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Theory of Thermodynamic Measurements of Quantum Systems Far from Equilibrium (Springer Theses)
by Abhay ShastryThis thesis presents several related advances in the field of nonequilibrium quantum thermodynamics. The central result is an ingenious proof that the local temperature and voltage measurement in a nonequilibrium system of fermions exists and is unique, placing the concept of local temperature on a rigorous mathematical footing for the first time. As an intermediate step, a proof of the positivity of the Onsager matrix of linear response theory is given -- a statement of the second law of thermodynamics that had lacked an independent proof for 85 years. A new experimental method to measure the local temperature of an electron system using purely electrical techniques is also proposed, which could enable improvements to the spatial resolution of thermometry by several orders of magnitude. Finally, a new mathematically-exact definition for the local entropy of a quantum system in a nonequilibrium steady state is derived. Several different measures of the local entropy are discussed, relating to the thermodynamics of processes that a local observer with varying degrees of information about the microstates of the system could carry out, and it is shown that they satisfy a hierarchy of inequalities. Proofs of the third law of thermodynamics for generic open quantum systems are presented, taking into account the entropic contribution due to localized states. Appropriately normalized (per-state) local entropies are defined and are used to quantify the departure from local equilibrium.
Theory of Third-Order Differential Equations
by Seshadev Padhi Smita PatiThis book discusses the theory of third-order differential equations. Most of the results are derived from the results obtained for third-order linear homogeneous differential equations with constant coefficients. M. Gregus, in his book written in 1987, only deals with third-order linear differential equations. These findings are old, and new techniques have since been developed and new results obtained. Chapter 1 introduces the results for oscillation and non-oscillation of solutions of third-order linear differential equations with constant coefficients, and a brief introduction to delay differential equations is given. The oscillation and asymptotic behavior of non-oscillatory solutions of homogeneous third-order linear differential equations with variable coefficients are discussed in Ch. 2. The results are extended to third-order linear non-homogeneous equations in Ch. 3, while Ch. 4 explains the oscillation and non-oscillation results for homogeneous third-order nonlinear differential equations. Chapter 5 deals with the z-type oscillation and non-oscillation of third-order nonlinear and non-homogeneous differential equations. Chapter 6 is devoted to the study of third-order delay differential equations. Chapter 7 explains the stability of solutions of third-order equations. Some knowledge of differential equations, analysis and algebra is desirable, but not essential, in order to study the topic.
Theory of Translation Closedness for Time Scales: With Applications in Translation Functions and Dynamic Equations (Developments in Mathematics #62)
by Chao Wang Ravi P. Agarwal Rathinasamy Sakthivel Donal O' ReganThis monograph establishes a theory of classification and translation closedness of time scales, a topic that was first studied by S. Hilger in 1988 to unify continuous and discrete analysis. The authors develop a theory of translation function on time scales that contains (piecewise) almost periodic functions, (piecewise) almost automorphic functions and their related generalization functions (e.g., pseudo almost periodic functions, weighted pseudo almost automorphic functions, and more). Against the background of dynamic equations, these function theories on time scales are applied to study the dynamical behavior of solutions for various types of dynamic equations on hybrid domains, including evolution equations, discontinuous equations and impulsive integro-differential equations.The theory presented allows many useful applications, such as in the Nicholson`s blowfiles model; the Lasota-Wazewska model; the Keynesian-Cross model; in those realistic dynamical models with a more complex hibrid domain, considered under different types of translation closedness of time scales; and in dynamic equations on mathematical models which cover neural networks. This book provides readers with the theoretical background necessary for accurate mathematical modeling in physics, chemical technology, population dynamics, biotechnology and economics, neural networks, and social sciences.
The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, & Emerged Triumphant from Two Centuries of C
by Sharon Bertsch McGrayne"This account of how a once reviled theory, Baye&’s rule, came to underpin modern life is both approachable and engrossing" (Sunday Times). A New York Times Book Review Editors&’ Choice Bayes' rule appears to be a straightforward, one-line theorem: by updating our initial beliefs with objective new information, we get a new and improved belief. To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok. In the first-ever account of Bayes' rule for general readers, Sharon Bertsch McGrayne explores this controversial theorem and the generations-long human drama surrounding it. McGrayne traces the rule&’s discovery by an 18th century amateur mathematician through its development by French scientist Pierre Simon Laplace. She reveals why respected statisticians rendered it professionally taboo for 150 years—while practitioners relied on it to solve crises involving great uncertainty and scanty information, such as Alan Turing's work breaking Germany's Enigma code during World War II. McGrayne also explains how the advent of computer technology in the 1980s proved to be a game-changer. Today, Bayes' rule is used everywhere from DNA de-coding to Homeland Security. Drawing on primary source material and interviews with statisticians and other scientists, The Theory That Would Not Die is the riveting account of how a seemingly simple theorem ignited one of the greatest controversies of all time.
