Showing papers on "Antisymmetric relation published in 1998"

Basis set convergence study of the atomization energy, geometry, and anharmonic force field of SO2: The importance of inner polarization functions

Abstract: The total atomization energies, geometries, and anharmonic force fields of the SO and SO2 molecules have been studied at the augmented coupled cluster [CCSD(T)] level near the one-particle basis set limit. The effect of core correlation has been accounted for. The addition of high-exponent d and f “inner polarization functions” to the sulfur basis set was found to be essential for obtaining reliable molecular geometries. The differential effect of core correlation on computed properties is in fact much less important. The CCSD(T) one-particle basis set limit for the symmetric stretching frequencies appears to be higher than the exact value, while the antisymmetric stretching frequency benefits from an error cancellation. The basis set extension effects of diffuse functions and inner polarization functions appear to be nearly perfectly additive. Our best computed atomization energies and geometries agree to within 0.1 kcal/mol, 0.0004 A, and 0.03 degrees with experiment: The errors in the fundamentals of SO2 are +3.9, −0.4, and +0.4 cm−1. The best computed quartic force field for SO2 should provide a good starting point for a new experimental refinement.

Linear analysis of the instability of two-dimensional non-Newtonian liquid sheets

Abstract: The instability of two-dimensional non-Newtonian liquid sheets moving in an inviscid gaseous environment is investigated. A linearized stability analysis shows that non-Newtonian liquid sheets have a higher growth rate than Newtonian liquid sheets for both symmetric and antisymmetric disturbances, indicating that non-Newtonian liquid sheets are more unstable than Newtonian liquid sheets. It is found that the surface tension effects always resist, whereas the aerodynamic effects promote, the occurrence and development of instability of non-Newtonian liquid sheets. Similar results were obtained for inviscid and Newtonian liquid sheets by many other authors before. It is observed that in non-Newtonian liquid sheets the liquid viscosity tends to damp the instability, whereas the liquid elasticity results in an enhancement of instability. It is seen that both the growth rate and the instability range of non-Newtonian liquid sheets increase greatly with the gas Weber number, the Reynolds number, and the ratio of gas to liquid density for symmetric and antisymmetric disturbances, indicating that non-Newtonian liquid sheets destabilize more easily at high values of these three parameters. When the liquid viscosity is increased, the growth rate of symmetric and antisymmetric disturbances on Newtonian and non-Newtonian liquid sheets decreases, but the cutoff wave number remains unchanged. At low liquid viscosity, the growth rate of non-Newtonian liquid sheets is close to that of Newtonian ones. The growth rates of symmetric and antisymmetric disturbances decrease with the ratio of deformation retardation to stress relaxation time but increase with the liquid elasticity, whereas the instability range does not change with these two parameters. Moreover, increasing the gas Weber number, the Reynolds number, and the ratio of gas to liquid density substantially, enhances the maximum growth rate and the dominant wave number of non-Newtonian liquid sheets for symmetric and antisymmetric types of disturbances. However, the effects of the ratio of deformation retardation to stress relaxation time, the Ohnesorge number, and the Elasticity number on both the maximum growth rate and the dominant wave number are relatively weak. It is discovered that the maximum growth rate of antisymmetric disturbances is always larger than that of symmetric disturbances, while the dominant wave number of antisymmetric disturbances is always smaller than that of symmetric disturbances. This indicates that antisymmetric disturbances always prevail over symmetric disturbances for non-Newtonian liquid sheets.

Dynamics of tautomerism in porphine: An instanton approach

Abstract: Ab initio calculations are reported of the rate of tautomerization by double-hydrogen transfer of porphine and three of its isotopomers. Both synchronous (one-step) and asynchronous (two-step) hydrogen tunneling mechanisms are considered. Geometries and force fields are calculated at the stationary points by means of a nonlocal density functional method that yields accurate equilibrium structures and vibrational spectra. Potential-energy surfaces are constructed in terms of all 73 in-plane normal-mode coordinates at the transition state, the mode with imaginary frequency being taken as the reaction coordinate. Hydrogen tunneling calculations are performed by means of a simplified instanton method that has proved reliable in calculations on smaller systems. The full multidimensional potential is used, and adiabatic separation of the normal modes from the reaction coordinate is avoided. The coordinates of the transverse modes are coupled linearly to the reaction coordinate and all modes are allowed to mix freely with each other along the reaction path. Direct evaluation of the instanton path is not necessary. To calculate the tunneling rate constant, it is sufficient to evaluate the one-dimensional instanton action along the reaction coordinate and to correct it for coupling with transverse vibrations. This makes the method computationally very efficient compared to other multidimensional approaches. For the synchronous mechanism, the calculations closely follow the previously established procedure, but for the asynchronous mechanism, generalization to an asymmetric barrier is required. This is achieved by dividing the normal-mode displacements that determine the couplings into symmetric and antisymmetric components which enhance and suppress the tunneling rate, respectively. The relative energies at the stationary points of the density-functional potential are calculated both by density functional theory (DFT) and by the Hartree–Fock method at the DFT geometry. The two methods yield results that are quite different. Comparison with a large set of experimental data comprising four isotopomers and a wide range of temperatures, indicates that neither method yields accurate energies but that some adjustment of the barrier height and the cis–trans energy difference is necessary to obtain satisfactory rate constants for the asynchronous mechanism. The other calculated parameters are used without adjustment. All parameters are combined to construct the potential required for the instanton calculations. A good fit to all available kinetic data is obtained, indicating that the method accounts accurately both for the isotope and the temperature dependence of the rate of tautomerization. It is shown that, in order to achieve this result, it is essential to include all linear couplings, since the balance between symmetric couplings, which enhance the tunneling rate, and antisymmetric couplings, which suppress it, varies between isotopomers. All dynamics calculations are performed with a newly developed code, which is designed to use the output of standard quantum-chemical codes and requires only minutes of CPU time on a standard workstation.

