Heterogeneity and disorder: Contributions of Rolf Landauer

Halperin, Bertrand I.; Bergman, David J.

doi:10.1016/j.physb.2010.01.002

Cited by 6 publications

(4 citation statements)

References 78 publications

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“…The data with which we are comparing has been collected during one day of loading, and is subject to natural variations in moisture content as well as possibly random instrumental errors and variability in physical parameters like porosity and solid permittivity with time. The sensitivity of our model to moisture content exhibited in Figure 13 suggests that moisture content only varies by up to ±1% during one day, which is consistent with laboratory measurements taken during that day that gave actual moisture values in the range [9,11]%. The high sensitivity seen in Figures 14 and 15 to the distance between the bauxite and the upper antenna, as seen in D 0 and sag values, means it is important to accurately measure this distance and its variability to an accuracy of millimetres rather than centimetres.…”

Section: Discussion Of Sensitivity and Fitsupporting

confidence: 83%

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Detecting Moisture in Bauxite Using Microwaves

PAEA,

MCGUINNESS

2023

ANZIAM J.

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Mathematical modelling of microwaves travelling through bauxite ore provides a way to compute moisture content in the free space transmission method given data on signal attenuation, phase shift and variable bauxite depth. We extend a recently developed four-layer model that uses coupled ordinary differential wave equations for the electric field together with continuity boundary conditions at interfaces between ore, air and antenna to find a solution that incorporates multiple internal reflections in ore and air. The model provides good fits to data, depending on ore permittivity and conductivity. Our extensions are to use effective medium models to obtain electromagnetic properties of the ore mixture from moisture content and to incorporate the damping effects of scattering from the ore surface. Our model leads to a formula for the received signal showing how signal strengths SS and phase shifts depend on the moisture content of the bauxite ore, through the effects of moisture on permittivity and conductivity. We show that SS may be noninvertible, indicating that attenuation data alone cannot be used to infer moisture content. Combining with phase data typically corrects the noninvertibility. Reducing the operating frequency dramatically improves the usefulness of signal strength data for inferring moisture content.

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Section: Discussion Of Sensitivity and Fitsupporting

confidence: 83%

“…Pecharroman and Iglesias [26] note that Landauer [20] has also obtained Bruggeman's symmetric formula, which is easily extended to cases with more than one inclusion [21]. It seems that Landauer was at first unaware of Bruggeman's results [9] from 1935.…”

Section: Mixture Permittivitymentioning

confidence: 99%

Detecting Moisture in Bauxite Using Microwaves

PAEA,

MCGUINNESS

2023

ANZIAM J.

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“…The mixture of occupied and empty sites of given lattice may exhibit some features of real physical systems. Among typical applications of the percolation theory one may find material science [4], immunology [5] or forest fires problems [6] and studies of liquids moving in porous media [7], etc. [8,9].…”

Section: Introductionmentioning

confidence: 99%

Simple Cubic Random-Site Percolation Thresholds for Complex Neighbourhoods

Kurzawski

Malarz

2012

Reports on Mathematical Physics

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In this communication with computer simulation we evaluate simple cubic randomsite percolation thresholds for neighbourhoods including the nearest neighbours (NN), the next-nearest neighbours (2NN) and the next-next-nearest neighbours (3NN). Our estimations base on finite-size scaling analysis of the percolation probability vs. site occupation probability plots. The Hoshen-Kopelman algorithm has been applied for cluster labelling. The calculated thresholds are 0., respectively. In contrast to the results obtained for a square lattice the calculated percolation thresholds decrease monotonically with the site coordination number z, at least for our inspected neighbourhoods.

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“…The concept of percolation has been useful in describing a variety of physical, chemical, and biological phenomena [15,16,17]. Among the typical applications of the percolation theory one may also find material science [18,19,20], immunology [21,22,23,24], or forest fires problems [25,26,27] and studies of liquids moving in porous media [28,29,30], etc. Generally speaking, the percolation theory deals with statistical properties of the clusters of occupied nodes (site percolation) or occupied edges (bond percolation) for a given graph, network or regular lattice.…”

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confidence: 99%

An Adaptation of the Hoshen-Kopelman Cluster Counting Algorithm for Honeycomb Networks

Popova

2015

SJC

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We develop a simplified implementation of the Hoshen-Kopelman cluster countingalgorithm adapted for honeycomb networks.In our implementation of the algorithm we assume that all nodes in the networkare occupied and links between nodes can be intact or broken. The algorithm counts how many clusters there are in the network and determineswhich nodes belong to each cluster. The network information is stored intotwo sets of data. The first one is related to the connectivity of the nodes andthe second one to the state of links. The algorithm finds all clusters in onlyone scan across the network and thereafter cluster relabeling operates on avector whose size is much smaller than the size of the network. Countingthe number of clusters of each size, the algorithm determines the clustersize probability distribution from which the mean cluster size parameter canbe estimated. Although our implementation of the Hoshen-Kopelman algorithmworks only for networks with a honeycomb (hexagonal) structure, itcan be easily changed to be applied for networks with arbitrary connectivitybetween the nodes (triangular, square, etc.).The proposed adaptation of the Hoshen-Kopelman cluster counting algorithmis applied to studying the thermal degradation of a graphene-like honeycombmembrane by means of Molecular Dynamics simulation with a Langevin thermostat.ACM Computing Classification System (1998): F.2.2, I.5.3.

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Heterogeneity and disorder: Contributions of Rolf Landauer

Cited by 6 publications

References 78 publications

Detecting Moisture in Bauxite Using Microwaves

Detecting Moisture in Bauxite Using Microwaves

Simple Cubic Random-Site Percolation Thresholds for Complex Neighbourhoods

An Adaptation of the Hoshen-Kopelman Cluster Counting Algorithm for Honeycomb Networks

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