3,613 research outputs found
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 and the thermodynamics of the non pinned particles is observed
at a lower temperature . 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 for an integer and introduce the related
Markov pseudo-process . In this paper, we study the sojourn
time in the interval up to a fixed time for this
pseudo-process. We provide explicit expressions for the joint distribution of
the couple
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
for . If we show that
almost surely there exists a point x in the plane such that , but if almost surely simultaneously for all . 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
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