Stein’s Method: Some Perspectives with Applications

Abstract: This paper presents Stein’s method from both a concrete and an abstract point of view. A proof of the Berry-Esseen theorem using the method is given. Two approaches to the construction of Stein identities are discussed: the antisymmetric function approach and an L2 space approach. A brief history of the developments of Stein’s method and some possible prospects are also mentioned.

Finite-Element Analysis of Convection Problems in Spatially Periodic Domains

Abstract: The finite-element method is used to solve fully developed convection problems in spatially periodic domains. Symmetric and antisymmetric periodicity in temperature is imposed in an original way that allows for different thermal boundary conditions at the walls. The formulation is first validated by comparing the numerical results with the analytical solutions for fully developed velocity and temperature distributions in a parallel-plate channel. Afterward, the accuracy and the capabilities of the procedure are demonstrated by two examples involving laminar flow and heat transfer in a periodic corrugated channel and in a parallel-plate channel with staggered fins.

Quantized (1, 0) % (0, 1) Fields

Abstract: We find a mapping between antisymmetric tensormatter fields and the Weinberg 2(2j + 1)-component“bispinor” fields. Equations which describethe j = 1 antisymmetric tensor field coincide with the Hammer-Tucker equations entirely and withthe Weinberg ones within a subsidiary condition, theKlein-Gordon equation. A new Lagrangian for the Weinbergtheory is proposed which is scalar and Hermitian. It is built on the basis of the concept of“Weinberg doubles.” The origin of acontradiction between the classical theory, the Weinbergtheorem B – A = λ for quantum relativisticfields, and the claimed ‘longitudity’ of the antisymmetrictensor field [transformed on the (1, 0) ⊕ (0, 1)Lorentz group representation] after quantization isclarified. Analogs of the j = 1/2 Feynman–Dysonpropagator are presented in the framework of the j = 1 Weinberg theory.It is then shown that under a definite choice of fieldfunctions and initial and boundary conditions themassless j = 1 Weinberg–Tucker–Hammerequations contain all the information that the Maxwell equationsfor the electromagnetic field have. Thus, the formerappear to be of use in describing some physicalprocesses.

USp(2k) Matrix Model: F Theory Connection

Abstract: We present a zero-dimensional matrix model based on USp(2k) with supermultiplets in symmetric, antisymmetric and fundamental representations. The four-dimensional com­ pactification of this model naturally captures the exact results of Sen 1) in F theory. Eight dynamical and eight kinematical supercharges are found, as required for critical string inter­ pretation. The classical vacuum has ten coordinates and is equipped with orbifold structure. We clarify the issue of spacetime dimensions which F theory represented by this matrix model produces.

Examples of embedded eigenvalues for problems in acoustic waveguides

Abstract: This short article discusses the spectrum of the Neumann Laplacian in the infinite domain Ω ⊂ R n , n ≥ 2 created by inserting a compact obstacle P into the uniform cylinder Ω 0 = (- ∞, ∞) × Ω'. The main result is the existence of at least one embedded eigenvalue when P is an (n - 2)-dimensional surface whose unit normal is parallel to Ω' at each point of P. The special case when P is symmetric about {0} × Ω' is also treated. It is shown that there is at least one symmetric eigenvector and, when P is sufficiently long, at least one antisymmetric eigenvector.

Multidimensional sigma-models with composite electric p-branes

Abstract: We consider a gravitational model on a manifold M = M_0 x M_1 x...x M_n with oriented connected Einstein internal spaces M_1,...,M_n. The matter part of the action contains several scalar fields and antisymmetric forms. With Ricci-flat internal spaces, the model has a midisuperspace representation in form of a sigma-model on M_0. The latter can be used to determine exact composite electric p-brane solutions, which depend on a set of harmonic functions on M_0.

Sum-frequency generation from an isotropic chiral medium

Abstract: We report a theoretical analysis of nonlinear optical sum-frequency generation from the bulk of a chiral liquid in the dipole approximation. In our theoretical formulation the circular birefringence effect of a chiral medium was properly taken into account. The angular dependence of the reflected and transmitted sum-frequency signals on the incident angles of two input beams was calculated to yield the optimal geometry for probing bulk chirality. We also derived a microscopic expression for the totally antisymmetric part of a second-order nonlinear optical susceptibility to elaborate unique features in the studies of chirality-related properties with sum-frequency generation.

