scholarly journals On the three-dimensional spatial correlations of curved dislocation systems

2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Joseph Pierre Anderson ◽  
Anter El-Azab
Keyword(s):  
Correlation Function ◽  
Slip System ◽  
Correlation Functions ◽  
Mean Field ◽  
Coarse Graining ◽  
Dislocation Dynamics ◽  
Coarse Grained ◽  
Spatial Correlation Function ◽  
Line System ◽  
Dislocation Densities

AbstractCoarse-grained descriptions of dislocation motion in crystalline metals inherently represent a loss of information regarding dislocation-dislocation interactions. In the present work, we consider a coarse-graining framework capable of re-capturing these interactions by means of the dislocation-dislocation correlation functions. The framework depends on a convolution length to define slip-system-specific dislocation densities. Following a statistical definition of this coarse-graining process, we define a spatial correlation function which will allow the arrangement of the discrete line system at two points—and thus the strength of their interactions at short range—to be recaptured into a mean field description of dislocation dynamics. Through a statistical homogeneity argument, we present a method of evaluating this correlation function from discrete dislocation dynamics simulations. Finally, results of this evaluation are shown in the form of the correlation of dislocation densities on the same slip-system. These correlation functions are seen to depend weakly on plastic strain, and in turn, the dislocation density, but are seen to depend strongly on the convolution length. Implications of these correlation functions in regard to continuum dislocation dynamics as well as future directions of investigation are also discussed.

scholarly journals Spatial Correlation Functions of Bright Radio Galaxies

1988 ◽  
Vol 130 ◽  
pp. 580-580 ◽  
Author(s):  
You-yuan Zhou ◽  
Yi-peng Jing
Keyword(s):  
Correlation Function ◽  
Spatial Correlation ◽  
Correlation Functions ◽  
Radio Galaxies ◽  
Radio Sources ◽  
Spatial Correlation Function ◽  
Extragalactic Radio Sources ◽  
Large Separation ◽  
The Universe

Because of their large separation bright radio galaxies characterize the structure of the universe on the scales of clusters and superclusters. In order to calculate the spatial correlation function we choose radio galaxies in radio surveys, for which the redshift values have been measured. One is from Bright Radio Sources at 178 MHz (Liang, Riley and Longair 1983), and another is from All-Sky Catalogue of Bright Extragalactic Radio Sources at 2.7 GHz (Wall and Peacock 1985).

scholarly journals Comparative analysis of continuum angiogenesis models

2021 ◽  
Vol 82 (4) ◽  
Author(s):  
W. Duncan Martinson ◽  
Hirokazu Ninomiya ◽  
Helen M. Byrne ◽  
Philip K. Maini
Keyword(s):  
Mean Field ◽  
Cell Movement ◽  
Coarse Graining ◽  
Population Level ◽  
Coarse Grained ◽  
Continuum Models ◽  
Biological Phenomena ◽  
Complex Population ◽  
The Mean ◽  
Work Done

AbstractAlthough discrete approaches are increasingly employed to model biological phenomena, it remains unclear how complex, population-level behaviours in such frameworks arise from the rules used to represent interactions between individuals. Discrete-to-continuum approaches, which are used to derive systems of coarse-grained equations describing the mean-field dynamics of a microscopic model, can provide insight into such emergent behaviour. Coarse-grained models often contain nonlinear terms that depend on the microscopic rules of the discrete framework, however, and such nonlinearities can make a model difficult to mathematically analyse. By contrast, models developed using phenomenological approaches are typically easier to investigate but have a more obscure connection to the underlying microscopic system. To our knowledge, there has been little work done to compare solutions of phenomenological and coarse-grained models. Here we address this problem in the context of angiogenesis (the creation of new blood vessels from existing vasculature). We compare asymptotic solutions of a classical, phenomenological “snail-trail” model for angiogenesis to solutions of a nonlinear system of partial differential equations (PDEs) derived via a systematic coarse-graining procedure (Pillay et al. in Phys Rev E 95(1):012410, 2017. https://doi.org/10.1103/PhysRevE.95.012410). For distinguished parameter regimes corresponding to chemotaxis-dominated cell movement and low branching rates, both continuum models reduce at leading order to identical PDEs within the domain interior. Numerical and analytical results confirm that pointwise differences between solutions to the two continuum models are small if these conditions hold, and demonstrate how perturbation methods can be used to determine when a phenomenological model provides a good approximation to a more detailed coarse-grained system for the same biological process.

