measurements have been carried out in orientationally disordered (OD) phases I and I′ of solid HBr, which yielded the first determination of acoustic velocities for all directions, the refractive index, the polarizability, the density, adiabatic elastic constants (C11, C12, and C44), bulk modulus, and the elastic anisotropy as a function of pressure up to 7 GPa and at room temperature. The I→I′ phase transition in solid HBr was confirmed on the discontinuous pressure dependence at P=2.3 GPa for average errors of the least-squares fit by the analysis of in situ Brillouin spectroscopy. These elastic properties of solid HBr are compared with recent results in the OD phase I of solid HCl. We suggest that the form of the potential energy function for intermolecular forces in solid HBr is similar to that in HCl.
Liquid–vapor coexistence by molecular dynamics simulation
Authors: Baranyai András , Cummings Peter T.
Published: July 2002

We present a simple and consistent molecular dynamics algorithm for determining the equilibrium properties of a bulk liquid and its coexisting vapor phase. The simulation follows the dynamics of the two systems simultaneously while maintaining the volume and the number of particles of the composite system fixed. The thermostat can constrain either the total energy or the temperature at a desired value. Division of the extensive properties between the two phases is governed by the difference of the corresponding intensive state variables. Particle numbers are continuous variables and vary only in virtual sense, i.e., the real sizes of the two systems are the same and do not change during the course of the simulation. Calculation of the chemical potential is separate from the dynamics; thus, one can replace the particle exchange step with other method if it improves the efficiency of the code.
Gas phase ion chemistry and ab initio theoretical study of phosphine. III. Reactions of PH2+ and PH3+ with PH3
Authors: Antoniotti Paola , Operti Lorenza , Rabezzana Roberto , Tonachini Glauco , Vaglio Gian Angelo
Published: July 2002

The gas phase ion chemistry of phosphine has been investigated by ab initio theoretical calculations and experimental techniques. Following previous studies dealing with P+3 and PH+ reacting with PH3, the quantum chemical study of these processes has been extended to the ion/molecule reactions starting from PH2+ and PH3 (reaction a) or PH3+ and PH3 (reaction b), as observed by ion trapping. In these experiments, PH2+ reacts to give P2Hn+ (n=1,3) product ions, with loss of H2 through different pathways. These processes take place at quite different rates, their constants being 2.6 and 7.6×10−10 cm3 molecule−1 s−1, respectively. The geometrical structures and energies of transition structures, reaction intermediates, and final products have been determined by ab initio theoretical methods. The initial step of the reaction of PH2+ with PH3 is formation of the H2P–PH3+ adduct. Then, a hydrogen molecule can be directly lost either from tricoordinated or tetracoordinated phosphorus, to give P–PH3+ or HP=PH2+, respectively. The shift of one H atom in HP=PH2+ produces the bridged HP(H)PH+ ion, from which further dissociation of H2 yields PPH+. The initial step of the reaction of PH3+ with PH3 is formation of the H3P–PH3+ adduct. Then inversion of the H atoms in the PH3 group transforms the adduct in an electrostatic complex. This last species is related by a dissociation process to the PH2 and PH4+ products. The heats of formation of the P2Hn+ (n=1–6) ionic species have been computed and compared with the experimental data in the literature.
Do “grow and exchange” simulations of polymers obey detailed balance?
Authors: Alexandrowicz Z.
Published: July 2002

Efficient simulations grow a polymer chain in a sequence of steps that occasionally branches out, seeking optimal pathways. The fraction of optimal pathways from among all possible ones has to be evaluated, in order to determine a new chain’s ensemble weight and hence its detailed balance acceptance into a multi-chain system. The total number of all possible pathways, however, is huge and has to be sampled. The consequent use of a sampled detailed balance may be questioned. Here it is shown to be exact (at least in the athermal case).
Potential of interaction of a counterion with a two-dimensional array of fixed charges
Authors: Vaughan Worth E.
Published: July 2002

