scholarly journals Long range correlations and slow time scales in a boundary driven granular model

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Andrea Plati ◽  
Andrea Puglisi
Keyword(s):  
Long Range ◽  
Time Scales ◽  
Statistical Physics ◽  
Spatial Correlations ◽  
Slow Time ◽  
Finite Characteristic ◽  
Long Range Correlations ◽  
Scale Free ◽  
Temporal Correlations ◽  
Free Cooling

AbstractWe consider a velocity field with linear viscous interactions defined on a one dimensional lattice. Brownian baths with different parameters can be coupled to the boundary sites and to the bulk sites, determining different kinds of non-equilibrium steady states or free-cooling dynamics. Analytical results for spatial and temporal correlations are provided by analytical diagonalisation of the system’s equations in the infinite size limit. We demonstrate that spatial correlations are scale-free and time-scales become exceedingly long when the system is driven only at the boundaries. On the contrary, in the case a bath is coupled to the bulk sites too, an exponential correlation decay is found with a finite characteristic length. This is also true in the free cooling regime, but in this case the correlation length grows diffusively in time. We discuss the crucial role of boundary driving for long-range correlations and slow time-scales, proposing an analogy between this simplified dynamical model and dense vibro-fluidized granular materials. Several generalizations and connections with the statistical physics of active matter are also suggested.

scholarly journals Non-homogeneous Heating induces Scale-free Correlations and Slow time Scales in a Granular-like Velocity Field

2021 ◽  
Author(s):  
Andrea Plati ◽  
Andrea Puglisi
Keyword(s):  
Velocity Field ◽  
Statistical Physics ◽  
Spatial Correlations ◽  
Finite Characteristic ◽  
Long Range Correlations ◽  
Scale Free ◽  
Temporal Correlations ◽  
Correlation Decay ◽  
Free Cooling

Abstract We consider a velocity field with linear viscous interactions defined on a one dimensional lattice. Brownian baths with different parameters can be coupled to the boundary sites and to the bulk sites, determining different kinds of non-equilibrium steady states or free-cooling dynamics. Analytical results for spatial and temporal correlations are provided by analytical diagonalisation of the system’s equations in the infinite size limit. We demonstrate that spatial correlations are scale-free and timescales become exceedingly long when the system is driven only at the boundaries. On the contrary, in the case a bath is coupled to the bulk sites too, an exponential correlation decay is found with a finite characteristic length. This is also true in the free cooling regime, but in this case the correlation length grows diffusively in time. We discuss the crucial role of non-homogeneous energy injection for long-range correlations and slow timescales , proposing an analogy between this simplified dynamical model and recent experiments with dense vibro-fluidized granular materials. Several generalizations and connections with the statistical physics of active matter are also suggested.

Long-range correlations and burstiness in written texts: Universal and language-specific aspects

2016 ◽  
Vol 30 (15) ◽  
pp. 1541005 ◽  
Author(s):  
Vassilios Constantoudis ◽  
Maria Kalimeri ◽  
Fotis Diakonos ◽  
Konstantinos Karamanos ◽  
Constantinos Papadimitriou ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Long Range ◽  
Word Length ◽  
Statistical Physics ◽  
Long Range Correlations ◽  
Specific Effects ◽  
Written Texts ◽  
Relative Standard ◽  
Germanic Languages ◽  
The Impact

Recently, methods from the statistical physics of complex systems have been applied successfully to identify universal features in the long-range correlations (LRCs) of written texts. However, in real texts, these universal features are being intermingled with language-specific influences. This paper aims at the characterization and further understanding of the interplay between universal and language-specific effects on the LRCs in texts. To this end, we apply the language-sensitive mapping of written texts to word-length series (wls) and analyse large parallel (of same content) corpora from 10 languages classified to four families (Romanic, Germanic, Greek and Uralic). The autocorrelation functions of the wls reveal tiny but persistent LRCs decaying at large scales following a power-law with a language-independent exponent [Formula: see text]0.60–0.65. The impact of language is displayed in the amplitude of correlations where a relative standard deviation [Formula: see text]40% among the analyzed languages is observed. The classification to language families seems to play a significant role since, the Finnish and Germanic languages exhibit more correlations than the Greek and Roman families. To reveal the origins of the LRCs, we focus on the long words and perform burst and correlation analysis in their positions along the corpora. We find that the universal features are linked more to the correlations of the inter-long word distances while the language-specific aspects are related more to their distributions.

scholarly journals Non-extensivity and long-range correlations in the earthquake activity at the West Corinth rift (Greece)

2013 ◽  
Vol 20 (5) ◽  
pp. 713-724 ◽  
Author(s):  
G. Michas ◽  
F. Vallianatos ◽  
P. Sammonds
Keyword(s):  
Long Range ◽  
Statistical Physics ◽  
Statistical Properties ◽  
Fluctuation Analysis ◽  
Earthquake Activity ◽  
The West ◽  
Seismic Region ◽  
Long Range Correlations ◽  
Interevent Time ◽  
Stationary Signals

