Chakraborty lab provides new understanding on the physics of granular materials

By Kabir Ramola, Ph.D

In the late 1980’s Sir Sam Edwards proposed a framework for describing the large scale properties of granular materials, such as sand or salt. In this description, similar to the well-established framework of statistical mechanics, the global properties of a complex system are determined by an average over all possible microscopic configurations consistent with a given global property. This is usually attributable to the very fast dynamics of the constituent particles making up the system. The extension of such treatments to granular systems where particles are static or ‘jammed’ represents a fundamental challenge in this field. Even so, Edwards’ conjecture postulated that for given external parameters such as volume, all possible packings of a granular material are equally likely. Such a conjecture, like Boltzmann’s hypothesis in statistical mechanics, can then be used as a starting point to develop new physical theories for such materials based on statistical principles. Indeed, several frameworks have been developed assuming this conjecture to be true.

Figure 1 : Snapshot of the system studied and illustration of the associated energy landscape at different volume fractions.

A simple illustration of this conjecture would be, if one were to pour sand into a bowl, and not bias the preparation in any way, then all the trillion trillions of configurations allowed for the grains would be equally likely. Clearly such a conjecture is utterly infeasible to test experimentally.  In a recent paper that appeared in Nature Physics, we instead performed detailed numerical computations on a theoretical system of soft disks (in two dimensions) with hard internal cores. We focused on a system of 64 disks which already pushed the limits of current computational power. We found that if one fixes the density of a given system of disks, the probability of a packing occurring depends on the pressure, violating Edwards’ proposition. However, at a critical density, where particles just begin to touch or ‘jam’, this probability remarkably becomes independent of the pressure, and all configurations are indeed equally likely to occur. This jamming point is in fact very interesting in its own right since most granular materials are found at the threshold of being jammed and ‘unjammed’. To be fair to Edwards, the hypothesis was made for ‘hard’ grains in which particles are precisely at this threshold, and therefore our numerics seem to confirm the original statement. This is the first time that this statement has been out to a direct test and will no doubt lead to many interesting directions in the future.

Links to news sources describing this article:

doi: 10.1038/nphys4168
Numerical test of the Edwards conjecture shows that all packings are equally probable at jamming.
Stefano Martiniani, K. Julian Schrenk, Kabir Ramola, Bulbul Chakraborty & Daan Frenkel.
Nature Physics


Colleagues and Students Gather for Astrophysics Symposium

by Roopesh Ojha (PhD ’98)

Radio Galaxy NGC 4261. (credit: Teddy Cheung)

From June 28th through 30th, about fifty former and current students, colleagues and friends of Brandeis astrophysics Professors John Wardle and David Roberts gathered in the Physics building for a symposium titled “When Brandeis met Jansky: astrophysics and beyond.” This event was organized to celebrate their achievements in astrophysics and their impact on generations of students. Their work has established Brandeis as a major player in radio astronomy.

The symposium title refers to Karl Jansky who is credited with starting an entirely new means of studying the cosmos using radio waves. Radio astronomy arrived at Brandeis with Professor Wardle in 1972. He was joined in 1980 by Professor Roberts and together they pioneered a very powerful observational technique called Very Long Baseline Polarimetry. This involves the use of telescopes separated by thousands of kilometers to produce the sharpest images available to astronomers. Their methods allow astronomers to map the magnetic fields in and near celestial objects. With their students and colleagues, John and Dave have exploited this technique to study the magnetic fields in quasars and active galaxies, and near super massive black holes far outside our Milky Way galaxy as well as black holes closer to home.

Physics Conference Group

Professors John Wardle and David Roberts (front right) with former students and colleagues on the steps of the Abelson physics building (photo: Mike Lovett)

The reach of John and Dave’s work was reflected in the content of the presentations and the composition of the attendees, some of whom had traveled from as far afield as South Korea, India, and Europe. All major centers of radio astronomy were represented. At the conference dinner, several former students expressed their appreciation for the roles Dave and John have played as their mentors.

In their presentations, Dave and John described their current projects and highlighted the work of their undergraduates, graduate students and postdoctoral fellows, who have all gone on to successful careers in academia and industry.

The nineteen PhD theses produced by the Brandeis Radio Astronomy group

Professor Roberts has decided to retire at the end of August, though his retirement plans include a huge program of continuing research into unusual-shaped radio galaxies. These may represent galaxy mergers and the possible merger of their central black holes, and is being carried out with colleagues in India. Professor Wardle has no intention of retiring and is expanding his horizons so to speak — he is part of the Event Horizon Telescope collaboration, an international team of astronomers that is attempting to make the first image of the ‘event horizon’* of a black hole!

The symposium was organized by Teddy Cheung (PhD ’05, now at the Naval Research Laboratory) and Roopesh Ojha (PhD ’98, now at NASA, Goddard Space Flight Center), with generous help and support from the Physics Department.

