Supplemental Material for Emergence of Border-Ownership by Large-Scale Consistency and Long-Range Interactions: Neuro-Computational Model to Reflect Global Configurations

2021 ◽  
Keyword(s):  
Computational Model ◽  
Long Range ◽  
Large Scale ◽  
Long Range Interactions

Single-mutation-induced stability loss in protein lysozyme

2007 ◽  
Vol 35 (6) ◽  
pp. 1551-1557 ◽  
Author(s):  
L. Ye ◽  
Z. Wu ◽  
M. Eleftheriou ◽  
R. Zhou
Keyword(s):  
Molecular Mechanism ◽  
Long Range ◽  
Large Scale ◽  
Stability Loss ◽  
Single Mutation ◽  
Wild Type ◽  
Range Interaction ◽  
Local Cluster ◽  
Long Range Interactions ◽  
Arginine Residues

Recent NMR experiments have revealed that a single residue mutation W62G on protein hen's-egg white lysozyme can cause a dramatic loss of long-range interactions and protein stability; however, the molecular mechanism for this surprising phenomenon is not completely clear. In this mini-review, we have summarized some of our recent work on the molecular mechanism with large-scale molecular modelling, and also utilized a new wavelet method to analyse the local structural clusters present in both the wild-type and mutant folding trajectories. These extensive MD (Molecular Dynamics) simulations (10+ μs) were performed in 8 M urea, mimicking the experimental condition. Detailed analyses revealed that the Trp62 residue is the key to a co-operative long-range interaction within the wild-type protein: it acts as a bridge between neighbouring basic residues, mainly arginine residues, through π-type hydrogen bonds or π-cation interactions to form an Arg-Trp-Arg ‘sandwich-like’ local structure. The local cluster near Trp62 further extends its interaction to other clusters, such as the one near Trp111, through Arg112, which is involved in such an Arg-Trp-Arg bridging structure, thus achieving the long-range interactions for the wild-type. On the other hand, the mutant does not have this bridging effect and forms much less local clusters or contacts, and therefore results in a much less stable structure. Overall, these findings not only support the general conclusions of the experiment, but also provide a detailed but somewhat different molecular picture of the disruption of the long-range interactions.

scholarly journals A nonextensive entropy path to probability distributions in solar wind turbulence

2005 ◽  
Vol 12 (2) ◽  
pp. 171-180 ◽  
Author(s):  
M. P. Leubner ◽  
Z. Vörös
Keyword(s):  
Solar Wind ◽  
Long Range ◽  
Large Scale ◽  
Probability Distributions ◽  
Spatial Separation ◽  
Scale Dependence ◽  
Small Scale ◽  
Time Lags ◽  
Turbulent Fluctuations ◽  
Long Range Interactions

Abstract. The observed scale dependence of the probability distributions of the differences of characteristic solar wind variables is analyzed. Intermittency of the turbulent fluctuations at small-scale spatial separations is accompanied by strongly non-Gaussian distributions that turn into a normal distribution for large-scale separation. Conventional theoretical models are subject to insufficient physical justification since nonlocality in turbulence should be based on long-range interactions, provided recently by the bi-kappa distribution in the context of nonextensive thermo-statistics. Observed WIND and ACE probability distributions are accurately reproduced for different time lags by the one-parameter bi-kappa functional, a core-halo convolution, where kappa measures the degree of nonlocality or nonextensivity in the system. Gradual decoupling is obtained by enhancing the spatial separation scale corresponding to increasing kappa values, where a Gaussian is approached for infinite kappa. Consequently, long-range interactions introduced on the fundamental level of entropy generalization, are able to provide physically the source of the observed scale dependence of the turbulent fluctuations in the intermittent interplanetary medium.

Dynamics of direct large-small scale couplings in coherently forced turbulence: concurrent physical- and Fourier-space views

1995 ◽  
Vol 283 ◽  
pp. 43-95 ◽  
Author(s):  
P. K. Yeung ◽  
James G. Brasseur ◽  
Qunzhen Wang
Keyword(s):  
Long Range ◽  
Large Scale ◽  
Three Dimensional ◽  
Physical Space ◽  
Small Scale ◽  
Fourier Space ◽  
Distant Interactions ◽  
Long Range Interactions ◽  
Small Scales ◽  
Non Local

