Linear Planar Research Articles

Spatial soliton switching modes of nonlinear optical slab waveguides

A planar nonlinear waveguide, consisting of a linear substrate, a linear film, and a Kerr-type cladding and end-fire excited by the TE0 mode of a linear planar waveguide, is studied both numerically and analytically (by means of the equivalent-particle model). It is shown that a switching device whose output is controlled by the input optical power can operate not only in the well-known soliton-breakup mode but also in a low-power mode. Furthermore, the device is shown to be highly sensitive to ak0, the product of the guide half-width times the wave number of the incoming beam.

Metal-clad graded-index planar optical waveguides: accurate perturbation analysis

We present a perturbation analysis of propagation constants and attenuation coefficients of TE and TM modes in a metal-clad linear index planar optical waveguide. The imaginary part N″ of the complex modal index N= N′ + iN″ is given by N″ = ( ∂N′ / ∂∈′), where ∈=∈′ + i∈″ is the complex dielectric constant of the metal cladding and ∂ N′ / ∂∈′ is obtained by numerical differentiation of the solution of the real eigenvalue equation. The cumbersome solution of a complex transcendental equation is thus completely eliminated. The results are in good agreement with those obtained by solving the eigenvalue equation in the complex plane. By taking the metal-clad linear planar waveguide as a preselected waveguide, we can use our RWKB method to solve metal-clad planar waveguides with parabolic, exponential, gaussian and complementary error function index profiles.

Decision analysis and optimality in air traffic control conflict resolution: II. Optimal heading (vectoring) control in a linear planar configuration

This manuscript is concerned with the effects of a heading advisory dispensed by an air traffic controller on a resolution of a pending or an in-progress potential aerial conflict. It is assumed that the aircraft traverse two linear, planar, intersecting air routes with fixed velocities. A potential conflict is defined as a violation of a given safety distance between two airplanes traveling different paths. The controller, upon discerning that the two craft are in potential conflict or about to enter one, issues, at the appropriate instant, corrective vectoring to them in order to obtain an effective dissolution of the conflict. The interpretation of “effective” in this paper is construed as either of the following: a new direction is put forth by the controller so as to maintain an inviolable separation between the two planes while introducing a minimal disturbance to their flight paths, or alternatively, while minimizing the duration of the potential conflict. An analysis of the impact of the controller's instructions on a single conflict involving two planes only, accompanied with illustrative numerical examples, is carried out under two pilot response suppositions. The first stipulates that pilots execute precisely the controller's remedial commands whereas the second allows for a built-in randomness in their response time.

Gold Complexes with Selenium Ligands, II [1] Preparation and Crystal Structures of the Gold Diphenylselenide Complexes Ph2SeAuCl and Ph2SeAuCl3

The complexes Ph2SeAuCl (green) and Ph2SeAuCl3 (brown) are prepared by direct reaction between the diphenylselenide ligand and the corresponding gold chloride. The crystal structures confirm the presence of monomeric, linear (AuI) or square planar (AuIII) coordinated complexes with bond lengths A u(I)-Se 2.378(1), Au(III)-Se 2.445(1) Å. Short non-bonded contacts Au(I) ··· Au(I) and Au(III) ··· Cl are observed.

Convective Diffusion in Two-Dimensional Incompressible Linear Flow

Previous article Next article Convective Diffusion in Two-Dimensional Incompressible Linear FlowPeter S. BernardPeter S. Bernardhttps://doi.org/10.1137/1032125PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractAn exact solution for the Green’s function governing convective diffusion in two-dimensional, linear, incompressible flow is computed by elementary means.Keywordsdiffusionconvection Previous article Next article FiguresRelatedReferencesCited ByDetails Lie group solutions of advection-diffusion equationsPhysics of Fluids, Vol. 33, No. 4 | 1 Apr 2021 Cross Ref Analytical approximations of the diffusive dispersion in fluid flowsEPL (Europhysics Letters), Vol. 108, No. 4 | 25 November 2014 Cross Ref Secondary Splitting of Zero Gradient Points in Turbulent Scalar FieldsProgress in Turbulence and Wind Energy IV | 1 Jan 2012 Cross Ref The secondary splitting of zero-gradient points in a scalar fieldJournal of Engineering Mathematics, Vol. 71, No. 1 | 15 January 2011 Cross Ref A Physics-Based Modeling and Real-Time Simulation of Biomechanical Diffusion Process Through Optical Imaged Alveolar Tissues on Graphical Processing UnitsRecent Advances in the 3D Physiological Human | 31 July 2009 Cross Ref Advection of a passive scalar by a vortex couple in the small-diffusion limitJournal of Fluid Mechanics, Vol. 270, No. -1 | 26 April 2006 Cross Ref Effective diffusion in time‐periodic linear planar flowPhysics of Fluids A: Fluid Dynamics, Vol. 5, No. 10 | 1 Oct 1993 Cross Ref Volume 32, Issue 4| 1990SIAM Review537-722 History Submitted:11 October 1989Accepted:05 December 1989Published online:18 July 2006 InformationCopyright © 1990 Society for Industrial and Applied MathematicsKeywordsdiffusionconvectionMSC codes76R5035K0535K15PDF Download Article & Publication DataArticle DOI:10.1137/1032125Article page range:pp. 660-666ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics

The two basic linear time Planarity algorithms: Are they the same?

