Raymond Brun
- Published in print:
- 2009
- Published Online:
- May 2009
- ISBN:
- 9780199552689
- eISBN:
- 9780191720277
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199552689.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
The high enthalpy gas flows, associating high velocities, and high temperatures, are the scene of physical and chemical processes such as molecular vibrational excitation, dissociation, ionization, ...
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The high enthalpy gas flows, associating high velocities, and high temperatures, are the scene of physical and chemical processes such as molecular vibrational excitation, dissociation, ionization, or various reactions. The characteristic times of these processes are of the same order of magnitude as aerodynamic characteristic times so that these reactive media are generally in thermodynamic and chemical non-equilibrium. This book presents a general introductory study of these media. In a first part their fundamental statistical aspects are described, starting from their discrete structure and taking into account the interactions between elementary particles: the transport phenomena, relaxation, and kinetics as well as their coupling are thus analysed and illustrated by many examples. The second part of the work is devoted to the macroscopic aspects of the reactive flows including shock waves, hypersonic expansions, flows around bodies, and boundary layers. Experimental data on vibrational relaxation times, vibrational populations, and kinetic rate constants are also presented. Finally, experimental aspects of reactive flows, their simulation in shock tube and shock tunnel are described as well as their applications, particularly in the aero-spatial domain.Less
The high enthalpy gas flows, associating high velocities, and high temperatures, are the scene of physical and chemical processes such as molecular vibrational excitation, dissociation, ionization, or various reactions. The characteristic times of these processes are of the same order of magnitude as aerodynamic characteristic times so that these reactive media are generally in thermodynamic and chemical non-equilibrium. This book presents a general introductory study of these media. In a first part their fundamental statistical aspects are described, starting from their discrete structure and taking into account the interactions between elementary particles: the transport phenomena, relaxation, and kinetics as well as their coupling are thus analysed and illustrated by many examples. The second part of the work is devoted to the macroscopic aspects of the reactive flows including shock waves, hypersonic expansions, flows around bodies, and boundary layers. Experimental data on vibrational relaxation times, vibrational populations, and kinetic rate constants are also presented. Finally, experimental aspects of reactive flows, their simulation in shock tube and shock tunnel are described as well as their applications, particularly in the aero-spatial domain.
C. N. Hinshelwood
- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198570257
- eISBN:
- 9780191717659
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570257.003.0019
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter discusses the role of energy and entropy in chemical reactions. Topics covered include chain reactions, branching chains, catalysis, and the development of chemical kinetics.
This chapter discusses the role of energy and entropy in chemical reactions. Topics covered include chain reactions, branching chains, catalysis, and the development of chemical kinetics.
Daniel T. Gillespie and Linda R. Petzold
- Published in print:
- 2006
- Published Online:
- August 2013
- ISBN:
- 9780262195485
- eISBN:
- 9780262257060
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262195485.003.0016
- Subject:
- Mathematics, Mathematical Biology
This chapter discusses concepts and techniques for mathematically describing and numerically simulating chemical systems that into account discreteness and stochasticity. The chapter is organized as ...
