Long-time behaviour of degenerate diffusions: UFG-type SDEs and time-inhomogeneous hypoelliptic processes

We study the long time behaviour of a large class of diffusion processes on $R^N$, generated by second order differential operators of (possibly) degenerate type. The operators that we consider {\em need not} satisfy the H\"ormander condition. Instead, they satisfy the so-called UFG condition, introduced by Herman, Lobry and Sussman in the context of geometric control theory and later by Kusuoka and Stroock, this time with probabilistic motivations. In this paper we study UFG diffusions and demonstrate the importance of such a class of processes in several respects: roughly speaking i) we show that UFG processes constitute a family of SDEs which exhibit multiple invariant measures and for which one is able to describe a systematic procedure to determine the basin of attraction of each invariant measure (equilibrium state). ii) We use an explicit change of coordinates to prove that every UFG diffusion can be, at least locally, represented as a system consisting of an SDE coupled with an ODE, where the ODE evolves independently of the SDE part of the dynamics. iii) As a result, UFG diffusions are inherently "less smooth" than hypoelliptic SDEs; more precisely, we prove that UFG processes do not admit a density with respect to Lebesgue measure on the entire space, but only on suitable time-evolving submanifolds, which we describe. iv) We show that our results and techniques, which we devised for UFG processes, can be applied to the study of the long-time behaviour of non-autonomous hypoelliptic SDEs and therefore produce several results on this latter class of processes as well. v) Because processes that satisfy the (uniform) parabolic H\"ormander condition are UFG processes, our paper contains a wealth of results about the long time behaviour of (uniformly) hypoelliptic processes which are non-ergodic, in the sense that they exhibit multiple invariant measures.Comment: 66 page

The sensitivity of r-process nucleosynthesis to the properties of neutron-rich nuclei

About half of the heavy elements in the Solar System were created by rapid neutron capture, or r-process, nucleosynthesis. In the r-process, heavy elements are built up via a sequence of neutron captures and beta decays in which an intense neutron flux pushes material out towards the neutron drip line. The nuclear network simulations used to test potential astrophysical scenarios for the r-process therefore require nuclear physics data (masses, beta decay lifetimes, neutron capture rates, fission probabilities) for thousands of nuclei far from stability. Only a small fraction of this data has been experimentally measured. Here we discuss recent sensitivity studies that aim to determine the nuclei whose properties are most crucial for r-process calculations.Comment: 8 pages, 4 figures, submitted to the Proceedings of the Fifth International Conference on Fission and Properties of Neutron-Rich Nuclei (ICFN5

How to Compose a Laboratory Animal Use Report for the USDA

All research facilities must submit an annual report on laboratory animal use to the U.S. Department of Agriculture Animal Care Staff as part of the legal requirements of the Federal Laboratory Animal Welfare Act (P.L. 89-544) and its subsequent amendments. This report (USDA: V.C. Form 18-23, Annual Report of Research Facility) must include an explanation of the scientific bases for conducting any research and tests that involve unalleviated distress (the Pain-No Drugs situation) in animal subjects. In some cases, only one of these reports is required

Sensitivity studies for r-process nucleosynthesis in three astrophysical scenarios

In rapid neutron capture, or r-process, nucleosynthesis, heavy elements are built up via a sequence of neutron captures and beta decays that involves thousands of nuclei far from stability. Though we understand the basics of how the r-process proceeds, its astrophysical site is still not conclusively known. The nuclear network simulations we use to test potential astrophysical scenarios require nuclear physics data (masses, beta decay lifetimes, neutron capture rates, fission probabilities) for all of the nuclei on the neutron-rich side of the nuclear chart, from the valley of stability to the neutron drip line. Here we discuss recent sensitivity studies that aim to determine which individual pieces of nuclear data are the most crucial for r-process calculations. We consider three types of astrophysical scenarios: a traditional hot r-process, a cold r-process in which the temperature and density drop rapidly, and a neutron star merger trajectory.Comment: 8 pages, 4 figures, submitted to the Proceedings of the International Nuclear Physics Conference (INPC) 201

On small time asymptotics for rough differential equations driven by fractional Brownian motions

We survey existing results concerning the study in small times of the density of the solution of a rough differential equation driven by fractional Brownian motions. We also slightly improve existing results and discuss some possible applications to mathematical finance.Comment: This is a survey paper, submitted to proceedings in the memory of Peter Laurenc

Paper Session II-C - Alternative Launch Site Selection

Due to circumstances beyond its control, Lockheed Martin\u27s Athena Small Launch Vehicle Program is being forced to relocate from the current Space Launch Complex (SLC) 6 at Vandenberg AFB, CA, to an alternate location. The objective of this study is to recommend highly favorable launch sites to Lockheed Martin Astronautics management for further development. We develop and use a hierarchical, multiobjective value model, to analyze and evaluate alternative launch sites capable of performing SLC-6 polar orbiting missions, as well as future easterly launches

Fuel Alcohol Production : Conversion of Cellulose to Glucose

Cellulose, a complex sugar, can be broken down through saccharification by some microorganisms in the soil to yield glucose. After further action by other microorganisms, it may be converted to ethyl alcohol (grain alcohol) for use as a fuel. The discussion that follows deals with some work done at South Dakota State University (SDSU) to ascertain the feasibility of this process in a farm or community-scale fuel alcohol production facility. Presently, the limiting factor in obtaining fuel alcohol from cellulose wastes is the cost of producing the complex of the three enzymes needed to carry out the process of saccharification. To date, improvements in enzyme production have been made only in the research laboratory. An owner-operator system that would convert cellulose to glucose has yet to be economically developed. The fuel alcohol production facility at SDSU is similar in size to what might be used by an individual owner-operator. This study sought to determine how effective it would be to scale up from the laboratory production level to a rudimentary pilot plant

Protection of Works of Art From Atmospheric Ozone

Assesses the colorfastness of organic colorants and watercolor pigments tested in atmospheric ozone. A summary of a full report of the Environmental Quality Laboratory, California Institute of Technology, Pasadena

Technical note - A method of inoculating and lime pelleting leguminous seeds

Since the report by Loneragan and co-workers (1), the use of lime-pelleted legume seeds has attracted considerable attention. Many queries have been received from farmers requesting information on the method of pelleting clover seed and its possible application to local conditions