Comparison of approximate and numerical analyses of nonlinear combustion instability

At the present time, there are three general analytical techniques available to study problems of unsteady motions in rocket motors: linear stability analysis; approximate nonlinear analysis, founded on examining the behavior of coupled normal modes; and numerical calculations based on the conservation equations for one-dimensional flows. The last two yield the linear results as a limit. It is the main purpose of this paper to check the accuracy of the approximate analysis against the numerical analysis for some special cases. The results provide some justification for using the approximate analysis to study three dimensional problems

Scenarios of energy efficiency and CO2 emissions reduction potential in the buildings sector in China to year 2050

As China’s rapid urbanization continues and urban dwellers become more affluent, energy use in buildings is expected to grow. To understand how this growth can be slowed, we explore four scenarios for Chinese buildings, ranging from a high-energy-demand scenario with no new energy policies to lowest energy demand under a techno-economic-potential scenario that assumes full deployment of cost-effective efficient and renewable technologies by 2050. We show that, in the high energy demand scenario, building energy demand has an average annual growth rate of about 2.8%, with slower growth rates in the other three scenarios. In all scenarios, CO2 emissions grow slower than energy, with building CO2 peaking around 2045 in the high energy demand scenario, and as early as 2030 in the techno-economic-potential scenario. We show that although various technological solutions, systems and practices can be very effective in minimizing building energy use, rigorous policies are needed to overcome multiple implementation barriers

Transonic flow in a converging-diverging nozzle Final report

Transonic equations of motion for convergent-divergent nozzl

Internet Ethics, American Law, and Jewish Law: A Comparative Overview

Societies are governed by codes of ethics. In developed societies, parts of these codes form a set of laws, enforceable by legal authorities, with or without assistance from the populace. At times, laws are crafted for the benefit of the powerful members of the society, ensuring preservation of their positions and property, while other constituents may ignore, actively disobey, or challenge laws they believe do not support their ethics. Developing and maintaining appropriate social norms is thus particularly critical for sustaining rapidly changing heterogeneous populaces. The Internet, devised for the purpose of interconnecting diverse computer networks of research and educational communities, has become a global communication system that joins together widely disparate populaces with different ethical codes. The World Wide Web (WWW), hosted by the Internet, serves both to propagate existing ethos and to undermine them. Communities of the WWW, as well as their governments, are striving to establish fundamental guidelines. This Essay suggests that Jewish law contains principles that may be relevant to this endeavor. Specifically, a comparative overview of elements of the ethics and regulation of speech in American law and Jewish law may help us understand ethical guidelines of online communities. We investigate the posting and retrieval of content containing libel (slander), gossip (scandal), unauthorized personal information (privacy violation), pornography, obscenity, and other objectionable material. We first briefly review the history of the Internet in order to identify ways in which its development influenced and was influenced by pre-existing technologies. We then examine American and Jewish law in terms of speech (output and input of content) and privacy (in this Essay, restricted to output and input of personal content), and compare these to content guidelines on some prominent social networks. We claim that Jewish law and ethics, which place broader restrictions on speech than those in American law, have the potential to positively influence the norms of both traditional and social media. Incorporating social norms can be particularly beneficial in the context of Internet-based ethics. First, to the extent that formal laws are unfair and/or ineffective, they can be supplemented by informal rules that better reflect the shared values of the community. Second, because they have not been decreed by the government, informal rules are generally not subject to constitutional protections. Therefore, ethical restrictions that are accepted by the community potentially provide a means for placing broader limits on speech than would be permissible under governmental laws. In both respects, social norms share characteristics of Jewish ethics, which often rely on a consensus of communal obligation as a primary motivation for adherence, and which include a range of obligations and prohibitions beyond those enacted in most legal systems

Transpiration and film cooling boundary layer computer program. Volume 1: Numerical solutions of the turbulent boundary layer equations with equilibrium chemistry

A finite difference turbulent boundary layer computer program has been developed. The program is primarily oriented towards the calculation of boundary layer performance losses in rocket engines; however, the solution is general, and has much broader applicability. The effects of transpiration and film cooling as well as the effect of equilibrium chemical reactions (currently restricted to the H2-O2 system) can be calculated. The turbulent transport terms are evaluated using the phenomenological mixing length - eddy viscosity concept. The equations of motion are solved using the Crank-Nicolson implicit finite difference technique. The analysis and computer program have been checked out by solving a series of both laminar and turbulent test cases and comparing the results to data or other solutions. These comparisons have shown that the program is capable of producing very satisfactory results for a wide range of flows. Further refinements to the analysis and program, especially as applied to film cooling solutions, would be aided by the acquisition of a firm data base

Detecting many-body entanglements in noninteracting ultracold atomic fermi gases

We explore the possibility of detecting many-body entanglement using time-of-flight (TOF) momentum correlations in ultracold atomic fermi gases. In analogy to the vacuum correlations responsible for Bekenstein-Hawking black hole entropy, a partitioned atomic gas will exhibit particle-hole correlations responsible for entanglement entropy. The signature of these momentum correlations might be detected by a sensitive TOF type experiment.Comment: 5 pages, 5 figures, fixed axes labels on figs. 3 and 5, added reference

Zero dimensional area law in a gapless fermion system

The entanglement entropy of a gapless fermion subsystem coupled to a gapless bulk by a "weak link" is considered. It is demonstrated numerically that each independent weak link contributes an entropy proportional to lnL, where L is linear dimension of the subsystem.Comment: 6 pages, 11 figures; added 3d computatio

A well-posedness theory in measures for some kinetic models of collective motion

We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the behavior of large groups of animals, such as flocks of birds, swarms, or schools of fish. Our aim is to give a well-posedness theory for general models which possibly include a variety of effects: an interaction through a potential, such as a short-range repulsion and long-range attraction; a velocity-averaging effect where individuals try to adapt their own velocity to that of other individuals in their surroundings; and self-propulsion effects, which take into account effects on one individual that are independent of the others. We develop our theory in a space of measures, using mass transportation distances. As consequences of our theory we show also the convergence of particle systems to their corresponding kinetic equations, and the local-in-time convergence to the hydrodynamic limit for one of the models

Diassociative algebras and Milnor's invariants for tangles

We extend Milnor's mu-invariants of link homotopy to ordered (classical or virtual) tangles. Simple combinatorial formulas for mu-invariants are given in terms of counting trees in Gauss diagrams. Invariance under Reidemeister moves corresponds to axioms of Loday's diassociative algebra. The relation of tangles to diassociative algebras is formulated in terms of a morphism of corresponding operads.Comment: 17 pages, many figures; v2: several typos correcte

Quantum Versus Mean Field Behavior of Normal Modes of a Bose-Einstein Condensate in a Magnetic Trap

Quantum evolution of a collective mode of a Bose-Einstein condensate containing a finite number N of particles shows the phenomena of collapses and revivals. The characteristic collapse time depends on the scattering length, the initial amplitude of the mode and N. The corresponding time values have been derived analytically under certain approximation and numerically for the parabolic atomic trap. The revival of the mode at time of several seconds, as a direct evidence of the effect, can occur, if the normal component is significantly suppressed. We also discuss alternative means to verify the proposed mechanism.Comment: minor corrections are introduced into the tex