Practical matching of principal stress field geometries in composite components

A simple composite design methodology has been developed from the basic principles of composite component failure. This design approach applies the principles of stress field matching to develop suitable reinforcement patterns around three-dimensional details such as lugs in mechanical components. The resulting patterns are essentially curvilinear orthogonal meshes, adjusted to meet the restrictions imposed by geometric restraints and the intended manufacturing process. Whilst the principles behind the design methodology can be applied to components produced by differing manufacturing processes, the results found from looking at simple generic example problems suggest a realistic and practical generic manufacturing approach. The underlying principles of the design methodology are described and simple analyses are used to help illustrate both the methodology and how such components behave. These analyses suggest it is possible to replace high-strength steel lugs with composite components whose strength-to-weight ratio is some 4-5 times better. © 1998 Elsevier Science Ltd. All rights reserved.

Nucleated polymerization with secondary pathways. I. Time evolution of the principal moments.

Self-assembly processes resulting in linear structures are often observed in molecular biology, and include the formation of functional filaments such as actin and tubulin, as well as generally dysfunctional ones such as amyloid aggregates. Although the basic kinetic equations describing these phenomena are well-established, it has proved to be challenging, due to their non-linear nature, to derive solutions to these equations except for special cases. The availability of general analytical solutions provides a route for determining the rates of molecular level processes from the analysis of macroscopic experimental measurements of the growth kinetics, in addition to the phenomenological parameters, such as lag times and maximal growth rates that are already obtainable from standard fitting procedures. We describe here an analytical approach based on fixed-point analysis, which provides self-consistent solutions for the growth of filamentous structures that can, in addition to elongation, undergo internal fracturing and monomer-dependent nucleation as mechanisms for generating new free ends acting as growth sites. Our results generalise the analytical expression for sigmoidal growth kinetics from the Oosawa theory for nucleated polymerisation to the case of fragmenting filaments. We determine the corresponding growth laws in closed form and derive from first principles a number of relationships which have been empirically established for the kinetics of the self-assembly of amyloid fibrils.

Generalized power method for sparse principal component analysis

In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant principal component of a data matrix, or more components at once, respectively. While the initial formulations involve nonconvex functions, and are therefore computationally intractable, we rewrite them into the form of an optimization program involving maximization of a convex function on a compact set. The dimension of the search space is decreased enormously if the data matrix has many more columns (variables) than rows. We then propose and analyze a simple gradient method suited for the task. It appears that our algorithm has best convergence properties in the case when either the objective function or the feasible set are strongly convex, which is the case with our single-unit formulations and can be enforced in the block case. Finally, we demonstrate numerically on a set of random and gene expression test problems that our approach outperforms existing algorithms both in quality of the obtained solution and in computational speed. © 2010 Michel Journée, Yurii Nesterov, Peter Richtárik and Rodolphe Sepulchre.

Refining sparse principal components

In this paper, we discuss methods to refine locally optimal solutions of sparse PCA. Starting from a local solution obtained by existing algorithms, these methods take advantage of convex relaxations of the sparse PCA problem to propose a refined solution that is still locally optimal but with a higher objective value. © 2010 Springer -Verlag Berlin Heidelberg.