Size-Distribution Analysis of Macromolecules by Sedimentation Velocity Ultracentrifugation and Lamm Equation Modeling

The development of regional metamorphism in areas of thickened continental crust is investigated in terms of the major controls on regional-scale thermal regimes. These are: the total radiogenic heat supply within the thickened crust, the supply of heat from the mantle, the thermal conductivity of the medium and the length and time scales of erosion of the continental crust. The orogenic episode is regarded as consisting of a relatively rapid phase of crustal thickening, during which little temperature change occurs in individual rocks, followed by a lengthier phase of erosion, at the end of which the crust is at its original thickness. The principal features of pressure-temperature-time (PTt) paths followed by rocks in this environment are a period of thermal relaxation, during which the temperature rises towards the higher geotherm that would be supported by the thickened crust, followed by a period of cooling as the rock approaches the cold land surface. The temperature increase that occurs is governed by the degree of thickening of the crust, its conductivity and the time that elapses before the rock is exhumed sufficiently to be affected by the proximity of the cold upper boundary. For much of the parameter range considered, the heating phase encompasses a considerable portion of the exhumation (decompression) part of the PTt path. In addition to the detailed calculation of PTt paths we present an idealized model of the thickening and exhumation process, which may be used to make simple calculations of the amount of heating to be expected during a given thickening and exhumation episode and of the depth at which a rock will start to cool on its ascent path. An important feature of these PTt paths is that most of them lie within 50 °C of the maximum temperature attained for one third or more of the total duration of their burial and uplift, and for a geologically plausible range of erosion rates the rocks do not begin to cool until they have completed 20 to 40 per cent of the total uplift they experience. Considerable melting of the continental crust is a likely consequence of thickening of crust with an average continental geotherm. A companion paper discusses these results in the context of attempts to use metamorphic petrology data to give information on tectonic processes. © 1984 Oxford University Press.

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Pressure-Temperature-Time Paths of Regional Metamorphism I. Heat Transfer during the Evolution of Regions of Thickened Continental Crust

Computational Fluid Dynamics: Principles and Applications, Third Edition presents students, engineers, and scientists with all they need to gain a solid understanding of the numerical methods and principles underlying modern computation techniques in fluid dynamics By providing complete coverage of the essential knowledge required in order to write codes or understand commercial codes, the book gives the reader an overview of fundamentals and solution strategies in the early chapters before moving on to cover the details of different solution techniques

	This updated edition includes new worked programming examples, expanded coverage and recent literature regarding incompressible flows, the Discontinuous Galerkin Method, the Lattice Boltzmann Method, higher-order spatial schemes, implicit Runge-Kutta methods and parallelization

	An accompanying companion website contains the sources of 1-D and 2-D Euler and Navier-Stokes flow solvers (structured and unstructured) and grid generators, along with tools for Von Neumann stability analysis of 1-D model equations and examples of various parallelization techniques



	
		Will provide you with the knowledge required to develop and understand modern flow simulation codes
	
		Features new worked programming examples and expanded coverage of incompressible flows, implicit Runge-Kutta methods and code parallelization, among other topics
	
		Includes accompanying companion website that contains the sources of 1-D and 2-D flow solvers as well as grid generators and examples of parallelization techniques

Computational Fluid Dynamics: Principles and Applications Ed. 3

Advances in scientific computing have made modelling and simulation an important part of the decision-making process in engineering, science, and public policy. This book provides a comprehensive and systematic development of the basic concepts, principles, and procedures for verification and validation of models and simulations. The emphasis is placed on models that are described by partial differential and integral equations and the simulations that result from their numerical solution. The methods described can be applied to a wide range of technical fields, from the physical sciences, engineering and technology and industry, through to environmental regulations and safety, product and plant safety, financial investing, and governmental regulations. This book will be genuinely welcomed by researchers, practitioners, and decision makers in a broad range of fields, who seek to improve the credibility and reliability of simulation results. It will also be appropriate either for university courses or for independent study.

