Showing papers on "Antisymmetric relation published in 2006"

Analytical models for bistable cylindrical shells

Abstract: Thin cylindrical shell structures can show interesting bistable behaviour. If made unstressed from isotropic materials they are only stable in the initial configuration, but if made from fibre-reinforced composites they may also have a second, stable configuration. If the layup of the composite is antisymmetric, this alternative stable configuration forms a tight coil; if the layup is symmetric the alternative stable configuration is helical. A simple two-parameter model for these structure is presented that is able to distinguish between these different behaviours.

A new approach for the two‐electron cumulant in natural orbital functional theory

Abstract: The cumulant expansion gives rise to a useful decomposition of the two-matrix D in which the pair correlated matrix (cumulant) is disconnected from the antisymmetric product of the one-matrix Γ. A new explicit antisymmetric approach for the two-particle cumulant matrix in terms of two symmetric matrices, Δ and Λ, as functionals of the occupation numbers is proposed for singlet ground states of closed-shell systems. It produces a natural orbital functional that reduces to the exact expression for the total energy in two-electron systems. The functional form of matrix Λ is readily generalized to any system with an even number of electrons. The diagonal elements of Δ equal the square of the occupation numbers, and the N-representability positivity necessary conditions of the two-matrix impose several bounds on the off-diagonal elements of matrix Δ. The well-known mean value theorem and the partial sum rule obtained for the off-diagonal elements of Δ provide a prescription for deriving a practical functional. In particular, when the mean values {J} of the Coulomb interactions {Jij} for a given orbital i taking over all orbitals j ≠ i are assumed to be equal {Kii/2}, a functional close to self-interaction-corrected GU functional is obtained, but the two-matrix fermionic antisymmetric holds. An additional term for the matrix elements of Λ between HF occupied orbitals is proposed to ensure a correct description of the occupation numbers for the lowest occupied levels. The functional is tested in fully variational finite basis set calculations of 57 molecules. It gives reasonable molecular energies at the equilibrium geometries. The calculated values of dipole moments are in good agreement with the available experimental data. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

Operator product expansion of higher rank Wilson loops from D-branes and matrix models

Abstract: In this paper we study correlation functions of circular Wilson loops in higher dimensional representations with chiral primary operators of = 4 super Yang-Mills theory. This is done using the recently established relation between higher rank Wilson loops in gauge theory and D-branes with electric fluxes in supergravity. We verify our results with a matrix model computation, finding perfect agreement in both the symmetric and the antisymmetric case.

Three-flat test solutions based on simple mirror symmetry

Abstract: In interferometric surface and wavefront metrology, three-flat tests are the archetypes of measurement procedures to separate errors in the interferometer reference wavefront from errors due to the test part surface, so-called absolute tests. What is believed to be a new class of solutions of the three-flat problem for circular flats is described in terms of functions that are symmetric or antisymmetric with respect to reflections at a single line passing through the center of the flat surfaces. The new solutions are simpler and easier to calculate than the known solutions based on twofold mirror symmetry or rotation symmetry. Strategies for effective azimuthal averaging and a method for determining the averaging error are also discussed.

Operator product expansion of higher rank Wilson loops from D-branes and matrix models

Abstract: In this paper we study correlation functions of circular Wilson loops in higher dimensional representations with chiral primary operators of N=4 super Yang-Mills theory. This is done using the recently established relation between higher rank Wilson loops in gauge theory and D-branes with electric fluxes in supergravity. We verify our results with a matrix model computation, finding perfect agreement in both the symmetric and the antisymmetric case.