Abstract. In the present work the statistical properties of the earthquake activity in a highly seismic region, the West Corinth rift (Central Greece), are being studied by means of generalized statistical physics. By using a dataset that covers the period 2001–2008, we investigate the earthquake energy distribution and the distribution of the time intervals (interevent times) between the successive events. As has been reported previously, these distributions exhibit complex statistical properties and fractality. By using detrended fluctuation analysis (DFA), a well-established method for detection of long-range correlations in non-stationary signals, it is shown that long-range correlations are also present in the earthquake activity. The existence of these properties motivates us to use non-extensive statistical physics (NESP) to investigate the statistical properties of the frequency-magnitude and the interevent time distributions, along with other well-known relations in seismology, such as the gamma distribution for interevent times. The results of the analysis indicate that the statistical properties of the earthquake activity can be successfully reproduced by means of NESP and that the earthquake activity at the West Corinth rift is correlated at all-time scales.

scholarly journals Patterns and Long Range Correlations in Idealized Granular Flows

1997 ◽  
Vol 08 (04) ◽  
pp. 953-965 ◽  
Author(s):  
J. A. G. Orza ◽  
R. Brito ◽  
T. P. C. van Noije ◽  
M. H. Ernst
Keyword(s):  
Long Range ◽  
Size Effects ◽  
Hard Spheres ◽  
Finite Size ◽  
System Size ◽  
Spatial Correlations ◽  
Finite Size Effects ◽  
Long Range Correlations ◽  
Intrinsic Length ◽  
Dynamics Simulations

An initially homogeneous freely evolving fluid of inelastic hard spheres develops inhomogeneities in the flow field u(r, t) (vortices) and in the density field n (r, t)(clusters), driven by unstable fluctuations, δa = {δn, δu}. Their spatial correlations, <δa(r, t)δa(r′,t)>, as measured in molecular dynamics simulations, exhibit long range correlations; the mean vortex diameter grows as [Formula: see text]; there occur transitions to macroscopic shearing states, etc. The Cahn–Hilliard theory of spinodal decomposition offers a qualitative understanding and quantitative estimates of the observed phenomena. When intrinsic length scales are of the order of the system size, effects of physical boundaries and periodic boundaries (finite size effects in simulations) are important.

scholarly journals Multivariate and Multiscale Complexity of Long-Range Correlated Cardiovascular and Respiratory Variability Series

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 315 ◽  
Author(s):  
Aurora Martins ◽  
Riccardo Pernice ◽  
Celestino Amado ◽  
Ana Paula Rocha ◽  
Maria Eduarda Silva ◽  
...  
Keyword(s):  
Time Series ◽  
Long Range ◽  
Time Scales ◽  
Multivariate Time Series ◽  
Multiscale Entropy ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Control Mechanisms ◽  
Long Range Correlations ◽  
Dynamical Complexity

Assessing the dynamical complexity of biological time series represents an important topic with potential applications ranging from the characterization of physiological states and pathological conditions to the calculation of diagnostic parameters. In particular, cardiovascular time series exhibit a variability produced by different physiological control mechanisms coupled with each other, which take into account several variables and operate across multiple time scales that result in the coexistence of short term dynamics and long-range correlations. The most widely employed technique to evaluate the dynamical complexity of a time series at different time scales, the so-called multiscale entropy (MSE), has been proven to be unsuitable in the presence of short multivariate time series to be analyzed at long time scales. This work aims at overcoming these issues via the introduction of a new method for the assessment of the multiscale complexity of multivariate time series. The method first exploits vector autoregressive fractionally integrated (VARFI) models to yield a linear parametric representation of vector stochastic processes characterized by short- and long-range correlations. Then, it provides an analytical formulation, within the theory of state-space models, of how the VARFI parameters change when the processes are observed across multiple time scales, which is finally exploited to derive MSE measures relevant to the overall multivariate process or to one constituent scalar process. The proposed approach is applied on cardiovascular and respiratory time series to assess the complexity of the heart period, systolic arterial pressure and respiration variability measured in a group of healthy subjects during conditions of postural and mental stress. Our results document that the proposed methodology can detect physiologically meaningful multiscale patterns of complexity documented previously, but can also capture significant variations in complexity which cannot be observed using standard methods that do not take into account long-range correlations.

scholarly journals Long-range temporal correlations in scale-free neuromorphic networks

2020 ◽  
Vol 4 (2) ◽  
pp. 432-447 ◽  
Author(s):  
Shota Shirai ◽  
Susant Kumar Acharya ◽  
Saurabh Kumar Bose ◽  
Joshua Brian Mallinson ◽  
Edoardo Galli ◽  
...  
Keyword(s):  
Long Range ◽  
Neuronal Networks ◽  
Temporal Dynamics ◽  
Structural Characteristics ◽  
Small World ◽  
Mammalian Brain ◽  
Scale Free ◽  
Temporal Correlations ◽  
Significant Step ◽  
Computational Ability

