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Published: 14 March 2023

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1

United States. National Aeronautics and Space Administration., ed. Mechanical system reliability for long life space systems: Final report. Nashville, Tenn: Dept. of Mechanical Engineering, Vanderbilt University, 1994.

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2

1938-, Stephansson Ove, Hudson J. A, and Jing Lanru, eds. Coupled thermo-hydro-mechanical processes in geo-systems: Fundamentals, modelling, experiments, and applications. Boston: Elsevier, 2004.

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3

GeoProc2003, (2003 Stockholm Sweden). Coupled thermo-hydro-mechanical-chemical processes in geo-systems: Fundamentals, modelling, experiments and applications. Amsterdam: Elsevier, 2004.

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4

E, Kennedy F., United States. Office of Naval Research., and Workshop on Thermomechanical Effects in Sliding Systems (3rd : 1984 : Dartmouth College), eds. Thermomechanical effects in sliding systems. Lausanne: Elsevier Sequoia S.A., 1985.

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5

A, Bajura R., Marston C. H. 1932-, Tsatsaronis G, American Society of Mechanical Engineers. Winter Meeting. (1989 : San Francisco, Calif.), American Society of Mechanical Engineers. Advanced Energy Systems Division., American Society of Mechanical Engineers. Advanced Energy Systems Division. Systems Analysis Committee., and Symposium on the Analysis and Design of Energy Systems (1989 : San Francisco, CA), eds. Analysis and design of energy systems: Computer-aided engineering : presented at the Winter Annual Meeting of the American Society of Mechanical Engineers, San Francisco, California, December 10-15, 1989. New York, NY: The Society, 1989.

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6

H, Amon Cristina, American Society of Mechanical Engineers. Heat Transfer Division., American Society of Mechanical Engineers. Electrical and Electronic Packaging Division., and International Mechanical Engineering Congress and Exposition (1995 : San Francisco, Calif.), eds. Cooling and thermal design of electronic systems: Presented at the 1995 ASME International Mechanical Engineering Congress and Exposition, November 12-17, 1995, San Francisco, California. New York: American Society of Mechanical Engineers, 1995.

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7

Karl-Heinz, Remmers, and Schnauss Martin, eds. Solar thermal systems: Successful planning and construction. Berlin: Solarpraxis, 2002.

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8

Yuriy, Pyr'yev, ed. Nonsmooth dynamics of contacting thermoelastic bodies. New York, NY: Springer, 2009.

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9

Evtushenko, Sergej, and Viktor Logvinov. Resistance of materials. Laboratory works. 4th edition. 4th ed. ru: Publishing Center RIOR, 2016. http://dx.doi.org/10.12737/16966.

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Data on laboratory works on resistance of materials are provided, the assessment of errors of results of measurements and experiments is given, statistical processing of experimental data is in detail stated. The book contains information on nondestructive methods and control devices of characteristics and diagnostics of materials and designs. In a grant the International system of units (SI) (tab. 1 of the Appendix) is used, designations of sizes are accepted according to the international recommendations of ISO. Data on physicomechanical characteristics of steel, cast iron, non-ferrous metals, wood and polymers and the allowed tension for them are provided in tab. 2-8 of the Appendix. The grant is intended for the students studying courses of resistance of materials, mechanics of materials and designs, applied mechanics, construction mechanics and construction designs.

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10

Nazarov, Vyacheslav, Roman Sandu, and Dmitriy Makarenkov. Technique and technology of combined processing of solid waste. ru: INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/996365.

