Tensor Technique Research Articles

The twisted open string partition function and Yukawa couplings

We use the operator formalism to derive the bosonic contribution to the twisted open string partition function in toroidal compactifications. This amplitude describes, for instance, the planar interaction between g+1 magnetized or intersecting D-branes. We write the result both in the closed and in the open string channel in terms of Prym differentials on the appropriate Riemann surface. Then we focus on the g=2 case for a 2-torus. By factorizing the twisted partition function in the open string channel we obtain an explicit expression for the 3-twist field correlator, which is the main ingredient in the computation of Yukawa couplings in D-brane phenomenological models. This provides an alternative method for computing these couplings that does not rely on the stress-energy tensor technique.

MODELING THE RELATIVE MOTION OF MAGNETIC LEVITATING TRAIN

The expediency of studying the relative movement of magnetically levitated train with the use of mathematical modeling has been substantiated. Proceeding from results of alternative options of such modeling, advantages of its tensor techniques are shown. The order of required model construction with the use of these techniques has been tracked.

Use of the Nye tensor in analyzing HREM images of bcc screw dislocations

The Nye tensor characterizes the strength of infinitesimal dislocations at each point in a continuously dislocated crystal, and provides a measure of the Burgers vector and the extent of dislocation dissociation. The present work employs this description to analyze ½ screw dislocations in bcc Mo obtained by Finnis–Sinclair, Bond Order Potential and first-principles simulations in an attempt to detect misfit in the core region. The spatial distribution and strength of the fractional dislocations are calculated and compared between the different simulated core structures. The Nye tensor technique is also applied to HREM images of end-on screw dislocations in Mo to detect the edge fractional dislocations predicted by simulation. The advantage of the Nye tensor for this purpose arises from its insensitivity to the Eshelby twist due to surface relaxation in a thin TEM foil (this is not the case for the more conventional methods of depicting misfit, such as direct and differential displacement maps). Although the Eshelby twist was removed from the experimental HREM images, some residual, mottled contrast structure was observed in the Nye tensor plots. This contrast was found to be due to the experimental noise, which masks the true structure of the dislocation core and precludes experimental characterization of screw dislocations in Mo by HREM.

The Linear Combination of Vibrational Wave Functions (LCVW) Method in a Morse–Gaussian Double Well Molecular Potential

The linear combinations of harmonic oscillator wave functions (LCWV) method is proposed to solve the Schrodinger equation, for a particle of a mass μ moving in a one dimensional double-well potential field, in which, the energy barrier has a gaussian shape. The general double well potential, whether symmetric or not, is constructed from appropriate combinations of Morse-like potentials and a Gaussian function and the problem is solved variationally, using as trial functions, linear combinations of harmonic oscillator wave functions (LCWV) centered at the two minima. The relevant matrix elements are calculated using the Harmonic Oscillator Tensor (HOT) technique. A generalization to multiple well problems is also advanced.

Diquarks in nonaquark states

We study the nonaquark states ${S}^{0}(3115)$ and ${S}^{+}(3140)$ which are reported by [T. Suzuki (KEK-PS), Phys. Lett. B 597, 236 (2004)M. Iwasaki et al., nucl-ex/0310018] by means of the quark model with diquark correlation. The nonaquark states form $\mathbf{1},\mathbf{8},\mathbf{10},\overline{\mathbf{10}},\mathbf{27},\overline{\mathbf{35}}$ SU(3) multiplets. The flavor wave functions of all the nonaquark states are constructed through the standard tensor technique. The mass spectrum is studied by using the Gell-Mann-Okubo mass formula. Some nonaquark mass sum rules are obtained. We further investigate the decay of ${S}^{0}(3115)$ and ${S}^{+}(3140)$ under the assumption of the ``fall-apart'' mechanism. It has been found that the main decay mode is $\ensuremath{\Sigma}NN$ rather than $\ensuremath{\Lambda}NN$ which is consistent with experiment. Also we have uniquely determined the flavor wave function of ${S}^{0}(3115)$ which belongs to the $\mathbf{27}$-plet with the quantum number $Y=2,I=1,{I}_{z}=\ensuremath{-}1$. Whereas the exotic states ${S}^{+}(3140)$ can belong to either the $\mathbf{27}$-plet or the $\overline{\mathbf{35}}$-plet. In the exact $\mathrm{SU}(3{)}^{\mathrm{flavor}}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3{)}^{\mathrm{color}}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2{)}^{\mathrm{spin}}$ limit, both ${S}^{0}(3115)$ and ${S}^{+}(3140)$ belong to the $\mathbf{27}$-plet with negative parity. We predict that its flavor structure can be determined by measuring the branch fractions of its decay channels. The experiments to check this prediction are as expected.

Efficient Scattering Calculations in Complex Backgrounds

The utilization of the Green's tensor associated with a complex optical background (surface, cavity or stratified medium) leads to a dramatic reduction of the computation effort associated with scattering calculations in that background. This approach is illustrated with examples where a mere change of the background Green's tensor makes possible the investigation of completely different physical situations. Two different discretization approaches are compared and similarities between the Green's tensor technique and the Method of Lines are emphasized; in the latter, the utilization of analytic solutions in one specific direction also reduces the discretization of the system.

