scholarly journals Dynamic cross-correlations between entangled biofilaments as they diffuse

2017 ◽  
Vol 114 (13) ◽  
pp. 3322-3327 ◽  
Author(s):  
Boyce Tsang ◽  
Zachary E. Dell ◽  
Lingxiang Jiang ◽  
Kenneth S. Schweizer ◽  
Steve Granick
Keyword(s):  
Long Range ◽  
Relaxation Times ◽  
Extended Period ◽  
Tube Diameter ◽  
Constant Density ◽  
Physical Reason ◽  
Rigid Rods ◽  
Intermediate Time ◽  
Correlation Hole ◽  
Cross Correlations

Entanglement in polymer and biological physics involves a state in which linear interthreaded macromolecules in isotropic liquids diffuse in a spatially anisotropic manner beyond a characteristic mesoscopic time and length scale (tube diameter). The physical reason is that linear macromolecules become transiently localized in directions transverse to their backbone but diffuse with relative ease parallel to it. Within the resulting broad spectrum of relaxation times there is an extended period before the longest relaxation time when filaments occupy a time-averaged cylindrical space of near-constant density. Here we show its implication with experiments based on fluorescence tracking of dilutely labeled macromolecules. The entangled pairs of aqueous F-actin biofilaments diffuse with separation-dependent dynamic cross-correlations that exceed those expected from continuum hydrodynamics up to strikingly large spatial distances of ≈15 µm, which is more than 104 times the size of the solvent water molecules in which they are dissolved, and is more than 50 times the dynamic tube diameter, but is almost equal to the filament length. Modeling this entangled system as a collection of rigid rods, we present a statistical mechanical theory that predicts these long-range dynamic correlations as an emergent consequence of an effective long-range interpolymer repulsion due to the de Gennes correlation hole, which is a combined consequence of chain connectivity and uncrossability. The key physical assumption needed to make theory and experiment agree is that solutions of entangled biofilaments localized in tubes that are effectively dynamically incompressible over the relevant intermediate time and length scales.

scholarly journals RELAXATION OF SPHERICAL SYSTEMS WITH LONG-RANGE INTERACTIONS: A NUMERICAL INVESTIGATION

2011 ◽  
Vol 21 (08) ◽  
pp. 2279-2283 ◽  
Author(s):  
PIERFRANCESCO DI CINTIO ◽  
LUCA CIOTTI
Keyword(s):  
Long Range ◽  
Superposition Principle ◽  
Relaxation Times ◽  
Stellar Dynamics ◽  
Mixing Times ◽  
Spherical Shells ◽  
Phase Mixing ◽  
Long Range Interactions ◽  
System Of Particles ◽  
Classical Gravity

The process of relaxation of a system of particles interacting with long-range forces is relevant to many areas of physics. For obvious reasons, in Stellar Dynamics much attention has been paid to the case of r-2force law. However, recently the interest in alternative gravities has emerged, and significant differences with respect to Newtonian gravity have been found in relaxation phenomena. Here we begin to explore this matter further, by using a numerical model of spherical shells interacting with an r-αforce law obeying the superposition principle. We find that the virialization and phase-mixing times depend on the exponent α, with small values of α corresponding to longer relaxation times, similarly to what happens when comparing for N-body simulations in classical gravity and in Modified Newtonian Dynamics.

Power-law autocorrelated stochastic processes with long-range cross-correlations

2007 ◽  
Vol 56 (1) ◽  
pp. 47-52 ◽  
Author(s):  
B. Podobnik ◽  
D. F. Fu ◽  
H. E. Stanley ◽  
P. Ch. Ivanov
Keyword(s):  
Stochastic Processes ◽  
Long Range ◽  
Power Law ◽  
Cross Correlations

Correlations versus causality in Stochastic Long-range Forecasting as a Past Value Problem

2021 ◽  
Author(s):  
Lenin Del Rio Amador ◽  
Shaun Lovejoy
Keyword(s):  
Granger Causality ◽  
Long Range ◽  
Power Law ◽  
Weather Prediction ◽  
Emergent Properties ◽  
Relaxation Processes ◽  
Initial Value ◽  
Relaxation Equation ◽  
Cross Correlations

<p>Over time scales between 10 days and 10-20 years – the macroweather regime – atmospheric fields, including the temperature, respect statistical scale symmetries, such as power-law correlations, that imply the existence of a huge memory in the system that can be exploited for long-term forecasts. The Stochastic Seasonal to Interannual Prediction System (StocSIPS) is a stochastic model that exploits these symmetries to perform long-term forecasts. It models the temperature as the high-frequency limit of the (fractional) energy balance equation (fractional Gaussian noise) which governs radiative equilibrium processes when the relevant equilibrium relaxation processes are power law, rather than exponential. They are obtained when the order of the relaxation equation is fractional rather than integer and they are solved as past value problems rather than initial value problems.</p><p>Long-range weather prediction is conventionally an initial value problem that uses the current state of the atmosphere to produce ensemble forecasts. In contrast, StocSIPS predictions for long-memory processes are “past value” problems that use historical data to provide conditional forecasts. Cross-correlations can be used to define teleconnection patterns, and for identifying possible dynamical interactions, but they do not necessarily imply any causation. Using the precise notion of Granger causality, we show that for long-range stochastic temperature forecasts, the cross-correlations are only relevant at the level of the innovations – not temperatures. Extended here to the multivariate case, (m-StocSIPS) produces realistic space-time temperature simulations. Although it has no Granger causality, we are able to reproduce emergent properties including realistic teleconnection networks and El Niño events and indices.</p>

