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A Single Twist-Angle Selection Method for the Electronic Structure of Bilayer Materials
Authors:
Ryan A. Baker,
William Z. Van Benschoten,
James J. Shepherd
Abstract:
Structure factor twist averaging (sfTA) is a newer method that has been shown to reproduce twist-averaged (TA) CCSD energies for bulk systems at a low computational cost. In this work, we extend this method for the treatment of low-dimensional materials in the form of two variants: paired sfTA and binding sfTA. These variants affect which twist angles are used in the sfTA protocol, as well as how…
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Structure factor twist averaging (sfTA) is a newer method that has been shown to reproduce twist-averaged (TA) CCSD energies for bulk systems at a low computational cost. In this work, we extend this method for the treatment of low-dimensional materials in the form of two variants: paired sfTA and binding sfTA. These variants affect which twist angles are used in the sfTA protocol, as well as how the special twist angle is selected, namely by using the binding structure factor. These changes are meant to incorporate the binding interaction into the twist-angle selection algorithm within sfTA. Both variants are tested on a variety of bilayer systems, and the resulting binding correlation energies are compared to original sfTA results. We show that the variants are able to produce results approaching TA, with binding sfTA producing the most accurate energies. We also use contour plots of the test systems to show that these improvements are most likely caused by a cancellation of errors.
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Submitted 25 April, 2026;
originally announced April 2026.
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Patterning perovskite colour converters for AR/VR microdisplays
Authors:
Ruairi Baker,
Maria Pervez,
Angus Hawkey,
Nobuya Sakai,
Valerie Berryman-Bousquet,
Bernard Wenger
Abstract:
Colour conversion offers the clearest path to achieve RGB colours in high resolution microdisplays for AR/VR. With resolutions beyond 5000 ppi (i.e. RGB pitch of 5 um), the thickness of the conversion layers is critical for efficiency and manufacturing. Perovskites outperform other conversion materials (quantum dots or phosphors) with their high absorption coefficients for blue light. In this cont…
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Colour conversion offers the clearest path to achieve RGB colours in high resolution microdisplays for AR/VR. With resolutions beyond 5000 ppi (i.e. RGB pitch of 5 um), the thickness of the conversion layers is critical for efficiency and manufacturing. Perovskites outperform other conversion materials (quantum dots or phosphors) with their high absorption coefficients for blue light. In this contribution, we show how perovskite materials, engineered for high optical density and colour purity, can be patterned to produce colour converting pixels. We demonstrate patterning using three approaches (lift-off, negative photoresist and dry etch), and discuss their advantages and disadvantages. The results consolidate the choice of perovskites for AR/VR applications by demonstrating their robustness and compatibility with multiple patterning strategies suitable for high resolution microdisplays.
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Submitted 27 November, 2025;
originally announced November 2025.
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Spatial correlations in SIS processes on random regular graphs
Authors:
Alexander Leibenzon,
Samuel W. S. Johnson,
Ruth E. Baker,
Michael Assaf
Abstract:
In network-based SIS models of infectious disease transmission, infection can only occur between directly connected individuals. This constraint naturally gives rise to spatial correlations between the states of neighboring nodes, as the infection status of connected individuals becomes interdependent. Although mean-field approximations and the standard pairwise model are commonly used to simplify…
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In network-based SIS models of infectious disease transmission, infection can only occur between directly connected individuals. This constraint naturally gives rise to spatial correlations between the states of neighboring nodes, as the infection status of connected individuals becomes interdependent. Although mean-field approximations and the standard pairwise model are commonly used to simplify disease forecasting on networks, they inadequately capture spatial correlations; mean-field frameworks assume that populations are well-mixed, while the pairwise model neglects correlations beyond nearest-neighbor connections, which leads to inaccurate predictions of infection numbers over time. As such, the development of approximations that account for higher order spatially correlated infections is of great interest, as they offer a compromise between accurate disease forecasting and analytic tractability. Here, we use existing corrections to mean-field theory on the regular lattice to construct a more general framework for equivalent corrections on random regular graph topologies. We derive and simulate a hierarchical system of ordinary differential equations for the time evolution of the spatial correlation function at various geodesic distances on random networks. Solving these equations allows us to predict the time-dependent global infection density, which agrees well with numerical simulations. Our results substantially improve on existing corrections to mean-field theory for infectious individuals in SIS processes and provide an in-depth characterization of how structural randomness in networks affects the dynamical trajectories of infectious diseases on networks.
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Submitted 17 March, 2026; v1 submitted 29 September, 2025;
originally announced September 2025.
