Formulation and performance of variational integrators for rotating bodies

Variational integrators are obtained for two mechanical systems whose configuration spaces are, respectively, the rotation group and the unit sphere. In the first case, an integration algorithm is presented for Euler’s equations of the free rigid body, following the ideas of Marsden et al. (Nonlinearity 12:1647–1662, 1999). In the second example, a variational time integrator is formulated for the rigid dumbbell. Both methods are formulated directly on their nonlinear configuration spaces, without using Lagrange multipliers. They are one-step, second order methods which show exact conservation of a discrete angular momentum which is identified in each case. Numerical examples illustrate their properties and compare them with existing integrators of the literature

A New Acoustic Portal into the Odontocete Ear and Vibrational Analysis of the Tympanoperiotic Complex

Global concern over the possible deleterious effects of noise on marine organisms was catalyzed when toothed whales stranded and died in the presence of high intensity sound. The lack of knowledge about mechanisms of hearing in toothed whales prompted our group to study the anatomy and build a finite element model to simulate sound reception in odontocetes. The primary auditory pathway in toothed whales is an evolutionary novelty, compensating for the impedance mismatch experienced by whale ancestors as they moved from hearing in air to hearing in water. The mechanism by which high-frequency vibrations pass from the low density fats of the lower jaw into the dense bones of the auditory apparatus is a key to understanding odontocete hearing. Here we identify a new acoustic portal into the ear complex, the tympanoperiotic complex (TPC) and a plausible mechanism by which sound is transduced into the bony components. We reveal the intact anatomic geometry using CT scanning, and test functional preconceptions using finite element modeling and vibrational analysis. We show that the mandibular fat bodies bifurcate posteriorly, attaching to the TPC in two distinct locations. The smaller branch is an inconspicuous, previously undescribed channel, a cone-shaped fat body that fits into a thin-walled bony funnel just anterior to the sigmoid process of the TPC. The TPC also contains regions of thin translucent bone that define zones of differential flexibility, enabling the TPC to bend in response to sound pressure, thus providing a mechanism for vibrations to pass through the ossicular chain. The techniques used to discover the new acoustic portal in toothed whales, provide a means to decipher auditory filtering, beam formation, impedance matching, and transduction. These tools can also be used to address concerns about the potential deleterious effects of high-intensity sound in a broad spectrum of marine organisms, from whales to fish

Simulating the effect of high-intensity sound on cetaceans: Modeling approach and a case study for Cuvier’s beaked whale ( Ziphius cavirostris

A finite element model is formulated to study the steady-state vibration response of the anatomy of a whale (Cetacea) submerged in seawater. The anatomy was reconstructed from a combination of two-dimensional (2D) computed tomography (CT) scan images, identification of Hounsfield units with tissue types, and mapping of mechanical properties. A partial differential equation model describes the motion of the tissues within a Lagrangean framework. The computational model was applied to the study of the response of the tissues within the head of a neonate Cuvier's beaked whale Ziphius cavirostris. The characteristics of the sound stimulus was a continuous wave excitation at 3500 Hz and 180 dB re: 1 mu Pa received level, incident as a plane wave. We model the beaked whale tissues embedded within a volume of seawater. To account for the finite dimensions of the computational volume, we increased the damping for viscous shear stresses within the water volume, in an attempt to reduce the contribution of waves reflected from the boundaries of the computational box. The mechanical response of the tissues was simulated including: strain amplitude; dissipated power; and pressure. The tissues are not likely to suffer direct mechanical or thermal damage, within the range of parameters tested. (c) 2006 Acoustical Society of America