As discussed in a recent paper by Brasseur & Wei (1994), scale interactions in fully developed turbulence are of two basic types in the Fourier-spectral view. The cascade of energy from large to small scales is embedded within ‘local-to-non-local’ triadic interactions separated in scale by a decade or less. ‘Distant’ triadic interactions between widely disparate scales transfer negligible energy between the largest and smallest scales, but directly modify the structure of the smallest scales in relationship to the structure of the energy-dominated large scales. Whereas cascading interactions tend to isotropize the small scales as energy moves through spectral shells from low to high wavenumbers, distant interactions redistribute energy within spectral shells in a manner that leads to anisotropic redistributions of small-scale energy and phase in response to anisotropic structure in the large scales. To study the role of long-range interactions in small-scale dynamics, Yeung & Brasseur (1991) carried out a numerical experiment in which the marginally distant triads were purposely stimulated through a coherent narrow-band anisotropic forcing at the large scales readily interpretable in both the Fourier- and physical-space views. It was found that, after one eddy turnover time, the smallest scales rapidly became anisotropic as a direct consequence of the marginally distant triadic group in a manner consistent with the distant triadic equations. Because these asymptotic equations apply in the infinite Reynolds number limit, Yeung & Brasseur argued that the observed long-range effects should be applicable also at high Reynolds numbers.We continue the analysis of forced simulations in this study, focusing (i) on the detailed three-dimensional restructuring of the small scales as predicted by the asymptotic triadic equations, and (ii) on the relationship between Fourier- and physical-space evolution during forcing. We show that the three-dimensional restructuring of small-scale energy and vorticity in Fourier space from large-scale forcing is predicted in some detail by the distant triadic equations. We find that during forcing the distant interactions alter small-scale structure in two ways: energy is redistributed anisotropically within high-wavenumber spectral shells, and phase correlations are established at the small scales by the distant interactions. In the numerical experiments, the long-range interactions create two pairs of localized volumes of concentrated energy in three-dimensional Fourier space at high wavenumbers in which the Fourier modes are phase coupled. Each pair of locally phase-correlated volumes of Fourier modes separately corresponds to aligned vortex tubes in physical space in two orthogonal directions. We show that the dynamics of distant interactions in creating small-scale anisotropy may be described in physical space by differential advection and distortion of small-scale vorticity by the coherent large-scale energy-containing eddies, producing anisotropic alignment of small-scale vortex tubes.Scaling arguments indicate a disparity in timescale between distant triadic interactions and energy-cascading local-to-non-local interactions which increases with scale separation. Consequently, the small scales respond to forcing initially through the distant interactions. However, as energy cascades from the large-scale to the small-scale Fourier modes, the stimulated distant interactions become embedded within a sea of local-to-non-local energy cascading interactions which reduce (but do not eliminate) small-scale anisotropy at later times. We find that whereas the small-scale structure is still anisotropic at these later times, the second-order velocity moment tensor is insensitive to this anisotropy. Third-order moments, on the other hand, do detect the anisotropy. We conclude that whereas a single statistical measure of anisotropy can be used to indicate the presence of anisotropy, a null result in that measure does not necessarily imply that the signal is isotropic. The results indicate that non-equilibrium non-stationary turbulence is particularly sensitive to long-range interactions and deviations from local isotropy.

scholarly journals On the thermal equilibrium state of large-scale flows

2019 ◽  
Vol 872 ◽  
pp. 594-625 ◽  
Author(s):  
Alexandros Alexakis ◽  
Marc-Etienne Brachet
Keyword(s):  
Energy Spectrum ◽  
Turbulent Flow ◽  
Equilibrium State ◽  
Long Range ◽  
Thermal Equilibrium ◽  
Large Scale ◽  
Thermal Equilibrium State ◽  
Triadic Interactions ◽  
Long Range Interactions ◽  
Small Scales

In a forced three-dimensional turbulent flow the scales larger than the forcing scale have been conjectured to reach a thermal equilibrium state forming a $k^{2}$ energy spectrum, where $k$ is the wavenumber. In this work we examine the properties of these large scales in turbulent flows with the use of numerical simulations. We show that the choice of forcing can strongly affect the behaviour of the large scales. A spectrally dense forcing (a forcing that acts on all modes inside a finite-width spherical shell) with long correlation times may lead to strong deviations from the $k^{2}$ energy spectrum, while a spectrally sparse forcing (a forcing that acts only on a few modes) with short correlated time scale can reproduce the thermal spectrum. The origin of these deviations is analysed and the involved mechanisms is unravelled by examining: (i) the number of triadic interactions taking place, (ii) the spectrum of the nonlinear term, (iii) the amplitude of interactions and the fluxes due to different scales and (iv) the transfer function between different shells of wavenumbers. It is shown that the spectrally dense forcing allows for numerous triadic interactions that couple one large-scale mode with two forced modes and this leads to an excess of energy input at the large scales. This excess of energy is then moved back to the small scales by self-interactions of the large-scale modes and by interactions with the turbulent small scales. The overall picture that arises from the present analysis is that the large scales in a turbulent flow resemble a reservoir that is in (non-local) contact with a second out-of-equilibrium reservoir consisting of the smaller (forced, turbulent and dissipative) scales. If the injection of energy at the large scales from the forced modes is relative weak (as is the case for the spectrally sparse forcing) then the large-scale spectrum remains close to a thermal equilibrium and the role of long-range interactions is to set the global energy (temperature) of the equilibrium state. If, on the other hand, the long-range interactions are dominant (as is the case for the spectrally dense forcing), the large-scale self-interactions cannot respond fast enough to bring the system into equilibrium. Then the large scales deviate from the equilibrium state with energy spectrum that may display exponents different from the $k^{2}$ spectrum.

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