/pdf/verification-and-validation-in-scientific-computing-262w5ti0ia.pdf

Verification and Validation in Scientific Computing

Elucidation of the mechanisms of cardiac conduction disturbances leading to reentry will require resolution of the details of multidimensional propagation at a microscopic size scale (less than 200 micron). In practice, this will necessitate the combined analysis of extracellular and transmembrane action potentials. The purpose of this paper is to demonstrate the relationships between the time derivatives of the extracellular waveforms and the underlying action potentials in the experimental analysis of anisotropic propagation at this small size scale, and apply these relationships to human atrial muscle at different ages. The extracellular waveforms and their derivatives changed from a smooth contour during transverse propagation in young preparations to complex polyphasic waveforms in the older preparations. The major problem was to estimate the size and location of small groups of fibers that generated the complex waveforms in the older preparations. We found dissimilarities in the derivatives that distinguished source (bundle) size from the distance of the source to the measurement site. The differences in the extracellular waveforms and their derivatives indicated that there was electrical uncoupling of the side-to-side connections between small groups of fibers with aging. These changes produced a prominent zigzag course of transverse propagation at a microscopic level which, in turn, accounted for the increased complexity of the waveforms. The waveform differences also correlated with the development of extensive collagenous septa that separated small groups of fibers. The electrophysiological consequence was an age-related decrease in the "effective" transverse conduction velocities to the range of the very slow conduction (less than 0.08 m/sec) which makes it possible for reentry to occur in small regions of cardiac muscle with normal cellular electrophysiological properties.

Relating extracellular potentials and their derivatives to anisotropic propagation at a microscopic level in human cardiac muscle. Evidence for electrical uncoupling of side-to-side fiber connections with increasing age.

This paper is concerned with methods of evaluating numerical solutions of the non-linear partial differential equationwheresubject to the boundary conditionsA, k, q are known constants.Equation (1) is of the type which arises in problems of heat flow when there is an internal generation of heat within the medium; if the heat is due to a chemical reaction proceeding at each point at a rate depending upon the local temperature, the rate of heat generation is often defined by an equation such as (2).

A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type

A, k, q are known constants. Equation (1) is of the type which arises in problems of heat flow when there is an internal generation of heat within the medium; if the heat is due to a chemical reaction proceeding at each point at a rate depending upon the local temperature, the rate of heat generation is often defined by an equation such as (2). The presence of the non-linear term q(Ow/at) in (1) and the empirical nature, in many cases, of the surface heat transfer function Hi (0), render the use of formal methods unsuitable. Now Hartree [3-5] has suggested two methods (methods I and II below) of evaluating approximate solutions of partial differential equations in two

Numerical methods have been applied to the problem of the diffusion of $\text{CO}$$\text{and}$$\text{O}_{2}$ through the red blood corpuscle membrane, accompanied by diffusion and chemical reaction of these substances in the layer of concentrated haemoglobin solution inside the corpuscle. The methods are applied to recent data on (i) the rates of CO uptake by corpuscle suspensions and haemoglobin solutions, prepared from the blood of rams and pregnant ewes, (ii) the rates of $\text{O}_{2}$ egress from ram corpuscle suspensions and haemoglobin solutions. In the case of the ram blood the slower overall rates of exchange in the corpuscle suspensions, as compared with the haemoglobin solution, can be accounted for by the limiting effect of diffusion inside the corpuscle, without the necessity of attributing any limiting effect to the corpuscle membrane. In the pregnant ewe blood, on the other hand, the corpuscle membrane appears to have a definite limiting effect on the passage of CO and preliminary values of its permeability to this substance are given. It is also shown how the special methods of computation developed in this paper can be generalized and thus made applicable to other processes in which diffusion and chemical reaction velocity are jointly involved.

A theoretical study of the influence of diffusion and chemical reaction velocity on the rate of exchange of carbon monoxide and oxygen between the red blood corpuscle and the surrounding fluid.

The experimental data on the cosmic-ray geomagnetic effects are used to provide information on the nature of the primary cosmic rays and on the mode of production of the meson component. The relevant arguments are first reviewed in a qualitative way and then elaborated by a quantitative analysis, which is not dependent upon any specific theory of meson production. Three main possibilities are discussed, the so-called proton, 'mixed' and soft component hypotheses (see section 1 for definitions). It is concluded that the bulk of the mesons must arise from protons (or possibly other heavier positively charged particles). The analysis suggests that the average multiplicity of the process of meson production is about nine. From consideration of the asymmetry at high altitudes it seems likely that the primary radiation consists of protons and electrons (equally positive and negative) in the ratio of about one proton to four electrons.

P. Nicolson

Papers

A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type

A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type

A theoretical study of the influence of diffusion and chemical reaction velocity on the rate of exchange of carbon monoxide and oxygen between the red blood corpuscle and the surrounding fluid.

Meson formation and the geomagnetic effects