Averaged topological equations for dispersed two-phase flows

A general relationship between the volume fraction and the specific interfacial area for averaged dispersed two-phase flows is proposed. This relationship, expressed as a basic set of two scalar evolution equations and two vectorial non-uniformity state equations, is an analytical result obtained by a systematic approach using the derivatives of some generalized functions and a local volume-averaging technique. The proposed set of equations was expressed for measurable macroscopic parameters of the system and has the same generality as the averaged transport equations of two-phase flows. By combination of the basic set of equations, called the averaged topological equations (ATEs), second-order ATEs for the volume fraction were found. The second-order ATEs were expressed both by a Lagrangian formulation and by a Eulerian formulation. The importance and physical meaning of the ATEs developed in this study were clarified within the framework of the theory of kinematic waves.     

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.     

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.     

Crystalline structure of polyamide 12 as revealed by solid‐state 13C NMR and synchrotron WAXS and SAXS

The crystalline structure of polyamide‐12 (PA12) was studied by solid‐state ¹³C nuclear magnetic resonance (NMR) as well as by synchrotron wide‐ and small‐angle X‐ray scattering (WAXS and SAXS). Isotropic and oriented PA12 showed different NMR spectra ascribed to γ‐ and γ′‐crystalline modifications, respectively. On the basis of the position of the first diffraction peak, the isotropic γ‐form and the oriented γ′‐form were shown to be with hexagonal crystalline lattice at room temperature. When heated, the two PA12 polymorphs demonstrated different behaviors. Above 140 °C, the isotropic γ‐PA12 partially transformed into α‐modification. No such transition was observed with the oriented γ′‐PA12 phase even after annealing at temperatures close to melting. A γ′–γ transition was observed here only after isotropization by melting point. Various structural parameters were extracted from the WAXS and SAXS patterns and analyzed as a function of temperature and orientation: the degree of crystallinity, the d‐spacings, the Bragg's long spacings, the average thicknesses of the crystalline (l_c) and amorphous (l_a) phases, and the linear crystallinity x_cl within the lamellar stacks. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3720–3733, 2005     

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     

Lie point symmetries of the Lane-Emden systems

It is shown that a Lie point symmetry of the Lane-Emden system is a Noether symmetry if and only if its parameters belong to the critical hyperbola.     

Asymptotic Properties of Random Multidimensional Assignment Problems

The multidimensional assignment problem (MAP) is a NP-hard combinatorial optimization problem, occurring in many applications, such as data association. In this paper, we prove two conjectures made in Ref. 1 and based on data from computational experiments on MAPs. We show that the mean optimal objective function cost of random instances of the MAP goes to zero as the problem size increases, when assignment costs are independent exponentially or uniformly distributed random variables. We prove also that the mean optimal solution goes to negative infinity when assignment costs are independent normally distributed random variables.