Numerical Simulations to Explore Deviations from the Beer-Lambert-Bouguer Law in a Correlated Random Medium

2021 ◽  
Author(s):  
Christopher K. Blouin ◽  
Michael Larsen
Keyword(s):  
Random Media ◽  
Spatial Clustering ◽  
Random Medium ◽  
Computational Simulation ◽  
Experimental Setting ◽  
Cloud Droplets ◽  
Field Representation ◽  
Simulation Domain ◽  
Atmospheric Radiative Transfer ◽  
Technological University

<p>The Beer-Lambert-Bouguer Law of exponential attenuation is ubiquitous in the study of atmospheric radiative transfer. However, previous work has shown that adherence to the classical Beer-Lambert-Bouguer law requires the scatterers in the medium to be spatially uncorrelated. As particulates in the atmosphere are often statistically correlated/clustered, it is useful to identify the magnitude of the deviation from the classical expectation under different degrees of spatial clustering.</p><p>Measuring this deviation is difficult in an experimental setting both because it is challenging to measure the spatial clustering and the deviations from the classical expectation are expected to be modest. Thus, we approach this question through a simplified “ballistic-photon” computational simulation.</p><p>Here, we use a simplified numerical model to track the extinction of a collimated light source through correlated random media. The geometry is taken to mimic a sub-volume of the Michigan Technological University Pi Chamber, and the scatterers (cloud droplets) are explicitly resolved using a variety of increasingly realistic techniques for a frozen-field representation of the particle positions.</p><p>We report on the anticipated deviations from the classical Beer-Lambert-Bouguer law through examination of the resulting intensity of the illumination leaving through different walls of the simulation domain.</p>

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.

Accurate and efficient seismic modeling in random media

Geophysics ◽  
1993 ◽  
Vol 58 (4) ◽  
pp. 576-588 ◽  
Author(s):  
Guido Kneib ◽  
Claudia Kerner
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Random Media ◽  
Polynomial Interpolation ◽  
Random Medium ◽  
High Order ◽  
Numerical Dispersion ◽  
Staggered Grid ◽  
Finite Difference Schemes ◽  
Seismic Modeling

The optimum method for seismic modeling in random media must (1) be highly accurate to be sensitive to subtle effects of wave propagation, (2) allow coarse sampling to model media that are large compared to the scale lengths and wave propagation distances which are long compared to the wavelengths. This is necessary to obtain statistically meaningful overall attributes of wavefields. High order staggered grid finite‐difference algorithms and the pseudospectral method combine high accuracy in time and space with coarse sampling. Investigations for random media reveal that both methods lead to nearly identical wavefields. The small differences can be attributed mainly to differences in the numerical dispersion. This result is important because it shows that errors of the numerical differentiation which are caused by poor polynomial interpolation near discontinuities do not accumulate but cancel in a random medium where discontinuities are numerous. The differentiator can be longer than the medium scale length. High order staggered grid finite‐difference schemes are more efficient than pseudospectral methods in two‐dimensional (2-D) elastic random media.

THE MEAN-FIELD THEORY OF DIRECTED POLYMERS IN RANDOM MEDIA AND SPIN GLASS MODELS

1995 ◽  
Vol 07 (02) ◽  
pp. 183-192 ◽  
Author(s):  
F. KOUKIOU
Keyword(s):  
Field Theory ◽  
Phase Diagram ◽  
Spin Glass ◽  
Spin Glasses ◽  
Random Media ◽  
Random Medium ◽  
Mean Field Theory ◽  
Mean Field ◽  
Directed Polymers ◽  
The Mean

We give a unifying framework for the mean-field theory for models of spin glasses and directed polymers in a random medium defined on homogeneous graphs. Their phase diagram is studied in the complex plane of temperature.

Wave propagation in random media

1971 ◽  
Vol 45 (4) ◽  
pp. 769-783 ◽  
Author(s):  
M. S. Howe
Keyword(s):  
Wave Propagation ◽  
General Theory ◽  
Random Media ◽  
Random Medium ◽  
Dispersive Media ◽  
Transverse Waves ◽  
Small Deviations ◽  
The Mean ◽  
Density Inhomogeneities ◽  
Rough Boundaries

This paper discusses a general theory of wave propagation through a random medium whose random inhomogeneities are confined to small deviations from the mean. The theory is initially worked out in detail for the propagation of transverse waves along an infinite stretched string whose density is a random function of position. The manner in which the mean wave profile is modified by scattering from the density inhomogeneities is discussed in great detail, with particular emphasis on physical interpretation. The general theory of wave propagation in arbitrary dispersive or non-dispersive media is then discussed, and it is shown how the theory may be extended to wave propagation problems involving scattering from rough boundaries.

scholarly journals SCALING IN A SIMPLE MODEL FOR SURFACE GROWTH IN A RANDOM MEDIUM

