Geometry and Topology of Escape II: Homotopic Lobe Dynamics

We continue our study of the fractal structure of escape-time plots for chaotic maps. In the preceding paper, we showed that the escape-time plot contains regular sequences of successive escape segments, called epistrophes, which converge geometrically upon each endpoint of every escape segment. In the present paper, we use topological techniques to: (1) show that there exists a minimal required set of escape segments within the escape-time plot; (2) develop an algorithm which computes this minimal set; (3) show that the minimal set eventually displays a recursive structure governed by an ``Epistrophe Start Rule'': a new epistrophe is spawned Delta = D+1 iterates after the segment to which it converges, where D is the minimum delay time of the complex.Comment: 13 pages, 8 figures, to appear in Chaos, second of two paper

Geometry and Topology of Escape I: Epistrophes

We consider a dynamical system given by an area-preserving map on a two-dimensional phase plane and consider a one-dimensional line of initial conditions within this plane. We record the number of iterates it takes a trajectory to escape from a bounded region of the plane as a function along the line of initial conditions, forming an ``escape-time plot''. For a chaotic system, this plot is in general not a smooth function, but rather has many singularities at which the escape time is infinite; these singularities form a complicated fractal set. In this article we prove the existence of regular repeated sequences, called ``epistrophes'', which occur at all levels of resolution within the escape-time plot. (The word ``epistrophe'' comes from rhetoric and means ``a repeated ending following a variable beginning''.) The epistrophes give the escape-time plot a certain self-similarity, called ``epistrophic'' self-similarity, which need not imply either strict or asymptotic self-similarity.Comment: 15 pages, 9 figures, to appear in Chaos, first of two paper

Geometry and Topology of Escape. II. Homotopic Lobe Dynamics

We continue our study of the fractal structure of escape-time plots for chaotic maps. In the preceding paper, we showed that the escape-time plot contains regular sequences of successive escape segments, called epistrophes, which converge geometrically upon each end point of every escape segment. In the present paper, we use topological techniques to: (1) show that there exists a minimal required set of escape segments within the escape-time plot; (2) develop an algorithm which computes this minimal set; (3) show that the minimal set eventually displays a recursive structure governed by an “Epistrophe Start Rule:” a new epistrophe is spawned Δ=D+1 role= presentation style= display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eΔ=D+1Δ=D+1 iterates after the segment to which it converges, where D role= presentation style= display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eD is the minimum delay time of the complex

The Double Disparity Facing Rural Local Health Departments

Residents of rural jurisdictions face significant health challenges, including some of the highest rates of risky health behaviors and worst health outcomes of any group in the country. Rural communities are served by smaller local health departments (LHDs) that are more understaffed and underfunded than their suburban and urban peers. As a result of history and current need, rural LHDs are more likely than their urban peers to be providers of direct health services, leading to relatively lower levels of population-focused activities. This review examines the double disparity faced by rural LHDs and their constituents: pervasively poorer health behaviors and outcomes and a historical lack of investment by local, state, and federal public health entities

A VARIABLE LOAD LVDT-BASED CREEP TEST RIG FOR USE

The INL developed the Variable Load Creep Test Ri

Evaluation of Candidate In-Pile Thermal Conductivity Techniques

Thermophysical properties of materials must be known for proper design, test, and application of new fuels and structural properties in nuclear reactors. In the case of nuclear fuels during irradiation, the physical structure and chemical composition change as a function of time and position within the rod. Typically, thermal conductivity changes, as well as other thermophysical properties being evaluated during irradiation in a materials and test reactor, are measured out-of-pile in “hot-cells.” Repeatedly removing samples from a test reactor to make out-of-pile measurements is expensive, has the potential to disturb phenomena of interest, and only provide understanding of the sample's end state at the time each measurement is made. There are also limited thermophysical property data for advanced fuels. Such data are needed for the development of next generation reactors and advanced fuels for existing nuclear plants. Having the capacity to effectively and quickly characterize fuels and material properties during irradiation has the potential to improve the fidelity of nuclear fuel data and reduce irradiation testing costs

Simulating High-Dimensional Multivariate Data using the bigsimr R Package

It is critical to accurately simulate data when employing Monte Carlo techniques and evaluating statistical methodology. Measurements are often correlated and high dimensional in this era of big data, such as data obtained in high-throughput biomedical experiments. Due to the computational complexity and a lack of user-friendly software available to simulate these massive multivariate constructions, researchers resort to simulation designs that posit independence or perform arbitrary data transformations. To close this gap, we developed the Bigsimr Julia package with R and Python interfaces. This paper focuses on the R interface. These packages empower high-dimensional random vector simulation with arbitrary marginal distributions and dependency via a Pearson, Spearman, or Kendall correlation matrix. bigsimr contains high-performance features, including multi-core and graphical-processing-unit-accelerated algorithms to estimate correlation and compute the nearest correlation matrix. Monte Carlo studies quantify the accuracy and scalability of our approach, up to $d=10,000$. We describe example workflows and apply to a high-dimensional data set -- RNA-sequencing data obtained from breast cancer tumor samples.Comment: 22 pages, 10 figures, https://cran.r-project.org/web/packages/bigsimr/index.htm

[Arctic] Greenland ice sheet [in “State of the Climate in 2012”]

Melting at the surface of the Greenland Ice Sheet set new records for extent and melt index (i.e., the number of days on which melting occurred multiplied by the area where melting was detected) for the period 1979–2012, according to passive microwave observations (e.g., Tedesco 2007, 2009; Mote and Anderson 1995). Melt extent reached ~97% of the ice sheet surface during a rare, ice-sheet-wide event on 11–12 July (Fig. 5.13a; Nghiem et al. 2012). This was almost four times greater than the average melt extent for 1981–2010. The 2012 standardized melting index (SMI, defined as the melting index minus its average and divided by its standard deviation) was +2.4, almost twice the previous record of about +1.3 set in 2010

Analytically Derived Switching-Functions For Exact H-2(+) Eigenstates

Electron translation factors (ETF\u27s) appropriate for slow atomic collisions may be constructed using switching functions. In this paper we derive a set of switching functions for the H2+ system by an analytical two-center decomposition of the exact molecular eigenstates. These switching functions are closely approximated by the simple form f=bη, where η is the angle variable of prolate spheroidal coordinates. For given united atom angular momentum quantum numbers (l,m), the characteristic parameter blm depends only on the quantity c2=-∊R22, where ∊ is the electronic binding energy and R the internuclear distance in a.u. The resulting parameters are in excellent agreement with those found in our earlier work by a heuristic optimization scheme based on a study of coupling matrix-element behavior for a number of H2+ states. An approximate extension to asymmetric cases (HeH2+) has also been made. Nonadiabatic couplings based on these switching functions have been used in recent close-coupling calculations for H+-H(1s) collisions and He2+-H(1s) collisions at energies 1.0-20 keV