Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh

A numerical scheme is presented for accurate simulation of fluid flow using the lattice Boltzmann equation (LBE) on unstructured mesh. A finite volume approach is adopted to discretize the LBE on a cell-centered, arbitrary shaped, triangular tessellation. The formulation includes a formal, second order discretization using a Total Variation Diminishing (TVD) scheme for the terms representing advection of the distribution function in physical space, due to microscopic particle motion. The advantage of the LBE approach is exploited by implementing the scheme in a new computer code to run on a parallel computing system. Performance of the new formulation is systematically investigated by simulating four benchmark flows of increasing complexity, namely (1) flow in a plane channel, (2) unsteady Couette flow, (3) flow caused by a moving lid over a 2D square cavity and (4) flow over a circular cylinder. For each of these flows, the present scheme is validated with the results from Navier-Stokes computations as well as lattice Boltzmann simulations on regular mesh. It is shown that the scheme is robust and accurate for the different test problems studied.

Electron-electron interactions in polyacetylene

Experimental evidence for strong electron-electron interactions in polyacetylene is presented. These include (i) observation of a dipole forbidden state below the optical gap, (ii) observation of negative spin densities at sites at which noninteracting models predict zero spin density (iii) vanishing optical gap, in the infinite chain limit, in the closely related symmetrical linear cyanine dyes. To correctly explain these features it is necessary to solve correlated model Hamiltonians. Using diagrammatic valence bond method model exact solutions of correlated models of finite-size systems can be obtained and various physical properties of the low-lying states can be computed. These properties, when extrapolated to the infinite chain limit explain many of the experimental features observed in polyacetylene.

An elementary approach to gap theorems

Using elementary comparison geometry, we prove: Let (M, g) be a simply-connected complete Riemannian manifold of dimension >= 3. Suppose that the sectional curvature K satisfies -1-s(r) <= K <= -1, where r denotes distance to a fixed point in M. If lim(r ->infinity) e(2r) s(r) = 0, then (M, g) has to be isometric to H-n.The same proof also yields that if K satisfies -s(r) <= K <= 0 where lim(r ->infinity) r(2) s(r) = 0, then (M, g) is isometric to R-n, a result due to Greene and Wu.Our second result is a local one: Let (M, g) be any Riemannian manifold. For a E R, if K < a on a geodesic ball Bp (R) in M and K = a on partial derivative B-p (R), then K = a on B-p (R).

Modeling Finite Buffer Effects on TCP Traffic over an IEEE 802.11 Infrastructure WLAN

The network scenario is that of an infrastructure IEEE 802.11 WLAN with a single AP with which several stations (STAs) are associated. The AP has a finite size buffer for storing packets. In this scenario, we consider TCP controlled upload and download file transfers between the STAs and a server on the wireline LAN (e.g., 100 Mbps Ethernet) to which the AP is connected. In such a situation, it is known (see, for example, (3), [9]) that because of packet loss due to finite buffers at the Ap, upload file transfers obtain larger throughputs than download transfers. We provide an analytical model for estimating the upload and download throughputs as a function of the buffer size at the AP. We provide models for the undelayed and delayed ACK cases for a TCP that performs loss recovery only by timeout, and also for TCP Reno.

Sol → gel transition with rings in a finite polycondensing system in solution

We report a theoretical formulation for the mean cluster size distribution in a finite polycondensing system. Expressions for the mean number of n-mers with j bonds ( nj) are developed. Numerical calculations show that while the non-cyclic molecules make the dominant contribution to the small clusters, the large clusters are dominated by cyclic structures. The number of particles in ringless chains, n n,n-1, decays monotonically with n at all extents of reaction, but n n becomes bimodal near the gel point. We also find that the solvent plays an important role in the cluster size distribution.

Spectral analysis of finite section normal integral operators

Some continuity and differentiability properties of the eigenvalues and eigenfunctions of finite section normal integral operators are proved. These are the extension of corresponding results for symmetric operators ([4.], 554–566; K. B. Athreya and R. Vittal Rao, to appear; [10.], 463–471.

Periodic Rayleigh waves of finite amplitude on an isotropic solid

Existence of a periodic progressive wave solution to the nonlinear boundary value problem for Rayleigh surface waves of finite amplitude is demonstrated using an extension of the method of strained coordinates. The solution, obtained as a second-order perturbation of the linearized monochromatic Rayleigh wave solution, contains harmonics of all orders of the fundamental frequency. It is shown that the higher harmonic content of the wave increases with amplitude, but the slope of the waveform remains finite so long as the amplitude is less than a critical value.

Recognition and enforcement in cross-border insolvency law: A proposal for judicial gap-filling

This Article analyzes the recognition and enforcement of cross-border insolvency judgments from the United States, United Kingdom, and Australia to determine whether the UNCITRAL Model Law’s goal of modified universalism is currently being practiced, and subjects the Model Law to analysis through the lens of international relations theories to elaborate a way forward. We posit that courts could use the express language of the Model Law text to confer recognition and enforcement of foreign insolvency judgments. The adoption of our proposal will reduce costs, maximize recovery for creditors, and ensure predictability for all parties.

