Geometric Stability Analysis for Periodic Solutions of the Swift-Hohenberg Equation

In this paper we describe invariant geometrical ~structures in the phase space of the Swift-Hohenberg equation in a neighborhood of its periodic stationary states. We show that in spite of the fact that these states are only marginally stable (i.e., the linearized problem about these states has continuous spectrum extending all the way up to zero), there exist finite dimensional invariant manifolds in the phase space of this equation which determine the long-time behavior of solutions near these stationary solutions. In particular, using this point of view, we obtain a new demonstration of Schneider's recent proof that these states are nonlinearly stable.Comment: 44 pages, plain tex, 0 figure

Experiments on identification and control of inflow disturbances in contracting streams

Vorticity from all surfaces and isolated objects in the vicinity of the fan intake, including the outside surfaces of the fan housing, were identified as the major sources for disturbances leading to blade passing frequency noise. The previously proposed mechanism based on atmospheric turbulence is refuted. Flow visualization and hot wire techniques were used in three different facilities to document the evolution of various types of disturbances, including the details of the mean flow and turbulence characteristics. The results suggest that special attention must be devoted to the design of the inlet and that geometric modeling may not lead to adequate simulation of the in flight characteristics. While honeycomb type flow manipulators appear to be effective in reducing some of the disturbances, higher pressure drop devices that generate adequate turbulence, for mixing of isolated nonuniformities, may be necessary to suppress the remaining disturbances. The results are also applicable to the design of inlets of open return wind tunnels and similar flow facilities

Asymptotic description of solutions of the exterior Navier Stokes problem in a half space

We consider the problem of a body moving within an incompressible fluid at constant speed parallel to a wall, in an otherwise unbounded domain. This situation is modeled by the incompressible Navier-Stokes equations in an exterior domain in a half space, with appropriate boundary conditions on the wall, the body, and at infinity. We focus on the case where the size of the body is small. We prove in a very general setup that the solution of this problem is unique and we compute a sharp decay rate of the solution far from the moving body and the wall

A Renormalization Group for Hamiltonians: Numerical Results

We describe a renormalization group transformation that is related to the breakup of golden invariant tori in Hamiltonian systems with two degrees of freedom. This transformation applies to a large class of Hamiltonians, is conceptually simple, and allows for accurate numerical computations. In a numerical implementation, we find a nontrivial fixed point and determine the corresponding critical index and scaling. Our computed values for various universal constants are in good agreement with existing data for area-preserving maps. We also discuss the flow associated with the nontrivial fixed point.Comment: 11 Pages, 2 Figures. For future updates, check ftp://ftp.ma.utexas.edu/pub/papers/koch

Effect of substrate thermal resistance on space-domain microchannel

In recent years, Fluorescent Melting Curve Analysis (FMCA) has become an almost ubiquitous feature of commercial quantitative PCR (qPCR) thermal cyclers. Here a micro-fluidic device is presented capable of performing FMCA within a microchannel. The device consists of modular thermally conductive blocks which can sandwich a microfluidic substrate. Opposing ends of the blocks are held at differing temperatures and a linear thermal gradient is generated along the microfluidic channel. Fluorescent measurements taken from a sample as it passes along the micro-fluidic channel permits fluorescent melting curves to be generated. In this study we measure DNA melting temperature from two plasmid fragments. The effects of flow velocity and ramp-rate are investigated, and measured melting curves are compared to those acquired from a commercially available PCR thermocycler