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We develop a theoretical description of the critical zipping dynamics of a self-folding polymer. We use tension propagation theory and the formalism of the generalized Langevin equation applied to a polymer that contains two complementary parts which can bind to each other. At the critical temperature, the (un)zipping is unbiased and the two strands open and close as a zipper. The number of closed base pairs $n(t)$ displays a subdiffusive motion characterized by a variance growing as $\langle \Delta n^2(t) \rangle \sim t^\alpha$ with $\alpha < 1$ at long times. Our theory provides an estimate of both the asymptotic anomalous exponent $\alpha$ and of the subleading correction term, which are both in excellent agreement with numerical simulations. The results indicate that the tension propagation theory captures the relevant features of the dynamics and shed some new insights on related polymer problems characterized by anomalous dynamical behavior.

Commentaires: 8 pages, 3 figures, submitted

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DOI: 10.1103/PhysRevLett.119.028101
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Efficient bacterial chromosome segregation typically requires the coordinated action of a three-component machinery, fueled by adenosine triphosphate, called the partition complex. We present a phenomenological model accounting for the dynamic activity of this system that is also relevant for the physics of catalytic particles in active environments. The model is obtained by coupling simple linear reaction-diffusion equations with a proteophoresis, or “volumetric” chemophoresis, force field that arises from protein-protein interactions and provides a physically viable mechanism for complex translocation. This minimal description captures most known experimental observations: dynamic oscillations of complex components, complex separation, and subsequent symmetrical positioning. The predictions of our model are in phenomenological agreement with and provide substantial insight into recent experiments. From a nonlinear physics view point, this system explores the active separation of matter at micrometric scales with a dynamical instability between static positioning and traveling wave regimes triggered by the dynamical spontaneous breaking of rotational symmetry.

Commentaires: 6 pages, 3 figures

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DOI: 10.1007/s10955-017-1828-5
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In previous papers, [M1, M2], [M3], we proved the existence as well as regularity of a finite range decomposition for the resolvent $G_{\alpha} (x-y,m^2) = ((-\Delta)^{\alpha\over 2} + m^{2})^{-1} (x-y) $, for $0<\alpha <2$ and all real $m$, in the lattice ${\bf Z}^{d}$ for dimension $d\ge 2$. In this paper, which is a continuation of the previous one, we extend those results by proving the existence as well as regularity of a finite range decomposition for the same resolvent but now on the lattice torus ${\bf Z}^{d}/L^{N+1}{\bf Z}^{d} $ for $d\ge 2$ provided $m\neq 0$ and $0<\alpha <2$. We also prove differentiability and uniform continuity properties with respect to the resolvent parameter $m^{2}$. Here $L$ is any odd positive integer and $N\ge 2$ is any positive integer.

Commentaires: 17 pages

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Erratum to: On a Finite Range Decomposition of the Resolvent of a Fractional Power of the Laplacian

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We investigate the opto-electronic properties of hexagonal boron nitride grown by high temperature plasma-assisted molecular beam epitaxy. We combine atomic force microscopy, spectroscopic ellipsometry, and photoluminescence spectroscopy in the deep ultraviolet to compare the quality of hexagonal boron nitride grown either on sapphire or highly oriented pyrolytic graphite. For both substrates, the emission spectra peak at 235 nm, indicating the high optical quality of hexagonal boron nitride grown by molecular beam epitaxy. The epilayers on highly oriented pyrolytic graphite demonstrate superior performance in the deep ultraviolet (down to 210 nm) compared to those on sapphire. These results reveal the potential of molecular beam epitaxy for the growth of hexagonal boron nitride on graphene, and more generally, for fabricating van der Waals heterostructures and devices by means of a scalable technology.

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Ref Arxiv: 1612.07036
DOI: 10.21468/SciPostPhys.2.1.006
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We show that an inhomogeneous coagulation/decoagulation model can be mapped to a quadratic fermionic model via a Jordan-Wigner transformation. The spectrum for this inhomogeneous model is computed exactly and the spectral gap is described for some examples. We construct our inhomogeneous model from two different homogeneous models joined by one special bond (impurity). The homogeneous models we started with are the coagulation/decoagulation models studied previously using the Jordan-Wigner transformation.

Commentaires: . Réf Journal: SciPost Phys. 2, 006 (2017)

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DOI: 10.1103/PhysRevE.95.012112
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Ising spin-glass models with bimodal, Gaussian, uniform, and Laplacian interaction distributions in dimension five are studied through detailed numerical simulations. The data are analyzed in both the finite-size scaling regime and the thermodynamic limit regime. It is shown that the values of critical exponents and of dimensionless observables at criticality are model dependent. Models in a single universality class have identical values for each of these critical parameters, so Ising spin-glass models in dimension five with different interaction distributions each lie in different universality classes. This result confirms conclusions drawn from measurements in dimension four and dimension two.