Using global invariant manifolds to understand metastability in Burgers equation with small viscosity

The large-time behavior of solutions to Burgers equation with small viscosity is described using invariant manifolds. In particular, a geometric explanation is provided for a phenomenon known as metastability, which in the present context means that solutions spend a very long time near the family of solutions known as diffusive N-waves before finally converging to a stable self-similar diffusion wave. More precisely, it is shown that in terms of similarity, or scaling, variables in an algebraically weighted $L^2$ space, the self-similar diffusion waves correspond to a one-dimensional global center manifold of stationary solutions. Through each of these fixed points there exists a one-dimensional, global, attractive, invariant manifold corresponding to the diffusive N-waves. Thus, metastability corresponds to a fast transient in which solutions approach this "metastable" manifold of diffusive N-waves, followed by a slow decay along this manifold, and, finally, convergence to the self-similar diffusion wave

Understanding Physical Processes Represented by the Monin–Obukhov Bulk Formula for Momentum Transfer

Physical processes represented by the Monin–Obukhov bulk formula for momentum are investigated with field observations. We discuss important differences between turbulent mixing by the most energetic non-local, large, coherent turbulence eddies and local turbulent mixing as traditionally represented by K-theory (analog to molecular diffusion), especially in consideration of developing surface-layer stratification. The study indicates that the neutral state in a horizontally homogeneous surface layer described in the Monin–Obukhov bulk formula represents a special neutrality regardless of wind speed, for example, the surface layer with no surface heating/cooling. Under this situation, the Monin–Obukhov bulk formula agrees well with observations for heights to at least 30 m. As the surface layer is stratified, stably or unstably, the neutral state is achieved by mechanically generated turbulent mixing through the most energetic non-local coherent eddies. The observed neutral relationship between u∗ role= presentation style= box-sizing: inherit; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eu∗u∗ (the square root of the momentum flux magnitude) and wind speed V at any height is different from that described by the Monin–Obukhov formula except within several metres of the surface. The deviation of the Monin–Obukhov neutral u∗−V role= presentation style= box-sizing: inherit; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eu∗−Vu∗−V linear relation from the observed one increases with height and contributes to the deteriorating performance of the bulk formula with increasing height, which cannot be compensated by stability functions. Based on these analyses, estimation of drag coefficients is discussed as well

Chandra and ROSAT observations of Abell 194: detection of an X-ray cavity and mapping the dynamics of the cluster

Based on Chandra and ROSAT observations, we investigated the nearby poor cluster Abell 194, which hosts two luminous radio galaxies, NGC547 (3C 40B) and NGC541 (3C 40A). We demonstrated the presence of a large X-ray cavity (r~34 kpc) formed by the giant southern radio lobe arising from 3C 40B in NGC547. The estimated age of the cavity is t=7.9 x 10^7 years and the total work of the AGN is 3.3 x 10^59 erg, hence the cavity power is P_cav=1.3 x 10^44 erg/s. Furthermore, in the Chandra images of NGC545 and NGC541 we detected sharp surface brightness edges, identified as merger cold fronts, and extended tails. Using the pressure ratios between inside and outside the cold fronts we estimated that the velocities of NGC545 and NGC541 correspond to Mach-numbers of M=1.0^{+0.3}_{-0.5} and M=0.9^{+0.2}_{-0.5}, respectively. The low radial velocities of these galaxies relative to the mean radial velocity of Abell 194 imply that their motion is oriented approximately in the plane of the sky. Based on these and earlier observations, we concluded that NGC545 and NGC541 are falling through the cluster, whose center is NGC547, suggesting that Abell 194 is undergoing a significant cluster merger event. Additionally, we detected 20 bright X-ray sources around NGC547 and NGC541, a surprisingly large number, since the predicted number of resolved LMXBs and CXB sources is 2.2 and 4.1, respectively. To explain the nature of additional sources, different possibilities were considered, none of which are satisfactory. We also studied the origin of X-ray emission in Minkowski's Object, and concluded that it is most likely dominated by the population of HMXBs rather than by hot diffuse ISM. Moreover, in view of the galaxy dynamics in Abell 194, we explored the possibility that the starburst in Minkowski's Object was triggered by its past interaction with NGC541, and concluded that it may be a viable path.Comment: 12 pages, 7 figures, accepted for publication in Ap

A many-core software framework for embedded space computing

Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 66-67).Space computing has long called for powerful yet power-efficient hardware for on-board computation. The emergence of many-core CPUs on a single die provides one potential solution. The development of processors like Maestro strives for the balance between computational power and energy efficiency. However, development in software has not kept up. Not a single dominant programming framework has emerged to allow developers to easily write applications to take advantage of the new multi-core paradigm. As a result, in NASA's technology roadmap, fault management, programmability, and energy management under the new multi-core paradigm have been listed as top challenges. The goal of this thesis is to develop a framework that streamlines programming for multi-core processors, in the form of a programming model and a C++ programming library. A 49-core Maestro Development Board (MDB) serves as the development and testing hardware platform. The framework's usability is tested through a software simulation of a vision-based crater recognition algorithm for a lunar lander. A parallel version of the algorithm is written under the framework and tested, and a performance gain of about 300%, using 21 Maestro cores, is observed over the RAD750. The uniqueness of this framework lies in the principle that task blocks, not CPU cores, are the fundamental abstraction for individual processes. Each task block is allocated an arbitrary number of CPUs, completes one task, and communicates with other task blocks through message passing. Fault tolerance, power management, and communication among task blocks are abstracted out so that programmers can concentrate on the implementation of the application. The resulting programming library provides developers with the right tools to design and test parallel programs, port serial versions of applications to their parallelized counterparts, and develop new parallel programs with ease.by Eugene Yu-Ting Sun.M. Eng

