Localization transition for a copolymer in an emulsion

Article / Letter to editorMathematisch Instituu

Localization transition for a copolymer in an emulsion

Article / Letter to editorMathematisch Instituu

Contrasting roles of axonal (pyramidal cell) and dendritic (interneuron) electrical coupling in the generation of neuronal network oscillations

Electrical coupling between pyramidal cell axons, and between interneuron dendrites, have both been described in the hippocampus. What are the functional roles of the two types of coupling? Interneuron gap junctions enhance synchrony of γ oscillations (25-70 Hz) in isolated interneuron networks and also in networks containing both interneurons and principal cells, as shown in mice with a knockout of the neuronal (primarily interneuronal) connexin36. We have recently shown that pharmacological gap junction blockade abolishes kainate-induced γ oscillations in connexin36 knockout mice; without such gap junction blockade, γ oscillations do occur in the knockout mice, albeit at reduced power compared with wild-type mice. As interneuronal dendritic electrical coupling is almost absent in the knockout mice, these pharmacological data indicate a role of axonal electrical coupling in generating the γ oscillations. We construct a network model of an experimental γ oscillation, known to be regulated by both types of electrical coupling. In our model, axonal electrical coupling is required for the γ oscillation to occur at all; interneuron dendritic gap junctions exert a modulatory effect

The critical fugacity for surface adsorption of self-avoiding walks on the honeycomb lattice is 1+21+\sqrt{2}

In 2010, Duminil-Copin and Smirnov proved a long-standing conjecture of Nienhuis, made in 1982, that the growth constant of self-avoiding walks on the hexagonal (a.k.a. honeycomb) lattice is $\mu=\sqrt{2+\sqrt{2}}.$ A key identity used in that proof was later generalised by Smirnov so as to apply to a general O(n) loop model with $n\in [-2,2]$ (the case $n=0$ corresponding to SAWs). We modify this model by restricting to a half-plane and introducing a surface fugacity $y$ associated with boundary sites (also called surface sites), and obtain a generalisation of Smirnov's identity. The critical value of the surface fugacity was conjectured by Batchelor and Yung in 1995 to be $y_{\rm c}=1+2/\sqrt{2-n}.$ This value plays a crucial role in our generalized identity, just as the value of growth constant did in Smirnov's identity. For the case $n=0$, corresponding to \saws\ interacting with a surface, we prove the conjectured value of the critical surface fugacity. A crucial part of the proof involves demonstrating that the generating function of self-avoiding bridges of height $T$, taken at its critical point $1/\mu$, tends to 0 as $T$ increases, as predicted from SLE theory.Comment: Major revision, references updated, 25 pages, 13 figure

Supernova neutrino detection in NOvA

The NOvA long-baseline neutrino experiment uses a pair of large, segmented, liquid-scintillator calorimeters to study neutrino oscillations, using GeV-scale neutrinos from the Fermilab NuMI beam. These detectors are also sensitive to the flux of neutrinos which are emitted during a core-collapse supernova through inverse beta decay interactions on carbon at energies of O(10 MeV). This signature provides a means to study the dominant mode of energy release for a core-collapse supernova occurring in our galaxy. We describe the data-driven software trigger system developed and employed by the NOvA experiment to identify and record neutrino data from nearby galactic supernovae. This technique has been used by NOvA to self-trigger on potential core-collapse supernovae in our galaxy, with an estimated sensitivity reaching out to 10 kpc distance while achieving a detection efficiency of 23% to 49% for supernovae from progenitor stars with masses of 9.6 M☉ to 27 M☉, respectively

Almost unknotted embeddings of graphs and surfaces(Knots and soft-matter physics: Topology of polymers and related topics in physics, mathematics and biology)

この論文は国立情報学研究所の電子図書館事業により電子化されました。We consider the number of embeddings of almost unknotted Θ_k-graphs, 3≤k≤6, in the simple cubic lattice Z^3. We show that to exponential order this number is the same as the number of unknotted Θ_k-graphs. This implies that almost unknotted Θ_k-graphs are exponentially rare in the set of embeddings of Θ_k-graphs. We construct almost unknotted surfaces in Z^4 by spinning and show that to exponential order the numbers of almost unknotted spun Θ_k are equal to the numbers of unknotted spun Θ_k, 4≤k≤6. The case of k=3 is open

Localization transition for a copolymer in an emulsion

In this paper we study a two-dimensional directed self-avoiding walk model of a random copolymer in a random emulsion. The polymer is a random concatenation of monomers of two types, A and B, each occurring with density 1/2. The emulsion is a random mixture of liquids of two types, A and B, organized in large square blocks occurring with density p and 1-p, respectively, where p ¿ (0, 1). The polymer in the emulsion has an energy that is minus a times the number of AA-matches minus ß times the number of BB-matches, where a, ß ¿ R are interaction parameters. Symmetry considerations show that without loss of generality we may restrict our attention to the cone {(a, ß) ¿ R2 : a ?? |ß|}. We derive a variational expression for the quenched free energy per monomer in the limit as the length n of the polymer tends to infinity and the blocks in the emulsion have size Ln such that Ln ¿ 8 and Ln/n ¿ 0. To make the model mathematically tractable, we assume that the polymer can only enter and exit a pair of neighboring blocks at diagonally opposite corners. Although this is an unphysical restriction, it turns out that the model exhibits rich and physically relevant behavior. Let pc ˜ 0.64 be the critical probability for directed bond percolation on the square lattice. We show that for p ?? pc the free energy has a phase transition along one curve in the cone, which turns out to be independent of p. At this curve, there is a transition from a phase where the polymer is fully A-delocalized (i.e., it spends almost all of its time deep inside the A-blocks) to a phase where the polymer is partially AB-localized (i.e., it spends a positive fraction of its time near those interfaces where it diagonally crosses the A-block rather than the B-block). We show that for p <pc the free energy has a phase transition along two curves in the cone, both of which turn out to depend on p. At the first curve there is a transition from a phase where the polymer is fully A,B-delocalized (i.e., it spends almost all of its time deep inside the A-blocks and the B-blocks) to a partially BA-localized phase, while at the second curve there is a transition from a partially BA-localized phase to a phase where both partial BA-localization and partial AB-localization occur simultaneously. We derive a number of qualitative properties of the critical curves. The supercritical curve is nondecreasing and concave with a finite horizontal asymptote. Remarkably, the first subcritical curve does not share these properties and does not converge to the supercritical curve as p ¿ pc. Rather, the second subcritical curve converges to the supercritical curve as p ¿ 0