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Macroscopic QED and noise currents in time-varying media
Authors:
S. A. R. Horsley,
R. K. Baker
Abstract:
Macroscopic QED (MQED) is the field theory for computing quantum electromagnetic effects in dispersive media. Here we extend MQD to treat time-varying, dispersive media. For a time dependent Drude model, we find that the expected replacement $ε(ω) {\to} ε(t,ω)$ within standard MQED leads to nonphysical polarization currents, becoming singular in the limit of a step change in the carrier density. W…
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Macroscopic QED (MQED) is the field theory for computing quantum electromagnetic effects in dispersive media. Here we extend MQD to treat time-varying, dispersive media. For a time dependent Drude model, we find that the expected replacement $ε(ω) {\to} ε(t,ω)$ within standard MQED leads to nonphysical polarization currents, becoming singular in the limit of a step change in the carrier density. We show this singular behaviour can be removed through modifying the reservoir dynamics, quantizing the resulting theory and finding the non-equilibrium, time-varying noise currents, which exhibit extra correlations due to temporal reflections within the material dynamics.
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Submitted 26 September, 2024; v1 submitted 18 September, 2024;
originally announced September 2024.
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3-D Printed Swimming Microtori for Cargo Transport and Flow Manipulation
Authors:
Remmi Baker,
Thomas Montenegro-Johnson,
Anton D. Sediako,
Murray J. Thomson,
Ayusman Sen,
Eric Lauga,
Igor. S. Aranson
Abstract:
Through billions of years of evolution, microorganisms mastered unique swimming behaviors to thrive in complex fluid environments. Limitations in nanofabrication have thus far hindered the ability to design and program synthetic swimmers with the same abilities. Here we encode multi-behavioral responses in artificial swimmers such as microscopic, self-propelled tori using nanoscale 3D printing. We…
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Through billions of years of evolution, microorganisms mastered unique swimming behaviors to thrive in complex fluid environments. Limitations in nanofabrication have thus far hindered the ability to design and program synthetic swimmers with the same abilities. Here we encode multi-behavioral responses in artificial swimmers such as microscopic, self-propelled tori using nanoscale 3D printing. We show experimentally and theoretically that the tori continuously transition between two primary swimming modes in response to a magnetic field. The tori also manipulate and transport other artificial swimmers, bimetallic nanorods, as well as passive colloidal particles. In the first behavioral mode, the tori accumulate and transport nanorods; in the second mode, nanorods align along the tori's self-generated streamlines. Our results indicate that such shape-programmed microswimmers have the potential to manipulate biological active matter, e.g. bacteria or cells.
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Submitted 1 April, 2020;
originally announced April 2020.
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The effect of habitats and fitness on species coexistence in systems with cyclic dominance
Authors:
Ryan Baker,
Michel Pleimling
Abstract:
Cyclic dominance between species may yield spiral waves that are known to provide a mechanism enabling persistent species coexistence. This observation holds true even in presence of spatial heterogeneity in the form of quenched disorder. In this work we study the effects on spatio-temporal patterns and species coexistence of structured spatial heterogeneity in the form of habitats that locally pr…
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Cyclic dominance between species may yield spiral waves that are known to provide a mechanism enabling persistent species coexistence. This observation holds true even in presence of spatial heterogeneity in the form of quenched disorder. In this work we study the effects on spatio-temporal patterns and species coexistence of structured spatial heterogeneity in the form of habitats that locally provide one of the species with an advantage. Performing extensive numerical simulations of systems with three and six species we show that these structured habitats destabilize spiral waves. Analyzing extinction events, we find that species extinction probabilities display a succession of maxima as function of time, that indicate a periodically enhanced probability for species extinction. Analysis of the mean extinction time reveals that as a function of the parameter governing the advantage of one of the species a transition between stable coexistence and unstable coexistence takes place. We also investigate how efficiency as a predator or a prey affects species coexistence.
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Submitted 20 November, 2019;
originally announced November 2019.
