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FIG. 4. Dimensionless integral I*( ${tau}$ ) as defined by Eq. [40]. It is the spatial integral of the Fréchet kernel F*(X,Y, ${tau}$ ) across a small region of radius R₂ = b centered at (X,Y) = ( $1/2$ ,0), the location of the temperature probe. Results are from Eq. [A5] with b = 1/12. Note that I*( ${tau}$ ) varies smoothly near ${tau}$ = 0.25, despite the fact that the kernel F*(X,Y, ${tau}$ ) has a negative singularity at (X,Y) = ( $1/2$ ,0) for ${tau}$ < 0.25 and a positive singularity at (X,Y) = ( $1/2$ ,0) for ${tau}$ > 0.25.