Professor of Chemical Engineering
rziff@umich.eduOffice Information:
B28-G060W NCRC
2800 Plymouth Road
Ann Arbor, MI 48109-2800
phone: 734.764.5498
Education/Degree:
Ph.D. The Rockefeller University, Statistical Physics, 1976B.S. University of California at Los Angeles, Physics, 1971
About
Professor Ziff carries out computational and theoretical studies of various physical problems, most notably percolation but also catalysis modeling and several reaction/diffusion systems. For percolation, he has developed various algorithms that have allowed substantial increases in performance, for the study of threshold behavior, crossing probability, etc. He also studies algorithms for efficiently simulating rare-event simulations such as chemical reactions and diffusion-limited aggregation.
Included in his research history are research in the area of cryogenics (especially in liquid helium) at Los Alamos National Laboratory in New Mexico and the study of statistical mechanics of gas and polymer systems while in the mechanical engineering and chemistry departments at the State University of New York at Stony Brook.
Society Memberships
Physical Review E, Associate Editor, 2002 – 2007
Physical Review E, Editorial Board, 1993-1995, 1996-1998
Fractals, Editorial Board, 1993-2002
Philosophical Magazine Letters B, Editorial Board, 1995-2007
Awards:
Department of Chemical Engineering Award for Excellence in Research 1996
Fellow of the American Physical Society
Outstanding Referee award of the Physical Review, 2009
Publications:
Robert M. Ziff, “Scaling behavior of explosive percolation on the square lattice,” Physical Review E 82, 051105 (3 November 2010).doi: 10.1103/PhysRevE.82.051105
Christian R. Scullard and Robert M. Ziff, “Critical surfaces for general inhomogeneous bond percolation problems,” J. Stat. Mech. 2010, P03021 (March 2010) doi: 10.1088/1742-5468/2010/03/P03021
David A Adams, Leonard M Sander and Robert M Ziff, “Fractal dimensions of the Q-state Potts model for complete and external hulls,” J. Stat. Mech. P03004 (March, 2010). doi: 10.1088/1742-5468/2010/03/P03004
Stefan Boettcher, Jessica L. Cook and Robert M. Ziff, “Patchy percolation on a hierarchical network with small-world bonds,” Physical Review E 80 (4), 041115 (13 October 2009). http://link.aps.org/abstract/PRE/v80/e041115
Adam M. Becker and Robert M. Ziff, “Percolation thresholds on two-dimensional Voronoi networks and Delaunay triangulations,” Physical Review E 80 (4), 041101 (1 October 2009). http://link.aps.org/abstract/PRE/v80/e041101
D. A. Adams, Yen Ting Lin, L. M. Sander and R. M. Ziff, “Harmonic measure for critical Potts clusters,” Physical Review E 80 (3), 031141 (28 September 2009). http://link.aps.org/abstract/PRE/v80/e031141
R. M. Ziff, S. N. Majumdar, and A. Comtet, “Capture of particles undergoing discrete random walks,” J. Chem. Phys., 130, 204104 (27 May 2009). http://link.aip.org/link/JCPSA6/v130/i20/p204104/s1
Robert M. Ziff, “Explosive growth in biased dynamic percolation on two-dimensional regular lattice networks,” Phys. Rev. Lett. 103, 045701 (22 July 2009) http://link.aps.org/doi/10.1103/PhysRevLett.103.045701
D. A. Adams, L. M. Sander, E. Somfai and R. M.Ziff, “The harmonic measure of diffusion-limited aggregates including rareevents,” Europhysics Letters 87 (2), 20001 (16 July 2009) http://stacks.iop.org/0295-5075/87/20001.
