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Books > Science & Mathematics > Physics > Thermodynamics & statistical physics

Water (R718) Turbo Compressor and Ejector Refrigeration / Heat Pump Technology (Paperback): Milan N. Sarevski, Vasko N. Sarevski Water (R718) Turbo Compressor and Ejector Refrigeration / Heat Pump Technology (Paperback)
Milan N. Sarevski, Vasko N. Sarevski
R2,365 R2,214 Discovery Miles 22 140 Save R151 (6%) Ships in 12 - 17 working days

Water (R718) Turbo Compressor and Ejector Refrigeration/Heat Pump Technology provides the latest information on efficiency improvements, a main topic in recent investigations of thermal energy machines, plants, and systems that include turbo compressors, ejectors, and refrigeration/heat pump systems. This, when coupled with environmental concerns, has led to the application of eco-friendly refrigerants and to a renewed interest in natural refrigerants. Within this context, readers will find valuable information that explores refrigeration and heat pump systems using natural refrigerants, polygeneration systems, the energy efficiency of thermal systems, the utilization of low temperature waste heat, and cleaner production. The book also examines the technical, economic, and environmental reasons of R718 refrigeration/heat pump systems and how they are competitive with traditional systems, serving as a valuable reference for engineers who work in the design and construction of thermal plants and systems, and those who wish to specialize in the use of R718 as a refrigerant in these systems.

A Random Walk in Physics - Beyond Black Holes and Time-Travels (Hardcover, 1st ed. 2021): Massimo Cencini, Andrea Puglisi,... A Random Walk in Physics - Beyond Black Holes and Time-Travels (Hardcover, 1st ed. 2021)
Massimo Cencini, Andrea Puglisi, Davide Vergni, Angelo Vulpiani
R1,210 Discovery Miles 12 100 Ships in 12 - 17 working days

This book offers an informal, easy-to-understand account of topics in modern physics and mathematics. The focus is, in particular, on statistical mechanics, soft matter, probability, chaos, complexity, and models, as well as their interplay. The book features 28 key entries and it is carefully structured so as to allow readers to pursue different paths that reflect their interests and priorities, thereby avoiding an excessively systematic presentation that might stifle interest. While the majority of the entries concern specific topics and arguments, some relate to important protagonists of science, highlighting and explaining their contributions. Advanced mathematics is avoided, and formulas are introduced in only a few cases. The book is a user-friendly tool that nevertheless avoids scientific compromise. It is of interest to all who seek a better grasp of the world that surrounds us and of the ideas that have changed our perceptions.

Simulation of Complex Systems (Hardcover): Giovanni Volpe, Agnese Callegari, Aykut Argun Simulation of Complex Systems (Hardcover)
Giovanni Volpe, Agnese Callegari, Aykut Argun
R2,156 Discovery Miles 21 560 Ships in 12 - 17 working days
Newtonian Dynamics - An Introduction (Hardcover): Richard Fitzpatrick Newtonian Dynamics - An Introduction (Hardcover)
Richard Fitzpatrick
R2,612 Discovery Miles 26 120 Ships in 12 - 17 working days

- A brief and accessible introduction to a complex topic - Contains a thorough treatment of the motions of heavenly bodies than conventional elementary mechanics texts. - Provides a wealth of end-of-chapter exercises to test understanding

Mathematical Physics for Nuclear Experiments (Paperback): Andrew E. Ekpenyong Mathematical Physics for Nuclear Experiments (Paperback)
Andrew E. Ekpenyong
R1,894 Discovery Miles 18 940 Ships in 12 - 17 working days

Mathematical Physics for Nuclear Experiments presents an accessible introduction to the mathematical derivations of key equations used in describing and analysing results of typical nuclear physics experiments. Instead of merely showing results and citing texts, crucial equations in nuclear physics such as the Bohr's classical formula, Bethe's quantum mechanical formula for energy loss, Poisson, Gaussian and Maxwellian distributions for radioactive decay, and the Fermi function for beta spectrum analysis, among many more, are presented with the mathematical bases of their derivation and with their physical utility. This approach provides readers with a greater connection between the theoretical and experimental sides of nuclear physics. The book also presents connections between well-established results and ongoing research. It also contains figures and tables showing results from the author's experiments and those of his students to demonstrate experimental outcomes. This is a valuable guide for advanced undergraduates and early graduates studying nuclear instruments and methods, medical and health physics courses as well as experimental particle physics courses. Key features Contains over 500 equations connecting theory with experiments. Presents over 80 examples showing physical intuition and illustrating concepts. Includes 80 exercises, with solutions, showing applications in nuclear and medical physics.

