Antisymmetric Field Research Articles

구동중인 자동차 배기계의 진동 특성 측정

In this work, the operational deflection shape(ODS) of an automobile exhaust system is measured by using a recently-developed magnetic sensor. The magnetic sensor is composed of a solenoid and two pairs of permanent magnets generating an antisymmetric magnetic field in the lateral direction inside the solenoid. Lateral movement of a ferromagnetic pipe inside the magnetic field of the suggested sensor induces an electromotive force in the solenoid corresponding to the lateral velocity of the pipe. Due to the simplicity and non-contact characteristics of the magnetic sensor, dynamic behaviors of the structures operating under high temperature such as an exhaust pipe can be efficiently observed. It is shown that the lateral ODS of an exhaust system can be successfully measured by the suggested sensors.

The geometrical form for the string space-time action

In the present article, we derive the space-time action of the bosonic string in terms of geometrical quantities. First, we study the space-time geometry felt by a probe bosonic string moving in antisymmetric and dilaton background fields. We show that the presence of the antisymmetric field leads to space-time torsion, and the presence of the dilaton field leads to space-time non-metricity. Using these results we obtain the integration measure for space-time with stringy non-metricity, requiring its preservation under parallel transport. We derive the Lagrangian depending on stringy curvature, torsion and non-metricity.

Generating mass and topological terms to the antisymmetric tensor matter field by Higgs mechanism

The interaction between the complex antisymmetric tensor matter field and a scalar field is constructed. We analyze the Higgs mechanism and show the generation of mass and topological terms by spontaneous symmetry breaking.

Frequency spectra of elliptic cylindrical shells

The kinetic and strain energy densities were derived for the vibration of an elliptic cylindrical shell of constant thickness. The elastic strain energy density has seven independent kinematic variables: Three displacements, two thickness‐shear, and two thickness‐stretch. The shell has a constant thickness h, finite length L, and is simply supported at its ends (z=0, L), where z is the axial coordinate. The elliptic cross section is defined by the shape parameter a, and the half‐length of the major axis l. Using appropriate comparison functions that satisfy the boundary conditions for a simply supported elliptic cylindrical shell, the system is solved using the Galerkin method. Since the shell has an elliptic cross section, the frequency spectra are categorized into distinct symmetric and antisymmetric displacement fields whose spectra coalesce as the elliptic cross section approaches a circular cross section. Numerical results are presented for two h/l and L/l ratios, and various shape parameters, including the limiting case of a simply supported cylindrical shell (a∼100). [Work supported by the ONR/ASEE Summer Faculty Research Program.]

Symmetry and stability of the geomagnetic field

Computer simulations of the geodynamo reveal a strong inverse correlation between stability and equatorial symmetry of the simulated field. This result is consistent with the paleomagnetically inferred degree of symmetry of Earth's magnetic field during the past 150 Ma, which reversed polarity more frequently when it was more symmetrical. A geodynamo simulation with solid inner core much smaller than it is today produced an exceptionally antisymmetric field, raising the possibility that reversals may have been much less common in the distant geologic past than more recently. Paleomagnetic evidence suggests that this might well be true.

On Chern–Simons (super) gravity, E8 Yang–Mills and polyvector-valued gauge theories in Clifford spaces

It is shown how the E8 Yang–Mills theory is a small sector of a Cl(16) algebra gauge theory and why the 11D Chern–Simons (super) gravity theory can be embedded into a Cl(11) algebra gauge theory. These results may shed some light into the origins behind the hidden E8 symmetry of 11D supergravity. To finalize, we explain how the Clifford algebra gauge theory (that contains the Chern–Simons gravity action in D=11, for example) can itself be embedded into a more fundamental polyvector-valued gauge theory in Clifford spaces involving tensorial coordinates xμ1μ2,xμ1μ2μ3,…,xμ1μ2…μD in addition to antisymmetric tensor gauge fields Aμ1μ2,Aμ1μ2μ3,…,Aμ1μ2…μD. The polyvector-valued supersymmetric extension of this polyvector valued bosonic gauge theory in Clifford spaces may reveal more important features of a Clifford-algebraic structure underlying M, F theory.

Metal foil method for noncontact measurement of lateral vibrations of a nonmetallic cylinder by a solenoid

This investigation shows that if a solenoid encircles a metal foil loop wound around a nonmetallic cylinder vibrating laterally, an electromotive force is induced in the solenoid. The induction is possible only when the foil loop is complete and an antisymmetric magnetic field is applied to the foil. In this work, stationary permanent magnets were used. Because the solenoid is the sensing element, no physical contact between the element and a test specimen is required. The effects of the metal foil thickness and width on the measurement sensitivity were studied and vibration modal testing of an acryl cylinder was performed.

