Showing papers on "Antisymmetric relation published in 2005"

Algorithms for Numerical Analysis in High Dimensions

Abstract: Nearly every numerical analysis algorithm has computational complexity that scales exponentially in the underlying physical dimension. The separated representation, introduced previously, allows many operations to be performed with scaling that is formally linear in the dimension. In this paper we further develop this representation by (i) discussing the variety of mechanisms that allow it to be surprisingly efficient; (ii) addressing the issue of conditioning; (iii) presenting algorithms for solving linear systems within this framework; and (iv) demonstrating methods for dealing with antisymmetric functions, as arise in the multiparticle Schrodinger equation in quantum mechanics. Numerical examples are given.

Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities

Abstract: We describe a method to project photonic two-qubit states onto the symmetric and antisymmetric subspaces of their Hilbert space. This device utilizes an ancillary coherent state, together with a weak cross-Kerr nonlinearity, generated, for example, by electromagnetically induced transparency. The symmetry analyzer is nondestructive, and works for small values of the cross-Kerr coupling. Furthermore, this device can be used to construct a nondestructive Bell-state detector.

Algebraic Flux Correction I. Scalar Conservation Laws

Abstract: An algebraic approach to the design of multidimensional high-resolution schemes is introduced and elucidated in the finite element context. A centered space discretization of unstable convective terms is rendered local extremum diminishing by a conservative elimination of negative off-diagonal coefficients from the discrete transport operator. This modification leads to an upwind-biased low-order scheme which is nonoscillatory but overly diffusive. In order to reduce the incurred error, a limited amount of compensating antidiffusion is added in regions where the solution is sufficiently smooth. Two closely related flux correction strategies are presented. The first one is based on a multidimensional generalization of total variation diminishing (TVD) schemes, whereas the second one represents an extension of the FEM-FCT paradigm to implicit time-stepping. Nonlinear algebraic systems are solved by an iterative defect correction scheme preconditioned by the low-order evolution operator which enjoys the M-matrix property. The dffusive and antidiffusive terms are represented as a sum of antisymmetric internodal fluxes which are constructed edge-by-edge and inserted into the global defect vector. The new methodology is applied to scalar transport equations discretized in space by the Galerkin method. Its performance is illustrated by numerical examples for 2D benchmark problems.

Critical points of the Onsager functional on a sphere

Abstract: We study Onsager's model of isotropic–nematic phase transitions with orientation parameter on a sphere. We consider two interaction potentials: the antisymmetric (with respect to orientation inversion) dipolar potential and symmetric Maier–Saupe potential. We prove the axial symmetry and derive explicit formulae for all critical points, thus obtaining their complete classification. Finally, we investigate their stability and construct the corresponding bifurcation diagrams.

FENE Dumbbell Model and Its Several Linear and Nonlinear Closure Approximations

Abstract: We present some analytical and numerical studies on the finite extendible nonlinear elasticity (FENE) model of polymeric fluids and its several moment-closure approximations. The well-posedness of the FENE model is established under the influence of a steady flow field. We further infer existence of long-time and steady-state solutions for purely symmetric or antisymmetric velocity gradients. The stability of the steady-state solution for a general velocity gradient is illuminated by the analysis of the FENE-P closure approximation. We also propose a new linear closure approximation utilizing higher moments, which is shown to generate more accurate approximations than other existing closure models for moderate shear or extension rates. An instability phenomenon under a large strain is also investigated. This paper is a sequel to our earlier work [P. Yu, Q. Du, and C. Liu, Multiscale Model. Simul., 3 (2005), pp. 895--917].

Fluxed minimal supersymmetric standard model

Abstract: Recent developments in string compactifications in the presence of antisymmetric field backgrounds suggest a new simple and predictive structure for soft terms in the MSSM depending only on two parameters. They give rise to a positive definite scalar potential, a solution to the $\ensuremath{\mu}$-problem, flavor universality and absence of a SUSY-CP problem.

Physical interpretation of the NUT family of solutions

Abstract: We demonstrate by the use of Komar integrals that the aggregate mass of two semi-infinite sources which are present in the general family of NUT solutions is a negative nonzero quantity, while the corresponding angular momentum always assumes an infinitely large value except for one particular case when it is equal to zero. In the latter case the solution is equatorially antisymmetric and represents the exterior field of two identical counter-rotating semi-infinite sources possessing negative masses and infinite angular momenta which are attached to the poles of a static Schwarzschild-like finite rod of positive mass.

