Collective behaviors in active matter

Active matter is describes systems whose constituent elements consume energy and are thus out-of-equilibrium. Examples include flocks or herds of animals, collections of cells, and components of the cellular cytoskeleton. When these objects interact with each other, collective behavior can emerge that is unlike anything possible with an equilibrium system. The types of behaviors and the factors that control them however, remain incompletely understood. In a recent paper in Physical Review Letters, “Excitable patterns in active nematics“, Giomi and coworkers develop a continuum theoretical description motivated by recent experiments from the Dogic group at Brandeis in which microtubules (filamentous cytoskeletal molecules) and clusters of kinesin (a molecular motor) exhibit dramatic spatiotemporal fluctuations in density and alignment. Specifically, they consider a hydrodynamic description for density, flow, and nematic alignment. In contrast to previous theories of this type, the degree of nematic alignment is allowed to vary in space and time.  Remarkably, the theory predicts that the interplay between non-uniform nematic order, activity and flow results in spatially modulated relaxation oscillations, similar to those seen in excitable media and biological examples such as the cardiac cycle. At even higher activity the dynamics is chaotic and leads to large-scale swirling patterns which resemble those seen in recent experiments. An example of the flow pattern is shown below left, and the nematic order parameter, which describes the degree of alignment of the filaments, as shown for the same configuration below right. These predictions can be tested in future experiments on systems of microtubules and motor proteins.

The system behavior for an active nematic at high activity. (left) The velocity field (arrows) is superimposed on a plot of the concentration of active nematogens (green=large concentration, red=small concentration). (right) A plot of the nematic order parameter, S,  (blue=large S, brown=small S) is superimposed on a plot of the nematic director (arrows). The flow under high activity is characterized by large vortices that span lengths of the order of the system size and the director field is organized in grains.

 

A lattice of interacting chemical oscillators

At Brandeis, there is a long tradition of interesting experiments on the Belousov-Zhabostinsky reaction system, with the legendary Zhabotinsky himself having been a part of the fraternity. This reaction system shows interesting oscillatory and stable patterns (see videos on Youtube). In the Fraden lab, an oil emulsion of micron-sized water droplets containing the BZ reactions, was shown to show interesting synchronization properties and complex spatial patterns [Toiya et al, J. Phys. Chem. Lett. 1, 1241 (2010)]. A coupling between the droplets due to preferential diffusion of an inhibitory reactant (bromine) in the oil medium was seen to be responsible for these collective phenomena.

In a new paper titled “Phase and frequency entrainment in locally coupled phase oscillators with repulsive interactions” in Phys. Rev. E, Physics Ph. D student Michael Giver, postdoc Zahera Jabeen and Prof. Bulbul Chakraborty show that neighboring oscillators can be modeled as Kuramoto phase oscillators, coupled nonlinearly to its nearest neighbors. The form of the coupling chosen is repulsive, which favors out of phase synchronization. They show using linear stability analysis as well as numerical study that the stable phase patterns depend on the geometry of the lattice. A linear chain of these repulsively coupled oscillators shows anti-phase synchronization, in which neighboring oscillators show a phase difference of π The phase difference between the neighboring oscillators when placed on a ring however depends on the number of oscillators. In such a case, the locally preferred phase difference of π is ruled out for an odd number of oscillators, as this may lead to frustration. When these oscillators are placed on a triangular lattice in two dimensions, the geometry of the lattice constrains the phase difference between two neighboring oscillators to 2 π /3. Interestingly, domains with different helicities form in the lattice. In each domain, the phases of any three neighboring oscillators can vary continuously in either clockwise or an anti-clockwise direction. Hence, phase difference between the nearest neighbors are seen to be ±2π /3 in the two domains (See figure). A phase difference of π is seen at the interfaces of these domains. These domains can grow in time, resembling domain coarsening in other statistical studies. At large coupling strengths, the domains freeze in size due to frequency synchronization of all the oscillators. Hence, an interplay between frequency synchronization and phase synchronization was seen in this system. Ongoing studies in the BZ experimental setup at the Fraden Lab, find correlations with the above results. Hence, insights into a complex system like the BZ oscillators could be gained using the phase oscillator formalism.