Gauge symmetries decrease the number of Dp-brane dimensions

It is known that the presence of the antisymmetric background field ${B}_{\ensuremath{\mu}\ensuremath{\nu}}$ leads to the noncommutativity of the Dp-brane manifold. The addition of the linear dilaton field in the form $\ensuremath{\Phi}(x)={\ensuremath{\Phi}}_{0}+{a}_{\ensuremath{\mu}}{x}^{\ensuremath{\mu}}$ causes the appearance of the commutative Dp-brane coordinate $x={a}_{\ensuremath{\mu}}{x}^{\ensuremath{\mu}}$. In the present article we show that for some particular choices of the background fields, ${a}^{2}\ensuremath{\equiv}{G}^{\ensuremath{\mu}\ensuremath{\nu}}{a}_{\ensuremath{\mu}}{a}_{\ensuremath{\nu}}=0$ and ${\stackrel{\texttildelow{}}{a}}^{2}\ensuremath{\equiv}[(G\ensuremath{-}4B{G}^{\ensuremath{-}1}B{)}^{\ensuremath{-}1}{]}^{\ensuremath{\mu}\ensuremath{\nu}}{a}_{\ensuremath{\mu}}{a}_{\ensuremath{\nu}}=0$, the local gauge symmetries appear in the theory. They turn some Neuman boundary conditions into the Dirichlet ones, and consequently decrease the number of the Dp-brane dimensions.

Black holes with quantum massive spin-2 hair

We show that black holes can posses a long range quantum-mechanical hair associated with a massive spin-2 field, which can be detected by a stringy generalization of the Aharovon-Bohm effect, in which a string loop lassoes the black hole. The long distance effect persist for arbitrarily high mass of the spin-2 field. An analogous effect is exhibited by a massive antisymmetric two-form field. We make a close parallel between the two and the ordinary Aharonov-Bohm phenomenon, and also show that in the latter case the effect can be experienced even by the electrically-neutral particles, provided some boundary terms are added to the action.

Instabilities in the nonsymmetric theory of gravitation

We consider the linearized nonsymmetric theory of gravitation (NGT) within the background of an expanding universe and near a Schwarzschild metric. We show that the theory always develops instabilities unless the linearized nonsymmetric Lagrangian reduces to a particularly simple form. This theory contains a gauge invariant kinetic term, a mass term for the antisymmetric metric field and a coupling with the Ricci curvature scalar. This form cannot be obtained within NGT. Next we discuss NGT beyond the linearized level and conjecture that the instabilities are not a relic of the linearization, but are a general feature of the full theory. Finally we show that one cannot add ad hoc constraints to remove the instabilities.

Interplay Between Wetting and Phase Behavior in Binary Polymer Films and Wedges: Monte Carlo Simulations and Mean Field Calculations

Confining a binary mixture, one can profoundly alter its miscibility behavior. The qualitative features of miscibility in confined geometry are ratheruniversal and 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. 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 is studied. 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. The dependence of the phase diagram on the film thickness Δ for antisymmetric surface fields is investigated. Upon decreasing the film thickness, the two critical points approach the symmetry axis of the phase diagram, and below a certain thickness Δtri, there remains only a single critical point at the 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 thickness, Δtri, tricritical behavior is found. The behavior of antisymmetric films is compared with the phase behavior in an antisymmetric double wedge. While the former is the analog of the wetting transition of a planar surface, the latter is related to the filling behavior of a single wedge. Evidence for a second-order interface localization/delocalization transition in an antisymmetric double wedge is presented, and its unconventional critical behavior is related to the predictions of Parry et al. (Phys. Rev. Lett. 83:5535 (1999)) for wedge filling. The critical behavior differs from the Ising universality class and is characterized by strong anisotropic fluctuations.

Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization

We present a numerical analysis of surface plasmon waveguides exhibiting both long-range propagation and spatial confinement of light with lateral dimensions of less than 10% of the free-space wavelength. Attention is given to characterizing the dispersion relations, wavelength-dependent propagation, and energy density decay in two-dimensional Ag/SiO2/Ag structures with waveguide thicknesses ranging from 12 nm to 250 nm. As in conventional planar insulator-metal-insulator (IMI) surface plasmon waveguides, analytic dispersion results indicate a splitting of plasmon modes—corresponding to symmetric and antisymmetric electric field distributions—as SiO2 core thickness is decreased below 100 nm. However, unlike IMI structures, surface plasmon momentum of the symmetric mode does not always exceed photon momentum, with thicker films (d~50 nm) achieving effective indices as low as n=0.15. In addition, antisymmetric mode dispersion exhibits a cutoff for films thinner than d=20 nm, terminating at least 0.25 eV below resonance. From visible to near infrared wavelengths, plasmon propagation exceeds tens of microns with fields confined to within 20 nm of the structure. As the SiO2 core thickness is increased, propagation distances also increase with localization remaining constant. Conventional waveguiding modes of the structure are not observed until the core thickness approaches 100 nm. At such thicknesses, both transverse magnetic and transverse electric modes can be observed. Interestingly, for nonpropagating modes (i.e., modes where propagation does not exceed the micron scale), considerable field enhancement in the waveguide core is observed, rivaling the intensities reported in resonantly excited metallic nanoparticle waveguides.

Rotational and magnetic instability in the diffusive tachocline

In this article we study the linear instability of the two-dimensional strongly stratified model for global MHD in the diffusive solar tachocline. Gilman and Fox [Gilman, P.A. and Fox, P., Joint instability of the latitudinal differential rotation and toroidal magnetic fields below the solar convection zone. Astrophys. J., 1997, 484, 439–454] showed that for ideal MHD, the observed surface differential rotation becomes more unstable than is predicted by Watson's [Watson, M., Shear instability of differential rotation in stars. Geophys. Astrophys. Fluid Dyn., 1981, 16, 285–298] nonmagnetic analysis. They showed that the solar differential rotation is unstable for essentially all reasonable values of the differential rotation in the presence of an antisymmetric toroidal field. They found that for the broad field case B φ∼sinθcosθ, θ being the co-latitude, instability occurs only for the azimuthal m = 1 mode, and concluded that modes which are symmetric (meridional flow in the same direction) about the equator onset at lower field strengths than the antisymmetric modes. We study the effect of viscosity and magnetic diffusivity in the strongly stably stratified case where diffusion is primarily along the level surfaces. We show that antisymmetric modes are now strongly preferred over symmetric modes, and that diffusion can sometimes be destabilising. Even solid body rotation can be destabilised through the action of magnetic field. In addition, we show that when diffusion is present, instability can occur when the longitudinal wavenumber m = 2.

Spherical magnetic instabilities in the Earth’s core and equatorial symmetries

The Boussinesq rotating magnetohydrodynamic equations in a conducting fluid sphere, linearised about a steady basic state, are discretised using scalar and vector spherical harmonics. Vector spherical harmonic representations are used for the basic state vector fields as well as the interaction terms in the equations. The solenoidal property of the perturbation magnetic and velocity fields are imposed on the fields and equations using relations between vector spherical harmonics and toroidal–poloidal representations. The method has several distinct advantages over previous discretisation methods: it produces compact angular spectral equations which require only five core subroutines to generate all interactions and product terms, and only six core subroutines to radially discretise the equations using finite-differences; the core subroutines can be extensively tested using only simple models; and its generality permits very flexible code. We apply our approach to the magnetic instabilities of a steady axisymmetric azimuthal magnetic field. To isolate magnetic instabilities and suppress other instabilities the magnetostrophic approximation is made. The perturbation velocity and magnetic field satisfy the inviscid boundary and insulating exterior conditions, respectively. Results are presented for the simplest equatorially symmetric (quadrupole) and equatorially antisymmetric (dipole) magnetic field models which vanish on a single spherical surface. For each model the perturbation fields decouple into two subproblems, in which the perturbation magnetic field has the same or opposite symmetry to the basic state field. A strong preference is found for the equatorially symmetric perturbation magnetic field in the equatorially symmetric model. However, there is only a marginal preference for the equatorial antisymmetric perturbation magnetic field in the equatorially antisymmetric model. We also consider a class of equatorially unsymmetric basic state magnetic fields which are convex combinations of the first two models. Although the critical Elsasser number does not change appreciably, the most unstable mode changes totally from equatorially symmetric to equatorially antisymmetric. Finally, we consider the effect on the equatorially symmetric model of varying the spherical surface on which the field vanishes. The most unstable mode is always equatorially symmetric. When the dimensionless magnetic-zero radius is decreased below about 0.7 the most unstable mode switches from eastward to westward propagation. The magnetic field perturbation in the westward (eastward) case is strongly confined to the region outside (inside) the magnetic-zero radius.