There Is No One Way to Teach Math: Actionable Ideas for Grades 6–12
by Robin Pemantle Henri PicciottoA collaboration between a seasoned math teacher and a research mathematician, this resource offers balanced instructional ideas based on student intellectual engagement and skilled teacher leadership. It is solidly grounded in many areas of classroom practice, but rather than serving as a prescriptive how-to manual, the authors invite reflection and discussion across classrooms and math departments, much in the way you would share ideas in the teachers’ lounge or across the table at a conference.Chapters offer practical suggestions and concrete examples to teachers of grades 6–12 on just about every aspect of the job: manipulatives, technology, lesson planning, group work, classroom discussion, and more. In opposition to the idea of a “one-size-fits-all” curriculum, the authors explain how to integrate teaching techniques: formal and informal, student-centered and teacher-led, experiential and rigorous.Chapters also include vignettes, as well as many links to curricular materials. Ideal for math educators of grades 6–12, this book is both comprehensive in its strategies and sensitive to the complexities of teaching. For these reasons, math departments, coaches, teacher leaders, and faculty at other levels can also easily reference its content where relevant. This book offers multiple entry points for teachers and departments to discuss and enhance their practice, making it essential reading for any math educator or professional development opportunity.
There's Math in My Origami!: 35 Fun Projects For Hands-on Math Learning
by Fumiaki Shingu35 creative origami designs plus brain-teasing math questions add up to the perfect math activity for kids Discover how fractions, shapes, and symmetry turn a flat sheet of paper into a 3D work of art! Each one of the 35 amazing projects in There’s Math in My Origami!invites kids to: Follow the simple, step-by-step instructions Flex their math skills by answering a fun quiz question Fold adorable origami like they’ve never seen before! Includes educational projects for kids ages 7 and up—plus 2 pages of eye stickers, and 80 sheets of origami paper!
Thermal and Statistical Physics: Concepts and Applications
by Sandeep SharmaThis textbook presents the fundamental concepts and theories in thermal physics and elementary statistical mechanics in a very simple, systematic and comprehensive way. This book is written in a way that it presents the topics in a holistic manner with end-of-chapter exercises and examples where concepts are supported by numerous solved examples and multiple-choice questions to aid self-learning. The textbook also contains illustrated diagrams for better understanding of the concepts. The book will benefit students who are taking introductory courses in thermal physics, thermodynamics and statistical mechanics.
Thermal Distribution Principle and Nonlinear Optimal Control for HVAC Water System (Indoor Environment and Sustainable Building)
by Tianyi Zhao Jiaming Wang Yiting WangThis book introduces the intelligent control technology of heating ventilation and air conditioning (HVAC) water system in detail, studying its thermal distribution characteristics and optimal control methods combining the nonlinearity, strong coupling and delay characteristics to improve the overall operation and maintenance level as well as the energy efficiency of HVAC water system. Intelligent control technology of HVAC water systems involves various fields such as electrical, mechanical, environmental and civil engineering. The book establishes a basic research framework for this topic using a sub-total approach, emphasizing the importance of thermodynamic properties and the significant influence of nonlinear properties in the optimal control of the system. This book is intended for undergraduate and postgraduate students interested in automated control of HVAC water systems, researchers investigating methods for system energy conservation and optimization and design engineers working on intelligent operation and maintenance of HVAC water system.
Thermal Protection Modeling of Hypersonic Flying Apparatus (Innovation And Discovery In Russian Science And Engineering Ser.)
by A. S. YakimovThis book is devoted to studies of unsteady heat and mass exchange processes taking into account thermochemical destruction of thermal protective materials, research of transpiration cooling systems, thermal protection of composite materials exposed to low-energy disturbances, as well as the numerical solution of heat and mass transfer of the exchange. It proposes several mathematical models of passive and active thermal protection systems with regard to factors such as surface ablation, surface roughness, phase transition of a liquid in porous materials, rotation of the body around its longitudinal axis, and exposure to low-energy disturbances. The author studies the possibilities to control thermochemical destruction and heat mass exchange processes in transpiration cooling systems exposed to low-energy disturbances. The numerical analysis of the heat and mass exchange process in carbon plastics under repeated impulse action is also presented. The numerical solutions of problems are compared with the known experimental data. The book is intended for specialists in the field of thermal protection and heat mass exchange, as well as graduate and undergraduates in physics and mathematics.
