This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents t…
This book is dedicated to the recent developments in RET with the aim to explore polyatomic gas, dense gas and mixture of gases in non-equilibrium. In particular we present the theory of dense gases with 14 fields, which reduces to the Navier-Stokes Fourier classical theory in the parabolic limit. Molecular RET with an arbitrary number of field-variables for polyatomic gases is also discussed a…
This monograph provides both an introduction to and a thorough exposition of the theory of rate-independent systems, which the authors have been working on with a lot of collaborators over 15 years. The focus is mostly on fully rate-independent systems, first on an abstract level either with or even without a linear structure, discussing various concepts of solutions with full mathematical rigo…
Focusing on the mathematics that lies at the intersection of probability theory, statistical physics, combinatorics and computer science, this volume collects together lecture notes on recent developments in the area. The common ground of these subjects is perhaps best described by the three terms in the title: Random Walks, Random Fields and Disordered Systems. The specific topics covered incl…
This is a first book to show that the theory of the Gaussian random matrix is essential to understand the universal correlations with random fluctuations and to demonstrate that it is useful to evaluate topological universal quantities. We consider Gaussian random matrix models in the presence of a deterministic matrix source. In such models the correlation functions are known exactly for an ar…
This book is the first volume of the SpringerBriefs in the Mathematics of Materials and provides a comprehensive guide to the interaction of mathematics with materials science. The anterior part of the book describes a selected history of materials science as well as the interaction between mathematics and materials in history. The emergence of materials science was itself a result of an interd…
This book covers the basics of aeroelasticity or the dynamics of fluid-structure interaction. While the field began in response to the rapid development of aviation, it has now expanded into many branches of engineering and scientific disciplines and treat physical phenomena from aerospace engineering, bioengineering, civil engineering, and mechanical engineering in addition to drawing the atte…
Joseph W. Dauben, a leading authority on the history of mathematics in Europe, China, and North America, has played a pivotal role in promoting international scholarship over the last forty years. This Festschrift volume, showcasing recent historical research by leading experts on three continents, offers a global perspective on important themes in this field.
This book provides the first critical edition of Ibn al-Haytham’s On the Shape of the Eclipse with English translation and commentary, which records the first scientific analysis of the camera obscura. On the Shape of the Eclipse includes pioneering research on the conditions of formation of the image, in a time deemed to be committed to aniconism. It also provides an early attempt to merge t…
This book takes an in depth look at a novel methodology for analyzing Global Positioning System (GPS) data to obtain the highest possible resolution surface imaging of tectonic deformation sources without prescribing the nature of either the sources or the subsurface medium. GPS methods are widely used to track the surface expression of crustal deformation at tectonic plate boundaries, and are …