Delocalization transition of the selective interface model: distribution of pseudo-critical temperatures

According to recent progress in the finite size scaling theory of critical disordered systems, the nature of the phase transition is reflected in the distribution of pseudo-critical temperatures $T_c(i,L)$ over the ensemble of samples $(i)$ of size $L$. In this paper, we apply this analysis to the delocalization transition of an heteropolymeric chain at a selective fluid-fluid interface. The width $\Delta T_c(L)$ and the shift $[T_c(\infty)-T_c^{av}(L)]$ are found to decay with the same exponent $L^{-1/\nu_{R}}$, where $1/\nu_{R} \sim 0.26$. The distribution of pseudo-critical temperatures $T_c(i,L)$ is clearly asymmetric, and is well fitted by a generalized Gumbel distribution of parameter $m \sim 3$. We also consider the free energy distribution, which can also be fitted by a generalized Gumbel distribution with a temperature dependent parameter, of order $m \sim 0.7$ in the critical region. Finally, the disorder averaged number of contacts with the interface scales at $T_c$ like $L^{\rho}$ with $\rho \sim 0.26 \sim 1/\nu_R$.Comment: 9 pages,6 figure

Lyman Alpha and MgII as Probes of Galaxies and their Environments

Ly{\alpha} emission, Ly{\alpha} absorption and MgII absorption are powerful tracers of neutral hydrogen. Hydrogen is the most abundant element in the universe and plays a central role in galaxy formation via gas accretion and outflows, as well as being the precursor to molecular clouds, the sites of star formation. Since 21cm emission from neutral hydrogen can only be directly observed in the local universe, we rely on Ly{\alpha} emission, and Ly{\alpha} and MgII absorption to probe the physics that drives galaxy evolution at higher redshifts. Furthermore, these tracers are sensitive to a range of hydrogen densities that cover the interstellar medium, the circumgalactic medium and the intergalactic medium, providing an invaluable means of studying gas physics in regimes where it is poorly understood. At high redshift, Ly{\alpha} emission line searches have discovered thousands of star-forming galaxies out to z = 7. The large Ly{\alpha} scattering cross-section makes observations of this line sensitive to even very diffuse gas outside of galaxies. Several thousand more high-redshift galaxies are known from damped Ly{\alpha} absorption lines and absorption by the MgII doublet in quasar and GRB spectra. MgII, in particular, probes metal-enriched neutral gas inside galaxy haloes in a wide range of environments and redshifts (0.1 < z < 6.3), including the so-called redshift desert. Here we review what observations and theoretical models of Ly{\alpha} emission, Ly{\alpha} and MgII absorption have told us about the interstellar, circumgalactic and intergalactic medium in the context of galaxy formation and evolution.Comment: 59 Pages, 19 Figures, 1 Table. Accepted for publication in Publications of the Astronomical Society of the Pacifi

Smoothening of Depinning Transitions for Directed Polymers with Quenched Disorder

We consider disordered models of pinning of directed polymers on a defect line, including (1+1)-dimensional interface wetting models, disordered Poland--Scheraga models of DNA denaturation and other (1+d)-dimensional polymers in interaction with columnar defects. We consider also random copolymers at a selective interface. These models are known to have a (de)pinning transition at some critical line in the phase diagram. In this work we prove that, as soon as disorder is present, the transition is at least of second order: the free energy is differentiable at the critical line, and the order parameter (contact fraction) vanishes continuously at the transition. On the other hand, it is known that the corresponding non-disordered models can have a first order (de)pinning transition, with a jump in the order parameter. Our results confirm predictions based on the Harris criterion.Comment: 4 pages, 1 figure. Version 2: references added, minor changes made. To appear on Phys. Rev. Let

Numerical study of the disordered Poland-Scheraga model of DNA denaturation

We numerically study the binary disordered Poland-Scheraga model of DNA denaturation, in the regime where the pure model displays a first order transition (loop exponent $c=2.15>2$). We use a Fixman-Freire scheme for the entropy of loops and consider chain length up to $N=4 \cdot 10^5$, with averages over $10^4$ samples. We present in parallel the results of various observables for two boundary conditions, namely bound-bound (bb) and bound-unbound (bu), because they present very different finite-size behaviors, both in the pure case and in the disordered case. Our main conclusion is that the transition remains first order in the disordered case: in the (bu) case, the disorder averaged energy and contact densities present crossings for different values of $N$ without rescaling. In addition, we obtain that these disorder averaged observables do not satisfy finite size scaling, as a consequence of strong sample to sample fluctuations of the pseudo-critical temperature. For a given sample, we propose a procedure to identify its pseudo-critical temperature, and show that this sample then obeys first order transition finite size scaling behavior. Finally, we obtain that the disorder averaged critical loop distribution is still governed by $P(l) \sim 1/l^c$ in the regime $l \ll N$, as in the pure case.Comment: 12 pages, 13 figures. Revised versio

Estimation and comparison of signed symmetric covariation coefficient and generalized association parameter for alpha-stable dependence modeling

Accepté à Communications in Statistics - Theory and methodsInternational audienceIn this paper we study the estimators of two measures of dependence: the signed symmetric covariation coefficient proposed by Garel and Kodia and the generalized association parameter put forward by Paulauskas. In the sub-Gaussian case, the signed symmetric covariation coefficient and the generalized association parameter coincide. The estimator of the signed symmetric covariation coefficient proposed here is based on fractional lower-order moments. The estimator of the generalized association parameter is based on estimation of a stable spectral measure. We investigate the relative performance of these estimators by comparing results from simulations

