Lewis F. Richardson
Bio: Lewis F. Richardson is an academic researcher from University of Cambridge. The author has contributed to research in topics: Differential equation & Numerical weather prediction. The author has an hindex of 22, co-authored 64 publications receiving 9744 citations.
Papers published on a yearly basis
01 Jan 1922
TL;DR: This chapter discusses the arrangement of points and instants in sequence, and some remaining problems of computing forms.
Abstract: The idea of forecasting the weather by calculation was first dreamt of by Lewis Fry Richardson. He set out in this book a detailed algorithm for systematic numerical weather prediction. The method of computing atmospheric changes, which he mapped out in great detail in this book, is essentially the method used today. He was greatly ahead of his time because, before his ideas could bear fruit, advances in four critical areas were needed: better understanding of the dynamics of the atmosphere; stable computational algorithms to integrate the equations; regular observations of the free atmosphere; and powerful automatic computer equipment. Over the ensuing years, progress in numerical weather prediction has been dramatic. Weather prediction and climate modelling have now reached a high level of sophistication, and are witness to the influence of Richardson's ideas. This new edition contains a new foreword by Peter Lynch that sets the original book in context.
TL;DR: In this paper, the diffusivity K of a substance whose mass per volume of atmosphere is χ is defined by an equation of Fick's type ū ∂ χ /∂ x + v - ∂χ/∂ y + w - ∆ χ/ ∂ z + ∆ ∆ t = ∆/∆ x (K ∆π x )+ ∆∆ y ) ∀ ∆ ǫ (k ∆ p x ) + ∁ p y )
Abstract: If the diffusivity K of a substance whose mass per volume of atmosphere is χ be defined by an equation of Fick’s type ū ∂ χ /∂ x + v - ∂ χ /∂ y + w - ∂ χ /∂ z + ∂ χ /∂ t = ∂/∂ x (K ∂ χ /∂ x ) + ∂/∂ y (K ∂ χ /∂ y ) ∂/∂ z (K ∂ χ /∂ z ), (1) x , y , z , t being Cartesian co-ordinates and time, ū , v -, w - being the components of mean velocity, then the measured values of K have been found to be 0·2 cm.2 sec.-1 in capillary tubes (Kaye and Laby’s Tables), 105 cm.2 sec.-1 when gusts are smoothed out of the mean wind (Akerblom, G. I. Taylor, Hesselberg, etc.), 108 cm.2 sec.-1 when the means extend over a time comparable with 4 hours (L. F. Richardson and D. Proctor), 1011 cm.2 sec.-1 when the mean wind is taken to be the general circulation characteristic of the latitude (Defant). Thus the so-called constant K varies in a ratio of 2 to a billion. The present paper records an attempt to comprehend all this range of diffusivity in one coherent scheme. Lest the method which I shall adopt should strike the reader as queer and roundabout, I wish to justify it by showing first why some known methods are in difficulties.
TL;DR: In this paper, the authors developed methods where by the differential equations of physics may be applied more freely than hitherto in the approximate form of difference equations to problems concerning irregular bodies, and all that was there said, as to the need for new methods, may be taken to apply here also.
Abstract: 1. Introduction.— 1·0. The object of this paper is to develop methods where by the differential equations of physics may be applied more freely than hitherto in the approximate form of difference equations to problems concerning irregular bodies. Though very different in method, it is in purpose a continuation of a former paper by the author, on a “Freehand Graphic Way of Determining Stream Lines and Equipotentials” (‘Phil. Mag.,’February, 1908; also ‘Proc. Physical Soc.,’ London, vol. xxi.). And all that was there said, as to the need for new methods, may be taken to apply here also. In brief, analytical methods are the foundation of the whole subject, and in practice they are the most accurate when they will work, but in the integration of partial equations, with reference to irregular-shaped boundaries, their field of application is very limited.
01 Jan 1982
TL;DR: This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.
Abstract: "...a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) ...and the illustrations include many superb examples of computer graphics that are works of art in their own right." Nature
01 Jan 1972
TL;DR: Gregory Bateson was a philosopher, anthropologist, photographer, naturalist, and poet, as well as the husband and collaborator of Margaret Mead as discussed by the authors, and his major work will continue to delight and inform generations of readers.
Abstract: Gregory Bateson was a philosopher, anthropologist, photographer, naturalist, and poet, as well as the husband and collaborator of Margaret Mead. With a new foreword by his daughter Mary Katherine Bateson, this classic anthology of his major work will continue to delight and inform generations of readers. "This collection amounts to a retrospective exhibition of a working life...Bateson has come to this position during a career that carried him not only into anthropology, for which he was first trained, but into psychiatry, genetics, and communication theory...He ...examines the nature of the mind, seeing it not as a nebulous something, somehow lodged somewhere in the body of each man, but as a network of interactions relating the individual with his society and his species and with the universe at large."--D. W. Harding, New York Review of Books "[Bateson's] view of the world, of science, of culture, and of man is vast and challenging. His efforts at synthesis are tantalizingly and cryptically suggestive...This is a book we should all read and ponder."--Roger Keesing, American Anthropologist Gregory Bateson (1904-1980) was the author of Naven and Mind and Nature.
TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.
Abstract: Fractional kinetic equations of the diffusion, diffusion–advection, and Fokker–Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns. These fractional equations are derived asymptotically from basic random walk models, and from a generalised master equation. Several physical consequences are discussed which are relevant to dynamical processes in complex systems. Methods of solution are introduced and for some special cases exact solutions are calculated. This report demonstrates that fractional equations have come of age as a complementary tool in the description of anomalous transport processes.
TL;DR: The mathematical theory of the method is explained in detail, followed by a thorough description of MEG instrumentation, data analysis, and practical construction of multi-SQUID devices.
Abstract: Magnetoencephalography (MEG) is a noninvasive technique for investigating neuronal activity in the living human brain. The time resolution of the method is better than 1 ms and the spatial discrimination is, under favorable circumstances, 2-3 mm for sources in the cerebral cortex. In MEG studies, the weak 10 fT-1 pT magnetic fields produced by electric currents flowing in neurons are measured with multichannel SQUID (superconducting quantum interference device) gradiometers. The sites in the cerebral cortex that are activated by a stimulus can be found from the detected magnetic-field distribution, provided that appropriate assumptions about the source render the solution of the inverse problem unique. Many interesting properties of the working human brain can be studied, including spontaneous activity and signal processing following external stimuli. For clinical purposes, determination of the locations of epileptic foci is of interest. The authors begin with a general introduction and a short discussion of the neural basis of MEG. The mathematical theory of the method is then explained in detail, followed by a thorough description of MEG instrumentation, data analysis, and practical construction of multi-SQUID devices. Finally, several MEG experiments performed in the authors' laboratory are described, covering studies of evoked responses and of spontaneous activity in both healthy and diseased brains. Many MEG studies by other groups are discussed briefly as well.