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1
Warren, Patricia F. A mathematical model of knee kinematics utilizing the principle of minimum energy. Monterey, Calif: Naval Postgraduate School, 1998.
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2
Ko, William L. Predictions of thermal buckling strengths of hypersonic aircraft sandwich panels using minimum potential energy and finite element methods. [Washington, D.C.]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1995.
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3
Henriksen, Niels Engholm, and Flemming Yssing Hansen. Potential Energy Surfaces. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805014.003.0003.
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This chapter discusses potential energy surfaces, that is, the electronic energy as a function of the internuclear coordinates as obtained from the electronic Schrödinger equation. It focuses on the general topology of such energy surfaces for unimolecular and bimolecular reactions. To that end, concepts like saddle point, barrier height, minimum-energy path, and early and late barriers are discussed. It concludes with a discussion of approximate analytical solutions to the electronic Schrödinger equation, in particular, the interaction of three hydrogen atoms expressed in terms of Coulomb and exchange integrals, as described by the so-called London equation. From this equation it is concluded that the total electronic energy is not equal to the sum of H–H pair energies. Finally, a semi-empirical extension of the London equation—the LEPS method—allows for a simple but somewhat crude construction of potential energy surfaces.
4
A Mathematical Model of Knee Kinematics Utilizing the Principle of Minimum Energy. Storming Media, 1998.
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5
Mann, Peter. Energy and Work. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0002.
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This chapter discusses the work–energy theorem, which is developed from Newton’s second law, and defines the kinetic and potential energies of the system. While there is some vector calculus involved, it has been kept to the bare minimum and the reader should not require in-depth knowledge to understand the salient points. If there is a net force on the particle, it accelerates in the direction of the unbalanced force. The force is a central force if it depends only on the distance between the point on which the force acts and the coordinate origin. Using Stokes’s theorem, potential energies are thoroughly discussed. The chapter also discusses spherically symmetric potentials, isotropic force, force on systems of particles, centre of mass coordinates and rigid bodies.
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Steigmann, David J. Stability and the energy criterion. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198567783.003.0011.
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This chapter motivates the criterion of minimum potential energy as a stability criterion for conservative problems. It examines the role played by various convexity conditions (ordinary convexity, quasiconvexity, polyconvexity, rank-one convexity) in the energy-minimization problem. Applications to simple phase-transition problems involving discontinuous deformation gradients are presented.
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Hoskin, Peter J. Radiotherapy in symptom management. Oxford University Press, 2015. http://dx.doi.org/10.1093/med/9780199656097.003.0123.
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Radiotherapy has a major role in symptom control and over 40% of all radiation treatments are given with palliative intent. In the palliative setting, radiotherapy will usually be delivered using high-energy external beam treatment from a linear accelerator. Bone metastases may be treated with intravenous systemic radioisotopes and dysphagia with endoluminal brachytherapy. A general principle of palliative radiotherapy is that it should be delivered in as few treatment visits as possible and be associated with minimal acute toxicity. The main indications for palliative radiotherapy are in the management of symptoms due to local tumour growth and infiltration. These include pain from bone metastases, visceral pain from soft tissue metastases, and neuropathic pain from spinal, pelvic, and axillary tumour. Local pressure symptoms are particularly onerous and potentially dangerous when they affect the nervous system; thus spinal canal compression remains one of the few true emergency situations in which radiotherapy is indicated. Similarly brain, meningeal, or skull base metastases require urgent assessment and can be helped with local radiotherapy. Obstruction of a hollow tube or drainage channels can lead to significant symptoms and again local radiotherapy can be valuable in addressing this scenario. Such indications would include dysphagia, bronchial obstruction, leg or arm oedema, vena cava obstruction, or hydrocephalus. Finally haemorrhage can be distressing if rarely life-threatening. Local radiotherapy to bleeding tumours in the lung, bronchus, bowel, genitourinary tract, and skin is very effective at control of bleeding.
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Office, General Accounting. Tax policy: Revenue potential of restoring excise taxes to past levels : report to the Joint Committee on Taxation. Washington, D.C: GAO, 1989.
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9
Sherwood, Dennis, and Paul Dalby. Macromolecular conformations and interactions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198782957.003.0025.
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As a polymer of many amino acids, any given protein can, in principle, adopt a huge number of configurations. In reality, however, the biologically stable protein adopts a single configuration that is stable over time. Thermodynamically, this configuration must represent a Gibbs free energy minimum. This chapter therefore explores how the thermodynamics and kinetics of protein folding and unfolding can be investigated experimentally (using, for example, chaotropes, heating or ligand interactions), and how these measurements can be used to enrich our understanding of protein configurations and stability.