The Fourier expansion coefficients of the potential of interaction of a test charge with a two-dimensional array of fixed charges were evaluated as a function of the size of the square array and as a function of the distance of the test charge from the array. Fourier coefficients were also found for the interaction with a continuous charge density corresponding to the fixed charge density. Similar coefficients were found indicating that the continuous distribution is a reasonable approximation to the potential of the discrete array. The (discrete) coefficient corresponding to the periodicity of the fixed charges is larger than expected (and the effect is greater at short distances) from the overall trend of the other coefficients, but this special term does not contribute appreciably to the total potential.
Molecular wire conductance: Electrostatic potential spatial profile
Authors: Mujica Vladimiro , Roitberg Adrian E. , Ratner Mark
Published: July 2002

We have studied the effect of the electrostatic potential on the current across a one-dimensional tight-binding molecular wire by solving self-consistently the Poisson and Schrödinger equations. The results indicate that electrostatic effects on the current are very important in the nonlinear regime. They manifest themselves through a strong variation of the voltage drop in the interfacial region compared to the linear ramp expected in the absence of charge in the wire and also in the nature of the current–voltage characteristics.
Coupled-cluster studies of the hyperfine splitting constants of the thioformyl radical
Authors: Petraco Nicholas D. K. , Wesolowski Steven S. , Leininger Matthew L. , Schaefer Henry F.
Published: July 2002

Hyperfine splitting constants (hfs) of the X̃ 2A′ electronic ground state of the thioformyl radical (HCS) have been determined at the coupled-cluster level with single, double, and perturbatively applied connected triple excitations [CCSD(T)] using 39 basis sets. Variation of the CCSD(T) hyperfine splittings with basis set was ascertained using a fixed geometry, optimized at the CCSD(T) level with Dunning’s correlation-consistent polarized valence quadruple-ζ basis set (cc-pVQZ). Pople basis sets, 6-311G++(2d,2p) and 6-311G++(3df,3pd), give 1H isotropic coupling constants (1H Aiso) in good agreement with the experimental vibrationally averaged value of 127.4 MHz, deviating by 5.5 and 9.3 MHz, respectively. Dunning’s valence correlation-consistent basis sets (cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, aug-cc-pVTZ, cc-pVQZ, aug-cc-pVQZ) deviate 6.4 MHz (aug-cc-pVQZ) to 14.9 MHz (cc-pVDZ) from the experimental value. The correlation-consistent core valence analogues of these sets give very similar values with deviations from experiment of 7.4 MHz (cc-pCVQZ) to 14.2 MHz (cc-pCVDZ). A direct comparison with the vibrationally averaged experimental value is not precisely possible since the hyperfine splittings are strongly geometry dependent and all theoretical predictions refer to the equilibrium geometry. Small Pople basis sets (3-12G, 6-31G, and 6-311G) give the worst results, deviating by 49.5, 34.1, and 31.8 MHz, respectively. All CCSD(T) 1H Aiso values fall below the experimental value. The 13C and 33S hyperfine splittings are not known experimentally, but the equilibrium values are predicted here to be 274.7 MHz (13C) and 21.7 MHz (33S) at the cc-pCVQZ CCSD(T) level of theory. Significantly different values are predicted by density functional theory (DFT) for the 13C and 33S hyperfine splittings.
Tortuosity factor for permeant flow through a fractal solid
Authors: Garza-López Roberto A. , Naya Lewis , Kozak John J.
Published: July 2002

The theory of finite Markov processes is used to calculate a normalized tortuosity for a porous solid with a well-defined internal structure characterized by an interconnected network of serial and parallel channels. The model introduced is based on the Menger sponge, a symmetric fractal set of dimension D=ln 20/ln 3. Numerically exact values of the mean walklength 〈n〉 for a permeant diffusing through this system are calculated both in the presence and absence of a uniform gradient (bias or external field) acting on the permeant. The ratio of walklengths is then used to define unambiguously a normalized tortuosity for the medium. Different assumptions on the initial spatial distribution of the permeant are investigated and the study is designed so that the effects of one or multiple exit sites are quantified. As expected, the tortuosity factor is dependent on system size, and quantitative results are presented for the first- and second-generation Menger sponge. Our calculations document that for a given system size: (1) the mean passage time can change by an order of magnitude depending on the number of exit pores available to the permeant; and (2) restricting the number of exit pores suppresses differences between values of 〈n〉 calculated for different initial conditions. Finally, we study whether the geometrical self-similarity of Menger sponge translates into a corresponding scaling of diffusion times for different system sizes; we find that there exists a remarkable correspondence in values calculated for a defined ratio of walklengths for the first two generations of this fractal set.
Multiple simultaneous distance determinations: Application of rotational echo double resonance nuclear magnetic resonance to IS2 spin networks
Authors: Liivak Oskar , Zax David B.
Published: July 2002