Mathematical Physics for Nuclear Experiments (Hardcover): Andrew E. Ekpenyong Mathematical Physics for Nuclear Experiments (Hardcover)
Andrew E. Ekpenyong
R4,819 Discovery Miles 48 190 Ships in 12 - 17 working days

Mathematical Physics for Nuclear Experiments presents an accessible introduction to the mathematical derivations of key equations used in describing and analysing results of typical nuclear physics experiments. Instead of merely showing results and citing texts, crucial equations in nuclear physics such as the Bohr's classical formula, Bethe's quantum mechanical formula for energy loss, Poisson, Gaussian and Maxwellian distributions for radioactive decay, and the Fermi function for beta spectrum analysis, among many more, are presented with the mathematical bases of their derivation and with their physical utility. This approach provides readers with a greater connection between the theoretical and experimental sides of nuclear physics. The book also presents connections between well-established results and ongoing research. It also contains figures and tables showing results from the author's experiments and those of his students to demonstrate experimental outcomes. This is a valuable guide for advanced undergraduates and early graduates studying nuclear instruments and methods, medical and health physics courses as well as experimental particle physics courses. Key features Contains over 500 equations connecting theory with experiments. Presents over 80 examples showing physical intuition and illustrating concepts. Includes 80 exercises, with solutions, showing applications in nuclear and medical physics.

Superconcentration and Related Topics (Hardcover, 2014): Sourav Chatterjee Superconcentration and Related Topics (Hardcover, 2014)
Sourav Chatterjee
R2,571 R1,574 Discovery Miles 15 740 Save R997 (39%) Ships in 12 - 17 working days

A certain curious feature of random objects, introduced by the author as "super concentration," and two related topics, "chaos" and "multiple valleys," are highlighted in this book. Although super concentration has established itself as a recognized feature in a number of areas of probability theory in the last twenty years (under a variety of names), the author was the first to discover and explore its connections with chaos and multiple valleys. He achieves a substantial degree of simplification and clarity in the presentation of these findings by using the spectral approach.

Understanding the fluctuations of random objects is one of the major goals of probability theory and a whole subfield of probability and analysis, called concentration of measure, is devoted to understanding these fluctuations. This subfield offers a range of tools for computing upper bounds on the orders of fluctuations of very complicated random variables. Usually, concentration of measure is useful when more direct problem-specific approaches fail; as a result, it has massively gained acceptance over the last forty years. And yet, there is a large class of problems in which classical concentration of measure produces suboptimal bounds on the order of fluctuations. Here lies the substantial contribution of this book, which developed from a set of six lectures the author first held at the Cornell Probability Summer School in July 2012.

The book is interspersed with a sizable number of open problems for professional mathematicians as well as exercises for graduate students working in the fields of probability theory and mathematical physics. The material is accessible to anyone who has attended a graduate course in probability.

Problems And Solutions On Thermodynamics And Statistical Mechanics (Hardcover, Second Edition): Swee Cheng Lim, Choy Heng Lai,... Problems And Solutions On Thermodynamics And Statistical Mechanics (Hardcover, Second Edition)
Swee Cheng Lim, Choy Heng Lai, Leong-Chuan Kwek
R3,154 Discovery Miles 31 540 Ships in 10 - 15 working days

This volume is a compilation of carefully selected questions at the PhD qualifying exam level, including many actual questions from Columbia University, University of Chicago, MIT, State University of New York at Buffalo, Princeton University, University of Wisconsin and the University of California at Berkeley over a twenty-year period. Topics covered in this book include the laws of thermodynamics, phase changes, Maxwell-Boltzmann statistics and kinetic theory of gases.This latest edition has been updated with more problems and solutions and the original problems have also been modernized, excluding outdated questions and emphasizing those that rely on calculations. The problems range from fundamental to advanced in a wide range of topics on thermodynamics and statistical physics, easily enhancing the student's knowledge through workable exercises. Simple-to-solve problems play a useful role as a first check of the student's level of knowledge whereas difficult problems will challenge the student's capacity on finding the solutions.

