scholarly journals Characteristics of Displacement Data Due to Time Scale for the Combination of Brownian Motion with Intermittent Adsorption

2014 ◽  
Vol 29 ◽  
pp. 281-288 ◽  
Author(s):  
Itsuo Hanasaki ◽  
Satoshi Uehara ◽  
Satoyuki Kawano
Keyword(s):  
Brownian Motion ◽  
Time Scale

Observation of Brownian motion on the time scale of hydrodynamic interactions

1993 ◽  
Vol 70 (2) ◽  
pp. 242-245 ◽  
Author(s):  
M. H. Kao ◽  
A. G. Yodh ◽  
D. J. Pine
Keyword(s):  
Brownian Motion ◽  
Time Scale ◽  
Hydrodynamic Interactions

Smooth first-passage densities for one-dimensional diffusions

1987 ◽  
Vol 24 (02) ◽  
pp. 370-377 ◽  
Author(s):  
E. J. Pauwels
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Stochastic Differential Equation ◽  
Time Scale ◽  
First Passage ◽  
One Dimensional ◽  
Drift Coefficient

The purpose of this paper is to show that smoothness conditions on the diffusion and drift coefficient of a one-dimensional stochastic differential equation imply the existence and smoothness of a first-passage density. In order to be able to prove this, we shall show that Brownian motion conditioned to first hit a point at a specified time has the same distribution as a Bessel (3)-process with changed time scale.

Brownian Motion Indexed by a Time Scale

2011 ◽  
Vol 29 (3) ◽  
pp. 457-472 ◽  
Author(s):  
David Grow ◽  
Suman Sanyal
Keyword(s):  
Brownian Motion ◽  
Time Scale

scholarly journals Urea-mediated anomalous diffusion in supported lipid bilayers

2018 ◽  
Vol 8 (5) ◽  
pp. 20180028 ◽  
Author(s):  
E. E. Weatherill ◽  
H. L. E. Coker ◽  
M. R. Cheetham ◽  
M. I. Wallace
Keyword(s):  
Brownian Motion ◽  
Polyethylene Glycol ◽  
Lipid Bilayer ◽  
Lipid Bilayers ◽  
Anomalous Diffusion ◽  
Incubation Time ◽  
Time Scale ◽  
Biological Membranes ◽  
Model Systems ◽  
Supported Lipid Bilayers

Diffusion in biological membranes is seldom simply Brownian motion; instead, the rate of diffusion is dependent on the time scale of observation and so is often described as anomalous. In order to help better understand this phenomenon, model systems are needed where the anomalous diffusion of the lipid bilayer can be tuned and quantified. We recently demonstrated one such model by controlling the excluded area fraction in supported lipid bilayers (SLBs) through the incorporation of lipids derivatized with polyethylene glycol. Here, we extend this work, using urea to induce anomalous diffusion in SLBs. By tuning incubation time and urea concentration, we produce bilayers that exhibit anomalous behaviour on the same scale as that observed in biological membranes.

The quadratic variation of Brownian motion on a time scale

2012 ◽  
Vol 82 (9) ◽  
pp. 1677-1680 ◽  
Author(s):  
David Grow ◽  
Suman Sanyal
Keyword(s):  
Brownian Motion ◽  
Time Scale ◽  
Quadratic Variation

Smooth first-passage densities for one-dimensional diffusions

1987 ◽  
Vol 24 (2) ◽  
pp. 370-377 ◽  
Author(s):  
E. J. Pauwels
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Stochastic Differential Equation ◽  
Time Scale ◽  
First Passage ◽  
One Dimensional ◽  
Drift Coefficient

The purpose of this paper is to show that smoothness conditions on the diffusion and drift coefficient of a one-dimensional stochastic differential equation imply the existence and smoothness of a first-passage density.In order to be able to prove this, we shall show that Brownian motion conditioned to first hit a point at a specified time has the same distribution as a Bessel (3)-process with changed time scale.

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