Directed polymer in a random medium of dimension 1+1 and 1+3: weights statistics in the low-temperature phase

We consider the low-temperature $T<T_c$ disorder-dominated phase of the directed polymer in a random potentiel in dimension 1+1 (where $T_c=\infty$) and 1+3 (where $T_c<\infty$). To characterize the localization properties of the polymer of length $L$, we analyse the statistics of the weights $w_L(\vec r)$ of the last monomer as follows. We numerically compute the probability distributions $P_1(w)$ of the maximal weight $w_L^{max}= max_{\vec r} [w_L(\vec r)]$, the probability distribution $\Pi(Y_2)$ of the parameter $Y_2(L)= \sum_{\vec r} w_L^2(\vec r)$ as well as the average values of the higher order moments $Y_k(L)= \sum_{\vec r} w_L^k(\vec r)$. We find that there exists a temperature $T_{gap}<T_c$ such that (i) for $T<T_{gap}$, the distributions $P_1(w)$ and $\Pi(Y_2)$ present the characteristic Derrida-Flyvbjerg singularities at $w=1/n$ and $Y_2=1/n$ for $n=1,2..$. In particular, there exists a temperature-dependent exponent $\mu(T)$ that governs the main singularities $P_1(w) \sim (1-w)^{\mu(T)-1}$ and $\Pi(Y_2) \sim (1-Y_2)^{\mu(T)-1}$ as well as the power-law decay of the moments $\bar{Y_k(i)} \sim 1/k^{\mu(T)}$. The exponent $\mu(T)$ grows from the value $\mu(T=0)=0$ up to $\mu(T_{gap}) \sim 2$. (ii) for $T_{gap}<T<T_c$, the distribution $P_1(w)$ vanishes at some value $w_0(T)<1$, and accordingly the moments $\bar{Y_k(i)}$ decay exponentially as $(w_0(T))^k$ in $k$. The histograms of spatial correlations also display Derrida-Flyvbjerg singularities for $T<T_{gap}$. Both below and above $T_{gap}$, the study of typical and averaged correlations is in full agreement with the droplet scaling theory.Comment: 13 pages, 29 figure

Cross-border care and healthcare quality improvement in Europe: the MARQuIS research project

Citizens are increasingly crossing borders within the European Union (EU). Europeans have always been free to travel to receive care abroad, but if they wished to benefit from their statutory social protection scheme, they were subject to their local or national legislation on social protection. This changed in 1991 with the European Court of Justice defining healthcare as a service, starting a debate on the right balance between different principles in European treaties: movement of persons, goods and services, versus the responsibility of member states to organise their healthcare systems. Simultaneously, cross-border cooperation has developed between member states

Effects of tidal-forcing variations on tidal properties along a narrow convergent estuary

A 1D analytical framework is implemented in a narrow convergent estuary that is 78 km in length (the Guadiana, Southern Iberia) to evaluate the tidal dynamics along the channel, including the effects of neap-spring amplitude variations at the mouth. The close match between the observations (damping from the mouth to ∼ 30 km, shoaling upstream) and outputs from semi-closed channel solutions indicates that the M2 tide is reflected at the estuary head. The model is used to determine the contribution of reflection to the dynamics of the propagating wave. This contribution is mainly confined to the upper one third of the estuary. The relatively constant mean wave height along the channel (< 10% variations) partly results from reflection effects that also modify significantly the wave celerity and the phase difference between tidal velocity and elevation (contradicting the definition of an “ideal” estuary). Furthermore, from the mouth to ∼ 50 km, the variable friction experienced by the incident wave at neap and spring tides produces wave shoaling and damping, respectively. As a result, the wave celerity is largest at neap tide along this lower reach, although the mean water level is highest in spring. Overall, the presented analytical framework is useful for describing the main tidal properties along estuaries considering various forcings (amplitude, period) at the estuary mouth and the proposed method could be applicable to other estuaries with small tidal amplitude to depth ratio and negligible river discharge.info:eu-repo/semantics/publishedVersio

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

Lyapunov exponents as a dynamical indicator of a phase transition

We study analytically the behavior of the largest Lyapunov exponent $\lambda_1$ for a one-dimensional chain of coupled nonlinear oscillators, by combining the transfer integral method and a Riemannian geometry approach. We apply the results to a simple model, proposed for the DNA denaturation, which emphasizes a first order-like or second order phase transition depending on the ratio of two length scales: this is an excellent model to characterize $\lambda_1$ as a dynamical indicator close to a phase transition.Comment: 8 Pages, 3 Figure

Proportion of various types of thyroid disorders among newborns with congenital hypothyroidism and normally located gland: A regional cohort study