Thermal Quantum Field Theory and Perturbative Non-Equilibrium Dynamics
by Peter MillingtonThe author develops a new perturbative formalism of non-equilibrium thermal quantum field theory for non-homogeneous backgrounds. As a result of this formulation, the author is able to show how so-called pinch singularities can be removed, without resorting to ad hoc prescriptions, or effective resummations of absorptive effects. Thus, the author arrives at a diagrammatic approach to non-equilibrium field theory, built from modified Feynman rules that are manifestly time-dependent from tree level. This new formulation provides an alternative framework in which to derive master time evolution equations for physically meaningful particle number densities, which are valid to all orders in perturbation theory and to all orders in gradient expansion. Once truncated in a loop-wise sense, these evolution equations capture non-equilibrium dynamics on all time-scales, systematically describing energy-violating processes and the non-Markovian evolution of memory effects
Thermal System Design and Optimization
by C. BalajiThis highly informative and carefully presented textbook introduces the general principles involved in system design and optimization as applicable to thermal systems, followed by the methods to accomplish them. It introduces contemporary techniques like Genetic Algorithms, Simulated Annealing, and Bayesian Inference in the context of optimization of thermal systems. There is a separate chapter devoted to inverse problems in thermal systems. It also contains sections on Integer Programming and Multi-Objective optimization. The linear programming chapter is fortified by a detailed presentation of the Simplex method. A major highlight of the textbook is the inclusion of workable MATLAB codes for examples of key algorithms discussed in the book. Examples in each chapter clarify the concepts and methods presented and end-of-chapter problems supplement the material presented and enhance the learning process.
Thermal Transport in Semiconductors: First Principles and Phonon Hydrodynamics (Springer Theses)
by Pol Torres AlvarezStarting from a broad overview of heat transport based on the Boltzmann Transport Equation, this book presents a comprehensive analysis of heat transport in bulk and nanomaterials based on a kinetic-collective model (KCM). This has become key to understanding the field of thermal transport in semiconductors, and represents an important stride. The book describes how heat transport becomes hydrodynamic at the nanoscale, propagating very much like a viscous fluid and manifesting vorticity and friction-like behavior. It introduces a generalization of Fourier’s law including a hydrodynamic term based on collective behavior in the phonon ensemble. This approach makes it possible to describe in a unifying way recent experiments that had to resort to unphysical assumptions in order to uphold the validity of Fourier’s law, demonstrating that hydrodynamic heat transport is a pervasive type of behavior in semiconductors at reduced scales.
Thermally-driven Mesoscale Flows and their Interaction with Atmospheric Boundary Layer Turbulence (Springer Theses)
by Jon Ander Arrillaga MitxelenaThis book presents developments of novel techniques and applies them in order to understand the interactions between thermally driven mesoscale flows (sea and mountain breezes) and the turbulent exchange within the atmospheric boundary layer. These interactions are not accurately reproduced in the meteorological models currently employed for weather forecasting. Consequently, important variables such as air temperature and wind speed are misrepresented. Also, the concentrations of relevant greenhouse gases such as CO2 are considerably affected by these interactions.By applying a systematic algorithm based on objective criteria (presented here), the thesis explores complete observational databases spanning up to 10 years. Further, it presents statistically significant and robust results on the topic, which has only been studied in a handful of cases in the extant literature. Lastly, by applying the algorithm directly to the outputs of the meteorological model, the thesis helps readers understand the processes discussed and reveals the biases in such models.
Thermo-Hydro-Mechanical-Chemical Processes in Fractured Porous Media: From Benchmarking To Tutoring (Terrestrial Environmental Sciences Ser.)
by Olaf Kolditz Thomas Nagel Hua Shao Wenqing Wang Sebastian BauerThe book comprises the 3rd collection of benchmarks and examples for porous and fractured media mechanics. Analysis of thermo-hydro-mechanical-chemical (THMC) processes is essential to a wide area of applications in environmental engineering, such as geological waste deposition, geothermal energy utilization (shallow and deep systems), carbon capture and storage (CCS) as well as water resources management and hydrology. In order to assess the feasibility, safety as well as sustainability of geoenvironmental applications, model-based simulation is the only way to quantify future scenarios. This charges a huge responsibility concerning the reliability of conceptual models and computational tools. Benchmarking is an appropriate methodology to verify the quality and validate the concept of models based on best practices. Moreover, benchmarking and code comparison are building strong community links. The 3rd THMC benchmark book also introduces benchmark-based tutorials, therefore the subtitle is selected as “From Benchmarking to Tutoring”. The benchmark book is part of the OpenGeoSys initiative - an open source project to share knowledge and experience in environmental analysis and scientific computation. The new version of OGS-6 is introduced and first benchmarks are presented therein (see appendices).
