Stochastic and deterministic models for agricultural production networks.

An approach to modeling the impact of disturbances in an agricultural production network is presented. A stochastic model and its approximate deterministic model for averages over sample paths of the stochastic system are developed. Simulations, sensitivity and generalized sensitivity analyses are given. Finally, it is shown how diseases may be introduced into the network and corresponding simulations are discussed.

Sensitivity of dynamical systems to parameters in a convex subset of a topological vector space.

We develop a theory for sensitivity with respect to parameters in a convex subset of a topological vector space of dynamical systems in a Banach space. Specific motivating examples for probability measure dependent differential, partial differential and delay differential equations are given. Schemes that approximate the measures in the Prohorov sense are illustrated with numerical simulations for distributed delay differential equations.

Nonlinear frequency-dependent attenuation in sandy sediments.

This paper summarizes evidence of a nonlinear frequency dependence of attenuation for compressional waves in shallow-water waveguides with sandy sediment bottoms. Sediment attenuation is found consistent with alpha(f) = alpha(f(o)) x (f/f(o))n, n approximately 1.8 +/- 0.2 at frequencies less than 1 kHz in agreement with the theoretical expectation, (n = 2), of Biot [J. Acoust. Soc. Am. 28(2), 168-178, 1956]. For frequencies less than 10 kHz, the sediment layers, within meters of the water-sediment interface, appear to play a role in the attenuation that strongly depends on the power law. The accurate calculation of sound transmission in a shallow-water waveguide requires the depth-dependent sound speed, density, and frequency-dependent attenuation.