Level-line moirés by superposition of cylindrical microlens gratings

2020 ◽  
Vol 37 (2) ◽  
pp. 209 ◽  
Author(s):  
Thomas Walger ◽  
Théophane Besson ◽  
Valentin Flauraud ◽  
Roger D. Hersch ◽  
Juergen Brugger
Keyword(s):  

It is shown in general that the exact solution to every non-degenerate unsteady water-wave problem in a straight channel inclined at arbitrary slope, governed by the non-linear hydraulic equations, can be obtained in terms of the complete elliptic integral of the second kind, E . By means of a non-Newtonian reference frame, every such wave problem for a sloping channel can be replaced by an associated problem for a horizontal channel. For the latter, the partial differential equations become reducible and thus permit hodograph inversion. The Riemann integration method for the resulting Euler-Poisson equation yields an auxiliary function for these hydraulic problems which is transformable into a Legendre function and then into the elliptic integral. In particular, the procedure is applied to obtain the exact solution for the water wave in a sloping channel produced by sudden release of the triangular wedge of water (the reservoir) initially at rest behind a vertical wall. The behaviour of the solution is exhibited for convenience in two level-line charts, and representative wave profiles and velocity distributions are presented.


1982 ◽  
Vol 3 ◽  
pp. 77-82 ◽  
Author(s):  
Christopher S. M. Doake

Data from ice rises on the east coast of the Antarctic Peninsula can be interpreted as showing that the ice is thinning at rates of up 0.5 m a−1. However, a level line between two nunataks in Palmer Land showed no change in surface elevation over a period of 5 a. Melt rates on George VI Ice Shelf vary with position and may indicate that parts of the ice shelf are thickening at the rate of several m a−1, presumably in response to a higher accumulation rate over the peninsula a few hundred years ago. A small valley glacier, Spartan Glacier, is wasting away at about 0.27 m a−1. Ice fronts on both east and west coasts of the peninsula have been retreating for the last 30 a. It seems that there is general glacier recession in response to a wanner climate and decreased snowfall for at least the last 30 a, while parts of the peninsula are still thickening in response to a high accumulation rate several hundred years ago.


1982 ◽  
Vol 3 ◽  
pp. 77-82 ◽  
Author(s):  
Christopher S. M. Doake

Data from ice rises on the east coast of the Antarctic Peninsula can be interpreted as showing that the ice is thinning at rates of up 0.5 m a−1. However, a level line between two nunataks in Palmer Land showed no change in surface elevation over a period of 5 a. Melt rates on George VI Ice Shelf vary with position and may indicate that parts of the ice shelf are thickening at the rate of several m a−1, presumably in response to a higher accumulation rate over the peninsula a few hundred years ago. A small valley glacier, Spartan Glacier, is wasting away at about 0.27 m a−1. Ice fronts on both east and west coasts of the peninsula have been retreating for the last 30 a. It seems that there is general glacier recession in response to a wanner climate and decreased snowfall for at least the last 30 a, while parts of the peninsula are still thickening in response to a high accumulation rate several hundred years ago.


1839 ◽  
Vol 129 ◽  
pp. 151-161 ◽  

In former communications to the Society, the laws of high water at Plymouth and other places have been the subject of my researches. These being obtained, the laws of low water are a subject of importance and interest on many accounts. The first ground of my pursuing this subject was the desire to ascertain how far the mean water , that is, the height midway between high and low water, is permanent during the changes which high and low water undergo. That it is approximately so at Ply­mouth, had been ascertained both by Mr. Walker and myself, by means of a com­parison of a short series of observations. But it was desirable to know with more exactness what was the real amount of this permanency, when, by using a long series of observations of high and low water, the irregularities arising from accident, and from taking imperfect cycles of inequalities, were eliminated. There was another reason which made this inquiry important at the present time. An operation has been recently carried on by the direction and at the expense of the British Association, with a view of ascertaining what surface ought to be taken as the permanent level of the sea. A Level Line has been carried with great care and accuracy from the north shore of Somerset to the south shore of Devon ; and the po­sition of this line has been fixed, so as to be recognised at any future time, by means of marks at Axmouth, at East Quantockshead, at Stolford, and at Portishead. This line has also been referred to the sea at its extremities ; and the observations show that the height of mean water coincides, at least very nearly, at different places, as well as at the same place at different times. While the difference of levels of low water at Axmouth on the English Channel, and Wick Rocks on the Bristol Channel, is not less than twelve feet; the mean water at those two places coincides in level within a few inches. In order to determine further what accuracy may be attained in this result, we are led to inquire what is the degree of permanency at one place. I may further add, that it cannot but be instructive to know how far the corrections of the height and time of low water, for lunar parallax and declination, agree in form and amount with the same corrections already obtained for high water.


CORROSION ◽  
1958 ◽  
Vol 14 (5) ◽  
pp. 55-58
Author(s):  
G. BlANCHI

Abstract Tests were made to study the differential aeration corrosion of zinc in molar NaCl solutions under varying conditions of aeration, pH, and length of test time. Test results led to the conclusion that formation of differential aeration macrocells is due to passivity of zinc on the zones of the specimen where cathodic reduction of oxygen takes place, and that the principal process of corrosion is accompanied by local corrosion processes at the cathodic and anodic areas of the macrocell. With buffered solutions which do not permit the passivation of zinc, distribution of corrosion changes radically, a localized attack taking place at the water level line where the oxygen flux is at a maximum.3.6.2


1988 ◽  
Vol 123 ◽  
pp. 63-65
Author(s):  
J.R. Kuhn ◽  
C.M. O'Neill ◽  
L.B. Gilliam

Several measurements of 5-min velocity amplitudes have yielded confusing and conflicting information on the l and m dependence of the modal excitation (Kuhn and O'hanlon, 1983 – henceforth KO; Deubner, 1985; and Hill et al. 1985). We have obtained considerably more data than was described in KO using similar observing techniques. Additional analysis has illuminated a systematic effect related to the finite spatial resolution, and line asymmetry of the data that can lead to errors in inferred velocity amplitudes. Even though Doppler shifts are calculated from the Fraunhofer line center positions the effect can lead to 5-min oscillation amplitude errors at the 10 percent or greater level. Line wing observations should be more susceptible, and comparable resolution 2-dimensional data may be less sensitive to this systematic.


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