Theory Journal Club

 

Date: October 4, 2017

Presenter: Valentin Slepukhin

Paper: "Rhythmogenic neuronal networks, pacemakers, and k-cores" by David J. Schwab, Robijn F. Bruinsma and Alex J. Levine.

Abstract:  The authors of the paper consider the model for describing the preBotzinger Complex of neurons producing rhythmic bursts to govern breathing of mammals. The model consists of N identical excitatory neurons with a connectivity matrix M_{i j}. It appears that the system under such conditions can exist in low or high activity fixed point, or oscillate between these two states. The regime as function of voltage depends solely on geometrical factors, as a number of neurons and connectivity matrix. It appears that transition from low to high activity state is governed by so-called emergent pacemakers, the neurons with the highest number of third-degree neighbors, and the phase transition between oscillating and high activity fixed point is well-described in terms of k-cores, the concept of which will be introduced during the talk.

Read notes here.


Date: September 27, 2017

Presenter: Alec Stein

Paper: “General method for analyzing Higgs potentials,” by J. S. Kim from 1981.

Abstract: The paper is by J. S. Kim from 1981. He was looking at how to find the symmetry group of the absolute minimum of a Landau (group-invariant) potential. (The symmetry group of the minimum will generally be a subgroup of the potential.)  He observed that finding the minimum could be interpreted geometrically, by moving the problem to “orbit space”.  I will discuss this orbit space picture and some consequences of it.


Paper: Statistical theory of equations of state and phase transitions I. Theory of condensation
Authors: C.N. Yang and T.D. Lee Physical Review 87, 404 (1952).

Paper: Statistical theory of equations of state and phase transitions II. Lattice gas and Ising model
Authors: C.N. Yang and T.D. Lee Physical Review 87, 410 (1952).

Presenter: Alex Levine

Dates: July 26 and August 2, 2017

Abstract: These papers address the question of how one may account generally for phase transitions in many body systems.  In short, the pose the problem as follows.  If one may compute the grand partition function of a system as a power series in fugacity (following say the Meyer cluster expansion), the result is an analytic function in that variable. As such it can have none of the singular behavior associated with a phase transition.  Lee and Yang show that this analysis is mistaken.  They show that that the Meyer expansion fails in the thermodynamic limit (V —> infinity)  in precisely the way necessary to admit phase transitions (paper I) and then go on to demonstrate this specifically for the Ising model (paper II).

Notes can be found here: 

Notes on Yang-Lee (1)

Notes on Yang-Lee (2)


Paper: "Fluctuation-Response Theorem for the Active Noisy Oscillator of the Hair-Cell Bundle"

Authors: L. Dinis, P. Martin, J. Barral,  J. Prost, and J. F. Joanny

Presenter: Janaki Sheth

Date: July, 5, 2017

Abstract: "The hair bundle of sensory cells in the vertebrate ear provides an example of a noisy oscillator close to a
Hopf bifurcation. The analysis of the data from both spontaneous and forced oscillations shows a strong
violation of the fluctuation-dissipation theorem, revealing the presence of an underlying active process
that keeps the system out of equilibrium. Nevertheless, we show that a generalized fluctuation-dissipation
theorem, valid for nonequilibrium steady states, is fulfilled within the limits of our experimental accuracy
and computational approximations, when the adequate conjugate degrees of freedom are chosen."


Paper: "Discontinous bundling transition in semiflexible polymer networks induced by Casimir interactions"

Authors: D. Kachan, K. Muller, W. Wall and A. Levine

Presenter: Valentin Slepukhin

Date: June 23, 2017

Abstract: "Fluctuation-induced interactions are an important organizing principle in a variety of soft matter systems. We
investigate the role of fluctuation-based or thermal Casimir interactions between cross linkers in a semiflexible
network. One finds that, by integrating out the polymer degrees of freedom, there is an attractive logarithmic
potential between nearest-neighbor cross linkers in a bundle, with a significantly weaker next-nearest-neighbor
interaction. Here we show that a one-dimensional gas of these strongly interacting linkers in equilibrium with a
source of unbound ones admits a discontinuous phase transition between a sparsely and a densely bound bundle.
This discontinuous transition induced by the long-ranged nature of the Casimir interaction allows for a similarly
abrupt structural transition in semiflexible filament networks between a low cross linker density isotropic phase
and a higher cross link density bundle network. We support these calculations with the results of finite element
Brownian dynamics simulations of semiflexible filaments and transient cross linkers."