Rotational Echo DOuble Resonance (REDOR) NMR is an oft-demonstrated tool for measuring distance between isolated IS spin pairs. Its application to more complex ISn spin networks (n>1), however, is rare, as in these systems the interpretation of the results is model-dependent–while it is precisely the measurement of multiple distances which is required for molecular structure elucidation. Recently, Θ-REDOR was introduced and was shown to improve interpretability at the cost of signal intensity. In this paper we analyze generalizations to the REDOR pulse sequence, and present a new experimental procedure which allows for simultaneous distance determinations in larger spin systems with improved signal intensity. Experimental data are presented for the IS2 spin system glycine-C213-N15.
Hamilton–Jacobi equation and Poissonian gluing for an inhomogeneous autocatalytic reaction
Authors: Gaveau Bernard , Latrémolière Daniel , Moreau Michel
Published: July 2002

The solution to the Hamilton–Jacobi equation which approximates the master equation of a nonlinear chemical system is, in general, impossible to obtain explicitly. In this work, we introduce a natural method for approximating the solution of the Hamilton–Jacobi equation, called “Poissonian gluing,” which has a general range of application. We show on a specific two-dimensional example (autocatalytic reaction in two cells coupled by diffusion) that this new approximation leads to explicit analytic results which are in good agreement with numerical simulations.
Experimental transition dipole moment for the four lowest Δv=1 bands of ArH+ in the Σ+1 fundamental state
Authors: Picqué Nathalie , Guelachvili Guy , Civis Svatopluk
Published: July 2002

Vibration–rotation bands of the Δv=1 sequence of ArH+ are recorded from the emission of a discharge tube with a Fourier spectrometer, between 1800 and 2830 cm−1. The analysis of the relative line intensities of the four lowest transitions made possible the determination of their Herman–Wallis factors. The derived ratios of first- and second-order coefficients of the dipole moment function to the permanent dipole moment M0 are equal to M1/M0=1.89, and M2/M0=0.96. The absolute values of the vibrational transition moments are respectively found, with no need of the ion concentration, equal to 0.194, 0.565, 1.049, and 1.623 debye for the 1–0, 2–1, 3–2, 4–3 transitions, with the assumption of M0 equal to 1.42 debye as experimentally given by K. B. Laughlin et al., Phys. Rev. Lett. 58, 996, (1987).
Hydration of cis- and trans-platin: A pseudopotential treatment in the frame of a G3-type theory for platinum complexes
Authors: Burda J. V. , Zeizinger M. , Šponer J. , Leszczynski J.
Published: July 2002

Hydration of selected platinum complexes [PtCl42−, Pt(NH3)42+, and cis- and trans-platin–PtCl2(NH3)2] have been studied. Up to two solvent molecules have been considered to replace the ligands. In order to be able to draw conclusions about pH changes in the course of the hydration process, both H2O and OH− species were considered in the solvating process. The modified Gaussian 3 theory was adapted for the pseudopotential treatment of platinum complexes. Since a heavy element was present in the complexes, an additional stabilization due to the spin–orbit coupling and core-polarization potentials have been evaluated above the scheme of a G3 treatment. This spin–orbit coupling stabilization amounts to 2–5 kcal/mol but does not qualitatively change the hydration preferences. In accord with the experiment, neutral Pt(NH3)2(OH)2 was found to be the most stable complex for hydration of both cis- and trans-platin.
A simplification of selective control using field optimized initial state with application to HI and IBr photodissociation
Authors: Vandana K. , Mishra Manoj K.
Published: July 2002

An examination of the dependence of total flux from competing photodissociation channels on the photolysis field parameters and initial vibrational states for IBr and HI molecules reveals that, for a range of field attributes, considerable selectivity and yield may be obtained by using only the ground or the ground and the first excited vibrational states in the optimal linear combination constituting the field optimized initial state (FOIST). The new simplifications obviate the need for overtone excitations or multicolor photolysis fields making it easier to implement FOIST experimentally. Concrete specifications of field attributes for achieving selective control of IBr photodissociation products is provided.
Atomic force microscopy study of oscillatory surface roughening in anodic dissolution of sputter-deposited nickel films
Authors: Saitou M. , Makabe A. , Tomoyose T.
Published: July 2002

