I am interested in the properties of large networks occurring in everyday life (social networks of contact, the Internet and the WWW, networks of flight connections, of neurons in the brain, etc.) and I use tools from statistical physics for their analysis. The study of networks has numerous applications, from devising more efficient networks of transportation, to improving the resilience of the Internet to random breakdown or to intentional attack, to finding strategies for arresting the spread of epidemics that propagate by social interaction.
I am also interested in diffusion-limited kinetics, that is, the way reaction processes evolve when the reactants take a much longer time to encounter each other (by diffusion) than to undergo reaction. The situation is dominated by fluctuations at all length scales and gives rise to anomalous kinetics -- quite different from reaction-limited kinetics (where the reaction time is very large), which can be analyzed by classical rate equations.
At a more fundamental level, I study diffusion and random walks in fractals and disordered media. In all regular lattices, regardless of dimensionality (e.g., square, triangular, cubic, etc.) diffusion follows a universal scaling law: the mean square displacement increases linearly with time. However, in fractals and disordered media diffusion is anomalous - the mean square displacement grows slower than linearly with time.
Other interests of mine include nonequilibrium kinetics and kinetics phase transitions, heterogeneous catalysis (catalytic reactions occurring on surfaces, or the interface of different media), and self avoiding walks (a model for linear polymers). I am also interested in various aspects of biological physics, such as the structure and motility of proteins (normal modes analysis), actin filaments in muscle and the scaffolding of cells, and the role of diffusion in signal transduction.
Recent Publications:
Entropy Production in Nonequilibrium Steady States: A Different Approach and an Exactly Solvable Canonical Model,
D. ben-Avraham, S. Dorosz, and M. Pleimling, Phys. Rev. E 84, 011115 (2011).
Exact Solution of the Nonconsensus Model on the Line,
Daniel ben-Avraham,
Physical Review E, 83, 050101(R), link.aps.org/doi/10.1103/Phys.RevE.83.050101 (2011)
Realm of Validity of the Crooks Relation,
D. ben-Avraham, S. Dorosz, M. Pleimling,
Physical Review E, 83, 041129, pre.aps.org/abstract/PRE/v83/i4/e041129 (2011)
Small-scale behavior in deterministic reaction models,
D. ben-Avraham, P. Paolo,
Journal of Physics A, 43, 405002 (2010)
Greedy connectivity of geographically embedded graphs,
Sun, J., D. Ben-Avraham,
Physical Review E, 82, 016109, pre.aps.org/absract/PRE/v82/i1/e016109 (2010)
Past Publications:
On the Google-Fame of Scientists and other Populations,
James P. Bagrow and Daniel ben-Avraham,
Conference Proceedings: 8th Granada Seminar on Computational and Statistical Physics,
"Modeling Cooperative Behavior in the Social Sciences," Granada, Spain, February 7-11, 2005. phys/0504034, pdf
What is Special about Diffusion in Scale-Free Networks?
E. Bollt and D. ben-Avraham, New J. Phys. 7, 26 (2005) open access.
cond-mat/0409465, pdf
On the Relation between One-Species Diffusion-Limited Coalescence and Annihilation in One Dimension,
E. Brunet and D. ben-Avraham, J. Phys. A 38, 3247-3252 (2005).
cond-mat/0412745, pdf
First Passage Properties of the Erdös-Rényi Random Graph,
V. Sood, S. Redner, and D. ben-Avraham, J. Phys. A 38, 109-123 (2005).
cond-mat/0410309, pdf
A Generalization of both the Method of Images and of the Classical Integral Transforms, A. S. Fokas and D. ben-Avraham, in Advances in Scattering and Biomedical Engineering, D. I. Fotiadis and C. V. Massalas, eds., pp. 260-276 (World Scientific, New Jersey 2004). cond-mat/0307020, pdf
Tomography and Stability of Complex Networks,
T. Kalisky, R. Cohen, D. ben-Avraham, and S. Havlin,
Lect. Notes Phys. 650, 3-34 (2004).
Conference Proceedings: ``Networks: Structure, Dynamics, and Function," Santa-Fe, NM, May 12-16, 2003.