Development of 2 underseat energy absorbers for application to crashworthy passenger seats for general aviation aircraft

This report presents the methodology and results of a program conducted to develop two underseat energy absorber (E/A) concepts for application to nonadjustable crashworthy passenger seats for general aviation aircraft. One concept utilizes an inflated air bag, and the other, a convoluted sheet metal bellows. Prototypes of both were designed, built, and tested. Both concepts demonstrated the necessary features of an energy absorber (load-limiter); however, the air bag concept is particularly encouraging because of its light weight. Several seat frame concepts also were investigated as a means of resisting longitudinal and lateral loads and of guiding the primary vertical stroke of the underseat energy absorber. Further development of a seat system design using the underseat energy absorbers is recommended because they provide greatly enhanced crash survivability as compared with existing general aviation aircraft seats

Root number of the twists of an elliptic curve

We give an explicit description of the behaviour of the root number in the family given by twists of an elliptic curve $E$ by the rational values of a polynomial $f(T)$. In particular, we give a criterion (on $f$ depending on $E$) for the family to have a constant root number over $\mathbb{Q}$. This completes a work of Rohrlich: we detail the behaviour of the root number when $E$ has bad reduction over $\mathbb{Q}^{ab}$ and we treat the cases $j(E)=0,1728$ which were not considered previously

On the density of rational points on rational elliptic surfaces

Let $\mathscr{E}\rightarrow\mathbb{P}^1_\mathbb{Q}$ be a non-trivial rational elliptic surface over $\mathbb{Q}$ with base $\mathbb{P}^1_\mathbb{Q}$ (with a section). We conjecture that any non-trivial elliptic surface has a Zariski-dense set of $\mathbb{Q}$-rational points. In this paper we work on solving the conjecture in case $\mathscr{E}$ is rational by means of geometric and analytic methods. First, we show that for $\mathscr{E}$ rational, the set $\mathscr{E}(\mathbb{Q})$ is Zariski-dense when $\mathscr{E}$ is isotrivial with non-zero $j$-invariant and when $\mathscr{E}$ is non-isotrivial with a fiber of type $II^*$, $III^*$, $IV^*$ or $I^*_m$ ($m\geq0$). We also use the parity conjecture to prove analytically the density on a certain family of isotrivial rational elliptic surfaces with $j=0$, and specify cases for which neither of our methods leads to the proof of our onjecture

The GEMPAK Barnes objective analysis scheme

GEMPAK, an interactive computer software system developed for the purpose of assimilating, analyzing, and displaying various conventional and satellite meteorological data types is discussed. The objective map analysis scheme possesses certain characteristics that allowed it to be adapted to meet the analysis needs GEMPAK. Those characteristics and the specific adaptation of the scheme to GEMPAK are described. A step-by-step guide for using the GEMPAK Barnes scheme on an interactive computer (in real time) to analyze various types of meteorological datasets is also presented

Monomization of power Ideals and parking functions

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 47-48).A zonotopal algebra is the quotient of a polynomial ring by an ideal generated by powers of linear forms which are derived from a zonotope, or dually it's hyperplane arrangement. In the case that the hyperplane arrangement is of Type A, we can rephrase the definition in terms of graphs. Using the symmetry of these ideals, we can find monomial ideals which preserve much of the structure of the zonotopal algebras while being computationally very efficient, in particular far faster than Gröbner basis techniques. We extend this monomization theory from the known case of the central zonotopal algebra to the other two main cases of the external and internal zonotopal algebras.by Craig J. Desjardins.Ph.D

Multi-scale analysis of compressible viscous and rotating fluids

We study a singular limit for the compressible Navier-Stokes system when the Mach and Rossby numbers are proportional to certain powers of a small parameter \ep. If the Rossby number dominates the Mach number, the limit problem is represented by the 2-D incompressible Navier-Stokes system describing the horizontal motion of vertical averages of the velocity field. If they are of the same order then the limit problem turns out to be a linear, 2-D equation with a unique radially symmetric solution. The effect of the centrifugal force is taken into account

An interactive visualization tool to explore the biophysical properties of amino acids and their contribution to substitution matrices

BACKGROUND: Quantitative descriptions of amino acid similarity, expressed as probabilistic models of evolutionary interchangeability, are central to many mainstream bioinformatic procedures such as sequence alignment, homology searching, and protein structural prediction. Here we present a web-based, user-friendly analysis tool that allows any researcher to quickly and easily visualize relationships between these bioinformatic metrics and to explore their relationships to underlying indices of amino acid molecular descriptors. RESULTS: We demonstrate the three fundamental types of question that our software can address by taking as a specific example the connections between 49 measures of amino acid biophysical properties (e.g., size, charge and hydrophobicity), a generalized model of amino acid substitution (as represented by the PAM74-100 matrix), and the mutational distance that separates amino acids within the standard genetic code (i.e., the number of point mutations required for interconversion during protein evolution). We show that our software allows a user to recapture the insights from several key publications on these topics in just a few minutes. CONCLUSION: Our software facilitates rapid, interactive exploration of three interconnected topics: (i) the multidimensional molecular descriptors of the twenty proteinaceous amino acids, (ii) the correlation of these biophysical measurements with observed patterns of amino acid substitution, and (iii) the causal basis for differences between any two observed patterns of amino acid substitution. This software acts as an intuitive bioinformatic exploration tool that can guide more comprehensive statistical analyses relating to a diverse array of specific research questions