Mathematical modeling of materially nonlinear problems in structural analyses, Part I: Theoretical fundamentals

Part I Fundamentals

FUNDAMENTALS Part I of our book lays the physical and conceptual foundations of hydrologic optics, the quantitative study of the interactions of light with the earth's oceans, estuaries, lakes, rivers and other water bodies. Radiative transfer theory is the physical and mathematical framework for hydrologic optics. Chapter 1 begins with a few comments upon the nature of light itself and upon th...

Part I Fundamentals and Concepts

Nonlinear Local Electro - Vascular Coupling . Part I : A Theoretical Model

In this paper, we present a detailed biophysical model of how brain electrical and vascular dynamics are generated within a basic cortical unit. The model is obtained from coupling a canonical neuronal mass and an expandable vasculature. In this proposal, we address several aspects related to electroencephalographic and functional magnetic resonance imaging data fusion: a) the impact of the cer...

PWL approximation of nonlinear dynamical systems, Part–I: structural stability

This paper and its companion address the problem of the approximation/identification of nonlinear dynamical systems depending on parameters, with a view to their circuit implementation. The proposed method is based on a piecewise-linear approximation technique. In particular, this paper describes the approximation method and applies it to some particularly significant dynamical systems (topolog...

PARALLEL TREE CONTRACTION ' PART I : FUNDAMENTALS Gary

This paper introduces parallel tree contraction: a new bottom-up technique for constructing parallel algorithms on trees. Contraction can be used to solve a wide variety of problems. Two examples included in this article are expression evaluation and subexpression elimination. In this paper we show these applications only require O(1ogn) time and O(n/logn) processors on a Q-sided randomized PRA...