Definite Integrals in the Fluid Force on a Vertical Surface

Author(s):  
George C. Ruben

Single molecule resolution in electron beam sensitive, uncoated, noncrystalline materials has been impossible except in thin Pt-C replicas ≤ 150Å) which are resistant to the electron beam destruction. Previously the granularity of metal film replicas limited their resolution to ≥ 20Å. This paper demonstrates that Pt-C film granularity and resolution are a function of the method of replication and other controllable factors. Low angle 20° rotary , 45° unidirectional and vertical 9.7±1 Å Pt-C films deposited on mica under the same conditions were compared in Fig. 1. Vertical replication had a 5A granularity (Fig. 1c), the highest resolution (table), and coated the whole surface. 45° replication had a 9Å granulartiy (Fig. 1b), a slightly poorer resolution (table) and did not coat the whole surface. 20° rotary replication was unsuitable for high resolution imaging with 20-25Å granularity (Fig. 1a) and resolution 2-3 times poorer (table). Resolution is defined here as the greatest distance for which the metal coat on two opposing faces just grow together, that is, two times the apparent film thickness on a single vertical surface.


2017 ◽  
Vol 20 (10) ◽  
pp. 865-879
Author(s):  
S.V.S.S.N.V.G. Krishna Murthy ◽  
Frédéric Magoulès ◽  
B. V. Rathish Kumar ◽  
Vinay Kumar

2019 ◽  
Vol 10 (1) ◽  
pp. 222-237
Author(s):  
M. I. Qureshi ◽  
Kaleem A. Quraishi ◽  
Dilshad Ahamad

1999 ◽  
Vol 45 (151) ◽  
pp. 533-538 ◽  
Author(s):  
Niels Reeh ◽  
Søren Nørvang Madsen ◽  
Johan Jakob Mohr

AbstractUntil now, an assumption of surface-parallel glacier flow has been used to express the vertical velocity component in terms of the horizontal velocity vector, permitting all three velocity components to be determined from synthetic aperture radar interferometry. We discuss this assumption, which neglects the influence of the local mass balance and a possible contribution to the vertical velocity arising if the glacier is not in steady state. We find that the mass-balance contribution to the vertical surface velocity is not always negligible as compared to the surface-slope contribution. Moreover, the vertical velocity contribution arising if the ice sheet is not in steady state can be significant. We apply the principle of mass conservation to derive an equation relating the vertical surface velocity to the horizontal velocity vector. This equation, valid for both steady-state and non-steady-state conditions, depends on the ice-thickness distribution. Replacing the surface-parallel-flow assumption with a correct relationship between the surface velocity components requires knowledge of additional quantities such as surface mass balance or ice thickness.


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