Antisymmetric magnetoresistance in magnetic multilayers with perpendicular anisotropy.

Abstract: While magnetoresistance (MR) has generally been found to be symmetric in applied field in nonmagnetic or magnetic metals, we have observed antisymmetric MR in $\mathrm{C}\mathrm{o}/\mathrm{P}\mathrm{t}$ multilayers. Simultaneous domain imaging and transport measurements show that the antisymmetric MR is due to the appearance of domain walls that run perpendicular to both the magnetization and the current, a geometry existing only in materials with perpendicular magnetic anisotropy. As a result, the extraordinary Hall effect gives rise to circulating currents in the vicinity of the domain walls that contributes to the MR. The antisymmetric MR and extraordinary Hall effect have been quantitatively accounted for by a theoretical model.

Finite-band solitons in the Kronig-Penney model with the cubic-quintic nonlinearity

Abstract: We present a model combining a periodic array of rectangular potential wells [the Kronig-Penney (KP) potential] and the cubic-quintic (CQ) nonlinearity. A plethora of soliton states is found in the system: fundamental single-humped solitons, symmetric and antisymmetric double-humped ones, three-peak solitons with and without the phase shift pi between the peaks, etc. If the potential profile is shallow, the solitons belong to the semi-infinite gap beneath the band structure of the linear KP model, while finite gaps between the Bloch bands remain empty. However, in contrast with the situation known in the model combining a periodic potential and the self-focusing Kerr nonlinearity, the solitons fill only a finite zone near the top of the semi-infinite gap, which is a consequence of the saturable character of the CQ nonlinearity. If the potential structure is much deeper, then fundamental and double (both symmetric and antisymmetric) solitons with a flat-top shape are found in the finite gaps. Computation of stability eigenvalues for small perturbations and direct simulations show that all the solitons are stable. In the shallow KP potential, the soliton characteristics, in the form of the integral power Q (or width w) versus the propagation constant k, reveal strong bistability, with two and, sometimes, four different solutions found for a given k (the bistability disappears with the increase of the depth of the potential). Disobeying the Vakhitov-Kolokolov criterion, the solution branches with both dQ/dk > 0 and dQ/dk < 0 are stable. The curve Q(k) corresponding to each particular type of the solution (with a given number of local peaks and definite symmetry) ends at a finite maximum value of Q (breathers are found past the end points). The increase of the integral power gives rise to additional peaks in the soliton's shape, each corresponding to a subpulse trapped in a local channel of the KP structure (a beam-splitting property). It is plausible that these features are shared by other models combining saturable nonlinearity and a periodic substrate.

Simulation of excited states and the sign problem in the path integral Monte Carlo method

Abstract: An approach is presented to compute properties of excited states in path integral Monte Carlo simulations of quantum systems. The approach is based on the introduction of several images of the studied system which have the total wavefunction antisymmetric over permutations of these images, and a simulation of the whole system at low enough temperature. The success of the approach relies, however, on the solution of the sign problem for the corresponding system. In the cases when the sign problem may be resolved (as for fermions in one dimension), properties of excited states can be computed with high precision. This was demonstrated by a simulation of excited states of a single particle in one- and two-dimensional harmonic oscillators. An example of the simulation of excited states of several interacting electrons in one dimension is also given.

Wave Propagation in a Micropolar Elastic Plate with Voids

Abstract: Frequency equations are obtained for Rayleigh–Lamb wave propagation in a plate of micropolar elastic material with voids. The thickness of the plate is taken to be finite and the faces of the plate are assumed to be free from stresses. The frequency equations are obtained corresponding to symmetric and antisymmetric modes of vibrations of the plate, and some limiting cases of these equations are discussed. Numerical computations are made for a specific model to solve the frequency equations for symmetric and antisymmetric modes of propagation. It is found that both modes of vibrations are dispersive and the presence of voids has a negligible effect on these dispersion curves. However, the attenuation coefficient is found to be influenced by the presence of voids. The results of some earlier works are also deduced from the present formulation.

