Embeddings of Star Graphs into Optical Meshes without Bends

We show an embedding of the star graph into a rectangular optical multichannel mesh ofddimensions such that the embedding has no bends; that is, neighbors in the star graph always differ in exactly one coordinate in the mesh, to facilitate one-hop optical communication. To embed ann-star, the mesh can have any number of dimensionsdbetween 1 andn− 1. The embedding has load 1 and an expansion of at mostn^{d − 1}/d!. The size of the mesh will be at most We optimize the size of the host mesh using clique-partitioning to produce embeddings with expansions as low as unity. In two dimensions, for evenn, the mesh will be no larger thann×n(n− 2)!, and have an expansion of no more than 1 1/(n− 1). Further, we show how we can use a contraction method to efficiently embed the star graph into an optical mesh with near-unity aspect ratios. Contraction on a two-dimensional embedding will yield a mesh of size no larger thann×nfor evennwith a load of (n− 2)!.     

Calorimetrically measured enthalpies for the reaction of H2(D2) (g) with Ti and Ti-Ni alloys at 323 K

Reaction enthalpies have been measured calorimetrically at 323 K for the reaction 1/2H₂ (g) + Ti (α, hcp) → TiH_1.5 and for the partial molar solution of H₂ in the δ phase. The magnitude of the enthalpy decreases from 68 at H/Ti = 0 to 65 kJ/mol H at H/Ti = 1.5. The enthalpy continues to slowly fall in magnitude with the increase of H content, and then, for (H/Ti) > 1.9, it falls more precipituously. ΔH _f ⁰ (TiH_1.5) = −98.4 kJ and ΔH _f ⁰ (TiH₂) = −130.3 kJ evaluated at 323 K. No differences in enthalpies were found between H and D. The results are discussed in terms of the existing solvus data for this system, which are important for the quantitative understanding of hydride-induced fracture. Enthalpies of reaction with H₂ have been determined for several Ti-Ni alloys which lie in the (Ti(α) + Ti₂Ni) two-phase field. The reaction with H₂ initially occurs with the Ti phase and then with the Ti₂Ni phase. The enthalpies are similar for the Ti phase as for pure Ti, indicating that this phase is relatively pure Ti. Reaction with the Ti₂Ni phase shows a plateau region with an enthalpy of reaction with 1/2H₂ of about −30 kJ/ mol H. Formerly Graduate Student, Department of Chemistry, University of Vermont.     

Non-linear transient finite element analysis with convected co-ordinates

A finite element method is presented for the transient analysis of large-displacement, small-strain problems with material non-linearities. The method employs a convected co-ordinate technique and a direct nodal force computational scheme of considerable efficiency. Detailed formulations are given for a plane, constant strain triangular element and a Euler-Bernoulli beam element. Results are presented for several example problems and compared with experimental data and other numerical solutions.     

The roles of self-esteem and self-consciousness in the Wortman-Brehm model of reactance and learned helplessness.

Studied the conditions under which failure would enhance or inhibit subsequent task performance. Based on the theory of C. B. Wortman and J. W. Brehm (1975), it was expected that small amounts of failure would produce reactance (manifested by improved performance at a subsequent task); large amounts would lead to learned helplessness (i.e., impaired later performance). It was further expected that individual differences in self-esteem and private self-consciousness would serve as moderator variables for the effects. In Exp I, 78 college students were exposed to either a small amount or no failure before working on an anagrams task. As predicted, Ss high in self-consciousness, who showed greater reactance arousal in attitude change studies, performed better on the anagrams task than Ss low in self-consciousness in the small-failure condition, but not in the no-failure condition. In Exp II, 119 Ss were pretreated with either a small amount of failure, an extended amount of failure, or no failure before working on the task. A significant Self-Esteem by Helplessness Training interaction emerged. Low self-esteem Ss (low SEs) performed marginally better than did high SEs in the small-failure condition but significantly worse than high SEs in the extended-failure condition. Questionnaire data from Exp II were consistent with the notion that enhanced performance reflected reactance, whereas impaired performance signified helplessness. (20 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Postprocessing of finite element transient response calculations by digital filters

A method of postprocessing output from linear transient response calculations by a nonrecursive digital filter is presented. The method is applied to postprocess a series of calculations performed with an explicit temporal integration and a lumped mass matrix; both one dimensional and two dimensional meshes are considered. It is shown that the digital filter is quite effective in eliminating spurious frequencies.     

A survey of numerical methods and computer programs for dynamic structural analysis

The safety analysis of nuclear reactors often involves the solution of non-linear, transient structure-continuum problems. Many general-purpose and special-purpose programs are available for this class of problems. The methods of integration found in these programs are described, particularly from the viewpoint of computational efficiency for the various classes of problems that are found in reactor safety analysis. The methods of time integration, in the usual manner, are subdivided into two categories: explicit and implicit. These methods are summarized along with their advantages and disadvantages and some recent results on their stability and accuracy. Customary practice in the use of these methods is outlined. The programs used in reactor structural safety analysis are surveyed and their salient features tabulated.     

Efficient linear and nonlinear heat conduction with a quadrilateral element

A method is presented for performing efficient and stable finite element calculations of heat conduction with quadrilaterals using one-point quadrature. The stability in space is obtained by using a stabilization matrix which is orthogonal to all linear fields and its magnitude is determined by a stabilization parameter. It is shown that the accuracy is almost independent of the value of the stabilization parameter over a wide range of values; in fact, the values 3, 2 and 1 for the normalized stabilization parameter lead to the 5-point finite difference, 9-point finite difference and fully integrated finite element operators, respectively, for rectangular meshes; numerical experiments reported here show that the three have identical rates of convergence in the L₂ norm. Eigenvalues of the element matrices, which are needed for stability limits, are also given. Numerical applications are used to show that the method yields accurate solutions with large increases in efficiency, particularly in nonlinear problems.     

Distributed call rerouting in multiclass broadband networks

Broadband integrated services digital networks (B-ISDN) must handle multiclass traffic with diverse quality of service requirements. We consider a multiclass routing model in which routes are calculated in a distributed fashion by the call originating nodes. Within this general context, we address the problem of rerouting a set of previously routed calls to avoid a failed link. Under the approach we propose, a single node executes an aggregate, global rerouting of all affected calls and then converts the set of aggregate routes into an allocation of bandwidth on each link to call origination nodes for the purpose of rerouting. The bandwidth allocation is distributed to each origination node, which in turn then calculates routes for the individual calls. The problem faced by each call origination node is a variant of the socalled bandwidth packing problem. We develop and analyze an approximate algorithm for solving this problem in the specific context that arises in our setting.The research was supported by IBM Corporation and by NSF Grant No. CDR-8803012.On personal leave from IBM RTP.     

Flexural wave propagation behavior of lumped mass approximations

The suitability of lumped masses for elastic wave propagation problems in beams is investigated. Dispersion relations are presented for lumped mass Euler-Bernoulli elements and an element with shear correction; for purposes of comparison, the dispersive properties of consistent masses are also given. It is shown that by increasing the rotational mass through a rotational mass factor , a good approximation can be obtained to the Timoshenko dispersion relation. Comparison with an exact solution for the propagation of a velocity discontinuity shows that the shear correction is required for a good solution and indicates optimal values for .