Machine-checked proofs of the design and implementation of a fault-tolerant circuit

A formally verified implementation of the 'oral messages' algorithm of Pease, Shostak, and Lamport is described. An abstract implementation of the algorithm is verified to achieve interactive consistency in the presence of faults. This abstract characterization is then mapped down to a hardware level implementation which inherits the fault-tolerant characteristics of the abstract version. All steps in the proof were checked with the Boyer-Moore theorem prover. A significant results is the demonstration of a fault-tolerant device that is formally specified and whose implementation is proved correct with respect to this specification. A significant simplifying assumption is that the redundant processors behave synchronously. A mechanically checked proof that the oral messages algorithm is 'optimal' in the sense that no algorithm which achieves agreement via similar message passing can tolerate a larger proportion of faulty processor is also described

Refraction of swell by surface currents

Using recordings of swell from pitch-and-roll buoys, we have reproduced the classic observations of long-range surface wave propagation originally made by Munk et al. (1963) using a triangular array of bottom pressure measurements. In the modern data, the direction of the incoming swell fluctuates by about $\pm 10^\circ$ on a time scale of one hour. But if the incoming direction is averaged over the duration of an event then, in contrast with the observations by Munk et al. (1963), the sources inferred by great-circle backtracking are most often in good agreement with the location of large storms on weather maps of the Southern Ocean. However there are a few puzzling failures of great-circle backtracking e.g., in one case, the direct great-circle route is blocked by the Tuamoto Islands and the inferred source falls on New Zealand. Mirages like this occur more frequently in the bottom-pressure observations of Munk et al. (1963), where several inferred sources fell on the Antarctic continent. Using spherical ray tracing we investigate the hypothesis that the refraction of waves by surface currents produces the mirages. With reconstructions of surface currents inferred from satellite altimetry, we show that mesoscale vorticity significantly deflects swell away from great-circle propagation so that the source and receiver are connected by a bundle of many rays, none of which precisely follow a great circle. The $\pm 10^\circ$ directional fluctuations at the receiver result from the arrival of wave packets that have travelled along the different rays within this multipath. The occasional failure of great-circle backtracking, and the associated mirages, probably results from partial topographic obstruction of the multipath, which biases the directional average at the receiver.Comment: Journal of Marine Research, in pres

Gas-Phase Photodegradation of Decane and Methanol on TiO_2: Dynamic Surface Chemistry Characterized by Diffuse Reflectance FTIR

Diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) was used to study illuminated TiO2 surfaces under both vacuum conditions, and in the presence of organic molecules (decane and methanol). In the presence of hole scavengers, electrons are trapped at Ti(III)–OH sites, and free electrons are generated. These free electrons are seen to decay by exposure either to oxygen or to heat; in the case of heating, reinjection of holes into the lattice by loss of sorbed hole scavenger leads to a decrease in Ti(III)–OH centers. Decane adsorption experiments lend support to the theory that removal of surficial hydrocarbon contaminants is responsible for superhydrophilic TiO2 surfaces. Oxidation of decane led to a mixture of surface-bound organics, while oxidation of methanol leads to the formation of surface-bound formic acid

The vertical structure of the wind-driven circulation

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution August 1981This thesis consists of three loosely related theoretical studies. In chapters 1 - 3 the physical mechanisms which determine the three dimensional structure of the currents in the Sverdrup interior of a wind-driven gyre are discussed. A variety of simple analytic models suggest that the subsurface geostrophic contours in a wind gyre are closed and so the flow in these regions is not determined by lateral boundary conditions. Instead a turbulent, quasigeostrophic extension of the Batchelor-Prandtl theorem suggests that the potential vorticity is uniform inside these laterally isolated regions. The requirement that the potential vorticity be uniform leads simply and directly to predictions of the shape and extent of the wind gyre and the vertical structure of the currents within it. In chapter 4 the propogation of Rossby wave trains through slowly varying forced mean flows is examined by solving the linearized potential vorticity equation using the WKB method. If the mean flow is forced the action defined by Bretherton and Garrett (1968) is not conserved. Surprisingly, there is another quadratic wave property which is conserved, the wave enstrophy. In chapter 5 shear dispersion in an oscillatory velocity field, similar to that of an inertial oscillation, is discussed. The goal of this section is to develop intuition about the role of internal waves in horizontal ocean mixing. The problem is examined using a variety of models and techniques. The most important result is (23.2) which is an expression for the effective horizontal diffusivity produced by the interaction of vertical diffusivity and oscillatory vertical shear. Given an empirical velocity shear spectrum and an estimate of the vertical diffusivity this result could be used to calculate a horizontal eddy diffusivity which parameterizes the horizontal mixing due to the internal wave field.NSF Grant OCE-78-25692 has supported me throughout my stay in the Joint Program

Methods to Determine the Deformation of the IRVE Hypersonic Inflatable Aerodynamic Decelerator

Small resonant targets used in conjunction with a microwave reflectometer to determine the deformation of the Hypersonic Inflatable Aerodynamic Decelerator (HIAD) during reentry are investigated. The reflectometer measures the distance to the targets and from this the HIAD deformation is determined. The HIAD is used by the Inflatable Reentry Vehicle Experiment (IRVE) which investigates the use of inflatable heat shields for atmospheric reentry. After several different microwave reflectometer systems were analyzed and compared it was determined that the most desirable for this application is the Frequency Doubling Target method

ECONOMICALLY OPTIMAL NITROGEN FERTILIZATION FOR YIELD AND PROTEIN IN HARD RED SPRING WHEAT

This analysis determines profit maximizing N fertilization levels of hard red spring wheat (HRSW) for various wheat prices, N prices, and protein-based HRSW price premium/discount (P/D) structures for south eastern Washington data. Fertilizer response data consisting of rates of N fertilization (lb/ac), grain yield (bu/ac), and grain protein (%) were used to statistically estimate regression relationships that predicted yield and protein in response to N. All predicted net return maximizing N, protein, and yield levels were within the data range. Increasing P/D incentives for protein increased optimal N, the expected economic result. At the high P/D structures, the P/D structure dominated N and wheat prices in determining optimal N application levels. Overall, net return-maximizing yields varied only modestly with changes in both N and wheat price in this data set. However, in all scenarios, as P/D incentives increased, net return maximizing N levels were beyond the level that resulted in maximum yield. At the two lowest P/D structures, which provided the lowest reward for protein, it was most profitable to fertilize for slightly less than 14% expected protein. These results indicate that it is not always profitable to use 14% protein as an N fertilization goal. Abbreviations: CT, conventional tillage; HRSW, hard red spring wheat; HRWW, hard red winter wheat; N, nitrogen; NO3, nitrate; NT, No Tillage; P/D, premium/discount; SWSW, soft white spring wheat; SWW, soft white wheat.Crop Production/Industries,

The design and proof of correctness of a fault-tolerant circuit

The flowing achievements are presented in view graph form: (1) a formal statement of interactive consistency conditions in the Boyer-Moore logic; (2) a formal statement of the oral messages (OM) algorithm in the Boyer-Moore logic; (3) a mechanically checked proof that OM satisfies the interactive consistency conditions; (4) a mechanically checked proof of the optimality result--no algorithm can tolerate fewer faults than OM yet still achieve interactive consistency; (5) the use of OM in a functional specification for a fault-tolerant device; (6) a formal description of the design of the device; (7) a mechanically checked proof that the device design satisfies the specification; and (8) an implementation of the design in programmable logic arrays