Problems And Solutions On Thermodynamics And Statistical Mechanics (Paperback, Second Edition): Swee Cheng Lim, Choy Heng Lai,... Problems And Solutions On Thermodynamics And Statistical Mechanics (Paperback, Second Edition)
Swee Cheng Lim, Choy Heng Lai, Leong-Chuan Kwek
R1,387 Discovery Miles 13 870 Ships in 10 - 15 working days

This volume is a compilation of carefully selected questions at the PhD qualifying exam level, including many actual questions from Columbia University, University of Chicago, MIT, State University of New York at Buffalo, Princeton University, University of Wisconsin and the University of California at Berkeley over a twenty-year period. Topics covered in this book include the laws of thermodynamics, phase changes, Maxwell-Boltzmann statistics and kinetic theory of gases.This latest edition has been updated with more problems and solutions and the original problems have also been modernized, excluding outdated questions and emphasizing those that rely on calculations. The problems range from fundamental to advanced in a wide range of topics on thermodynamics and statistical physics, easily enhancing the student's knowledge through workable exercises. Simple-to-solve problems play a useful role as a first check of the student's level of knowledge whereas difficult problems will challenge the student's capacity on finding the solutions.

Microchannel Phase Change Transport Phenomena (Paperback): Sujoy Kumar Saha Microchannel Phase Change Transport Phenomena (Paperback)
Sujoy Kumar Saha
R2,493 R2,332 Discovery Miles 23 320 Save R161 (6%) Ships in 12 - 17 working days

Microchannel Heat transfer is the cooling application of high power density microchips in the CPU system, micropower systems and many other large scale thermal systems requiring effective cooling capacity. This book offers the latest research and recommended models on the microsize cooling system which not only significantly reduces the weight load, but also enhances the capability to remove much greater amount of heat than any of large scale cooling systems. A detailed reference in microchannel phase change (boiling and condensation) including recommended models and correlations for various requirements such as pressure loss, and heat transfer coefficient. Researchers, engineers, designers and students will benefit from the collated, state-of-the-art of the research put together in this book and its systematic, addressing all the relevant issues and providing a good reference for solving problems of critical analysis.

Statistical Physics - An Entropic Approach (Hardcover, New): II Ford Statistical Physics - An Entropic Approach (Hardcover, New)
II Ford
R2,957 R2,376 Discovery Miles 23 760 Save R581 (20%) Out of stock

This undergraduate textbook provides a statistical mechanical foundation to the classical laws of thermodynamics via a comprehensive treatment of the basics of classical thermodynamics, equilibrium statistical mechanics, irreversible thermodynamics, and the statistical mechanics of non-equilibrium phenomena.This timely book has a unique focus on the concept of entropy, which is studied starting from the well-known ideal gas law, employing various thermodynamic processes, example systems and interpretations to expose its role in the second law of thermodynamics. This modern treatment of statistical physics includes studies of neutron stars, superconductivity and the recently developed fluctuation theorems. It also presents figures and problems in a clear and concise way, aiding the student's understanding.

Quantum Statistical Mechanics in Classical Phase Space (Hardcover): Phil Attard Quantum Statistical Mechanics in Classical Phase Space (Hardcover)
Phil Attard
R3,401 Discovery Miles 34 010 Ships in 12 - 17 working days
Simulating Complex Systems by Cellular Automata (Hardcover, 2010 ed.): Alfons G. Hoekstra, Jiri Kroc, Peter M. A. Sloot Simulating Complex Systems by Cellular Automata (Hardcover, 2010 ed.)
Alfons G. Hoekstra, Jiri Kroc, Peter M. A. Sloot
R3,027 Discovery Miles 30 270 Ships in 10 - 15 working days