Using atomic force microscopy (AFM), the kinetic surface roughening in electrochemical dissolution of nickel films at a low constant current density was studied in order to reveal the scaling laws. The surface measurements of AFM exhibited the oscillatory variation of the interface width with time, which made it impossible to determine the growth exponent β. The oscillatory behavior of surface roughening was explained by the presence of unstable passive films formed on the nickel film surface. The roughness exponent α=0.94±0.04 calculated from the AFM images of the anodic dissolved surface was almost equal to that predicted by the diffusion-driven growth model.
Group-theoretic determination of normal coordinates for molecular vibration
Authors: Watanabe Hiroshi
Published: July 2002

It is shown that the normal coordinates for molecular vibration are determined by simply taking those linear combinations of mass-weighted displacements that are irreducible bases of the group relevant to the molecule.
Periodic fixed points of Bäcklund transformations and the Korteweg–de Vries equation
Authors: Weiss John
Published: July 2002

A new method for studying integrable systems based on the ‘‘periodic fixed points’’ of Bäcklund transformations (BT’s) is presented. Normally the BT maps an ‘‘old’’ solution into a ‘‘new’’ solution and requires a known ‘‘seed’’ solution to get started. Besides this limitation, it can also be difficult to qualitatively classify the result of applying the BT several times to a known solution. By studying the periodic fixed points of the BT (regarded as a nonlinear map in a function space), integrable systems of equations of finite degree (equal to the order of the fixed point) and a method for the systematic classification of the solutions of the original system are obtained.
Some practical observations on the predictor jump method for solving the Laplace equation
Authors: Duque-Carrillo J. F. , Vega-Fernández J. M. , Peña-Bernal J. J. , Rossell-Bueno M. A.
Published: July 2002

The best conditions for the application of the predictor jump (PJ) method in the solution of the Laplace equation are discussed and some practical considerations for applying this new iterative technique are presented. The PJ method was remarked on in a previous article entitled ‘‘A new way for solving Laplace’s problem (the predictor jump method)’’ [J. M. Vega-Fernández, J. F. Duque-Carrillo, and J. J. Peña-Bernal, J. Math. Phys. 26, 416 (1985)].
Exterior differentiation in the Regge calculus
Authors: Brewin Leo
Published: July 2002

Regge manifolds are piecewise continuous manifolds constructed from a finite number of basic building blocks. On such manifolds piecewise continuous forms can be defined in a way similar to differential forms on a differentiable manifold. Regge manifolds are used extensively in the construction of space-times in numerical general relativity. In this paper a definition of exterior differentiation suitable for use on piecewise continuous forms on a Regge manifold is presented. It is shown that this definition leads to a version of Stokes’ theorem and also to the usual result that d2=0. This is preceded by a discussion of certain geometrical properties of the Regge manifolds. It is shown that the version of Stokes’ theorem presented here coincides with the usual definition when the Regge manifold is refined, by increasing the number of cells while keeping the total volume constant, to a smooth manifold.
Crossing rules in Cartesian and standard coordinate systems
Authors: Elbaz E.
Published: July 2002

A vectorial and a tensorial crossing rule are defined in Cartesian coordinate systems. Different applications are given. With a particular choice of the standardization coefficient of vectors the same expression of dot and vector products in the standard and Cartesian coordinate systems results. The crossing rules are thus redefined in a standard coordinate system. Applications are obtained in the simplification of some particular ‘‘3nj’’ coefficients.
Quasiresonance of long life
Authors: Meyer R. E.
Published: July 2002

Schrödinger’s equation for two-body scattering is analyzed in the tunneling range of energy for arbitrary, analytic potentials with one barrier. An exact scattering representation is given which furnishes a rigorous and efficient basis for the determination of all the eigenvalues of very long life and the associated linewidths and resonant responses. The approach is direct and simple enough to avoid computation or estimation of wave functions and asymptotic or perturbation expansions.
Magnetized diagonal Weyl metrics
Authors: Salazar I. Humberto
Published: July 2002