Paper: "Confined induced nematic ordering" (to be appear)

Authors: Steven van Duijnhoven, Robijn Bruinsma

Presenter: Steven van Duijnhoven

Date: June 16, 2017


Paper: "Theory of spin glasses"

Authors: S F Edwardst and P W Anderson

Presenter: Alec Stein

Date: June 2, 2017

Description: "A new theory of the class of dilute magnetic alloys. called the spin glasses.
is proposed which offers a simple explanation of the cusp found experimentally in the
susceptibility. The argument is that because the interaction between the spins dissolved
in the matrix oscillates in sign according to distance. there will be no mean ferro-
or antiferromagnetism, but there will be a ground state with the spins aligned in definite
directions. even if these directions appear to be at random. At the critical temperature.
the existence of these preferred directions affects the orientation of the spins. leading
to a cusp in the susceptibility. This cusp is smoothed by an external field. If the potential
between spins on sites i. j is Jijsi.sJ then it is shown that
where e i j is unity or zero according to whether sites i and j are occupied. Although the
behaviour at low T needs a quantum mechanical treatment, it is interesting to complete
the classical calculations down to 7 = 0. Classically the susceptibility tends to a constant
value at T+O. and the specific heat to a constant value."


Paper: "Statistical mechanics of neural networks near saturation"
Authors: Amit, Gutfreund and Sompolinsky

Presenter: Valentin Slepukhin

Date: May, 26, 2017

Description:  "The Hopfield model of a neural network is studied near its saturation, i.e., when the number p of stored patterns increases with the size of the network N, as p = αN. The mean-field theory for this system is described in detail. The system possesses, at low α, both a spin-glass phase and 2p dynamically stable degenerate ferromagnetic phases. The latter have essentially full macroscopic overlaps with the memorized patterns, and provide effective associative memory, despite the spin-glass features. The network can retrieve patterns, at T = 0, with an error of less than 1.5% for α <αc = 0.14."


Paper:  "Coevolutionary Immune System Dynamics Driving Pathogen Speciation"
http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0102821

Authors:  K.J.Schlesinger, S.P.Stromberg, J.M.Carlson.

Presenter: Hongda Jiang

Date: May 19, 2017

Description: The immune system is a complex adaptive system whose richness makes it an excellent model for nonlinear dynamics and biological complexity. We introduce and analyze a predator-prey model of co-evolution between mutating pathogens and the adaptive immune response. Several remarkable properties of the immune system including the cross reactivity of antibody and specificity of antigens will be investigated.


Paper: "Synchronization of Spontaneous Active Motility of Hair Cell Bundles" 

Authors: Tracy-Ying Zhang , Seung Ji  and Dolores Bozovic

Presenter: Tracy Zhang

Date: May, 12, 2017

Description:  "Hair cells of the inner ear exhibit an active process, believed to be crucial for achieving the
sensitivity of auditory and vestibular detection. One of the manifestations of the active pro-
cess is the occurrence of spontaneous hair bundle oscillations in vitro. Hair bundles are
coupled by overlying membranes in vivo; hence, explaining the potential role of innate bun-
dle motility in the generation of otoacoustic emissions requires an understanding of the
effects of coupling on the active bundle dynamics. We used microbeads to connect small
groups of hair cell bundles, using in vitro preparations that maintain their innate oscillations.
Our experiments demonstrate robust synchronization of spontaneous oscillations, with
either 1:1 or multi-mode phase-locking. The frequency of synchronized oscillation was
found to be near the mean of the innate frequencies of individual bundles. Coupling also led
to an improved regularity of entrained oscillations, demonstrated by an increase in the qual-
ity factor."


