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.

MRSEC summer course in Optical Microscopy (June 20-24, 2011)

Optical microscopy has become a powerful experimental tool capable of simultaneously visualizing large scale structures such as entire cells, and fluorescently labeled single molecules within these complex structures. It has found important applications in diverse scientific fields.  The Brandeis Materials Science Research and Enginering Center will offer a one-week intense summer course in optical microscopy from June 20 – June 24, 2011, “Introduction to Optical Microscopy.“  The primary goal of the course is to train students in the fundamentals of microscopy and optics. The students will start by constructing a bright field and fluorescence microscope from simple optical components before learning how to use research grade optical microscopes. After completing the course, students will acquire knowledge necessary for using optical microscopes at limits of their capabilities and critically evaluating their performance.

This summer course is a condensed version of a popular graduate level course in  Quantitative Biology (Quantitative Biology Instrumentation Laboratory QB 120 b).  Our goal is to make this course accessible to students with all scientific backgrounds.  The course will be taught by Zvonimir Dogic, who is a faculty member in the Physics Department at Brandeis University.

More information and application procedures are available at the following website: http://www.brandeis.edu/mrsec/summercourses.html.

MRSEC summer course in Microfluidics (June 27- July 1, 2011)

Microfluidics is a recently introduced field of research area in which scientists study the behavior, precise control, and manipulation of fluids that are geometrically constrained to a small, typically sub-millimeter scale, where the dominant phenomena include diffusion, laminar flow, surface tension, and evaporation.  By incorporating these new tools, researchers are able to create novel functions and methods. Emerging application areas for this technology include micro total analysis system (μTAS), tissue engineering, and drug screening. One of the major benefits of this technology is its ability to make an economical device that requires very small sample and small quantities of expensive reagent.  It may also be possible to integrate more components in a device at higher resolution with this technology.

The Brandeis Materials Science Research and Enginering Center offers a one-week summer course from June 27 – July 1, 2011, “Introduction to Microfludics Technology“. The course will introduce students to the microfabrication technologies available to build microfluidic devices. This course has been created in response to the great interest from industry, government and academia in the field of microfluidics. We will build several microfluidic devices to understand the microscale phenomena and their applications. Throughout the course, we will place an emphasis on hands-on experimentation with microfluidic systems where laminar flow, surface tension, and molecular diffusion dominate.

Students having fun in the cleanroom

The instructor, Dr. Dongshin Kim, received his Ph.D. (2006) degree in Mechanical Engineering, MS degrees in both Biomedical (2004) and Mechanical (2001) Engineering from the University of Wisconsin-Madison. After his Ph.D. program, Dr. Kim received biological training on tissue engineering in the Department of Animal Sciences at the University of Illinois as a postdoctoral associate in 2006. In January of 2009, Dr. Kim joined the Materials Research Science and Engineering Center (MRSEC) at Brandeis University. Since then, Dr. Kim has been collaborating with many faculty members and scientists in the field of life science to implement the microfluidics technology into their researches.

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.

Chirality leads to self-limited self-assembly

Simple building blocks that self-assemble into ordered structures with controlled sizes are essential for nanomaterials applications, but what are the general design principles for molecules that undergo self-terminating self-assembly? The question is addressed in a recent paper in Physical Review Letters by Yasheng Yang, graduate student in Physics, working together with Profs. Meyer and Hagan,  The paper considers molecules that self assemble to form filamentous bundles, and shows that chirality, or asymmetry with respect to a molecule’s mirror image, can result in stable self-limited structures. Using modern computational techniques, the authors demonstrate that chirality frustrates long range order and thereby terminates assembly upon formation of regular self-limited bundles.  With strong interactions, however, the frustration is relieved by defects, which give rise to branched networks or irregular bundles.

Figure: (a) Snapshots of regular chiral bundles. Free energy calculations and dynamics demonstrate that the optimal diameter decreases with increasing chirality. (b) Branched bundles form with strong interactions

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