Robert M. Ziff, Satya N.Majumdar, and Alain Comtet, “Capture of particles undergoing discrete randomwalks,” J. Chem. Phys. 130, 204104 (27 May 2009) http://link.aip.org/link/?JCPSA6/130/204104/1
Robert M. Ziff, Satya N.Majumdar, and Alain Comtet, “Capture of particles undergoing discrete randomwalks,” J. Chem. Phys. 130, 204104 (27 May 2009) http://link.aip.org/link/?JCPSA6/130/204104/1
Jacob J. H. Simmons, Robert M.Ziff and Peter Kleban,“Factorization of percolation density correlation functions for clusters touching the sides of a rectangle,”, J. Stat. Mech. Th. Exp. 2009, P02067 (33pages) (27 Feb 2009) doi: 10.1088/1742-5468/2009/02/P02067
Robert M. Ziff and Hang Gu, “Universal condition for critical percolation thresholds of kagomé-likelattices,” Phys. Rev. E 79, 020102(18 Feb 2009) http://link.aps.org/doi/10.1103/PhysRevE.79.020102
Amir Haji-Akbari and Robert M. Ziff, “Percolation in networks with voids and bottlenecks,” Phys.Rev. E 79, 021118 (18 Feb 2009) http://link.aps.org/doi/10.1103/PhysRevE.79.021118
Satya N. Majumdar and Robert M. Ziff, “Universal Record Statistics of Random Walks and Lévy Flights,” Phys. Rev. Lett., 101, 050601, 2008.
Christian R. Scullard and Robert M. Ziff, “Critical Surfaces for General Bond Percolation Problems,” Phys. Rev. Lett., 100, 185701, 2008.
Jacob J. H. Simmons, Peter Kleban, and Robert M. Ziff, “Exact factorization of correlation functions in two-dimensional critical percolation,” Phys. Rev. E, 76, 041106, 2007.
Peter Kleban, Jacob J. Simmons, and Robert M. Ziff , “Anchored Critical Percolation Clusters and 2D Electrostatics,” Phys. Rev. Lett., 97, 115702, 2006.
R. M. Ziff and P. Grassberger, “Efficient algorithms for rare-event multiple cluster crossing in critical percolation.” In preparation.
R. M. Ziff and M. E. J. Newman, “Convergence of threshold estimates for two-dimensional percolation,” Physical Review E 66, 016129 (10 pages) (29 July 2002).
R. M. Ziff and John Cardy, “Exact area distribution for critical percolation, Ising and Potts model clusters,” Journal of Statistical Physics (in press, 2002)
Christian D. Lorenz, Ramin Haghgooie, Chevarous Kennebrew, and R. M. Ziff, “The effects of surface defects in a catalysis model,” Surface Science (in press, 2002)
R. M. Ziff, “The hull-gradient method and site percolation on the square lattice, “International Journal of Modern Physics C (Computational) (being revised).
M. E. J. Newman, I. Jensen, and R. M. Ziff, “Percolation and epidemics in a two-dimensional small world network,” Physical Review E 65, 021904 (7 pages) (16 January 2002).
Gerald Paul, R. M. Ziff, H. E. Stanley, “Percolation Threshold, Fisher Exponent, and Shortest Path Exponent for 4 and 5 Dimensions,” Physical Review E 64, 026115 (23 July 2001).
M. E. J. Newman and R. M. Ziff, “A fast Monte Carlo algorithm for site or bond percolation,” Physical Review E 64, 016706 (27 June 2001)
C. D. Lorenz and R. M. Ziff, “Excess number of percolation clusters on a sphere,” Physica A 296: 1-8 (2001).
C. D. Lorenz and R. M. Ziff, “Precise determination of the critical percolation threshold for the three-dimensional ‘Swiss Cheese” model using a growth algorithm,” Journal of Chemical Physics 114 (8): 3659-3661 (22 February 2001)
M. E. J. Newman and R. M. Ziff, “Efficient Monte Carlo algorithm and high-precision results for percolation,” Physical Review Letters 85 (19): 4104-4107 (6 Nov 2000)
J. Quintanilla, S. Torquato, and R. M. Ziff, “Efficient measurement of the percolation threshold for fully penetrable discs,” Journal of Physics A 33 (42): L399-L407 (27 October 2000).