Multidimensional cosmology for intersecting p-branes with static internal spaces.

Abstract: Multidimensional cosmological model with static internal spaces describing the evolution of an Einstein space of non-zero curvature and n internal spaces is considered. The action contains several dilatonic scalar fields φ and antisymmetric forms A and Λ -term. When forms are chosen to be proportional to volume forms of p -brane submanifolds of internal space manifold, the Toda-like Lagrange representation arises. Exact solutions for the model are obtained, when scale factors of internal spaces are constant. It is shown that they are de Sitter or anti-de Sitter. Behaviour of cosmological constant and its generation by p-branes is demonstrated.

An Antisymmetric Formula for Euler's Constant

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Vibrational excitation of carbon dioxide by electron impact: symmetric and antisymmetric stretching modes

Abstract: Vibrational excitation of a molecule by electron impact is studied theoretically. Differential and integral cross sections in the incident energy region 4-35 eV for symmetric stretching and 4-50 eV for antisymmetric stretching modes are calculated. The calculation is based on the rotational sudden and vibrationally two-state close-coupling method with an ab initio electrostatic potential and approximate exchange and target polarization. The cross sections obtained are compared with experimental data. For symmetric stretching, differential cross sections are in a qualitative agreement with experimental data and two resonance peaks appear at around 14 and 32 eV. These resonances correspond to those found by Tronc et al in 1979 in their relative measurement of differential cross section at . For antisymmetric stretching, the present cross sections reproduce experimental data well. The energy dependence of cross sections shows resonances similar to those seen in the differential cross section for symmetric stretching.

Generation of spatial solitons using non-linear guided modes

Abstract: We investigate how two-dimensional spatial optical solitons can be generated in a non-linear Kerr medium using the non-linear guided modes of a weakly-guiding slab waveguide with a linear core and a non-linear cladding as the source of excitation. Symmetric, antisymmetric and asymmetric non-linear modes are considered, from which we determine the parameters of single solitons, oscillating two-soliton bound states, and two repelling solitons, respectively. Both the beam propagation method and inverse scattering transform are used.

Higher dimensional Yang–Mills theories and topological terms

Abstract: Higher dimensional generalisations of self-duality conditions and of theta angle terms are analysed in Yang-Mills theories. For the theory on a torus, the torus metric and various antisymmetric tensors are viewed as coupling constants related by U-duality, arising from background expectation values of supergravity fields for D-brane or matrix theories. At certain special points in the moduli space of coupling constants certain branes or instantons are found to dominate the functional integral. The possibility of lifting chiral or supersymmetric theories to higher dimensions is discussed.

Linear phase and symmetries for multidimensional FIR filters over lattices

Abstract: We present in this paper multidimensional FIR filters over arbitrary lattices having the linear phase property. The extended definitions of phase, group delay, and linear phase are first presented. This leads us to consider four types of filters as in the one-dimensional (1-D) case (symmetric or antisymmetric with odd or even support). The zeros in frequencies inherent to each type are presented. Hyper-octantal symmetry, in which all coefficients of a filter depend on those in one hyper-octant, is then introduced. We show conditions on lattices and filters for this kind of symmetry to be possible. We finally give equations relating dependent coefficients to independent ones.

Fermion Monte Carlo

Abstract: We review the fundamental challenge of fermion Monte Carlo for continuous systems, the "sign problem". We seek that eigenfunction of the many-body Schriodinger equation that is antisymmetric under interchange of the coordinates of pairs of particles. We describe methods that depend upon the use of correlated dynamics for pairs of correlated walkers that carry opposite signs. There is an algorithmic symmetry between such walkers that must be broken to create a method that is both exact and as effective as for symmetric functions, In our new method, it is broken by using different "guiding" functions for walkers of opposite signs, and a geometric correlation between steps of their walks, With a specific process of cancellation of the walkers, overlaps with antisymmetric test functions are preserved. Finally, we describe the progress in treating free-fermion systems and a fermion fluid with 14 3 He atoms.

Morita equivalence of multidimensional noncommutative tori

Abstract: One can describe an $n$-dimensional noncommutative torus by means of an antisymmetric $n\times n$-matrix $\theta$. We construct an action of the group $SO(n,n|\bf Z)$ on the space of antisymmetric matrices and show that, generically, matrices belonging to the same orbit of this group give Morita equivalent tori. Some applications to physics are sketched.

Topological mass mechanism from dimensional reduction

Abstract: We show that the abelian topological mass mechanism in four dimensions, described by the Cremmer-Sherk action, can be obtained from dimensional reduction in five dimensions. Starting from a gauge invariant action in five dimensions, where the dual equivalence between a massless vector field and a massless second-rank antisymmetric field in five dimensions is established, the dimensional reduction is performed keeping only one massive mode. Furthermore, the Kalb-Ramond action and the Stuckelberger formulation for massive spin-1 are recovered.