A general approach to systems with randomly pinned particles: unfolding and clarifying the Random Pinning Glass Transition

Pinning a fraction of particles from an equilibrium configuration in supercooled liquids has been recently proposed as a way to induce a new kind of glass transition, the Random Pinning Glass Transition (RPGT). The RPGT has been predicted to share some features of standard thermodynamic glass transitions and usual first order ones. Thanks to its special nature, the approach and the study of the RPGT appears to be a fairly reachable task compared to the daunting problem of inspecting standard glass transitions. In this Letter we generalize the pinning particle procedure. We study a mean-field system where the pinned configuration is extracted from the equilibrium distribution at temperature $T'$ and the thermodynamics of the non pinned particles is observed at a lower temperature $T$. A more complicated physics emerges from this generalization eventually clarifying the origin and the peculiar characteristics of the RPGT.Comment: 7 pages, 1 figur

Estimating the turning point location in shifted exponential model of time series

We consider the distribution of the turning point location of time series modeled as the sum of deterministic trend plus random noise. If the variables are modeled by shifted exponentials, whose location parameters define the trend, we provide a formula for computing the distribution of the turning point location and consequently to estimate a confidence interval for the location. We test this formula in simulated data series having a trend with asymmetric minimum, investigating the coverage rate as a function of a bandwidth parameter. The method is applied to estimate the confidence interval of the minimum location of the time series of RT intervals extracted from the electrocardiogram recorded during the exercise test. We discuss the connection with stochastic ordering

Fluctuations and shape of cooperative rearranging regions in glass-forming liquids

We develop a theory of amorphous interfaces in glass-forming liquids. We show that the statistical properties of these surfaces, which separate regions characterized by different amorphous arrangements of particles, coincide with the ones of domain walls in the random field Ising model. A major consequence of our results is that supercooled liquids are characterized by two different static lengths: the point-to-set ξPS, which is a measure of the spatial extent of cooperative rearranging regions, and the wandering length ξ⊥, which is related to the fluctuations of their shape. We find that ξ⊥ grows when approaching the glass transition but slower than ξPS. The wandering length increases as s−1/2c, where sc is the configurational entropy. Our results strengthen the relationship with the random field Ising model found in recent works. They are in agreement with previous numerical studies of amorphous interfaces and provide a theoretical framework for explaining numerical and experimental findings on pinned particle systems and static lengths in glass-forming liquids

Joint distribution of the process and its sojourn time for pseudo-processes governed by high-order heat equation

Consider the high-order heat-type equation $\partial u/\partial t=\pm \partial^N u/\partial x^N$ for an integer $N>2$ and introduce the related Markov pseudo-process $(X(t))_{t\ge 0}$. In this paper, we study the sojourn time $T(t)$ in the interval $[0,+\infty)$ up to a fixed time $t$ for this pseudo-process. We provide explicit expressions for the joint distribution of the couple $(T(t),X(t))$

Numerical evidences of universal trap-like aging dynamics

Trap models have been initially proposed as toy models for dynamical relaxation in extremely simplified rough potential energy landscapes. Their importance has considerably grown recently thanks to the discovery that the trap like aging mechanism is directly controlling the out-of-equilibrium relaxation processes of more sophisticated spin models, that are considered as the solvable counterpart of real disordered systems. Establishing on a firmer ground the connection between these spin model out-of-equilibrium behavior and the trap like aging mechanism would shed new light on the properties, still largely mysterious, of the activated out-of-equilibrium dynamics of disordered systems. In this work we discuss numerical evidences of emergent trap-like aging behavior in a variety of disordered models. Our numerical results are backed by analytic derivations and heuristic discussions. Such exploration reveals some of the tricks needed to analyze the trap behavior in spite of the occurrence of secondary processes, of the existence of dynamical correlations and of finite system's size effects.Comment: 25 pages, 15 figure

On the most visited sites of planar Brownian motion

Let (B_t : t > 0) be a planar Brownian motion and define gauge functions $\phi_\alpha(s)=log(1/s)^{-\alpha}$ for $\alpha>0$. If $\alpha<1$ we show that almost surely there exists a point x in the plane such that $H^{\phi_\alpha}({t > 0 : B_t=x})>0$, but if $\alpha>1$ almost surely $H^{\phi_\alpha} ({t > 0 : B_t=x})=0$ simultaneously for all $x\in R^2$. This resolves a longstanding open problem posed by S.,J. Taylor in 1986

Trend extraction in functional data of R and T waves amplitudes of exercise electrocardiogram

The R and T waves amplitudes of the electrocardiogram recorded during the exercise test undergo strong modifications in response to stress. We analyze the time series of these amplitudes in a group of normal subjects in the framework of functional data, performing reduction of dimensionality, smoothing and principal component analysis. These methods show that the R and T amplitudes have opposite responses to stress, consisting respectively in a bump and a dip at the early recovery stage. We test these features computing a confidence band for the trend of the population mean and analyzing the zero crossing of its derivative. Our findings support the existence of a relationship between R and T wave amplitudes and respectively diastolic and systolic ventricular volumes