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The educational manual provides information about industrial and domestic waste. The properties of the lithosphere and the soil components. The estimation of soil pollution by industrial and household waste. The peculiarities of classification of wastes and provides criteria for determining risk. Describe the General pattern of the combined methods of processing that use mechanical, physical, thermal and biothermal recycling processes. In detail the construction described granulating equipment, methods of intensification of processes, process flow sheets and engineering calculation methods. Special attention is given to the thermal methods of waste treatment, process lines, constructions of furnaces and reactors. On the basis of the system approach with use of data of environmental monitoring are considered the methodology for selecting the most available technology. Meets the requirements of Federal state educational standards of higher education of the last generation. Intended for independent work of undergraduates majoring in 20.04.01 "Technospheric safety" (master level), 20.03.01 "Technosphere safety" (bachelor level), 18.03.01 "Chemical technology" 18.03.02 "Energy and resource saving processes in chemical technology, petrochemistry and biotechnology". Can be useful for engineers and technicians of chemical industry and related industries.

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11

Heat transfer: Thermal management of electronics. Boca Raton: Taylor & Francis, 2010.

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12

Orlik, Lyubov', and Galina Zhukova. Operator equation and related questions of stability of differential equations. ru: INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1061676.

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The monograph is devoted to the application of methods of functional analysis to the problems of qualitative theory of differential equations. Describes an algorithm to bring the differential boundary value problem to an operator equation. The research of solutions to operator equations of special kind in the spaces polutoratonny with a cone, where the limitations of the elements of these spaces is understood as the comparability them with a fixed scale element of exponential type. Found representations of the solutions of operator equations in the form of contour integrals, theorems of existence and uniqueness of such solutions. The spectral criteria for boundedness of solutions of operator equations and, as a consequence, sufficient spectral features boundedness of solutions of differential and differential-difference equations in Banach space. The results obtained for operator equations with operators and work of Volterra operators, allowed to extend to some systems of partial differential equations known spectral stability criteria for solutions of A. M. Lyapunov and also to generalize theorems on the exponential characteristic. The results of the monograph may be useful in the study of linear mechanical and electrical systems, in problems of diffraction of electromagnetic waves, theory of automatic control, etc. It is intended for researchers, graduate students functional analysis and its applications to operator and differential equations.

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13

Garofalo, Giuseppe, ed. Capitalismo distrettuale, localismi d'impresa, globalizzazione. Florence: Firenze University Press, 2008. http://dx.doi.org/10.36253/978-88-8453-605-1.

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From the late Sixties on, industrial development in Italy evolved through the spread of small and medium sized firms, aggregated in district networks, with an elevated propensity to enterprise and the marked presence of owner-families. Installed within the local systems, the industrial districts tended to simulate large-scale industry exploiting lower costs generated by factors that were not only economic. The districts are characterised in terms of territorial location (above all the thriving areas of the North-east and Centre) and sector, since they are concentrated in the "4 As" (clothing-fashion, home-decor, agri-foodstuffs, automation-mechanics), with some overlapping with "Made in Italy". How can this model be assessed? This is the crucial question in the debate on the condition and prospects of the Italian productive system between the supporters of its capacity to adapt and the critics of economic dwarfism. A dispassionate judgement suggests that the prospects of "small is beautiful" have been superseded, but that the "declinist" view, that sees only the dangers of globalisation and the IT revolution for our SMEs is risky. The concept of irreversible crisis that prevails at present is limiting, both because it is not easy either to "invent", or to copy, a model of industrialisation, and because there is space for a strategic repositioning of the district enterprises. The book develops considerations in this direction, showing how an evolution of the district model is possible, focusing on: gains in productivity, scope economies (through diversification and expansion of the range of products), flexibility of organisation, capacity to meld tradition and innovation aiming at product quality, dimensional growth of the enterprises, new forms of financing, active presence on the international markets and valorisation of the resources of the territory. It is hence necessary to reactivate the behavioural functions of the entrepreneurs.

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14

Jing, Lanru, Ove Stephansson, and Hudson John. Coupled Thermo-Hydro-Mechanical-Chemical Processes in Geo-Systems. Elsevier Science & Technology Books, 2004.

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15

James, Jose, Sabu Thomas, and Pramoda Kumari Pallathadka. Polymers and Multicomponent Polymeric Systems: Thermal, Thermo-Mechanical and Dielectric Analysis. Taylor & Francis Group, 2020.

