Geometric mechanics involves the application of geometric and symmetry techniques to the study of Lagrangian or Hamiltonian mechanics. The goal of computational geometric mechanics is to construct computational algorithms which preserve the geometric properties of mechanical systems [1]. My research is focused on developing computational geometric methods for numerical integration, optimal cont...

Through extensive ab initio total energy calculations of the S5 ~210! grain boundary in TiO2 ~rutile!, the remarkably large rigid-body contractions found by high resolution electron microscopy and Z-contrast imaging are explored. Unlike previous calculations, this work emphasizes the importance of the displacements of the two halves of the bicrystal towards one another. Previous experimental wo...

We introduce a class of polynomials, which we call subspace polynomials and show that the problem of explicitly constructing a rigid matrix can be reduced to the problem of explicitly constructing a small hitting set for this class. We prove that small-bias sets are hitting sets for the class of subspace polynomials, though their size is larger than desired. Furthermore, we give two alternative...

This paper reports on the following: (1) Simple experimental investigations of pultruded fiber-reinforced plastic (PFRP) material behavior and tests of simple epoxied joints to verify and enhance the reported database; (2) cyclic tests of an attempted PFRP rigid beam-column connections; and (3) preliminary observations regarding the seismic-resistance worthiness of PFRP structures. These are si...

A graph with a trivial automorphism group is said to be rigid. Wright proved [11] that for logn n + ω( 1 n) ≤ p ≤ 1 2 a random graph G ∈ G(n, p) is rigid whp. It is not hard to see that this lower bound is sharp and for p < (1− ) logn n with positive probability aut(G) is nontrivial. We show that in the sparser case ω( 1 n) ≤ p ≤ logn n + ω( 1 n), it holds whp that G’s 2-core is rigid. We concl...

this study proposes a new linear approximation for solving the dynamic response equations of a rocking rigid block. linearization assumptions which have already been used by hounser and other researchers cannot be valid for all rocking blocks with various slenderness ratios and dimensions; hence, developing new methods which can result in better approximation of governing equations while keepin...

this study proposes a new linear approximation for solving the dynamic response equations of a rocking rigid block. linearization assumptions which have already been used by hounser and other researchers cannot be valid for all rocking blocks with various slenderness ratios and dimensions; hence, developing new methods which can result in better approximation of governing equations while keepin...

A comprehensive review of the fundamental rheology of dilute disperse systems is presented. The exact rheological constitutive equations based on rigorous single-particle mechanics are discussed for a variety of disperse systems. The different types of inclusions (disperse phase) considered are: rigid-solid spherical particles with and without electric charge, rigid-porous spherical particles, ...

An amphiphilic heteroarm star polymer containing 12 alternating hydrophobic/hydrophilic arms of polystyrene (PS) and poly(acrylic acid) (PAA) connected to a well-defined rigid aromatic core was studied at the air-water and the air-solid interfaces. At the air-water interface, the molecules spontaneously form pancakelike micellar aggregates which measure up to several microns in diameter and 5 n...

Membrane-bound transport proteins are expected to proceed via different conformational states during the translocation of a solute across the membrane. Tryptophan phosphorescence spectroscopy is one of the most sensitive methods used for detecting conformational changes in proteins. We employed this technique to study substrate-induced conformational changes in the mannitol permease, EnzymeII(m...