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This chapter discusses concepts and techniques for mathematically describing and numerically simulating chemical systems that into account discreteness and stochasticity. The chapter is organized as follows. Section 16.2 outlines the foundations of “stochastic chemical kinetics” and derives the chemical master equation (CME)—the time-evolution equation for the probability function of the system’s state. The CME, however, cannot be solved, for any but the simplest of systems. But numerical realizations (sample trajectories in state space) of the stochastic process defined by the CME can be generated using a Monte Carlo strategy called the stochastic simulation algorithm (SSA), which is derived and discussed in Section 16.3. Section 16.4 describes an approximate accelerated algorithm known as tau-leaping. Section 16.5 shows how, under certain conditions, tau-leaping further approximates to a stochastic differential equation called the chemical Langevin equation (CLE), and then how the CLE can in turn sometimes be approximated by an ordinary differential equation called the reaction rate equation (RRE). Section 16.6 describes the problem of stiffness in a deterministic (RRE) context, along with its standard numerical resolution: implicit method. Section 16.7 presents an implicit tau-leaping algorithm for stochastically simulating stiff chemical systems. Section 16.8 concludes by describing and illustrating yet another promising algorithm for dealing with stiff stochastic chemical systems, which is called the slow-scale SSA.Less
This chapter discusses concepts and techniques for mathematically describing and numerically simulating chemical systems that into account discreteness and stochasticity. The chapter is organized as follows. Section 16.2 outlines the foundations of “stochastic chemical kinetics” and derives the chemical master equation (CME)—the time-evolution equation for the probability function of the system’s state. The CME, however, cannot be solved, for any but the simplest of systems. But numerical realizations (sample trajectories in state space) of the stochastic process defined by the CME can be generated using a Monte Carlo strategy called the stochastic simulation algorithm (SSA), which is derived and discussed in Section 16.3. Section 16.4 describes an approximate accelerated algorithm known as tau-leaping. Section 16.5 shows how, under certain conditions, tau-leaping further approximates to a stochastic differential equation called the chemical Langevin equation (CLE), and then how the CLE can in turn sometimes be approximated by an ordinary differential equation called the reaction rate equation (RRE). Section 16.6 describes the problem of stiffness in a deterministic (RRE) context, along with its standard numerical resolution: implicit method. Section 16.7 presents an implicit tau-leaping algorithm for stochastically simulating stiff chemical systems. Section 16.8 concludes by describing and illustrating yet another promising algorithm for dealing with stiff stochastic chemical systems, which is called the slow-scale SSA.
Dennis Sherwood and Paul Dalby
- Published in print:
- 2018
- Published Online:
- August 2018
- ISBN:
- 9780198782957
- eISBN:
- 9780191826177
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198782957.003.0014
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
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, ...
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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.Less
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.
Giovanni Zocchi
- Published in print:
- 2018
- Published Online:
- January 2019
- ISBN:
- 9780691173863
- eISBN:
- 9781400890064
- Item type:
- book
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691173863.001.0001
- Subject:
- Physics, Soft Matter / Biological Physics
This book presents a dynamic new approach to the physics of enzymes and DNA from the perspective of materials science. Unified around the concept of molecular deformability—how proteins and DNA ...
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This book presents a dynamic new approach to the physics of enzymes and DNA from the perspective of materials science. Unified around the concept of molecular deformability—how proteins and DNA stretch, fold, and change shape—the book describes the complex molecules of life from the innovative perspective of materials properties and dynamics, in contrast to structural or purely chemical approaches. It covers a wealth of topics, including nonlinear deformability of enzymes and DNA; the chemo-dynamic cycle of enzymes; supra-molecular constructions with internal stress; nano-rheology and viscoelasticity; and chemical kinetics, Brownian motion, and barrier crossing. Essential reading for researchers in materials science, engineering, and nanotechnology, the book also describes the landmark experiments that have established the materials properties and energy landscape of large biological molecules. The book gives graduate students a working knowledge of model building in statistical mechanics, making it an essential resource for tomorrow's experimentalists in this cutting-edge field. In addition, mathematical methods are introduced in the bio-molecular context. The result is a generalized approach to mathematical problem solving that enables students to apply their findings more broadly.Less
This book presents a dynamic new approach to the physics of enzymes and DNA from the perspective of materials science. Unified around the concept of molecular deformability—how proteins and DNA stretch, fold, and change shape—the book describes the complex molecules of life from the innovative perspective of materials properties and dynamics, in contrast to structural or purely chemical approaches. It covers a wealth of topics, including nonlinear deformability of enzymes and DNA; the chemo-dynamic cycle of enzymes; supra-molecular constructions with internal stress; nano-rheology and viscoelasticity; and chemical kinetics, Brownian motion, and barrier crossing. Essential reading for researchers in materials science, engineering, and nanotechnology, the book also describes the landmark experiments that have established the materials properties and energy landscape of large biological molecules. The book gives graduate students a working knowledge of model building in statistical mechanics, making it an essential resource for tomorrow's experimentalists in this cutting-edge field. In addition, mathematical methods are introduced in the bio-molecular context. The result is a generalized approach to mathematical problem solving that enables students to apply their findings more broadly.