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16

James, Jose, Sabu Thomas, and Pramoda Kumari Pallathadka. Polymers and Multicomponent Polymeric Systems: Thermal, Thermo-Mechanical and Dielectric Analysis. Taylor & Francis Group, 2020.

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17

James, Jose, Sabu Thomas, and Pramoda Kumari Pallathadka. Polymers and Multicomponent Polymeric Systems: Thermal, Thermo-Mechanical and Dielectric Analysis. Taylor & Francis Group, 2020.

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18

James, Jose, Sabu Thomas, and Pramoda Kumari Pallathadka. Polymers and Multicomponent Polymeric Systems: Thermal, Thermo-Mechanical and Dielectric Analysis. Taylor & Francis Group, 2020.

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19

Mechanical system reliability for long life space systems: Final report. Nashville, Tenn: Dept. of Mechanical Engineering, Vanderbilt University, 1994.

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20

Coupled Thermo-Hydro-Mechanical-Chemical Processes in Geo-Systems - Fundamentals, Modelling, Experiments and Applications. Elsevier, 2004. http://dx.doi.org/10.1016/s1571-9960(04)x8014-9.

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21

Stephansson, Ove, John Hudson, and Lanru Jing. Coupled Thermo-Hydro-Mechanical-Chemical Processes in Geo-systems, Volume 2 (Geo-Engineering Book Series). Elsevier Science, 2004.

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22

Stephansson, Ove, John Hudson, and Lanru Jing. Coupled Thermo-Hydro-Mechanical-Chemical Processes in Geo-systems, Volume 2 (Geo-Engineering Book Series). Elsevier Science, 2004.

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23

Darrigol, Olivier. The Analogical Turn (1884–1887). Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198816171.003.0006.

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This chapter recounts how Boltzmann reacted to Hermann Helmholtz’s analogy between thermodynamic systems and a special kind of mechanical system (the “monocyclic systems”) by grouping all attempts to relate thermodynamics to mechanics, including the kinetic-molecular analogy, into a family of partial analogies all derivable from what we would now call a microcanonical ensemble. At that time, Boltzmann regarded ensemble-based statistical mechanics as the royal road to the laws of thermal equilibrium (as we now do). In the same period, he returned to the Boltzmann equation and the H theorem in reply to Peter Guthrie Tait’s attack on the equipartition theorem. He also made a non-technical survey of the second law of thermodynamics seen as a law of probability increase.

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24

Chiarandini, Paolo, and Giorgio Della Rocca. Post-operative ventilatory dysfunction management in the ICU. Oxford University Press, 2016. http://dx.doi.org/10.1093/med/9780199600830.003.0362.

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Alterations in respiratory function and gas exchanges are frequently seen in patients during anaesthesia and in the post-operative period. Mechanical ventilation and drugs such as neuromuscular blocking agents can alter normal function of the respiratory system and cause damage to lungs. Protective ventilation strategies should always be adopted intra-operatively in mechanically-ventilated patients. A neuromuscular monitoring-guided use of decurarizating agents and post-operative adequate analgesia techniques are recommended to avoid post-operative residual curarization and pain. Pneumonia is the most frequent infective complication, but at the moment there are no recommended clinical tools (scoring systems) to identify patients at high. A fast-track surgical approach and early can decrease the risk. Early mobilization and prophylactic low molecular weight heparins use have a well-documented efficacy on prevention of pulmonary embolism. There is still no general consensus on the widespread use of early NIV in post-operative patients, although in selected high-risk patients it could help respiratory recovery and reduce complications.

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25

Horing, Norman J. Morgenstern. Quantum Mechanical Ensemble Averages and Statistical Thermodynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0006.