* The boundary around a black hole beyond which nothing can escape.

Two Brandeis Professors Receive 2017 Simons Fellowships, part II

Spectral Flow

Spectral Flow (full caption below)

Two Brandeis professors have been awarded highly prestigious and competitive Simons Fellowships for 2017. Daniel Ruberman received a 2017 Simons Fellowship in Mathematics. Matthew Headrick was awarded a 2017 Simons Fellowship in Theoretical Physics. This is the second of two articles where each recipient describes their award-winning research.

Daniel Ruberman’s research asks “What is the large-scale structure of our world?” Einstein’s unification of physical space and time tells us that the universe is fundamentally 4-dimensional. Paradoxically, the large-scale structure, or topology, of 4-dimensional spaces, is much less understood than the topology in other dimensions. Surfaces (2-dimensional spaces) are completely classified, and the study of 3-dimensional spaces is largely dominated by geometry. In contrast, problems about spaces of dimension greater than 4 are translated, using the technique called surgery theory, into the abstract questions of algebra.

Ruberman will work on several projects studying the large-scale topology of 4-dimensional spaces. His work combines geometric techniques with the study of partial differential equations arising in physics. One major project, with Nikolai Saveliev (Miami) is to test a prediction of the high-dimensional surgery theory, that there should be `exotic’ manifolds that resemble a product of a circle and a 3-dimensional sphere. The proposed method, which would show that this prediction is incorrect, is to compare numerical invariants derived from the solutions to the Yang-Mills and Seiberg-Witten equations, by embedding both in a more complicated master equation. The study of the Seiberg-Witten invariants is complicated by their instability with respect to varying geometric parameters in the theory. A key step in their analysis is the introduction of the notion of end-periodic spectral flow, which compensates for that instability, as illustrated below.

Other projects for the year will apply techniques from 4-dimensional topology to classical problems of combinatorics and geometry about configurations of lines in projective space. In recent years, combinatorial methods have been used to decide if a specified incidence relation between certain objects (“lines”) and other objects (“points”) can be realized by actual points and lines in a projective plane. For the real and complex fields, one can weaken the condition to look for topologically embedded lines (circles in the real case, spheres in the complex case) that meet according to a specified incidence relation. Ruberman’s work with Laura Starkston (Stanford) gives new topological restrictions on the realization of configurations of spheres in the complex projective plane.

Caption: Solutions to the Seiberg-Witten equations of quantum field theory provide topological information about 4-dimensional spaces. However, the set of solutions, or moduli space, can undergo a phase transition as a parameter T is varied, making those solutions hard to count. This figure illustrates a key calculation: the phase transition is equal to the end-periodic spectral flow, a new concept introduced in work of Mrowka-Ruberman-Saveliev. In the figure, the spectral set, illustrated by the red curves, evolves with the parameter T. Every time the spectral set crosses the cylinder, the moduli space changes, gaining or losing points according to the direction of the crossing.

Physics department mourns passing of Professor Emeritus Sam Schweber

Sam SchweberSam Schweber, Professor Emeritus of Physics, died May 14th at the age of 89. A theoretical physicist and historian of science, Sam was among that first generation of Brandeis faculty whose genius turned a fledgling institution into a university of the first rank. He published his first book in 1956, when not yet thirty, and his last in 2012, in his mid-eighties. His was an extraordinary life and career.

Sam was born in Strasbourg and came to this country at the age of 14. Like many immigrants and children of immigrants, he attended college at City College of New York, and he then went on to earn an M.S. from the University of Pennsylvania and a Ph.D. from Princeton. A postdoctoral fellowship at Cornell gave him the special opportunity to work under Hans Bethe (whose biography he wrote, many years later). Sam came to Brandeis in 1955 as associate professor of physics and quickly became involved in building the young department. In 1957, the Physics Department started a graduate program, and the following year it established, at Sam’s initiative, a summer institute in theoretical physics, bringing to campus leading physicists as well as selected graduate students and postdocs, for weeks of seminars and colloquia. The institute ran annually for fifteen years, until the federal funding ceased.

The young Sam Schweber had clearly impressed Hans Bethe. In 1955 he co-authored with Bethe (and a third physicist) the two-volume Mesons and Fields, and in 1960, the same three authors published Quantum Theory of Fields. A year after that, in his foreword to Sam’s new book, An Introduction to Relativistic Quantum Field Theory, Bethe observed, “It is always astonishing to see one’s children grow up, and to find that they can do things which their parents no longer fully understand.” This book remains in print five decades after its initial publication.

Sam continued to conduct research and publish in the field of quantum field theory, while also playing an integral part in the growth of Brandeis University. His scholarly interests then started to shift. Volunteering to teach a course on how probability entered the sciences, he became fascinated with the history of science and chose to spend his next sabbatical in the History of Science Department at Harvard. In the third decade of his career, Sam became a historian of science. He joined our interdepartmental program in History of Ideas, and in 1982 was appointed to the Koret Chair in the History of Ideas.

