scholarly journals Sur l'équation aux dérivées fonctionnelles partielles relative à l'aire d'une surface minima limitée à une courbe gauche et sur la recherche de ses solutions homogènes

1928 ◽  
Vol 20 ◽  
pp. 129-236
Author(s):  
Jules Sebag
Keyword(s):  
Surface Minima

High accuracy block-matching sub-pixel motion estimation through detection of error surface minima

2017 ◽  
Vol 77 (5) ◽  
pp. 5837-5856 ◽  
Author(s):  
Konstantinos Konstantoudakis ◽  
Lazaros Vrysis ◽  
George Papanikolaou ◽  
Charalampos Dimoulas
Keyword(s):  
Motion Estimation ◽  
High Accuracy ◽  
Block Matching ◽  
Error Surface ◽  
Surface Minima

Spectra of zinc tetrabenzporphyrin in n-octane

1976 ◽  
Vol 29 (5) ◽  
pp. 933 ◽  
Author(s):  
PE Fielding ◽  
AWH Mau
Keyword(s):  
Excited States ◽  
Energy Surface ◽  
Soret Band ◽  
Relative Magnitude ◽  
Host Matrix ◽  
Solvent Interaction ◽  
Band Emission ◽  
Hot Band ◽  
Franck Condon ◽  
Surface Minima

A detailed spectroscopic study of zinc tetrabenzporphyrin in n-octane reveals the following: (i) the relative magnitude of solute-solvent interaction in the ground and excited states increases in the order T1 < S0 < S1 < S2. (ii) The potential energy surface minima of the ground and excited states are very similar within the framework of the Franck-Condon principle. (iii) The absence of any hot-band emission from the Q band (S1) and any emission from the Soret band (S2) indicates that significant amounts of energy degrade to the lowest vibrational level of S1. (iv) An earlier report on monomer phosphorescence is mainly due to aggregation. Selective narrow-band excitation is shown to be a useful technique to unravel complex spectra of porphyrins in Shpolskii-type matrices. Accurate measurements can be made of the energies for electronic transitions between the ground and excited states of molecules isolated in the various sites of the host matrix. The intensity ratios for electronic and vibronic bands can also be determined.

scholarly journals Time-resolved imaging of a compressible air disc under a drop impacting on a solid surface

2015 ◽  
Vol 780 ◽  
pp. 636-648 ◽  
Author(s):  
E. Q. Li ◽  
S. T. Thoroddsen
Keyword(s):  
Solid Surface ◽  
High Speed ◽  
Theoretical Models ◽  
Adiabatic Compression ◽  
Time Resolved ◽  
Time Resolved Imaging ◽  
Rapid Deceleration ◽  
Drop Impacts ◽  
The Impact ◽  
Surface Minima

When a drop impacts on a solid surface, its rapid deceleration is cushioned by a thin layer of air, which leads to the entrapment of a bubble under its centre. For large impact velocities the lubrication pressure in this air layer becomes large enough to compress the air. Herein we use high-speed interferometry, with 200 ns time-resolution, to directly observe the thickness evolution of the air layer during the entire bubble entrapment process. The initial disc radius and thickness shows excellent agreement with available theoretical models, based on adiabatic compression. For the largest impact velocities the air is compressed by as much as a factor of 14. Immediately following the contact, the air disc shows rapid vertical expansion. The radial speed of the surface minima just before contact, can reach 50 times the impact velocity of the drop.

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