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Adopting a multidisciplinary approach, this edited volume brings together a diverse range of contributions to look beyond the strictly mathematical view of modelling and instead examine the social nature of models, their biases and responsibilities.

Mathematical models --- Social aspects. --- Models, Mathematical --- Simulation methods --- Policy sciences --- Political planning --- Politics and Government. --- Politics & government. --- Mathematical models.

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This book contains reports made at the International Conference on Differential Equations, Mathematical Modeling and Computational Algorithms, held in Belgorod, Russia, in October 2021 and is devoted to various aspects of the theory of differential equations and their applications in various branches of science. Theoretical papers devoted to the qualitative analysis of emerging mathematical objects, theorems of the existence and uniqueness of solutions to the boundary value problems under study are presented, and numerical algorithms for their solution are described. Some issues of mathematical modeling are also covered; in particular, in problems of economics, computational aspects of the theory of differential equations and boundary value problems are studied. The articles are written by well-known experts and are interesting and useful to a wide audience: mathematicians, representatives of applied sciences and students and postgraduates of universities engaged in applied mathematics.

Differential equations. --- Mathematical models. --- Mathematics—Data processing. --- Differential Equations. --- Mathematical Modeling and Industrial Mathematics. --- Computational Science and Engineering. --- Models, Mathematical --- Simulation methods --- 517.91 Differential equations --- Differential equations

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This monograph provides a comprehensive and self-contained treatment of continuum physics, illustrating a systematic approach to the constitutive equations for wide-ranging classes of materials. Derivations of results are detailed through careful proofs, and the contents have been developed to ensure a self-contained and consistent presentation. Part I reviews the kinematics of continuous bodies and illustrates the general setting of balance laws. Essential preliminaries to continuum physics – such as reference and current configurations, transport relations, singular surfaces, objectivity, and objective time derivatives – are covered in detail. A chapter on balance equations then develops the balance laws of mass, linear momentum, angular momentum, energy, and entropy, as well as the balance laws in electromagnetism. Part II is devoted to the general requirements on constitutive models, emphasizing the application of objectivity and consistency with the second law of thermodynamics. Common models of simple materials are then reviewed, and in this framework, detailed descriptions are given of solids (thermoelastic, elastic, and dissipative) and fluids (elastic, thermoelastic, viscous, and Newtonian). A wide of variety of constitutive models are investigated in Part III, which consists of separate chapters focused on several types of non-simple materials: materials with memory, aging and higher-order grade materials, mixtures, micropolar media, and porous materials. The interaction of the electromagnetic field with deformation is also examined within electroelasticity, magnetoelasticity, and plasma theory. Hysteretic effects and phase transitions are considered in Part IV. A new approach is established by treating entropy production as a constitutive function in itself, as is the case for entropy and entropy flux. This proves to be conceptually and practically advantageous in the modelling of nonlinear phenomena, such as those occurring in hysteretic continua (e.g., plasticity, electromagnetism, and the physics of shape memory alloys). Mathematical Modelling of Continuum Physics will be an important reference for mathematicians, engineers, physicists, and other scientists interested in research or applications of continuum mechanics. .

Mathematical models. --- Physics. --- Mathematical Modeling and Industrial Mathematics. --- Classical and Continuum Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Models, Mathematical --- Simulation methods --- Teoria de camps (Física) --- Models matemàtics

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The content of the book collects some contributions related to the talks presented during the INdAM Workshop "Fractional Differential Equations: Modelling, Discretization, and Numerical Solvers", held in Rome, Italy, on July 12–14, 2021. All contributions are original and not published elsewhere. The main topic of the book is fractional calculus, a topic that addresses the study and application of integrals and derivatives of noninteger order. These operators, unlike the classic operators of integer order, are nonlocal operators and are better suited to describe phenomena with memory (with respect to time and/or space). Although the basic ideas of fractional calculus go back over three centuries, only in recent decades there has been a rapid increase in interest in this field of research due not only to the increasing use of fractional calculus in applications in biology, physics, engineering, probability, etc., but also thanks to the availability of new and more powerful numerical tools that allow for an efficient solution of problems that until a few years ago appeared unsolvable. The analytical solution of fractional differential equations (FDEs) appears even more difficult than in the integer case. Hence, numerical analysis plays a decisive role since practically every type of application of fractional calculus requires adequate numerical tools. The aim of this book is therefore to collect and spread ideas mainly coming from the two communities of numerical analysts operating in this field - the one working on methods for the solution of differential problems and the one working on the numerical linear algebra side - to share knowledge and create synergies. At the same time, the book intends to realize a direct bridge between researchers working on applications and numerical analysts. Indeed, the book collects papers on applications, numerical methods for differential problems of fractional order, and related aspects in numerical linear algebra. The target audience of the book is scholars interested in recent advancements in fractional calculus.

Differential equations. --- Mathematics --- Mathematical models. --- Numerical analysis. --- Differential Equations. --- Computational Mathematics and Numerical Analysis. --- Mathematical Modeling and Industrial Mathematics. --- Numerical Analysis. --- Data processing. --- Models, Mathematical --- Simulation methods --- 517.91 Differential equations --- Differential equations --- Mathematical analysis

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This book investigates in detail long-term health state estimation technology of energy storage systems, assessing its potential use to replace common filtering methods that constructs by equivalent circuit model with a data-driven method combined with electrochemical modeling, which can reflect the battery internal characteristics, the battery degradation modes, and the battery pack health state. Studies on long-term health state estimation have attracted engineers and scientists from various disciplines, such as electrical engineering, materials, automation, energy, and chemical engineering. Pursuing a holistic approach, the book establishes a fundamental framework for this topic, while emphasizing the importance of extraction for health indicators and the significant influence of electrochemical modeling and data-driven issues in the design and optimization of health state estimation in energy storage systems. The book is intended for undergraduate and graduate students who are interested in new energy measurement and control technology, researchers investigating energy storage systems, and structure/circuit design engineers working on energy storage cell and pack.

Energy storage. --- Electronics --- Mathematical models. --- Mechanical and Thermal Energy Storage. --- Electronic Materials. --- Mathematical Modeling and Industrial Mathematics. --- Materials. --- Models, Mathematical --- Simulation methods --- Electronic materials --- Storage of energy --- Force and energy --- Power (Mechanics) --- Flywheels --- Pulsed power systems