Observable signals in a string inspired axion-dilaton background and Randall-Sundrum scenario

Rotation angle of the plane of polarization of the distant galactic radio waves has been estimated in a string inspired axion-dilaton background. It is found that the axion,dual to the field strength of the second rank antisymmetric massless Kalb-Ramond field in the string spectrum, produces a wavelength independent optical rotation which is much larger than that produced by the dilaton. Detection of such rotation has been reported in some recent cosmological experiments. The observed value has been compared with our estimated theoretical value following various cosmological constraints. The effects of warped extra dimensions in a braneworld scenario on such an optical rotation have been investigated.

BOSONIC STRING THEORY IN BACKGROUND FIELDS BY CANONICAL METHODS

We investigate classical dynamics of the bosonic string in the background metric, antisymmetric and dilaton fields. We use canonical methods to find Hamiltonian in terms of energy–momentum tensor components. The later are secondary constraints of the theory. Due to the presence of the dilaton field the Virasoro generators have nonlinear realization. We find that, in the curve space–time, opposite chirality currents do not commute. As a consequence of the two-dimensional general covariance, the energy–momentum tensor components satisfy two Virasoro algebras, even in the curve space–time. We emphasize that background antisymmetric and dilaton fields are the origin of space–time torsion and space–time nonmetricity, respectively.

Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model

A numerical analysis of surface plasmon dispersion, propagation, and localization on smooth lossy films is presented. Particular attention is given to determining wavelength-dependent behavior of thin Ag slab waveguides embedded in a symmetric $\mathrm{Si}{\mathrm{O}}_{2}$ environment. Rather than considering Ag as a damped free electron gas, the metal is defined by the experimentally determined optical constants of Johnson and Christy and Palik. As in free electron gas models, analytic dispersion results indicate a splitting of plasmon modes---corresponding to symmetric and antisymmetric field distributions---as film thickness is decreased below $50\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. However, unlike free electron gas models, the surface plasmon wave vector remains finite at resonance with the antisymmetric-field plasmon converging to a pure photon mode for very thin films. In addition, allowed excitation modes are found to exist between the bound and radiative branches of the dispersion curve. The propagation characteristics of all modes are determined, and for thin films (depending upon electric field symmetry), propagation distances range from microns to centimeters in the near infrared. Propagation distances are correlated with both the field decay (skin depth) and energy density distribution in the metal and surrounding dielectric. While the energy density of most long-range surface plasmons exhibits a broad spatial extent with limited confinement in the waveguide, it is found that high-field confinement does not necessarily limit propagation. In fact, enhanced propagation is observed for silver films at ultraviolet wavelengths despite strong field localization in the metal. The surface plasmon characteristics described in this paper provide a numerical springboard for engineering nanoscale metal plasmon waveguides, and the results may provide a new avenue for integrated optoelectronic applications.

Spinning test particle in Kalb-Ramond background

In this work we explore the geodesic deviations of spinning test particles in a string inspired Einstein-Kalb Ramond background. Such a background is known to be equivalent to a spacetime geometry with torsion. We have shown here that the antisymmetric Kalb-Ramond field has significant effect on the geodesic deviation of a spinning test particle. A search for an observational evidence of such an effect in astrophysical experiments may lead to a better undestanding of the geometry of the background spacetime.

Integrability of Generalized (Matrix) Ernst Equations in String Theory

The integrability structures of the matrix generalizations of the Ernst equation for Hermitian or complex symmetric $d\times d$-matrix Ernst potentials are elucidated. These equations arise in the string theory as the equations of motion for a truncated bosonic parts of the low-energy effective action respectively for a dilaton and $d\times d$ - matrix of moduli fields or for a string gravity model with a scalar (dilaton) field, U(1) gauge vector field and an antisymmetric 3-form field, all depending on two space-time coordinates only. We construct the corresponding spectral problems based on the overdetermined $2d\times 2d$-linear systems with a spectral parameter and the universal (i.e. solution independent) structures of the canonical Jordan forms of their matrix coefficients. The additionally imposed conditions of existence for each of these systems of two matrix integrals with appropriate symmetries provide a specific (coset) structures of the related matrix variables. An equivalence of these spectral problems to the original field equations is proved and some approach for construction of multiparametric families of their solutions is envisaged.

TOPOLOGICAL MASS IN SEVEN DIMENSIONS AND DUALITIES IN FOUR DIMENSIONS

The massive topologically and self-dual theories in seven dimensions are considered. The local duality between these theories is established and the dimensional reduction leads to different dualities for massive antisymmetric fields in four dimensions.