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... Nature 329, 32 - 37 (03 September 1987); doi:10.1038/329032a0. Viscous fingering on percolation clusters. Unni Oxaal * , Michael Murat , Finn Boger * , Amnon Aharony , Jens Feder * & Torstein Jøssang *. ... | Article |... more
... Nature 329, 32 - 37 (03 September 1987); doi:10.1038/329032a0. Viscous fingering on percolation clusters. Unni Oxaal * , Michael Murat , Finn Boger * , Amnon Aharony , Jens Feder * & Torstein Jøssang *. ... | Article | ChemPort |. 8. Ben-Jacob, et al. Phys. Rev. Lett. ...
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Growth models and viscous fingers are studied on simple percolation models of porous media. Studies include computer and real experiments on square lattice models, at the percolation threshold, and exact calculations of deterministic flow... more
Growth models and viscous fingers are studied on simple percolation models of porous media. Studies include computer and real experiments on square lattice models, at the percolation threshold, and exact calculations of deterministic flow on non-random fractal models. Crossover away from the threshold is also analyzed, using both computer simulations and scaling theory.
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The critical exponents which describe quantities which are measured per unit 'mass' of the infinite cluster near percolation are shown to be shifted by beta p (the exponent describing the probability of belonging to this... more
The critical exponents which describe quantities which are measured per unit 'mass' of the infinite cluster near percolation are shown to be shifted by beta p (the exponent describing the probability of belonging to this cluster). The fractal dimensionality of the infinite cluster then replaces the Euclidean one in hyperscaling relations. The crossover exponent for the effects of random fields on dilute Ising models are zero temperature is then shown to be phi h= gamma p+ beta p. Similarly, that for random local concentrations is phi p= alpha p+ beta p.
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... and CN YA~G: Phys. Rev., t06, 340 (1957). (*' TD LEE and CS ~vVu: ~4nn. Rev. N~L ~c~., 17, 513 (1967). ... Page 5. 866 A. AtlAtlON'Y and Y. NE~EMAN In a. time-inverted co-erdinatc scheme one obtains equationssimilar to (10),... more
... and CN YA~G: Phys. Rev., t06, 340 (1957). (*' TD LEE and CS ~vVu: ~4nn. Rev. N~L ~c~., 17, 513 (1967). ... Page 5. 866 A. AtlAtlON'Y and Y. NE~EMAN In a. time-inverted co-erdinatc scheme one obtains equationssimilar to (10), except for a change in the sign of e in cq. ...
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Research Interests: Physics, Quantum Mechanics, Magnetic field, Quantum Dots, Kondo effect, and 13 moreAharonov-Bohm Effect, Anderson Model, Physical sciences, Low Energy Buildngs, Oscillations, Numerical Renormalization Group, CHEMICAL SCIENCES, Quantum Tunnelling, Quantum Dot, Heavy Fermion, Coulomb blockade, Bethe Ansatz, and Degree of Freedom
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ABSTRACT The fractal geometry of dilute fractal networks influences the dynamics of physical systems superimposed on such networks. The paper reviews some recent results on random walks, non-linear resistors, noise, spin dynamics and... more
ABSTRACT The fractal geometry of dilute fractal networks influences the dynamics of physical systems superimposed on such networks. The paper reviews some recent results on random walks, non-linear resistors, noise, spin dynamics and viscous fingering.
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The fractal dimensionality of the infinite cluster at the percolation threshold for dimensionalities d>6 is shown to be D=4 (rather than the naive finite size scaling prediction D=d-2). Similarly, the conductivity of a... more
The fractal dimensionality of the infinite cluster at the percolation threshold for dimensionalities d>6 is shown to be D=4 (rather than the naive finite size scaling prediction D=d-2). Similarly, the conductivity of a sample of size L scales as L-d (rather than L-6). This anomalous behaviour is related to a dangerous irrelevant variable, associated with the probability to have vertices
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The finite size scaling method is used to study the critical properties of the spin-1 Baxter-Wu model as function of the fugacity, z, of the vacant (spin zero) sites. For z=0, the thermal exponent converges very quickly to the (exact)... more
The finite size scaling method is used to study the critical properties of the spin-1 Baxter-Wu model as function of the fugacity, z, of the vacant (spin zero) sites. For z=0, the thermal exponent converges very quickly to the (exact) value yt=3/2. For z>0, yt monotonically increases beyond the value 2. This increase is interpreted as indicating a first-order transition. Out of several possible renormalisation group flows, the results seem to favour the one in which the critical Baxter-Wu Hamiltonian flows to the fixed point of the 4-state Potts model, with the amplitude of the marginal operator equal to zero.
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For pt.I see ibid., vol.16, p.1267 (1983). The authors construct and investigate a family of fractals which are generalisations of the Sierpinski gaskets (SGs) to all Euclidean dimensionalities. These fractal lattices have a finite order... more
For pt.I see ibid., vol.16, p.1267 (1983). The authors construct and investigate a family of fractals which are generalisations of the Sierpinski gaskets (SGs) to all Euclidean dimensionalities. These fractal lattices have a finite order of ramification, and can be considered 'marginal' between one-dimensional and higher-dimensional geometries. Physical models defined on them are exactly solvable. The authors argue that short-range
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... (10) (ii) (ij) This is exactly of the form of the Ashkin and Teller (1943) model; for K = 0 we have two decoupled Ising models, with exchange &T, while non-zero values of K introduce coupling of the energy-energy type between them... more
... (10) (ii) (ij) This is exactly of the form of the Ashkin and Teller (1943) model; for K = 0 we have two decoupled Ising models, with exchange &T, while non-zero values of K introduce coupling of the energy-energy type between them (see also Kadanoff and Wegner 1971). ...
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Research Interests: Mathematics, Physics, Condensed Matter Physics, Quantum Physics, Graph Theory, and 15 morePhase Transitions, Mathematical Sciences, Ising Model, Physical sciences, Nearest Neighbor, Series expansions, Critical exponents, High Temperature, Renormalization Group, Exchange Interactions, Pade Approximation, Random Distribution, Distribution Function, Padé Approximant, and Distribution Functions
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Magnetic spin models and resistor networks are studied on certain self-similar fractal lattices, which are described as 'quasi-linear', because they share a significant property of the line: finite portions can be isolated... more
Magnetic spin models and resistor networks are studied on certain self-similar fractal lattices, which are described as 'quasi-linear', because they share a significant property of the line: finite portions can be isolated from the rest by removal of two points (sites). In all cases, there is no long-range order at finite temperature. The transition at zero temperature has a discontinuity
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We develop a microscopic magnetoelectric coupling in Ni3V2O8 (NVO) which gives rise to the trilinear phenomenological coupling used previously to explain the phase transition in which magnetic and ferroelectric order parameters appear... more
We develop a microscopic magnetoelectric coupling in Ni3V2O8 (NVO) which gives rise to the trilinear phenomenological coupling used previously to explain the phase transition in which magnetic and ferroelectric order parameters appear simultaneously. Using combined neutron scattering measurements and first-principles calculations of the phonons in NVO, we determine eleven phonons which can induce the observed spontaneous polarization. Among these eleven phonons, we find that a few of them can actually induce a significant dipole moment. Using the calculated atomic charges, we find that the required distortion to induce the observed dipole moment is very small (˜0.001 å) and therefore it would be very difficult to observe the distortion by neutron-powder diffraction. Finally, we identify the derivatives of the exchange tensor with respect to atomic displacements which are needed for a microscopic model of a spin-phonon coupling in NVO and which we hope to obtain from a fundamental qu...