Large time behaviour of solutions of a system of generalized Burgers equation

In this paper we study the asymptotic behaviour of solutions of a system of $N$ partial differential equations. When $N = 1$ the equation reduces to the Burgers equation and was studied by Hopf. We consider both the inviscid and viscous case and show a new feature in the asymptotic behaviour.Comment: 9 page

Singular limits in phase dynamics with physical viscosity and capillarity

Following pioneering work by Fan and Slemrod who studied the effect of artificial viscosity terms, we consider the system of conservation laws arising in liquid-vapor phase dynamics with {\sl physical} viscosity and capillarity effects taken into account. Following Dafermos we consider self-similar solutions to the Riemann problem and establish uniform total variation bounds, allowing us to deduce new existence results. Our analysis cover both the hyperbolic and the hyperbolic-elliptic regimes and apply to arbitrarily large Riemann data. The proofs rely on a new technique of reduction to two coupled scalar equations associated with the two wave fans of the system. Strong $L^1$ convergence to a weak solution of bounded variation is established in the hyperbolic regime, while in the hyperbolic-elliptic regime a stationary singularity near the axis separating the two wave fans, or more generally an almost-stationary oscillating wave pattern (of thickness depending upon the capillarity-viscosity ratio) are observed which prevent the solution to have globally bounded variation.Comment: 30 page

Boundary layers in weak solutions to hyperbolic conservation laws

This paper is concerned with the initial-boundary value problem for a nonlinear hyperbolic system of conservation laws. We study the boundary layers that may arise in approximations of entropy discontinuous solutions. We consider both the vanishing viscosity method and finite difference schemes (Lax-Friedrichs type schemes, Godunov scheme). We demonstrate that different regularization methods generate different boundary layers. Hence, the boundary condition can be formulated only if an approximation scheme is selected first. Assuming solely uniform L\infty bounds on the approximate solutions and so dealing with L\infty solutions, we derive several entropy inequalities satisfied by the boundary layer in each case under consideration. A Young measure is introduced to describe the boundary trace. When a uniform bound on the total variation is available, the boundary Young measure reduces to a Dirac mass. Form the above analysis, we deduce several formulations for the boundary condition which apply whether the boundary is characteristic or not. Each formulation is based a set of admissible boundary values, following Dubois and LeFloch's terminology in ``Boundary conditions for nonlinear hyperbolic systems of conservation laws'', J. Diff. Equa. 71 (1988), 93--122. The local structure of those sets and the well-posedness of the corresponding initial-boundary value problem are investigated. The results are illustrated with convex and nonconvex conservation laws and examples from continuum mechanics.Comment: 43 page

The Rocketdyne Multifunction Tester. Part 1: Test Method

The Rocketdyne Multifunction Tester is a general purpose test apparatus which utilizes axial and radial magnetic bearings as shaft excitation devices. The tester is modular in design so that different seal and bearing packages can be tested on the same test stand. The tester will be used for rotordynamic coefficient extraction, as well as life and fluid/material compatibility evaluations. Use of a magnetic bearing as a shaft excitation device opens up many possibilities for shaft excitation and rotordynamic coefficient extraction. In addition to describing the basic apparatus, some of the excitation and extraction methods are described. Some of the excitation methods to be discussed include random, aperiodic, harmonic, impulse and chirp

Price Formation under Small Numbers Competition: Evidence from Land Auctions in Singapore

This paper examines the price formation process under small numbers competition using data from Singapore land auctions. The theory predicts that bid prices are less than the zero-profit asset value in these first-price sealed-bid auctions. The model also shows that expected sales price increases with the number of bidders both because each bidder has an incentive to offer a higher price and because of a greater likelihood that a high-value bidder is present. The empirical estimates are consistent with auction theory and show that the standard land attributes are reflected in auction prices as expected. Working Paper No. 04-0

Suppression of Subsynchronous Vibration in the SSME HPFTP

Space Shuttle Main Engine (SSME) High Pressure Fuel Turbopump (HPFTP) hot-fire dynamic data evaluation and rotordynamic analysis both confirm that two of the most significant turbopump attributes in determining susceptibility to subsynchronous vibration are impeller interstage seal configuration and rotor sideload resulting from turbine turnaround duct configuration and hot gas manifold. Recent hot-fire testing has provided promising indications that the incorporation of roughened damping seals at the impeller interstages may further increase the stability margin of this machine. A summary of the analysis which led to the conclusion that roughened seals would enhance the stability margin is presented along with a correlation of the analysis with recent test data

Effect of additives on the mechanical properties of polyacrylonitrile fibres

In spinning of synthetic fibers, several additives are used for various purpose. Some organic compounds are known to reduce viscostly and facilitate many technical operations besides increasing solid content of the dope in wet spinning process. Gelation if preceeded by phase separation increases the mechanical properties of the fibers. The effect organic additives and gelating agents (of inorganic compounds and non-solvents) on the mechanical properties of the PAN fibers have been reported here. The organic additives decreased both the modulus and the strength, the inorganic additives increase them whereas non solvent has no effect. When all the additives are added the overall strength and modulus of the fibers increase as compared to the fibers without any additive. Carbon fibers from the PAN fibers produced in the presence of all the additives have comparable mechanical properties with those of some of the industrial fibers carbonized at 1000°C

The role of the individual in the coming era of process-based therapy

For decades the development of evidence-based therapy has been based on experimental tests of protocols designed to impact psychiatric syndromes. As this paradigm weakens, a more process-based therapy approach is rising in its place, focused on how to best target and change core biopsychosocial processes in specific situations for given goals with given clients. This is an inherently more idiographic question than has normally been at issue in evidence-based therapy over the last few decades. In this article we explore methods of assessment and analysis that can integrate idiographic and nomothetic approaches in a process-based era.Accepted manuscrip