Antisymmetric contribution to the planar Hall effect of Fe 3 Si films grown on GaAs ( 113 ) A substrates

Abstract: The planar Hall effect (PHE) in ferromagnets is believed to result from the anisotropic magnetoresistance (AMR) and hence does not change the sign by reversing the direction of the applied in-plane magnetic field. Our studies of the ferromagnetic Heusler alloy ${\mathrm{Fe}}_{3}\mathrm{Si}$ films grown on low-symmetric GaAs(113)A substrates however show a change in the sign of the PHE by reversing the direction of the applied field, indicating the existence of an additional antisymmetric component superimposed with the usual symmetric AMR term. This antisymmetric component shows a maximum along the major in-plane $⟨33\overline{2}⟩$ axes and vanishes along the other major in-plane $⟨\overline{1}10⟩$ axes. A phenomenological model based on the symmetry of the crystal provides a good explanation of the observed antisymmetric contribution to the PHE. The model shows that this component arises from the antisymmetric part of the magnetoresistivity tensor and is basically a second order Hall effect. It is shown that the observed effect can be ascribed to the Umkehr effect, which refers to the coexistence of even and odd terms in the component of magnetoresistivity tensor. A sign reversal of this antisymmetric component is also found for a Si content above 21 at. % and at temperatures below a certain critical temperature which increases with increasing Si content.

The interplay between wetting and phase behaviour in binary polymer films and wedges: Monte Carlo simulations and mean field calculations

Abstract: By confining a binary mixture, one can profoundly alter its miscibility behaviour. The qualitative features of miscibility in confined geometry are rather universal and are shared by polymer mixtures as well as small molecules, but the unmixing transition in the bulk and the wetting transition are typically well separated in polymer blends. We study the interplay between wetting and miscibility of a symmetric polymer mixture via large scale Monte Carlo simulations in the framework of the bond fluctuation model and via numerical self-consistent field calculations. The film surfaces interact with the monomers via short-ranged potentials, and the wetting transition of the semi-infinite system is of first order. It can be accurately located in the simulations by measuring the surface and interface tensions and using Young's equation. If both surfaces in a film attract the same component, capillary condensation occurs and the critical point is close to the critical point of the bulk. If surfaces attract different components, an interface localization/delocalization occurs which gives rise to phase diagrams with two critical points in the vicinity of the pre-wetting critical point of the semi-infinite system. The crossover between these two types of phase diagrams as a function of the surface field asymmetry is studied. We investigate the dependence of the phase diagram on the film width Δ for antisymmetric surface fields. Upon decreasing the film width the two critical points approach the symmetry axis of the phase diagram, and below a certain width, Δtri, there remains only a single critical point at symmetric composition. This corresponds to a second order interface localization/delocalization transition even though the wetting transition is of first order. At a specific film width, Δtri, tricritical behaviour is found. The behaviour of antisymmetric films is compared with the phase behaviour in an antisymmetric double wedge. While the former is the analogy of the wetting transition of a planar surface, the latter is the analogy of the filling behaviour of a single wedge. We present evidence for a second order interface localization/delocalization transition in an antisymmetric double wedge and relate its unconventional critical behaviour to the predictions of Parry et al (1999 Phys. Rev. Lett. 83 5535) for wedge filling. The critical behaviour differs from the Ising universality class and is characterized by strong anisotropic fluctuations. We present evidence that the transition in large double wedges can be of second order although there is a first order wetting transition on a planar substrate.

Mu-tau 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 mu-tau 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.

Nonlinear Dual-core Photonic Crystal Fiber Couplers

Abstract: We study nonlinear modes of dual-core photonic crystal fiber couplers made of a material with the focusing Kerr nonlinearity. We find numerically the profiles of symmetric, antisymmetric, and asymmetric nonlinear modes and analyze all-optical switching generated by the instability of the symmetric mode. We also describe elliptic spatial solitons controlled by the waveguide boundaries.

Few-electron molecular states and their transitions in a single InAs quantum dot molecule.

Abstract: We study electronic configurations in a single pair of vertically coupled self-assembled InAs quantum dots, holding just a few electrons. By comparing the experimental data of nonlinear single-electron transport spectra in a magnetic field with many-body calculations, we identify the spin and orbital configurations to confirm the formation of molecular states by filling both the quantum mechanically coupled symmetric and antisymmetric states. Filling of the antisymmetric states is less favored with increasing magnetic field, and this leads to various magnetic field induced transitions in the molecular states.

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(N_1)xSU(N_2) model with (N_1,N_2) or (N_1,\bar{N}_2) bifundamental matter. Solutions 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.

