Structure of a Plane Shock Layer

The structure of a plane shock wave is discussed and the expected range of applicability of the Navier‐Stokes equations within the shock layer is outlined. The shock profiles are computed using the Bhatnagar‐Gross‐Krook model of the Boltzmann equation and a uniformly converging iteration scheme starting from the Navier‐Stokes solution. It is shown that the Navier‐Stokes solution remains a good approximation in the high‐pressure region of the shock layer up to approximately the point of maximum stress for all shock strengths. In the low‐pressure region, the correct profiles deviate with increasing shock strength from the Navier‐Stokes solution. The physical significance of the kinetic model used and the relation of the present study to previous theoretical and experimental work is discussed

The Blackhole-Dark Matter Halo Connection

We explore the connection between the central supermassive blackholes (SMBH) in galaxies and the dark matter halo through the relation between the masses of the SMBHs and the maximum circular velocities of the host galaxies, as well as the relationship between stellar velocity dispersion of the spheroidal component and the circular velocity. Our assumption here is that the circular velocity is a proxy for the mass of the dark matter halo. We rely on a heterogeneous sample containing galaxies of all types. The only requirement is that the galaxy has a direct measurement of the mass of its SMBH and a direct measurement of its circular velocity and its velocity dispersion. Previous studies have analyzed the connection between the SMBH and dark matter halo through the relationship between the circular velocity and the bulge velocity dispersion, with the assumption that the bulge velocity dispersion stands in for the mass of the SMBH, via the well{}-established SMBH mass{}-bulge velocity dispersion relation. Using intermediate relations may be misleading when one is studying them to decipher the active ingredients of galaxy formation and evolution. We believe that our approach will provide a more direct probe of the SMBH and the dark matter halo connection. We find that the correlation between the mass of supermassive blackholes and the circular velocities of the host galaxies is extremely weak, leading us to state the dark matter halo may not play a major role in regulating the blackhole growth in the present Universe.Comment: Accepted for publication in the Ap

The GLAS physical inversion method for analysis of HIRS2/MSU sounding data

Goddard Laboratory for Atmospheric Sciences has developed a method to derive atmospheric temperature profiles, sea or land surface temperatures, sea ice extent and snow cover, and cloud heights and fractional cloud, from HIRS2/MSU radiance data. Chapter 1 describes the physics used in the radiative transfer calculations and demonstrates the accuracy of the calculations. Chapter 2 describes the rapid transmittance algorithm used and demonstrates its accuracy. Chapter 3 describes the theory and application of the techniques used to analyze the satellite data. Chapter 4 shows results obtained for January 1979

Investigations carried out under the Director's Discretionary Fund

This annual report comprises a set of summaries, describing task objectives, progress and results or accomplishments, future outlook, and financial status for each director's discretionary fund (DDF) task that was active during fiscal year 1984. Publications and conference presentations related to the work are listed. The individual reports are categorized as interim or final according to whether the task efforts are ongoing or completed. A partial list of new tasks to be initiated with fiscal year 1985 funds and a glossary of abbreviations and acronyms, used by the task authors in their summaries are included. The table of contents lists the DDF reports in sequence by their task number, which is derived from the 13-digit code assigned to account for the fund awarded to the task project

Collaborative Evaluative Inquiry: A Model for Improving Mathematics Instruction in Urban Elementary Schools

In this article, the authors describe the cyclical process of a collaborative evaluative inquiry project and the data collected throughout the project—data that not only informed next steps during the project but also show promise in documenting the benefits of such projects. Over a period of 18 months, seven elementary teachers from a K–6 urban elementary school collaborated with university personnel using Parsons’s (2002) Evaluative Inquiry Model, a 5-stage, cyclical model that includes defining, planning, and investigating challenges; collecting, analyzing, and synthesizing data; and communicating findings that transpire through collaborative inquiry. Overall, the project focused on improving the elementary teachers’ skills of inquiry and, in turn, their mathematics instruction and students’ learning outcomes. The long-term goal was to enhance teachers’ roles in their schools by affording them the opportunities to make informed decisions throughout their teaching based on an effective and skillful use of data

Financial Contracting in Islamic Venture Capital: The Form-Substance Dichotomy

Based on a series of interviews in Malaysia and the United Arab Emirates, we conduct a comprehensive exploratory study of Islamic Venture Capital focusing on the distinguishing features of its financial rights and securities and the context which affect their design. We use a qualitative methodology, the Grounded Theory approach, to generate new theory. We find that while Islamic contractual rights and securities may have formal differences with their conventional counterparts, they are very close in economic substance. This form-substance dichotomy is a central characteristic of Islamic Venture Capital. Market demand for an Islamic brand of venture capital based on ideals of fairness and solidarity clashes with the reality of an array of agency issues and claims venture capitalists need to address. The capacity of Islamic venture capitalists to address these conflicting forces increases with their experience. Their ability is, however, constrained by their fiscal and legal environments. In form, commitment to Islamic ideals is therefore signaled through an investment policy excluding a small number of industries and through the use of Islamic financial instruments with little economic difference, if any, with their conventional counterparts. Minor economic inefficiencies can result, although overall, they are insignificant. In substance, Islamic Venture Capital is thus operationally and economically a near-equivalent to conventional venture capital. Following our analysis of the interviews, we position our theoretical contribution within related literature through an extensive survey. To further support our theory of form-substance dichotomy, that is the process by which the difference in form is maintained, but not in economic substance, we demonstrate the near-equivalence of Islamic financial instruments’ economic substance with their conventional counterparts’ through a systematic comparison of economic payouts for the entire Islamic venture capital asset class. This research is unique in that it is the first to our knowledge to address the topic of financial contracting in Islamic venture capital. Previous research in Islamic finance is heavily normative, and there is generally a dearth of research publications dealing with either Islamic financial contracting or Islamic venture capital

Simulation studies of improved sounding systems

Two instrument designs for indirect satellite sounding of the atmosphere in the infrared are represented by the High Resolution Infra-Red Sounder, Model 2 (HIRS-2) and by the Advanced Meteorological Temperature Sounder (AMTS). The relative capabilities of the two instruments were tested by simulating satellite measurements from a group of temperature soundings, allowing the two participants to retrieve the temperature profiles from the simulated data, and comparing the results with the original temperature profiles. Four data sets were produced from radiosondes data extrapolated to a suitable altitude, representing continents and oceans, between 30S and 30N. From the information available, temperature profiles were retrieved by two different methods, statistical regression and inversion of the radiative transfer equation. Results show the consequence of greater spectral purity, concomitant increase in the number of spectral intervals, and the better spatial resolution in partly clouded areas. At the same time, the limitation of the HIRS-2 without its companion instrument leads to some results which should be ignored in comparing the two instruments. A clear superiority of AMTS results is shown

Exact relations between damage spreading and thermodynamic functions for the N-color Ashkin-Teller model

Exact results are derived relating quantities computable by the so-called damage spreading method and thermodynamic functions for the N-color Ashkin-Teller model. The results are valid for any ergodic dynamics. Since we restrict our analysis to the ferromagnetic case the results are also valid for any translational invariant lattice. The derived relations should be used in order to determine numerically the N-color Ashkin-Teller critical exponents with better accuracy and less computational efforts than standard Monte Carlo simulations.Comment: 6 pages, to be published in JSTAT (Journal of Statistical Mechanics: Theory and Experiment). The results of a computer simulation were included for N=3 as an example on how to use the analytical relations derived in the paper as a guide to obtain the critical temperature and critical exponent