Search Results

What is Special Relativity?

Harvey R. Brown

in Physical Relativity: Space-time structure from a dynamical perspective

This chapter begins with a discussion of Minkowski's geometrization of special relativity (SR). It then discusses Minkowski space-time, what absolute geometry explains, and special relativity. It is ... More

This chapter begins with a discussion of Minkowski's geometrization of special relativity (SR). It then discusses Minkowski space-time, what absolute geometry explains, and special relativity. It is argued that Einstein's contribution was not to establish a clear-cut divide between kinematics and dynamics, but the demonstration (a) of the full operational significance of the Lorentz transformations, and (b) that the latter could be obtained by imposing simple phenomenological constraints on the nature of the fundamental interactions in physics.Less

 Karlsruhe: 1919–1920

William Taussig Scott and Martin X. Moleski

in Michael Polanyi: Scientist and Philosopher

In preparation for a scientific career in Germany, Polanyi chose Australian citizenship and was baptized as a Roman Catholic. During his doctoral studies at Karlsruhe, Polanyi completed his thesis on ... More

In preparation for a scientific career in Germany, Polanyi chose Australian citizenship and was baptized as a Roman Catholic. During his doctoral studies at Karlsruhe, Polanyi completed his thesis on adsorption and began to work on reaction kinetics. He became engaged to Magda Kemeny, who was also working on a doctorate at the University.Less

Introduction to neutron powder diffraction

Erich H. Kisi and Christopher J. Howard

in Applications of Neutron Powder Diffraction

This chapter opens with brief descriptions of neutrons, powders (polycrystalline materials), and diffraction, followed by an account of how the unique properties of neutrons and their interaction ... More

This chapter opens with brief descriptions of neutrons, powders (polycrystalline materials), and diffraction, followed by an account of how the unique properties of neutrons and their interaction with matter define a role for neutron powder diffraction in the study of condensed matter. The concepts are refined within an historical account of the development of neutron powder diffraction and its applications. Reference are made to the earliest demonstration of neutron diffraction, to the development of neutron sources (research reactors and accelerator-based sources), and to applications ranging from early investigation of simple crystal and magnetic structures to the more recent investigations of kinetic processes and complex crystal structures (high-temperature superconductors, fullerenes).Less

New directions

Erich H. Kisi and Christopher J. Howard

in Applications of Neutron Powder Diffraction

This chapter highlights some recent and forthcoming developments that impact on the practice of neutron powder diffraction. New and more powerful neutron sources are now in service or under ... More

This chapter highlights some recent and forthcoming developments that impact on the practice of neutron powder diffraction. New and more powerful neutron sources are now in service or under construction. At the same time, there has been continuing development of critical components, such as neutron guides (supermirrors), compact collimators, focussing monochromators, and fast detection systems. These developments have been incorporated into new neutron powder diffractometers, for high resolution, high intensity, and residual stress applications. Advances in data analysis discussed include an increased focus on the use of group theory, the analysis of the total scattering, e.g., via pair distribution functions, mapping by the maximum entropy method, and rapid handling of extensive data sets. Frontier applications range from fast reaction kinetics (combustion synthesis) to the structure refinement of biological molecules. It is suggested that application of neutron powder diffraction for simultaneous investigation of structure and microstructure will assume increasing importance.Less

ENERGY AND ENTROPY FACTORS IN REACTION VELOCITY

C. N. Hinshelwood

in The Structure of Physical Chemistry

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.

Epilogue: A theory of crystallization?