Quantifying Drop Size Distribution Variability over Areas: Some Implications for Ground Validation Experiments

2016 ◽  
Vol 17 (10) ◽  
pp. 2689-2698 ◽  
Author(s):  
A. R. Jameson
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Ground Truth ◽  
Network Size ◽  
Relative Dispersion ◽  
Spatial Correlation Function ◽  
Temporal Correlations ◽  
Ground Validation ◽  
Radar Measurements ◽  
The Fourier Transform

Abstract In previous work it was found that over a small network of disdrometers, the variability of probability size distributions (PSDs) expressed using the relative dispersion (RD; the ratio of the standard deviation to the mean) increased with the expansion of the network size. The explanation is that the network acts to integrate the Fourier transform of the spatial correlation function from smallest wavelengths to those comparable to the network size . Consequently, as increases, so do the variances at the different drop sizes. Thus, RD and PSD variability grow as increases. The limits to this growth, however, were not determined quantitatively. This finding is given fuller theoretical quantitative meaning over much larger dimensions by explicitly deriving the variance contributions at all the different drop sizes as well as for a variety of moments of the PSD by using spatial radial correlation functions estimated from temporal correlations. This is justifiable when the time for each observation is short. One example is provided. The relative dispersion of the PSD is dominated by fluctuations in the occurrences of the larger drops. The RDs of the raw moments are only a few percent of the PSD. Thus, approaches attempting to estimate radial correlation functions using, say, radar measurements of moments are of limited utility, a usefulness further compromised by the distortion of the correlation function by filtering over the beam dimension. These findings present a challenge for efforts to validate remote sensing measurements by ground truth experiments using networks.

scholarly journals A Possibility of Reveal of Parent Populations for the Objects by Active Nuclei on the Basis of Comparing their Spatial Correlation Functions

1994 ◽  
Vol 159 ◽  
pp. 512-512
Author(s):  
B.V. Romberg ◽  
A.V. Kravtsov
Keyword(s):  
Correlation Function ◽  
Spatial Correlation ◽  
Correlation Functions ◽  
Seyfert Galaxies ◽  
Spatial Correlation Function ◽  
The World

For a model of the World with q0 = 0.5 and H0 = 100h−1 there was received a 2-point spatial correlation function (CF) (The sample of 300 objects with z < 0.045 and δ > 0 was used) for Seyfert Galaxies with the following parameters: r0 = (9 ± 2)h−1Mpc, γ = –(1.7 ± 0.2).

Grand-Reaction Method for Simulations of Ionization Equilibria and Ion Partitioning in a Broad Range of pH and Ionic Strength

2019 ◽  
Author(s):  
Jonas Landsgesell ◽  
Oleg Rud ◽  
Pascal Hebbeker ◽  
Raju Lunkad ◽  
Peter Košovan ◽  
...  
Keyword(s):  
Mean Field ◽  
Coarse Grained ◽  
Reactive System ◽  
Acid Base ◽  
Buffer Solution ◽  
Reaction Method ◽  
Ionization Equilibria ◽  
Coarse Grained Simulations ◽  
Ph Range ◽  
Weak Polyelectrolytes

