Mean-Field Spin Glass models from the Cavity--ROSt Perspective

The Sherrington-Kirkpatrick spin glass model has been studied as a source of insight into the statistical mechanics of systems with highly diversified collections of competing low energy states. The goal of this summary is to present some of the ideas which have emerged in the mathematical study of its free energy. In particular, we highlight the perspective of the cavity dynamics, and the related variational principle. These are expressed in terms of Random Overlap Structures (ROSt), which are used to describe the possible states of the reservoir in the cavity step. The Parisi solution is presented as reflecting the ansatz that it suffices to restrict the variation to hierarchal structures which are discussed here in some detail. While the Parisi solution was proven to be correct, through recent works of F. Guerra and M. Talagrand, the reasons for the effectiveness of the Parisi ansatz still remain to be elucidated. We question whether this could be related to the quasi-stationarity of the special subclass of ROSts given by Ruelle's hierarchal `random probability cascades' (also known as GREM).Comment: Based on talks given at `Young Res. Symp.', Lisbon 2003, and `Math. Phys. of Spin Glasses', Cortona 200

The Development of NDE Techniques for Large Cryogenic Storage Tanks

Objectives of this project are: (1) Develop and demonstrate NDE techniques to evaluate the condition of large cryogenic Dewars (typically 50,000 to 900,000 gaL). (2) These tanks are used across NASA for launch pads, engine test stands, cryogenic wind tunnels and other facilities: they represent a major investment. (3) Issues addressed: (1) Insulation integrity of existing Dewars (powdered insulation under vacuum or sometimes ambient pressure (LO2), (2) Post fabrication insulation verification without full chill-down to avoid thermal cycling the tank (fatigue limitation of piping and compaction of Perlite)

Measuring Air Leaks into the Vacuum Space of Large Liquid Hydrogen Tanks

Large cryogenic liquid hydrogen tanks are composed of inner and outer shells. The outer shell is exposed to the ambient environment while the inner shell holds the liquid hydrogen. The region between these two shells is evacuated and typically filled with a powderlike insulation to minimize radiative coupling between the two shells. A technique was developed for detecting the presence of an air leak from the outside environment into this evacuated region. These tanks are roughly 70 ft (approx. equal 21 m) in diameter (outer shell) and the inner shell is roughly 62 ft (approx. equal 19 m) in diameter, so the evacuated region is about 4 ft (approx. equal 1 m) wide. A small leak's primary effect is to increase the boil-off of the tank. It was preferable to install a more accurate fill level sensor than to implement a boil-off meter. The fill level sensor would be composed of an accurate pair of pressure transducers that would essentially weigh the remaining liquid hydrogen. This upgrade, allowing boil-off data to be obtained weekly instead of over several months, is ongoing, and will then provide a relatively rapid indication of the presence of a leak

Measuring Moisture Levels in Graphite Epoxy Composite Sandwich Structures

Graphite epoxy composite (GEC) materials are used in the construction of rocket fairings, nose cones, interstage adapters, and heat shields due to their high strength and light weight. However, they absorb moisture depending on the environmental conditions they are exposed to prior to launch. Too much moisture absorption can become a problem when temperature and pressure changes experienced during launch cause the water to vaporize. The rapid state change of the water can result in structural failure of the material. In addition, heat and moisture combine to weaken GEC structures. Diffusion models that predict the total accumulated moisture content based on the environmental conditions are one accepted method of determining if the material strength has been reduced to an unacceptable level. However, there currently doesn t exist any field measurement technique to estimate the actual moisture content of a composite structure. A multi-layer diffusion model was constructed with Mathematica to predict moisture absorption and desorption from the GEC sandwich structure. This model is used in conjunction with relative humidity/temperature sensors both on the inside and outside of the material to determine the moisture levels in the structure. Because the core materials have much higher diffusivity than the face sheets, a single relative humidity measurement will accurately reflect the moisture levels in the core. When combined with an external relative humidity measurement, the model can be used to determine the moisture levels in the face sheets. Since diffusion is temperaturedependent, the temperature measurements are used to determine the diffusivity of the face sheets for the model computations

Thermographic Methods of Detecting Insulation Voids in Large Cryogenic Tanks

Four very large (900Kgal) cryogenic liquid hydrogen and oxygen storage tanks at Kennedy Space Center's LC-39 launch pads were constructed in 1965 to support the Apollo/Saturn V Program and continue to support the Space Shuttle Program. These double-walled spherical tanks with powdered insulation in the annular region, have received minimal refurbishment or even inspection over the years. Intrusively inspecting these tanks would mean a significant down time to the program as the cryogenic liquid and the perlite insulation would have to be removed which would be a significant task and long-term schedule disruption. A study of the tanks was performed to determine the extent to which performance and structural information could be revealed without intrusive inspection. Thermal images of the tanks were taken over a variety of environmental conditions to determine the best conditions under which to compare and use thermography as a health monitoring technique as the tanks continue to age. The settling and subsequent compaction of insulation is a serious concern for cryogenic tanks. Comparison of images from the tanks reveals significant variations in the insulation in the annual regions and point to the use of thermography as a way to monitor for insulation migration and possible compaction. These measurements, when combined with mathematical models of historical boil-off data provide key insight to the condition of the vessels. Acceptance testing methods for new tanks, before they are filled with cryogenic commodity (and thereby thermally cycled), are needed and we explore how thermography can be used to accomplish this

Two-dimensional Inductive Position Sensing System

A two-dimensional inductive position sensing system uses four drive inductors arranged at the vertices of a parallelogram and a sensing inductor positioned within the parallelogram. The sensing inductor is movable within the parallelogram and relative to the drive inductors. A first oscillating current at a first frequency is supplied to a first pair of the drive inductors located at ends of a first diagonal of the parallelogram. A second oscillating current at a second frequency is supplied to a second pair of the drive inductors located at ends of a second diagonal of the parallelogram. As a result, the sensing inductor generates a first output voltage at the first frequency and a second output voltage at the second frequency. A processor determines a position of the sensing inductor relative to the drive inductors using the first output voltage and the second output voltage