Thermo-hydrodynamic Lubrication in Hydrodynamic Bearings
by Dominique Bonneau Aurelian Fatu Dominique SouchetThis Series provides the necessary elements to the development and validation of numerical prediction models for hydrodynamic bearings. This book describes the thermo-hydrodynamic and the thermo-elasto-hydrodynamic lubrication. The algorithms are methodically detailed and each section is thoroughly illustrated.
Thermodynamics: For Physicists, Chemists and Materials Scientists (Undergraduate Lecture Notes in Physics)
by Reinhard HentschkeConcise, detailed, and transparently structured, this upper-level undergraduate textbook is an excellent resource for a one-semester course on thermodynamics for students majoring in physics, chemistry, or materials science. Throughout the seven chapters and three-part appendix, students benefit from numerous practical examples and solved problems ranging in broad scope from cosmic to molecular evolution; cloud formation to rubber elasticity; and Carnot engines to Monte Carlo simulation of phase equilibria.Lauded in Physics Today as “a valuable resource for students and faculty”, Hentschke’s Thermodynamics presents in this long-anticipated second edition new and extended coverage of a range of topical material, such as thermodynamics of the universe and atmospheric thermodynamics, while also featuring a more application-oriented treatment of surfaces, interfaces, and polymers. Touching on subjects throughout soft-matter physics, superconductors, and complex fluids, this textbook delivers the foundation and breadth of scope necessary to prepare undergraduate students for further study in this timeless yet ever-changing field.
Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions (Fundamental Theories of Physics #195)
by Felix Binder Luis A. Correa Christian Gogolin Janet Anders Gerardo AdessoQuantum Thermodynamics is a novel research field which explores the emergence of thermodynamics from quantum theory and addresses thermodynamic phenomena which appear in finite-size, non-equilibrium and finite-time contexts. Blending together elements from open quantum systems, statistical mechanics, quantum many-body physics, and quantum information theory, it pinpoints thermodynamic advantages and barriers emerging from genuinely quantum properties such as quantum coherence and correlations. Owing to recent experimental efforts, the field is moving quickly towards practical applications, such as nano-scale heat devices, or thermodynamically optimised protocols for emergent quantum technologies. Starting from the basics, the present volume reviews some of the most recent developments, as well as some of the most important open problems in quantum thermodynamics. The self-contained chapters provide concise and topical introductions to researchers who are new to the field. Experts will find them useful as a reference for the current state-of-the-art. In six sections the book covers topics such as quantum heat engines and refrigerators, fluctuation theorems, the emergence of thermodynamic equilibrium, thermodynamics of strongly coupled systems, as well as various information theoretic approaches including Landauer's principle and thermal operations. It concludes with a section dedicated to recent quantum thermodynamics experiments and experimental prospects on a variety of platforms ranging from cold atoms to photonic systems, and NV centres.
Thermodynamics of Information Processing in Small Systems
by Takahiro SagawaThis thesis presents a general theory of nonequilibrium thermodynamics for information processing. Ever since Maxwell's demon was proposed in the nineteenth century, the relationship between thermodynamics and information has attracted much attention because it concerns the foundation of the second law of thermodynamics. From the modern point of view, Maxwell's demon is formulated as an information processing device that performs measurement and feedback at the level of thermal fluctuations. By unifying information theory, measurement theory, and the recently developed theory of nonequilibrium statistical mechanics, the author has constructed a theory of "information thermodynamics," in which information contents and thermodynamic variables are treated on an equal footing. In particular, the maximum work that can be extracted by the demon and the minimum work that is needed for measurement and information erasure by the demon has been determined. Additionally, generalizations of nonequilibrium relations such as a Jarzynski equality for classical stochastic systems in the presence of feedback control have been derived. One of the generalized equalities has recently been verified experimentally by using sub-micron colloidal particles. The results obtained serve as fundamental principles for information processing in small thermodynamic systems, and are applicable to nanomachines and nanodevices.
