Time-decoupled high order continuous space-time finite element schemes for the heat equation

Copyright © by SIAMIn Comput. Methods Appl. Mech. Engrg., 190 (2001), pp. 6685—6708 Werder et al. demonstrated that time discretizations of the heat equation by a temporally discontinuous Galerkin finite element method could be decoupled by diagonalising the temporal ‘Gram matrices’. In this article we propose a companion approach for the heat equation by using a continuous Galerkin time discretization. As a result, if piecewise polynomials of degree d are used as the trial functions in time and the spatial discretization produces systems of dimension M then, after decoupling, d systems of size M need to be solved rather than a single system of sizeMd. These decoupled systems require complex arithmetic, as did Werder et al.’s technique, but are amenable to parallel solution on modern multi-core architectures. We give numerical tests for temporal polynomial degrees up to six for three different model test problems, using both Galerkin and spectral element spatial discretizations, and show convergence and temporal superconvergence rates that accord with the bounds given by Aziz and Monk, Math. Comp. 52:186 (1989), pp. 255—274. We also interpret error as a function of computational time and see that our high order schemes may offer greater efficiency that the Crank-Nicolson method in terms of accuracy per unit of computational time—although in a multi-core world, with highly tuned iterative solvers, one has to be cautious with such claims. We close with a speculation on the application of these ideas to the Navier-Stokes equations for incompressible fluids

On the Pricing of Forward Starting Options under Stochastic Volatility

We consider the problem of pricing European forward starting options in the presence of stochastic ­volatility. By performing a change of measure using the asset price at the time of strike determination as a numeraire, we derive a closed-form solution based on Heston’s model of stochastic volatility

Computer program to assess impact of fatigue and fracture criteria on weight and cost of transport aircraft

A preliminary design analysis tool for rapidly performing trade-off studies involving fatigue, fracture, static strength, weight, and cost is presented. Analysis subprograms were developed for fatigue life, crack growth life, and residual strength; and linked to a structural synthesis module which in turn was integrated into a computer program. The part definition module of a cost and weight analysis program was expanded to be compatible with the upgraded structural synthesis capability. The resultant vehicle design and evaluation program is named VDEP-2. It is an accurate and useful tool for estimating purposes at the preliminary design stage of airframe development. A sample case along with an explanation of program applications and input preparation is presented

Substrate rigidity deforms and polarizes active gels

We present a continuum model of the coupling between cells and substrate that accounts for some of the observed substrate-stiffness dependence of cell properties. The cell is modeled as an elastic active gel, adapting recently developed continuum theories of active viscoelastic fluids. The coupling to the substrate enters as a boundary condition that relates the cell's deformation field to local stress gradients. In the presence of activity, the coupling to the substrate yields spatially inhomogeneous contractile stresses and deformations in the cell and can enhance polarization, breaking the cell's front-rear symmetry.Comment: 6 pages, 4 figures, EPL forma

Current State of Co-Employee Immunity under Workers\u27 Compensation Law, The

The exclusivity provision of Missouri\u27s Workers\u27 Compensation Act ( the Act ) essentially constitutes a statutory mandated quid-pro-quo agreement amongst employees and their employers. Under the terms of the Act, employers incur the burden of no-fault liability for workplace injuries. The Act states that [e]very employer ... shall be liable, irrespective of negligence, to furnish compensation . . . for personal injury or death of the employee by accident arising out of and in the course of [his] employment. In exchange for employers incurring this burden, the Act statutorily abrogates any common law right of action the employee may hold against the employer for the injury. In this regard, the Act states that [e]very employer subject to the provisions of this chapter ... shall be released from all other liability... whatsoever, whether to the employee or any other person. The exclusivity provision of the Act, however, does nothing to prevent injured employees from bringing suit against negligent third parties for their workplace injuries. The Act recognizes the potential for such situations by providing employers with a right of subrogation against any recovery since they remain liable for the workplace injury under the no-fault scheme. If the Act provides an injured employee with less in benefits than the employee would have likely recovered as damages under a common law negligence suit, the ability to sue a negligent third party is an attractive option. Many times, workplace injuries occur because of the negligence of an injured party\u27s co-employee. Therefore, to gain the benefits of the third-party suit option, injured parties may argue that their negligent co-employee is a third person not entitled to the exclusivity provision of the Act. Missouri courts have dealt with the issue of whether negligent coemployees constitute third persons many times, but they have struggled to formulate a workable rule. In principle, Missouri courts have accepted the premise that a co-employee can potentially constitute a third person subject to a common law suit for acts of workplace negligence. In application, the courts only allow injured employees to bring such suits when they allege that the co-employee committed something more than a mere negligent act. This Comment will attempt to identify what constitutes something more

Polariton lasing in high-quality Selenide-based micropillars in the strong coupling regime

We have designed and fabricated all-epitaxial ZnSe-based optical micropillars exhibiting the strong coupling regime between the excitonic transition and the confined optical cavity modes. At cryogenic temperatures, under non-resonant pulsed optical excitation, we demonstrate single transverse mode polariton lasing operation in the micropillars. Owing to the high quality factors of these microstructures, the lasing threshold remains low even in micropillars of the smallest diameter. We show that this feature can be traced back to a sidewall roughness grain size below 3 nm, and to suppressed in-plane polariton escape.Comment: 5 pages, 3 figure