Oscillations and concentrations in weak solutions of the incompressible fluid equations

The authors introduce a new concept of measure-valued solution for the 3-D incompressible Euler equations in order to incorporate the complex phenomena present in limits of approximate solutions of these equations. One application of the concepts developed here is the following important result: a sequence of Leray-Hopf weak solutions of the Navier-Stokes equations converges in the high Reynolds number limit to a measure-valued solution of 3-D Euler defined for all positive times. The authors present several explicit examples of solution sequences for 3-D incompressible Euler with uniformly bounded local kinetic energy which exhibit complex phenomena involving both persistence of oscillations and development of concentrations. An extensions of the concept of Young measure is developed to incorporate these complex phenomena in the measure-valued solutions constructed here.Partially supported by N.S.F. GrantPartially supported by N.S.F. Grant 84-0223 and 86-11110     

Single-Shot Diffusion Measurement in Laser-Polarized Gas

A single-shot pulsed gradient stimulated echo sequence is introduced to address the challenges of diffusion measurements of laser polarized 3He and 129Xe gas. Laser polarization enhances the NMR sensitivity of these noble gases by >10(3), but creates an unstable, nonthermal polarization that is not readily renewable. A new method is presented which permits parallel acquisition of the several measurements required to determine a diffusive attenuation curve. The NMR characterization of a sample's diffusion behavior can be accomplished in a single measurement, using only a single polarization step. As a demonstration, the diffusion coefficient of a sample of laser-polarized 129Xe gas is measured via this method.     

Is there a universal scale of time?

The assumption that the same universal scale of time applies for different physical laws depends uponthe hypothesis that there is a unique universal scale of time in the universe. Intrinsic to that hypothesis is the assumption that if extraneous factors that affect physical clocks and processes that run on different physical principles could be removed, all clocks are synchronizable with one another. The consequences of that hypothesis not being true are considered. It was found thatclock asynchrony implies that: (1) a mass variation theory is probable; (2) there is a need for multiple clocks; and (3) t in the equations of physics is referring to clocks rather than time such that the properties of time are reduced to its direction (as characterized by thermodynamics and cosmology).     

Dynamic glottal pressures in an excised hemilarynx model

During phonation, air pressures act upon the vocal folds to help maintain their oscillation. The air pressures vary dynamically along the medial surface of the vocal folds, although no live human or excised studies have shown how those pressure profiles vary in time. The purpose of this study was to examine time-dependent glottal pressure profiles using a canine hemilarynx approach. The larynx tissue was cut in the midsaggital plane from the top to about 5 mm below the vocal folds. The right half was replaced with a Plexiglas pane with imbedded pressure taps. Simultaneous recordings were made of glottal pressure signals, subglottal pressure, particle velocity, and average airflow at various levels of adduction. The data indicate that the pressures in the glottis (on the Plexiglas) vary both vertically and longitudinally throughout the phonatory cycle. Pressures vary most widely near the location of maximum vibratory amplitude, and can include negative pressures during a portion of the cycle. Pressures anterior and posterior to the maximum amplitude location may have less variation and may remain positive throughout the cycle, giving rise to a new concept called dynamic bidirectional pressure gradients in the glottis. This is an important concept that may relate strongly to tissue health as well as basic oscillatory mechanics.     

The Hamiltonian structure of general relativistic perfect fluids

We show that the evolution equations for a perfect fluid coupled to general relativity in a general lapse and shift, are Hamiltonian relative to a certain Poisson structure. For the fluid variables, a Lie-Poisson structure associated to the dual of a semi-direct product Lie algebra is used, while the bracket for the gravitational variables has the usual canonical symplectic structure. The evolution is governed by a Hamiltonian which is equivalent to that obtained from a canonical analysis. The relationship of our Hamiltonian structure with other approaches in the literature, such as Clebsch potentials, Lagrangian to Eulerian transformations, and its use in clarifying linearization stability, are discussed.Research supported in part by NSF grant MCS 81-08814(A02)Research supported in part by NSF grant MCS 81-07086     

Tracking regression and progression of atherosclerosis in human carotid arteries using high-resolution magnetic resonance imaging