A Green's tensor approach to the modeling of nanostructure replication and characterization

We use the Green's tensor technique to study the optical processes taking place in configurations typically used for the replication and characterization of nanostructures. For the replication process we investigate light‐coupling masks for optical contact lithography and for the characterization process the mode scattered by a defect or a short grating in a planar waveguide. Both configurations consist of structures embedded in a stratified background composed of a stack of material layers with different permittivities. We perform calculations for two‐dimensional and three‐dimensional structures and compare their optical behavior. Our results show that the additional material interfaces in three‐dimensional systems can lead to significantly different field distributions and must be taken into account for a complete understanding of the electromagnetic properties of the systems.

Scattering experiments with a diving cylinder

We present numerical experiments of light scattering by a circular dielectric cylinder embedded in a stratified background, using the Green's tensor technique. The stratified background consists of two or three dielectric layers, the latter forming an anti-reflection system. We show movies of the scattered field as a function of different parameters: polarization, angle of incidence, and relative position of the cylinder with respect to the background interfaces.

Contrast mechanisms in high-resolution contact lithography: A comparative study

We compare three different approaches to high-resolution contact lithography with special emphasis on contrast mechanisms for subwavelength structures. Masks with protruding metal absorbers, masks with absorbers embedded in the transparent background, and masks with air gaps and recessed absorbers are studied. Using the Green’s tensor technique we compute the light intensity distribution in the photoresist. The intensity and contrast functions are investigated for different mask geometries (absorber thickness, height of protruding elements), and the difference between chrome and gold as absorber material is discussed. Our results show that embedding the absorbers in a transparent mask material enhances the transmitted intensity and the contrast compared with a mask having protruding metal absorbers. A further improvement is achieved by a topographically patterned mask with air gaps and recessed absorbers. Optimized mask dimensions can be found for which the contrast and the depth of focus are increased.

How to tap an innocent waveguide

We study the interaction of a mode propagating in a planar waveguide with a three--dimensional rectangular defect (protrusion or notch) in the structure. The scattering by the defect disturbes the propagation of the mode and light is coupled out of the waveguide. To investigate these phenomena we compute electric field distributions with the Green's tensor technique and show movies with varying defect geometries and different mode polarizations. These calculations should be useful for optimizing specific elements in complex photonic circuits.

Green's tensor technique for scattering in two-dimensional stratified media.

We present an accurate and self-consistent technique for computing the electromagnetic field in scattering structures formed by bodies embedded in a stratified background and extending infinitely in one direction (two-dimensional geometry). With this fully vectorial approach based on the Green's tensor associated with the background, only the embedded scatterers must be discretized, the entire stratified background being accounted for by the Green's tensor. We first derive the formulas for the computation of this dyadic and discuss in detail its physical substance. The utilization of this technique for the solution of scattering problems in complex structures is then illustrated with examples from photonic integrated circuits (waveguide grating couplers with varying periodicity).

Macroseismic field generated by 29 March, 1999 Chamoli Earthquake and its seismotectonics

A damaging earthquake of magnitude 6.4 mb (USGS) rocked the Garhwal region on 29 March, 1999 at 00:35:00 hours (IST). Maximum intensities of VIII and VII on the Medvedev–Sponheaer–Karnik (MSK-64) scale and the European Macroseismic Scale-98 (EMS-98) were observed in the affected region. Extensive damage was noticed both in the Chamoli and Rudraprayag regions of the Garhwal Himalaya. In the Chamoli region, damage of intensity VIII was confined to the right bank of the river Alaknanda. In the Rudraprayag region, the damage was widespread between Chandrapuri and Cantha villages. An isoseismal map prepared on the basis of a damage survey shows a NW–SE trend with its major axis in the NW–SE direction and minor axis in the NE–SW direction in the Rudraprayag region. The major axis is 11 km long and minor axis 8 km long. Thus the VIII isoseismal zone covers an area of approximately 88 km 2. The damage survey revealed that maximum damage has been either along major faults or to adobe houses, locally called Pathal houses. The damage was also higher than expected because of the use of undressed stones and heavy Pathal (slate) roofing. The villages of Kansali, Pingalpani, Akhori, Kiyunja, Sena, Cantha, Tewri, Talsari, and Chamoli were the most affected in the Rudraprayag and Chamoli regions. Grade 4 and Grade 3 damage has been observed in many adobe houses in the intensity zone VII. The study of damage distribution and intensity attenuation has demonstrated an asymmetric distribution and heterogeneous behaviour. The heterogeneous pattern could be related to rupture asperity distribution. A noteworthy feature of this earthquake was that it has produced a lot of ground fissures, some traceable for many tens to hundreds of meters affecting both rocks and overburden. One such fissure was traced for nearly 500 m trending NW–SE with a downthrow of 20–25 cm. This fissure shows thrust faulting with the foot wall having moved down towards the NE and the hanging wall upwards toward the SW side. This is in conformity with the fault plane solution given by the USGS using the moment tensor technique, which indicates that the earthquake originated by slip along a low angle thrust fault dipping NE. Changes in hydrological conditions have been noticed in a number of villages, for example Kiyunja, Kansali, Talsari, Pingalpani, Mukku, Sena, Akhori, Tewri, Gurpunga and Bhatwari etc.

