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Spatschek K: Theoretische Plasmaphysik

Theoretische Plasmaphysik

Eine Einführung in die Grundlagen klassischer Plasmen

Grunds¨atzliches im Uberblick.- Bewegung einzelner Teilchen.- Gleichgewichtsstatistik eines Plasmas .- Kinetische Beschreibung eines Plasmas.- Makroskopische Beschreibung.- &nbsp;Wellen und Instabilit¨aten in Vlasov-Systemen.- Welle-Plasma-Wechselwirkung.- Nichtlineare Schwingungen in Plasmen.- Stabilit¨at von MHD Systemen.- Plasmaeinschluss und anomaler Transport.- &nbsp;Laser-Plasma-Physik bei hohen Intensit¨aten.- Komplexe Plasmen.- Hilfreiche Grundgleichungen.

This&nbsp;updated, second edition features a new sectionhow to document and measure all the mass and charge transport properties of a material and a comprehensive solution manual for end-of-chapter exercise problems, that is designed to help readers themselves grasp and apply the fundamental knowledge of kinetics.&nbsp;&nbsp;It remains an essential primer for beginning graduate or senior undergraduate students in materials discipline, presenting fundamental and quantitative ideas on kinetic processes in materials. &nbsp;Kinetics is concerned with the rate of change of the state of existence of a material system under thermodynamic driving forces. Typically, kinetic processes in materials involve chemical reactions and diffusion either in parallel or in tandem. Thus, mathematics of diffusion in continuum is first dealt with in some depth, followed by the atomic theory of diffusion and a brief review of chemical reaction kinetics. As applications, then follow chemical diffusion in multi-component materials ( e.g., metallic alloys &nbsp;and mixed ionic electronic conductors), &nbsp;the kinetics of phase transformations, and the kinetics of gas-solid reactions. Through this course of learning and practice, a student will become able to predict quantitatively how fast a kinetic process takes place, to understand the inner workings of the process, and to design an optimal process for state changes in materials used in processing applications.

Lectures on Kinetic Processes in Materials

Dieses Buch bereitet auf die Mathematik eines MINT-Studiums vor.
&nbsp;
Besonderheiten
Neben dem Überprüfen des Wissensstandes und dem Reaktivieren bekannter Inhalte geht es v. a. um das selbstständige Üben handschriftlicher Umformungen von Gleichungen und Ungleichungen, den Umgang mit Termen und Funktionen, die Parameter enthalten sowie um eine zügige Bearbeitung der Aufgaben.
In jedem Kapitel werden zuerst die theoretischen Sachverhalte bereitgestellt und an Beispielen erläutert. Übungen und Tests regen dann zum selbstständigen Arbeiten und Lösen an.
In den Lösungswegen zu allen Übungsaufgaben und Tests werden ausführlich die wichtigen Teilschritte präsentiert, häufig anzutreffende Fehler kommentiert und falsche Herangehensweisen analysiert. Zum Schluss werden Links zu Lernvideos angeboten.
&nbsp;
Der Inhalt
Bruchrechnung und Umstellen von Gleichungen ¿ Potenzen u. Wurzeln&nbsp;¿ Binomische Formeln u. binomischer Lehrsatz&nbsp;¿ Polynomdivision&nbsp;¿ Mengenlehre&nbsp;¿ Funktionen&nbsp;¿ Lineare Funktionen&nbsp;¿ Quadratische Funktionen&nbsp;¿ Potenz- u. Wurzelfunktionen&nbsp;¿ Exponential- u. Logarithmusfunktionen&nbsp;¿ Trigonometrische Funktionen&nbsp;¿&nbsp;Funktionen in Polarkoordinaten ¿&nbsp;Hinweise u. Lösungen zu den Übungen ¿&nbsp;Hinweise u. Lösungen zu den Tests ¿&nbsp;Hinweise zum Studium u. Tipps für Klausuren
&nbsp;
Neuerungen (2. Aufl.)
Die inhaltliche und methodisch-didaktische Gestaltung wurden grundlegend überarbeitet. Neu sind die Kapitel lineare Gleichungssysteme, Vektorrechnung und komplexe Zahlen/komplexe Rechnung.
&nbsp;
Die Zielgruppe
Das Buch richtet sich an diejenigen, die ihre Kenntnisse vor Studienbeginn und in den ersten Semestern verbessern möchten, speziell bei einer längeren Pause nach der Reifeprüfung oder ohne Abitur.
&nbsp;
Vorkenntnisse
Um unterschiedliche Vorkenntnisse auszugleichen, einen erfolgreichen Studienstart zu ermöglichen und Abbruchzahlen zu senken, entwickelte Prof. Siegert über Jahrzehnte einen Brückenkurs, woraus das vorliegende Buch entstanden ist.
&nbsp;
Der Autor und die Autorin
Joachim Siegert war Professor an der HTW Berlin. Schwerpunktmäßig engagiert er sich in der Grundlagenausbildung im Fach Mathematik in MINT-Studiengängen.
Nataliya Togobytska&nbsp;lehrt als Professorin im Studiengang Wirtschaftsmathematik der HTW Berlin. Sie ist zusätzlich in der Grundlagenausbildung von Ingenieurstudiengängen involviert.

Womit man im MINT-Studium rechnen muss

Mathematik trainieren: Brüche, Funktionen & Co

De Gruyter Studies in Mathematics

Multiplier Method and Morawetz Estimate

Regularity and Scattering of Dispersive Wave Equations

The Navier-Stokes equations - modeling the motion of viscous, incompressible Newtonian fluids - have been capturing the attention of an increasing number of mathematicians over the years and has now become one of the most intensely studied subjects in applied analysis. This project is dedicated to a complete and updated mathematical analysis of fundamental topics related to these equations. Every subject will be analyzed using different approaches. The main ideas behind them as well as their differences will also be emphasized and discussed. The book aims at being self-contained, however, it will also be supported by a vast bibliography for further reading.