Deeply rooted in fundamental research in Mathematics and Computer Science, Cellular Automata (CA) are recognized as an intuitive modeling paradigm for Complex Systems. Already very basic CA, with extremely simple micro dynamics such as the Game of Life, show an almost endless display of complex emergent behavior. Conversely, CA can also be designed to produce a desired emergent behavior, using either theoretical methodologies or evolutionary techniques. Meanwhile, beyond the original realm of applications - Physics, Computer Science, and Mathematics - CA have also become work horses in very different disciplines such as epidemiology, immunology, sociology, and finance. In this context of fast and impressive progress, spurred further by the enormous attraction these topics have on students, this book emerges as a welcome overview of the field for its practitioners, as well as a good starting point for detailed study on the graduate and post-graduate level. The book contains three parts, two major parts on theory and applications, and a smaller part on software. The theory part contains fundamental chapters on how to design and/or apply CA for many different areas. In the applications part a number of representative examples of really using CA in a broad range of disciplines is provided - this part will give the reader a good idea of the real strength of this kind of modeling as well as the incentive to apply CA in their own field of study. Finally, we included a smaller section on software, to highlight the important work that has been done to create high quality problem solving environments that allow to quickly and relatively easily implement a CA model and run simulations, both on the desktop and if needed, on High Performance Computing infrastructures.

Endoreversible Thermodynamics of Solar Energy Conversion (Hardcover): Alexis De Vos Endoreversible Thermodynamics of Solar Energy Conversion (Hardcover)
Alexis De Vos
R2,890 Discovery Miles 28 900 Ships in 12 - 17 working days

This book describes various forms of solar energy conversion techniques in a unified way. The physical framework used to describe the various conversions is endoreversible thermodynamics, a recently developed subset of irreversible thermodynamics . It thus studies situations which are not in equilibrium and in which therefore entropy is continuously created. Nevertheless the mathematics is simple, because the authors consider only stationary situations. Most undergraduate textbooks on thermodynamics emphasize equilibrium thermodynamics and reversible processes. No entropy is created and conversion efficiencies are maximal, equal to the Carnot efficiency. For irreversible conversion processes, the reader learns only that entropy production is positive and that conversion efficiency is lower than the Carnot efficiency. But how great the entropy creation is, and how low the efficiency, is usually not expressed. Endoreversible thermodynamics gives the opportunity to calculate explicit values for a broad class of these processes, including solar energy conversion, which is particularly suited to being described in this way. The book is intended for physicists and engineers interested in renewable energy and irreversible thermodynamics.

Open Quantum Systems - A Mathematical Perspective (Hardcover, 1st ed. 2019): Dorothea Bahns, Anke Pohl, Ingo Witt Open Quantum Systems - A Mathematical Perspective (Hardcover, 1st ed. 2019)
Dorothea Bahns, Anke Pohl, Ingo Witt
R3,206 Discovery Miles 32 060 Ships in 10 - 15 working days

This book presents four survey articles on various aspects of open quantum systems, specifically addressing quantum Markovian processes, Feller semigroups and nonequilibrium dynamics. The contributions are based on lectures given by distinguished experts at a summer school in Goettingen, Germany. Starting from basic notions, the authors of these lecture notes accompany the reader on a journey up to the latest research, highlighting new challenges and addressing unsolved problems at the interface between mathematics and physics. Though the book is primarily addressed to graduate students, it will also be of interest to researchers.

Product of Random Stochastic Matrices and Distributed Averaging (Hardcover, 2012 ed.): Behrouz Touri Product of Random Stochastic Matrices and Distributed Averaging (Hardcover, 2012 ed.)
Behrouz Touri
R2,927 Discovery Miles 29 270 Ships in 10 - 15 working days

The thesis deals with averaging dynamics in a multiagent networked system, which is a main mechanism for diffusing the information over such networks. It arises in a wide range of applications in engineered physical networks (such as mobile communication and sensor networks), as well as social and economic networks. The thesis provides in depth study of stability and other phenomena characterizing the limiting behavior of both deterministic and random averaging dynamics. By developing new concepts, and using the tools from dynamic system theory and non-negative matrix theory, several novel fundamental results are rigorously developed. These contribute significantly to our understanding of averaging dynamics as well as to non-negative random matrix theory. The exposition, although highly rigorous and technical, is elegant and insightful, and accompanied with numerous illustrative examples, which makes this thesis work easily accessible to those just entering this field and will also be much appreciated by experts in the field.