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Coopersmith, Jennifer. Lagrangian Mechanics. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198743040.003.0006.
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It is demonstrated how d’Alembert’s Principle can be used as the basis for a more general mechanics – Lagrangian Mechanics. How this leads to Hamilton’s Principle (the Principle of Least Action) is shown mathematically and in words. It is further explained why Lagrangian Mechanics is so general, why forces of constraint may be ignored, and how external conditions lead to “curved space.” Also, it is explained why the Lagrangian, L, has the form L = T − V (where T is the kinetic energy and V is the potential energy), and why T is in “quadratic form” (T = 1/2mv2). It is shown how Noether’s Theorem leads to a more fundamental definition of energy and links the conservation of energy to the homogeneity of time. The ingenious Lagrange multipliers are explained, and also generalized forces and generalized coordinates.
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Sherwood, Dennis, and Paul Dalby. Chemical equilibrium and chemical kinetics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198782957.003.0014.
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Building on the previous chapter, this chapter examines gas phase chemical equilibrium, and the equilibrium constant. This chapter takes a rigorous, yet very clear, ‘first principles’ approach, expressing the total Gibbs free energy of a reaction mixture at any time as the sum of the instantaneous Gibbs free energies of each component, as expressed in terms of the extent-of-reaction. The equilibrium reaction mixture is then defined as the point at which the total system Gibbs free energy is a minimum, from which concepts such as the equilibrium constant emerge. The chapter also explores the temperature dependence of equilibrium, this being one example of Le Chatelier’s principle. Finally, the chapter links thermodynamics to chemical kinetics by showing how the equilibrium constant is the ratio of the forward and backward rate constants. We also introduce the Arrhenius equation, closing with a discussion of the overall effect of temperature on chemical equilibrium.
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Rau, Jochen. Constructing the State. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780199595068.003.0003.
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The limited data available about a macroscopic system may come in various forms: sharp constraints, expectation values, or control parameters. While these data impose constraints on the state, they do not specify it uniquely; a further principle—the maximum entropy principle—must be invoked to construct it. This chapter discusses basic notions of information theory and why entropy may be regarded as a measure of ignorance. It shows how the state—called a Gibbs state—is constructed using the maximum entropy principle, and elucidates its generic properties, which are conveniently summarized in a thermodynamic square. The chapter further discusses the second law and how it is linked to the reproducibility of macroscopic processes. It introduces the concepts of equilibrium and temperature, as well as pressure and chemical potential. Finally, this chapter considers statistical fluctuations of the energy and of other observables in case these are given as expectation values.
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Deruelle, Nathalie, and Jean-Philippe Uzan. Lagrangian mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0008.
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This chapter shows how the Newtonian law of motion of a particle subject to a gradient force derived from a ‘potential energy’ can always be obtained from an extremal principle, or ‘principle of least action’. According to Newton’s first law, the trajectory representing the motion of a free particle between two points p1 and p2 is a straight line. In other words, out of all the possible paths between p1 and p2, the trajectory effectively followed by a free particle is the one that minimizes the length. However, even though the use of the principle of extremal length of the paths between two points gives the straight line joining the points, this does not mean that the straight-line path is traced with constant velocity in an inertial frame. Moreover, the trajectory describing the motion of a particle subject to a force is not uniform and rectilinear.
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Blockley, David. 2. Does form follow function? Oxford University Press, 2014. http://dx.doi.org/10.1093/actrade/9780199671939.003.0002.
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In c.15 bc, the Roman Vitruvius stated that a good building should satisfy three requirements: durability, utility, and beauty. ‘Does form follow function?’ examines utility and beauty. It explains that structures are naturally lazy because they contain minimum potential energy. Each piece of structure, however small or large, will move, but not freely as the neighbouring pieces will get in the way. When this happens internal forces are created as the pieces bump up against each other. Force pathways are degrees of freedom and the structure has to be strong enough to resist these internal forces along these pathways. Form-finding structures are exciting and innovative examples of the fusion of engineering and architecture.
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Deruelle, Nathalie, and Jean-Philippe Uzan. Conservation laws. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0007.
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This chapter defines the conserved quantities associated with an isolated dynamical system, that is, the quantities which remain constant during the motion of the system. The law of momentum conservation follows directly from Newton’s third law. The superposition principle for forces allows Newton’s law of motion for a body Pa acted on by other bodies Pa′ in an inertial Cartesian frame S. The law of angular momentum conservation holds if the forces acting on the elements of the system depend only on the separation of the elements. Finally, the conservation of total energy requires in addition that the forces be derivable from a potential.
