Radiation of charge moving in one-dimensional fine-scale random medium

1991 ◽  
Vol 34 (7) ◽  
pp. 691-693
Author(s):  
F. G. Bass ◽  
S. I. Khankina
Keyword(s):  
Random Medium ◽  
Fine Scale ◽  
One Dimensional

Dynamical properties of a random walk in a one-dimensional random medium

1991 ◽  
Vol 171 (1) ◽  
pp. 47-68 ◽  
Author(s):  
C. Aslangul ◽  
M. Barthélémy ◽  
N. Pottier ◽  
D. Saint-James
Keyword(s):  
Random Walk ◽  
Random Medium ◽  
One Dimensional ◽  
Dynamical Properties

ANALYSIS OF PULSE PROPAGATION THROUGH A ONE-DIMENSIONAL RANDOM MEDIUM USING COMPLEX MARTINGALES

2008 ◽  
Vol 08 (01) ◽  
pp. 127-138 ◽  
Author(s):  
JOSSELIN GARNIER ◽  
GEORGE PAPANICOLAOU
Keyword(s):  
Frequency Domain ◽  
Transmission Coefficient ◽  
Pulse Propagation ◽  
Random Medium ◽  
Asymptotic Limit ◽  
Diffusion Approximations ◽  
Martingale Representation ◽  
One Dimensional

We show that the propagation of pulses in a one-dimensional random medium can be characterized using a new complex martingale representation of the transmission coefficient. This representation holds in the frequency domain and in a certain asymptotic limit where diffusion approximations can be used.

Numerically statistical simulation of the intensity field of the radiation transmitted through a random medium

2018 ◽  
Vol 33 (3) ◽  
pp. 161-171 ◽  
Author(s):  
Andrey Yu. Ambos ◽  
Gennadii A. Mikhailov
Keyword(s):  
Random Media ◽  
Radiation Transfer ◽  
Random Medium ◽  
Statistical Simulation ◽  
Angular Distributions ◽  
One Dimensional ◽  
Different Types ◽  
Intensity Field

Abstract The radiation transfer through random media of three different types was simulated numerically and statistically with the same one-dimensional distributions and correlation radii. The averaged probabilities of passages of quanta and their angular distributions practically coincide, although the calculations of correlation radii and visualizations of the corresponding brightness fields give slightly distinct results. In the calculations we used the methods of ‘double randomization’ and ‘delta-scattering’ and also statistical nuclear estimates.

scholarly journals Getting started with controlled-source electromagnetic 1D modeling

2017 ◽  
Vol 36 (4) ◽  
pp. 352-355 ◽  
Author(s):  
Dieter Werthmüller
Keyword(s):  
Forward Modeling ◽  
Higher Dimensions ◽  
Hydrocarbon Exploration ◽  
Fine Scale ◽  
One Dimensional ◽  
Controlled Source ◽  
1D Modeling ◽  
Resistivity Anisotropy ◽  
Complex Models ◽  
Diffusive Term

Forward modeling is an important part of understanding controlled-source electromagnetic (CSEM) responses. The diffusive term in the electromagnetic wave equation is dominant over the displacement term at these frequencies. It is the diffusive behavior that makes it difficult to imagine the actual propagation of the signal. An important tool in gaining experience therefore is forward modeling, and lots of it. The advantage of one-dimensional (1D) forward modeling, besides its speed, is to study isolated effects (see for instance Key, 2009): What is the influence of resistivity anisotropy, or of fine-scale resistivity variations? What is the influence of the airwave? With 1D modeling you can quickly study these effects in isolation before you go on to more complex models in higher dimensions. For an introduction to CSEM for hydrocarbon exploration see, for instance, Constable (2010).

The statistics of waves propagating in a one-dimensional random medium

1985 ◽  
Vol 398 (1815) ◽  
pp. 341-363 ◽  
Keyword(s):  
Brownian Motion ◽  
Decay Rate ◽  
Normal Distribution ◽  
Random Medium ◽  
Transmitted Intensity ◽  
One Dimensional ◽  
Time Harmonic ◽  
Log Normal ◽  
The Waves ◽  
Log Normal Distribution

We consider the one-dimensional scattering of waves in a time-independent random medium. The waves considered are time-harmonic. It is assumed that the wavelength of the waves and the correlation length of the scatterers are small compared with the distance required for significant scattering. Stochastic process theory is used to investigate the statistics of the wavefield. The problem of a wave incident on a length of random medium is investigated in two cases. The first is where the medium is backed by a perfectly reflecting boundary. Here the intensity is shown to be a product of two factors; an exponential term that decays into the medium and the exponential of a ‘Brownian motion’ that describes the fluctuations of intensity with different realizations of the random medium. Because a Brownian motion has a normal distribution, the intensity has a log–normal distribution at any fixed point in the interior of the medium. For a typical realization of the random medium the exponential decay leads to most of the wave energy being near the front of a long medium. However, it is shown that the average intensity is independent of position in the medium. This is because of the long tail of the log–normal distribution and comes about because the average is heavily weighted by exceptional realizations of the medium. Thus the average value of the intensity, unlike the average of the logarithm of the intensity, is not representative of the intensity in a typical realization. The exponential decay of intensity is a result of the phenomenon of Anderson localization, which has received much attention in solid-state physics. The second case considered is where there is no barrier at the back of the medium. For large lengths of the random medium, it is shown that the transmitted intensity has an approximately log–normal distribution. The typical transmitted intensity is exponentially small as a result of localization, the decay rate with length being the same as the decay rate for the previous case. The average transmitted intensity is also exponentially small, but with a different decay rate because of weighting by exceptional realizations. The third problem discussed is that of the response of a random medium to time-harmonic forcing in the interior. The boundaries are taken to be perfectly reflecting and the response is found to be localized near the source for a typical realization. This result is related to the existence of localized normal modes in a long medium.

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