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

Potential Milk Production in the Point MacKenzie Area of Southcentral Alaska

Point MacKenzie is an area northwest of Anchorage directly across the Knik Arm of Cook Inlet (Figure 1 ). This area contains a substantial amount of latent agricultural land and discussion regarding its potential has been going on for some time. The catalyst which activated the recent planning process directed at Point MacKenzie was concern over potential loss of the southcentral Alaska dairy industry expressed on May 4, 1979, in a letter from Jack Flint, General Manager, Matanuska Maid, Inc., to Governor Jay Hammond: "It is my opinion that if we do not take immediate steps to stabilize this important phase of agriculture, [the dairy industry] will pass from the scene. I think that if it should occur, it would be a serious blow to the State of Alaska, economically and socially. I believe we should also realize that if the dairy industry should cease to exist within the state, it is going to be very difficult to re-establish it." Mr. Flint's letter and corresponding action by the Matanuska-Susitna Borough have directed planning processes of the State of Alaska toward Poinr Mac- Kenzie. The Alaska Agricultural Action Council, created by the 1979 state legislature to plan, recommend, and administer agricultural development projects on state lands in Alaska, held a meeting in the Matanuska Valley in September, 1979, and determined that an economic feasibility study, directed toward dairy production, should be undertaken for the Point MacKenzie area. This report is that feasibility study.The information presented in this bulletin is part of a report prepared for the Agricultural Action Council of the State of Alaska. The group was formed in 1979 by legislative action and is chaired by W. I. "Bob" Palmer, Special Projects Director, Office of the Governor. The purpose of the group is to plan and manage agricultural development projects within the state. The report on the feasibility of milk production in the Point MacKenzie Area presented to Governor Hammond through the Alaska Agricultural Action Council was prepared by the authors of this bulletin and Dr. Boyd Buxton, Agricultural Economist, U.S. D.A., stationed at the University of Minnesota at St. Paul and Dr. Paul Fuglestad, Agricultural Economist, U.S.D .A., stationed in Anchorage, Alaska, both of whom are acknowledged with gratitude. The authors also wish to thank Cathy Warren who reviewed extensively the tabular data

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

Higher Order Modulation Equations for a Boussinesq Equation

In order to investigate corrections to the common KdV approximation to long waves, we derive modulation equations for the evolution of long wavelength initial data for a Boussinesq equation. The equations governing the corrections to the KdV approximation are explicitly solvable and we prove estimates showing that they do indeed give a significantly better approximation than the KdV equation alone. We also present the results of numerical experiments which show that the error estimates we derive are essentially optimal

LoCoH: nonparameteric kernel methods for constructing home ranges and utilization distributions.

Parametric kernel methods currently dominate the literature regarding the construction of animal home ranges (HRs) and utilization distributions (UDs). These methods frequently fail to capture the kinds of hard boundaries common to many natural systems. Recently a local convex hull (LoCoH) nonparametric kernel method, which generalizes the minimum convex polygon (MCP) method, was shown to be more appropriate than parametric kernel methods for constructing HRs and UDs, because of its ability to identify hard boundaries (e.g., rivers, cliff edges) and convergence to the true distribution as sample size increases. Here we extend the LoCoH in two ways: "fixed sphere-of-influence," or r-LoCoH (kernels constructed from all points within a fixed radius r of each reference point), and an "adaptive sphere-of-influence," or a-LoCoH (kernels constructed from all points within a radius a such that the distances of all points within the radius to the reference point sum to a value less than or equal to a), and compare them to the original "fixed-number-of-points," or k-LoCoH (all kernels constructed from k-1 nearest neighbors of root points). We also compare these nonparametric LoCoH to parametric kernel methods using manufactured data and data collected from GPS collars on African buffalo in the Kruger National Park, South Africa. Our results demonstrate that LoCoH methods are superior to parametric kernel methods in estimating areas used by animals, excluding unused areas (holes) and, generally, in constructing UDs and HRs arising from the movement of animals influenced by hard boundaries and irregular structures (e.g., rocky outcrops). We also demonstrate that a-LoCoH is generally superior to k- and r-LoCoH (with software for all three methods available at http://locoh.cnr.berkeley.edu)

Testable polarization predictions for models of CMB isotropy anomalies

Anomalies in the large-scale CMB temperature sky measured by WMAP have been suggested as possible evidence for a violation of statistical isotropy on large scales. In any physical model for broken isotropy, there are testable consequences for the CMB polarization field. We develop simulation tools for predicting the polarization field in models that break statistical isotropy locally through a modulation field. We study two different models: dipolar modulation, invoked to explain the asymmetry in power between northern and southern ecliptic hemispheres, and quadrupolar modulation, posited to explain the alignments between the quadrupole and octopole. For the dipolar case, we show that predictions for the correlation between the first 10 multipoles of the temperature and polarization fields can typically be tested at better than the 98% CL. For the quadrupolar case, we show that the polarization quadrupole and octopole should be moderately aligned. Such an alignment is a generic prediction of explanations which involve the temperature field at recombination and thus discriminate against explanations involving foregrounds or local secondary anisotropy. Predicted correlations between temperature and polarization multipoles out to l = 5 provide tests at the ~ 99% CL or stronger for quadrupolar models that make the temperature alignment more than a few percent likely. As predictions of anomaly models, polarization statistics move beyond the a posteriori inferences that currently dominate the field.Comment: 17 pages, 15 figures; published in PRD; references adde

Integrated Bush Management Systems (IBMS): Strategies and Economics.

12 p

An Examination of the Challenges Experienced by Canadian Ice-Hockey Players in the National Hockey League

Semistructured interviews were used in this study to learn about the challenges experienced by four groups of National Hockey League (NHL) players (N=11): prospects (n=3), rookies (n=3), veterans (n=2), and retirees (n=3). The database is comprised of 757 meaning units grouped into 11 contextual challenges pertaining to scouting demands, training camp, increased athletic demands, team expectations, and earning team trust. The veterans spoke mostly of challenges including scouting demands, athletic demands, and team expectations. Retirees considered mostly challenges pertaining to team expectations, athletic demands, lifestyle, media demands, transactions, cross-cultural encounters, and playoffs. An expert panel ensured that the interview guide, data analysis, and the findings represented the participants’ experiences in the NHL. Recommendations for practitioners and researchers working with NHL players are proposed

Impact of reionization on CMB polarization tests of slow-roll inflation

Estimates of inflationary parameters from the CMB B-mode polarization spectrum on the largest scales depend on knowledge of the reionization history, especially at low tensor-to-scalar ratio. Assuming an incorrect reionization history in the analysis of such polarization data can strongly bias the inflationary parameters. One consequence is that the single-field slow-roll consistency relation between the tensor-to-scalar ratio and tensor tilt might be excluded with high significance even if this relation holds in reality. We explain the origin of the bias and present case studies with various tensor amplitudes and noise characteristics. A more model-independent approach can account for uncertainties about reionization, and we show that parametrizing the reionization history by a set of its principal components with respect to E-mode polarization removes the bias in inflationary parameter measurement with little degradation in precision.Comment: 9 pages, 6 figures; submitted to Phys. Rev.

Thermo-mechanical sensitivity calibration of nanotorsional magnetometers

We report on the fabrication of sensitive nanotorsional resonators, which can be utilized as magnetometers for investigating the magnetization dynamics in small magnetic elements. The thermo-mechanical noise is calibrated with the resonator displacement in order to determine the ultimate mechanical torque sensitivity of the magnetometer.Comment: 56th Annual Conference on Magnetism and Magnetic Material