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Displacement of transport processes on networked topologies
Authors:
Daniel B. Wilson,
Ruth E. Baker,
Francis G. Woodhouse
Abstract:
Consider a particle whose position evolves along the edges of a network. One definition for the displacement of a particle is the length of the shortest path on the network between the current and initial positions of the particle. Such a definition fails to incorporate information of the actual path the particle traversed. In this work we consider another definition for the displacement of a part…
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Consider a particle whose position evolves along the edges of a network. One definition for the displacement of a particle is the length of the shortest path on the network between the current and initial positions of the particle. Such a definition fails to incorporate information of the actual path the particle traversed. In this work we consider another definition for the displacement of a particle on networked topologies. Using this definition, which we term the winding distance, we demonstrate that for Brownian particles, confinement to a network can induce a transition in the mean squared displacement from diffusive to ballistic behaviour, $\langle x^2(t) \rangle \propto t^2$ for long times. A multiple scales approach is used to derive a macroscopic evolution equation for the displacement of a particle and uncover a topological condition for whether this transition in the mean squared displacement will occur. Furthermore, for networks satisfying this topological condition, we identify a prediction of the timescale upon which the displacement transitions to long-time behaviour. Finally, we extend the investigation of displacement on networks to a class of anomalously diffusive transport processes, where we find that the mean squared displacement at long times is affected by both network topology and the character of the transport process.
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Submitted 25 November, 2019; v1 submitted 12 February, 2019;
originally announced February 2019.
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Topology-dependent density optima for efficient simultaneous network exploration
Authors:
Daniel B. Wilson,
Ruth E. Baker,
Francis G. Woodhouse
Abstract:
A random search process in a networked environment is governed by the time it takes to visit every node, termed the cover time. Often, a networked process does not proceed in isolation but competes with many instances of itself within the same environment. A key unanswered question is how to optimise this process: how many concurrent searchers can a topology support before the benefits of parallel…
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A random search process in a networked environment is governed by the time it takes to visit every node, termed the cover time. Often, a networked process does not proceed in isolation but competes with many instances of itself within the same environment. A key unanswered question is how to optimise this process: how many concurrent searchers can a topology support before the benefits of parallelism are outweighed by competition for space? Here, we introduce the searcher-averaged parallel cover time (APCT) to quantify these economies of scale. We show that the APCT of the networked symmetric exclusion process is optimised at a searcher density that is well predicted by the spectral gap. Furthermore, we find that non-equilibrium processes, realised through the addition of bias, can support significantly increased density optima. Our results suggest novel hybrid strategies of serial and parallel search for efficient information gathering in social interaction and biological transport networks.
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Submitted 15 March, 2018; v1 submitted 25 September, 2017;
originally announced September 2017.
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Disorder induced Dirac-point physics in epitaxial graphene from temperature-dependent magneto-transport measurements
Authors:
J. Huang,
J. A. Alexander-Webber,
A. M. R. Baker,
T. J. B. M. Janssen,
A. Tzalenchuk,
V. Antonov,
T. Yager,
S. Lara-Avila,
S. Kubatkin,
R. Yakimova,
R. J. Nicholas
Abstract:
We report a study of disorder effects on epitaxial graphene in the vicinity of the Dirac point by magneto-transport. Hall effect measurements show that the carrier density increases quadratically with temperature, in good agreement with theoretical predictions which take into account intrinsic thermal excitation combined with electron-hole puddles induced by charged impurities. We deduce disorder…
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We report a study of disorder effects on epitaxial graphene in the vicinity of the Dirac point by magneto-transport. Hall effect measurements show that the carrier density increases quadratically with temperature, in good agreement with theoretical predictions which take into account intrinsic thermal excitation combined with electron-hole puddles induced by charged impurities. We deduce disorder strengths in the range 10.2 $\sim$ 31.2 meV, depending on the sample treatment. We investigate the scattering mechanisms and estimate the impurity density to be $3.0 \sim 9.1 \times 10^{10}$ cm$^{-2}$ for our samples. An asymmetry in the electron/hole scattering is observed and is consistent with theoretical calculations for graphene on SiC substrates. We also show that the minimum conductivity increases with increasing disorder potential, in good agreement with quantum-mechanical numerical calculations.
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Submitted 14 May, 2015;
originally announced May 2015.
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Weak localization scattering lengths in epitaxial, and CVD graphene
Authors:
A. M. R. Baker,
J. A. Alexander-Webber,
T. Altebaeumer,
T. J. B. M. Janssen,
A. Tzalenchuk,
S. Lara-Avila,
S. Kubatkin,
R. Yakimova,
C. -T. Lin,
L. -J. Li,
R. J. Nicholas
Abstract:
Weak localization in graphene is studied as a function of carrier density in the range from 1 x $10^{11}$\,cm$^{-2}$ to 1.43 x $10^{13}$\,cm$^{-2}$ using devices produced by epitaxial growth onto SiC and CVD growth on thin metal film. The magnetic field dependent weak localization is found to be well fitted by theory, which is then used to analyse the dependence of the scattering lengths L…
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Weak localization in graphene is studied as a function of carrier density in the range from 1 x $10^{11}$\,cm$^{-2}$ to 1.43 x $10^{13}$\,cm$^{-2}$ using devices produced by epitaxial growth onto SiC and CVD growth on thin metal film. The magnetic field dependent weak localization is found to be well fitted by theory, which is then used to analyse the dependence of the scattering lengths L$_\varphi$, L$_i$, and L$_*$ on carrier density. We find no significant carrier dependence for L$_\varphi$, a weak decrease for L$_i$ with increasing carrier density just beyond a large standard error, and a n$^{-\frac{1}{4}}$ dependence for L$_*$. We demonstrate that currents as low as 0.01\,nA are required in smaller devices to avoid hot-electron artefacts in measurements of the quantum corrections to conductivity.