An improved game-theoretic approach to uncover overlapping communities

How can we uncover overlapping communities from complex networks to understand the inherent structures and functions? Chen et al. firstly proposed a community game (Game) to study this problem, and the overlapping communities have been discovered when the game is convergent. It is based on the assumption that each vertex of the underlying network is a rational game player to maximize its utility. In this paper, we investigate how similar vertices affect the formation of community game. The Adamic–Adar Index (AA Index) has been employed to define the new utility function. This novel method has been evaluated on both synthetic and real-world networks. Experimental study shows that it has significant improvement of accuracy (from 4.8% to 37.6%) compared with the Game on 10 real networks. It is more efficient on Facebook networks (FN) and Amazon co-purchasing networks than on other networks. This result implicates that “friend circles of friends” of Facebook are valuable to understand the overlapping community division

Safety, Tolerability, and Pharmacokinetic Properties of Intravenous Delafloxacin After Single and Multiple Doses in Healthy Volunteers

AbstractPurposeThe objective of this report was to determine the pharmacokinetic properties, safety, and tolerability of single and multiple doses of intravenous delafloxacin. In addition, the absolute bioavailability (BA) of the 450-mg tablet formulation of delafloxacin was determined.MethodsThree clinical trials are summarized. The first study was a randomized, double-blind, placebo-controlled, single- (300, 450, 600, 750, 900, and 1200 mg) ascending-dose study of IV delafloxacin in 62 (52 active, 10 placebo) healthy volunteers. The second study was a randomized, double-blind, placebo-controlled study of IV delafloxacin (300 mg) given as a single dose on day 1, followed by twice-daily dosing on days 2 through 14; 12 (8 active, 4 placebo) healthy volunteers were enrolled. The third study was an open-label, randomized, 2-period, 2-sequence crossover study in which 56 healthy volunteers were randomly assigned to 1 of 2 sequences of a single oral dose of delafloxacin (450-mg tablet) or IV delafloxacin (300 mg). Serial blood samples were collected, and plasma pharmacokinetic parameters of delafloxacin were calculated.FindingsDelafloxacin Cmax values increased proportionally with increasing single IV dose for the dose range of 300 to 1200 mg, whereas the AUC values increased more than proportionally to dose for the same dose range. The mean terminal half-life of delafloxacin was approximately 12 hours (ranging from 8 to 17 hours). The volume of distribution (Vd) at steady state was approximately 35 L, which is similar to the volume of total body water. There was minimal accumulation of delafloxacin after twice-daily IV administration of 300 mg with an accumulation ratio of 1.09. The delafloxacin total exposure after a single 1-hour IV infusion of 300 mg and a single oral dose of a 450-mg tablet were equivalent with geometric least square mean ratio (90% CI) of 0.8768 (0.8356–0.9200) for AUC0–∞ and 0.8445 (0.8090–0.8815) for AUC0–t, respectively. The Cmax values of delafloxacin were not equivalent for the 2 formulations with a ratio (90% CI) of 0.5516 (0.5150–0.5908), respectively. The mean absolute bioavailability of delafloxacin was 58.8%.ImplicationsDelafloxacin was well tolerated in healthy volunteers after single and multiple IV doses. The total systemic exposure to IV (300 mg) and oral (450 mg) delafloxacin is comparable, supporting that a switch between the 2 formulations is appropriate

Single and Multiple Ascending-dose Studies of Oral Delafloxacin: Effects of Food, Sex, and Age

AbstractPurposeThe objective of this report is describe the results of 2 studies that examined the pharmacokinetic parameters, safety profile, and tolerability of single and multiple ascending doses of oral delafloxacin and the effects of food, sex, and age on oral delafloxacin pharmacokinetic parameters, safety profile, and tolerability.MethodsThe first study contained 3 parts and used unformulated delafloxacin in a capsule. Part 1 was a randomized, double-blind, placebo-controlled, single (50, 100, 200, 400, 800, 1200, and 1600 mg) ascending-dose study of oral delafloxacin in healthy men. Part 2 was a single-dose crossover study in which 20 men received 250 mg delafloxacin with or without food. Part 2 also included a parallel group, double-blind, placebo-controlled study in 16 women and 16 elderly men and women who were randomized (3:1) to receive 250 mg delafloxacin or placebo. Part 3 was a randomized, double-blind, placebo-controlled, multiple (100, 200, 400, 800, 1200 mg once daily for 5 days) ascending-dose study of oral delafloxacin in healthy men. The second study was a single-dose, randomized, 3-period crossover study in which participants received 900 mg delafloxacin (2 × 450-mg tablets) under fasted conditions, with a high-fat meal, or fasted with a high-fat meal 2 hours after dosing. Serial blood samples were collected, and plasma pharmacokinetic parameters of delafloxacin were determined.FindingsDelafloxacin Cmax and AUC0–∞ increased with increasing oral dose over the dose range of 50 to 1600 mg. The increases in delafloxacin AUC0–∞ were dose proportional at doses of ≥200 mg. Steady state was reached by day 3 of dosing with minimal accumulation of delafloxacin. The Cmax of delafloxacin was decreased slightly in the presence of food. No sex difference in delafloxacin pharmacokinetic parameters was observed. In the elderly men and women, mean delafloxacin Cmax and AUC0–∞ were 35% higher than observed for young adults, which could be partially explained by a decrease in the creatinine clearance in the elderly men and women. Delafloxacin was well tolerated at the tested doses, with gastrointestinal adverse effects observed more commonly at doses ≥1200 mg.ImplicationsDelafloxacin exhibits linear pharmacokinetic parameters that reached steady state after 3 days of daily oral dosing with minimal accumulation. Delafloxacin was well tolerated throughout both studies, with gastrointestinal effects observed at the higher doses (≥1200 mg)