New Perspectives in Fluid Dynamics: Mathematical Analysis of a Model Proposed by Howard Brenner

George Gabriel Stokes

10.1093/oso/9780198822868.001.0001 ◽

2019 ◽

Cited By ~ 2

Keyword(s):

Fluid Dynamics ◽

History Of Science ◽

Mathematical Analysis ◽

Royal Society ◽

Science And Religion ◽

Cambridge University ◽

Public Servant ◽

History Of ◽

The Many ◽

Natural Philosophers

George Gabriel Stokes was one of the most significant mathematicians and natural philosophers of the nineteenth century. Serving as Lucasian professor at Cambridge he made wide-ranging contributions to optics, fluid dynamics and mathematical analysis. As Secretary of the Royal Society he played a major role in the direction of British science acting as both a sounding board and a gatekeeper. Outside his own area he was a distinguished public servant and MP for Cambridge University. He was keenly interested in the relation between science and religion and wrote extensively on the matter. This edited collection of essays brings together experts in mathematics, physics and the history of science to cover the many facets of Stokes’s life in a scholarly but accessible way.

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Density waves in disk galaxies

Symposium - International Astronomical Union ◽

10.1017/s0074180900101135 ◽

1967 ◽

Vol 31 ◽

pp. 313-317 ◽

Cited By ~ 8

Author(s):

C. C. Lin ◽

F. H. Shu

Keyword(s):

Mathematical Analysis ◽

Spiral Structure ◽

Stellar System ◽

Collective Modes ◽

Disk Galaxies ◽

Spiral Pattern ◽

Density Waves ◽

The Galaxy ◽

Detailed Mathematical Analysis

Density waves in the nature of those proposed by B. Lindblad are described by detailed mathematical analysis of collective modes in a disk-like stellar system. The treatment is centered around a hypothesis of quasi-stationary spiral structure. We examine (a) the mechanism for the maintenance of this spiral pattern, and (b) its consequences on the observable features of the galaxy.

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Computing cell tractions from particle displacements on silicone rubber substrata

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100168542 ◽

1994 ◽

Vol 52 ◽

pp. 162-163

Author(s):

Tim Oliver ◽

Akira Ishihara ◽

Ken Jacobsen ◽

Micah Dembo

Keyword(s):

Plane Stress ◽

Linear Elasticity ◽

Silicone Rubber ◽

Mathematical Analysis ◽

Elastic Recovery ◽

Video Images ◽

Cell Traction Forces ◽

Latex Beads ◽

Cell Traction ◽

Better Than

In order to better understand the distribution of cell traction forces generated by rapidly locomoting cells, we have applied a mathematical analysis to our modified silicone rubber traction assay, based on the plane stress Green’s function of linear elasticity. To achieve this, we made crosslinked silicone rubber films into which we incorporated many more latex beads than previously possible (Figs. 1 and 6), using a modified airbrush. These films could be deformed by fish keratocytes, were virtually drift-free, and showed better than a 90% elastic recovery to micromanipulation (data not shown). Video images of cells locomoting on these films were recorded. From a pair of images representing the undisturbed and stressed states of the film, we recorded the cell’s outline and the associated displacements of bead centroids using Image-1 (Fig. 1). Next, using our own software, a mesh of quadrilaterals was plotted (Fig. 2) to represent the cell outline and to superimpose on the outline a traction density distribution. The net displacement of each bead in the film was calculated from centroid data and displayed with the mesh outline (Fig. 3).

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