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Submitted 10 May, 2013;
originally announced May 2013.
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Phase-space for the breakdown of the quantum Hall effect in epitaxial graphene
Authors:
J. A. Alexander-Webber,
A. M. R. Baker,
T. J. B. M. Janssen,
A. Tzalenchuk,
S. Lara-Avila,
S. Kubatkin,
R. Yakimova,
B. A. Piot,
D. K. Maude,
R. J. Nicholas
Abstract:
We report the phase-space defined by the quantum Hall effect breakdown in polymer gated epitaxial graphene on SiC (SiC/G) as a function of temperature, current, carrier density, and magnetic fields up to 30T. At 2K breakdown currents ($I_c$) almost two orders of magnitude greater than in GaAs devices are observed. The phase boundary of the dissipationless state ($ρ_{xx}=0$) shows a (1-$(T/T_c)^2$)…
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We report the phase-space defined by the quantum Hall effect breakdown in polymer gated epitaxial graphene on SiC (SiC/G) as a function of temperature, current, carrier density, and magnetic fields up to 30T. At 2K breakdown currents ($I_c$) almost two orders of magnitude greater than in GaAs devices are observed. The phase boundary of the dissipationless state ($ρ_{xx}=0$) shows a (1-$(T/T_c)^2$) dependence and persists up to $T_c>45K$ at 29T. With magnetic field $I_c$ was found to increase $\propto B^{3/2}$ and $T_c \propto B^{1.88}$. As the Fermi energy approaches the Dirac point, the $ν=2$ quantized Hall plateau appears continuously from fields as low as 1T up to at least 19T due to a strong magnetic field dependence of the carrier density.
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Submitted 17 April, 2013;
originally announced April 2013.
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Discrepancy between Monte-Carlo Results and Analytic Values for the Average Excluded Volume of Rectangular Prisms
Authors:
Sameet Sreenivasan,
Don R. Baker,
Gerald Paul,
H. Eugene Stanley
Abstract:
We perform Monte Carlo simulations to determine the average excluded volume <V_{ex}> of randomly oriented rectangular prisms, randomly oriented ellipsoids and randomly oriented capped cylinders in 3-D. There is agreement between the analytically obtained <V_{ex}> and the results of simulations for randomly oriented ellipsoids and randomly oriented capped cylinders. However, we find that the <V_{…
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We perform Monte Carlo simulations to determine the average excluded volume <V_{ex}> of randomly oriented rectangular prisms, randomly oriented ellipsoids and randomly oriented capped cylinders in 3-D. There is agreement between the analytically obtained <V_{ex}> and the results of simulations for randomly oriented ellipsoids and randomly oriented capped cylinders. However, we find that the <V_{ex}> for randomly oriented prisms obtained from the simulations differs from the analytically obtained results. In particular, for cubes, the percentage difference is 3.92, far exceeding the bounds of statistical error in our simulation.{\bf Added in Revision 2: We recently found the cause of the discrepancy between the simulation result and the analytic value of the excluded volume to be the effect of an error in our simulation code. Upon rectification of the simulation code, the simulation yields $ 11.00 \pm 0.002 $ as the excluded volume of a pair of randomly oriented cubes of unit volume. The simulation also yields results as predicted by the analytic formula for all other cases of rectangular prisms that we study.}
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Submitted 3 October, 2002; v1 submitted 7 August, 2002;
originally announced August 2002.
