Exact analysis of simply supported rhombic plates under uniform pressure

The simply supported rhombic plate under transverse load has received extensive attention from elasticians, applied mathematicians and engineers. All known solutions are based on approximate procedures. Now, an exact solution in a fast converging explicit series form is derived for this problem, by applying Stevenson's tentative approach with complex variables. Numerical values for the central deflexion and moments are obtained for various corner angles. The present solution provides a basis for assessing the accuracy of approximate methods for analysing problems of skew plates or domains.

Rotating anisotropic disc of uniform strength

A procedure to design a constant thickness composite disc of uniform strength by radially tailoring the anisotropic elastic constants is proposed. A special case of an isotropic disc with radially varying modulus is also examined. Analytical results are also compared with FEM calculations for two cases of radially varying anisotropy and for an isotropic disc with variable modulus. (C) 1999 Elsevier Science Ltd. All rights reserved.

On Uniform Approximate Solutions in Bending of Symmetric Laminated Plates

A layer-wise theory with the analysis of face ply independent of lamination is used in the bending of symmetric laminates with anisotropic plies. More realistic and practical edge conditions as in Kirchhoff's theory are considered. An iterative procedure based on point-wise equilibrium equations is adapted. The necessity of a solution of an auxiliary problem in the interior plies is explained and used in the generation of proper sequence of two dimensional problems. Displacements are expanded in terms of polynomials in thickness coordinate such that continuity of transverse stresses across interfaces is assured. Solution of a fourth order system of a supplementary problem in the face ply is necessary to ensure the continuity of in-plane displacements across interfaces and to rectify inadequacies of these polynomial expansions in the interior distribution of approximate solutions. Vertical deflection does not play any role in obtaining all six stress components and two in-plane displacements. In overcoming lacuna in Kirchhoff's theory, widely used first order shear deformation theory and other sixth and higher order theories based on energy principles at laminate level in smeared laminate theories and at ply level in layer-wise theories are not useful in the generation of a proper sequence of 2-D problems converging to 3-D problems. Relevance of present analysis is demonstrated through solutions in a simple text book problem of simply supported square plate under doubly sinusoidal load.

On Precoding for Constant K-User MIMO Gaussian Interference Channel With Finite Constellation Inputs

This paper considers linear precoding for the constant channel-coefficient K-user MIMO Gaussian interference channel (MIMO GIC) where each transmitter-i (Tx-i) requires the sending of d(i) independent complex symbols per channel use that take values from fixed finite constellations with uniform distribution to receiver-i (Rx-i) for i = 1, 2, ..., K. We define the maximum rate achieved by Tx-i using any linear precoder as the signal-to-noise ratio (SNR) tends to infinity when the interference channel coefficients are zero to be the constellation constrained saturation capacity (CCSC) for Tx-i. We derive a high-SNR approximation for the rate achieved by Tx-i when interference is treated as noise and this rate is given by the mutual information between Tx-i and Rx-i, denoted as I(X) under bar (i); (Y) under bar (i)]. A set of necessary and sufficient conditions on the precoders under which I(X) under bar (i); (Y) under bar (i)] tends to CCSC for Tx-i is derived. Interestingly, the precoders designed for interference alignment (IA) satisfy these necessary and sufficient conditions. Furthermore, we propose gradient-ascentbased algorithms to optimize the sum rate achieved by precoding with finite constellation inputs and treating interference as noise. A simulation study using the proposed algorithms for a three-user MIMO GIC with two antennas at each node with d(i) = 1 for all i and with BPSK and QPSK inputs shows more than 0.1-b/s/Hz gain in the ergodic sum rate over that yielded by precoders obtained from some known IA algorithms at moderate SNRs.