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Chapter 6 introduces quantum-mechanical ensemble theory by proving the asymptotic equivalence of the quantum-mechanical, microcanonical ensemble average with the quantum grand canonical ensemble average for many-particle systems, based on the method of Darwin and Fowler. The procedures involved identify the grand partition function, entropy and other statistical thermodynamic variables, including the grand potential, Helmholtz free energy, thermodynamic potential, Gibbs free energy, Enthalpy and their relations in accordance with the fundamental laws of thermodynamics. Accompanying saddle-point integrations define temperature (inverse thermal energy) and chemical potential (Fermi energy). The concomitant emergence of quantum statistical mechanics and Bose–Einstein and Fermi–Dirac distribution functions are discussed in detail (including Bose condensation). The magnetic moment is derived from the Helmholtz free energy and is expressed in terms of a one-particle retarded Green’s function with an imaginary time argument related to inverse thermal energy. This is employed in a discussion of diamagnetism and the de Haas-van Alphen effect.

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26

Lei, Yuan. Introduction. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780198784975.003.0001.

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The ‘Introduction’ chapter presents the concept of the entire ventilator system, whose understanding is crucial for the clinician performing mechanical ventilation. Mechanical ventilation is a risky, expensive, and error-prone therapy, the author asserts, which is why it is so important to understand not just the clinical application of ventilation, but also the equipment used in ventilation therapy. Furthermore, the ventilator must be viewed within the context of the larger ventilation system. This chapter defines the book’s audiences and discusses its value to them.

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27

Shankar, R., Tangellapalli Srinivas, and N. Shankar Ganesh. Flexible Kalina Cycle Systems. Apple Academic Press, Incorporated, 2019.

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28

Braham, William W. Architecture and Systems Ecology: Thermodynamic Principles of Environmental Building Design, in Three Parts. Taylor & Francis Group, 2015.

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29

Braham, William W. Architecture and Systems Ecology: Thermodynamic Principles of Environmental Building Design, in Three Parts. Taylor & Francis Group, 2015.

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30

Swendsen, Robert H. An Introduction to Statistical Mechanics and Thermodynamics. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198853237.001.0001.

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This is a textbook on statistical mechanics and thermodynamics. It begins with the molecular nature of matter and the fact that we want to describe systems containing many (1020) particles. The first part of the book derives the entropy of the classical ideal gas using only classical statistical mechanics and Boltzmann’s analysis of multiple systems. The properties of this entropy are then expressed as postulates of thermodynamics in the second part of the book. From these postulates, the structure of thermodynamics is developed. Special features are systematic methods for deriving thermodynamic identities using Jacobians, the use of Legendre transforms as a basis for thermodynamic potentials, the introduction of Massieu functions to investigate negative temperatures, and an analysis of the consequences of the Nernst postulate. The third part of the book introduces the canonical and grand canonical ensembles, which are shown to facilitate calculations for many models. An explanation of irreversible phenomena that is consistent with time-reversal invariance in a closed system is presented. The fourth part of the book is devoted to quantum statistical mechanics, including black-body radiation, the harmonic solid, Bose–Einstein and Fermi–Dirac statistics, and an introduction to band theory, including metals, insulators, and semiconductors. The final chapter gives a brief introduction to the theory of phase transitions. Throughout the book, there is a strong emphasis on computational methods to make abstract concepts more concrete.

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31

Goodman, Lawrence R. Imaging the respiratory system in the critically ill. Oxford University Press, 2016. http://dx.doi.org/10.1093/med/9780199600830.003.0078.

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Routine radiographs are not cost effective in the intensive care unit (ICU) setting. Most published guidelines agree that radiographs are worthwhile after insertion of tubes or catheters, and in patients receiving mechanical ventilation. Otherwise, they are required only for change in the patient’s clinical status. Picture archiving and communication systems utilize digital imaging technology. They provide superior quality images, rapid image availability at multiple sites, and fewer repeat examinations, reducing both cost and patient radiation. Disadvantages of picture archiving and communication systems include expensive equipment and personnel required to keep them functioning. The majority of chest X-ray abnormalities in the ICU are best understood by paying careful attention to the initial appearance of the X-ray in relation to the patient’s onset of symptoms and the progression of abnormalities over the next few days.

