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  • 1
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    Non-Linearity and Breakdown in Soft Condensed Matter : Proceedings of a Workshop Held at Calcutta, India 1–9 December 1993 (1994)
    Berlin ; Heidelberg : Springer
    Details
    ISBN: 9783540586524
    URL: http://www.springerlink.com/openurl.asp?genre=book&isbn=978-3-540-58652-4
    Language: English
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  • 2
    Electronic Resource
    Electronic Resource
    Study of tracer dispersion in self-affine fractures using lattice–gas automata (1995)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 7 (1995), S. 1938-1948 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: This paper studies the problem of hydrodynamic dispersion of a tracer in a fluid flowing through a two-dimensional rough channel bounded by self-affine surfaces. Changing the surface roughness exponent H, rough walls having different microstructure are obtained. In order to simulate hydrodynamics, a lattice–gas automata modified to introduce two different species of particles is used. In the studied range of Péclet numbers (20–50), the concentration profiles along the channel are well described by Gaussian-type dispersion. A clear enhancement of the dispersion due to roughness is observed. For the studied regime of Péclet numbers, a simple approach is proposed which allows us to interpret the dispersion enhancement in terms of surface roughness. It is shown that the dispersion enhancement in the rough channel is due to the presence of two characteristic lengths, the hydraulic diameter δH which determines the velocity in the channel and the average aperture δav which determines the transverse diffusion length; next shown is that the dispersion in the rough channel varies as D(parallel)∼(δav/δH)2. The values of δH obtained from the dispersion results are compared with those obtained from permeability measures and a good agreement is observed. In the studied domain of Péclet numbers, the roughness exponent H has only a weak influence on the dispersion. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868508
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  • 3
    Electronic Resource
    Electronic Resource
    Propagation of order in the dilute antiferromagnetic three-state Potts model (1989)
    Springer
    Journal of statistical physics 55 (1989), S. 341-350 
    Details
    ISSN: 1572-9613
    Keywords: Potts model ; percolation ; central-force percolation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A recent analysis of the propagation of order in a dilute 3-state Potts antiferromagnetic model on a triangular lattice at zero temperature by Adleret al. has shown the importance of nonlocality in the propagation of order. We study a linearized continuous version of this model, which can be mapped onto three independent percolation problems. We discuss the respective roles of nonlocality and nonlinearity, in particular in connection with central-force percolation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01042604
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  • 4
    Electronic Resource
    Electronic Resource
    Minimal path on the hierarchical diamond lattice (1991)
    Springer
    Journal of statistical physics 65 (1991), S. 183-204 
    Details
    ISSN: 1572-9613
    Keywords: Minimal path ; directed polymer ; hierarchical lattice ; percolation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider the minimal paths on a hierarchical diamond lattice, where bonds are assigned a random weight. Depending on the initial distribution of weights, we find all possible asymptotic scaling properties. The different cases found are the small-disorder case, the analog of Lévy's distributions with a power-law decay at-∞, and finally a limit of large disorder which can be identified as a percolation problem. The asymptotic shape of the stable distributions of weights of the minimal path are obtained, as well as their scaling properties. As a side result, we obtain the asymptotic form of the distribution of effective percolation thresholds for finite-size hierarchical lattices.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01329855
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  • 5
    Electronic Resource
    Electronic Resource
    Resistivity exponent of two-dimensional lattice animals (1988)
    Springer
    Journal of statistical physics 52 (1988), S. 447-451 
    Details
    ISSN: 1572-9613
    Keywords: Lattice animal ; resistivity exponent ; fractal dimension ; spectral dimension
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We calculate the average resistanceR(L) of lattice animals spanningL×L cells on the square lattice using exact and Monte Carlo methods. The dynamical resistivity exponent, defined asR(L) ∼ L ζ, is found to be ζ=1.36±0.07. This contradicts the Alexander-Orbach conjecture, which predicts ζ≈ 0.8. Our value for ζ differs from earlier measurements of this quantity by other methods yielding ζ=1.17±0.05 and 1.22±0.08 by Havlin et al.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01016425
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  • 6
    Electronic Resource
    Electronic Resource
    Multifractality in elastic percolation (1988)
    Springer
    Journal of statistical physics 53 (1988), S. 759-771 
    Details
    ISSN: 1572-9613
    Keywords: Percolation ; multifractality ; elasticity ; critical exponents
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present numerical results on the distribution of forces in the central-force percolation model at threshold in two dimensions. We conjecture a relation between the multifractal spectrum of scalar and vector percolation that we test for central-foce percolation. This relation is in excellent agreement with our numerical data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01014224
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  • 7
    Electronic Resource
    Electronic Resource
    Abstracts from the CECAM workshop on computer simulations of cellular automata (1989)
    Springer
    Journal of statistical physics 55 (1989), S. 1333-1359 
    Details
    ISSN: 1572-9613
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01041096
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  • 8
    Electronic Resource
    Electronic Resource
    Rupture of heterogeneous media in the limit of infinite disorder (1988)
    Springer
    Journal of statistical physics 52 (1988), S. 237-244 
    Details
    ISSN: 1572-9613
    Keywords: Fracture ; percolation ; heterogeneous media
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider a random fuse or random fragile element model. We show that, in the limit of infinite disorder in the bond-breaking thresholds, the rupture of a lattice is a “disguised” percolation process. Therefore, just before the final overall rupture of the lattice, we obtain scaling relations of various physical properties as a function of the number of bonds broken.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01016411
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  • 9
    Electronic Resource
    Electronic Resource
    Fourier acceleration of iterative processes in disordered systems (1988)
    Springer
    Journal of statistical physics 52 (1988), S. 747-773 
    Details
    ISSN: 1572-9613
    Keywords: Fourier acceleration ; critical slowing down ; relaxation ; conjugate gradient algorithm ; disordered systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Technical details are given on how to use Fourier acceleration with iterative processes such as relaxation and conjugate gradient methods. These methods are often used to solve large linear systems of equations, but become hopelessly slow very rapidly as the size of the set of equations to be solved increases. Fourier acceleration is a method designed to alleviate these problems and result in a very fast algorithm. The method is explained for the Jacobi relaxation and conjugate gradient methods and is applied to two models: the random resistor network and the random central-force network. In the first model, acceleration works very well; in the second, little is gained. We discuss reasons for this. We also include a discussion of stopping criteria.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01019728
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  • 10
    Electronic Resource
    Electronic Resource
    There is more to be learned from the Lorentz model (1997)
    Springer
    Journal of statistical physics 87 (1997), S. 1205-1228 
    Details
    ISSN: 1572-9613
    Keywords: Kinetic theory ; non-Markovian effects ; magnetotransport ; percolation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The classical Lorentz model for charged noninteracting point particles in a perpendicular magnetic field is reconsidered in 2D. We show that the standard Boltzmann equation is not valid for this model, even in the Grad limit. We construct a generalized Boltzmann equation which is, and solve the corresponding initial value problem exactly. By an independent calculation, we find the same solution by directly constructing the Green function from the dynamics of the model in the Grad limit. From this solution an expression for the diffusion tensor, valid for arbitrary short-range forces, is derived. For hard disks we calculate the diffusion tensor explicitly. Away from the Grad limit a percolation problem arises. We determine numerically the percolation threshold and the corresponding geometric critical exponents. The numerical evidence strongly suggests that this continuum percolation model is in the universality class of 2D lattice percolation. Although we have explicitly determined a number of limiting properties of the model, several intriguing open problems remain.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02181280
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