Navier-Stokes Equations: A Mathematical Analysis

Applied Mathematical Sciences

Explore the fascinating intersection of mathematics and combustion theory in this comprehensive monograph, inspired by the pioneering work of N. N. Semenov and D. A. Frank-Kamenetskii. Delving into the nonlinear functional analytic approach, this book examines semilinear elliptic boundary value problems governed by the Arrhenius equation and Newton's law of heat exchange.Key topics include:<ul><li>Detailed analysis of boundary conditions, including isothermal (Dirichlet) and adiabatic (Neumann) cases.</li><li>Critical insights into ignition and extinction phenomena in stable steady temperature profiles, linked to the Frank-Kamenetskii parameter.</li><li>Sufficient conditions for multiple positive solutions, revealing the S-shaped bifurcation curves of these problems.</li></ul>Designed for researchers and advanced students, this monograph provides a deep understanding of nonlinear functional analysis and elliptic boundary value problems through their application to combustion and chemical reactor models. Featuring detailed illustrations, clearly labeled figures, and tables, this book ensures clarity and enhances comprehension of complex concepts.Whether you are exploring combustion theory, functional analysis, or applied mathematics, this text offers profound insights and a thorough mathematical foundation.

Nonlinear Functional Analysis with Applications to Combustion Theory

Lecture Notes in Physics

Nonequilibrium and Irreversibility

Springer Theses

This thesis describes two groundbreaking measurements in the precision frontier at the LHC: the first ever differential measurement of the Z-associated single top quark (tZq) production, and the luminosity measurement using Z boson production rate for the first time in CMS. Observed only in 2018, the tZq process is of great importance in probing top quark electroweak couplings. These couplings are natural places for new phenomena to happen in the top quark sector of the standard model. Yet, they are the least explored directly. One has to obtain a firm understanding of the modeling of sensitive distributions to new top-Z interactions. The present analysis marks a major milestone in this long-term effort. All distributions relevant for new phenomena, and/or modeling of tZq, are studied in full depth using advanced Machine Learning techniques.The luminosity and its uncertainty contributes to every physics result of the experiment. The method minutely developed in this thesis provides a complementary measurement that results in a significant overall reduction of uncertainties.

First Differential Measurements of tZq Production and Luminosity Determination Using Z Boson Rates at the LHC

Forum for Interdisciplinary Mathematics

Finite Difference Methods for Compressible Two-Fluid Dynamics provides the essentials of high-order numerical methods for compressible single-fluid and two-fluid transport phenomena. This book can serve as a first course on the numerical methods for transport phenomena or fluid dynamics for students in mechanical, aerospace, and chemical engineering, applied mathematics, and physics at the senior level of an undergraduate or graduate degree. It also provides foundations and algorithmic details for implementing the most recent numerical schemes for compressible flows and extending them to include other physics, such as elasticity, reaction, and magnetohydrodynamics.The book's presented schemes enable computations for broad applications, including shock-induced interfacial instability and turbulence, shock-bubble interactions, and detonation, to name a few. For a broad reach and impact, the numerical schemes satisfy the simultaneous requirements of simplicity, extendibility, and efficiency on serial and parallel computers. The physics of the compressible single- and two-fluid system also guide the design and analysis of the numerical methods. The enabled direct numerical simulations also help obtain accurate data for tuning the emerging physics-based neuromorphic algorithms.

Finite Difference Methods for Compressible Two-Fluid Dynamics

De Gruyter Series in Applied and Numerical Mathematics

Non-Newtonian Fluids with Variable Power-Law

Regularity Theory for Generalized Navier–Stokes Equations

Phänomene, Grundlagen und Anwendungen

Plasmaphysik

This book introduces foundational topics such as group theory, fields, linear algebra, matrix theory, and graph theory, providing readers with the essential background needed to understand Feynman diagrams and their integral representations.&nbsp; 
The book highlights Feynman's parametrization as a central tool for studying Feynman integrals, starting with the traditional momentum representation. Schwinger and Lee-Pomeransky parametrizations are covered in a supplementary chapter. Readers will develop a clear understanding of the mathematical properties and practical applications of these techniques, with a particular emphasis on Feynman’s approach. Advanced topics such as integration-by-parts identities and intersection number theory are explored in the final chapter, offering readers a gateway to key mathematical structures. 
The prerequisites are minimal—only a basic familiarity with algebra and calculus is recommended. The content begins with introductory concepts and gradually progresses to more advanced material, ensuring a balanced learning curve. Practical examples throughout the book reinforce the main ideas, allowing readers to apply what they’ve learned and deepen their understanding as they move through the material. 
&nbsp;

Insights into Feynman Diagrams

Lectures on Graph Theory

This textbook offers you a profound understanding of the core concepts in electrodynamics and the special theory of relativity. Emphasis is placed on establishing strong mathematical fundamentals while also equipping you with problem-solving skills crucial for mastering these disciplines. It covers electromagnetic theory, encompassing Maxwell's equations and electromagnetic wave theory as well as special theory of relativity, including space-time principles and the Lorentz transformation. Reiner M. Dreizler, Professor emeritus of Theoretical Physics at Goethe University, Frankfurt/Main, works on many-body systems in quantum mechanics.Cora S. Lüdde, Diplom-physicist, research associate at Goethe University, Frankfurt/Main, Germany, working on application-oriented programming, researches computer arithmetic.

Electrodynamics and Special Theory of Relativity

Theoretische Plasmaphysik

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