Giovanni Zocchi
- Published in print:
- 2018
- Published Online:
- January 2019
- ISBN:
- 9780691173863
- eISBN:
- 9781400890064
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691173863.003.0004
- Subject:
- Physics, Soft Matter / Biological Physics
This chapter discusses the deformability of enzymes. This property allows enzymes to couple a chemical process to a cycle of deformations of the molecule, which can perform a task in the cell. This ...
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This chapter discusses the deformability of enzymes. This property allows enzymes to couple a chemical process to a cycle of deformations of the molecule, which can perform a task in the cell. This is the celebrated “molecular machine” aspect of enzymes. The dynamics of enzyme deformability presents universal features when ensemble-averaged trajectories are examined. The mechanical response is viscoelastic. The remainder of the chapter covers the nonlinearity of the enzyme's mechanics, timescales, enzymatic cycle and viscoelasticity, internal dissipation, origin of the restoring force g, models based on chemical kinetics, different levels of microscopic description, connection to information flow, normal mode analysis, many states of the folded protein, and interesting topics in nonequilibrium thermodynamics relating to enzyme dynamics.Less
This chapter discusses the deformability of enzymes. This property allows enzymes to couple a chemical process to a cycle of deformations of the molecule, which can perform a task in the cell. This is the celebrated “molecular machine” aspect of enzymes. The dynamics of enzyme deformability presents universal features when ensemble-averaged trajectories are examined. The mechanical response is viscoelastic. The remainder of the chapter covers the nonlinearity of the enzyme's mechanics, timescales, enzymatic cycle and viscoelasticity, internal dissipation, origin of the restoring force g, models based on chemical kinetics, different levels of microscopic description, connection to information flow, normal mode analysis, many states of the folded protein, and interesting topics in nonequilibrium thermodynamics relating to enzyme dynamics.
Mary Jo Nye
- Published in print:
- 2011
- Published Online:
- September 2013
- ISBN:
- 9780226610634
- eISBN:
- 9780226610658
- Item type:
- chapter
- Publisher:
- University of Chicago Press
- DOI:
- 10.7208/chicago/9780226610658.003.0004
- Subject:
- History, History of Science, Technology, and Medicine
This chapter examines Michael Polanyi's work in surface chemistry and X-ray diffraction by way of analyzing how he later drew upon his experiences in order to develop the notion of the “typical” or ...
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This chapter examines Michael Polanyi's work in surface chemistry and X-ray diffraction by way of analyzing how he later drew upon his experiences in order to develop the notion of the “typical” or ordinary scientist who is at the heart of everyday scientific practice. Polanyi's investigations in these two fields generated greater skepticism and less recognition from his colleagues than his results in chemical kinetics and reaction dynamics, which are the subject of the next chapter. Polanyi's reflections on resistance to his work turned him to sociological, rather than logical, explanation, for the mechanism by which scientific priority and recognition are accorded within the structure of scientific authority. The chapter concludes with an analysis of how Polanyi reinterpreted his work on surface chemistry and X-ray diffraction within a sociological framework in two essays published in the early 1960s.Less
This chapter examines Michael Polanyi's work in surface chemistry and X-ray diffraction by way of analyzing how he later drew upon his experiences in order to develop the notion of the “typical” or ordinary scientist who is at the heart of everyday scientific practice. Polanyi's investigations in these two fields generated greater skepticism and less recognition from his colleagues than his results in chemical kinetics and reaction dynamics, which are the subject of the next chapter. Polanyi's reflections on resistance to his work turned him to sociological, rather than logical, explanation, for the mechanism by which scientific priority and recognition are accorded within the structure of scientific authority. The chapter concludes with an analysis of how Polanyi reinterpreted his work on surface chemistry and X-ray diffraction within a sociological framework in two essays published in the early 1960s.