Motion Determination in Actin Filament Fluorescence Images with a Spatio-Temporal Orientation Analysis Method

We present a novel approach of automatically measuring motion in series of microscopic fluorescence images. As a differential method, the three-dimensional structure tensor technique is used to calculate the displacement vector field for every image of the sequence, from which the velocities are subsequently derived. We have used this method for the analysis of the movement of single actin filaments in the in vitro motility assay, where fluorescently labeled actin filaments move over a myosin decorated surface. With its fast implementation and subpixel accuracy, this approach is, in general, very valuable for analyzing dynamic processes by image sequence analysis.

Near-field distribution in light-coupling masks for contact lithography

We discuss the potential and limitations of light-coupling masks for high-resolution subwavelength optical lithography. Using a three-dimensional fully vectorial numerical approach based on Green’s tensor technique, the near-field distribution of the electric field in the photoresist is calculated. We study the dependence of the illuminating light and the angle of incidence on polarization. Furthermore, we investigate the replication of structures of various sizes and separations. It is predicted that the formation of features in the 60 nm range is possible using light with a 248 nm wavelength. However, with decreasing separation among the features, crosstalk limits the ultimate resolution.

Electromagnetic scattering in polarizable backgrounds

We develop a fully vectorial formalism for the investigation of electromagnetic scattering in polarizable backgrounds, i.e., where the scatterers are not in vacuum but situated in a medium with a dielectric permittivity different from unity. Our approach is based on the Green's tensor technique and the corresponding Green's tensors for two-dimensional (2D) and three-dimensional (3D) systems are developed. The analysis of 2D systems is not restricted to the case where transverse electric (TE) and transverse magnetic (TM) modes are decoupled, but treated in a general manner. Practical examples illustrate the application of the method: scattering by a microcavity for two dimensions and color formation in opal for three dimensions.

The harmonic oscillator tensor approach to the eigenspectra of multiple-well molecular potentials. I. Non-periodic potentials

Using an irreducible tensor technique, we have derived matrix elements for the non-periodical vibrational operators qk, qkeλη and qkeλq2 in the basis of the non-degenerate harmonic oscillator wave functions. The matrix elements are simple and computationally easy to evaluate which makes the method suitable for variational studies of multiple-well potentials.

The harmonic oscillator tensor approach to the eigenspectra of multiple-well molecular potentials II. Periodic potentials

We display the matrix elements for the vibrational operators q k sin( ω k q), q k cos( ω k q), q k sinh( ω k q) and q k cosh( ω k q) k = 0, 1, 2, 3, … derived using an irreducible tensor technique in the basis of the non-degenerate harmonic oscillator wave functions. We give an example of a variational eigenvalue calculation, using matrix elements calculated in this manner, of an arbitrary periodical and non-periodical potentials expanded in fourier series.

On the calculation of derivatives for Coulomb-type interaction energies and general anisotropic pair potentials

We derive efficient algorithms for the derivatives, in particular the forces, torques and the Hessian, for Coulomb-type interactions and for general anisotropic pair potentials. We use spherical tensor techniques and an intermediate transformation to a quasi-internal coordinate system, proposed recently to obtain a factorization of the multipole interaction tensors. By these means we obtain a unified approach to the derivatives at small extra computational cost to the energy calculation. For the special case of an electrostatic interaction the computational cost scales for a system of N molecules through rank L in the multiple expansion as N 2 x O(L 3) for both the energy and its derivatives.

SOLID-STATE CONTROLLED SINGLE-PHASE INDUCTION MOTOR

ABSTRACT Single-phase induction motors are widely used in domestic appliances, workshops and factories. Many conventional methods are used to control these motors. There is no one method by which single phase induction motors can be started, speed-controlled and reversed. This paper presents a new method for controlling single-phase induction motors with two symmetrical stator windings utilizing two triacs; one in series with the main winding and the other with the auxiliary one. Such a connection will perform all the required jobs namely; starting, speed control and reversing the direction of rotation, the motor is represented in the dqo reference frame. A rigorous state space mathematical model is developed to describe the system. Kron's tensor technique is applied using variable connection matrix to care for the nonlinearities introduced by the triacs. Computer results for transient and steady state conditions are presented. Also, the proposed method has been verified experimentally.

Dielectric versus topographic contrast in near-field microscopy

Using a fully vectorial three-dimensional numerical approach (generalized field propagator, based on Green’s tensor technique), we investigate the near-field images produced by subwavelength objects buried in a dielectric surface. We study the influence of the object index, size, and depth on the near field. We emphasize the similarity between the near field spawned by an object buried in the surface (dielectric contrast) and that spawned by a protrusion on the surface (topographic contrast). We show that a buried object with a negative dielectric contrast (i.e., with a smaller index than its surrounding medium) produces a near-field image that is reversed from that of an object with a positive contrast.