Focus on APS Topical Groups

Statistical and Nonlinear Physics

Editor's Note:  This article is the second in an occasional series that will highlight the activities of APS's ten topical groups, units that may be small in numbers but that are often the locus of cutting-edge research. The first article in the series appeared in the October 2007 issue.

The topical group on statistical and nonlinear physics (GSNP) brings together people studying widely diverse phenomena, from earthquakes and bird flocking to traditional nonlinear systems and chaos.

Work in statistical and nonlinear physics overlaps naturally with fluid dynamics, computational physics, biological physics, condensed matter physics, and polymer physics.

“It’s a very interdisciplinary group. GSNP includes researchers working on a wide spectrum of nonlinear and nonequilibrium problems that span many disciplines, from biology to earth science,” says GSNP chair Cristina Marchetti of Syracuse University. “One of the goals of the Group has been to strengthen and highlight the connections between these disparate fields and topics.”

Many GSNP members work in areas of nonlinear dynamical systems and chaos, including chaotic behavior that arises in nonlinear pendulums, turbulent fluid flow, and pattern formation. Some of these areas of study have a very natural overlap with fluid dynamics, says Marchetti.  In addition to classical chaotic systems, some GSNP members now study quantum chaos.

Other GSNP members are working on complex materials, or soft condensed matter. This area includes many important systems, such as understanding granular media, liquid crystals, colloids, cells, the collective behavior of bacteria, and the study of earthquakes and crack propagation. Self-assembly and self-organization play key roles in many of these systems.

Yet another class of problems that has caught the attention of statistical physicists lately is the study of networks. Examples of networks include the internet, cell signaling networks, and power grid networks.  “There are ideas and mathematical techniques that can address questions that are relevant to all these systems,” says Marchetti.

These seemingly disparate topics actually have a lot in common, says Marchetti. “What unifies them are the common ideas that are often used to study them,” she says. Principal among those are the notions of scaling and universality. The concept of universality, which has been around for some time, has its roots in the study of phase transitions and critical phenomena that occur in systems composed of many interacting units. At certain characteristic parameter values, these systems exhibit cooperative behavior and undergo a phase change. Near this phase transition, the system is universal in that the behavior of the system at large scales does not depend on the microscopic physics. Consequently, many seemingly disparate systems involving the onset of collective or emergent behavior, can be characterized using these concepts and techniques.

As physics itself has become more interdisciplinary, interest in statistical and nonlinear physics has grown. “The field has really exploded because statistical physics, particularly what we call nonequilibrium statistical physics, is now relevant to a very broad set of disciplines. It is also very important in biology,” says Marchetti.

The field has its roots in equilibrium statistical physics, but has evolved to encompass and emphasize nonequilibrium and dynamical phenomena. It is a field in rapid evolution, with a constantly changing focus. “For a long time physicists have focused on systems at or near thermal equilibrium. Equilibrium statistical mechanics is an old and well developed subject, although many open questions remain,” says Marchetti. On the other hand, the majority of phenomena in nature are not in equilibrium, Marchetti points out. This is clearly always the case in biology.

The membership of GSNP has grown steadily in recent years. Most of the GSNP activities take place at the March Meeting, where every year GSNP sponsors many Focus Sessions and Invited Symposia, often in conjunction with other units. Although most of the GSNP members attend the March Meeting, there is also significant GSNP representation at the annual DFD November meeting. Each year GSNP recommends several APS Fellows to Council for election.

GSNP also sponsors two other activities at the March Meeting. The first is the “Gallery of Images” modeled after a similar exhibition started years ago by DFD. GSNP members are invited to submit a poster or video that provides some striking, yet informative display of work in the area of statistical or nonlinear physics. Such images arise from experiments or from numerical studies, and can be strikingly beautiful while carrying critical scientific information. For example, drops splashing on surfaces create fascinating images when caught by a high speed camera. The entries are displayed at the March Meeting, and winning entries are published in the journal Chaos. Examples from recent contests include visual representations of the community structure in the U.S. House of Representatives, the crowd synchrony on the London Millennium Bridge, and the edge of chaos in pipe flow. Starting next year there will also be a cash prize for the winning entry.

The second GSNP-sponsored activity at the March Meeting is an award for the best graduate student talk in the field. GSNP members are invited to submit nominations of students for the award, and a number of students are selected to give a presentation in a special session at the March Meeting, with a cash prize awarded for the best presentation. 

The Group also has a deep interest in education. Last year, GSNP and the Forum on Education jointly held a symposium on the teaching of non-equilibrium statistical physics, a subject that is not systematically taught in graduate schools.

With nearly 900 members, GSNP, which was formed in 1998, is now one of the largest of the APS topical groups.