Bifurcation in growth patterns for arrays of parallel Griffith, edge and sliding cracks

This paper presents the recent finding by Muhlhaus et al [1] that bifurcation of crack growth patterns exists for arrays of two-dimensional cracks. This bifurcation is a result of the nonlinear effect due to crack interaction, which is, in the present analysis, approximated by the dipole asymptotic or pseudo-traction method. The nonlinear parameter for the problem is the crack length/ spacing ratio lambda = a/h. For parallel and edge crack arrays under far field tension, uniform crack growth patterns (all cracks having same size) yield to nonuniform crack growth patterns (i.e. bifurcation) if lambda is larger than a critical value lambda(cr) (note that such bifurcation is not found for collinear crack arrays). For parallel and edge crack arrays respectively, the value of lambda(cr) decreases monotonically from (2/9)(1/2) and (2/15.096)(1/2) for arrays of 2 cracks, to (2/3)(1/2)/pi and (2/5.032)(1/2)/pi for infinite arrays of cracks. The critical parameter lambda(cr) is calculated numerically for arrays of up to 100 cracks, whilst discrete Fourier transform is used to obtain the exact solution of lambda(cr) for infinite crack arrays. For geomaterials, bifurcation can also occurs when array of sliding cracks are under compression.

A numerical study of large sparse matrix exponentials arising in Markov chains

Krylov subspace techniques have been shown to yield robust methods for the numerical computation of large sparse matrix exponentials and especially the transient solutions of Markov Chains. The attractiveness of these methods results from the fact that they allow us to compute the action of a matrix exponential operator on an operand vector without having to compute, explicitly, the matrix exponential in isolation. In this paper we compare a Krylov-based method with some of the current approaches used for computing transient solutions of Markov chains. After a brief synthesis of the features of the methods used, wide-ranging numerical comparisons are performed on a power challenge array supercomputer on three different models. (C) 1999 Elsevier Science B.V. All rights reserved.AMS Classification: 65F99; 65L05; 65U05.

Axial Young's modulus prediction of single-walled carbon nanotube arrays with diameters from nanometer to meter scales

Based on a self-similar array model, we systematically investigated the axial Young's modulus (Y-axis) of single-walled carbon nanotube (SWNT) arrays with diameters from nanometer to meter scales by an analytical approach. The results show that the Y-axis of SWNT arrays decreases dramatically with the increases of their hierarchy number (s) and is not sensitive to the specific size and constitution when s is the same, and the specific Young's modulus Y-axis(s) is independent of the packing configuration of SWNTs. Our calculations also show that the Y-axis of SWNT arrays with diameters of several micrometers is close to that of commercial high performance carbon fibers (CFs), but the Y-axis(s) of SWNT arrays is much better than that of high performance CFs. (C) 2005 American Institute of Physics.

Population pharmacokinetics of perhexiline from very sparse, routine monitoring data

Using NONMEM, the population pharmacokinetics of perhexiline were studied in 88 patients (34 F, 54 M) who were being treated for refractory angina. Their mean +/- SD (range) age was 75 +/- 9.9 years (46-92), and the length of perhexiline treatment was 56 +/- 77 weeks (0.3-416). The sampling time after a dose was 14.1 +/- 21.4 hours (0.5-200), and the perhexiline plasma concentrations were 0.39 +/- 0.32 mg/L (0.03-1.56). A one-compartment model with first-order absorption was fitted to the data using the first-order (FO) approximation. The best model contained 2 subpopulations (obtained via the $MIXTURE subroutine) of 77 subjects (subgroup A) and 11 subjects (subgroup B) that had typical values for clearance (CL/F) of 21.8 L/h and 2.06 L/h, respectively. The volumes of distribution (V/F) were 1470 L and 260 L, respectively, which suggested a reduction in presystemic metabolism in subgroup B. The interindividual variability (CV%) was modeled logarithmically and for CL/F ranged from 69.1% (subgroup A) to 86.3% (subgroup B). The interindividual variability in V/F was 111%. The residual variability unexplained by the population model was 28.2%. These results confirm and extend the existing pharmacokinetic data on perhexiline, especially the bimodal distribution of CL/F manifested via an inherited deficiency in hepatic and extrahepatic CYP2D6 activity.

An equivalent waveguide approach to designing of reflect arrays with the use of variable-size microstrip patches

An equivalent unit cell waveguide approach (WGA) is described to study the behavior of a multilayer reflect array of variable-size patches/dipoles, The approach considers normal incidence of a plane wave on an infinite periodic array of identical radiating elements and introduces an equivalent unit cell waveguide to obtain the reflection coefficient. A field matching technique and method of moments (MoM) is used to determine fields in different layers of the equivalent waveguide. Good agreements for the phase of the reflection coefficient between the proposed model and those published in selected literatures are obtained. (C) 2002 Wiley Periodicals, Inc.

