James R. Brannan

COMPOUND RANDOM FIELD MODELS OF MULTIPLE SCALE HYDRAULIC CONDUCTIVITY

Enormous amounts of hydrologic data are required to accurately simulate subsurface contaminant transport. Effectively supplementing measurements of hydrologic parameters such as permeability and porosity with “soft” information obtained from the interpretation of geologic cores and geophysical logs can improve the simulation of contaminant transport while reducing the measured data that are required. A method is presented herein for generating hydraulic conductivity fields comprised of several geological materials with hydraulic conductivities that can range over several orders of magnitude. This method utilizes indicator fields that are designed to allow random variation at the megascopic scale but are constrained by observations inferred from geophysical logs and geologic core data. The statistical description of random hydraulic conductivity values of distinct geological materials at the macroscopic scale may be obtained by conventional parameter estimation techniques. The combined approach can then be used to generate realizations of a hydraulic conductivity field for subsequent use in flow and transport simulations. The structural constraints confine realizations to vary about a nominal model in a physically reasonable manner. The uncertainty may be viewed as arising from two different scales. Variation in hydraulic conductivity at the macroscale may be viewed as an intrinsic statistical property of the particular geologic material but where measurements may be made in order to ascertain the statistical description. On the other hand, uncertainty at the megascale level arises from the fact that the large-scale system structure is only partially observable. It is the latter area where soft geologic information and geological knowledge can be useful in confining the uncertainty in the model to geologically reasonable limits.

Escape probability, mean residence time and geophysical fluid particle dynamics

Abstract Stochastic dynamical systems arise as models for fluid particle motion in geophysical flows with random velocity fields. Escape probability (from a fluid domain) and mean residence time (in a fluid domain) quantify fluid transport between flow regimes of different characteristic motion. We consider a quasigeostrophic meandering jet model with random perturbations. This jet is parameterized by the parameter β=(2 Ω /r) cos (θ) , where Ω is the rotation rate of the earth, r the earth’s radius and θ the latitude. Note that Ω and r are fixed, so β is a monotonic decreasing function of the latitude. The unperturbed jet (for 0

The uniform WKB modal approach to pulsed and broadband propagation

A uniform asymptotic approach is utilized to consider pulsed and broadband propagation. For a given frequency, the WKB approach with boundary layer corrections is used to approximate the normal modes of the sound channel. This approach is demonstrated to yield significant reductions in computer processing time and high accuracy when compared to a conventional code. It is shown that a substantial amount of the calculations in the uniform WKB approach required at each frequency is frequency‐independent, and need be done only once in multiple frequency runs. Hence, further efficiencies in broadband or pulsed propagation result without any sacrifice in accuracy. Comparison of waveform predictions between uniform WKB and conventional techniques show excellent agreement in a complex propagation environment with use of the uniform WKB approach resulting in reductions of computer time by a factor of over 100.

Escape probability and mean residence time in random flows with unsteady drift

We investigate fluid transport in random velocity fields with unsteady drift. First, we propose to quantify fluid transport between flow regimes of different characteristic motion, by escape probability and mean residence time. We then develop numerical algorithms to solve for escape probability and mean residence time, which are described by backward Fokker-Planck type partial differential equations. A few computational issues are also discussed. Finally, we apply these ideas and numerical algorithms to a tidal flow model.

Spatially localized interactive neural populations—I. A mathematical model

A probabilistic model of a spatially localized, mutually exitatory (inhibitory) population of neurons is formulated to help explain average evoked potential and post-stimulus time histogram measurements. The model is based on the stochastic activity of single neurons within interactive masses of neurons which exhibit co-operative behavior. Macrostate variables corresponding to the above measurements are related through the model to features of neural operation at the individual and ensemble level. Steady-state solution are obtained and their physiological implications are discussed.

A Diffusion Model of Forest Succession

Based on a tree by tree replacement mechanism, a diffusion model of forest stand canopy composition is formulated and analyzed. The model is used to explore composition dichotomies by estimating coefficients from forest stand data and interpreting the results in terms of mechanisms for succession. The model yields a concrete characterization of the succession phenomenon known as the climax state.

Spatially localized interactive neural populations—II: Stability and dynamics of excitatory sets

The stability characteristics and dynamical behavior of a system of mutually excitatory neurons in close spatial proximity are investigated with a mathematical model. The model predicts the existence of uniform, intermediate levels of activity other than those of no activity and maximal activity. The model also, yeilds a good explanation of data obtained from periglomerular neurons in the olfactory bulb of the cat.

A robust, low precision, environmentally adapted receiver algorithm

For a model problem of source localization, it is shown that a receiver algorithm based on maximum likelihood theory and which also includes a priori knowledge of the environment has high precision but is extremely sensitive to deviations of environmental parameters from exact values. Consequently a computationally intensive search over the parameter space is required to estimate the source location. An alternative, physically motivated, low resolution estimation algorithm, the Levy receiver, based on the Levy metric for probability distributions is presented. The Levy receiver also incorporates a priori knowledge of environmental parameters but appears to be much less sensitive to uncertainty in these parameters. Furthermore, the amplitude of the surface generated by the Levy receiver over parameter space exhibits trends which permits restricting the search to a relatively coarse grid.

Relaxation spectra of interactive neural systems

A nonlinear model of spatially localized interactive neural systems is analyzed in the neighborhood of steady state solutions by computing relaxation spectra which govern the long time approach to steady state activity levels.

High-frequency numerical-analytic approximations for the separable acoustic wave equation

Abstract An algorithm which employs a combination of asymptotic and numerical methods to solve a Sturm-Liouville problem arising from a separable acoustic wave equation is presented. Error criteria for switching between methods are derived. Implementation requires a decomposition of the index of refraction profile into separable subprofiles. Computing times and accuracies are compared with conventional methods.