Summary of research in applied mathematics, numerical analysis, and computer sciences

The major categories of current ICASE research programs addressed include: numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; control and parameter identification problems, with emphasis on effective numerical methods; computational problems in engineering and physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and computer systems and software, especially vector and parallel computers

Vorticity wave interaction and exceptional points in shear flow instabilities

We establish a link between vorticity wave interaction and $\mathcal{PT}$-symmetry breaking in shear flow instabilities. The minimal dynamical system for two coupled counter-propagating vorticity waves is shown to be a non-Hermitian system that exhibits a saddle-node exceptional point. The mechanism of phase-locking and mutual growth of vorticity waves is then related to the Krein collision and the breaking of $\mathcal{PT}$-symmetry through the exceptional point. The key parameter that leads the system to spontaneous $\mathcal{PT}$-symmetry breaking is the ratio between frequency detuning and coupling strength of the vorticity waves. The critical behavior near the exceptional point is described as a transition between phase-locking and phase-slip dynamics of the vorticity waves. The phase-slip dynamics lead to non-modal, transient growth of perturbations in the regime of unbroken $\mathcal{PT}$-symmetry, and the phase-slip frequency $\Omega \propto |k-k_c|^{1/2}$ shares the same critical exponent with the phase rigidity of system eigenvectors. The results can be readily extended to the interaction of multiple vorticity waves with multiple exceptional points and rich transient dynamics.Comment: 10 pages, 13 figure

Energy Flux in the Cochlea: Evidence Against Power Amplification of the Traveling Wave

Traveling waves in the inner ear exhibit an amplitude peak that shifts with frequency. The peaking is commonly believed to rely on motile processes that amplify the wave by inserting energy. We recorded the vibrations at adjacent positions on the basilar membrane in sensitive gerbil cochleae and tested the putative power amplification in two ways. First, we determined the energy flux of the traveling wave at its peak and compared it to the acoustic power entering the ear, thereby obtaining the net cochlear power gain. For soft sounds, the energy flux at the peak was 1 ± 0.6 dB less than the middle ear input power. For more intense sounds, increasingly smaller fractions of the acoustic power actually reached the peak region. Thus, we found no net power amplification of soft sounds and a strong net attenuation of intense sounds. Second, we analyzed local wave propagation on the basilar membrane. We found that the waves slowed down abruptly when approaching their peak, causing an energy densification that quantitatively matched the amplitude peaking, similar to the growth of sea waves approaching the beach. Thus, we found no local power amplification of soft sounds and strong local attenuation of intense sounds. The most parsimonious interpretation of these findings is that cochlear sensitivity is not realized by amplifying acoustic energy, but by spatially focusing it, and that dynamic compression is realized by adjusting the amount of dissipation to sound intensity

Cumulative reports and publications through December 31, 1990

This document contains a complete list of ICASE reports. Since ICASE reports are intended to be preprints of articles that will appear in journals or conference proceedings, the published reference is included when it is available

Activities of the Institute for Computer Applications in Science and Engineering

Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period April 1, 1985 through October 2, 1985 is summarized

Cumulative reports and publications

A complete list of Institute for Computer Applications in Science and Engineering (ICASE) reports are listed. Since ICASE reports are intended to be preprints of articles that will appear in journals or conference proceedings, the published reference is included when it is available. The major categories of the current ICASE research program are: applied and numerical mathematics, including numerical analysis and algorithm development; theoretical and computational research in fluid mechanics in selected areas of interest to LaRC, including acoustics and combustion; experimental research in transition and turbulence and aerodynamics involving LaRC facilities and scientists; and computer science

Cumulative reports and publications through December 31, 1988

This document contains a complete list of ICASE Reports. Since ICASE Reports are intended to be preprints of articles that will appear in journals or conference proceedings, the published reference is included when it is available

Étude de la stabilité de quelques systèmes d'équations des ondes couplées sur des domaines bornés et non bornés

The thesis is driven mainly on indirect stabilization system of two coupled wave equations and the boundary stabilization of Rayleigh beam equation. In the case of stabilization of a coupled wave equations, the Control is introduced into the system directly on the edge of the field of a single equation in the case of a bounded domain or inside a single equation but in the case of an unbounded domain. The nature of thus coupled system depends on the coupling equations and arithmetic Nature of speeds of propagation, and this gives different results for the polynomial stability and the instability. In the case of stabilization of Rayleigh beam equation, we consider an equation with one control force acting on the edge of the area. First, using the asymptotic expansion of the eigenvalues and vectors of the uncontrolled system an observability result and a result of boundedness of the transfer function are obtained. Then a polynomial decay rate of the energy of the system is established. Then through a spectral study combined with a frequency method, optimality of the rate obtained is assured.La thèse est portée essentiellement sur la stabilisation indirecte d’un système de deux équations des ondes couplées et sur la stabilisation frontière de poutre de Rayleigh.Dans le cas de la stabilisation d’un système d’équations d’onde couplées, le contrôle est introduit dans le système directement sur le bord du domaine d’une seule équation dans le cas d’un domaine borne ou à l’intérieur d’une seule équation mais dans le cas d’un domaine non borné. La nature du système ainsi couplé dépend du couplage des équations et de la nature arithmétique des vitesses de propagations, et ceci donne divers résultats pour la stabilisation polynomiale ainsi la non stabilité.Dans le cas de la stabilisation de poutre de Rayleigh, l’équation est considérée avec un seul contrôle force agissant sur bord du domaine. D’abord, moyennant le développement asymptotique des valeurs propres et des vecteurs propres du système non contrôlé, un résultat d’observabilité ainsi qu’un résultat de bornétude de la fonction de transfert correspondant sont obtenus. Alors, un taux de décroissance polynomial de l’énergie du système est établi. Ensuite, moyennant une étude spectrale combinée avec une méthode fréquentielle, l’optimalité du taux obtenu est assurée

Institute for Computer Applications in Science and Engineering (ICASE)

Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis and computer science during the period April 1, 1983 through September 30, 1983 is summarized

Research in structural and solid mechanics, 1982

Advances in structural and solid mechanics, including solution procedures and the physical investigation of structural responses are discussed