Semiconductor waveguide directional couplers for coherent receivers

Optical waveguide 3-dB couplers integrated on semicondutors have been studied, designed and fabricated, using both bulk and diluted multi-quantum-well InGaAsP/InP-based materials, grown by MOCVD. The device structure is based on the two-mode interference (TMI) principle and is fully compatible for integration with the optoelectronic and electronic components of a coherent receiver. Bulk material couplers provide an output balanced within 0.05 dB per nanometer and an excess loss of 1.4 dB, compared to a straight guide, while coupling loss to a tapered-lensed single mode fibre is 4 dB.Improved coupling efficiency to single-mode fibres is achieved by use of moderately diluted multi-quantum-well waveguides, which include InGaAsP wells and InP barriers: coupling loss to a tapered-lensed single-mode fibre as low as 0.5 dB and excess loss of 1.8 dB are featured. Couplers fabricated with this waveguide structure have a balance sensitivity of 0.03 to 0.04 dB per nanometer.A moderately diluted multi-quantum-well 3-dB coupler has been permanently pigtailed and butt-coupled to a dual balanced PIN photoreceiver. This hybrid assembly was tested in a coherent transmission system at 155 and 622 Mbits^-1 showing sensitivities, for 10^-9 BER, of about-38.0 dBm and-28.8 dBm, respectively.     

Coupled lubrication and Stokes flow finite elements

A method is developed for performing a local reduction of the governing physics for fluid problems with domains that contain a combination of narrow and non‐narrow regions, and the computational accuracy and performance of the method are measured. In the narrow regions of the domain, where the fluid is assumed to have no inertia and the domain height and curvature are assumed small, lubrication, or Reynolds, theory is used locally to reduce the two‐dimensional Navier–Stokes equations to the one‐dimensional Reynolds equation while retaining a high degree of accuracy in the overall solution. The Reynolds equation is coupled to the governing momentum and mass equations of the non‐narrow region with boundary conditions on the mass and momentum flux. The localized reduction technique, termed ‘stitching,’ is demonstrated on Stokes flow for various geometries of the hydrodynamic journal bearing—a non‐trivial test problem for which a known analytical solution is available. The computational advantage of the coupled Stokes–Reynolds method is illustrated on an industrially applicable fully‐flooded deformable‐roll coating example. The examples in this paper are limited to two‐dimensional Stokes flow, but extension to three‐dimensional and Navier–Stokes flow is possible. Copyright © 2003 John Wiley & Sons, Ltd.     

Directed triangles in directed graphs

We show that each directed graph (with no parallel arcs) on n vertices, each with indegree and outdegree at least n/twhere t=2.888997… contains a directed circuit of length at most 3.     

The six semifield planes associated with a semifield flock

In 1965 Knuth (J. Algebra 2 (1965) 182) noticed that a finite semifield was determined by a 3-cube array (a_ijk) and that any permutation of the indices would give another semifield. In this article we explain the geometrical significance of these permutations. It is known that a pair of functions (f,g) where f and g are functions from GF(q) to GF(q) with the property that f and g are linear over some subfield and g(x)²+4xf(x) is a non-square for all x∈GF(q)∗, q odd, give rise to certain semifields, one of which is commutative of rank 2 over its middle nucleus, one of which arises from a semifield flock of the quadratic cone, and another that comes from a translation ovoid of Q(4,q). We show that there are in fact six non-isotopic semifields that can be constructed from such a pair of functions, which will give rise to six non-isomorphic semifield planes, unless (f,g) are of linear type or of Dickson-Kantor-Knuth type. These six semifields fall into two sets of three semifields related by Knuth operations.     

Basins of Attraction of Periodic Oscillations in Suspension Bridges

We consider the dynamics of the lowest order transversal vibration mode of a suspension bridge, for which the hangers are treated as one-sided springs, according to the model of Lazer and McKeena [SIAM Review 58, 1990, 537]. We analyze in particular the multi-stability of periodic attractors and the basin of attraction structure in phase space and its dependence with the model parameters. The parameter values used in numerical simulations have been estimated from a number of bridges built in the United States and in the United Kingdom, thus taking into account realistic, yet sometimes simplified, structural, aerodynamical, and physical considerations.     

Space–time integrated least squares: a time‐marching approach

A time‐marching formulation is derived from the space–time integrated least squares (STILS) method for solving a pure hyperbolic convection equation and is numerically compared to various known methods. Copyright © 2004 John Wiley & Sons, Ltd.     

Elasticity and inelasticity of biomorphic silicon carbide ceramics

The effect of the vibration strain amplitude on the Young modulus and ultrasonic absorption (internal friction) in biomorphic SiC ceramics is investigated in the temperature range 116–296 K. The biomorphic SiC ceramics is prepared through pyrolysis of eucalyptus with subsequent infiltration of silicon. It is demonstrated that the vibration loading of samples in air and under vacuum is accompanied by a number of unexpected effects. The behavior of the studied ceramics is governed by at least two mechanisms, which, to a large extent, are responsible for the elastic and inelastic properties of the material. One mechanism is associated with the adsorption-desorption of environmental molecules (hypothetically, owing to the presence of pores and residual carbon), and the other mechanism involves microplastic deformation due to the motion of dislocations or other (similar) structural units.     

A new technique for obtaining the activation energy distribution of a relaxing system

This paper describes a robust and fast fitting procedure applicable for relaxing processes that cannot be understood as a discrete sum of single processes but require an activation energy distribution. The method is based on a set of closed-form expressions that allow the computation of the relaxation parameters directly from the isochronal curves obtained experimentally. The usefulness of this method is checked by analyzing the isochronal curves given by a theoretical energy distribution and the magnetic disaccommodation spectra observed in yttrium iron garnet (YIG) samples. PACS 02.60.Ed; 75.60.Lr; 75.50.Gg     

A Borsuk–Ulam Theorem for Maps from a Sphere to a Generalized Manifold

H. J. Munkholm obtained a generalization for topological manifolds of the famous Borsuk–Ulam type theorem proved by Conner and Floyd. The purpose of this paper is to prove a version of Conner and Floyd's theorem for generalized manifolds.     

Relative morsification theory

In this paper we develop a Morsification Theory for holomorphic functions defining a singularity of finite codimension with respect to an ideal, which recovers most previously known morsification results for non-isolated singularities and generalise them to a much wider context. We also show that deforming functions of finite codimension with respect to an ideal within the same ideal respects the Milnor fibration. Furthermore we present some applications of the theory: we introduce new numerical invariants for non-isolated singularities, which explain various aspects of the deformation of functions within an ideal; we define generalisations of the bifurcation variety in the versal unfolding of isolated singularities; applications of the theory to the topological study of the Milnor fibration of non-isolated singularities are presented. Using intersection theory in a generalised jet-space we show how to interpret the newly defined invariants as certain intersection multiplicities; finally, we characterise which invariants can be interpreted as intersection multiplicities in the above mentioned generalised jet space.