A generalization of the diagonal Weyl metrics, which is obtained by a Harrison transformation over the Ernst potential ε, is presented. The Ernst potential is defined for a linear combination of the Killing vectors ∂τ and ∂σ. The cases which correspond to Kasner and Voorhees metrics are analyzed in some detail.
Parent potentials for an infinite class of reflectionless kinks
Authors: Trullinger S. E. , Flesch R. J.
Published: July 2002

The sine–Gordon and φ-four kinks are known to be reflectionless by virtue of the fact that their small oscillations are governed by the modified Pöschl–Teller potential Ul(x) =1−[(l+1)/l]sech2(x/l), with l=1 and 2, respectively. An infinite class of parent potentials Vl(φ) analogous to V1∼1−cos φ for sine–Gordon kinks and V2∼(1−φ2)2 for φ-four kinks, which bear reflectionless kinks, are constructed. This is done by requiring the lowest bound-state eigenfunction of Ul(x) to be proportional to the spatial derivative of the kink waveform φ(l)K(x), i.e., the translational mode of the kink. The resulting differential equation is solved for Vl(φ) to find that it can be expressed in terms of the student’s t distribution of probability theory. Various properties of the parent potentials and their reflectionless kinks are discussed.
Compatibility of observables represented by positive operator-valued measures
Authors: Kruszyński P. , de Muynck W. M.
Published: July 2002

The proof of a result analogous to that in Koelman and de Muynck [Phys. Lett. A 98, 1 (1983)] is given for the case of unbounded observables. If two, not necessarily bounded, observables are represented by a positive operator-valued measure, then the measurement of any of them is undisturbed if and only if they commute. The Naimark theorem on dilations of spectral functions is exploited. A stronger version of Wigner’s theorem is given.
On the physical properties of a nonquadratic solution for the McVittie metric
Authors: Knutsen Henning
Published: July 2002

A particular class of McVittie’s new nonquadratic solutions is examined with respect to its physical characteristics. It is found that center regularity is not compatible with negative pressure and density gradients. These solutions also have the strange geometric feature that the physical radius is a decreasing function of comoving radial coordinate. Models for nonstatic ‘‘gaseous’’ spheres (i.e., the density ρ vanishes at the outer surface of the perfect fluid sphere together with the pressure p) have been constructed. The global motion is studied, and it has been found that pulsations are not possible. It is shown, however, that the density and pressure gradients are both negative. The pressure and the density are thus positive within the boundary of these ‘‘gaseous’’ spheres, and it is also seen that the density is increasing for contracting models. For the layers close to the outer boundary, it is shown that the pressure is increasing when the sphere is contracting. The speed of sound is thus real, and it is further seen that this speed is less than the speed of light. It is found that there exist bouncing models where the rate of change of circumference as measured by an observer riding on the boundary of the ‘‘gaseous’’ sphere is zero just at the moment when the sphere starts its reexpansion.
On new substitutions connecting different Feynman diagrams
Authors: Anders Till B. , Jachmann Wolfgang
Published: July 2002

Feynman diagrams for electroweak reactions representing partial helicity amplitudes are considered. Substitutions connect all diagrams that differ only in the direction of fermion currents passing through the reaction and in the property of whether a particle is incoming or outgoing. The substitutions act on suitably introduced signatures of the particles and of the special currents. A special substitution that reverses the direction of a current is elaborated. It is used to construct a reversal of the sequence of the interactions in a current. The crossing symmetries, which are derived from the ‘‘substitution rule,’’ are different from these. The application of all these substitutions helps to reduce considerably the number of Feynman diagrams that have to be calculated explicitly. The method is illustrated by a treatment of the reactions ee→eeγγ and eγ→eZ0. Thereby calculational aids are given that refine the methods of an earlier paper for the evaluation of helicity amplitudes and cross sections for polarized particles in the standard model, including massive spin-1 bosons. A replacement of Dirac factors like p=pμ γμ by dyadic products of four-component helicity spinors helps to separate complicated fermion currents into sums of simple spinor scalars for which the optimal forms are given.
Islands of stability and complex universality relations
Authors: Delbourgo R. , Hughes P. , Kenny B. G.
Published: July 2002