Antisymmetric stresses in suspensions: vortex viscosity and energy dissipation

Abstract: When the individual particles in an otherwise quiescent suspension of freely suspended spherical particles are acted upon by external couples, the resulting suspension-scale fluid motion is characterized by a non-symmetric state of stress. Viewed at the interstitial scale (i.e. microscopic scale), this coupling between translational and rotational particle motions is a manifestation of particle-particle hydrodynamic interactions and vanishes with the volume fraction Φ of suspended spheres. The antisymmetric portion of the stress is quantified by the suspension-scale vortex viscosity μ v , different from the suspension's shear viscosity μ. Numerical boundary element method (BEM) simulations of such force-free suspensions of spheres uniformly dispersed in incompressible Newtonian liquids of viscosity μ 0 are performed for circumstances in which external couples (of any specified suspension-scale position-dependence) are applied individually to each of the suspended particles in order to cause them to rotate in otherwise quiescent fluids. In the absence of external forces acting on either the spheres or boundaries, such rotations indirectly, through interparticle coupling, cause translational motions of the individual spheres which, owing to the no-slip boundary condition, drag neighbouring fluid along with them. In turn, this combined particle-interstitial fluid movement is manifested as a suspension-scale velocity field, generated exclusively by the action of external couples. Use of this scheme to create suspension-scale particle-phase spin fields Ω and concomitant velocity fields v enables both the vortex and shear viscosities of suspensions to be determined as functions of 0 in disordered systems. This scheme is shown, inter alia, to confirm the constitutive equation, T a = 2μ v e · [(1/2)∇ x v - Ω], proposed in the continuum mechanics literature for the linear relation between the antisymmetric stress T a and the disparity existing between the particle-phase spin rate Ω and half the suspension's vorticity, V x v (with the third-rank pseudotensor e the permutation triadic). Our dynamically based BEM simulations confirm the previous computations of the Prosperetti et al. group for the dependence of the vortex viscosity upon the solids volume fraction in concentrated disordered suspensions, obtained by a rather different simulation scheme. Moreover, our dynamically based rheological calculations are confirmed by our semi-independent, energetically based, calculations that equate the rates of working (equivalently, the energy dissipation rates) at the respective interstitial and suspension scales. As an incidental by-product, the same BEM simulation results also verify the suspension-scale Newtonian constitutive equation, T s = μ[∇v + (∇v) † ], as well as the functional dependence of the shear viscosity μ upon Φ found in the literature.

Axiomatic Digital Topology

Abstract: The paper presents a new set of axioms of digital topology, which are easily understandable for application developers. They define a class of locally finite (LF) topological spaces. An important property of LF spaces satisfying the axioms is that the neighborhood relation is antisymmetric and transitive. Therefore any connected and non-trivial LF space is isomorphic to an abstract cell complex. The paper demonstrates that in an n-dimensional digital space only those of the (a, b)-adjacencies commonly used in computer imagery have analogs among the LF spaces, in which a and b are different and one of the adjacencies is the "maximal" one, corresponding to 3 n ? 1 neighbors. Even these (a, b)-adjacencies have important limitations and drawbacks. The most important one is that they are applicable only to binary images. The way of easily using LF spaces in computer imagery on standard orthogonal grids containing only pixels or voxels and no cells of lower dimensions is suggested.

Cubic curves from instanton counting

Abstract: We investigate the possibility to extract Seiberg-Witten curves from the formal series for the prepotential, which was obtained by the Nekrasov approach. A method for models whose Seiberg-Witten curves are not hyperelliptic is proposed. It is applied to the SU(N) model with one symmetric or antisymmetric representations as well as for SU(N1) × SU(N2) model with (N1,N2) or (N1,2) bifundamental matter. Solution are compared with known results. For the gauge group product we have checked the instanton corrections which follow from our curves against direct instanton counting computations up to two instantons.

Optical add-drop multiplexers based on the antisymmetric waveguide Bragg grating

Abstract: A novel optical add-drop multiplexer (OADM) based on a null coupler with an antisymmetric grating was designed and experimentally demonstrated. The antisymmetric grating exclusively produces a reflection with mode conversion in a two-mode waveguide. This improves the performance compared with previous demonstrations that used tilted Bragg gratings. Our design minimizes noise and cross talk produced by reflection without mode conversion. In addition, operational bandwidth and, versatility are improved while the compactness and simplicity of the null coupler OADM are maintained.

μ–τ antisymmetry and neutrino mass matrices

Abstract: Using the seesaw mechanism and a discrete symmetry, we construct a class of models for the neutrino mass matrix where the inverse of that matrix is the sum of a μ–τ antisymmetric background and a perturbation. We consider various possibilities for that perturbation. The simplest possible perturbations lead to four-parameter neutrino mass matrices which are unable to fit the experimental data. More complicated perturbations give rise to viable six-parameter mass matrices; we present detailed predictions of each of them.

