Structural tailoring of select fiber composite structures

A multidisciplinary design process for aerospace propulsion composite structures was formalized and embedded into computer codes. These computer codes are streamlined to obtain tailored designs for select composite structures. The codes available are briefly described with sample cases to illustrate their applications. The sample cases include aircraft engine blades, propfans (turboprops), flat, and cylindrical panels. Typical results illustrate that the use of these codes enable the designer to obtain designs which meet all the design requirements with maximum benefits in efficiency, noise, weight or thermal distortions

Probabilistic structural analysis to quantify uncertainties associated with turbopump blades

A probabilistic study of turbopump blades has been in progress at NASA Lewis Research Center for over the last two years. The objectives of this study are to evaluate the effects of uncertainties in geometry and material properties on the structural response of the turbopump blades to evaluate the tolerance limits on the design. A methodology based on probabilistic approach was developed to quantify the effects of the random uncertainties. The results indicate that only the variations in geometry have significant effects

Discretisation for odd quadratic twists

The discretisation problem for even quadratic twists is almost understood, with the main question now being how the arithmetic Delaunay heuristic interacts with the analytic random matrix theory prediction. The situation for odd quadratic twists is much more mysterious, as the height of a point enters the picture, which does not necessarily take integral values (as does the order of the Shafarevich-Tate group). We discuss a couple of models and present data on this question.Comment: To appear in the Proceedings of the INI Workshop on Random Matrix Theory and Elliptic Curve

Random Matrix Theory and the Fourier Coefficients of Half-Integral Weight Forms

Conjectured links between the distribution of values taken by the characteristic polynomials of random orthogonal matrices and that for certain families of L-functions at the centre of the critical strip are used to motivate a series of conjectures concerning the value-distribution of the Fourier coefficients of half-integral weight modular forms related to these L-functions. Our conjectures may be viewed as being analogous to the Sato-Tate conjecture for integral weight modular forms. Numerical evidence is presented in support of them.Comment: 28 pages, 8 figure

Tighter Relations Between Sensitivity and Other Complexity Measures

Sensitivity conjecture is a longstanding and fundamental open problem in the area of complexity measures of Boolean functions and decision tree complexity. The conjecture postulates that the maximum sensitivity of a Boolean function is polynomially related to other major complexity measures. Despite much attention to the problem and major advances in analysis of Boolean functions in the past decade, the problem remains wide open with no positive result toward the conjecture since the work of Kenyon and Kutin from 2004. In this work, we present new upper bounds for various complexity measures in terms of sensitivity improving the bounds provided by Kenyon and Kutin. Specifically, we show that deg(f)^{1-o(1)}=O(2^{s(f)}) and C(f) < 2^{s(f)-1} s(f); these in turn imply various corollaries regarding the relation between sensitivity and other complexity measures, such as block sensitivity, via known results. The gap between sensitivity and other complexity measures remains exponential but these results are the first improvement for this difficult problem that has been achieved in a decade.Comment: This is the merged form of arXiv submission 1306.4466 with another work. Appeared in ICALP 2014, 14 page

Autocorrelation of Random Matrix Polynomials

We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in three equivalent forms: as a determinant sum (and hence in terms of symmetric polynomials), as a combinatorial sum, and as a multiple contour integral. These formulae are analogous to those previously obtained for the Gaussian ensembles of Random Matrix Theory, but in this case are identities for any size of matrix, rather than large-matrix asymptotic approximations. They also mirror exactly autocorrelation formulae conjectured to hold for L-functions in a companion paper. This then provides further evidence in support of the connection between Random Matrix Theory and the theory of L-functions

Lower order terms in the full moment conjecture for the Riemann zeta function

We describe an algorithm for obtaining explicit expressions for lower terms for the conjectured full asymptotics of the moments of the Riemann zeta function, and give two distinct methods for obtaining numerical values of these coefficients. We also provide some numerical evidence in favour of the conjecture.Comment: 37 pages, 4 figure

Sliding friction between an elastomer network and a grafted polymer layer: the role of cooperative effects

We study the friction between a flat solid surface where polymer chains have been end-grafted and a cross-linked elastomer at low sliding velocity. The contribution of isolated grafted chains' penetration in the sliding elastomer has been early identified as a weakly velocity dependent pull-out force. Recent experiments have shown that the interactions between the grafted chains at high grafting density modify the friction force by grafted chain. We develop here a simple model that takes into account those interactions and gives a limit grafting density beyond which the friction no longer increases with the grafting density, in good agreement with the experimental dataComment: Submitted to Europhys. Letter