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Wigmans, Richard. Analysis and Interpretation of Test Beam Data. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786351.003.0009.
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This chapter describes some of the many pitfalls that may be encountered when developing the calorimeter system for a particle physics experiment. Several of the examples chosen for this chapter are based on the author’s own experience. Typically, the performance of a new calorimeter is tested in a particle beam provided by an accelerator. The potential pitfalls encountered in correctly assessing this performance both concern the analysis and the interpretation of the data collected in such tests. The analysis should be carried out with unbiased event samples. Several consequences of violating this principle are illustrated with practical examples. For the interpretation of the results, it is very important to realize that the conditions in a testbeam are fundamentally different than in practice. This has consequences for the meaning of the term “energy resolution”. It is shown that the way in which the results of beam tests are quoted may create a misleading impression of the quality of the tested instrument.
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Ellinson, Michelle, and Tommy Rampling. Normal nutritional function. Edited by Patrick Davey and David Sprigings. Oxford University Press, 2018. http://dx.doi.org/10.1093/med/9780199568741.003.0331.
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Normal nutritional function requires a healthy diet. Healthy eating incorporates a variety of nutrients that are essential for energy expenditure, prevention of disease, and maintenance of normal physiological function. An unhealthy diet can result in malnutrition, and this contributes to illness and death throughout the world. The core principle of healthy eating is obtaining an adequate balance, and the diseases resulting from overnourishment differ greatly from those resulting from undernourishment. In the third world, diets tend to rely heavily on staple crops, and can be very seasonal. Energy sources are predominantly cereals, whereas meat and fish are limited. Malnutrition tends to occur from a lack of essential nutrients, leading to conditions such as vitamin deficiencies, kwashiorkor, and iodine deficiency syndromes. In first-world countries, people have more freedom to choose what they eat. Thus, diets tend to be high in fat and dense in energy. Obesity, diabetes, coronary heart disease, cancer, and hypertension are major contributors to morbidity and mortality. A healthy diet should contain adequate proportions of carbohydrates, fats, proteins, vitamins, and trace elements. The intake of these constituents is sporadic, with meals constituting major boluses of potential energy. Energy expenditure, conversely, is continuous. The human body has, therefore, developed complex mechanisms directing nutrients into storage when in excess, and mobilizing these stores as they are needed, and it is essential that sufficient energy is always available to maintain the basal metabolic rate, which is the amount of energy expended while at rest in a neutrally temperate environment. This energy is sufficient only for the functioning of the vital organs, such as the heart, the lungs, the liver, the kidneys, and the CNS.
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Садовников, Василий. Теория гетерогенного катализа. Теория хемосорбции. Publishing House Triumph, 2021. http://dx.doi.org/10.32986/978-5-40-10-01-2001.
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This monograph is a continuation of the monograph by V.V. Sadovnikov. Lateral interaction. Moscow 2006. Publishing house "Anta-Eco", 2006. ISBN 5-9730-0017-6. In this work, the foundations of the theory of heterogeneous catalysis and the theory of chemisorption are more easily formulated. The book consists of two parts, closely related to each other. These are the theoretical foundations of heterogeneous catalysis and chemisorption. In the theory of heterogeneous catalysis, an experiment is described in detail, which must be carried out in order to isolate the stages of a catalytic reaction, to find the stoichiometry of each of the stages. This experiment is based on the need to obtain the exact value of the specific surface area of the catalyst, the number of centers at which the reaction proceeds, and the output curves of each of the reaction products. The procedures for obtaining this data are described in detail. Equations are proposed and solved that allow calculating the kinetic parameters of the nonequilibrium stage and the thermodynamic parameters of the equilibrium stage. The description of the quantitative theory of chemisorption is based on the description of the motion of an atom along a crystal face. The axioms on which this mathematics should be based are formulated, the mathematical apparatus of the theory is written and the most detailed instructions on how to use it are presented. The first axiom: an atom, moving along the surface, is present only in places with minima of potential energy. The second axiom: the face of an atom is divided into cells, and the position of the atom on the surface of the face is set by one parameter: the cell number. The third axiom: the atom interacts with the surrounding material bodies only at the points of minimum potential energy. The fourth axiom: the solution of the equations is a map of the arrangement of atoms on the surface. The fifth axiom: quantitative equations are based on the concept of a statistically independent particle. The formation energies of these particles and their concentration are calculated by the developed program. The program based on these axioms allows you to simulate and calculate the interaction energies of atoms on any crystal face. The monograph is intended for students, post-graduate students and researchers studying work and working in petrochemistry and oil refining.