Finite element analysis of laminated anisotropic thin-walled open-section beams

A finite element analysis of thin-walled open-section laminated anisotropic beams is presented herein. A two-noded, 8 degrees of freedom per node thin-walled open-section laminated anisotropic beam finite element has been developed and used. The displacements of the element reference axes are expressed in terms of one-dimensional first order Hermite interpolation polynomials and line member assumptions are invoked in the formulation of the stiffness matrix. The problems of: 1. (a) an isotropic material Z section straight cantilever beam, and 2. (b) a single-layer (0°) composite Z section straight cantilever beam, for which continuum solutions (exact/approximate) are possible, have been solved in order to evaluate the performance of the finite element. Its applicability has been shown by solving the following problems: 3. (c) a two-layer (45°/−45°) composite Z section straight cantilever beam, 4. (d) a three-layer (0°/45°/0°) composite Z section straight cantilever beam.

A laminated anisotropic curved beam and shell stiffening finite element

The details of development of the stiffness matrix of a laminated anisotropic curved beam finite element are reported. It is a 16 dof element which makes use of 1-D first order Hermite interpolation polynomials for expressing it's assumed displacement state. The performance of the element is evaluated considering various examples for which analytical or other solutions are available.

Performance of slotted ALOHA satellite channels with finite buffer

The behaviour of the slotted ALOHA satellite channel with a finite buffer at each of the user terminals is studied. Approximate relationships between the queuing delay, overflow probabilities and buffer size are derived as functions of the system input parameters (i.e. the number of users, the traffic intensity, the transmission and the retransmission probabilities) for two cases found in the literature: the symmetric case (same transmission and retransmission probabilities), and the asymmetric case (transmission probability far greater than the retransmission probability). For comparison, the channel performance with an infinite buffer is also derived. Additionally, the stability condition for the system is defined in the latter case. The analysis carried out in the paper reveals that the queuing delays are quite significant, especially under high traffic conditions.

Finite-amplitude love-waves on an isotropic layered half-space

A pair of semi-linear hyperbolic partial differential equations governing the slow variations in amplitude and phase of a quasi-monochromatic finite-amplitude Love-wave on an isotropic layered half-space is derived using the method of multiple-scales. The analysis of the exact solution of these equations for a signalling problem reveals that the amplitude of the wave remains constant along its characteristic and that the phase of the wave increases linearly behind the wave-front.

R-parameter: A local truncation error based adaptive framework for finite volume compressible flow solvers

A residual-based strategy to estimate the local truncation error in a finite volume framework for steady compressible flows is proposed. This estimator, referred to as the -parameter, is derived from the imbalance arising from the use of an exact operator on the numerical solution for conservation laws. The behaviour of the residual estimator for linear and non-linear hyperbolic problems is systematically analysed. The relationship of the residual to the global error is also studied. The -parameter is used to derive a target length scale and consequently devise a suitable criterion for refinement/derefinement. This strategy, devoid of any user-defined parameters, is validated using two standard test cases involving smooth flows. A hybrid adaptive strategy based on both the error indicators and the -parameter, for flows involving shocks is also developed. Numerical studies on several compressible flow cases show that the adaptive algorithm performs excellently well in both two and three dimensions.

Delay time of a vacuum gap triggered by an exploding wire

The experimental results of delay time of a vacuum gap triggered by an exploding wire plasma have been reported. It consists of explosion delay time and propagation delay time. The explosion delay time has been found to be dependent on the parameters of the exploding wire and the exploding wire circuit and is independent of vacuum gap configuration. The propagation delay time depends on the properties of the exploding wire plasma and vacuum gap parameters such as the number of injection slots, gap spacing, gap polarity, etc. In the absence of prebreakdown current in the vacuum gap, the breakdown can be initiated only after the plasma completely bridges the gap spacing. Under this specific condition, it has been shown that the delay time data can be used to calculate the plasma velocity.

Finite element analysis of bimodulus composite stiffened thin shells of revolution

This paper is a sequel to the work published by the first and third authors[l] on stiffened laminated shells of revolution made of unimodular materials (materials having identical properties in tension and compression). A finite element analysis of laminated bimodulus composite thin shells of revolution, reinforced by laminated bimodulus composite stiffeners is reported herein. A 48 dot doubly curved quadrilateral laminated anisotropic shell of revolution finite element and it's two compatible 16 dof stiffener finite elements namely: (i) a laminated anisotropic parallel circle stiffener element (PCSE) and (ii) a laminated anisotropic meridional stiffener element (MSE) have been used iteratively. The constitutive relationship of each layer is assumed to depend on whether the fiberdirection strain is tensile or compressive. The true state of strain or stress is realized when the locations of the neutral surfaces in the shell and the stiffeners remain unaltered (to a specified accuracy) between two successive iterations. The solutions for static loading of a stiffened plate, a stiffened cylindrical shell. and a stiffened spherical shell, all made of bimodulus composite materials, have been presented.