Verification of the theory of Brownian motion of a particle through a potential barrier in a viscous medium during experimental study of dislocation acoustic relaxation in normal and superconducting niobium

1997 ◽  
Vol 23 (11) ◽  
pp. 922-932 ◽  
Author(s):  
V. D. Natsik ◽  
P. P. Pal-Val
Keyword(s):  
Experimental Study ◽  
Brownian Motion ◽  
Potential Barrier ◽  
Viscous Medium

Experimental study of the Brownian motion of a harmonically bound particle

1979 ◽  
Vol 47 (9) ◽  
pp. 827-828
Author(s):  
Henry Unruh ◽  
Patrick M. Maxton ◽  
Jonathan Schwartz
Keyword(s):  
Experimental Study ◽  
Brownian Motion

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

Brownian motion with quadratic killing and some implications

1986 ◽  
Vol 23 (04) ◽  
pp. 893-903 ◽  
Author(s):  
Michael L. Wenocur
Keyword(s):  
Brownian Motion ◽  
Weibull Distribution ◽  
Special Function ◽  
Function Theory ◽  
Killing Rate

Brownian motion subject to a quadratic killing rate and its connection with the Weibull distribution is analyzed. The distribution obtained for the process killing time significantly generalizes the Weibull. The derivation involves the use of the Karhunen–Loève expansion for Brownian motion, special function theory, and the calculus of residues.

Experimental study on the restoration from a tilt-azimuth series for improvement in resolution

1995 ◽  
Vol 53 ◽  
pp. 636-637
Author(s):  
Norio Baba ◽  
Norihiko Ichise ◽  
Syunya Watanabe
Keyword(s):  
Experimental Study ◽  
Spherical Aberration ◽  
Incident Beam ◽  
Optical Parameters ◽  
Beam Tilting ◽  
Illumination Method ◽  
Restoration Method ◽  
Illumination Mode

The tilted beam illumination method is used to improve the resolution comparing with the axial illumination mode. Using this advantage, a restoration method of several tilted beam images covering the full azimuthal range was proposed by Saxton, and experimentally examined. To make this technique more reliable it seems that some practical problems still remain. In this report the restoration was attempted and the problems were considered. In our study, four problems were pointed out for the experiment of the restoration. (1) Accurate beam tilt adjustment to fit the incident beam to the coma-free axis for the symmetrical beam tilting over the full azimuthal range. (2) Accurate measurements of the optical parameters which are necessary to design the restoration filter. Even if the spherical aberration coefficient Cs is known with accuracy and the axial astigmatism is sufficiently compensated, at least the defocus value must be measured. (3) Accurate alignment of the tilt-azimuth series images.

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