2002 ◽  
Vol 13 (05) ◽  
pp. 603-612
Author(s):  
AMNON AHARONY ◽  
DIETRICH STAUFFER
Keyword(s):  
Surface Tension ◽  
Random Media ◽  
Random Number ◽  
Random Medium ◽  
Scaling Law ◽  
Biological Species ◽  
Surface Growth ◽  
Height Distribution ◽  
Local Surface ◽  
Simple Scaling

Surface growth in random media is usually governed by both the surface tension and the random local forces. Simulations on lattices mimic the former by imposing a maximum gradient m on the surface heights, and the latter by site-dependent random growth probabilities. Here we consider the limit m → ∞, where the surface grows at the site with minimal random number, independent of its neighbors. The resulting height distribution obeys a simple scaling law, which is destroyed when local surface tension is included. Our model is equivalent to Yee's simplification of the Bak–Sneppen model for the extinction of biological species, where the height represents the number of times a biological species is exchanged.

ON THE ELECTROMAGNETIC VACUUM OF RANDOM MEDIA

2012 ◽  
Vol 14 ◽  
pp. 291-305
Author(s):  
MANUEL DONAIRE
Keyword(s):  
Lamb Shift ◽  
Random Media ◽  
Vacuum Energy ◽  
Random Medium ◽  
Effective Medium ◽  
Polar Molecules ◽  
Leading Order ◽  
Molecular Density ◽  
Statistical Fluctuations ◽  
Medium Vacuum

We present a microscopical approach to the electromagnetic vacuum energy of a random medium made of non-polar molecules. We evaluate the contribution of statistical fluctuations to the average total vacuum energy. While the Lamb shift is a function of the electrical susceptibility only, the vacuum energy is generally not, except in the quasicrystalline approximation. We comment on the possibility of testing experimentally our results. We clarify why the effective medium vacuum energy (i.e., that of long-wavelengths) does not account for the total vacuum energy of a molecular dielectric. Consequently, the Lamb shift does not derive from the effective medium vacuum energy except at leading order in the molecular density.

On the kinetic theory of wave propagation in random media

1973 ◽  
Vol 274 (1242) ◽  
pp. 523-549 ◽  
Keyword(s):  
Wave Propagation ◽  
Energy Transfer ◽  
Scattering Theory ◽  
Random Media ◽  
Order Approximation ◽  
Random Medium ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Conservation Of Energy ◽  
Transfer Processes

This paper considers the theory of the multiple scattering of waves in extensive random media. The classical theory of wave propagation in random media is discussed with reference to its practical limitations, and in particular to the inability of the lowest order approximation to the Bethe-Salpeter equation, which describes the propagation of correlations, to account for conservation of energy. An alternative kinetic theory is formulated, based on the theory of energy transfer processes in random media. The proposed theory satisfies conservation of energy and the Second Law of Thermodynamics. It is illustrated by a consideration of three problems each of which is difficult or impossible to treat by classical scattering theory. These involve the transmission of energy through a slab of random medium; the scattering theory of geometrical optics; and scattering by a randomly inhomogeneous half-space.

Domain walls in random media driven by AC fields

2002 ◽  
Vol 12 (9) ◽  
pp. 275-275
Author(s):  
A. Glatz ◽  
T. Nattermann ◽  
V. Pokr vsky
Keyword(s):  
Random Media ◽  
Domain Walls ◽  
Random Medium ◽  
Low Frequency ◽  
Frequency Limit ◽  
Depinning Transition ◽  
First Time ◽  
Ac Fields ◽  
Adiabatic Case ◽  
Scaling Arguments

The viscous motion of an interface driven by an ac external field of frequency $\omega_0$ in a random medium is considered here for the first time. The velocity exhibits a smeared depinning transition showing a double hysteresis which is absent in the adiabatic case $\omega_0 \rightarrow 0$. Using scaling arguments and an approximate renormalization group calculation we explain the main characteristics of the hysteresis loop. In the low frequency limit these can be expressed in terms of the depinning threshold and the critical exponents of the adiabatic case.

Study on the Scattering Effect of Micro-Scale Inhomogeneity to the Elastic Wave

2013 ◽  
Vol 807-809 ◽  
pp. 2228-2231
Author(s):  
Ning Yang ◽  
Xu Qian
Keyword(s):  
Random Media ◽  
Random Medium ◽  
Wave Length ◽  
Seismic Record ◽  
Obvious Effect ◽  
Von Karman ◽  
Scale Inhomogeneity ◽  
Von Kármán ◽  
Dielectric Objects ◽  
The Impact

Some research on the wave propagation in random medium with Von Karman correlation has been developed in this paper. It focuses on the seismic record of circular disturbance in random medium with Von Karman autocorrelation function. Six different kinds of random medium become the background of the dielectric object. The study of the impact to the responds of the dielectric objects can be measured by applying the FDTD to random background medium model. The numerical results show that the random media make the most obvious effect when the scale of imhomogeneity is close to the wave length.

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