We introduce the grand-reaction method for coarse-grained simulations of acid-base equilibria in a system coupled to a reservoir at a given pH and concentration of added salt. It can be viewed as an extension of the constant-pH method and the reaction ensemble, combining explicit simulations of reactions within the system, and grand-canonical exchange of particles with the reservoir. Unlike the previously introduced methods, the grand-reaction method is applicable to acid-base equilibria in the whole pH range because it avoids known artifacts. However, the method is more general, and can be used for simulations of any reactive system coupled to a reservoir of a known composition. To demonstrate the advantages of the grand-reaction method, we simulated a model system: A solution of weak polyelectrolytes in equilibrium with a buffer solution. By carefully accounting for the exchange of all constituents, the method ensures that all chemical potentials are equal in the system and in the multi-component reservoir. Thus, the grand-reaction method is able to predict non-monotonic swelling of weak polyelectrolytes as a function of pH, that has been known from mean-field predictions and from experiments but has never been observed in coarse-grained simulations. Finally, we outline possible extensions and further generalizations of the method, and provide a set of guidelines to enable safe usage of the method by a broad community of users.<br><br>

scholarly journals From correlation functions to event shapes in QCD

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
D. Chicherin ◽  
J. M. Henn ◽  
E. Sokatchev ◽  
K. Yan
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Event Shape ◽  
Proof Of Concept ◽  
Yang Mills ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Event Shapes ◽  
A Charge ◽  
Conserved Currents

Abstract We present a method for calculating event shapes in QCD based on correlation functions of conserved currents. The method has been previously applied to the maximally supersymmetric Yang-Mills theory, but we demonstrate that supersymmetry is not essential. As a proof of concept, we consider the simplest example of a charge-charge correlation at one loop (leading order). We compute the correlation function of four electromagnetic currents and explain in detail the steps needed to extract the event shape from it. The result is compared to the standard amplitude calculation. The explicit four-point correlation function may also be of interest for the CFT community.

scholarly journals Mean-Field Models for EEG/MEG: From Oscillations to Waves

2021 ◽  
Author(s):  
Áine Byrne ◽  
James Ross ◽  
Rachel Nicks ◽  
Stephen Coombes
Keyword(s):  
Gap Junction ◽  
Large Scale ◽  
Mean Field ◽  
Coarse Grained ◽  
Neural Mass Model ◽  
Neuron Network ◽  
Mass Model ◽  
Mean Field Model ◽  
Neural Mass ◽  
The Rich

AbstractNeural mass models have been used since the 1970s to model the coarse-grained activity of large populations of neurons. They have proven especially fruitful for understanding brain rhythms. However, although motivated by neurobiological considerations they are phenomenological in nature, and cannot hope to recreate some of the rich repertoire of responses seen in real neuronal tissue. Here we consider a simple spiking neuron network model that has recently been shown to admit an exact mean-field description for both synaptic and gap-junction interactions. The mean-field model takes a similar form to a standard neural mass model, with an additional dynamical equation to describe the evolution of within-population synchrony. As well as reviewing the origins of this next generation mass model we discuss its extension to describe an idealised spatially extended planar cortex. To emphasise the usefulness of this model for EEG/MEG modelling we show how it can be used to uncover the role of local gap-junction coupling in shaping large scale synaptic waves.

The gas-liquid surface of the penetrable sphere model. II

1978 ◽  
Vol 358 (1694) ◽  
pp. 267-280 ◽  
Keyword(s):  
Surface Tension ◽  
Correlation Function ◽  
Liquid Surface ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Intermolecular Potential ◽  
Direct Correlation Function ◽  
Sphere Model ◽  
One Dimensional

The direct correlation function between two points in the gas-liquid surface of the penetrable sphere model is obtained in a mean-field approximation. This function is used to show explicitly that three apparently different ways of calculating the surface tension all lead to the same result. They are (1) from the virial of the intermolecular potential, (2) from the direct correlation function, and (3) from the energy density. The equality of (1) and (2) is shown analytically at all temperatures 0 < T < T c where T c is the critical temperature; the equality of (2) and (3) is shown analytically for T ≈ T c , and by numerical integration at lower temperatures. The equality of (2) and (3) is shown analytically at all temperatures for a one-dimensional potential.

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