ANGELO GAVEZZOTTI

in Molecular Aggregation: Structure analysis and molecular simulation of crystals and liquids

In molecular crystallisation there are no first-rate laws, very few second-rate laws and many third-rate laws. The first-rate laws of thermodynamics become in such a context third-rate laws because ... More

In molecular crystallisation there are no first-rate laws, very few second-rate laws and many third-rate laws. The first-rate laws of thermodynamics become in such a context third-rate laws because the concept of phase is ill-defined in most if not all of the transformations involved in the evolution from a disperse molecular system to a molecular aggregate. There is a wide gap between the ever increasing ease with which the aggregation and crystallisation phenomenon can be studied thanks to calorimetry, X-ray diffraction, nuclear magnetic resonance, atomic force microscopy, molecular simulation, and the degree of understanding and control that may be gained from these experiments. If even laws are weak, the way to a theory seems even more problematic. This chapter examines whether a theory of crystallisation currently exists, laws and theories in chemistry, stages of molecular aggregation in oligomers, nanoparticles and mesoparticles, aggregation of macroscopic crystals, and the thermodynamics, kinetics, and symmetry of molecular aggregation.Less

Modeling Biological Systems

Wolfgang Banzhaf and Lidia Yamamoto

in Artificial Chemistries

This chapter is devoted to one of the main applications of artificial chemistries, the modeling of biological systems. The chapter starts at the molecular level, with algorithms that model RNA and ... More

This chapter is devoted to one of the main applications of artificial chemistries, the modeling of biological systems. The chapter starts at the molecular level, with algorithms that model RNA and protein folding. An introduction to models of enzymatic reactions and the binding of proteins to genes then follows. Models of the dynamics of biochemical pathways are discussed next, with focus on metabolic networks. An overview of algorithms to simulate the large-scale reaction networks common in biology is presented afterwards. Genetic regulatory networks (GRNs) are examples of such large-scale reaction networks, and are discussed next. A treatment of cell differentiation, multicellularity and morphogenesis concludes the chapter.Less

Kinetic and perturbation studies

Dmitri I. Svergun, Michel H. J. Koch, Peter A. Timmins, and Roland P. May

in Small Angle X-Ray and Neutron Scattering from Solutions of Biological Macromolecules

Following a brief historical introduction, the difference between dynamics and kinetics is explained to clarify that SAS produces kinetic information. Data interpretation methods are based on those ... More

Following a brief historical introduction, the difference between dynamics and kinetics is explained to clarify that SAS produces kinetic information. Data interpretation methods are based on those developed for mixtures. An overview of the main perturbation methods (temperature, pressure, mixing, light and fields) and the relevant SAS instrumentation is presented. Examples of applications illustrate some of the results obtained for assembly and (un)folding phenomena induced by different rates of temperature or pressure change. An extensive survey of protein and RNA (un)folding studies, as well as studies of the kinetics of allosteric transitions and virus assembly relying mostly on fast mixing, is also made. Even if they miss the early stages of the transitions, time-resolved measurements have provided new insights into many of these processes. Further progress in time-resolution can be expected in cases where light-triggered fast pump–probe experiments are possible, as illustrated by recent experiments on CO-haemoglobin.Less

Conclusion

Alex C. Purves

in Homer and the Poetics of Gesture

This conclusion briefly restates the argument of the book and considers the broader implications of studying Homeric formularity and agency through embodied action. It places in juxtaposition the ... More

This conclusion briefly restates the argument of the book and considers the broader implications of studying Homeric formularity and agency through embodied action. It places in juxtaposition the kinetic reflexes of the hero and the aesthetic reflexes of the poet, in an attempt to open up new ways of reading literature through and within the body. The result is a book that thinks in new terms about epic repetition and the actions of Homeric characters within the constraints of oral poetry. I end the conclusion by suggesting that gesture’s quiet capacity to act on its own accord and to exhibit its own form of autonomy leads to novel possibilities for our consideration of Homeric character and agency.Less

Numerical Simulation for Biochemical Kinetics

Daniel T. Gillespie and Linda R. Petzold

in System Modeling in Cellular Biology: From Concepts to Nuts and Bolts

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 ... More

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

Introduction to Chemical Kinetic Processes

John Ross, Igor Schreiber, and Marcel O. Vlad

in Determination of Complex Reaction Mechanisms: Analysis of Chemical, Biological, and Genetic Networks

It is useful to have a brief discussion of some kinetic processes that we shall treat in later chapters. Some, but not all, of the material in this chapter is presented in [1] in more detail. A ... More