scholarly journals MULTIFRACTAL CROSS WAVELET ANALYSIS

Fractals ◽  
2017 ◽  
Vol 25 (06) ◽  
pp. 1750054 ◽  
Author(s):  
ZHI-QIANG JIANG ◽  
XING-LU GAO ◽  
WEI-XING ZHOU ◽  
H. EUGENE STANLEY
Keyword(s):  
Wavelet Analysis ◽  
Long Range ◽  
Cross Correlation ◽  
Multifractal Spectrum ◽  
Theoretical Formula ◽  
Cross Correlations ◽  
The Cross ◽  
Cross Wavelet Analysis ◽  
Multifractal Behavior ◽  
Cross Wavelet

Complex systems are composed of mutually interacting components and the output values of these components usually exhibit long-range cross-correlations. Using wavelet analysis, we propose a method of characterizing the joint multifractal nature of these long-range cross correlations, a method we call multifractal cross wavelet analysis (MFXWT). We assess the performance of the MFXWT method by performing extensive numerical experiments on the dual binomial measures with multifractal cross correlations and the bivariate fractional Brownian motions (bFBMs) with monofractal cross correlations. For binomial multifractal measures, we find the empirical joint multifractality of MFXWT to be in approximate agreement with the theoretical formula. For bFBMs, MFXWT may provide spurious multifractality because of the wide spanning range of the multifractal spectrum. We also apply the MFXWT method to stock market indices, and in pairs of index returns and volatilities we find an intriguing joint multifractal behavior. The tests on surrogate series also reveal that the cross correlation behavior, particularly the cross correlation with zero lag, is the main origin of cross multifractality.

COMBINED X-RAY AND STM STUDY OF THE OXYGEN-INDUCED RESTRUCTURING OF THE Au(111) SURFACE

1997 ◽  
Vol 04 (06) ◽  
pp. 1315-1319 ◽  
Author(s):  
L. ORTEGA ◽  
L. HUANG ◽  
J. CHEVRIER ◽  
P. ZEPPENFELD ◽  
J. M. GAY ◽  
...  
Keyword(s):  
High Pressure ◽  
High Temperature ◽  
Long Range ◽  
Extended Period ◽  
Grazing Incidence ◽  
Scanning Tunneling ◽  
X Ray Diffraction ◽  
Tunneling Microscopy ◽  
X Ray ◽  
New Evidence

Au(111) surfaces exposed to oxygen under high pressure (p O2 =1 bar) and at high temperature (T≈800°C) during an extended period of time (several hours) exhibit a ([Formula: see text]R30° structure and, at larger scales (a few nanometers), a long range hexagonal height modulation with a period of 72 Å. This is evidenced by X-ray diffraction at grazing incidence performed at the ESRF. These results confirm and complete previous surface analysis in direct space by scanning tunneling microscopy (STM). This new evidence for a long range superstructure by X-ray diffraction provides new insights into the origin of the moiré patterns observed in the STM study.

scholarly journals Optimal transport with discrete long-range mean-field interactions

2020 ◽  
Vol 10 (02) ◽  
pp. 2050011
Author(s):  
Jiakun Liu ◽  
Grégoire Loeper
Keyword(s):  
Force Field ◽  
Long Range ◽  
Interaction Potential ◽  
Velocity Potential ◽  
Optimal Transport ◽  
Mean Field ◽  
External Force Field ◽  
Intermediate Time ◽  
Optimal Transport Map ◽  
Intermediate Density

We study an optimal transport problem where, at some intermediate time, the mass is either accelerated by an external force field or self-interacting. We obtain the regularity of the velocity potential, intermediate density, and optimal transport map, under the conditions on the interaction potential that are related to the so-called Ma–Trudinger–Wang condition from optimal transport [X.-N. Ma, N. S. Trudinger and X.-J. Wang, Regularity of potential functions of the optimal transportation problems, Arch. Ration. Mech. Anal. 177 (2005) 151–183.].

A Lattice of Rigid Rods with Long Range Anisotropic Attractions

1978 ◽  
pp. 385-398
Author(s):  
Michael S. Rapport ◽  
Andrew G. De Rocco
Keyword(s):  
Long Range ◽  
Rigid Rods

scholarly journals A universal mechanism for long-range cross-correlations

2014 ◽  
Vol 105 (2) ◽  
pp. 26004 ◽  
Author(s):  
F. K. Diakonos ◽  
A. K. Karlis ◽  
P. Schmelcher
Keyword(s):  
Long Range ◽  
Cross Correlations ◽  
Universal Mechanism
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