Lefschetz Center for Dynamical Systems Seminar
Abstract: Wave turbulence formalism for long internal waves in a stratified fluid is developed, based on a natural Hamiltonian description. A kinetic equation appropriate for the description of spectral energy transfer is derived, and its self-similar stationary solution corresponding to a direct cascade of energy toward the short scales is found. This solution is very close to the high wavenumber limit of the Garrett-Munk spectrum of long internal waves in the ocean. In fact, a small modification of the Garrett-Munk formalism includes a spectrum consistent with the one predicted by wave turbulence.
Center for Fluid Mechanics Seminar
Abstract: Experiments have been performed to better understand the space-varying character of the fluctuating wall pressure field beneath a transitional boundary layer and to guide the development of an appropriate model for the space-varying (nonhomogeneous) wavenumber-frequency wall pressure spectrum. Although a great deal is understood regarding the structure of the wall pressure field beneath fully developed equilibrium turbulent boundary layers and the associated form of the homogeneous wavenumber-frequency wall pressure spectrum, the current understanding of the wall pressure field beneath the spatially evolving transitional boundary layer is incomplete. Overlooked have been critical issues concerning spatial variations in turbulence structure and the convection and decay of pressure producing disturbances -- properties that define the character of the field and resulting form of the wavenumber-frequency spectrum.
The experiments involve measurement of the space-time fluctuating wall pressure field across the transition region of a flat plate boundary layer by means of a 64-element linear array of subminiature hearing-aid microphones and hot wire velocity measurements in the adjacent laminar, transitional, and turbulent boundary layers. Unlike previous single-point or two-point transition zone measurements in the literature, the present array measurements clearly reveal the spatio-temporal formation, convection and growth of transitional flow structures across the transition zone. To examine the effect of these spatial variations in transitional pressure producing distrubances on the wavenumber-frequency spectrum, a preliminary model has been developed that introduces space-varying velocity and length scales into the equilibrium turbulent boundary layer wavenumber-frequency wall pressure model of Chase (1987). Measured single-point spectra and statistics computed from this equation have been evaluated and shown to produce the qualitatively correct behavior seen in the measured results.
This presentation will describe the experimental effort and present results from both the measurement and modeling efforts using conventional signal processing methods. The application of the wavelet based methods to the interpretation and modeling of the field is in progress and will be discussed also.
Stochastic Systems Seminar
Brown University Joint Mechanics/Materials Seminar
Abstract: Fatigue behaviour of SiC-fibre (SCS-6 of Textron USA) reinforced titanium alloy Timetal 834 has been investigated at room temperature and 600^o C. Matrix crack formation and growth is the dominating damage mechanism at room temperature. This leads to a strong drop in fatigue strength for a life of 10^3-10^6 cycles and the endurance limit measures ~800MPa. At 600^o C the matrix appears to be less susceptive to cracking which causes the endurance limit to be considerably higher (limit ~1200MPa). Fracture surfaces give information about the crack size, which give rise to ultimate failure. This is especially the case for the specimens broken during 600^o C fatigue testing, as at the moment oxygen has access to free crack surfaces colour patterns are formed.
The most important damage mechanism giving rise to the strong drop in fatigue strength (matrix cracks bridged by the fibres) at room temperature has been investigated with the aid of 3-dimensional finite element modelling. With the aid of 3D-models crack propagation rates in SCS-6/Timetal 834 at room temperature have been predicted making use of the known da/dN behaviour of Timetal 834 and compared with experimental results. It will be shown that the condition of interfacial stress transfer is the dominating parameter for the growth of fibre bridged matrix cracks.
Finally the parameters giving rise to the excellent high temperature fatigue behaviour are discussed. These are: stress relaxation of the matrix, creep properties of the fibres and lack of oxidation of the fibres (as long these are protected by the titanium).
Brown Analysis Seminar
Scientific Computing Seminar
North Carolina State University, Raleigh and Tel Aviv, Israel | |
Abstract: We consider a problem of eliminating the unwanted time- harmonic noise on a predetermined region of interest. The desired objective is achieved by active means, i.e., by introducing additional sources of sound called control sources, that generate the appropriate annihilating acoustic signal (anti-sound). A general solution for the control sources has been obtained previously in both continuous and discrete formulation of the problem. In the current talk, we focus on optimizing the overall absolute acoustic source strength of the control sources. Mathematically, this amounts to the minimization of multi- variable complex-valued functions in the sense of $L_1$ with conical constraints, which are only "marginally" convex. The corresponding numerical optimization problem appears very challenging even for the most sophisticated state-of-the-art methodologies, and even when the dimension of the grid is small, and the waves are long.
Our central result is that the global $L_1$-optimal solution, can, in fact, be obtained without solving a numerical optimization problem. This solution is given by a special layer of monopole sources on the perimeter of the protected region. We provide a rigorous proof of the global $L_1$ minimality for both continuous and discrete optimization problems in the one-dimensional case. We also provide numerical evidence that corroborates our result in the two-dimensional case, when the protected domain is a cylinder. Even though we cannot fully justify it, we believe that the same result holds in the general case, because the combination of 2D computations and 1D proof cannot be a mere coincidence. We formulate it as a conjecture in the end of the talk.
Brown University - Joint Mechanics/Materials Seminar
Abstract: I will start by talking about our group's development of a modern, flexible and powerful MD package, called DigitalMaterial. What makes this package different from others is the use of a component-based approach based on software engineering methods known as Design Patterns. The interfaces for these components are very clearly defined, allowing components to be quite interoperable. I will then talk about three applications whose common theme is interfacing or embedding atomistic models with/in continuum models. The first example is the Peierls barrier for dislocation glide in a two dimensional material. The second application, which particularly makes use of the flexibility in DigitalMaterial, is the initiation of fracture at sharp notches in single crystal silicon. Finally I will describe some current work concerning the coupling of MD to finite-element modeling.
PDE Seminar
<--- 2002 Index