D. Stauffer and R. M. Ziff, “Reexamination of seven-dimensional site percolation thresholds,” International Journal of Modern Physics C (Computational) 11 (1): 205-209 (February 2000).
Christian D. Lorenz, Raechelle May, and Robert M. Ziff, “Similarity of percolation thresholds on the HCP and FCC lattices,” Journal of Statistical Physics 98 (3-4): 961-970 (February 2000).
Robert M. Ziff, “Exact critical exponent for the shortest-path scaling function in percolation,” Journal of Physics A 32 (43): L457-L459 (29 October 1999).
Robert M. Ziff and Filip Babalievski, “Site percolation threshold on the Penrose rhomb lattice,” Physica A 269 (2-4): 201-210 (15 July 1999).
Paul N. Suding and Robert M. Ziff, “Site percolation thresholds for Archimedean lattices,” Physical Review E 60 (1): 275-283 (July 1999).
Robert M. Ziff, Christian D. Lorenz and Peter Kleban, “Shape-dependent universality in percolation,” Physica A 266 (1-4): 17-26 (15 April 1999).
Christian D. Lorenz and Robert M. Ziff, “Universality of the excess number of clusters and the crossing probability function in three-dimensional percolation,” Journal of Physics A 31 (40): 8147-8157 (9 October 1998).
Robert M. Ziff, “Four-tap shift-register-sequence random-number generators, “Computers in Physics 12 (4): 385-392 (Jul/Aug 1998).
R. Dennis Vigil and Robert M. Ziff, “On the scaling theory of two-component aggregation,” Chemical Engineering Science 53 (9): 1725-1729 (May 1998).
Peter Kleban and Robert M. Ziff, “Exact results at the two-dimensional percolation point,” Physical Review B – Condensed Matter (Rapid Communications) 57 (14): R8075-R8078 (1 April 1998).
Christian D. Lorenz and Robert M. Ziff, “Precise determination of the bond percolation thresholds and finite-size scaling corrections for the sc, fcc and bcc lattices,” Physical Review E 57 (1): 230-236 (January 1998).
About
Professor Ziff carries out computational and theoretical studies of various physical problems, most notably percolation but also catalysis modeling and several reaction/diffusion systems. For percolation, he has developed various algorithms that have allowed substantial increases in performance, for the study of threshold behavior, crossing probability, etc. He also studies algorithms for efficiently simulating rare-event simulations such as chemical reactions and diffusion-limited aggregation.
Included in his research history are research in the area of cryogenics (especially in liquid helium) at Los Alamos National Laboratory in New Mexico and the study of statistical mechanics of gas and polymer systems while in the mechanical engineering and chemistry departments at the State University of New York at Stony Brook.