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32

Amon, Cristina H. Cooling and Thermal Design of Electronic Systems: Presented at the 1995 Asme International Mechanical Engineering Congress and Exposition, November 12 (Htd). American Society of Mechanical Engineers, 1995.

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33

Price, Susanna, and Pascal Vranckx. Portable (short-term) mechanical circulatory support. Oxford University Press, 2015. http://dx.doi.org/10.1093/med/9780199687039.003.0030.

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Mechanical circulatory support can be used to resuscitate patients, as a stabilizing measure for angiography and prompt revascularization, or to buy time until more definite measures can be taken. In addition, there is experimental evidence that ventricular unloading of the left ventricle can significantly reduce the infarct size. Different systems for mechanical circulatory support are available to the medical community. Treatment options for mechanical circulatory support must be tailored to each patient in order to maximize the potential benefits and minimize the risk of detrimental effects. Intra-aortic balloon pumping is still the most widely used mechanical circulatory support therapy. The relative ease and speed with which this device can be applied to patients with a rapidly deteriorating haemodynamic picture have led to its widespread use as a first-line intervention among critically unstable patients. Where intra-aortic balloon pumping is inadequate, an immediate triage to a more advanced percutaneous (short-term) mechanical circulatory support may be warranted. Despite their extensive use, the utility of mechanical circulatory support devices in acute heart failure syndromes and cardiogenic shock remains uncertain. This chapter concentrates on the application of mechanical circulatory support relevant to the interventional cardiologist and cardiac intensive care physician.

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34

Price, Susanna, and Pascal Vranckx. Portable (short-term) mechanical circulatory support. Oxford University Press, 2016. http://dx.doi.org/10.1093/med/9780199687039.003.0030_update_001.

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Mechanical circulatory support can be used to resuscitate patients, as a stabilizing measure for angiography and prompt revascularization, or to buy time until more definite measures can be taken. In addition, there is experimental evidence that ventricular unloading of the left ventricle can significantly reduce the infarct size. Different systems for mechanical circulatory support are available to the medical community. Treatment options for mechanical circulatory support must be tailored to each patient in order to maximize the potential benefits and minimize the risk of detrimental effects. Intra-aortic balloon pumping is still the most widely used mechanical circulatory support therapy. The relative ease and speed with which this device can be applied to patients with a rapidly deteriorating haemodynamic picture have led to its widespread use as a first-line intervention among critically unstable patients. Where intra-aortic balloon pumping is inadequate, an immediate triage to a more advanced percutaneous (short-term) mechanical circulatory support may be warranted. Despite their extensive use, the utility of mechanical circulatory support devices in acute heart failure syndromes and cardiogenic shock remains uncertain. This chapter concentrates on the application of mechanical circulatory support relevant to the interventional cardiologist and cardiac intensive care physician.

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35

Price, Susanna, and Pascal Vranckx. Portable (short-term) mechanical circulatory support. Oxford University Press, 2018. http://dx.doi.org/10.1093/med/9780199687039.003.0030_update_002.

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Mechanical circulatory support can be used to resuscitate patients, as a stabilizing measure for angiography and prompt revascularization, or to buy time until more definite measures can be taken. In addition, there is experimental evidence that ventricular unloading of the left ventricle can significantly reduce the infarct size. Different systems for mechanical circulatory support are available to the medical community. Treatment options for mechanical circulatory support must be tailored to each patient in order to maximize the potential benefits and minimize the risk of detrimental effects. Intra-aortic balloon pumping is still the most widely used mechanical circulatory support therapy. The relative ease and speed with which this device can be applied to patients with a rapidly deteriorating haemodynamic picture have led to its widespread use as a first-line intervention among critically unstable patients. Where intra-aortic balloon pumping is inadequate, an immediate triage to a more advanced percutaneous (short-term) mechanical circulatory support may be warranted. Despite their extensive use, the utility of mechanical circulatory support devices in acute heart failure syndromes and cardiogenic shock remains uncertain. This chapter concentrates on the application of mechanical circulatory support relevant to the interventional cardiologist and cardiac intensive care physician.