Design of microchannel free-space optical interconnects based on vertical-cavity surface-emitting laser arrays

We investigate the design of free-space optical interconnects (FSOIs) based on arrays of vertical-cavity surface-emitting lasers (VCSELs), microlenses, and photodetectors. We explain the effect of the modal structure of a multimodeVCSEL beam on the performance of a FSOI with microchannel architecture. A Gaussian-beam diffraction model is used in combination with the experimentally obtained spectrally resolved VCSEL beam profiles to determine the optical channel crosstalk and the signal-to-noise ratio (SNR) in the system. The dependence of the SNR on the feature parameters of a FSOI is investigated. We found that the presence of higher-order modes reduces the SNR and the maximum feasible interconnect distance. We also found that the positioning of a VCSEL array relative to the transmitter microlens has a significant impact on the SNR and the maximum feasible interconnect distance. Our analysis shows that the departure from the traditional confocal system yields several advantages including the extended interconnect distance and/or improved SNR. The results show that FSOIs based on multimode VCSELs can be efficiently utilized in both chip-level and board-level interconnects. (C) 2002 Optical Society of America.

An augmented Lanczos algorithm for the efficient computation of a dot-product of a function of a large sparse symmetric matrix

The Lanczos algorithm is appreciated in many situations due to its speed. and economy of storage. However, the advantage that the Lanczos basis vectors need not be kept is lost when the algorithm is used to compute the action of a matrix function on a vector. Either the basis vectors need to be kept, or the Lanczos process needs to be applied twice. In this study we describe an augmented Lanczos algorithm to compute a dot product relative to a function of a large sparse symmetric matrix, without keeping the basis vectors.

Comparison of three commercial sparse-matrix crystallization screens

Sparse-matrix sampling using commercially available crystallization screen kits has become the most popular way of determining the preliminary crystallization conditions for macromolecules. In this study, the efficiency of three commercial screening kits, Crystal Screen and Crystal Screen 2 (Hampton Research), Wizard Screens I and II (Emerald BioStructures) and Personal Structure Screens 1 and 2 (Molecular Dimensions), has been compared using a set of 19 diverse proteins. 18 proteins yielded crystals using at least one crystallization screen. Surprisingly, Crystal Screens and Personal Structure Screens showed dramatically different results, although most of the crystallization formulations are identical as listed by the manufacturers. Higher molecular weight polyethylene glycols and mixed precipitants were found to be the most effective precipitants in this study.

Nonlinear dynamics of a satellite with deployable solar panel arrays

The multibody dynamics of a satellite in circular orbit, modeled as a central body with two hinge-connected deployable solar panel arrays, is investigated. Typically, the solar panel arrays are deployed in orbit using preloaded torsional springs at the hinges in a near symmetrical accordion manner, to minimize the shock loads at the hinges. There are five degrees of freedom of the interconnected rigid bodies, composed of coupled attitude motions (pitch, yaw and roll) of the central body plus relative rotations of the solar panel arrays. The dynamical equations of motion of the satellite system are derived using Kane's equations. These are then used to investigate the dynamic behavior of the system during solar panel deployment via the 7-8th-order Runge-Kutta integration algorithms and results are compared with approximate analytical solutions. Chaotic attitude motions of the completely deployed satellite in circular orbit under the influence of the gravity-gradient torques are subsequently investigated analytically using Melnikov's method and confirmed via numerical integration. The Hamiltonian equations in terms of Deprit's variables are used to facilitate the analysis. (C) 2003 Published by Elsevier Ltd.

Effect of mutual coupling on the interference rejection capabilities of linear and circular arrays in CDMA systems

This paper is concerned with assessing the interference rejection capabilities of linear and circular array of dipoles that can be part of a base station of a code-division multiple-access cellular communication system. The performance criteria for signal-to-interference ratio (SIR) improvement employed in this paper is the spatial interference suppression coefficient. We first derive an expression for this figure of merit and then analyze and compare the SIR performance of the two types of arrays. For a linear array, we quantitatively assess the degradation in SIR performance, as we move from array broadside to array end-fire direction. In addition, the effect of mutual coupling is taken into account.

Quantum-error correction on linear-nearest-neighbor qubit arrays

A quantum circuit implementing 5-qubit quantum-error correction on a linear-nearest-neighbor architecture is described. The canonical decomposition is used to construct fast and simple gates that incorporate the necessary swap operations allowing the circuit to achieve the same depth as the current least depth circuit. Simulations of the circuit's performance when subjected to discrete and continuous errors are presented. The relationship between the error rate of a physical qubit and that of a logical qubit is investigated with emphasis on determining the concatenated error correction threshold.

Packing-dependent pore structure in single-walled carbon nanotube arrays

Based on a self-similar array model of single-walled carbon nanotubes (SWNTs), the pore structure of SWNT bundles is analyzed and compared with that obtained from the conventional triangular model and adsorption experimental results. In addition to the well known cylindrical endo-cavities and interstitial pores, two types of newly defined pores with diameters of 2-10 and 8-100 nm are proposed, inter-bundle pores and inter-array pores. In particular, the relationship between the packing configuration of SWNTs and their pore structures is systematically investigated. (c) 2005 American Institute of Physics.