The research was supported by the ACS Petroleum Research Fund and the Brandeis MRSEC. Michael Giver is a trainee in the Brandeis NSF-sponsored IGERT program Time, Space & Structure: Physics and Chemistry of BIological Systems

Physics students present research at 20th Annual Berko Symposium on May 16

On Monday, May 16, the Physics Department will hold the Twentieth Annual Student Research Symposium in Memory of Professor Stephan Berko in Abelson 131. The symposium will end with talks by the two Berko Prize winning students, undergraduate Netta Engelhardt and graduate student Tim Sanchez. The whole department then gathers for a lunch of cold cuts, cookies and conversation. “It’s a great way to close out the academic year,” said Professor of Astrophysics and Department Chair John Wardle. “We come together to celebrate our students’ research and hear what the different research groups are doing.”

The undergraduate speakers will describe their senior thesis honors research. This is the final step in gaining an honors degree in physics, and most of them will also be co-authors on a paper published in a mainline science journal. The graduate student speakers are in the middle of their PhD research, and will disucss their progress and their goals.

The prize winners are nominated and chosen by the faculty for making particularly noteworthy progress in their research. Graduate student winner Sanchez’ talk is titled “Reconstructing cilia beating from the ground up.” He works in Professor Zvonimir Dogic’s lab studying soft condensed matter. Undergraduate winner Engelhardt’s talk is titled “A New Approach to Solving the Hermitian Yang-Mills Equations”. She works with Professors Matt Headrick and Bong Lian (Math) on problems in theoretical physics and string theory. The schedule for Monday morning and abstracts of all the talks can be found on the Physics Department website.

Sanchez’ research very much represents the growing interdisciplinary nature of science at Brandeis. Here, a physicist’s approach is used to study a biological organism. Professor Zvonimir Dogic says of his work “He has made a whole series of important discoveries that are going to have a measurable impact on a number of diverse fields ranging from cell biology, biophysics, soft matter physics and non-equilibrium statistical mechanics.  His discoveries have fundamentally transformed the direction of my laboratory and probably of many other laboratories as well.”

Engelhardt’s research is much more abstract and mathematical, and concerns fundamental problems in string theory, not usually an area tackled by undergraduates. Professor Headrick says “Netta really, really wants to be a theoretical physicist, preferably a string theorist. She has a passion for mathematics, physics, and the connections between them.” He adds that she is utterly fearless in tackling hard problems. Netta has been awarded an NSF Graduate Research Fellowship based on her undergraduate work here.  Next year she will enter graduate school at UC Santa Barbara and will likely work with eminent string theorist Gary Horowitz, who has already supervised the PhD research of two other Brandeis physics alumni, Matthew Roberts ’05, and Benson Way ’08.

This Student Research Symposium is now in its 20th year. The “First Annual…..” (two words which are always unwise to put next to each other) was initiated in 1992 by Wardle to honor Professor Stephan Berko, who had died suddenly the previous year. Family, friends and colleagues contributed to a fund to support and celebrate student research in his memory. This provides the prize money which Netta and Tim will share.

Stephan Berko was a brilliant and volatile experimental physicist who was one of the founding members of the physics department. He was born in Romania in 1924 and was a survivor of both the Auschwitz and Dachau concentration camps. He came to the United States under a Hillel Foundation scholarship and obtained his PhD at the University of Virginia. He came to Brandeis in 1961 to establish a program in experimental physics and worked tirelessly to build up the department. Together with Professors Karl Canter (dec. 2006) and Alan Mills (now at UC Riverside) he established Brandeis as a world center for research into positrons (the anti-matter mirror image of ordinary electrons). In a series of brilliant experiments they achieved many “firsts,” culminating in election to the National Academy of Sciences for Steve, and, it has been rumored, in a Nobel Prize nomination for the three of them. Steve was as passionate about teaching as he was about research, and when he died, it seemed most appropriate to honor his memory by celebrating the research of our graduate and undergraduate students. During the coffee break on Monday, we will show a movie of Steve lecturing on “cold fusion,” a headline-grabbing but phony claim for producing cheap energy from 1989.

