摘要:

There are three ways in which an expected symmetry may not hold exactly: first, if the basic laws do not respect the symmetry exactly; second, if the initial or boundary conditions do not obey the symmetry; and third, by a spontaneous breakdown, which can happen in two ways, here called SBS1 and SBS2, which will be defined and illustrated. Similar to them is the symmetry-breaking approximation, in which a symmetric system is approximated by an asymmetric formalism to make it easier to handle certain correlations.

ISSN:0010-7514    

DOI:10.1080/00107519208223971

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

A short history of observations on the shapes of snow crystals starts in ancient China, summarizes the remarkable but little-known essay by Kepler in 1611, includes contributions by Descartes and Hooke, and ends with the beautiful collections of microphotographs by Bentley and Humphreys (1931) and Nakaya (1954). Modern observations from aircraft and mountain observatories reveal that the dominant crystal habits, hexagonal plates, columns, needles and dendritic stellar forms, and transition from one to another, are strongly correlated with air temperature, with the supersaturation of the vapour having only a secondary influence. There follows a review of laboratory experiments to determine the nature and origin of natural ice-forming nuclei and the properties of artificial nuclei, such as silver iodide, through the study of epitaxial growth of ice crystals on single crystalline substrates. Growth of snow crystals under carefully controlled conditions in laboratory cloud chambers has established that the crystal habit changes sharply six times over the temperature range 0 to—25°C. The author argues that the basic habit is determined in the very early stages of growth by the relative rates of surface diffusion of water molecules across the basal and prism faces. He deduces the average migration distance, xs, for molecules on the basal face from measurements on the velocity of growth layers and of that on the prism faces from measurements on the axial ratios of small crystals. In both cases, xs, varies rapidly between 1 and 6 μm with temperature, and the two curves intersect at three temperatures that correspond to transitions between crystal habits. A theory is developed to explain the transition from regular plates to dendritic stellar crystals; the corners sprout when material from the vapour phase arrives at corners more rapidly than it can be carried away by surface diffusion and occurs only when the diameter of the plate exceeds a critical value dc, ∝ Ds, /Dv, = αx2p, /Dv, where Ds, Dv, are the coefficients of surface and volume diffusion and xp, is the surface migration distance on the (prism) edge of the plate. The predictions of the theory are compared with observations on natural snow crystals. Equations are derived for the growth rates of snow crystals as they fall through the atmosphere. The predicted maximum attainable diameters of the various shapes are in good agreement with observations.

ISSN:0010-7514    

DOI:10.1080/00107519208223972

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

The words‘fluidization of a non-cohesive granular material by low-frequency vibrations’cover the whole scope of phenomena which are described briefly with the use of precise examples. In most of them, the fluidized medium has a free surface since this condition seems to be required to obtain fluid-like behaviour and convective flows. I also give the example of sand liquefaction which occurs sometimes during seisms for which the existence of a free-boundary condition is not needed. I separate problems linked to the presence of air from those which are induced directly by slight changes in boundary conditions or by the vibrations themselves. If most of the time the convective patterns are produced with vertical vibrations, I demonstrate that other convective patterns are obtained with horizontal vibrations. All these convections occur above an amplitude threshold, which is higher for horizontal vibrations than for vertical vibrations. I demonstrate also that vertical vibrations may stop an hourglass, the physics of which we do not understand. One of the main goals of this paper is to demonstrate that the physics of the sand pile (and then of convection in the sand pile) is mostly governed by friction and dilatancy, which are two nonlinear phenomena; this implies in particular that sand-pile mechanics is quite sensitive to rotations of the principal stress axis, which make these convection patterns quite sensitive to any change in boundary conditions at some stage of vibration, so that their macroscopic behaviour depends on small changes and are quite difficult to predict ab initio, unless the situation is well characterized.

ISSN:0010-7514    

DOI:10.1080/00107519208223973

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

ISSN:0010-7514    

DOI:10.1080/00107519208223974

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

ISSN:0010-7514    

DOI:10.1080/00107519208223975

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

ISSN:0010-7514    

DOI:10.1080/00107519208223976

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

ISSN:0010-7514    

DOI:10.1080/00107519208223977

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

摘要:

Scattering and Diffraction in Physical Optics.By Manuel Nieto Vesperinas. 1991, £47.50 (hbk), pp. xvii + 397. Wiley, ISBN 0471 61529 3. Scope: Monograph. Level: Postgraduate.

ISSN:0010-7514    

DOI:10.1080/00107519208223978

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor

ISSN:0010-7514    

DOI:10.1080/00107519208223979

出版商:Taylor & Francis Group    

年代:1992

数据来源: Taylor