Objective To determine the proportion of the various types of thyroid disorders among newborns detected by the neonatal TSH screening programme, with a normally located thyroid gland.Patients and methods Of the 882 575 infants screened in our centre between 1981 and 2002, 85 infants with a normally located gland had persistent elevation of serum TSH values (an incidence of 1/10 383). Six of these 85 patients were lost to follow-up and were therefore excluded from the study. During follow-up, patients were classified as having permanent or transient hypothyroidism.Results Among the 79 patients included in the study, transient (n = 30, 38% of cases) and permanent (n = 49, 62% of cases) congenital hypothyroidism (CH) was demonstrated during the follow-up at the age of 0.7 +/- 0.6 years and 2.6 +/- 1.8 years (P &lt; 0.0001), respectively. The proportion of premature births was significantly higher in the group with transient CH (57%) than in the group with permanent CH (2%) (P &lt; 0.0001). A history of iatrogenic iodine overload was identified during the neonatal period in 69% of transient cases. Among permanent CH cases (n = 49), patients were classified as having a goitre (n = 27, 55% of cases), a normal sized and shaped thyroid gland (n = 14, 29% of cases) or a hypoplastic gland (n = 8, 16% of cases). The latter patients demonstrated global thyroid hypoplasia (n = 3), a right hemithyroid (n = 2), hypoplasia of the left lobe (n = 2), or asymmetry in the location of the two lobes (n = 1). Patients with a normal sized and shaped thyroid gland showed a significantly less severe form of hypothyroidism than those with a goitre or a hypoplastic thyroid gland (P &lt; 0.0002). Among permanent CH cases, those with a goitre (n = 27) had an iodine organification defect (n = 10), Pendred syndrome (n = 1), a defect of thyroglobulin synthesis (n = 8), or a defect of sodium iodine symporter (n = 1), and in seven patients no aetiology could be determined. Among permanent cases with a normal sized and shaped thyroid gland (n = 14), a specific aetiology was found in only one patient (pseudohypoparathyroidism) and two patients had Down's syndrome. Among those with a globally hypoplastic gland, a TSH receptor gene mutation was found in two patients.Conclusions A precise description of the phenotype can enhance our understanding of various forms of neonatal hypothyroidism as well as their prevalence and management. It also helps to identify cases of congenital hypothyroidism of unknown aetiology, which will need to be investigated in collaboration with molecular biologists

Statistical physics of the melting of inhomogeneous DNA

We studied how the inhomogeneity of a sequence affects the phase transition that takes place at DNA melting. Unlike previous works, which considered thermodynamic quantities averaged over many different inhomogeneous sequences, we focused on precise sequences and investigated the succession of local openings that lead to their dissociation. For this purpose, we performed Transfer Integral type calculations with two different dynamical models, namely the heterogeneous Dauxois-Peyrard-Bishop model and the model based on finite stacking enthalpies we recently proposed. It appears that, for both models, the essential effect of heterogeneity is to let different portions of the investigated sequences open at slightly different temperatures. Besides this macroscopic effect, the local aperture of each portion indeed turns out to be very similar to that of a homogeneous sequence with the same length. Rounding of each local opening transition is therefore merely a size effect. For the Dauxois-Peyrard-Bishop model, sequences with a few thousands base pairs are still far from the thermodynamic limit, so that it is inappropriate, for this model, to discuss the order of the transition associated with each local opening. In contrast, sequences with several hundreds to a few thousands base pairs are pretty close to the thermodynamic limit for the model we proposed. The temperature interval where power laws holds is consequently broad enough to enable the estimation of critical exponents. On the basis of the few examples we investigated, it seems that, for our model, disorder does not necessarily induce a decrease of the order of the transition

Marine aggregate extraction regulation in EU member states

This paper provides a brief review of regulations and procedures relevant to the authorization of marine aggregate (MA) operations in eight EU Member States. MA operations are affected by a multi-level legislative/regulatory regime, consisting of international conventions (e.g. the UNCLOS 1982, OSPAR, Helsinki, ICES, Barcelona and Espoo Conventions), secondary EC legislation (e.g. the Environmental Impact Assessment Directives (85/337/EEC and 97/11 EC) and the Freedom of Access to Environmental Information Directive (2003/4/EC)) and national legislation or regulation. It appears that rules and procedures relevant to MA extraction vary considerably between the considered Member States. In general, relevant information is not easily available in accurate, comprehensive and up-to date form. As a result, it is difficult to assess whether and to which extent national practice in relation to MA extraction authorization is in substantive compliance with the requirements of existing international and European rules and regulations aimed at sustainable development and protection of the marine and coastal environment

THERMODYNAMICS OF A BROWNIAN BRIDGE POLYMER MODEL IN A RANDOM ENVIRONMENT

We consider a directed random walk making either 0 or $+1$ moves and a Brownian bridge, independent of the walk, conditioned to arrive at point $b$ on time $T$. The Hamiltonian is defined as the sum of the square of increments of the bridge between the moments of jump of the random walk and interpreted as an energy function over the bridge connfiguration; the random walk acts as the random environment. This model provides a continuum version of a model with some relevance to protein conformation. The thermodynamic limit of the specific free energy is shown to exist and to be self-averaging, i.e. it is equal to a trivial --- explicitly computed --- random variable. An estimate of the asymptotic behaviour of the ground state energy is also obtained.Comment: 20 pages, uuencoded postscrip

Bubble dynamics in DNA

The formation of local denaturation zones (bubbles) in double-stranded DNA is an important example for conformational changes of biological macromolecules. We study the dynamics of bubble formation in terms of a Fokker-Planck equation for the probability density to find a bubble of size n base pairs at time t, on the basis of the free energy in the Poland-Scheraga model. Characteristic bubble closing and opening times can be determined from the corresponding first passage time problem, and are sensitive to the specific parameters entering the model. A multistate unzipping model with constant rates recently applied to DNA breathing dynamics [G. Altan-Bonnet et al, Phys. Rev. Lett. 90, 138101 (2003)] emerges as a limiting case.Comment: 9 pages, 2 figure