Graduate Student Andreas Rauch awarded Outstanding Teaching Fellow in Physics

Graduate student Andreas Rauch has been awarded the Outstanding Teaching Fellow award in Physics based on his overall teaching excellence, student and course instructor evaluations, and letters from faculty.  According to Professor John Wardle, Chair of the Physics Department, “Andreas’ several years of teaching math in German schools has helped make him one of the best and most experienced Teaching Fellows I have known. This award is very well deserved.”  Andreas has been a teaching fellow in Physics 29a, Electronics Laboratory with Professor Larry Kirsch; Physics 25b, Astrophysics with Professor John Wardle; Physics 19b, Physics Laboratory II with Professor Zvonimir Dogic; and Physics 31a, Quantum Theory I with Professor Matthew Headrick.

Four other teaching fellows in the sciences will also be recognized at this year’s TF Award reception on May 6:

Mark Bezpalko (Chemistry)
Ryan Broderick (Mathematics)
Xiaochuan Cai (Chemistry)
Fan Zhao (Chemistry)

NSF CAREER Award for Headrick

Assistant Professor of Physics Matthew Headrick has received a Faculty Early Career Development (CAREER) award from the National Science Foundation. Headrick’s project “CAREER: Holography, Quantum Information, and Elliptic Relativity” will fund his research exploring issues in string theory and classical and quantum gravity. The two projects address 1) study of the thermal and statistical physics of holographic systems, and quantum gravity more generally, through the lens of quantum information theory, and 2) continuing the development of practical, general methods for numerically solving the elliptic Einstein equation to find static, stationary, and Euclidean metrics for higher-dimensional black holes and compactification spaces. NSF grants require broader impact activites. Headrick will participate in TheoryNet, an NSF-funded program in which high-energy physicists visit high-school science classrooms, and will also work with the Brandeis Science Posse program.

Associate Professor Zvonimir Dogic, also in the Physics department, was a 2010 recipient of an NSF CAREER award.

Barry and Dogic receive 2010 Cozzarelli Prize

Physics graduate student Edward Barry and Professor Zvonimir Dogic have been selected to receive the 2010 Cozzarelli Prize in Engineering and Applied Sciences from the Proceedings of the National Academy of Sciences (PNAS) for their work entitled “Entropy driven self-assembly of non-amphiphilic colloidal membranes.”

The work of Barry and Dogic was selected for exploring a novel pathway for the self-assembly of 2D fluid-like surfaces or monolayer membranes from non-amphiphilic molecules. Amphiphilic molecules consist of immiscible components, such as a hydrophobic tail and a hydrophilic head, which are irreversibly linked to each other, thus frustrating their bulk separation. When added to water, these molecules self-assemble into a variety of structures in order to satisfy competing affinities for the solvent. One particular structure, a bilayer membrane, which is a thin flexible sheet with remarkable mechanical and chemical properties, plays an essential role in biology, physics, and material science. Over the past decade the paramount example of conventional amphiphilic self-assembly has inspired the synthesis of numerous amphiphilic-type building blocks for studies of membrane self-assembly including various block-copolymers, heterogeneous nanorods, and hybrid protein-polymer complexes. Underlying all of these studies is the belief that amphiphilic molecules are an essential requirement for membrane assembly.

Barry and Dogic, using a combination of theory and experiments, describe for the first time a set of design principles required for the assembly of non-amphiphilic membranes in which the constituent rod-like molecules are chemically homogeneous.  Using a simple mixture of filamentous bacteriophages and non-adsorbing polymer, they were able to assemble macroscopic membranes roughly 4-5 orders of magnitude larger than the constituent molecules themselves. Due to unique properties of their system, Barry and Dogic were able to characterize the physical behavior of the resulting non-amphiphilic membranes at all relevant length scales and provide an entropic mechanism that explains their stability. The importance of these results lies in their potential to establish a fundamentally different route toward solution based self-assembly of 2D materials.

Papers selected for the Cozzarelli Prize were chosen from more than 3,700 research articles published by PNAS in 2010 and represent the six broadly defined classes under which the National Academy of Sciences is organized. The award was established in 2005 and named the Cozzarelli Prize in 2007 to honor late PNAS Editor-in-Chief Nicholas R. Cozzarelli. The annual award acknowledges recently published papers that reflect scientific excellence and originality. The 2010 awards will be presented at the PNAS Editorial Board Meeting, and awardees are recognized at the awards ceremony, during the National Academy of Sciences Annual Meeting on May 1, 2011, in National Harbor, Maryland.

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