For complex mappings of the type z→λz(1−z), universality constants α and δ can be defined along islands of stability lying on filamentary sequences in the complex λ plane. As the end of the filament is approached, asymptotic values αN∼λN−1∞, δN/α2N∼1 are attained, where μ∞=λ∞(λ∞−2)/4, is associated with the limiting form of the universal function for that sequence, g(z)=1−μ∞z2. These results are complex generalizations of the real mapping case (applying to tangent bifurcations and windows of stability) where μ∞=2 and δ/α2→ (2)/(3) correspond to the filament running along the real axis.
Geometrical and kinematical characterization of parallax-free world models
Authors: Hasse W. , Perlick V.
Published: July 2002

An arbitrary general relativistic world model, i.e., a pseudo-Riemannian manifold along with a timelike vector field V, is considered. Such a kinematical world model is called ‘‘parallax-free’’ iff the angle under which any two observers (i.e., integral curves of V) are seen by any third observer remains constant in the course of time. It is shown that a model is parallax-free iff V is proportional to some conformal Killing field. In this case V, especially, has to be shear-free. Furthermore a relationship between parallaxes and red shift is presented and a reference is made to considerations concerning the visibility of cosmic rotation.
Three-dimensional scattering of impulsive acoustic waves by a semi-infinite crack in the plane interface of a half-space and a layer
Authors: Kooij Bert Jan , Quak Dirk
Published: July 2002

The three-dimensional diffraction of a pulsed acoustic wave by a semi-infinite crack located in the interface of a uniform layer and a half-space is investigated theoretically. In the analysis the influence of shear stresses in the material structure is neglected. The incident acoustic wave is taken to be generated by an impulsive compressional point source located at the top boundary of the layer. With the aid of the Wiener–Hopf technique and a modified version of the Cagniard–de Hoop technique implemented in an iterative scheme, closed-form expressions for the particle velocity within any finite time window anywhere at the top boundary of the layer are obtained.
Polynomial icosahedral invariants
Authors: Cummins C. J. , Patera J.
Published: July 2002

In this paper the ring of polynomial invariants of the icosahedral group I is studied. It begins by reviewing the surprising connections that this group and its double cover II have with various areas of mathematics and physics of current interest. Information concerning the representation theory of these groups is then given. After a brief discussion of the methods involved, the integrity basis of the ring of polynomial invariants for each irreducible representation of I is given, together with syzygies. These are expressed in terms of the invariants of the tetrahedral subgroup T of I. Finally other methods of finding these invariants are discussed.
On the representation of Slater-type densities by Gaussian densities
Authors: Braunss G. , Teubner E.
Published: July 2002

It is proved that for arbitrary m, n∈N0 and α>0, β>0, there exists an integral representation ‖x‖m ‖y‖n exp(−α‖x‖−β‖y‖) =∫R+×RKmn(s,t)exp[−(s +it)‖x‖2−(s−it)‖y‖2]d(s,t), x,y∈R3, where Kmn(s,t) is a singular distribution in 𝒟′ (R)⊗𝒵′(R).
The existence of regular partially future asymptotically predictable space-times
Authors: Królak Andrzej
Published: July 2002

A new definition of asymptotically flat space-times is proposed. It is shown that singularities in these new space-times arise from regular initial data. This leads to a simplification of the assumptions of the cosmic censorship theorem recently proved by the author [Class. Quantum Gravit. 3, 267 (1986)]. It is also shown that in the new asymptotically flat space-times a stronger censorship theorem than that proved so far by the author holds.
Generalized exponential, circular, and hyperbolic functions for nonlinear wave equations
Authors: Díaz Bejarano J. , Martín Sánchez A.
Published: July 2002

Wave functions are presented in the form of generalized exponentials that are solutions of some of the most usual linear and nonlinear wave equations. The solutions are given in terms of the elliptic functions of Jacobi and presented in a form as similar as possible to the usual circular functions. Some simple theorems are demonstrated to present the solutions as the simplest possible extension of the usual exponentials.
Proper conformal symmetries of conformal symmetric space-times
Authors: Sharma Ramesh
Published: July 2002

It is shown that conformal symmetric space-times admitting an infinitesimal conformal symmetry are either of type O or N. Those of type N represent plane gravitational waves with parallel rays, provided the Einstein tensor is invariant of the infinitesimal conformal symmetry.
On the Kerr–Newman metric in cosmological background
Authors: Koppar Sharda S. , Patel L. K.
Published: July 2002