Thermodynamik für das Bachelorstudium
by Klaus StierstadtDas Verständnis der Thermodynamik ist nicht nur Voraussetzung für die moderne Physik, Chemie, Biologie und Technik, sondern auch für die Frage der Energieversorgung der Zukunft. Der Autor führt in die Prinzipien, Methoden und Ergebnisse der Thermodynamik ein, indem er die Größen Temperatur, Wärme und Entropie auf die Eigenschaften der Atome und auf ihr Zusammenwirken zurückgeführt. Basierend auf den vier Hauptsätzen der Thermodynamik werden die wichtigsten Anwendungen, z. B. Energieumwandlung und Nanotechnologie, ausführlich besprochen.
Thermodynamik für das Bachelorstudium
by Klaus StierstadtDas Verständnis der Thermodynamik ist nicht nur Voraussetzung für die moderne Physik, Chemie, Biologie und Technik, sondern auch für die Frage der Energieversorgung der Zukunft. Der Autor führt in die Prinzipien, Methoden und Ergebnisse der Thermodynamik ein, indem er die Größen Temperatur, Wärme und Entropie auf die Eigenschaften der Atome und auf ihr Zusammenwirken zurückgeführt. Basierend auf den vier Hauptsätzen der Thermodynamik werden die wichtigsten Anwendungen, z. B. Energieumwandlung und Nanotechnologie, ausführlich besprochen.
Thermodynamische Potenziale und Zustandssumme: Ein Überblick über die Definitionen in der Thermodynamik (essentials)
by Klaus StierstadtDieses essential gibt einen Überblick über die Definitionen und die Bedeutung thermodynamischer Potenziale und ermöglicht auch Einsteigern ein Verständnis der Thematik, welche eine Voraussetzung für die moderne Physik, die Chemie, Biologie und Technik ist. Der Schwerpunkt liegt auf den Grundlagen und aktuellen Fragestellungen. Es schlägt eine Brücke zwischen den beiden Thermodynamik-Vorlesungen: der einfachen Wärmelehre im 1. oder 2. Semester und der anspruchsvollen Statistischen Physik im 5. Semester. Das essential ist Teil einer dreiteiligen Reihe zur Thermodynamik zusammen mit Temperatur und Wärme – was ist das wirklich? und Die Eigenschaften der Stoffe: Suszeptibilitäten und Transportkoeffizienten.
Thermofluid Dynamics of Turbulent Flows: Fundamentals and Modelling (UNIPA Springer Series)
by Michele CiofaloThe book provides the theoretical fundamentals on turbulence and a complete overview of turbulence models, from the simplest to the most advanced ones including Direct and Large Eddy Simulation. It mainly focuses on problems of modeling and computation, and provides information regarding the theory of dynamical systems and their bifurcations. It also examines turbulence aspects which are not treated in most existing books on this subject, such as turbulence in free and mixed convection, transient turbulence and transition to turbulence. The book adopts the tensor notation, which is the most appropriate to deal with intrinsically tensor quantities such as stresses and strain rates, and for those who are not familiar with it an Appendix on tensor algebra and tensor notation are provided.
Thermomechanical Industrial Processes: Modeling and Numerical Simulation (Wiley-iste Ser.)
by Jean Michel BergheauThe numerical simulation of manufacturing processes and of their mechanical consequences is of growing interest in industry. However, such simulations need the modeling of couplings between several physical phenomena such as heat transfer, material transformations and solid or fluid mechanics, as well as to be adapted to numerical methodologies. This book gathers a state of the art on how to simulate industrial processes, what data are needed and what numerical simulation can bring. Assembling processes such as welding and friction stir welding, material removal processes, elaboration processes of composite structures, sintering processes, surface-finishing techniques, and thermo-chemical treatments are investigated.This book is the work of a group of researchers who have been working together in this field for more than 12 years. It should prove useful for both those working in industry and those studying the numerical methods applied to multiphysics problems encountered in manufacturing processes.
The Thermophysics of Porous Media (Monographs and Surveys in Pure and Applied Mathematics)
by null T.J.T. SpanosModels for the mechanical behavior of porous media introduced more than 50 years ago are still relied upon today, but more recent work shows that, in some cases, they may violate the laws of thermodynamics. In The Thermophysics of Porous Media, the author shows that physical consistency requires a unique description of dynamic processes that involv
Thicker Than Blood: How Racial Statistics Lie
by Tukufu ZuberiTukufu Zuberi offers a concise account of the historical connections between the development of the idea of race and the birth of social statistics. Zuberi describes the ways race-differentiated data is misinterpreted in the social sciences and asks searching questions about the ways racial statistics are used. He argues that statistical analysis can and must be deracialized, and that this deracialization is essential to the goal of achieving social justice for all.