It is useful to have a brief discussion of some kinetic processes that we shall treat in later chapters. Some, but not all, of the material in this chapter is presented in [1] in more detail. A macroscopic, deterministic chemical reacting system consists of a number of different species, each with a given concentration (molecules or moles per unit volume). The word “macroscopic” implies that the concentrations are of the order of Avogadro’s number (about 6.02 × 1023) per liter. The concentrations are constant at a given instant, that is, thermal fluctuations away from the average concentration are negligibly small (more in section 2.3). The kinetics in many cases, but far from all, obeys mass action rate expressions of the type . . . dA/dt = k(T )AαBβ . . . (2.1) . . . where T is temperature, A is the concentration of species A, the same for B, and possibly other species indicated by dots in the equation, and α and β are empirically determined “orders” of reaction. The rate coefficient k is generally a function of temperature and frequently a function of T only. The dependence of k on T is given empirically by the Arrhenius equation . . . k(T ) = C exp−Ea/RT (2.2) . . . where C, the frequency factor, is either nearly constant or a weakly dependent function of temperature, and Ea is the activation energy. Rate coefficients are averages of reaction cross-sections, as measured for example by molecular beam experiments. The a priori calculation of cross-sections from quantum mechanical fundamentals is extraordinarily difficult and has been done to good accuracy only for the simplest trimolecular systems (such as D + H2). A widely used alternative approach is based on activated complex theory. In its simplest form, two reactants collide and form an activated complex, said to be in equilibrium. One degree of freedom of the complex, a vibration, is allowed to lead to the dissociation of the complex to products, and the rate of that dissociation is taken to be the rate of the reaction. Less

Kinetics of heterogeneous processes

Boris S. Bokstein, Mikhail I. Mendelev, and David J. Srolovitz

in Thermodynamics and Kinetics in Materials Science: A Short Course

Most practical reactions that occur in synthesizing or processing materials are heterogeneous. These include oxidation, reduction reactions, dissolution of solids in ... More

Most practical reactions that occur in synthesizing or processing materials are heterogeneous. These include oxidation, reduction reactions, dissolution of solids in liquids, and most solid-state phase transformations. Consider the oxidation of a metal by exposure of a solid metal to an atmosphere with a finite partial pressure of oxygen. In order for oxidation to occur, molecular oxygen must dissociate into atomic oxygen on the metal surface. In some cases, atomic oxygen diffuses into the metal and reacts to form an internal oxide, while in others, the reaction occurs at the surface. In the latter case, thickening of the oxide layer requires either metal or oxygen diffusion through the growing oxide layer. This example demonstrates that heterogeneous processes commonly involve several steps. The first step is usually the transport of a reactant through one of the phases to the interface. The second is the adsorption (segregation) or chemical reaction on the interface. Finally, the last third step is the diffusion of the products into the growing phase or the desorption of the product. Since the entire heterogeneous process is a type of complex reaction, there is usually one step that controls the rate of the process, that is, is the rate-determining step. Recall that the rate-determining step is the slowest (fastest) step for a consecutive (parallel) reaction (see Sections 8.2.1 and 8.2.2). Consider the case of a consecutive heterogeneous reaction in which one of the reactants is transported through the fluid phase to the solid–fluid interface, where a first-order reaction takes place. The reaction rate ωr in such a case is ωr=kcx, where cx is the concentration of the reactant on the interface. Since the reactant is consumed at the interface, cx is smaller than the reactant concentration far from the interface, c0. It is usually easier to measure the reactant concentration in the bulk fluid. Therefore, it is convenient, to rewrite the reaction rate in terms of the bulk concentration in the fluid and an effective rate constant . . . ωr = kcx = keffc0. (11.1) . . . It is easiest to see the relation between keff and k by considering the steady-state case. Less

