Homogenization in integral viscoelasticity

A multi-phase periodic composite subjected to inhomogeneous shrinkage and mechanical loads including prescribed interface jumps of displacements and tractions is considered. The composite components are anisotropic linear viscoelastic and aging (described by the non-convolution Volterra integral operators). The paper presents some results about asymptotic homogenization and 2-scale convergence in appropriate function spaces

Homogenization in strength and durability analysis of reinforced tooth filling

An asymptotic homogenization procedure is employed to obtain effective elastic properties of the composite tooth filling, a homogenized macro– stress field and a first approximation to the micro-stress field, from properties of the components and applied macro–loads. Using the approximate micro–stress field, a non–local initial strength and fatigue durability macro–conditions for the composite filling material is expressed in terms of the homogenized macro–stresses. An illustrative example with the stress singularity on the tooth–filling interface is presented showing the need in the non-local analysis. Effective elastic properties of the tooth filling is numerically simulated for some size distributions of the reinforcing particles

Static and dynamic pitching moment measurements on a family of elliptic cones at Mach number 11 in helium

Static and dynamic pitching moment measurements were made on a family of constant volume elliptic cones about two fixed axes of oscillation in the NAE helium hypersonic wind tunnel at a Mach number of 11 and at Reynolds numbers based on model length of up to 14 million. Viscous effects on the stability derivatives were investigated by varying the Reynolds number for certain models by a factor as large as 10. The models investigated comprised a 7.75 deg circular cone, elliptic cones of axis ratios 3 and 6, and an elliptic cone with conical protuberances

Pressure seal Patent

Pressure seals suitable for use in environmental test chamber

Homogenization of contact problem with Coulomb's friction on periodic cracks

We consider the elasticity problem in a %heterogeneous domain with contact on multiple periodic open cracks. The contact is described by the Signorini and Coulomb-friction conditions. Problem is non-linear, the dissipative functional depends on the un-known solution and the existence of the solution for fixed period of the structure is usually proven by the fix-point argument in the Sobolev spaces with a little higher regularity, $H^{1+\alpha}$. We rescaled norms, trace, jump and Korn inequalities in fractional Sobolev spaces with positive and negative exponent, using the unfolding technique, introduced by Griso, Cioranescu and Damlamian. Then we proved the existence and uniqieness of the solution for friction and period fixed. Then we proved the continuous dependency of the solution to the problem with Coulomb's friction on the given friction and then estimated the solution using fixed point theorem. However, we were not able to pass to the strong limit in the frictional dissipative term. For this reason, we regularized the problem by adding a fourth-order term, which increased the regularity of the solution and allowed the passing to the limit. This can be interpreted as micro-polar elasticity

Pinwheels and nullhomologous surgery on 4-manifolds with b^+ = 1

We present a method for finding embedded nullhomologous tori in standard 4-manifolds which can be utilized to change their smooth structure. As an application, we show how to obtain infinite families of simply connected smooth 4-manifolds with b^+ = 1 and b^- = 2,...,7, via surgery on nullhomologous tori embedded in the standard manifolds CP^2 # k (-CP^2), k=2,...,7.Comment: Final version. To appear in AG

On the fundamental group of the complement of a complex hyperplane arrangement

We construct two combinatorially equivalent line arrangements in the complex projective plane such that the fundamental groups of their complements are not isomorphic. The proof uses a new invariant of the fundamental group of the complement to a line arrangement of a given combinatorial type with respect to isomorphisms inducing the canonical isomorphism of the first homology groups.Comment: 12 pages, Latex2e with AMSLaTeX 1.2, no figures; this last version is almost the same as published in Functional Analysis and its Applications 45:2 (2011), 137-14

Survey of needs and capabilities for wind tunnel testing of dynamic stability of aircraft at high angles of attack

A survey was conducted relative to future requirements for dynamic stability information for such aerospace vehicles as the space shuttle and advanced high performance military aircraft. High-angle-of-attack and high-Reynolds number conditions were emphasized. A review was made of the wind-tunnel capabilities in North America for measuring dynamic stability derivatives, revealing an almost total lack of capabilities that could satisfy these requirements. Recommendations are made regarding equipment that should be constructed to remedy this situation. A description is given of some of the more advanced existing capabilities, which can be used to at least partly satisfy immediate demands

On Sasaki-Einstein manifolds in dimension five

We prove the existence of Sasaki-Einstein metrics on certain simply connected 5-manifolds where until now existence was unknown. All of these manifolds have non-trivial torsion classes. On several of these we show that there are a countable infinity of deformation classes of Sasaki-Einstein structures.Comment: 18 pages, Exposition was expanded and a reference adde