Non-uniform beams and stiff strings isospectral to axially loaded uniform beams and piano strings

In this paper, we derive analytical expressions for mass and stiffness functions of transversely vibrating clamped-clamped non-uniform beams under no axial loads, which are isospectral to a given uniform axially loaded beam. Examples of such axially loaded beams are beam columns (compressive axial load) and piano strings (tensile axial load). The Barcilon-Gottlieb transformation is invoked to transform the non-uniform beam equation into the axially loaded uniform beam equation. The coupled ODEs involved in this transformation are solved for two specific cases (pq (z) = k (0) and q = q (0)), and analytical solutions for mass and stiffness are obtained. Examples of beams having a rectangular cross section are shown as a practical application of the analysis. Some non-uniform beams are found whose frequencies are known exactly since uniform axially loaded beams with clamped ends have closed-form solutions. In addition, we show that the tension required in a stiff piano string with hinged ends can be adjusted by changing the mass and stiffness functions of a stiff string, retaining its natural frequencies.

Diffusive Wave Solutions for Open Channel Flows with Uniform and Concentrated Lateral Inflow

The diffusive wave equation with inhomogeneous terms representing hydraulics with uniform or concentrated lateral inflow intoa river is theoretically investigated in the current paper. All the solutions have been systematically expressed in a unified form interms of response function or so called K-function. The integration of K-function obtained by using Laplace transform becomesS-function, which is examined in detail to improve the understanding of flood routing characters. The backwater effects usuallyresulting in the discharge reductions and water surface elevations upstream due to both the downstream boundary and lateral infloware analyzed. With a pulse discharge in upstream boundary inflow, downstream boundary outflow and lateral inflow respectively,hydrographs of a channel are routed by using the S-functions. Moreover, the comparisons of hydrographs in infinite, semi-infiniteand finite channels are pursued to exhibit the different backwater effects due to a concentrated lateral inflow for various channeltypes.

Growth kinetics and uniform scaling-up of graphene synthesis

Chemical vapor deposition on copper is the most widely used method to synthesize graphene at large scale. However, the clear understanding of the fundamental mechanisms that govern this synthesis is lacking. Using a vertical-flow, cold-wall reactor with short gas residence time we observe the early growths to study the kinetics of chemical vapor deposition of graphene on copper foils and demonstrate uniform synthesis at wafer scale. Our results indicate that the growth is limited by the catalytic dissociative dehydrogenation on the surface and copper sublimation hinders the graphene growth. We report an activation energy of 3.1 eV for ethylene-based graphene synthesis. © The Electrochemical Society.

Effects of rapid thermal annealing on the emission properties of highly uniform self-assembled InAs/GaAs quantum dots emitting at 1.3 mu m

The authors report the effects of rapid thermal annealing (RTA) on the emission properties of highly uniform self-assembled InAs quantum dots (QDs) emitting at 1.3 mu m grown on GaAs substrate by metal organic chemical vapor deposition. Postgrowth RTA experiments were performed under N-2 flow at temperatures ranging from 600 to 900 degrees C for 30 s using GaAs proximity capping. Surprisingly, in spite of the capping, large blueshifts in the emission peak (up to about 380 meV at 850 degrees C) were observed (even at low annealing temperatures) along with enhanced integrated photoluminescence (PL) intensities. Moreover, pronounced peak broadenings occurred at low annealing temperatures (< 700 degrees C), indicating that RTA does not always cause peak narrowing, as is typically observed with traditional QDs with large inhomogeneous PL linewidths. The mechanism behind the large peak blueshift was studied and found to be attributed to the as-grown QDs with large size, which cause a larger dot-barrier interface and greater strain in and near the QD regions, thereby greatly promoting Ga-In intermixing across the interface during RTA. The results reported here demonstrate that it is possible to significantly shift the emission peak of the QDs by RTA without any additional procedures, even at lower annealing temperatures. (c) 2007 American Institute of Physics.

New method for the growth of highly uniform quantum dots

A new method is realized for the growth of self-formed quantum dots. We identify that dislocation-free islands can be formed by the strain from the strained superlattice taken as a whole. Unlike the Stranski-Krastanow (S-K) growth mode, the islands do not form during the growth of the corresponding strained single layers. Highly uniform quantum dots can be self-formed via this mechanism. The low temperature spectra of self-formed InGaAs/GaAs quantum dot superlattices grown on a (001) GaAs substrate have a full width at half maximum of 26-34 meV, indicating a better uniformity of quantum dot size than those grown in the S-K mode. This method can provide great degrees of freedom in designing possible quantum dot devices. 1998 Published by Elsevier Science B.V. All rights reserved.