Journal ArticleDOI
Geometry of optimal path hierarchies
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In this paper, the hierarchy of optimal paths in a disordered landscape, based on the best path, the second best path and so on in terms of an energy, was investigated, and it was shown that the density of spanning optimal paths scale as the length of the paths to −2/3 and the histogram of energy differences between consecutive paths scales as a power law in the difference size with exponent −2.5.Abstract:
We investigate the hierarchy of optimal paths in a disordered landscape, based on the best path, the second best path and so on in terms of an energy. By plotting each path at a height according to its energy above some zero level, a landscape appears. This landscape is self-affine and controlled by two Hurst exponents: the one controlling the height fluctuations is 1/3 and the one controlling the fluctuations of the equipotential lines in the landscape is 2/3. These two exponents correspond to the exponents controlling energy and shape fluctations in the directed polymer problem. We furthermore find that the density of spanning optimal paths scale as the length of the paths to −2/3 and the histogram of energy differences between consecutive paths scale as a power law in the difference size with exponent −2.5.read more
Citations
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Bingham’s model in the oil and gas industry
TL;DR: In this paper, yield stress fluid flows occur in a great many operations and unit processes within the oil and gas industry, including heavy oil, drilling fluids and operations, wellbore cementing, hydraulic fracturing and some open-hole completions, sealing/remedial operations.
Journal ArticleDOI
Simple yield stress fluids
TL;DR: In this article, the authors push back, in defence of the century-old simplicity, exploring what is new and useful and what these models have given in the past few decades.
Journal ArticleDOI
On the determination of a generalized Darcy equation for yield-stress fluid in porous media using a Lattice-Boltzmann TRT scheme
Laurent Talon,Daniela Bauer +1 more
TL;DR: A Lattice-Boltzmann TRT scheme is presented that allows the resolution of this type of flow in stochastically reconstructed porous media and a generalized Darcy equation is determined depending on the yield stress, the effective viscosity, the pressure drop and a characteristic length of the porous medium.
Journal ArticleDOI
Non-Darcy effects in fracture flows of a yield stress fluid
TL;DR: In this paper, the authors study non-inertial flows of single-phase yield stress fluids along uneven/rough-walled channels, e.g., approximating a fracture, with two main objectives.
Journal ArticleDOI
Effective rheology of Bingham fluids in a rough channel
TL;DR: In this paper, the authors derived the volumetric flow rate versus pressure drop of a Bingham fluid in one-dimensional channels of variable apertures in the lubrication approximation.
References
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Dynamic Scaling of Growing Interfaces
TL;DR: A model is proposed for the evolution of the profile of a growing interface that exhibits nontrivial relaxation patterns, and the exact dynamic scaling form obtained for a one-dimensional interface is in excellent agreement with previous numerical simulations.
Book
Numerical Recipes 3rd Edition: The Art of Scientific Computing
TL;DR: This new edition incorporates more than 400 Numerical Recipes routines, many of them new or upgraded, and adopts an object-oriented style particularly suited to scientific applications.
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Fractal Concepts in Surface Growth
TL;DR: The first chapter of this important new text is available on the Cambridge Worldwide Web server: http://www.cup.cam.ac.uk/onlinepubs/Textbooks/textbookstop.html as discussed by the authors.
Journal ArticleDOI
Self-Affine Fractals and Fractal Dimension
TL;DR: In this article, it was shown that the global fractal dimension of a self-affine fractal curve can be computed by walking a compass along the fractal path of a scalar Bownian record.