scholarly journals Signature of dynamical heterogeneity in spatial correlations of particle displacement and its temporal evolution in supercooled liquids

2020 ◽  
Vol 2 (2) ◽  
Author(s):  
Indrajit Tah ◽  
Smarajit Karmakar
Keyword(s):  
Temporal Evolution ◽  
Supercooled Liquids ◽  
Particle Displacement ◽  
Spatial Correlations ◽  
Dynamical Heterogeneity

scholarly journals Effects of a tungsten addition on the morphological evolution, spatial correlations and temporal evolution of a model Ni–Al–Cr superalloy

2008 ◽  
Vol 56 (3) ◽  
pp. 448-463 ◽  
Author(s):  
Chantal K. Sudbrack ◽  
Tiffany D. Ziebell ◽  
Ronald D. Noebe ◽  
David N. Seidman
Keyword(s):  
Temporal Evolution ◽  
Morphological Evolution ◽  
Spatial Correlations

scholarly journals Multiple dynamic regimes in concentrated microgel systems

2009 ◽  
Vol 367 (1909) ◽  
pp. 5013-5032 ◽  
Author(s):  
David A. Sessoms ◽  
Irmgard Bischofberger ◽  
Luca Cipelletti ◽  
Véronique Trappe
Keyword(s):  
Volume Fraction ◽  
Low Frequency ◽  
Qualitative Change ◽  
System Size ◽  
Packing Fraction ◽  
Contact Forces ◽  
Spatial Correlations ◽  
Dynamical Heterogeneity ◽  
Thermally Driven ◽  
System Properties

We investigate dynamical heterogeneities in the collective relaxation of a concentrated microgel system, for which the packing fraction can be conveniently varied by changing the temperature. The packing fraction-dependent mechanical properties are characterized by a fluid–solid transition, where the system properties switch from a viscous to an elastic low-frequency behaviour. Approaching this transition from below, we find that the range ξ of spatial correlations in the dynamics increases. Beyond this transition, ξ reaches a maximum, extending over the entire observable system size of approximately 5 mm. Increasing the packing fraction even further leads to a second transition, which is characterized by the development of large zones of lower and higher dynamical activity that are well separated from each other; the range of correlation decreases at this point. This striking non-monotonic dependence of ξ on volume fraction is reminiscent of the behaviour recently observed at the jamming/rigidity transition in granular systems. We identify this second transition as the transition to ‘squeezed’ states, where the constituents of the system start to exert direct contact forces on each other, such that the dynamics becomes increasingly determined by imbalanced stresses. Evidence of this transition is also found in the frequency dependence of the storage and loss moduli, which become increasingly coupled as direct friction between the particles starts to contribute to the dissipative losses within the system. To our knowledge, our data provide the first observation of a qualitative change in dynamical heterogeneity as the dynamics switches from purely thermally driven to stress driven.

Quadratic Discriminant Analysis of Spatially Correlated Data

2001 ◽  
Vol 6 (2) ◽  
pp. 15-28 ◽  
Author(s):  
K. Dučinskas ◽  
J. Šaltytė
Keyword(s):  
Discriminant Function ◽  
Error Rate ◽  
Gaussian Random Field ◽  
Correlated Data ◽  
Covariance Matrices ◽  
Classification Rule ◽  
Spatial Correlations ◽  
Linear Quadratic ◽  
Spatial Correlation Function ◽  
Spatially Correlated

The problem of classification of the realisation of the stationary univariate Gaussian random field into one of two populations with different means and different factorised covariance matrices is considered. In such a case optimal classification rule in the sense of minimum probability of misclassification is associated with non-linear (quadratic) discriminant function. Unknown means and the covariance matrices of the feature vector components are estimated from spatially correlated training samples using the maximum likelihood approach and assuming spatial correlations to be known. Explicit formula of Bayes error rate and the first-order asymptotic expansion of the expected error rate associated with quadratic plug-in discriminant function are presented. A set of numerical calculations for the spherical spatial correlation function is performed and two different spatial sampling designs are compared.

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