In physics, chemistry, and materials science, percolation refers to the movement and filtering of fluids through porous materials. It is described by Darcy's law. Broader applications have since been developed that cover connectivity of many systems modeled as lattices or graphs, analogous to connectivity of lattice components in the filtration problem that modulates capacity for percolation.
The edge of chaos is a transition space between order and disorder that is hypothesized to exist within a wide variety of systems. This transition zone is a region of bounded instability that engenders a constant dynamic interplay between order and disorder.
In applied mathematics, highly optimized tolerance (HOT) is a method of generating power law behavior in systems by including a global optimization principle. It was developed by Jean M. Carlson and John Doyle in the early 2000s. For some systems that display a characteristic scale, a global optimization term could potentially be added that would then yield power law behavior. It has been used to generate and describe internet-like graphs, forest fire models and may also apply to biological systems.
Per Bak was a Danish theoretical physicist who coauthored the 1987 academic paper that coined the term "self-organized criticality."
Tang Chao is a Chair Professor of Physics and Systems Biology at Peking University.
In physics, topological order is a kind of order in the zero-temperature phase of matter. Macroscopically, topological order is defined and described by robust ground state degeneracy and quantized non-Abelian geometric phases of degenerate ground states. Microscopically, topological orders correspond to patterns of long-range quantum entanglement. States with different topological orders cannot change into each other without a phase transition.
Extremal optimization (EO) is an optimization heuristic inspired by the Bak–Sneppen model of self-organized criticality from the field of statistical physics. This heuristic was designed initially to address combinatorial optimization problems such as the travelling salesman problem and spin glasses, although the technique has been demonstrated to function in optimization domains.
Kurt Wiesenfeld is an American physicist working primarily on non-linear dynamics. His works primarily concern stochastic resonance, spontaneous synchronization of coupled oscillators, and non-linear laser dynamics. Since 1987, he has been professor of physics at the Georgia Institute of Technology.
The percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in random systems. Below the threshold a giant connected component does not exist; while above it, there exists a giant component of the order of system size. In engineering and coffee making, percolation represents the flow of fluids through porous media, but in the mathematics and physics worlds it generally refers to simplified lattice models of random systems or networks (graphs), and the nature of the connectivity in them. The percolation threshold is the critical value of the occupation probability p, or more generally a critical surface for a group of parameters p1, p2, ..., such that infinite connectivity (percolation) first occurs.
The Abelian sandpile model (ASM) is the more popular name of the original Bak–Tang–Wiesenfeld model (BTW). The BTW model was the first discovered example of a dynamical system displaying self-organized criticality. It was introduced by Per Bak, Chao Tang and Kurt Wiesenfeld in a 1987 paper.
Subir Sachdev is Herchel Smith Professor of Physics at Harvard University specializing in condensed matter. He was elected to the U.S. National Academy of Sciences in 2014, received the Lars Onsager Prize from the American Physical Society and the Dirac Medal from the ICTP in 2018, and was elected Foreign Member of the Royal Society ForMemRS in 2023. He was a co-editor of the Annual Review of Condensed Matter Physics 2017–2019, and is Editor-in-Chief of Reports on Progress in Physics 2022-.
Dante R. Chialvo is a professor at Universidad Nacional de San Martin. Together with Per Bak, they put forward concrete models considering the brain as a critical system. Initial contributions focussed on mathematical ideas of how learning could benefit from criticality. Further work provided experimental evidence for this conjecture both at large and small scale. He was named Fulbright Scholar in 2005 and elected as a Fellow of the American Physical Society in 2007 and as Member of the Academia de Ciencias de America Latina in 2022.
In the context of the physical and mathematical theory of percolation, a percolation transition is characterized by a set of universal critical exponents, which describe the fractal properties of the percolating medium at large scales and sufficiently close to the transition. The exponents are universal in the sense that they only depend on the type of percolation model and on the space dimension. They are expected to not depend on microscopic details such as the lattice structure, or whether site or bond percolation is considered. This article deals with the critical exponents of random percolation.
Active matter is matter composed of large numbers of active "agents", each of which consumes energy in order to move or to exert mechanical forces. Such systems are intrinsically out of thermal equilibrium. Unlike thermal systems relaxing towards equilibrium and systems with boundary conditions imposing steady currents, active matter systems break time reversal symmetry because energy is being continually dissipated by the individual constituents. Most examples of active matter are biological in origin and span all the scales of the living, from bacteria and self-organising bio-polymers such as microtubules and actin, to schools of fish and flocks of birds. However, a great deal of current experimental work is devoted to synthetic systems such as artificial self-propelled particles. Active matter is a relatively new material classification in soft matter: the most extensively studied model, the Vicsek model, dates from 1995.
Maya Paczuski is the head and founder of the Complexity Science Group at the University of Calgary. She is a well-cited physicist whose work spans self-organized criticality, avalanche dynamics, earthquake, and complex networks. She was born in Israel in 1963, but grew up in the United States. Maya Paczuski received a B.S. and M.S. in Electrical Engineering and Computer Science from M.I.T. in 1986 and then went on to study with Mehran Kardar, earning her Ph.D in Condensed matter physics from the same institute.
In neuroscience, the critical brain hypothesis states that certain biological neuronal networks work near phase transitions. Experimental recordings from large groups of neurons have shown bursts of activity, so-called neuronal avalanches, with sizes that follow a power law distribution. These results, and subsequent replication on a number of settings, led to the hypothesis that the collective dynamics of large neuronal networks in the brain operates close to the critical point of a phase transition. According to this hypothesis, the activity of the brain would be continuously transitioning between two phases, one in which activity will rapidly reduce and die, and another where activity will build up and amplify over time. In criticality, the brain capacity for information processing is enhanced, so subcritical, critical and slightly supercritical branching process of thoughts could describe how human and animal minds function.
Amnon Aharony is an Israeli Professor (Emeritus) of Physics in the School of Physics and Astronomy at Tel Aviv University, Israel and in the Physics Department of Ben Gurion University of the Negev, Israel. After years of research on statistical physics, his current research focuses on condensed matter theory, especially in mesoscopic physics and spintronics. He is a member of the Israel Academy of Sciences and Humanities, a Foreign Honorary Member of the American Academy of Arts and Sciences and of several other academies. He also received several prizes, including the Rothschild Prize in Physical Sciences, and the Gunnar Randers Research Prize, awarded every other year by the King of Norway.
Vitaly Kocharovsky is a Russian-American physicist, academic and researcher. He is a Professor of Physics and Astronomy at Texas A&M University.
Vladimir Kocharovsky is a Russian physicist, academic and researcher. He is a Head of the Astrophysics and Space Plasma Physics Department at the Institute of Applied Physics of the Russian Academy of Sciences and a professor at N.I. Lobachevsky State University of Nizhny Novgorod.
Dov I. Levine is an American-Israeli physicist, known for his research on quasicrystals, soft condensed matter physics, and statistical mechanics out of equilibrium.
