Publications sorted by subject



Note that some papers address combinations of more than one theme and consequently they appear more than once. The papers in chronological order are listed in this publication list.

Random resistor networks, Percolation theory, Fractals, Multifractals

  1. R. Blumenfeld and A. Aharony, Nonlinear resistor fractal networks, topological distances, singly connected bonds and fluctuations J. Phys. A: Math. Gen. 18, L443-L448 (1985).
  2. R. Blumenfeld, Y. Meir, A. B. Harris and A. Aharony, Infinite set of exponents describing physics on fractal networks J. Phys. A: Math. Gen. 19, L791-L796 (1986).
  3. Y. Meir, R. Blumenfeld, A. Aharony and A. B. Harris, Series analysis of randomly diluted nonlinear resistor networks Phys. Rev. B 34, 3424-3428 (1986).
  4. R. Blumenfeld, Y. Meir, A. Aharony and A. B. Harris, Resistance fluctuations in randomly diluted networks Phys. Rev. B 35, 3524-3535 (1987).
  5. R. Blumenfeld and D. J. Bergman, Fluid flow in a random porous medium: A network model and effective medium approximation J. Appl. Phys. 62, 1616-1621 (1987).
  6. Y. Meir, R. Blumenfeld, A. B. Harris and A. Aharony, Series analysis of randomly diluted nonlinear networks with negative nonlinearity exponent Phys. Rev. B 36, 3950-3952 (1987).
  7. R. Blumenfeld, Probability densities of homogeneous functions: Explicit approximation and applications to percolating networks J. Phys. A: Math. Gen. 21, 815-825 (1988).
  8. U. Sivan, R. Blumenfeld, Y. Meir and O. Entin-Wohlman, Dynamic structure factor of a deterministic fractal Europhys. Lett. 7, 249-253 (1988).
  9. A. Aharony, R. Blumenfeld, P. Breton, B. Fourcade, A. B. Harris, Y. Meir and A. -M. S. Tremblay, Negative moments of currents in percolating resistor networks Phys. Rev. B 40, 7318 (1989).
  10. R. Blumenfeld, Universality and superuniversality of multifractals in nonlinear networks J. Stat. Phys. 56, 233-241 (1989).
  11. O. Entin-Wohlman, U. Sivan, R. Blumenfeld and Y. Meir, Dynamic structure factor of fractals Physica D 38, 93-97 (1989).
  12. R. C. Ball and R. Blumenfeld, Universal scaling of the stress field at the vicinity of a wedge crack in two dimensions and oscillatory self-similar corrections to scaling Phys. Rev. Lett. 65, 1784-1787 (1990).
  13. R. Blumenfeld and A. Aharony, Breakdown of multifractal behaviour in diffusion limited aggregates Phys. Rev. Lett. 64, 1843 (1990).
  14. R. Blumenfeld, Geometrical correlations and the origin of x values at the maximum and intersects of T{c}(x) in La{2-x}Sr{x}CuO{4} J. de Physique 1, 159-166 (1991).
  15. R. C. Ball, P. W. H. Barker and R. Blumenfeld, Sidebranch selection in fractal growth EuroPhys. Lett. 16, 47-52 (1991).
  16. R. Blumenfeld and R. C. Ball, Onset of scale-invariant pattern in growth processes: The cracking problem Physica A 177, 407-415 (1991).
  17. R. Blumenfeld and R. C. Ball, Onset of scaling behaviour in 2D slow cracking Modern Phys. Lett. B 5, 1567-1573 (1991).
  18. E. Duering, R. Blumenfeld, D. J. Bergman, A. Aharony and M. Murat, Current distributions in a two-dimensional random-resistor-network J. Stat. Phys. 67, 113-121 (1992).
  19. A. Aharony, R. Blumenfeld and A. B. Harris, The distribution of the logarithms of currents in percolating resistor networks, I. Theory Phys. Rev. B 47, 5756-5769 (1993).
  20. J. Adler, A. Aharony, R. Blumenfeld, A. B. Harris and Y. Meir, The distribution of the logarithms of currents in percolating resistor networks, II. Series expansion Phys. Rev. B 47, 5770-5782 (1993).
  21. R. Blumenfeld and R. C. Ball, A probe for morphology and hierarchical correlations in scale invariant structures Phys. Rev. E 47, 2298-2302 (1993).
  22. V. Milman, R. Blumenfeld, N. A. Stelmashenko and R. C. Ball, Experimental measurements of the roughness of brittle cracks Phys. Rev. Lett. 71, 204 (1993).
  23. R. Blumenfeld and R. C. Ball, Quantifying morphology of scale-invariant structures beyond the fractal dimension Fractals 1, 985-991 (1993).
  24. V. Milman, N. A. Stelmashenko and R. Blumenfeld, Fracture surfaces: A critical review and a morphological analysis of scanning tunneling microscopy measurements Progress in Materials Science 38, 425-474 (1994). Los Alamos National Laboratory Report LA-UR-94-2812.
  25. R. Blumenfeld and Benoit B. Mandelbrot Mass fractal lacunarity, L\'evy dusts, Mittag-Leffler statistics, and perceived dimension, Phys. Rev. E 56, 112 (1997).

