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.

Summer SciFest 2017 to Showcase Undergrad Research on August 3

SciFest 2016Brandeis Summer Scifest, an Undergraduate Research Poster Session, will be held on Thursday, August 3. The poster session will be 1:00 to 3:00 pm in the Shapiro Science Center atrium.

SciFest is an annual poster session for undergraduates who have spent their summers working in both on-campus and off-campus labs doing scientific research, usually alongside grad students, postdocs and faculty members. It an opportunity for undergraduates from across the Division of Science, including summer visitors and Brandeis students, to present posters summarizing their research.

There were 106 posters presented last year. Prospective presenters for this year should note that the deadline to register for this event is July 25. Early registrants will get the prime locations for their posters!

The public is invited to attend and to discuss research with the students. As always, refreshments will be served.

2nd Boston Symposium of Encoded Library Platforms to be held Aug. 4

BSELP imageThe Brandeis Chemistry Department, together with GlaxoSmithKline and Pharmaron, is hosting the 2nd Boston Symposium of Encoded Library Platforms on August 4th in the Shapiro Theater. This symposium will feature 8 speakers from industry and academic labs, covering the newest developments in the technology of encoded small molecule libraries and related topics.

For several decades, major efforts have gone into discovering drug leads by high-throughput screening, in which “libraries” of thousands to millions of random compounds are tested in a highly repetitive fashion for biological activity, such as the ability to inhibit an enzyme. A new and elegant alternative to this process is the use of encoded libraries, in which each random molecule within the library bears a “tag” of DNA with a unique sequence. Libraries containing hundreds of millions of DNA-tagged compounds can be incubated with a target protein in a single tube, and those which bind to the target can be identified by high-throughput sequencing of the DNA barcodes in the protein-bound fraction. This approach has gained great popularity in the last few years, and is just this week the cover story of Chemical & Engineering News.

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.

Learning to see

How do we learn to see? Proper visual experience during the first weeks and months of life is critical for the proper development of the visual system. But how does experience modify neural circuits so that they exhibit the proper responses to visual stimuli? Knowledge of the mechanisms by which the brain is constructed early in development should inspire new therapies for repairing the brain if it develops improperly or is damaged by disease or injury.

At the present time, it is not possible to directly view all or even most connections within a living neural circuit. Therefore, neuroscientists often build computational models to study how these circuits may be constructed and how they may change with experience. A good model allows scientists to understand how these circuits may work in principle, and offers testable predictions that can be examined in the living animal to either support or refute the model.

Undergraduate Ian Christie ’16 was interested in understanding how neural circuits in the ferret visual system become selective to visual motion. At the time of eye opening, neurons in ferret visual cortex respond to an object moving in either of two opposite directions. With about a week of visual experience, each neuron develops a preference for only one of these directions, and greatly reduces its responses to the opposite direction.

Previous models of this process posited that the primary source of the change was in the organization and pattern of inputs to the cortex. But, recent experiments from the Van Hooser lab (Roy/Osik/Ritter et al., 2016) showed that stimulating the cortex by itself was sufficient to cause the development of motion selectivity, which suggests that some changes within the cortex itself must be underlying the increase in selectivity, at least in part. Further, other experiments in the lab of former Brandeis postdoc Arianna Maffei (Griffen et al., 2012) have shown that the cortex becomes less excitable to focal stimulation over the first weeks after eye opening.

Ian constructed families of computational models that could account for both of these observations. In the model, columns of neurons in the cortex already receive input that is slightly selective for motion in one of two opposite directions, but the connections between these cortical columns are so strong that both columns respond to both directions. However, the activity that is caused by simulated visual experience activates synaptic plasticity mechanisms in the model, that served to greatly reduce the strength of these connections between the columns, allowing motion selectivity to emerge in the cortical columns. The project was supervised by faculty members Paul Miller and Stephen Van Hooser, and the results were published in Journal of Neurophysiology (Christie et al., 2017).

Future experiments will now look for evidence of weaker connectivity between cortical neurons with visual experience.

This work was supported by the “Undergraduate and Graduate Training in Computational Neuroscience” grant to Brandeis University from NIH, and by the National Eye Institute grant EY022122. It also used the Brandeis University High Performance Computing Cluster.

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