Society Memberships
Physical Review E, Associate Editor, 2002 – 2007
Physical Review E, Editorial Board, 1993-1995, 1996-1998
Fractals, Editorial Board, 1993-2002
Philosophical Magazine Letters B, Editorial Board, 1995-2007
Awards:
Department of Chemical Engineering Award for Excellence in Research 1996
Fellow of the American Physical Society
Outstanding Referee award of the Physical Review, 2009
Publications:
Robert M. Ziff, “Scaling behavior of explosive percolation on the square lattice,” Physical Review E 82, 051105 (3 November 2010).doi: 10.1103/PhysRevE.82.051105
Christian R. Scullard and Robert M. Ziff, “Critical surfaces for general inhomogeneous bond percolation problems,” J. Stat. Mech. 2010, P03021 (March 2010) doi: 10.1088/1742-5468/2010/03/P03021
David A Adams, Leonard M Sander and Robert M Ziff, “Fractal dimensions of the Q-state Potts model for complete and external hulls,” J. Stat. Mech. P03004 (March, 2010). doi: 10.1088/1742-5468/2010/03/P03004
Stefan Boettcher, Jessica L. Cook and Robert M. Ziff, “Patchy percolation on a hierarchical network with small-world bonds,” Physical Review E 80 (4), 041115 (13 October 2009). http://link.aps.org/abstract/PRE/v80/e041115
Adam M. Becker and Robert M. Ziff, “Percolation thresholds on two-dimensional Voronoi networks and Delaunay triangulations,” Physical Review E 80 (4), 041101 (1 October 2009). http://link.aps.org/abstract/PRE/v80/e041101
D. A. Adams, Yen Ting Lin, L. M. Sander and R. M. Ziff, “Harmonic measure for critical Potts clusters,” Physical Review E 80 (3), 031141 (28 September 2009). http://link.aps.org/abstract/PRE/v80/e031141
R. M. Ziff, S. N. Majumdar, and A. Comtet, “Capture of particles undergoing discrete random walks,” J. Chem. Phys., 130, 204104 (27 May 2009). http://link.aip.org/link/JCPSA6/v130/i20/p204104/s1
Robert M. Ziff, “Explosive growth in biased dynamic percolation on two-dimensional regular lattice networks,” Phys. Rev. Lett. 103, 045701 (22 July 2009) http://link.aps.org/doi/10.1103/PhysRevLett.103.045701
D. A. Adams, L. M. Sander, E. Somfai and R. M.Ziff, “The harmonic measure of diffusion-limited aggregates including rareevents,” Europhysics Letters 87 (2), 20001 (16 July 2009) http://stacks.iop.org/0295-5075/87/20001.
Robert M. Ziff, Satya N.Majumdar, and Alain Comtet, “Capture of particles undergoing discrete randomwalks,” J. Chem. Phys. 130, 204104 (27 May 2009) http://link.aip.org/link/?JCPSA6/130/204104/1
Robert M. Ziff, Satya N.Majumdar, and Alain Comtet, “Capture of particles undergoing discrete randomwalks,” J. Chem. Phys. 130, 204104 (27 May 2009) http://link.aip.org/link/?JCPSA6/130/204104/1
Jacob J. H. Simmons, Robert M.Ziff and Peter Kleban,“Factorization of percolation density correlation functions for clusters touching the sides of a rectangle,”, J. Stat. Mech. Th. Exp. 2009, P02067 (33pages) (27 Feb 2009) doi: 10.1088/1742-5468/2009/02/P02067
Robert M. Ziff and Hang Gu, “Universal condition for critical percolation thresholds of kagomé-likelattices,” Phys. Rev. E 79, 020102(18 Feb 2009) http://link.aps.org/doi/10.1103/PhysRevE.79.020102
Amir Haji-Akbari and Robert M. Ziff, “Percolation in networks with voids and bottlenecks,” Phys.Rev. E 79, 021118 (18 Feb 2009) http://link.aps.org/doi/10.1103/PhysRevE.79.021118
Satya N. Majumdar and Robert M. Ziff, “Universal Record Statistics of Random Walks and Lévy Flights,” Phys. Rev. Lett., 101, 050601, 2008.
Christian R. Scullard and Robert M. Ziff, “Critical Surfaces for General Bond Percolation Problems,” Phys. Rev. Lett., 100, 185701, 2008.
Jacob J. H. Simmons, Peter Kleban, and Robert M. Ziff, “Exact factorization of correlation functions in two-dimensional critical percolation,” Phys. Rev. E, 76, 041106, 2007.
Peter Kleban, Jacob J. Simmons, and Robert M. Ziff , “Anchored Critical Percolation Clusters and 2D Electrostatics,” Phys. Rev. Lett., 97, 115702, 2006.
R. M. Ziff and P. Grassberger, “Efficient algorithms for rare-event multiple cluster crossing in critical percolation.” In preparation.
R. M. Ziff and M. E. J. Newman, “Convergence of threshold estimates for two-dimensional percolation,” Physical Review E 66, 016129 (10 pages) (29 July 2002).