We compare the two most widely known planarity testing algorithms, the one due to Hoperoft and Tarjan, and the other to Lempel. Even, and Cederbaum. These two algorithms are generally viewed as very different approaches to the problems of planarity testing and graph embedding. In this paper, however, by utilizing previously unnoticed freedoms of choice in the order in which the operations of the Hoperoft-Tarjan algorithm can be performed, we create a variation of this algorithm which, in terms of the order in which vertices are processed, is indistinguishable on all planar graph inputs from the Lempel -Even-Cederbaum algorithm. This allows one to create hybridized algorithms which, when interpreted as embedding algorithms, combine all of the features of both procedures.

High-packing-density multichannel integrated-optic modules in LiNbO_3 for a programmable correlation of binary sequences

Two 10-channel integrated-optic device modules have been constructed and tested. The architecture common to both modules consists of a LiNbO(3) composite waveguide 1.0 cm x 2.0 cm in size in which a channel-waveguide array, a planar waveguide, a linear microlens array, an electro-optic Bragg modulator array or an acousto-optic and electro-optic Bragg modulator array, and a large-aperture lens are integrated. A novel scheme that employs a linear ionmilled planar microlens array was devised to excite the entire channel-waveguide array simultaneously, and thus greatly facilitate testing and application of the two device modules. The performance characteristics obtained in programmable correlation of binary sequences are also presented.

Soluble saturable refractive-index nonlinearity model

TE modes of an optically linear planar waveguide on a thick nonlinear substrate are described for a model substrate refractive index or dielectric permittivity of the form ϵ= ϵ s + ϵ satu(2+u) (1+u) 2 , where u= α|E| 2 2ϵ sat , which displays saturation at high guided-wave powers, yet for which wave equation integration and power integrals are elementary. The parameter γ= ϵ sat (ϵ f–ϵ s) where ϵ f is the guiding-layer permittivity, determines the guided-wave behavior. For γ<1, little effect is seen; for γ>1, power limiting and interface guiding are observed, similar to the Kerr model except for the saturation effect.

Decision analysis and optimality in air traffic control conflict resolution I. optimal timing of speed control in a linear planar configuration

This paper concerns itself with the effects of the air traffic controller's intervention on the progress of a potential aerial conflict and its resolution. The subsumed model consists of two planar intersecting air routes along which aircraft travel with fixed velocities. A potential conflict is declared whenever two airplanes on different routes violate a given safety distance. The task of the controller is to expediently resolve the conflict by modifying, at the right moment, the relative velocities of the planes involved. The intensity of the potential conflict—measured by its duration and minimum separation—depends, beside the approach pattern, on the variables manipulable by the controller. A complete analytical study of the conflict's intensity as a function of the controller's instructions is carried out, and consequently the optimal decisions that contribute most to the resolution of the conflict are laid out.

Conservation laws in elasticity. III. Planar linear anisotropic elastostatics

The first order conservation laws for an arbitrary homogeneous linear planar elastic material are completely classified. In all cases, both isotropic and anisotropic, besides the standard Betti reciprocity laws, there are two infinite-dimensional families of conservation laws, each depending on an arbitrary analytic function of two complex variables.

Canonical elastic moduli

Every linear planar anisotropic elastic material is equivalent, under a linear change of coordinates, to an orthotropic material. Consequently, up to linear changes of variables, there are just two “canonical” planar elastic moduli which determine the properties of any linearly elastic material. Extensions to three-dimensional elasticity and applications are indicated.

Irreversibility and reactant adsorption in differential pulse polarography

The influence of the adsorption of electractive species on DPP responses of non-reversible redox reactions is described. A linear isotherm and stationary planar diffusion were assumed. The DPP resposes influenced by the adsorption of both the reactant and product are enhanced if the redox reaction is quasi-reversible or totally irreversible. The dependence of the degree of enhancement on the various parameters of the redox reaction, the adsorption process and the excitation signal is analysed.