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The Approximate Invariance of the Average Number of Connections for the Continuum Percolation of Squares at Criticality
Authors:
Sameet Sreenivasan,
Don R. Baker,
Gerald Paul,
H. Eugene Stanley
Abstract:
We perform Monte Carlo simulations to determine the average excluded area $<A_{ex}>$ of randomly oriented squares, randomly oriented widthless sticks and aligned squares in two dimensions. We find significant differences between our results for randomly oriented squares and previous analytical results for the same. The sources of these differences are explained. Using our results for $<A_{ex}>$…
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We perform Monte Carlo simulations to determine the average excluded area $<A_{ex}>$ of randomly oriented squares, randomly oriented widthless sticks and aligned squares in two dimensions. We find significant differences between our results for randomly oriented squares and previous analytical results for the same. The sources of these differences are explained. Using our results for $<A_{ex}>$ and Monte Carlo simulation results for the percolation threshold, we estimate the mean number of connections per object $B_c$ at the percolation threshold for squares in 2-D. We study systems of squares that are allowed random orientations within a specified angular interval. Our simulations show that the variation in $B_c$ is within 1.6% when the angular interval is varied from 0 to $π/2$.
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Submitted 31 May, 2002;
originally announced May 2002.
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The continuum percolation threshold for interpenetrating squares and cubes
Authors:
Don R. Baker,
Gerald Paul,
Sameet Sreenivasan,
H. Eugene Stanley
Abstract:
Monte Carlo simulations are performed to determine the critical percolation threshold for interpenetrating square objects in two dimensions and cubic objects in three dimensions. Simulations are performed for two cases: (i) objects whose edges are aligned parallel to one another and (ii) randomly oriented objects. For squares whose edges are aligned, the critical area fraction at the percolation…
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Monte Carlo simulations are performed to determine the critical percolation threshold for interpenetrating square objects in two dimensions and cubic objects in three dimensions. Simulations are performed for two cases: (i) objects whose edges are aligned parallel to one another and (ii) randomly oriented objects. For squares whose edges are aligned, the critical area fraction at the percolation threshold phi_c=0.6666 +/- 0.0004, while for randomly oriented squares phi_c=0.6254 +/- 0.0002, 6% smaller. For cubes whose edges are aligned, the critical volume fraction at the percolation threshold phi_c=0.2773 +/- 0.0002, while for randomly oriented cubes phi_c=0.2236 +/- 0.0002, 24% smaller.
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Submitted 11 March, 2002;
originally announced March 2002.
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Nonlinearity and Multifractality of Climate Change in the Past 420,000 Years
Authors:
Yosef Ashkenazy,
Don R. Baker,
Hezi Gildor,
Shlomo Havlin
Abstract:
Evidence of past climate variations are stored in ice and indicate glacial-interglacial cycles characterized by three dominant time periods of 20kyr, 40kyr, and 100kyr. We study the scaling properties of temperature proxy records of four ice cores from Antarctica and Greenland. These series are long-range correlated in the time scales of 1-100kyr. We show that these series are nonlinear as expre…
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Evidence of past climate variations are stored in ice and indicate glacial-interglacial cycles characterized by three dominant time periods of 20kyr, 40kyr, and 100kyr. We study the scaling properties of temperature proxy records of four ice cores from Antarctica and Greenland. These series are long-range correlated in the time scales of 1-100kyr. We show that these series are nonlinear as expressed by volatility correlations and a broad multifractal spectrum. We present a stochastic model that captures the scaling and the nonlinear properties observed in the data.
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Submitted 7 February, 2002; v1 submitted 6 February, 2002;
originally announced February 2002.
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Scaling of Cluster and Backbone Mass Between Two Lines in 3d Percolation
Authors:
Luciano R. da Silva,
Gerald Paul,
Shlomo Havlin,
Don R. Baker,
H. Eugene Stanley
Abstract:
We consider the cluster and backbone mass distributions between two lines of arbitrary orientations and lengths in porous media in three dimensions, and model the porous media by bond percolation at the percolation threshold $p_c$. We observe that for many geometrical configurations the mass probability distribution presents power law behavior. We determine how the characteristic mass of the dis…
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We consider the cluster and backbone mass distributions between two lines of arbitrary orientations and lengths in porous media in three dimensions, and model the porous media by bond percolation at the percolation threshold $p_c$. We observe that for many geometrical configurations the mass probability distribution presents power law behavior. We determine how the characteristic mass of the distribution scales with such geometrical parameters as the line length, w, the minimal distance between lines, r, and the angle between the lines, $θ$. The fractal dimensions of both the cluster and backbone mass are independent of w, r, and $θ$. The slope of the power law regime of the cluster mass is unaffected by changes in these three variables. However, the slope of the power law regime of the backbone mass distribution is dependent upon $θ$. The characteristic mass of the cluster also depends upon $θ$, but the characteristic backbone mass is only weakly affected by $θ$. We propose new scaling functions that reproduce the $θ$ dependence of the characteristic mass found in the simulations.
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Submitted 26 December, 2001;
originally announced December 2001.