FE modeling of Lamb mode diffraction by defects in anisotropic viscoelastic plates

Abstract: A Finite Element code is used in a stationary mode to compute, at a single frequency, the stress and displacement fields in plates made of anisotropic, viscoelastic materials. An appropriated spatial load at one boundary of the plate is applied to generate a guided mode. This step is included in a frequency loop for which the number of iterations (≈ usually less than 50) is defined by the frequency spectrum of a temporal excitation. Then the temporal response at any location in the plate can be reconstructed with inverse Fourier transform. The phase velocity, attenuation and nature of one or several propagating modes can be identified in the classical frequency/wave number representation. The first example concerns the interaction of the symmetric Lamb mode S0 with an opening notch in a Perspex plate. The proportion of S0 and converted antisymmetric A0 mode, transmitted past the notch is evaluated by the FE method and validated by a comparison with measurements made on a real system using an air coupled transducer. The second example shows the effect of the viscoelasticity on the propagation of the symmetric Lamb mode S0 in a cross-ply, carbon-epoxy material plate. Focus is made on some difficulties that the attenuation causes on the detection of a delamination between plies.

Enhanced Recollisions for Antisymmetric Molecular Orbitals in Intense Laser Fields

Abstract: The peculiarities of antisymmetric molecular orbitals are investigated in very intense linearly polarized laser pulses. For this purpose, the ionization-recollision quantum dynamics is evaluated theoretically beyond the dipole approximation. As opposed to the usual situation, the laser magnetic field component is found to strongly enhance recollision probabilities for particularly oriented antisymmetric molecular orbitals. Harmonic generation and related processes are thus allowed at high laser intensities without the common limitations by the laser magnetic field.

Two-dimensional Raman spectra of atomic solids and liquids

Abstract: We calculate third- and fifth-order Raman spectra of simple atoms interacting through a soft-core potential by means of molecular-dynamics (MD) simulations. The total polarizability of molecules is treated by the dipole-induced dipole model. Two- and three-body correlation functions of the polarizability at various temperatures are evaluated from equilibrium MD simulations based on a stability matrix formulation. To analyze the processes involved in the spectroscopic measurements, we divide the fifth-order response functions into symmetric and antisymmetric integrated response functions; the symmetric one is written as a simple three-body correlation function, while the antisymmetric one depends on a stability matrix. This analysis leads to a better understanding of the time scales and molecular motions that govern the two-dimensional (2D) signal. The 2D Raman spectra show novel differences between the solid and liquid phases, which are associated with the decay rates of coherent motions. On the other hand, these differences are not observed in the linear Raman spectra.

Efficient Algorithm for Solving Semi-Infinite Programming Problems and Their Applications to Nonuniform Filter Bank Designs

Abstract: An efficient algorithm for solving semi-infinite programming problems is proposed in this paper. The index set is constructed by adding only one of the most violated points in a refined set of grid points. By applying this algorithm for solving the optimum nonuniform symmetric/antisymmetric linear phase finite-impulse-response (FIR) filter bank design problems, the time required to obtain a globally optimal solution is much reduced compared with that of the previous proposed algorithm

Fast magnetohydrodynamic waves in a two-slab coronal structure: collective behaviour

Abstract: Aims. We study fast magnetohydrodynamic waves in a system of two coronal loops modeled as smoothed, dense plasma slabs in a uniform magnetic field. This allows us to analyse in a simple configuration the collective behaviour of the structure due to the interaction between the slabs. Methods. We first calculate the normal modes of the system and find analytical expressions for the dispersion relation of the two-slab configuration. Next, we study the time-dependent problem of the excitation of slab oscillations by numerically solving the initial value problem. We investigate the behaviour of the system for several shapes of the initial disturbances. Results. The symmetric mode respect to the centre of the structure is the only trapped mode for all distances between the slabs while the antisymmetric mode is leaky for small slab separations. Nevertheless, there is a wide range of slab separations for which the fundamental symmetric and antisymmetric trapped modes are allowed and have very close frequencies. These modes are excited according to the parity of the initial perturbation. Conclusions. We find that for any initial disturbance the slabs oscillate with the normal modes of the coupled slab system, which are different from the modes of the individual slabs. We show that it is possible to excite the symmetric and antisymmetric trapped modes at the same time. This kind of excitation can produce the beating phenomenon, characterised by a continuous exchange of energy between the individual slabs.

Generating dyonic solutions in 5D Einstein-dilaton gravity with antisymmetric forms and dyonic black rings

Abstract: We consider five-dimensional Einstein-dilaton gravity with antisymmetric forms. Assuming staticity and a restriction on the dilaton coupling parameters, we derive a four-dimensional sigma model with a target space $SL(2,R)/SO(1,1)\ifmmode\times\else\texttimes\fi{}SL(2,R)/SO(1,1)$. On this basis, using the symmetries of the target space, we develop a solution-generating technique and employ it to construct new asymptotically flat and nonflat dyonic black rings solutions. The solutions are analyzed and the basic physical quantities are calculated.

