A note on tsunamis: their generation and propagation in an ocean of uniform depth

The waves generated in a two-dimensional fluid domain of infinite lateral extent and uniform depth by a deformation of the bounding solid boundary are investigated both theoretically and experimentally. An integral solution is developed for an arbitrary bed displacement (in space and time) on the basis of a linear approximation of the complete (nonlinear) description of wave motion. Experimental and theoretical results are presented for two specific deformations of the bed; the spatial variation of each bed displacement consists of a block section of the bed moving vertically either up or down while the time-displacement history of the block section is varied. The presentation of results is divided into two sections based on two regions of the fluid domain: a generation region in which the bed deformation occurs and a downstream region where the bed position remains stationary for all time. The applicability of the linear approximation in the generation region is investigated both theoretically and experimentally; results are presented which enable certain gross features of the primary wave leaving this region to be determined when the magnitudes of parameters which characterize the bed displacement are known. The results indicate that the primary restriction on the applicability of the linear theory during the bed deformation is that the total amplitude of the bed displacement must remain small compared with the uniform water depth; even this restriction can be relaxed for one type of bed motion. Wave behaviour in the downstream region of the fluid domain is discussed with emphasis on the gradual growth of nonlinear effects relative to frequency dispersion during propagation and the subsequent breakdown of the linear theory. A method is presented for finding the wave behaviour in the far field of the downstream region, where the effects of nonlinearities and frequency dispersion have become about equal. This method is based on the use of a model equation in the far field (which includes both linear and nonlinear effects in an approximate manner) first used by Peregrine (1966) and more recently advocated by Benjamin, Bona & Mahony (1972) as a preferable model to the more commonly used equation of Korteweg & de Vries (1895). An input-output approach is illustrated for the numerical solution of this equation where the input is computed from the linear theory in its region of applicability. Computations are presented and compared with experiment for the case of a positive bed displacement where the net volume of the generated wave is finite and positive; the results demonstrate the evolution of a train of solitary waves (solitons) ordered by amplitude followed by a dispersive train of oscillatory waves. The case of a negative bed displacement in which the net wave volume is finite and negative (and the initial wave is negative almost everywhere) is also investigated; the results suggest that only a dispersive train of waves evolves (no solitons) for this case

An Empirical Argument for Nontechnical Public Members on Advisory Committees: FDA As a Model

A discussion of the results of two surveys of present and past members of Food and Drug Administration Advisory Committees. The views and understanding of the issues before various categories of membership are compared and contrasted. It appears that technical members of advisory committees would generally welcome more participation by persons who lack special subject matter expertise

Infrared Imaging of Planetary Nebulae from the Ground Up

New ground-based telescopes and instruments, the return of the NICMOS instrument on the Hubble Space Telescope (HST), and the recent launch of the Spitzer Space Telescope have provided new tools that are being utilized in the study of planetary nebulae. Multiwavelength, high spatial resolution ground-based and HST imaging have been used to probe the inner regions of young PNe to determine their structure and evaluate formation mechanisms. Spitzer/IRAC and MIPS have been used to image more evolved PNe to determine the spatial distribution of molecular hydrogen, ionized gas, and dust in the nebulae and halos.Comment: 8 pages, 3 figures, invited review given at IAU Symp. 234, to appear in "Planetary Nebulae in Our Galaxy and Beyond", eds. M. J. Barlow & R. H. Mende

Drinking Bourbon with Cupid

It was Valentine’s Day, and rather than enjoying the suspiciously commercial holiday with a romantic partner, I was alone watching reruns of “How I Met Your Mother,” from a cozy armchair with a cigar in one hand and a glass of bourbon in the other. The show prompted me to examine the nature of relationships; specifically, how the media portrays them vastly different than reality and the implications that arise as a result. Romantic relationships in film and literature appear to be idealized to a ridiculous degree. Unfortunately for us, this means that we create unrealistic expectations for our partners that lead many to remain single while they search for a relationship that adheres to the media’s extravagant standards. [excerpt

Attractors for Damped Semilinear Wave Equations with Singularly Perturbed Acoustic Boundary Conditions

Under consideration is the damped semilinear wave equation $$u_{tt}+u_t-\Delta u+u+f(u)=0$$ in a bounded domain $\Omega$ in $\mathbb{R}^3$ subject to an acoustic boundary condition with a singular perturbation, which we term "massless acoustic perturbation," \ep\delta_{tt}+\delta_t+\delta = -u_t\quad\text{for}\quad \ep\in[0,1]. By adapting earlier work by S. Frigeri, we prove the existence of a family of global attractors for each \ep\in[0,1]. We also establish the optimal regularity for the global attractors, as well as the existence of an exponential attractor, for each \ep\in[0,1]. The later result insures the global attractors possess finite (fractal) dimension, however, we cannot yet guarantee that this dimension is independent of the perturbation parameter \ep. The family of global attractors are upper-semicontinuous with respect to the perturbation parameter \ep, a result which follows by an application of a new abstract result also contained in this article. Finally, we show that it is possible to obtain the global attractors using weaker assumptions on the nonlinear term $f$, however, in that case, the optimal regularity, the finite dimensionality, and the upper-semicontinuity of the global attractors does not necessarily hold.Comment: To appear in EJDE. arXiv admin note: substantial text overlap with arXiv:1503.01821 and text overlap with arXiv:1302.426