BACKGROUND AND PURPOSE: Magnetic resonance imaging (MRI) can accurately and reproducibly measure the volume of atherosclerotic plaque in human carotid arteries. Atherosclerotic plaques may either progress or regress over time, depending on individual risk factors and treatment regimens. This study was designed to determine if regression or progression of human carotid atherosclerosis in patients receiving statin therapy over 24 months can be detected by high-resolution MRI. METHODS: In 11 subjects who had undergone unilateral carotid endarterectomy and were on statin therapy, volumes for total carotid artery, concentric wall (normal wall), eccentric wall (plaque), and lumen were quantified at 0, 16 and 24 months using a 1.5-T human imager equipped with 6-cm phased array coils. RESULTS: The interobserver mean coefficient of variation (CV) was lowest for the lumen volume (3.1%) and highest for the plaque volume (9.8%). The interscan mean CV was lowest for the total artery volume (3.2%) and highest for the plaque volume (9.9%). As much as 26% regression and 35% progression were observed in individual subject's carotid artery eccentric wall (plaque) volumes over time. Mean eccentric wall volume increased 5% by 16 months and 8% by 24 months. Mean total wall volume increased slightly at both 16 and 24 months (+1.2% and +1.8%). CONCLUSIONS: High-resolution MRI provides a noninvasive reproducible method of tracking changes in carotid atherosclerosis. This pilot study detected changes in individual subjects at both 16 and 24 months. MRI tracking of changes in atherosclerotic plaques should prove useful in assessing vascular disease risk and monitoring the efficacy of interventions designed to induce regression or retard progression.     

Constants of Motion for Several One-Dimensional Systems and Problems Associated with Getting Their Hamiltonians

The constants of motion of the following systems are deduced: a relativistic particle with linear dissipation; a no-relativistic particle with a time explicitly depending force; a no-relativistic particle with a constant force and time depending mass; and a relativistic particle under a conservative force with position depending mass. The Hamiltonian for these systems, which is determined by getting the velocity as a function of position and generalized linear momentum, can be found explicitly at first approximation for the first system. The Hamiltonians for the other systems are kept implicitly in their expressions for their constants of motion.     

Dynamics of hairpin vortices and polymer-induced turbulent drag reduction

It has been known for over six decades that the dissolution of minute amounts of high molecular weight polymers in wall-bounded turbulent flows results in a dramatic reduction in turbulent skin friction by up to 70%. First principles simulations of turbulent flow of model polymer solutions can predict the drag reduction (DR) phenomenon. However, the essential dynamical interactions between the coherent structures present in turbulent flows and polymer conformation field that lead to DR are poorly understood. We examine this connection via dynamical simulations that track the evolution of hairpin vortices, i.e., counter-rotating pairs of quasistreamwise vortices whose nonlinear autogeneration and growth, decay and breakup are centrally important to turbulence stress production. The results show that the autogeneration of new vortices is suppressed by the polymer stresses, thereby decreasing the turbulent drag.     

Repeated Interaction Quantum Systems: Van Hove Limits and Asymptotic States

We establish the existence of two weak coupling regime effective dynamics for an open quantum system of repeated interactions (vanishing strength and individual interaction duration, respectively). This generalizes known results (Attal and Joye in J. Stat. Phys. 126:1241–1283, 2007) in that the von Neumann algebras describing the system and the chain element may not be of finite type. Then (but now assuming that the small system is of finite type), we prove that both effective dynamics capture the long-term behavior of the system: existence of a unique asymptotic state for them implies the same property for the respective exact dynamics—provided that the perturbation parameter is sufficiently small. The zero-th order term in a power series expansion in the perturbation parameter of such an asymptotic state is given by the asymptotic state of the effective dynamics. We conclude by working out the case in which the small system and the chain element are spins. Dedicated to Mariana Huerta. This work was partially funded by Nucleus Millennium Information and Randomness P04-069-F.     

Ignition delay times of methane and hydrogen highly diluted in carbon dioxide at high pressures up to 300 atm

The need for more efficient power cycles has attracted interest in super-critical CO₂ (sCO₂) cycles. However, the effects of high CO₂ dilution on auto-ignition at extremely high pressures has not been studied in depth. As part of the effort to understand oxy-fuel combustion with massive CO₂ dilution, we have measured shock tube ignition delay times (IDT) for methane/O₂/CO₂ mixtures and hydrogen/O₂/CO₂ mixtures using sidewall pressure and OH* emission near 306?nm. Ignition delay time was measured in two different facilities behind reflected shock waves over a range of temperatures, 1045–1578?K, in different pressures and mixture regimes, i.e., CH₄/O₂/CO₂ mixtures at 27–286 atm and H₂/O₂/CO₂ mixtures at 37–311 atm. The measured data were compared with the predictions of two recent kinetics models. Fair agreement was found between model and experiment over most of the operating conditions studied. For those conditions where kinetic models fail, the current ignition delay time measurements provide useful target data for development and validation of the mechanisms.