Introduction to Sustainable Energy Transformation (Paperback): Henryk Anglart Introduction to Sustainable Energy Transformation (Paperback)
Henryk Anglart
R2,616 Discovery Miles 26 160 Ships in 12 - 17 working days

This textbook provides an accessible introduction to various energy transformation technologies and their influences on the environment. Here the energy transformation is understood as any physical process induced by humans, in which energy is intentionally transformed from one form to another. This book provides an accessible introduction to the subject: covering the theory, principles of design, operation, and efficiency of the systems in addition to discerning concepts such as energy, entropy, exergy, efficiency, and sustainability. It is not assumed that readers have any previous exposure to such concepts as laws of thermodynamics, entropy, exergy, fluid mechanics or heat transfer, and is therefore an ideal textbook for advanced undergraduate students. Key features: Represents a complete source of information on sustainable energy transformation systems and their externalities. Includes all existing and major emerging technologies in the field. Chapters include numerous examples and problems for further learning opportunities.

Introduction to Sustainable Energy Transformation (Hardcover): Henryk Anglart Introduction to Sustainable Energy Transformation (Hardcover)
Henryk Anglart
R6,453 Discovery Miles 64 530 Ships in 12 - 17 working days

This textbook provides an accessible introduction to various energy transformation technologies and their influences on the environment. Here the energy transformation is understood as any physical process induced by humans, in which energy is intentionally transformed from one form to another. This book provides an accessible introduction to the subject: covering the theory, principles of design, operation, and efficiency of the systems in addition to discerning concepts such as energy, entropy, exergy, efficiency, and sustainability. It is not assumed that readers have any previous exposure to such concepts as laws of thermodynamics, entropy, exergy, fluid mechanics or heat transfer, and is therefore an ideal textbook for advanced undergraduate students. Key features: Represents a complete source of information on sustainable energy transformation systems and their externalities. Includes all existing and major emerging technologies in the field. Chapters include numerous examples and problems for further learning opportunities.

Nonequilibrium Statistical Physics (Paperback): Gerd Roepke Nonequilibrium Statistical Physics (Paperback)
Gerd Roepke
R2,406 R1,948 Discovery Miles 19 480 Save R458 (19%) Out of stock

Authored by a well-known expert in the field of nonequilibrium statistical physics, this book is a coherent presentation of the subject suitable for masters and PhD students, as well as postdocs in physics and related disciplines.
Starting from a general discussion of irreversibility and entropy, the method of nonequilibrium statistical operator is presented as a general concept. Stochastic processes are introduced as a necessary prerequisite to describe the evolution of a nonequilibrium state. Different standard approaches such as master equations, kinetic equations and linear response theory, are derived after special assumptions. This allows for an insight into the problems of nonequilibrium physics, a discussion of the limits of the approaches, and suggestions for improvements. The method of thermodynamic Green's function is outlined that allows for the systematic quantum statistical treatment of many-body systems. Applications and typical examples are given, as well as fully worked problems.

Modern Semiconductor Physics and Device Applications (Hardcover): Vitalii Dugaev, Vladimir Litvinov Modern Semiconductor Physics and Device Applications (Hardcover)
Vitalii Dugaev, Vladimir Litvinov
R3,631 Discovery Miles 36 310 Ships in 12 - 17 working days

* Explores concepts common in textbooks on semiconductors, in addition to topics not included in similar books currently available on the market, such as the topology of Hilbert space in crystals * Contains the latest research and developments in the field * Written in an accessible yet rigorous manner

Morphogenetic Engineering - Toward Programmable Complex Systems (Hardcover, 2013 ed.): Rene Doursat, Hiroki Sayama, Olivier... Morphogenetic Engineering - Toward Programmable Complex Systems (Hardcover, 2013 ed.)
Rene Doursat, Hiroki Sayama, Olivier Michel
R3,784 Discovery Miles 37 840 Ships in 10 - 15 working days

Generally, spontaneous pattern formation phenomena are random and repetitive, whereas elaborate devices are the deterministic product of human design.
Yet, biological organisms and collective insect constructions are exceptional examples of complex systems that are both self-organized and architectural.
This book is the first initiative of its kind toward establishing a new field of research, Morphogenetic Engineering, to explore the modeling and implementation of self-architecturing systems. Particular emphasis is placed on the programmability and computational abilities of self-organization, properties that are often underappreciated in complex systems science while, conversely, the benefits of self-organization are often underappreciated in engineering methodologies.
Altogether, the aim of this work is to provide a framework for and examples of a larger class of self-architecturing systems, while addressing fundamental questions such as
> How do biological organisms carry out morphogenetic tasks so reliably?
> Can we extrapolate their self-formation capabilities to engineered systems?
> Can physical systems be endowed with information (or informational systems be embedded in physics) so as to create autonomous morphologies and functions?
> What are the core principles and best practices for the design and engineering of such morphogenetic systems?
The intended audience consists of researchers and graduate students who are working on, starting to work on, or interested in programmable self-organizing systems in a wide range of scientific fields, including computer science, robotics, bioengineering, control engineering, physics, theoretical biology, mathematics, and many others.