Dynamics of Enzyme Action

Giovanni Zocchi

in Molecular Machines: A Materials Science Approach

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 ... More

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

Steady-state kinetics

Athel Cornish-Bowden

in Spectrophotometry and Spectrofluorimetry: A Practical Approach

All of chemical kinetics is based on rate equations, but this is especially true of steady-state enzyme kinetics: in other applications a rate equation can be regarded as a differential equation ... More

All of chemical kinetics is based on rate equations, but this is especially true of steady-state enzyme kinetics: in other applications a rate equation can be regarded as a differential equation that has to be integrated to give the function of real interest, whereas in steady-state enzyme kinetics it is used as it stands. Although the early enzymologists tried to follow the usual chemical practice of deriving equations that describe the state of reaction as a function of time there were too many complications, such as loss of enzyme activity, effects of accumulating product etc., for this to be a fruitful approach. Rapid progress only became possible when Michaelis and Menten (1) realized that most of the complications could be removed by extrapolating back to zero time and regarding the measured initial rate as the primary observation. Since then, of course, accumulating knowledge has made it possible to study time courses directly, and this has led to two additional subdisciplines of enzyme kinetics, transient-state kinetics, which deals with the time regime before a steady state is established, and progress-curve analysis, which deals with the slow approach to equilibrium during the steady-state phase. The former of these has achieved great importance but is regarded as more specialized. It is dealt with in later chapters of this book. Progress-curve analysis has never recovered the importance that it had at the beginning of the twentieth century. Nearly all steps that form parts of the mechanisms of enzyme-catalysed reactions involve reactions of a single molecule, in which case they typically follow first-order kinetics: . . . v = ka . . . . . . 1 . . . or they involve two molecules (usually but not necessarily different from one another) and typically follow second-order kinetics: . . . v = kab . . . . . . 2 . . . In both cases v represents the rate of reaction, and a and b are the concentrations of the molecules involved, and k is a rate constant. Because we shall be regarding the rate as a quantity in its own right it is not usual in steady-state kinetics to represent it as a derivative such as -da/dt. Less

Stopped-flow spectroscopy

M.T. Wilson and J. Torres

in Spectrophotometry and Spectrofluorimetry: A Practical Approach

There was a time, fortunately some years ago now, when to undertake rapid kinetic measurements using a stopped-flow spectrophotometer verged on the heroic. One needed to be armed with knowledge of ... More

There was a time, fortunately some years ago now, when to undertake rapid kinetic measurements using a stopped-flow spectrophotometer verged on the heroic. One needed to be armed with knowledge of amplifiers, light sources, oscilloscopes etc. and ideally one’s credibility was greatly enhanced were one to build one’s own instrument. Analysis of the data was similarly difficult. To obtain a single rate constant might involve a wide range of skills in addition to those required for the chemical/biochemical manipulation of the system and could easily include photography, developing prints and considerable mathematical agility. Now all this has changed and, from the point of view of the scientist attempting to solve problems through transient kinetic studies, a good thing too! Very high quality data can readily be obtained by anyone with a few hours training and the ability to use a mouse and ‘point and click’ programs. Excellent stopped -flow spectrophotometers can be bought which are reliable, stable, sensitive and which are controlled by computers able to signal-average and to analyse, in seconds, kinetic progress curves in a number of ways yielding rate constants, amplitudes, residuals and statistics. Because it is now so easy, from the technical point of view, to make measurement and to do so without an apprenticeship in kinetic methods, it becomes important to make sure that one collects data that are meaningful and open to sensible interpretation. There are a number of pitfalls to avoid. The emphasis of this article is, therefore, somewhat different to that written by Eccleston (1) in an earlier volume of this series. Less time will be spent on consideration of the hardware, although the general principles are given, but the focus will be on making sure that the data collected means what one thinks it means and then how to be sure one is extracting kinetic parameters from this in a sensible way. With the advent of powerful, fast computers it has now become possible to process very large data sets quickly and this has paved the way for the application of ‘rapid scan’ devices (usually, but not exclusively, diode arrays), which allow complete spectra to be collected at very short time intervals during a reaction. Less