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36

Chattopadhyay, Santanu. Thermal-Aware Testing of Digital VLSI Circuits and Systems. Taylor & Francis Group, 2018.

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37

Chattopadhyay, Santanu. Thermal-Aware Testing of Digital VLSI Circuits and Systems. Taylor & Francis Group, 2018.

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38

Chattopadhyay, Santanu. Thermal-Aware Testing of Digital VLSI Circuits and Systems. Taylor & Francis Group, 2018.

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39

Peuser, Felix A., Karl-Heinz Remmers, and Martin Schnauss. Solar Thermal Systems: Successful Planning and Construction. Earthscan Publications Ltd., 2002.

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40

Peuser, Felix A., Karl-Heinz Remmers, and Martin Schnauss. Solar Thermal Systems: Successful Planning and Construction. Taylor & Francis Group, 2013.

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41

Peuser, Felix A., Karl-Heinz Remmers, and Martin Schnauss. Solar Thermal Systems: Successful Planning and Construction. Taylor & Francis Group, 2013.

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42

Peuser, Felix A., Karl-Heinz Remmers, and Martin Schnauss. Solar Thermal Systems: Successful Planning and Construction. Taylor & Francis Group, 2013.

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43

Solar Thermal Systems: Successful Planning and Construction. Taylor & Francis Group, 2011.

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44

Peuser, Felix, Karl-Heinz Remmers, and Martin Schnauss. Solar Thermal Systems: Successful Planning and Construction. Routledge, 2013.

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45

Wentzel, Jolanda J., Ethan M. Rowland, Peter D. Weinberg, and Robert Krams. Biomechanical theories of atherosclerosis. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780198755777.003.0012.

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Atherosclerosis, the disease underlying most heart attacks and strokes, occurs predominantly at certain well-defined sites within the arterial system. Its development may therefore depend not only on systemic risk factors but also on locally varying biomechanical forces. There are three inter-related theories explaining the effect of biomechanics on atherosclerosis. In the first theory, a central role is played by lipid transport into the vessel wall, which varies as a result of mechanical forces. In the second theory, haemodynamic wall shear stress-the frictional force per unit area of endothelium arising from the movement of blood-activates signalling pathways that affect endothelial cell properties. In the third, strain-the stretch of the wall arising from changes in blood pressure-is the key biomechanical trigger. All three theories are discussed from historical, molecular, and clinical perspectives.

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46

Glennan, Stuart. Postscript. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198779711.003.0009.

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As I have worked on this book, I have often been struck by the audacity of its title. The phrase “the New Mechanical Philosophy” was not my own, but still, to appropriate the venerable tradition of mechanical philosophy, to call it new, and to add a definite article to boot—maybe that’s just too much. Nonetheless I have stuck with the title, and the project, because I think it reflects both the continuity with the history of science and its philosophy, and a sea change in philosophical thinking in the new century. Mechanical philosophy is as old as Democritus; it was a central theme in the scientific revolution; it has helped drive research and debates on the nature of life and the nature of mind. But the New Mechanical Philosophy is new in large part because it tracks changes in the way science is done. Over recent decades, the sciences have developed increasing, if still rudimentary, capacities to analyze complex and heterogeneous systems—cells, brains, ecosystems, economies, and so on. Whereas in earlier epochs many of the greatest scientific achievements have been to understand the basic building blocks—the laws of electricity and magnetism or the structure of the hydrogen atom—scientists are now able to greater and greater extents understand how these things are put together to make the universe we know. Mechanical philosophy is always about understanding how things are put together, so it is a philosophy for this time....

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47

Hough, Catherine L. Chronic critical illness. Oxford University Press, 2016. http://dx.doi.org/10.1093/med/9780199600830.003.0377.

