Fractional oscillator noise and its applications

It is shown that a fractional oscillator (FO) noise, which is a generalization of the ordinary overdamped linear oscillator driven by the white noise may be ‘applied to diverse systems; its stationary correlation function presents power-law-like function, exponential-like function, exponential function, and oscillatory decays. The model may be employed to describe the fluctuation of the distance between a fluorescein–tyrosine pair within a single protein complex and the internal dynamics of a lysozyme molecule in solution. It also has the possibility of describing a Brownian particle in an oscillatory viscoelastic shear flow.

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TESTING POWER-LAW RELAXATION SCENARIOS IN A METASTABLE LIQUID

International Journal of Modern Physics B ◽

10.1142/s0217979212501469 ◽

2012 ◽

Vol 26 (29) ◽

pp. 1250146 ◽

Cited By ~ 1

Author(s):

BHASKAR SEN GUPTA ◽

SHANKAR P. DAS

Keyword(s):

Correlation Function ◽

Power Law ◽

Hard Sphere ◽

Numerical Solutions ◽

Packing Fraction ◽

Equilibrium Density ◽

Density Correlation ◽

Density Correlation Function ◽

Basic Model ◽

The One

The renormalized dynamics described by the equations of nonlinear fluctuating hydrodynamics (NFH) treated at one loop order gives rise to the basic model of the mode coupling theory (MCT). We investigate here by analyzing the density correlation function, a crucial prediction of ideal MCT, namely the validity of the multi step relaxation scenario. The equilibrium density correlation function is calculated here from the direct solutions of NFH equations for a hard sphere system. We make first detailed investigation for the robustness of the correlation functions obtained from the numerical solutions by varying the size of the grid. For an optimum choice of grid size we analyze the decay of the density correlation function to identify the multi-step relaxation process. Weak signatures of two step power law relaxation is seen with exponents which do not match predictions from the one loop MCT. For the final relaxation stretched exponential (KWW) behavior is seen and the relaxation time grows with increase of density. But apparent power law divergences indicate a critical packing fraction much higher than the corresponding MCT predictions for a hard sphere fluid.

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On the closed-form output correlation function of power-law devices

Proceedings of the IEEE ◽

10.1109/proc.1966.5236 ◽

1966 ◽

Vol 54 (11) ◽

pp. 1625-1626 ◽

Cited By ~ 1

Author(s):

M. Fukada ◽

S. Rauch

Keyword(s):

Correlation Function ◽

Closed Form ◽

Power Law

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Drag and Lift Forces Acting on a Sphere in Shear Flow of Power-Law Fluid

Journal of Engineering Thermophysics ◽

10.1134/s1810232818040094 ◽

2018 ◽

Vol 27 (4) ◽

pp. 474-488 ◽

Cited By ~ 1

Author(s):

A. A. Gavrilov ◽

K. A. Finnikov ◽

Ya. S. Ignatenko ◽

O. B. Bocharov ◽

R. May

Keyword(s):

Shear Flow ◽

Power Law ◽

Power Law Fluid ◽

Lift Forces ◽

Drag And Lift

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Analysis of the buildup of spatiotemporal correlations and their bounds outside of the light cone

10.21468/scipostphys.5.5.052 ◽

2018 ◽

Vol 5 (5) ◽

Cited By ~ 1

Author(s):

Nils O. Abeling ◽

Lorenzo Cevolani ◽

Stefan Kehrein

Keyword(s):

Correlation Function ◽

Power Law ◽

Light Cone ◽

Relativistic Quantum ◽

Initial State ◽

Quantum Theories ◽

Luttinger Model ◽

Power Law Decay ◽

Exactly Solvable ◽

Exponentially Small

In non-relativistic quantum theories the Lieb-Robinson bound defines an effective light cone with exponentially small tails outside of it. In this work we use it to derive a bound for the correlation function of two local disjoint observables at different times if the initial state has a power-law decay. We show that the exponent of the power-law of the bound is identical to the initial (equilibrium) decay. We explicitly verify this result by studying the full dynamics of the susceptibilities and correlations in the exactly solvable Luttinger model after a sudden quench from the non-interacting to the interacting model.

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Single-protein study of photoresistance of pigment–protein complex in lipid bilayer

Chemical Physics Letters ◽

10.1016/j.cplett.2011.06.019 ◽

2011 ◽

Vol 511 (1-3) ◽

pp. 135-137 ◽

Cited By ~ 4

Author(s):

Daisuke Uchiyama ◽

Hajime Hoshino ◽

Kohei Otomo ◽

Taro Kato ◽

Ken-ichi Onda ◽

...

Keyword(s):

Lipid Bilayer ◽

Protein Complex ◽

Single Protein ◽

Pigment Protein Complex

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Numerical investigation of shear-flow free-surface turbulence and air entrainment at large Froude and Weber numbers

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.695 ◽

2019 ◽

Vol 880 ◽

pp. 209-238 ◽

Cited By ~ 3

Author(s):

Xiangming Yu ◽

Kelli Hendrickson ◽

Bryce K. Campbell ◽

Dick K. P. Yue

Keyword(s):

Surface Tension ◽

Free Surface ◽

Shear Flow ◽

Power Law ◽

Outer Surface ◽

Air Entrainment ◽

Entrainment Rate ◽

Surface Layers ◽

Surface Turbulence ◽

Free Surface Turbulence

We investigate two-phase free-surface turbulence (FST) associated with an underlying shear flow under the condition of strong turbulence (SFST) characterized by large Froude ($Fr$) and Weber ($We$) numbers. We perform direct numerical simulations of three-dimensional viscous flows with air and water phases. In contrast to weak FST (WFST) with small free-surface distortions and anisotropic underlying turbulence with distinct inner/outer surface layers, we find SFST to be characterized by large surface deformation and breaking accompanied by substantial air entrainment. The interface inner/outer surface layers disappear under SFST, resulting in nearly isotropic turbulence with ${\sim}k^{-5/3}$ scaling of turbulence kinetic energy near the interface (where $k$ is wavenumber). The SFST air entrainment is observed to occur over a range of scales following a power law of slope $-10/3$. We derive this using a simple energy argument. The bubble size spectrum in the volume follows this power law (and slope) initially, but deviates from this in time due to a combination of ongoing broad-scale entrainment and bubble fragmentation by turbulence. For varying $Fr$ and $We$, we find that air entrainment is suppressed below critical values $Fr_{cr}$ and $We_{cr}$. When $Fr^{2}>Fr_{cr}^{2}$ and $We>We_{cr}$, the entrainment rate scales as $Fr^{2}$ when gravity dominates surface tension in the bubble formation process, while the entrainment rate scales linearly with $We$ when surface tension dominates.

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