Observations of improved confinement in field reversed configurations sustained by antisymmetric rotating magnetic fields

Abstract: Rotating magnetic fields (RMF) have been employed to both form and sustain currents in field reversed configurations (FRC). A major concern about this method has been the fear of opening up magnetic field lines with even small ratios of vacuum RMF Bω to external confinement field Be. A recently proposed innovation was to use an antisymmetric arrangement of RMF, but vacuum calculations with full RMF penetration showed that very low values of Bω∕Be would still be required to provide field-line closure. Recent comparisons of symmetric and antisymmetric RMF drive on the translation, confinement, and sustainment (TCS) facility [A. L. Hoffman, H. Y. Guo, J. T. Slough et al., Fusion Sci. Technol. 41, 92 (2002)] have shown strong improvements in the basic confinement properties of the FRCs when using antisymmetric drive, even with ratios of Bω∕Be as high as 0.3. This is due to normal standard operation with only partial penetration of the RMF beyond the FRC separatrix. The uniform transverse RMF in vacuum is shie...

Low loss recursive filters for basestation applications without spurious modes

Abstract: In SAW filters spurious waveguide modes may seriously affect the performance: Undesired lobes in the upper pass- or stopband and ripples in the group delay are typical for devices suffering from waveguiding effects. In order to suppress spurious modes and to excite only the fundamental symmetric mode various approaches as overlap weighting or sawtooth shaping of the busbars in order to destroy the waveguide have been applied. Alternatively recently it was suggested to employ the first antisymmetric mode by splitting the acoustic track into two subtracks, which are longitudinally shifted by half a wavelength with respect to each other. The very reason of the excitation of higher modes is, however, the fact that the excitation profile is of different shape than the fundamental symmetric or antisymmetric mode. In most cases the excitation profile is of rectangular shape while the waveguide modes usually are of sinusoidal shape. While the approaches of prior arts aimed at changing the excitation profile to maximize excitation of the fundamental symmetric or antisymmetric mode we suggest an approach where the waveguide is changed in order to shape the fundamental symmetric mode rectangularly. The approach is applied to low loss recursive inline filters which are employed as intermediate frequency filters in GSM infrastructure systems. The method proves to be particulary successful in reducing group delay ripple and sidelobes. I. INTRODUCTION Spurious modes are a serious problem in SAW filters. They may lead to ripples in the passband, distortions of the group delay time and reduced out of band suppression.

Spin transfer in antisymmetric exchange-biased spin-valves

Abstract: In this letter, we report on measurements of current-induced magnetization switching (CIMS) in current-perpendicular-to-plane exchange-biased spin-valves (ESPVs). The structures of the ESPVs are all “antisymmetric,” but with different thickness of a ruthenium (Ru) layer. It is confirmed that the “antisymmetric” structures largely enhance the spin transfer effect and therefore reduce critical current densities for the CIMS. The effect of the Ru layer on the spin transfer in the ESPVs is also systematically studied. With a decrease of the Ru layer’s thickness, the critical current densities can be further reduced. The lowest critical current we achieved in an “antisymmetric” structure is 1×106A∕cm2, which realizes a reduction of more than one order of magnitude compared with all the reported works.

Phase space flows for non-Hamiltonian systems with constraints.

Abstract: In this paper, non-Hamiltonian systems with holonomic constraints are treated by a generalization of Dirac's formalism. Non-Hamiltonian phase space flows can be described by generalized antisymmetric brackets or by general Liouville operators which cannot be derived from brackets. Both situations are treated. In the first case, a Nos\'e-Dirac bracket is introduced as an example. In the second one, Dirac's recipe for projecting out constrained variables from time translation operators is generalized and then applied to non-Hamiltonian linear response. Dirac's formalism avoids spurious terms in the response function of constrained systems. However, corrections coming from phase space measure must be considered for general perturbations.

Linearized self-forces for branes

Abstract: We compute the regularized force density and renormalized action due to fields of external origin coupled to a brane of arbitrary dimension in a spacetime of any dimension. Specifically, we consider forces generated by gravitational, dilatonic, and generalized antisymmetric form-fields. The force density is regularized using a recently developed gradient operator. For the case of a Nambu-Goto brane, we show that the regularization leads to a renormalization of the tension, which is seen to be the same in both approaches. We discuss the specific couplings which lead to cancellation of the self-force in this case.