Biological neuronal networks are the computing engines of the mammalian brain. These networks exhibit structural characteristics such as hierarchical architectures, small-world attributes, and scale-free topologies, providing the basis for the emergence of rich temporal characteristics such as scale-free dynamics and long-range temporal correlations. Devices that have both the topological and the temporal features of a neuronal network would be a significant step toward constructing a neuromorphic system that can emulate the computational ability and energy efficiency of the human brain. Here we use numerical simulations to show that percolating networks of nanoparticles exhibit structural properties that are reminiscent of biological neuronal networks, and then show experimentally that stimulation of percolating networks by an external voltage stimulus produces temporal dynamics that are self-similar, follow power-law scaling, and exhibit long-range temporal correlations. These results are expected to have important implications for the development of neuromorphic devices, especially for those based on the concept of reservoir computing.

scholarly journals Long-range spatio-temporal correlations in multimode fibers for pulse delivery

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Wen Xiong ◽  
Chia Wei Hsu ◽  
Hui Cao
Keyword(s):  
Long Range ◽  
Temporal Correlation ◽  
Power Delivery ◽  
Arrival Times ◽  
Long Range Correlations ◽  
Multimode Fibers ◽  
Temporal Correlations ◽  
Wave Transport ◽  
Mode Space ◽  
Spatio Temporal

Abstract Long-range correlations play an essential role in wave transport through disordered media, but have rarely been studied in other complex systems. Here we discover spatio-temporal intensity correlations for an optical pulse propagating through a multimode fiber with strong random mode coupling. Positive long-range correlation arises from multiple scattering in fiber mode space and depends on the statistical distribution of arrival times. By optimizing the incident wavefront of a pulse, we maximize the power transmitted at a selected time, and such control is significantly enhanced by the long-range spatio-temporal correlation. We provide an explicit relation between the correlation and the power enhancement, which agrees with experimental results. Our work shows that multimode fibers provide a fertile ground for studying complex wave phenomena. The strong spatio-temporal correlation can be employed for efficient power delivery at a well-defined time.

scholarly journals Long-range Temporal Correlations in the Broadband Resting state Activity of the Human Brain revealed by Neuronal Avalanches

2020 ◽  
Author(s):  
Fabrizio Lombardi ◽  
Oren Shriki ◽  
Hans J. Herrmann ◽  
Lucilla de Arcangelis
Keyword(s):  
Long Range ◽  
Power Law ◽  
Resting State ◽  
Brain Activity ◽  
Neural Systems ◽  
Scaling Exponents ◽  
Long Range Correlations ◽  
Temporal Correlations ◽  
Neuronal Avalanches ◽  
The Brain

AbstractResting-state brain activity is characterized by the presence of neuronal avalanches showing absence of characteristic size. Such evidence has been interpreted in the context of criticality and associated with the normal functioning of the brain. At criticality, a crucial role is played by long-range power-law correlations. Thus, to verify the hypothesis that the brain operates close to a critical point and consequently assess deviations from criticality for diagnostic purposes, it is of primary importance to robustly and reliably characterize correlations in resting-state brain activity. Recent works focused on the analysis of narrow band electroencephalography (EEG) and magnetoencephalography (MEG) signal amplitude envelope, showing evidence of long-range temporal correlations (LRTC) in neural oscillations. However, this approach is not suitable for assessing long-range correlations in broadband resting-state cortical signals. To overcome such limitation, here we propose to characterize the correlations in the broadband brain activity through the lens of neuronal avalanches. To this end, we consider resting-state EEG and long-term MEG recordings, extract the corresponding neuronal avalanche sequences, and study their temporal correlations. We demonstrate that the broadband resting-state brain activity consistently exhibits long-range power-law correlations in both EEG and MEG recordings, with similar values of the scaling exponents. Importantly, although we observe that avalanche size distribution depends on scale parameters, scaling exponents characterizing long-range correlations are quite robust. In particular, they are independent of the temporal binning (scale of analysis), indicating that our analysis captures intrinsic characteristics of the underlying dynamics. Because neuronal avalanches constitute a fundamental feature of neural systems with universal characteristics, the proposed approach may serve as a general, systems- and experiment-independent procedure to infer the existence of underlying long-range correlations in extended neural systems, and identify pathological behaviors in the complex spatio-temporal interplay of cortical rhythms.

scholarly journals Network robustness improvement via long-range links

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Vincenza Carchiolo ◽  
Marco Grassia ◽  
Alessandro Longheu ◽  
Michele Malgeri ◽  
Giuseppe Mangioni
Keyword(s):  
Complex Networks ◽  
Long Range ◽  
Real World ◽  
Network Robustness ◽  
Scale Free ◽  
Area Of Interest ◽  
Before And After ◽  
Significant Area ◽  
Better Than

AbstractMany systems are today modelled as complex networks, since this representation has been proven being an effective approach for understanding and controlling many real-world phenomena. A significant area of interest and research is that of networks robustness, which aims to explore to what extent a network keeps working when failures occur in its structure and how disruptions can be avoided. In this paper, we introduce the idea of exploiting long-range links to improve the robustness of Scale-Free (SF) networks. Several experiments are carried out by attacking the networks before and after the addition of links between the farthest nodes, and the results show that this approach effectively improves the SF network correct functionalities better than other commonly used strategies.

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