Stabilization of projection-based reduced order models of the Navier–Stokes

A new method of stabilizing low-order, proper orthogonal decomposition based reduced-order models of the Navier?CStokes equations is proposed. Unlike traditional approaches, this method does not rely on empirical turbulence modeling or modification of the Navier?CStokes equations. It provides spatial basis functions different from the usual proper orthogonal decomposition basis function in that, in addition to optimally representing the solution, the new proposed basis functions also provide stable reduced-order models. The proposed approach is illustrated with two test cases: two-dimensional flow inside a square lid-driven cavity and a two-dimensional mixing layer.     

SOLVENT CHARACTERISTICS OF MOLTEN SULFUR AT 132°C

Abstract

The activity coefficient of 50 solutes in liquid sulfur have been measured at infinite dilution by gas chromatography. The solvent-solute interactions have been examined in terms of chromatographic models, activity coefficients, and solubility parameter theory. The classification of sulfur with polar chromatographic solvents is examined and attributed to enhanced dispersion of sulfur with compounds which have, relative to alkanes, loosely held electron clouds. Solubility parameter theory is found to provide a basis for the correlation of the behavior of n-alkanes in liquid sulfur.     

Active feedback control of a beam subjected to a nonconservative force

This study examines the possibility of controlling through feedback a thin cantilevered beam subjected to a nonconservative follower force. A converging frequency flutter instability which occurs in this model is similar to classical bending-torsion flutter of an aircraft wing. Because of the similar nature of the instabilities, the beam under the follower force can be a useful vehicle for investigating the fundamental aspects of stabilization of wing flutter by feedback control. A modal approach is used for obtaining the mathematical model and control laws. A standard root locus technique for simple analytical models is also used to understand and explain the control of the beam. Experiments are carried out to verify the validity of this theoretical model. Good correlation is shown between theoretically and experimentally determined stability boundaries as well as for modal frequency and damping variation with follower force.     

The Secondary Bifurcation of an Aeroelastic Airfoil Motion: Effect of High Harmonics

The nonlinear dynamical response of a two-degree-of-freedom aeroelastic airfoil motion with cubic restoring forces is investigated. A secondary bifurcation after the primary Hopf (flutter) bifurcation is detected for a cubic hard spring in the pitch degree-of-freedom. Furthermore, there is a hysteresis in the secondary bifurcation: starting from different initial conditions the motion may jump from one limit cycle to another at different fluid flow velocities. A high-order harmonic balance method is employed to investigate the possible bifurcation branches. Furthermore, a numerical time simulation procedure is used to confirm the stable and unstable bifurcation branches.     

A novel harmonic balance analysis for the Van Der Pol oscillator

This study focuses on a novel harmonic balance formulation, the high-dimensional harmonic balance method. To investigate a non-linearity in the damping term, the system chosen for study is the Van der Pol's oscillator. Both unforced and forced oscillators are analyzed. The results from the analysis are compared with those obtained from the classical harmonic balance and the time marching (Runge-Kutta) methods.     

Hopf-flip bifurcation of high dimensional maps and application to vibro-impact systems

This paper addresses the problem of Hopf-flip bifurcation of high dimensional maps. Using the center manifold theorem, we obtain a three dimensional reduced map through the projection technique. The reduced map is further transformed into its normal form whose coefficients are determined by that of the original system. The dynamics of the map near the Hopf-flip bifurcation point is approximated by a so called ‘‘time-2τ² map’’ of a planar autonomous differential equation. It is shown that high dimensional maps may result in cycles of period two, tori T¹ (Hopf invariant circles), tori 2T¹ and tori 2T² depending both on how the critical eigenvalues pass the unit circle and on the signs of resonant terms’ coefficients. A two-degree-of-freedom vibro-impact system is given as an example to show how the procedure of this paper works. It reveals that through Hopf-flip bifurcations, periodic motions may lead directly to different types of motion, such as subharmonic motions, quasi-periodic motions, motions on high dimensional tori and even to chaotic motions depending both on change in direction of the parameter vector and on the nonlinear terms of the first three orders.The project supported by the National Natural Science Foundation of China (10472096)The English text was polished by Ron Marshall.     

Non-linear oscillator models in bluff body aero-elasticity

A critique of non-linear oscillator models is offered and a systematic and self-consistent procedure for constructing such a model is proposed based upon theoretical and experimental fluid mechanical information. Numerical studies are conducted for the proposed model as well as for the earlier one of Skop and Griffin. A comparison with Jones' experimental results is also made.     

Speech processing studies using an acoustic model of a multiple-channel cochlear implant

The speech perception of two multiple-channel cochlear implant patients was compared with that of three normally hearing listeners using an acoustic model of the implant for 22 different speech tests. The tests used included a minimal auditory capabilities battery, both closed-set and open-set word and sentence tests, speech tracking and a 12-consonant confusion study using nonsense syllables. The acoustic model represented electrical current pulses by bursts of noise and the effects of different electrodes were represented by using bandpass filters with different center frequencies. All subjects used a speech processor that coded the fundamental voicing frequency of speech as a pulse rate and the second formant frequency of speech as the electrode position in the cochlea, or the center frequency of the bandpass filter. Very good agreement was found for the two groups of subjects, indicating that the acoustic model is a useful tool for the development and evaluation of alternative cochlear implant speech processing strategies.     

Experimental comparison of Jψ production by π±, K±, p and p̄ beams at 39.5 GeV/c

Measurements have been made of relative production cross sections of the $\text{J}\text{ψ}$ by π^±, K^±, p and p? at 39.5 GeV/c incident on copper. $\text{J}\text{ψ}$ production rates from π^?, K^? and p? are similar. The $\text{J}\text{ψ}$ relative particle/anti-particle production cross sections for x>0 are $\text{σ(π}{}^{\mathrm{+}}\text{)}\text{σ(π}{}^{\mathrm{?}}\text{)=(0.87±0.14)}$, σ(K⁺)/σ(K^?)=(0.85±0.5) and $\text{σ(}\text{p}\text{)}\text{σ(}\text{p}\text{?}\text{)=(0.15 ±0.08)}$. The small p/p? cross section ratio disagrees with models of J/ψ production by gluon amalgamation.