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In diffusion transport, the flux at a point is typically modeled in terms of the local gradient of a potential. When heterogeneities are present, this local model can break down and it may be more appropriate to model the diffusion flux as a weighted sum of gradients present throughout the domain. Here a discrete nonlocal flux model-consistent with control-volume implementations-is developed. This scheme is referred to as the control-volume weighted flux scheme (CVWFS). The key component is the modeling of the diffusion flux at a given control-volume face in terms of a weighted sum of gradients at that face and at faces up- and downstream. Criteria for choosing the weights are proposed. This results in numerical solution schemes in which the coefficient matrix is diagonally dominant, has positive off-diagonal elements, and zero row sums. For a particular power-law weighting scheme it is shown how the CVWFS is related to the definition of the Caputo fractional derivative and the one-shift Grunwald approximation of the Riemann-Liouville fractional derivative. On developing transients and boundary condition treatments, the accuracy and suitability of the CVWFS scheme is demonstrated by solving a number of problems governed by Caputo fractional diffusion equations. [ABSTRACT FROM AUTHOR]

The unwanted sensitivity of a plate pyroelectric detector to airborne acoustic noise is depends critically on the mounting conditions for the plate. We consider a plate in an isotropic acoustic pressure field oscillating at angular frequencyωd. We analyze the situation in terms of a mechanically isotropic material, and show that for one type of boundary conditions, the so-called clamped-boundary conditions, the strain-induced time-varying surface charges caused by the pressure in various regions of the plate, completely cancel out. This suggests that significantly reduced noise sensitivity of a practical free-standing pyroelectric detector can be achieved by paying careful attention to the mounting conditions. We also derive the strains for the case of the trigonal 3m class within the framework developed for the thin-plate approximation, and show that the result is unchanged. This has implications for the design of pyroelectric detectors based on a stiff material such as LiTaO3.∗Contribution of the National Institute of Standards and Technology, not subject to Copyright. [ABSTRACT FROM AUTHOR]