Exact(4)
However, it was also observed that if most traffic goes to and from an access point, spatial reuse alone does not lead to an increase in network throughput [5].
Unlike previous alternating direction methods of order higher than one, which only deliver unconditional stability for rectangular domains, the new high-order FC-AD (Fourier-Continuation Alternating-Direction) algorithm yields unconditional stability for general domains at an O(Nlog(N)) cost per time-step for an N point spatial discretization grid.
Let d t be the measured data point (spatial position or angle value) at time t.
The kernel R in equation (9) corresponds with the two point spatial correlation function, defined as follows: (10) R = 1 ℓ ∑ j = 1 ℓ x (ξ, t j ) x (ξ ′, t j ). with x(ξ t j ) denoting the value of the field at each instant t j and the summation extends over a sufficiently rich collection of uncorrelated snapshots at j = 1,⋯, ℓ[ 34].
Similar(56)
Finite-difference (5-point) and finite-element (9-point) spatial approximations are compared for different grid aspect ratios.
In all cases, the use of multi-point spatial derivative approximations are explored to find an optimum.
The presented framework is based on low dimensional representation of material structure obtained through principal component analysis (PCA) of 2-point spatial correlations.
It is shown that REV, REA and mean pore and grain size are effectively estimated using the two-point spatial correlation function.
Alternatively, one can identify a weighted set of statistical volume elements (WSVEs) that captures selected dominant components of n-point spatial correlations of the microstructure to prescribed accuracy.
In addition, LES data for the two-point spatial correlations of velocity fluctuations that provide structural information were computed and compared with PIV data.
We then utilize 3-D CNN learned features as estimators of higher-order spatial correlations, and formulate an integrated framework combining 3-D CNN features with 2-point spatial correlations.
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