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Although it is widely accepted that the diffusion of early reflections in acoustic spaces intended for music performance greatly improves the perceived quality of sound, current manufacturers of synthetic reverberation engines continue to model reflecting surfaces as having almost perfectly specular characteristics. This dissertation describes a hybrid method of simulating diffusion based on both physical and phenomenological modeling components. / In 1979, Manfred Schroeder described a method of designing and constructing diffusing surfaces based on a rather simple mathematical algorithm which provides diffused reflections in predictable frequency bands. This structural device, now known as a "Schroeder diffuser," has become a standard geometry used in constructing diffusive surfaces for spaces intended for music rehearsal, recording and performance. While it is possible to use DSP to model the characteristics of reflections off such a surface, a reflection model based exclusively on a surface constructed of a Schroeder diffuser has proven in informal tests to be as aesthetically inadequate as a perfectly specular model. Control of both the spatial and temporal envelopes of the diffusive reflection are required by an end user in order to tailor the reflection characteristics to the desired impression. / In 1974 an empirical model for computing light reflections off objects in a three-dimensional environment was developed by Phong Bui-Toung. This algorithm incorporated both a specular and diffuse component with relationships controlled by an end user. / This dissertation describes the adaptation and implementation of the Phong shading algorithm in conjunction with a physical model of components of the Schroeder diffuser for the modeling of diffuse reflections in synthetic acoustic environments. The inclusion of the Phong algorithm provides precise control over the balance between the spectral and diffusive components of the reflection. In addition, directivity functions for sound sources and receivers in the virtual space are described. / Analysis and evaluation of the model using mathematical and empirical methodologies are discussed and stereo and multichannel audio examples produced by the system are included.

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A deterministic computer model was developed to continuously simulate the runoff from surface and subsurface-drained fields in the St. Lawrence lowlands. The model simulates all of the major hydrologic and hydraulic processes occurring both above and below the ground. Input data requirements include hourly rainfall, daily potential evapotranspiration, soil physical properties, field dimensions, open channel geometry and drainage system specifications. / Events for the years 1978 to 1982 were simulated, to compare the runoff characteristics between 20 ha, clay loam, surface-drained and subsurface-drained fields. Further simulations were conducted to examine the hydrologic effects of wide-spaced, deep, parallel field ditches. / Hydrographs for the one-in-200-year storm were also simulated. All of the simulations confirmed that the peak flow rate on the subsurface-drained field was less than that of the surface-drained field. Longer times to peak and lag times occurred on the subsurface-drained field.

In this thesis I present a simple, computationally-inexpensive moist turbulence model in order to study the differences between moist and dry turbulence. The model is validated by comparing a moist-bubble simulation with ones presented in Grabowski and Clark (1993) using a more-sophisticated model. We show that the outputs compare well and that our model can easily be extended to higher resolutions due to its simplified equations and uncomplicated implementation. Measurements of liquid water content spectra from the 3843 validation run are shown having shallow slopes, implying that moist processes require high resolution. Consideration is also given to the issue of Gibb's oscillations near sharp gradients, such as at a cloud boundary. It is shown that, due to our high resolutions, the dynamics of our model are not seriously affected if corrections are not made to address them. / The model is used to study the small-scale predictability and dynamics of moist and dry shallow convective turbulence. Although moist flows are less predictable than their associated dry flows, we can account for the differences via a simple scaling. Using large-scale (the root-mean-squared vorticity) and small-scale (the dissipation wavenumber, kd) measures, we can reconcile classical predictability statistics from both wet and dry runs, with different lapse rates and relative humidities. / Finally, I present a more thorough investigation of the dynamical differences between wet and dry convective turbulence, and then consider the very small-scale (ℓ ≲ 10 m) variability of liquid water content and compare our high-resolution simulation results to existing in situ cumulus-cloud observations. We find that there is a small decrease in the spatial intermittency of vorticity in wet runs relative to dry ones. This is consistent with the idea that evaporation of the liquid water in the clouds reduces the instabilities that would lead to the most intense vortices. At the same time, the liquid water content spectra show that in these areas of intense mixing and cloud decay, the characteristic scale of variability is shifted to smaller scales compared to a passive scalar. Further integrations in which the convective forcing is removed show that as the amount of liquid water decreases through evaporation, there is delayed decay of the smallest scales of the cloud. These findings may explain the small-scale shallow liquid water content spectra from cumulus-cloud fly-through measurements reported in Davis et al. (1999).

Structural change and innovation in the market for financial services in recent years have drawn attention to the fact that traditional definitions of money as included in demand for money models and monetary aggregation measures may be misspecified. It is unclear whether or to what extent broader measures of money should be used as targets in monetary policy or as indicators of changes in the real economy. This thesis is a nonparametric empirical test of monetary asset, leisure and consumption good data which seeks to examine whether the underlying structure of preferences implied by monetary aggregation can be said to be justified. Using recent software routines, we test Canadian data for the years 1968-I to 1989-IV in order to determine whether it meets the criteria for utility maximization and for a structure of preferences represented by weak separability. We find that only a narrow grouping of monetary assets meets these requirements. Further, we conclude that many other studies in the literature which have merely assumed weak separability have been misspecified.

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