A wavelet based sparse grid method for the electronic Schrödinger equation

Abstract: We present a direct discretization of the electronic Schrodinger equation. It is based on one-dimensional Meyer wavelets from which we build an anisotropic multiresolution analysis for general particle spaces by a tensor product construction. We restrict these spaces to the case of antisymmetric functions. To obtain finite-dimensional subspaces we first discuss semidiscretization with respect to the scale parameter by means of sparse grids which relies on mixed regularity and decay properties of the electronic wave functions. We then propose different techniques for a discretization with respect to the position parameter. Furthermore we present the results of our numerical experiments using this new generalized sparse grid methods for Schrodinger�s equation.

The Complexity of Computing the Size of an Interval

Abstract: Given a p-order $A$ over a universe of strings (i.e., a transitive, reflexive, antisymmetric relation such that if $(x, y) \in A$, then $|x|$ is polynomially bounded by $|y|$), an interval size function of $A$ returns, for each string $x$ in the universe, the number of strings in the interval between strings $b(x)$ and $t(x)$ (with respect to $A$), where $b(x)$ and $t(x)$ are functions that are polynomial-time computable in the length of $x$. By choosing sets of interval size functions based on feasibility requirements for their underlying p-orders, we obtain new characterizations of complexity classes. We prove that the set of all interval size functions whose underlying p-orders are polynomial-time decidable is exactly mP. We show that the interval size functions for orders with polynomial-time adjacency checks are closely related to the class FPSPACE(poly). Indeed, FPSPACE(poly) is exactly the class of all nonnegative functions that are an interval size function minus a polynomial-time computable function. We study two important functions in relation to interval size functions. The function mDIV maps each natural number $n$ to the number of nontrivial divisors of $n$. We show that mDIV is an interval size function of a polynomial-time decidable partial p-order with polynomial-time adjacency checks. The function mMONSAT maps each monotone boolean formula $F$ to the number of satisfying assignments of $F$. We show that mMONSAT is an interval size function of a polynomial-time decidable total p-order with polynomial-time adjacency checks. Finally, we explore the related notion of cluster computation.

On a Completely Antisymmetric Cartan Torsion Tensor

Abstract: We discuss the general structure of metric geometries, and how metricity implies the complete antisymmetry of Cartan tensor; an application in the frame of Lie group theory is given. Interpretations of the completely antisymmetric torsion in physical models are reviewed.

Nonuniform Spin Triplet Superconductivity due to Antisymmetric Spin-Orbit Coupling in Noncentrosymmetric Superconductor CePt$_3$Si

Abstract: We show that the nonuniform state (Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state) of the spin triplet superconductivity in noncentrosymmetric systems is stabilized by antisymmetric spin-orbit coupling even if the magnetic field is absent. The transition temperature of the spin triplet superconductivity is reduced by the antisymmetric spin-orbit coupling in general. This pair breaking effect is shown to be similar to the Pauli pair breaking effect due to magnetic field for the spin singlet superconductivity, in which FFLO state is stabilized near the Pauli limit (or Chandrasekhar-Clogston limit) of external magnetic field. Since there are gapless excitations in nonuniform superconducting state, some physical quantities such as specific heat and penetration depth should obey the power low temperature-dependences. We discuss the possibility of the realization of nonuniform state in CePt$_3$Si.

Thermomechanical Postbuckling Analysis of Cross-Ply Laminated Cylindrical Shell Panels

Abstract: The postbuckling analysis of symmetric and antisymmetric cross-ply laminated cylindrical shell panels subjected to thermomechanical loading is examined in this paper The formulation is based on an extension of Reissner’s shallow shell simplifications and accounts for parabolic distribution of transverse shear strains Adopting a multiterm Galerkin’s method, the governing nonlinear partial differential equations are reduced into a set of nonlinear algebraic equations The nonlinear equilibrium paths through limit points are traced using the Newton–Raphson method in conjunction with Riks approach Numerical results are presented for symmetric [0∕90∕0] and antisymmetric [0∕90] cross-ply laminated cylindrical shell panels, that illustrate the influence of mechanical edge loads, lateral distributed load, initial imperfection, and temperature field on the limit loads and snap-through behavior