Invariant manifolds and the long-time asymptotics of the Navier-Stokes and vorticity equations on R^2

We construct finite-dimensional invariant manifolds in the phase space of the Navier-Stokes equation on R^2 and show that these manifolds control the long-time behavior of the solutions. This gives geometric insight into the existing results on the asymptotics of such solutions and also allows one to extend those results in a number of ways.Comment: 46 pages, 3 figure

Non-Linear Stability Analysis of Higher Order Dissipative Partial Differential Equations

We extend the invariant manifold method for analyzing the asymptotics of dissipative partial differential equations on unbounded spatial domains to treat equations in which the linear part has order greater than two. One important example of this type of equation which we analyze in some detail is the Cahn-Hilliard equation. We analyze the marginally stable solutions of this equation in some detail. A second context in which such equations arise is in the Ginzburg-Landau equation, or other pattern forming equations, near a codimension-two bifurcation

An Economic Analysis of Fluid Milk Processing in Alaska

Alaskan fluid milk is processed for market by a two-firm industry. In Delta Junction, the Northern Lights Dairy obtains milk from two producers and services an Interior market from Delta to Fairbanks. In Anchorage , Matanuska Maid (M-M) obtains milk from II producers and markets its products largely in southcentral Alaska and , to a less extent, in Fairbanks. Direct competition between the two is minimal. The principal source of competition is preprocessed fluid milk shipped in from Puget Sound

On the Debate Concerning the Proper Characterisation of Quantum Dynamical Evolution

There has been a long-standing and sometimes passionate debate between physicists over whether a dynamical framework for quantum systems should incorporate not completely positive (NCP) maps in addition to completely positive (CP) maps. Despite the reasonableness of the arguments for complete positivity, we argue that NCP maps should be allowed, with a qualification: these should be understood, not as reflecting 'not completely positive' evolution, but as linear extensions, to a system's entire state space, of CP maps that are only partially defined. Beyond the domain of definition of a partial-CP map, we argue, much may be permitted.Comment: To be presented at the 2012 biennial meeting of the Philosophy of Science Association (PSA), San Diego, Californi

Geometric Stability Analysis for Periodic Solutions of the Swift-Hohenberg Equation

In this paper we describe invariant geometrical ~structures in the phase space of the Swift-Hohenberg equation in a neighborhood of its periodic stationary states. We show that in spite of the fact that these states are only marginally stable (i.e., the linearized problem about these states has continuous spectrum extending all the way up to zero), there exist finite dimensional invariant manifolds in the phase space of this equation which determine the long-time behavior of solutions near these stationary solutions. In particular, using this point of view, we obtain a new demonstration of Schneider's recent proof that these states are nonlinearly stable.Comment: 44 pages, plain tex, 0 figure

Kinetics and mechanism of the reaction between atomic chlorine and dimethyl selenide; comparison with the reaction between atomic chlorine and dimethyl sulfide

Dimethyl selenide is the most abundant gaseous selenium species in marine environments. In this work, the value of the rate coefficient for the gas-phase reaction between dimethyl selenide and Cl atoms has been determined for the first time. The value of the second-order rate coefficient obtained was (5.0±1.4)×10–10 cm3 molecule–1 s–1. The very fast nature of the reaction means that, when estimating the lifetime of dimethyl selenide in the atmosphere, loss due to reaction with Cl atoms should be considered along with loss due to reaction with O3 and with OH and NO3 radicals. Analysis of the available kinetic data suggests that at 760 Torr the dominant reaction pathway for the reaction of Cl atoms with dimethyl selenide will be the addition of Cl to the Se atom forming an adduct of the type CH3Se(Cl)CH3. Theoretical calculations, at the B3LYP/6-311++G(2df,p)//B3LYP/6-311++G(d,p) level of theory, show that at 298 K the value of rH for the formation of the adduct is –111.4 kJ mol–1. This value may be compared to –97.0 kJ mol–1, the value calculated for rH for the formation of the analogous sulfur adduct, CH3S(Cl)CH3, following the reaction between Cl atoms and dimethyl sulfide. Variational RRKM theory was used to predict the thermal decomposition rates of the two adducts back to starting materials. The estimated rate constant for the decomposition of the selenium adduct to the reactants is 5×10–5 s–1, compared to 0.02 s–1 in the case of the sulfur adduct. However, our calculations suggest that the CH3Se(Cl)CH3 adduct, which is initially formed highly excited, will not be stabilised under atmospheric conditions, but rather will decompose to yield CH3SeCl and CH3, a process that is calculated to be exothermic with respect to the initial reactants by 5.8 kJ mol–1. The formation of CH3SCl and CH3 from the sulfur adduct, on the other hand, is endothermic by 20.8 kJ mol–1 with respect to the initial reactants, and is thus not expected to occur

Circular 89

A yield trial in which 43 named varieties and numbered selections of potatoes were compared was conducted during the 1991 growing season at the University of Alaska Fairbanks, Agricultural and Forestry Experiment Station’s Palmer Research Center, Matanuska Research Farm, located six miles west of Palmer, Alaska. Varieties with a history of commercial production in the Matanuska Valley (Alaska 114, Bake-King, Green Mountain, and Superior) are included and serve as a comparative base for newly developed varieties, numbered selections or older varieties that have not been tested at this location. Varieties that compare favorably with the above listed standards may warrant consideration by commercial growers. Nonirrigated trials have been conducted annually since 1982, whereas irrigated trials were initiated in 1985 (AFES Circulars 49, 54, 58, 65, 71, 77, and 84). These circulars are available at the AFES Offices in Fairbanks and Palmer. Included in this report are the results of abbreviated versions of the AFES potato yield trial conducted by cooperating individuals and agencies at other locations in Alaska including Delta Junction, Fairbanks, Homer, Kenai- Soldotna, and Kodiak.[Part 1: Potato Variety Performance] -- Introduction -- Matanuska Farm Yield Trials -- Trials at Other Locations in Alaska -- [Part 2: Commercial Potato Crop Data Summary] -- Introduction -- Potato Varieties and Yields -- Acreage per grower -- Irrigation -- Seed and Planting -- Fertilizer -- Other Cultural Practices -- Chemical Contro