Geometry and Physics of Spatial Random Systems

Erscheinungsjahr 2027
ISBN: 978-3-032-41050-4
Verlag: Springer

Buch, Englisch, 358 Seiten, Format (B × H): 155 mm x 235 mm

Reihe: Lecture Notes in Physics

This book introduces the geometry and physics of complex, disordered materials such as foams, granular assemblies, paper, catalysts, and amorphous solids. It explains how modern stochastic and integral geometry can be used to describe spatial structure and to understand how morphology influences physical properties. Key topics include the major stochastic models for random media: hard-core particle processes, random tessellations, Boolean models, random fields, and continuum percolation. These mathematical frameworks are consistently linked to physical systems ranging from structured fluids and cellular materials to transport in disordered environments. Integral geometric tools, in particular Minkowski tensors, provide a unifying approach that captures structural information beyond standard correlation measures. The book is designed for learning and self-study. It includes illustrative examples and practical guidance for applying geometric methods in image analysis and spatial statistics. Chapters are organized to help readers gradually build both intuition and a rigorous mathematical understanding. This volume is intended for graduate students and researchers in theoretical physics, mathematics, materials science, and related fields. A basic background in geometry, probability, and continuum physics is helpful, but no prior knowledge of stochastic geometry is required.

Zielgruppe

Graduate

Autoren/Hrsg.

Hug, Daniel

Klatt, Michael A.

Last, Günter

Mecke, Klaus

Schröder-Turk, Gerd E.

Winter, Steffen

Fachgebiete

• Naturwissenschaften Physik Thermodynamik Festkörperphysik, Kondensierte Materie
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme

Inhaltsverzeichnis

Introduction.- Integral geometry.- Tessellations and hard core particle systems.- Boolean models.- Random fields.- Percolation.- Image analysis and spatial statistics.

Über Autor(innen)

Prof. Dr. Daniel Hug obtained his doctoral degree in mathematics and completed his Habilitation at the University of Freiburg. He was an Assistant Professor at TU Vienna, trained and worked as a high-school teacher, served as a Professor at the University of Duisburg–Essen, and was an Associate Professor in Karlsruhe. He has been a Professor in Karlsruhe since 2011. He is the author of two books published by Springer.

Dr.  Michael Andreas Klatt obtained his doctoral degree in physics from the University of Erlangen. He subsequently held research positions at the Karlsruhe Institute of Technology, Princeton University, and the University of Düsseldorf, where he combined probabilistic modeling, geometry, and physical theory to design micro-structured materials with novel forms of short- and long-range order. In 2022, he was awarded a Helmholtz Young Investigator Group at the German Aerospace Center (DLR), where he has been building an interdisciplinary research team since 2023.

Prof. Dr.  Günter Last received his doctoral degree from Humboldt University in Berlin, where he worked as a scientific assistant until 1992. He then moved to the Technical University of Braunschweig, where he obtained his Dr. Sc. degree. In 1995/96 he spent one semester as a visiting professor at the University of Kaiserslautern, and in 1996/97 he spent one year as a visiting professor at the University of Bonn. Since 2000 he has been Professor at the Karlsruhe Institute of Technology. He has worked in various areas of probability theory, with a focus on random measures and point processes and their applications in stochastic geometry.

Prof. Dr.  Klaus Mecke received his doctoral degree from the University of Munich with a thesis on integral geometry in statistical physics. He held postdoctoral positions at the University of Texas at Austin, Northeastern University in Boston, and the University of Wuppertal, working primarily on interface physics and wetting phenomena. In 2001 he joined the Max Planck Institute for Metal Research in Stuttgart. Since 2004 he has been Full Professor of theoretical physics at Friedrich-Alexander Universität Erlangen-Nürnberg in Germany. His research focuses on the statistical physics of complex fluids and the morphometric description of spatial structures. More recently, he developed a theory of quantum spacetime based on the finite projective geometry of event processes. At the Erlangen Center for Literature and the Sciences (ELINAS), he also explores the diverse interactions between physics and literature.

Prof. Dr.  Gerd E. Schröder-Turk obtained his PhD from the Australian National University and his Habilitation from Friedrich-Alexander Universität Erlangen-Nürnberg (FAU). He has held academic positions at the Australian National University, FAU, and Murdoch University, and visiting appointments in Melbourne, Copenhagen, and Lund. He is currently Professor at Murdoch University in Perth, where he leads research on structured materials and their formation and function through geometric methods. He has held governance roles, including service on the Murdoch University Senate, and has been a member of the National Executive of the Australian Institute of Physics. He is a Fellow of the American Physical Society.

Dr.-habil.  Steffen Winter obtained his doctoral degree in mathematics at the University of Jena and his Habilitation at the Karlsruhe Institute of Technology, where he has worked since 2006. His research interests include fractals and stochastic geometry, as well as applications of complex geometric models in physics and engineering.