Sam became equally eminent in his new field, publishing a series of significant books and helping to found and then lead the Dibner Institute for the History of Science and Technology at MIT. Sam brought to his writing not only rigorous historical research and a deep understanding of science, but also a strong interest in the human dimension and social consequences of scientific research and discovery. Among his many books were Einstein and Oppenheimer: The Meaning of Genius, In the Shadow of the Bomb: Oppenheimer, Bethe and the Moral Responsibility of the Scientist, and Nuclear Forces: The Making of the Physicist Hans Bethe. Describing another of Sam’s books, Freeman Dyson wrote that “he has produced a lively and readable narrative history, with a lightness of touch than can come only to one who is absolute master of his subject.”

Sam continued to be an active scholar and author after his retirement from Brandeis in 2003. In 2011, he won the Abraham Pais Prize for History of Physics. The citation spoke of “his sophisticated, technically masterful historical studies” and his “broadly insightful biographical writing on several of the most influential physicists of the 20th century.” Sam was a Fellow of the American Physical Society, the American Association for the Advancement of Science, and the American Academy of Arts and Sciences. A further measure of his stature and influence came in the past few days, from the Max-Planck-Institut fur Wissenschaftsgeschichte: “It is with deep regret that we announce the passing on May 14, 2017 of the distinguished historian of science, Professor Sam S. Schweber. Sam was a dear colleague and mentor of many at the Institute and will be sorely missed by all those who had the great fortune and pleasure of knowing him.”

That sentiment will surely be echoed by the many former Brandeis colleagues and students who greatly admired Sam and learned from him.

Pump without pumps

By Kun-Ta Wu, Ph.D.

Pumping water through a pipe solves the need to provide water in every house. By turning on faucets, we retrieve water at home without needing to carry it from a reservoir with buckets. However, driving water through a pipe requires external pressure; such pressure increases linearly with pipe length. Longer pipes need to be more rigid for sustaining proportionally-increased pressure, preventing pipes from exploding. Hence, transporting fluids through pipes has been a challenging problem for physics as well as engineering communities.

To overcome such a problem, Postdoctoral Associate Kun-Ta Wu and colleagues from the Dogic and Fraden labs, and Brandeis MRSEC doped water with 0.1% v/v active matter. The active matter mainly consisted of kinesin-driven microtubules. These microtubules were extracted from cow brain tissues. In cells, microtubules play an important role in cell activity, such as cell division and nutrient transport. The activity originates from kinesin molecular motors walking along microtubules. In cargo transport, microtubules are like rail tracks; kinesin motors are like trains. When these tracks and trains are doped in water, their motion drives surrounding fluids, generating vortices. The vortices only circulate locally; there is no global net flow.

Wu-Pump without Pumps

Figure: Increasing the height of the annulus induces a transition from locally turbulent to globally coherent flows of a confined active isotropic fluid. The left and right half-plane of each annulus illustrate the instantaneous and time-averaged flow and vorticity map of the self-organized flows. The transition to coherent flows is an intrinsically 3D phenomenon that is controlled by the aspect ratio of the channel cross section and vanishes for channels that are either too shallow or too thin. Adapted from Wu et al. Science 355, eaal1979 (2017).

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Physics Graduate Student Receives Kavli Fellowship

Cesar Agon at Kavli Institute Cesar Agon, a graduate student in the High-Energy and Gravitational Theory group, was awarded a prestigious Graduate Fellowship at the Kavli Institute for Theoretical Physics (KITP) at the University of California, Santa Barbara. KITP is one of the world’s leading centers for research in all areas of theoretical physics. In addition to having its own faculty and postdocs, it hosts visiting faculty from around the world and holds conferences and semester-long programs on topics of current interest. The Graduate Fellowship program allows exceptional students to benefit from this activity and the scientific ambience of KITP by spending a semester there. This is a very competitive program, with only about half a dozen students coming from around the world each semester. Agon, who is advised by Profs. Matthew Headrick, Albion Lawrence, and Howard Schnitzer, is currently spending the spring term at KITP, before heading off to Stony Brook University as a postdoc in the fall.

Back in the summer of 2015, Agon had the opportunity to visit KITP during two important programs on the physics frontiers, both of special interest to him, namely ”Entanglement in Strongly-Correlated Quantum Matter” and ”Quantum Gravity Foundations: UV to IR”. That was a great opportunity to meet in person the leaders of the field from around the world in the relaxed and friendly atmosphere of the KITP. Discussions among the researchers and students were tremendously common all around the institute and there were many activities that facilitated such discussions such as daily coffees, lunches, and dinners.

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