Paper: "Magnetic Nanoparticles for Ultrafast Mechanical Control of Inner Ear Hair Cells" by Jae-Hyun Lee, Ji-wook Kim, Michael Levy,  Albert Kao,  Seung-hyun Noh,  Dolores Bozovic,  and Jinwoo Cheon 

and

"Magnetic Force Nanoprobe for Direct Observation of Audio Frequency Tonotopy of Hair Cells" by I-wook Kim, Jae-Hyun Lee, Ji-Hyun Ma,  Eunna Chung, Hongsuh Choi, Jinwoong Bok, and Jinwoo Cheon

Presenter: Elizabeth Mills

Date: May, 5, 2017

Description: The talk will follow the technology outlined in the following papers, with the application of this technology to my research questions involving mechanics and dynamics with inner ear bullfrog hair cells.


Paper: Localization as an alternative to Goldstone's theorem

Authors: A.J. McKaneM. Stone

Publication:Annals of Physics Volume 131, Issue 1, January 1981, Pages 36-55

Presenter: Johnathan Kernes

Date: April, 28, 2017

Description: This will continue the theme of last week's talk, specifically discussing how disorder induced phase transitions differ from thermodynamic ones. Specifically, we show that the breaking of a continuous symmetry need not create goldstone bosons in the presence of localized states. This is examined on an electron in a random potential (a very similar but simpler model than elasticity of last week)


Paper: Localization in a disordered elastic medium near two dimensions

Authors: Sajeev John, H. Sompolinsky, and Michael J. Stephen

Publication: Phys. Rev. B 27, 5592 – Published 1 May 1983

Presenter: Johnathan Kernes

Date: April, 21, 2017

Description: This talk will discuss the application of disorder on the localization of classical waves, particularly in the context of elastic waves. In analogy with the quantum mechanical localization of electrons, sufficiently strong placement of random scattering impurities leads to coherent backscattering. Functional integral methods are used to express an effective field theory of such diffusion modes.


Paper: Should All Crystals Be bcc? Landau Theory of Solidification and Crystal Nucleation

Authors: S.Alexander, J.McTague

Publication: Physical Review Letters, 41 10, Septmber, 4, 1978

Presenter: Alec Stein

Date: March, 22, 2017

Description: : The authors give an argument for why, upon cooling from a liquid to a solid, all solids should pass through a bcc phase (provided the "first-order-ness" of the transition is sufficiently weak.)


Paper: Fluctuations of dynamical scaling indices in nonlinear systems
Authors: Jean-Pierre Eckmann and Itamar Procaccia
Publication: Physical Review Letters A, 34, 659 (1986)
Presenter: Lu Shen
Date: October 6, 2016
Description: This paper is as a continuation of his previous talk, deriving how the Lyapunov exponents enter the invariant probability measure exactly for non-equilibrium chaotic systems , based on the strange attractor argument and fractal dimension scaling hypothesis.
Read the notes.


Paper: Probability of Second Law Violations in Shearing Steady States
Authors: D.J. Evans, E.G.D. Cohen, G.P. Evans
Publication: Physical Review Letters 71, Number 15, 2401 (1993).
Presenter: Lu Shen
Date: September 13, 2016
Description: This paper proposed an alternate formula and a non-equilibrium physical system(shearing fluid) to perform a measurable numerical test on the natural invariant measure which the authors showed in their earlier works. The authors have obtained a probability ratio for the reversed sign shear stress. They found out that in such a non-equilibrium system, when the shearing stress is opposite to the direction of the imposed fixed shear rate, the second law of thermodynamics is violated.
Read the notes.


Paper: Steady-State Thermodynamics of Langevin Systems
Authors: Takahiro Hatano and Shin-ichi Sasa
Publication: Physical Review Letters 86, Number 16, 3463 (2001).
Presenter: Alex Levine
Date: August 30, 2016
Description: The authors propose and derive an analog of the second law of thermodynamics applicable to nonequilibrium steady-states. Certain conditions for validity are discussed.
Read the notes.


Paper: Self-consistent Theory of Polymerized Membranes
Authors: Pierre Le Doussal and Leo Radzihovsky 
Publication: Physical Review Letters 69, 1209 (1992).
Presenter: Christian Vaca 
Time/Date: Tuesday 4pm October 7, 2014 in Geology 4606

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