Phase Transformations in Metals and Alloys (Hardcover, 4th edition): David A. Porter, Kenneth E. Easterling, Mohamed Y. Sherif Phase Transformations in Metals and Alloys (Hardcover, 4th edition)
David A. Porter, Kenneth E. Easterling, Mohamed Y. Sherif
R4,715 Discovery Miles 47 150 Ships in 12 - 17 working days

Discusses advances in the computation of phase diagrams Offers expanded treatment of eutectic solidification with practical examples and new coverage of ternary phase diagrams, covering the concepts of orthoequilibrium and paraequilibrium Updates discussion of bainite transformation to reflect current opinions Includes new case studies covering grain refiners in aluminium alloys, additive manufacturing, thin film growth, important aerospace Al-Li alloys, and quenched and partitioned steels, and metastable austenitic stainless steels. Each chapter now begins with a list of key concepts, includes simpler illustrative exercises with relevance to real practical applications, and references to scientific publications updated to reflect experimental and computational advances in metallurgy

Bimodal Oxidation - Coupling of Heterogeneous and Homogeneous Reactions (Paperback): Robert Bakhtchadjian Bimodal Oxidation - Coupling of Heterogeneous and Homogeneous Reactions (Paperback)
Robert Bakhtchadjian
R1,477 Discovery Miles 14 770 Ships in 12 - 17 working days

This book is devoted to the problems of oxidation chemical reactions and addresses bimodal reaction sequences. Chemical reactions of oxidation, occurring under certain conditions and in multicomponent systems are complex processes. The process of the oxidation essentially changes in the presence and contact of the solid substances with reactants. The role of solid substances and the appearance of this phenomenon in oxidation reaction are discussed. The reader will understand the "driving forces" of this phenomenon and apply it in practice. Written for chemists, physicists, biologists and engineers working in the domain of oxidation reactions. Key Selling Features: Covers the historical background, modern state of the art, and perspectives in investigations of the coupling between heterogeneous and homogeneous reactions Discusses the feasible pathways of the coupling of heterogeneous and homogeneous reactions in oxidation in man-made and natural chemical systems Addresses the abundance, peculiarities and mechanisms of the bimodal reaction sequences in oxidation with dioxygen in recent decades Discusses the existence of the bimodal reaction sequences in chemical systems investigations in atmospheric chemistry and heterogeneous photocatalysis Presented in a simple concise style, accessible for both specialists and non-specialists

Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols (Hardcover, 1st ed. 2015): Sabir Umarov Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols (Hardcover, 1st ed. 2015)
Sabir Umarov
R3,425 R2,180 Discovery Miles 21 800 Save R1,245 (36%) Ships in 12 - 17 working days

The book systematically presents the theories of pseudo-differential operators with symbols singular in dual variables, fractional order derivatives, distributed and variable order fractional derivatives, random walk approximants, and applications of these theories to various initial and multi-point boundary value problems for pseudo-differential equations. Fractional Fokker-Planck-Kolmogorov equations associated with a large class of stochastic processes are presented. A complex version of the theory of pseudo-differential operators with meromorphic symbols based on the recently introduced complex Fourier transform is developed and applied for initial and boundary value problems for systems of complex differential and pseudo-differential equations.

Quantitative Phase Field Modelling of Solidification (Hardcover): Nikolas Provatas, Tatu Pinomaa, Nana Ofori-Opoku Quantitative Phase Field Modelling of Solidification (Hardcover)
Nikolas Provatas, Tatu Pinomaa, Nana Ofori-Opoku
R3,180 Discovery Miles 31 800 Ships in 12 - 17 working days

Presents a clear path to developing quantitative multi-phase and multi-component phase field models for solidification and other phase transformation kinetics based on practical grand potential functional Derives explicitly and discusses the quantitative nature of the model formulations through matched interface asymptotic analysis Explores a framework for quantitative treatment of rapid solidification to control solute trapping and solute drag dynamics

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