The Experts below are selected from a list of 285 Experts worldwide ranked by ideXlab platform
H. E. Stanley - One of the best experts on this subject based on the ideXlab platform.
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Multifractal properties of the random Resistor Network
Physical Review E, 2000Co-Authors: Marc Barthelemy, Sergey V. Buldyrev, Shlomo Havlin, H. E. StanleyAbstract:We study the multifractal spectrum of the current in the two-dimensional random Resistor Network at the percolation threshold. We consider two ways of applying the voltage difference: ~i! two parallel bars, and ~ii! two points. Our numerical results suggest that in the infinite system limit, the probability distribution behaves for small i as P(i);1/i, where i is the current. As a consequence, the moments of i of order q
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multifractal properties of the random Resistor Network
Physical Review E, 2000Co-Authors: Marc Barthelemy, Sergey V. Buldyrev, Shlomo Havlin, H. E. StanleyAbstract:We study the multifractal spectrum of the current in the two-dimensional random Resistor Network at the percolation threshold. We consider two ways of applying the voltage difference: (i) two parallel bars, and (ii) two points. Our numerical results suggest that in the infinite system limit, the probability distribution behaves for small i as P(i) approximately 1/i, where i is the current. As a consequence, the moments of i of order q
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Multifractal Properties of the Random Resistor Network
Physical Review E : Statistical Nonlinear and Soft Matter Physics, 2000Co-Authors: Marc Barthelemy, Sergey V. Buldyrev, Shlomo Havlin, H. E. StanleyAbstract:We study the multifractal spectrum of the current in the two-dimensional random Resistor Network at the percolation threshold. We consider two ways of applying the voltage difference: (i) two parallel bars, and (ii) two points. Our numerical results suggest that in the infinite system limit, the probability distribution behaves for small current i as P(i) ~ 1/i. As a consequence, the moments of i of order q less than q_c=0 do not exist and all current of value below the most probable one have the fractal dimension of the backbone. The backbone can thus be described in terms of only (i) blobs of fractal dimension d_B and (ii) high current carrying bonds of fractal dimension going from $1/\\nu$ to d_B.
I L Aleiner - One of the best experts on this subject based on the ideXlab platform.
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random Resistor Network model of minimal conductivity in graphene
Physical Review Letters, 2007Co-Authors: Vadim V Cheianov, Vladimir I Falko, B L Altshuler, I L AleinerAbstract:Transport in undoped graphene is related to percolating current patterns in the Networks of n- and p-type regions reflecting the strong bipolar charge density fluctuations. Finite transparency of the p-n junctions is vital in establishing the macroscopic conductivity. We propose a random Resistor Network model to analyze scaling dependencies of the conductance on the doping and disorder, the quantum magnetoresistance and the corresponding dephasing rate.
Alison Kirkby - One of the best experts on this subject based on the ideXlab platform.
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relating permeability and electrical resistivity in fractures using random Resistor Network models
Journal of Geophysical Research, 2016Co-Authors: Alison Kirkby, Graham Heinson, Lars KriegerAbstract:We use random Resistor Network models to explore the relationship between electrical resistivity and permeability in a fracture filled with an electrically conductive fluid. Fluid flow and current are controlled by both the distribution and the volume of pore space. Therefore, the aperture distribution of fractures must be accurately modeled in order to realistically represent their hydraulic and electrical properties. We have constructed fracture surface pairs based on characteristics measured on rock samples. We use these to construct Resistor Networks with variable hydraulic and electrical resistance in order to investigate the changes in both properties as a fault is opened. At small apertures, electrical conductivity and permeability increase moderately with aperture until the fault reaches its percolation threshold. Above this point, the permeability increases by 4 orders of magnitude over a change in mean aperture of less than 0.1 mm, while the resistivity decreases by up to a factor of 10 over this aperture change. Because permeability increases at a greater rate than matrix to fracture resistivity ratio, the percolation threshold can also be defined in terms of the matrix to fracture resistivity ratio, M. The value of M at the percolation threshold, MPT, varies with the ratio of rock to fluid resistivity, the fault spacing, and the fault offset. However, MPT is almost always less than 10. Greater M values are associated with fractures above their percolation threshold. Therefore, if such M values are observed over fluid-filled fractures, it is likely that they are open for fluid flow.
Lars Krieger - One of the best experts on this subject based on the ideXlab platform.
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relating permeability and electrical resistivity in fractures using random Resistor Network models
Journal of Geophysical Research, 2016Co-Authors: Alison Kirkby, Graham Heinson, Lars KriegerAbstract:We use random Resistor Network models to explore the relationship between electrical resistivity and permeability in a fracture filled with an electrically conductive fluid. Fluid flow and current are controlled by both the distribution and the volume of pore space. Therefore, the aperture distribution of fractures must be accurately modeled in order to realistically represent their hydraulic and electrical properties. We have constructed fracture surface pairs based on characteristics measured on rock samples. We use these to construct Resistor Networks with variable hydraulic and electrical resistance in order to investigate the changes in both properties as a fault is opened. At small apertures, electrical conductivity and permeability increase moderately with aperture until the fault reaches its percolation threshold. Above this point, the permeability increases by 4 orders of magnitude over a change in mean aperture of less than 0.1 mm, while the resistivity decreases by up to a factor of 10 over this aperture change. Because permeability increases at a greater rate than matrix to fracture resistivity ratio, the percolation threshold can also be defined in terms of the matrix to fracture resistivity ratio, M. The value of M at the percolation threshold, MPT, varies with the ratio of rock to fluid resistivity, the fault spacing, and the fault offset. However, MPT is almost always less than 10. Greater M values are associated with fractures above their percolation threshold. Therefore, if such M values are observed over fluid-filled fractures, it is likely that they are open for fluid flow.
Shaffique Adam - One of the best experts on this subject based on the ideXlab platform.
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equivalence of effective medium and random Resistor Network models for disorder induced unsaturating linear magnetoresistance
Physical Review B, 2017Co-Authors: Navneeth Ramakrishnan, Ying Tong Lai, Silvia Lara, Meera M Parish, Shaffique AdamAbstract:A linear unsaturating magnetoresistance at high perpendicular magnetic fields, together with a quadratic positive magnetoresistance at low fields, has been seen in many different experimental materials, ranging from silver chalcogenides and thin films of InSb to topological materials like graphene and Dirac semimetals. In the literature, two very different theoretical approaches have been used to explain this classical magnetoresistance as a consequence of sample disorder. The phenomenological random Resistor Network model constructs a grid of four terminal Resistors, each with a varying random resistance. The effective medium theory model imagines a smoothly varying disorder potential that causes a continuous variation of the local conductivity. Here, we demonstrate numerically that both models belong to the same universality class and that a restricted class of the random Resistor Network is actually equivalent to the effective medium theory. Both models are also in good agreement with experiments on a diverse range of materials. Moreover, we show that in both cases, a single parameter, i.e., the ratio of the fluctuations in the carrier density to the average carrier density, completely determines the magnetoresistance profile.