Using the method of null tetrad, the Kerr–Newman metric in the background of the Robertson–Walker universe is derived in terms of a metric that is conformal to a generalized Kerr–Schild metric. A new two–fluid interpretation of this metric is presented. The Kerr–Newman metric in the background of the Einstein–de Sitter universe is discussed in detail.
Approximate eigenvalues of parameter-dependent systems from boundaries of level sets
Authors: Arteca Gustavo A. , Mezey Paul G.
Published: July 2002

Some basic properties of the energy level sets for parameter-dependent systems are analyzed. A class of Hamiltonians depending linearly on two parameters is considered as a working example. It is shown that an approximate computation of the boundary of the level set can be useful to derive analytical representations of the eigenvalues of the system. The expressions deduced for the eigenenergies have the correct analytic behavior in the whole range of all physical parameters. In the simplest case, a nonvariational upper bound to the ground state energy is derived that satisfies both virial and Hellmann–Feynman theorems, as well as first-order perturbation theory. Furthermore, some approximations are obtained, within the framework of the scaling variational method, that are numerical upper and lower bounds to the exact eigenvalues. Applications are illustrated with a family of anharmonic oscillators.
Vectorial continued fractions and an algebraic construction of effective Hamiltonians
Authors: Znojil M.
Published: July 2002

In the haromonic oscillator basis, the effective Hamiltonians are constructed for the polynomial interactions V(r)=∑ti=1gir2i and t≤4. Their form (factorized in terms of the vectorial continued fractions) is simpler in a semirelativistic (c<∞) reformulation. Its degeneracy in the c→∞ limit (confluence of the physical and unphysical solutions) is removed by solving a coupled set of the nonlinear algebraic equations in reduce.
Summable chains of instantons and their symmetries
Authors: Brihaye Yves , Kunz Jutta
Published: July 2002

Among its solutions, the self-duality equations of SU(2) Yang–Mills theory possess configurations called summable chains of instantons. The symmetry properties of these solutions are studied and it is shown that they are invariant under an O(3)⊗O(2) subgroup of the conformal group of Euclidian space-time. This exceptional invariance is exploited in order to establish new summability formulas and to characterize the action densities of these classical solutions of the SU(2) gauge theory.
Path-dependent techniques for electromagnetism with magnetic charges
Authors: Buendía G. M. , Percoco U. , Trias A.
Published: July 2002

An extension of the Green’s function formalism to the path dependent formulation of electromagnetism with magnetic charges is presented. The explicit form of the electromagnetic potential in terms of a generalized current density is calculated. As an example, the radiation field created by a moving particle with both types of charge is found. A technique is developed for the computation of ordinary potentials in terms of path dependent potentials. It is shown how the problem of a moving magnetic charge can be treated without the difficulty of dealing with moving strings of singularities. As an illustration of the method, the electromagnetic potential for a magnetic monopole moving in a straight line is calculated.
Proof of the family index theorem via a path integral
Authors: Li Miao
Published: July 2002

The integral formula of the family index theorem and its equivariant version are derived by use of a path integral, analogous to such a proof of the Atiyah–Singer index theorem, but without supersymmetry. Some formulas explicitly presented here should be useful in applications of the family index theorem to physics.
On the iterative solutions of some nonlinear eigenvalue problems
Authors: Wanelik Kazimierz
Published: July 2002

A simple refinement procedure of iteration methods for nonlinear systems is presented. It is based upon the introduction of a numerical measure of the ‘‘separation’’ between iterates, which themselves depend on parameters to be determined by requirements on the magnitude of this ‘‘separation.’’ As a simple but informative application of this idea the refined Picard iteration of the null Dirichlet problem for Δu+λf (x,u)=0 is considered. To illustrate the use of this technique the equation of Bratu and the so-called Gel’fand problem is observed. A discussion follows.
Null path model for classical interactions
Authors: Sutherland Roderick I.
Published: July 2002

It is shown that certain simple field interactions which are known to be reexpressible in direct interaction form can also be given an ‘‘action at no distance’’ interpretation. The solutions necessary for this interpretation are obtained by generalizing the mode of interaction in space-time from null lines (straight) to null paths (with corners).
Presentation of the constant r-term Krichever–Novikov-type algebras
Authors: Nuyts Jean , Platten Isabelle
Published: July 2002