Transport properties in strongly nonlinear media

  1. R. Blumenfeld and A. Aharony, Nonlinear resistor fractal networks, topological distances, singly connected bonds and fluctuations J. Phys. A: Math. Gen. 18, L443-L448 (1985).
  2. R. Blumenfeld, Y. Meir, A. B. Harris and A. Aharony, Infinite set of exponents describing physics on fractal networks J. Phys. A: Math. Gen. 19, L791-L796 (1986).
  3. Y. Meir, R. Blumenfeld, A. Aharony and A. B. Harris, Series analysis of randomly diluted nonlinear resistor networks Phys. Rev. B 34, 3424-3428 (1986).
  4. R. Blumenfeld and D. J. Bergman, Nonlinear dielectrics: electrostatics of random media and propagation of waves in a homogeneous slab Physica A 157, 428-436 (1989).
  5. R. Blumenfeld, Universality and superuniversality of multifractals in nonlinear networks J. Stat. Phys. 56, 233-241 (1989).
  6. R. Blumenfeld and D. J. Bergman, Exact calculation to second order of the effective dielectric constant of a strongly nonlinear composite Phys. Rev. B 40, 1987-1989 (1989).
  7. R. Blumenfeld, Novel flux solutions in nonlinear continuum systems with negative dynamic resistance Physica A 168, 697-704 (1990).
  8. R. Blumenfeld and D. J. Bergman, Nonlinear susceptibilities of granular matter Phys. Rev. B 43, 13682-13683 (1991).
  9. R. Blumenfeld and D. J. Bergman, Strongly nonlinear composite dielectrics: a method for exact solution for the potential field and effective bulk properties Phys. Rev. B 44, 7378-7386 (1991).
  10. R. Blumenfeld, An exact solution for electromagnetic waves in strongly nonlinear media J. Phys. A; Math. Gen. 25, L275-L282 (1992).
  11. R. Blumenfeld, Explicitly exact solutions for waves in a family of nonlinear media Physica D 66, 7-13 (1993).
  12. R. Blumenfeld and Sal Torquato, Estimates of the effective conductivity of strongly nonlinear composites, in preperation.
  13. R. J. Held and R. Blumenfeld, Quantification of pore space for a Sandstone probe, in preparation.

