Well-posedness via Monotonicity. An Overview

The idea of monotonicity (or positive-definiteness in the linear case) is shown to be the central theme of the solution theories associated with problems of mathematical physics. A "grand unified" setting is surveyed covering a comprehensive class of such problems. We elaborate the applicability of our scheme with a number examples. A brief discussion of stability and homogenization issues is also provided.Comment: Thoroughly revised version. Examples correcte

Modeling Axisymmetric Optical Precision Piezoelectric Membranes

The US Department of Defense (DOD), as well as the National Aeronautics and Astronautics Administration (NASA) and the Jet Propulsion Laboratory (JPL) are interested in developing and deploying precise, compliant, light-weight, space-based structures. More specifically, the Air Force’s core competencies ‘Aerospace Superiority’ and ‘Information Superiority’ demand ever-increasing depth and breadth of capability. Whether used for energy transmission or optical reconnaissance, current launch restraints limit rigid space-based optical reflector size. To support this requirement, the Air Force Research Laboratory (AFRL) is developing a large space-based optical membrane telescope. Inflatable reflectors can conceptually break this barrier, but controlling such a compliant structure presents significant problems. While inflatable technology is flight proven, the ability to control the shape of a flexible space structure to optical precision has yet to be demonstrated. A laminate of piezoelectric polymer material can deform a membrane optical surface; however, modeling this system must be improved. Analytic solutions to the beam and axisymmetric membrane models are produced providing insight into resulting behavior of these materials. Based on these results a new mathematical methodology rooted in fundamental perturbation techniques was developed: The Method of Integral Multiple Scales (MIMS). MIMS allows selectable precision when applied to a special class of dynamic systems which can be represented through a Lagrangian. This new method was first applied to a relatively simple linear beam problem for the purpose of illustration. The method is able to integrate spatial and temporal multiple scales directly producing boundary layer solutions. This method is fully realized through the finite element approach, where the solution was shown to be over three orders of magnitude more accurate than a standard finite element result. The finite element methodology is applied to nonlinear beam and axisymmetric circular membrane models producing insight for future design decisions. The results illustrate the capability of such an active membrane to modify a reflected wavefront and provide control for an inflatable optical reflector

Optimal control of first order distributed systems

The problem of characterizing optimal controls for a class of distributed-parameter systems is considered. The system dynamics are characterized mathematically by a finite number of coupled partial differential equations involving first-order time and space derivatives of the state variables, which are constrained at the boundary by a finite number of algebraic relations. Multiple control inputs, extending over the entire spatial region occupied by the system ("distributed controls') are to be designed so that the response of the system is optimal. A major example involving boundary control of an unstable low-density plasma is developed from physical laws

Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare?

A wide variety of techniques have been developed to homogenize transport equations in multiscale and multiphase systems. This has yielded a rich and diverse field, but has also resulted in the emergence of isolated scientific communities and disconnected bodies of literature. Here, our goal is to bridge the gap between formal multiscale asymptotics and the volume averaging theory. We illustrate the methodologies via a simple example application describing a parabolic transport problem and, in so doing, compare their respective advantages/disadvantages from a practical point of view. This paper is also intended as a pedagogical guide and may be viewed as a tutorial for graduate students as we provide historical context, detail subtle points with great care, and reference many fundamental works

Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare?

A wide variety of techniques have been developed to homogenize transport equations in multiscale and multiphase systems. This has yielded a rich and diverse field, but has also resulted in the emergence of isolated scientific communities and disconnected bodies of literature. Here, our goal is to bridge the gap between formal multiscale asymptotics and the volume averaging theory. We illustrate the methodologies via a simple example application describing a parabolic transport problem and, in so doing, compare their respective advantages/disadvantages from a practical point of view. This paper is also intended as a pedagogical guide and may be viewed as a tutorial for graduate students as we provide historical context, detail subtle points with great care, and reference many fundamental works

Contract stresses in hip replacements.

SIGLEAvailable from British Library Document Supply Centre- DSC:D172337 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

The 2nd International Conference on Mathematical Modelling in Applied Sciences, ICMMAS’19, Belgorod, Russia, August 20-24, 2019 : book of abstracts

The proposed Scientific Program of the conference is including plenary lectures, contributed oral talks, poster sessions and listeners. Five suggested special sessions / mini-symposium are also considered by the scientific committe

Nonlinear Systems

The editors of this book have incorporated contributions from a diverse group of leading researchers in the field of nonlinear systems. To enrich the scope of the content, this book contains a valuable selection of works on fractional differential equations.The book aims to provide an overview of the current knowledge on nonlinear systems and some aspects of fractional calculus. The main subject areas are divided into two theoretical and applied sections. Nonlinear systems are useful for researchers in mathematics, applied mathematics, and physics, as well as graduate students who are studying these systems with reference to their theory and application. This book is also an ideal complement to the specific literature on engineering, biology, health science, and other applied science areas. The opportunity given by IntechOpen to offer this book under the open access system contributes to disseminating the field of nonlinear systems to a wide range of researchers