R. M. Ziff and John Cardy, “Exact area distribution for critical percolation, Ising and Potts model clusters,” Journal of Statistical Physics (in press, 2002)
Christian D. Lorenz, Ramin Haghgooie, Chevarous Kennebrew, and R. M. Ziff, “The effects of surface defects in a catalysis model,” Surface Science (in press, 2002)
R. M. Ziff, “The hull-gradient method and site percolation on the square lattice, “International Journal of Modern Physics C (Computational) (being revised).
M. E. J. Newman, I. Jensen, and R. M. Ziff, “Percolation and epidemics in a two-dimensional small world network,” Physical Review E 65, 021904 (7 pages) (16 January 2002).
Gerald Paul, R. M. Ziff, H. E. Stanley, “Percolation Threshold, Fisher Exponent, and Shortest Path Exponent for 4 and 5 Dimensions,” Physical Review E 64, 026115 (23 July 2001).
M. E. J. Newman and R. M. Ziff, “A fast Monte Carlo algorithm for site or bond percolation,” Physical Review E 64, 016706 (27 June 2001)
C. D. Lorenz and R. M. Ziff, “Excess number of percolation clusters on a sphere,” Physica A 296: 1-8 (2001).
C. D. Lorenz and R. M. Ziff, “Precise determination of the critical percolation threshold for the three-dimensional ‘Swiss Cheese” model using a growth algorithm,” Journal of Chemical Physics 114 (8): 3659-3661 (22 February 2001)
M. E. J. Newman and R. M. Ziff, “Efficient Monte Carlo algorithm and high-precision results for percolation,” Physical Review Letters 85 (19): 4104-4107 (6 Nov 2000)
J. Quintanilla, S. Torquato, and R. M. Ziff, “Efficient measurement of the percolation threshold for fully penetrable discs,” Journal of Physics A 33 (42): L399-L407 (27 October 2000).
D. Stauffer and R. M. Ziff, “Reexamination of seven-dimensional site percolation thresholds,” International Journal of Modern Physics C (Computational) 11 (1): 205-209 (February 2000).
Christian D. Lorenz, Raechelle May, and Robert M. Ziff, “Similarity of percolation thresholds on the HCP and FCC lattices,” Journal of Statistical Physics 98 (3-4): 961-970 (February 2000).
Robert M. Ziff, “Exact critical exponent for the shortest-path scaling function in percolation,” Journal of Physics A 32 (43): L457-L459 (29 October 1999).
Robert M. Ziff and Filip Babalievski, “Site percolation threshold on the Penrose rhomb lattice,” Physica A 269 (2-4): 201-210 (15 July 1999).
Paul N. Suding and Robert M. Ziff, “Site percolation thresholds for Archimedean lattices,” Physical Review E 60 (1): 275-283 (July 1999).
Robert M. Ziff, Christian D. Lorenz and Peter Kleban, “Shape-dependent universality in percolation,” Physica A 266 (1-4): 17-26 (15 April 1999).
Christian D. Lorenz and Robert M. Ziff, “Universality of the excess number of clusters and the crossing probability function in three-dimensional percolation,” Journal of Physics A 31 (40): 8147-8157 (9 October 1998).
Robert M. Ziff, “Four-tap shift-register-sequence random-number generators, “Computers in Physics 12 (4): 385-392 (Jul/Aug 1998).
R. Dennis Vigil and Robert M. Ziff, “On the scaling theory of two-component aggregation,” Chemical Engineering Science 53 (9): 1725-1729 (May 1998).
Peter Kleban and Robert M. Ziff, “Exact results at the two-dimensional percolation point,” Physical Review B – Condensed Matter (Rapid Communications) 57 (14): R8075-R8078 (1 April 1998).
Christian D. Lorenz and Robert M. Ziff, “Precise determination of the bond percolation thresholds and finite-size scaling corrections for the sc, fcc and bcc lattices,” Physical Review E 57 (1): 230-236 (January 1998).