For each constant r-term Krichever–Novikov-type algebra, a minimal set of defining generators is given from which all the operators of the algebra can be constructed by sequential definitions. A finite system of polynomial conditions on the defining generators is given, guaranteeing the commutation relations of the full algebra.
On a Fourier integral over SO(3)
Authors: Wei Gaoyuan , Eichinger B. E.
Published: July 2002

A two-matrix function of general interest in the areas of configuration statistics of macromolecules, number theory, harmonic analysis, and multivariate statistics is studied. The function is defined as a Fourier integral over SO(3), the Lie group of orthogonal 3×3 matrices with unit determinant. This six-variable function is first expressed as a product of a three-variable function and an exponential function of an additional variable, thereby reducing the total number of independent variables by 2. The new function with three parameters is expressible either as a double integral or as a series in one of the variables with the coefficients being polynomials in the other two. A special, nontrivial case where one of three arguments of the function takes a particular value is explored thoroughly. The resulting two-variable function is real valued and is an oscillating function of one of the variables when the other is fixed. When this function is expanded as a power series in one of the two variables, it generates polynomials in the other variable. Numerical analysis of this series shows it to be rapidly convergent and it is of practical use in the numerical evaluation of the function. Although the connection between these newly found polynomials and zonal polynomials has not been investigated, the parametrization for the four new variables of the two-matrix function studied may well prove useful in the effective numerical evaluation of the function when expressed alternatively as a series in zonal polynomials with an exponential part factored out.
Extended supergravity: Chern–Simons theories in 2+1 dimensions
Authors: Koehler K. , Mansouri F. , Vaz Cenalo , Witten L.
Published: July 2002

In this paper de Sitter supergravity theories in 2+1 dimensions with positive cosmological constant as Chern–Simons gauge theories of the algebra OSp(M‖2;C) are constructed. Starting from anti-de Sitter supergravity theories based on OSp(M‖2;R)×OSp(M‖2;R) algebras, a particular Inonu–Wigner contraction is used to construct a large class of super Poincaré supergravity theories with nontrivial internal symmetries. Other models based on algebras SL(M‖N) and the exceptional super Lie algebras are also discussed. The classical consistency of our de Sitter supergravity theories is discussed.
On the quantization of linearly damped harmonic oscillator
Authors: Srivastava Sunita , Vishwamittar  , Minhas I. S.
Published: July 2002

Using the equation of motion for a linearly damped harmonic oscillator as fundamental equation, a condition has been obtained that must be satisfied by its Lagrangian and a number of functional forms has been critically investigated. The Lagrangians that successfully describe a classical damped oscillator have been quantized using Feynman’s elegant path integral method. However, it is found that the expectation value of energy of the damped oscillator in all the cases becomes infinitely large for t→∞, ruling out the possibility of treating the damped quantum system as a one-body problem.
An exact solution in Poincaré gauge theory: Monopole solution
Authors: Nakariki Shin-ichi
Published: July 2002

Poincaré gauge theory is treated such that a translational gauge field is actually identified with the Einstein’s gravitational field and the Lorentz gauge field is thought of as a pair of Yang–Mills-like field and its partner. An exact solution is investigated in this model, which is similar to the Wu–Yang solution in Yang–Mills theory. As a result, a solution is found. According to Kalb’s ansatz, the ‘‘Yang–Mills parts’’ of the solution are interpreted as ‘‘electric’’ and ‘‘magnetic’’ fields that are created by a point source with a unit ‘‘magnetic’’ charge and a certain ‘‘electric’’ charge. The translational gauge field then gives the Reissner–Nordström space-time.
Topological classification of defects in two-dimensional quasicrystals
Authors: Wu Yihren , Szeto K. Y.
Published: July 2002

A new topological classification of defects in two-dimensional quasicrystals generated by the ‘‘generalized dual method (GDM)’’ is presented. Two classes of defects can be obtained by considering the possible obstructions encountered during the inward growth from a loop of tiles. The first class of defects, which do not associate with Burgers’ vectors, is new. A classification scheme for this class of defects is given along with examples drawn from a computer growth model in two dimensions. The second class of defects is a generalization of the work of Kleman and Pavlovitch to the GDM cases.