An electron diffraction study of the gas-phase structure of a sterically hindered cadmium amide, bis(hexamethyldisilylamido)cadmium(II), Cd{N(Si(CH 3) 3) 2} 2

Gaseous bis(hexamethyldisilylamido)cadmium(II), Cd{N(SiMe 3) 2}, 2, has been studied by electron diffraction at a nozzle temperature of ca. 375K. The diffraction data are consistent with a model including only monomers. By assuming a linear NCdN chain and planar environments about the nitrogen atoms, an equilibrium conformer with a staggered Si 2NCdNSi 2 skeleton ( D 2d symmetry) may be brought into a nice agreement with the data. The large value of the amplitude of vibration for the inter-ligand Si…Si distances, 0.31(10) A, indicates that the ligands undergo large-amplitude vibrations about the NCdN axis. The value of the barrier to internal rotation about this axis is estimated to be in the range 1–2 kcal mol −1. A model with an eclipsed, co-planar Si 2NCdNSi 2 backbone ( D 2h symmetry) could not be brought into agreement with the observed intensity data. Some key parameters, including bond lengths ( τ a ) and valence angles, are: CdN 2.03(2) A, SiN 1.727(7) A, SiC 1.881(3) A; ∠CdNSi 114.0(0.6)°, ∠SiNSi 132.0(1.2)°, ∠NSiC 113.6(1.2)° and ∠SiCH 111.0(1.2) 0 (Parenthesized values denote least-squares standard deviations multiplied by a factor of three). The SiMe, groups are twisted 20(3) 0 away from the reference position typified by one SiC bond of each such group eclipsing the adjacent CdN bond, while the methyl groups themselves are essentially in staggered positions, the value of the relevant twist angle being 8(6) 0.

Exact results for a linear chain planar EQQ model

A linear chain planar EQQ model is studied using the transfer matrix method. The specific heat is found to vary as T 2 in the high-temperature limit and is linear in T in the low-temperature to the leading orders.

A Linear Time Planarity Algorithm for 2-Complexes

A linear time algorithm to decide whether a given finite 2- complex is planar is described. Topological results of Gross, Harary and Rosen are the mathematical basis for the algorithm. Optimal running time is achieved by constructing various lists simultaneously and keeping their orderings compatible. If the complex is simplical with p vertices, then the algorithm has O(p) time and space bounds. The algorithm uses depth-first search both in application of the graph planarity algorithm of Hopcroft and Tarjan and elsewhere

An additive treatment of 115In nuclear quadrupole coupling constants for organoindium compounds

Using previously measured 119Sn IV and 115In III e 2 Qq values, we use the additivity model to rationalize and calculate 115In e 2 Qq values for In III in a variety of coordination environments. A semiquantitative estimate of In III e 2 Qq values (in MHz) may be obtained by multiplying the 1 2 s 2Qq value (in mm sec −1) for the isostructural Sn IV compound by 310. Absolute partial quadrupole coupling constants ( pqcc) have been derived for the first time for linear ( sp hybridized metal) and trigonal planar ( sp 2 hybridized metal) species. The ratios of the pqcc values ( pqcc) Me tet:( pqcc) Me tba: ( pqcc) Me oct is 1.23:1.09:1. These are in good agreement with the corresponding 119Sn partial quadrupole splitting ( pqs) values. The relative pqce values for ligands in two to six coordination are in qualitative agreement with those expected from a simple molecular orbital approach. The pqcc parameters are used to calculate the expected e 2 Qq values for a number of methylindium species in four, five, and six coordination. These calculations should be very useful for structural elucidation. For the associated compounds MeInBr 2 and EtInI 2, these calculations suggest highly associated structures with In having a coordination number of greater than four. For the six coordinate Me 2In moieties, the trend in e 2 Qq with C-In-C angle is reproduced qualitatively by a simple distortion calculation.

The hepta(µ2-benzenethiolato)pentacuprate(I) dianion; X-ray crystal and molecular structure

Soluble benzenethiolato-cuprate(I) complexes [Me4N]n[{Cu2(SPh)3}n] and [Me4N]2[Cu5(SPh)7] are formed in ethanol; the crystal structure of the latter is composed of [Cu5(µ2-SPh)7]2– molecular clusters containing linear and trigonal planar copper co-ordination.

Tests of the CNDO method for the band structure of crystalline solids: I. Calculations on lithium fluoride

The feasibility of using the CNDO method for the calculation of the band structure of crystalline solids has been investigated by means of calculations on model systems comprising various configurations of lithium and fluorine atoms. These include a one dimensional linear chain and various planar and cubic structures containing up to 27 atoms. These results show that the typical band structure associated with ionic crystals is reproduced and that a comparison between these results and those of previous experimental and theoretical studies gives encouragement as to the applicability of this method to aspects of the properties of crystalline solids.