scholarly journals Non-local Discrete $$\infty $$ ∞ -Poisson and Hamilton Jacobi Equations

2015 ◽  
Vol 55 (2) ◽  
pp. 229-241 ◽  
Author(s):  
Matthieu Toutain ◽  
Abderrahim Elmoataz ◽  
François Lozes ◽  
Alamin Mansouri
Keyword(s):  
Non Local ◽  
Jacobi Equations

scholarly journals On unbounded solutions of ergodic problems for non-local Hamilton–Jacobi equations

2019 ◽  
Vol 180 ◽  
pp. 94-128
Author(s):  
Cristina Brändle ◽  
Emmanuel Chasseigne
Keyword(s):  
Unbounded Solutions ◽  
Non Local ◽  
Jacobi Equations

Dislocation dynamics described by non-local Hamilton–Jacobi equations

2005 ◽  
Vol 400-401 ◽  
pp. 162-165 ◽  
Author(s):  
O. Alvarez ◽  
E. Carlini ◽  
P. Hoch ◽  
Y. Le Bouar ◽  
R. Monneau
Keyword(s):  
Dislocation Dynamics ◽  
Non Local ◽  
Jacobi Equations

Toward High-Resolution Low-Voltage SEM

1988 ◽  
Vol 46 ◽  
pp. 218-219
Author(s):  
Zhifeng Shao
Keyword(s):  
Low Voltage ◽  
Spherical Aberration ◽  
Chromatic Aberration ◽  
Limiting Factor ◽  
Operating Voltage ◽  
Probe Radius ◽  
Non Local ◽  
Electron Microscopes ◽  
Image Position ◽  
Scanning Electron Microscopes

Recently, low voltage (≤5kV) scanning electron microscopes have become popular because of their unprecedented advantages, such as minimized charging effects and smaller specimen damage, etc. Perhaps the most important advantage of LVSEM is that they may be able to provide ultrahigh resolution since the interaction volume decreases when electron energy is reduced. It is obvious that no matter how low the operating voltage is, the resolution is always poorer than the probe radius. To achieve 10Å resolution at 5kV (including non-local effects), we would require a probe radius of 5∽6 Å. At low voltages, we can no longer ignore the effects of chromatic aberration because of the increased ratio δV/V. The 3rd order spherical aberration is another major limiting factor. The optimized aperture should be calculated as

Chromatic aberration and low-voltage SEM

1987 ◽  
Vol 45 ◽  
pp. 546-547
Author(s):  
Zhifeng Shao ◽  
A.V. Crewe
Keyword(s):  
Electron Energy ◽  
Low Voltage ◽  
Spherical Aberration ◽  
Chromatic Aberration ◽  
Primary Electron ◽  
Probe Size ◽  
Non Local ◽  
Optical Treatment ◽  
Electron Microscopes ◽  
Scanning Electron Microscopes

For scanning electron microscopes, it is plausible that by lowering the primary electron energy, one can decrease the volume of interaction and improve resolution. As shown by Crewe /1/, at V0 =5kV a 10Å resolution (including non-local effects) is possible. To achieve this, we would need a probe size about 5Å. However, at low voltages, the chromatic aberration becomes the major concern even for field emission sources. In this case, δV/V = 0.1 V/5kV = 2x10-5. As a rough estimate, it has been shown that /2/ the chromatic aberration δC should be less than ⅓ of δ0 the probe size determined by diffraction and spherical aberration in order to neglect its effect. But this did not take into account the distribution of electron energy. We will show that by using a wave optical treatment, the tolerance on the chromatic aberration is much larger than we expected.

Magic of signs: a non-local interpretation of homeopathy

2000 ◽  
Vol 89 (3) ◽  
pp. 127-140 ◽  
Author(s):  
H Walach
Keyword(s):  
Non Local

Imperfections in non-local elasticity

1998 ◽  
Vol 08 (PR8) ◽  
pp. Pr8-309-Pr8-316 ◽  
Author(s):  
Y. Z. Povstenko
Keyword(s):  
Non Local
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