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Chronic critical illness (CCI) is common and describes a state of prolonged critical illness, in which patients have persisting organ failures requiring treatment in an intensive care setting. There are many different definitions of CCI, with most including prolonged (> 96 hours) mechanical ventilation. Advanced age, higher severity of illness, and poor functional status prior to critical illness are all important risk factors, but prediction of CCI is imperfect. Although requirement for mechanical ventilation is the hallmark, CCI encompasses much more than the respiratory system, with effects on metabolism, skin, brain, and neuromuscular function. During CCI, patients have a high burden of symptoms and impaired capacity to communicate their needs. Mortality and quality of life are generally poor, but highly variable, with 1-year mortality over 50% and most survivors suffering permanent cognitive impairment and functional dependence. Patients at highest and lowest risk for mortality can be identified using a simple prediction rule. Caring for the chronically critically ill is a substantial burden both to patients’ families and to the health care system as a whole. Further research is needed in order to improve care and outcomes for CCI patients and their families.

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48

Deruelle, Nathalie, and Jean-Philippe Uzan. Interacting charges II. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0039.

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This chapter continues the discussion from the previous chapter. The motion of a charge (m,q) in the field of another charge (m′,q′) and in its own field can now be studied in the lowest orders of the velocities directly using the equation of motion obtained in the preceding chapter. However, the features of this motion are revealed more easily by deriving them from the Darwin Lagrangian. This allows for a rigorous establishment of a balance between the energy radiated by the system and the mechanical energy lost by the system. The chapter concludes this general study of the electromagnetic radiation of a system of charges by outlining the ‘post-Minkowski’ approach based on iteration in the ‘coupling constant’ qq′ rather than in the velocities.

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49

Nolte, David D. Introduction to Modern Dynamics. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198844624.001.0001.

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Introduction to Modern Dynamics: Chaos, Networks, Space and Time (2nd Edition) combines the topics of modern dynamics—chaos theory, dynamics on complex networks and the geometry of dynamical spaces—into a coherent framework. This text is divided into four parts: Geometric Mechanics, Nonlinear Dynamics, Complex Systems, and Relativity. These topics share a common and simple mathematical language that helps students gain a unified physical intuition. Geometric mechanics lays the foundation and sets the tone for the rest of the book by emphasizing dynamical spaces, like state space and phase space, whose geometric properties define the set of all trajectories through those spaces. The section on nonlinear dynamics has chapters on chaos theory, synchronization, and networks. Chaos theory provides the language and tools to understand nonlinear systems, introducing fixed points that are classified through stability analysis and nullclines that shepherd system trajectories. Synchronization and networks are central paradigms in this book because they demonstrate how collective behavior emerges from the interactions of many individual nonlinear elements. The section on complex systems contains chapters on neural dynamics, evolutionary dynamics, and economic dynamics. The final section contains chapters on metric spaces and the special and general theories of relativity. In the second edition, sections on conventional topics, like applications of Lagrangians, have been strengthened, as well as being updated to provide a modern perspective. Several of the introductory chapters have been rearranged for improved logical flow and there are expanded homework problems at the end of each chapter.

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50

Kaloshin, Vadim, and Ke Zhang. Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691202525.001.0001.

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Arnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was discovered by Vladimir Arnold in 1963, it has attracted the efforts of some of the most prominent researchers in mathematics. The question is whether a typical perturbation of a particular system will result in chaotic or unstable dynamical phenomena. This book provides the first complete proof of Arnold diffusion, demonstrating that that there is topological instability for typical perturbations of five-dimensional integrable systems (two and a half degrees of freedom). This proof realizes a plan John Mather announced in 2003 but was unable to complete before his death. The book follows Mather's strategy but emphasizes a more Hamiltonian approach, tying together normal forms theory, hyperbolic theory, Mather theory, and weak KAM theory. Offering a complete, clean, and modern explanation of the steps involved in the proof, and a clear account of background material, the book is designed to be accessible to students as well as researchers. The result is a critical contribution to mathematical physics and dynamical systems, especially Hamiltonian systems.

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