Diffusion-limited-aggregation (DLA), Laplacian growth, Growth of interfaces

  1. R. Blumenfeld and A. Aharony, Breakdown of multifractal behaviour in diffusion limited aggregates Phys. Rev. Lett. 62, 2977-2980 (1989).
  2. R. C. Ball and R. Blumenfeld, Universal scaling of the stress field at the vicinity of a wedge crack in two dimensions and oscillatory self-similar corrections to scaling Phys. Rev. Lett. 65, 1784-1787 (1990).
  3. R. C. Ball and R. Blumenfeld, Exact results on exponential screening in two-dimensional diffusion limited aggregation Phys. Rev. A 44, R828-R831 (1991).
  4. R. C. Ball, P. W. H. Barker and R. Blumenfeld, Sidebranch selection in fractal growth EuroPhys. Lett. 16, 47-52 (1991).
  5. R. Blumenfeld and R. C. Ball, Onset of scale-invariant pattern in growth processes: The cracking problem Physica A 177, 407-415 (1991).
  6. R. Blumenfeld and R. C. Ball, Onset of scaling behaviour in 2D slow cracking Modern Phys. Lett. B 5, 1567-1573 (1991).
  7. R. C. Ball and R. Blumenfeld, Universal scaling of the stress field at the vicinity of a wedge crack in two dimensions and oscillatory self-similar corrections to scaling Phys. Rev. Lett. 68, 2254 (1992).
  8. R. Blumenfeld, Two dimensional Laplacian growth can be mapped onto Hamiltonian dynamics Phys. Lett. A 186, 317-322 (1994). Los Alamos National Laboratory Report LA-UR-93-2800.
  9. R. Blumenfeld, Formulating a first-principles statistical theory of growing surfaces in two-dimensional Laplacian fields Phys. Rev. E 50, 2952 (1994). Los Alamos National Laboratory Report LA-UR-93-4338.
  10. R. Blumenfeld and R. C. Ball, Two dimensional Laplacian growth as a system of creating and annihilating particles Phys. Rev. E 51, 3434 (1995). Los Alamos National Laboratory Report LA-UR-94-2466.
  11. R. Blumenfeld, Pattern formation in Laplacian growth: Theory Center for Nonlinear Studies Newsletter 112, April (1995). Los Alamos National Laboratory Report LALP-95-012.
  12. Y. Jiang and R. Blumenfeld, First-principles estimates of the fractal dimension and the multifractal spectrum of diffusion-Limited-aggregates, in preparation.
  13. R. Blumenfeld, Towards a theory of growing surfaces: Mapping Laplacian growth onto Hamiltonian dynamics and statistics in Fluctuations and Order: The New Synthesis, ed. M. M. Millonas (Springer-Verlag, 1996). Los Alamos National Laboratory Report LA-UR-93-3591.
  14. R. Blumenfeld, A morphological theory for Laplacian nonlinear growth processes via statistics of equivalent many-body systems in Nonlinear Evolution Equations and Dynamical Systems (NEEDS94), eds. V.G. Makhankov, A.R. Bishop and D.D. Holm (World Scientific, 1995). Los Alamos National Laboratory Report LA-UR-94-3528.
  15. R. Blumenfeld, A theory for growing interfaces in Laplacian fields: a many-body formulation and statistical analysis 1994 MRS General Meeting, Boston, MA, USA. Los Alamos National Laboratory Report LA-UR-94-2076.
  16. R. Blumenfeld, A theory for the morphology of Laplacian growths from statistics of equivalent many-body hamiltonian systems in Fractal Reviews in the Natural and Applied Sciences, ed. M. M. Novak (Chapman-Hill, 1995). Los Alamos National Laboratory Report LA-UR-94-2077.
  17. R. Blumenfeld, First-principles formulation of a theory for growing surfaces in Laplacian fields: Mapping the growth onto Hamiltonian dynamics and statistical analysis of the surface Bulletin of the American Physical Society 39, 80 (1994). Los Alamos National Laboratory Report LA-UR-94-0700.
  18. R. Blumenfeld, Morphology of Laplacian growth: Theory Bulletin of the American Physical Society (1995).

High-temperature superconductivity

  1. R. Blumenfeld, Phase coherence oscillation of holes in La{2-x}Sr{x}CuO{4}, dynamics of single holes in the CuO plane and the typical pairing time Physica A 168, 705-713 (1990).
  2. G. Corsten, C. Liem, R. Blumenfeld and N. Jan, Pairing of holes via vortex/antivortex attraction in doped La{2-x}Sr{x}CuO{4} J. de Physique 51, 2229-2233 (1990).
  3. R. Blumenfeld, Geometrical correlations and the origin of x values at the maximum and intersects of T{c}(x) in La{2-x}Sr{x}CuO{4} J. de Physique 1, 159-166 (1991).
  4. R. Blumenfeld, The functional form of the T{c}(x) line in the phase diagram of high temperature superconductors Physica C 178, 119-124 (1991).
  5. C. Bowen, D. L. Hunter, R. Blumenfeld and N. Jan, Magnetism and high T{c} superconductors J. Physique I France 3, 83-92 (1993).

Fracture-related issues


Coarse-graining, Upscaling and Mesoscale issues


Magnetic systems


Polymer issues


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