A simple model for DNA denaturation

Following Poland and Scheraga, we consider a simplified model for the denaturation transition of DNA. The two strands are modeled as interacting polymer chains. The attractive interactions, which mimic the pairing between the four bases, are reduced to a single short range binding term. Furthermore, base-pair misalignments are forbidden, implying that this binding term exists only for corresponding (same curvilinear abscissae) monomers of the two chains. We take into account the excluded volume repulsion between monomers of the two chains, but neglect intra-chain repulsion. We find that the excluded volume term generates an effective repulsive interaction between the chains, which decays as $1/r^{d-2}$. Due to this long-range repulsion between the chains, the denaturation transition is first order in any dimension, in agreement with previous studies.Comment: 10 page

Statistics of first-passage times in disordered systems using backward master equations and their exact renormalization rules

We consider the non-equilibrium dynamics of disordered systems as defined by a master equation involving transition rates between configurations (detailed balance is not assumed). To compute the important dynamical time scales in finite-size systems without simulating the actual time evolution which can be extremely slow, we propose to focus on first-passage times that satisfy 'backward master equations'. Upon the iterative elimination of configurations, we obtain the exact renormalization rules that can be followed numerically. To test this approach, we study the statistics of some first-passage times for two disordered models : (i) for the random walk in a two-dimensional self-affine random potential of Hurst exponent $H$, we focus on the first exit time from a square of size $L \times L$ if one starts at the square center. (ii) for the dynamics of the ferromagnetic Sherrington-Kirkpatrick model of $N$ spins, we consider the first passage time $t_f$ to zero-magnetization when starting from a fully magnetized configuration. Besides the expected linear growth of the averaged barrier $\bar{\ln t_{f}} \sim N$, we find that the rescaled distribution of the barrier $(\ln t_{f})$ decays as $e^{- u^{\eta}}$ for large $u$ with a tail exponent of order $\eta \simeq 1.72$. This value can be simply interpreted in terms of rare events if the sample-to-sample fluctuation exponent for the barrier is $\psi_{width}=1/3$.Comment: 8 pages, 4 figure

On the multifractal statistics of the local order parameter at random critical points : application to wetting transitions with disorder

Disordered systems present multifractal properties at criticality. In particular, as discovered by Ludwig (A.W.W. Ludwig, Nucl. Phys. B 330, 639 (1990)) on the case of diluted two-dimensional Potts model, the moments $\bar{\rho^q(r)}$ of the local order parameter $\rho(r)$ scale with a set $x(q)$ of non-trivial exponents $x(q) \neq q x(1)$. In this paper, we revisit these ideas to incorporate more recent findings: (i) whenever a multifractal measure $w(r)$ normalized over space $\sum_r w(r)=1$ occurs in a random system, it is crucial to distinguish between the typical values and the disorder averaged values of the generalized moments $Y_q =\sum_r w^q(r)$, since they may scale with different generalized dimensions $D(q)$ and $\tilde D(q)$ (ii) as discovered by Wiseman and Domany (S. Wiseman and E. Domany, Phys Rev E {\bf 52}, 3469 (1995)), the presence of an infinite correlation length induces a lack of self-averaging at critical points for thermodynamic observables, in particular for the order parameter. After this general discussion valid for any random critical point, we apply these ideas to random polymer models that can be studied numerically for large sizes and good statistics over the samples. We study the bidimensional wetting or the Poland-Scheraga DNA model with loop exponent $c=1.5$ (marginal disorder) and $c=1.75$ (relevant disorder). Finally, we argue that the presence of finite Griffiths ordered clusters at criticality determines the asymptotic value $x(q \to \infty) =d$ and the minimal value $\alpha_{min}=D(q \to \infty)=d-x(1)$ of the typical multifractal spectrum $f(\alpha)$.Comment: 17 pages, 20 figure

On Heteropolymer Shape Dynamics

We investigate the time evolution of the heteropolymer model introduced by Iori, Marinari and Parisi to describe some of the features of protein folding mechanisms. We study how the (folded) shape of the chain evolves in time. We find that for short times the mean square distance (squared) between chain configurations evolves according to a power law, $D \sim t ^\nu$. We discuss the influence of the quenched disorder (represented by the randomness of the coupling constants in the Lennard-Jones potential) on value of the critical exponent. We find that $\nu$ decreases from $\frac{2}{3}$ to $\frac{1}{2}$ when the strength of the quenched disorder increases.Comment: 12 pages, very simple LaTeX file, 6 figures not included, sorry. SCCS 33

Copolymer adsorption kinetics at a selective liquid-liquid interface: Scaling theory and computer experiment

We consider the adsorption kinetics of a regular block-copolymer of total length $N$ and block size $M$ at a selective liquid-liquid interface in the limit of strong localization. We propose a simple analytic theory based on scaling considerations which describes the relaxation of the initial coil into a flat-shaped layer. The characteristic times for attaining equilibrium values of the gyration radius components perpendicular and parallel to the interface are predicted to scale with chain length $N$ and block length $M$ as $\tau_{\perp} \propto M^{1+2\nu}$ (here $\nu\approx 0.6$ is the Flory exponent) and as $\tau_{\parallel} \propto N^2$, although initially the rate of coil flattening is expected to decrease with block size as $\propto M^{-1}$. Since typically $N\gg M$ for multiblock copolymers, our results suggest that the flattening dynamics proceeds faster perpendicular rather than parallel to the interface. We also demonstrate that these scaling predictions agree well with the results of extensive Monte Carlo simulations of the localization dynamics.Comment: 4 pages, 4 figures, submited to Europhys. Let