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List of Events

All seminars take place at 2 pm on Thursdays in Abelson 229, unless otherwise indicated.

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Spring 2018 IGERT Seminars


Thursday, January 25
Jonathan Harper, Brandeis
Title: Lagrangian duality and its applications to holography
Abstract: Dualities are tools which enable us to perceive a problem from a new perspective or framework. In this talk I will illustrate a particular example, Lagrange duality, which has been essential to my own research. Lagrange duality allows one to map a class of constrained minimization problems to a corresponding maximization problem. I will provide several examples of Lagrange duality including application to the physically relevant problem of determining constrained minimal surfaces in spacetimes with holographic duals.

Thursday, March 15
Jonathan Touboul, Brandeis Mathematics
Title: Collective dynamics of random neural networks: complexity, synchronization and insights from random matrices theory
Abstract:
Neurons are electrically excitable cells that collectively process information to respond in a suitable, fast and adaptive manner to stimuli. I will present here a few thoughts and models on effective mathematical descriptions of large-scale neuronal networks and on the role of microscopic network parameters on collective dynamics of large neuronal networks. 
Neural networks, with their asymmetric interactions, communication delays and spatial extension, display dynamics vastly distinct from classical models of equilibrium statistical physics. Deriving limits of large-scale networks and investigating their dynamics, I will exhibit in particular a mysterious and somewhat paradoxical result: neural networks may synchronize when noise or disorder exceed a specific value. Along the same lines, I will come back to a much more classical but equally mysterious transition exhibited some 30 years ago by Sompolinsky and co-workers between a fixed point regime to a chaotic regime as disorder increases. Using random matrix theory, I will show that this transition is related to an exponential explosion of fixed points, and that the complexity happens to be equal to the Lyapunov exponent of the chaotic dynamics, suggesting a possible microscopic explanation for the emergence of chaos in these networks. 
If time allows, I will show that neural networks with balanced excitation and inhibition have a collective dynamics governed by the real or complex nature of an extreme eigenvalues of the connectivity matrix, and thus on new results we developed on the characterization of real eigenvalues of non-symmetric random matrices.

Thursday, March 29
Pathikrit Bhattacharya, Tufts University
Title: Do frictional interfaces really strengthen with age? Insights into the phenomenology and physics of re-strengthening of earthquake bearing faults
Abstract: The earthquake cycle in nature alternates between periods of little or no slip on locked faults interspersed by bursts of rapid slip to release the stored strain energy as seismic waves. In order for this cycle to operate, the fault needs to re-strengthen, i.e., re-lock, between successive seismic events. Laboratory friction experiments provide an important clue to the origins of fault re-strengthening – geological materials undergoing shear driven slip show similar strengthening when slip is (nearly) arrested by unloading a large fraction of the driving shear stress. This strengthening is evidenced by the fact that the peak static friction upon resliding the sample increases linearly with the logarithm of the duration of the period of arrested slip called ‘holds’. Such frictional strengthening shows a remarkable adherence to this linear with log time increase across a wide variety of materials suggesting a degree of universality in the underlying physical processes. Traditionally, this phenomenology has been ascribed to contact aging which can proceed even in the absence of slip. In this physical picture, contact age is considered a proxy for creep induced increase in real contact area of the interface which leads to an increase in the resistance to sliding. To date, the aging model of contact strength remains the most widely used constitutive description of laboratory rock friction.
In my talk, I will discuss recent theoretical and experimental results which instead demonstrate that this widely used aging model fails to capture the salient features of laboratory observed frictional strengthening. Additionally, I will show that frictional strengthening is not only sensitive to interfacial slip but is instead dominantly controlled by it across orders of magnitude variations in slip rate below microns/sec. One implication of this result is that increase in real area of contact through creep, which has been optically recorded in transparent plastic, does not necessarily translate to an increase in interfacial strength. I will discuss statistical physics models which might offer clues as to why.


IGERT Summer Institute 2018

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