A note on the 1-prevalence of continuous images with full Hausdorff dimension

We consider the Banach space consisting of real-valued continuous functions on an arbitrary compact metric space. It is known that for a prevalent (in the sense of Hunt, Sauer and Yorke) set of functions the Hausdorff dimension of the image is as large as possible, namely 1. We extend this result by showing that `prevalent' can be replaced by `1-prevalent', i.e. it is possible to \emph{witness} this prevalence using a measure supported on a one dimensional subspace. Such one dimensional measures are called \emph{probes} and their existence indicates that the structure and nature of the prevalence is simpler than if a more complicated `infinite dimensional' witnessing measure has to be used.Comment: 8 page

The Hausdorff dimension of graphs of prevalent continuous functions

We prove that the Hausdorff dimension of the graph of a prevalent continuous function is 2. We also indicate how our results can be extended to the space of continuous functions on $[0,1]^d$ for $d \in \mathbb{N}$ and use this to obtain results on the `horizon problem' for fractal surfaces. We begin with a survey of previous results on the dimension of a generic continuous function

Determination of complex absorbing potentials from the electron self-energy

The electronic conductance of a molecule making contact to electrodes is determined by the coupling of discrete molecular states to the continuum electrode density of states. Interactions between bound states and continua can be modeled exactly by using the (energy-dependent) self-energy, or approximately by using a complex potential. We discuss the relation between the two approaches and give a prescription for using the self-energy to construct an energy-independent, non-local, complex potential. We apply our scheme to studying single-electron transmission in an atomic chain, obtaining excellent agreement with the exact result. Our approach allows us to treat electron-reservoir couplings independent of single electron energies, allowing for the definition of a one-body operator suitable for inclusion into correlated electron transport calculations.Comment: 11 pages, 8 figures; to be published in the J. Chem. Phy

Observations of MMOD Impact Damage to the ISS

This paper describes meteoroid and orbital debris (MMOD) damage observations on the International Space Station (ISS). Several hundred MMOD damage sites on ISS have been documented using imagery taken from ISS windows. MMOD damage sites visible from ISS windows are typically larger approximately 5mm diameter and greater due to the larger viewer-to-surface distance. Closer inspection of these surfaces by astronauts during spacewalks reveals many smaller features that are typically less distinct. Characterization of these features as MMOD or non- MMOD is difficult, but can be partially accomplished by matching physical characteristics of the damage against typical MMOD impact damage observed on ground-based impact tests. Numerous pieces of space-exposed ISS hardware were returned during space shuttle missions. Subsequent ground inspection of this hardware has also contributed to the database of ISS MMOD impact damage. A handful of orbital replacement units (ORUs) from the ISS active thermal control and electrical power subsystems were swapped out and returned during the Space Shuttle program. In addition, a reusable logistics module was deployed on ISS for a total 59.4 days on 11 shuttle missions between 2001 and 2011 and then brought back in the shuttle payload bay. All of this returned hardware was subjected to detailed post-flight inspections for MMOD damage, and a database with over 1,400 impact records has been collected. A description of the largest observed damage features is provided in the paper. In addition, a discussion of significant MMOD impact sites with operational or design aspects is presented. MMOD impact damage to the following ISS modules/subsystems is described: (1) Solar Arrays, (2) US and Russian windows, (3) Extravehicular Activity (EVA) handrails, (4) Radiators, and (5) Russian Functional Cargo Block (FGB) module

Comparison of Risk from Orbital Debris and Meteoroid Environment Models on the Extravehicular Mobility Unit (EMU)

A well-known hazard associated with exposure to the space environment is the risk of failure from an impact from a meteoroid and orbital debris (MMOD) particle. An extravehicular mobility unit (EMU) spacesuit impact during a US extravehicular activity (EVA) is of great concern as a large leak could prevent an astronaut from safely reaching the airlock in time resulting in a loss of life. A risk assessment is provided to the EVA office at the Johnson Space Center (JSC) by the Hypervelocity Impact Technology (HVIT) group prior to certification of readiness for each US EVA. Need to understand the effect of updated meteoroid and orbital debris environment models to EMU risk

IDEAS: A Qualitative Inquiry into Project-Based Learning

As waves of the Global Educational Reform Movement, what Sahlberg (2015) identifies as GERM, still ripple around the world pushing for competition, standardization, the focus on the core subjects, and test-based accountability some schools like IDEAS choose what Hargreaves and Shirley (2012) call The Forth Way towards inspiration and innovation with their project-based learning pedagogy. IDEAS is a small public high school in Sheboygan, Wisconsin and a member of Ted Sizer’s Coalition of Essential Schools (CES). Our qualitative inquiry explores the implications of project-based learning on IDEAS’ students, teachers, academic program and school community. Data came from direct observation, interviews, curriculum documents, and teaching and learning artifacts. Our research informs IDEAS about the impact of their project-based learning pedagogy and validates its significance as part of their curricular program. It demonstrates that democratic principles are at work in some US schools, despite so many instances to the contrary. In the age of GERM this single-case study provides research-based evidence that alternative pedagogical methods and curriculum programs are potentially viable alternatives to many of the curriculum practices commonly found in today’s schools

Moving Difference (MDIFF) Non-adiabatic Rapid Sweep (NARS) EPR of Copper(II)

Non-adiabatic rapid sweep (NARS) EPR spectroscopy has been introduced for application to nitroxide-labeled biological samples (Kittell et al., 2011). Displays are pure absorption, and are built up by acquiring data in spectral segments that are concatenated. In this paper we extend the method to frozen solutions of copper-imidazole, a square planar copper complex with four in-plane nitrogen ligands. Pure absorption spectra are created from concatenation of 170 5-gauss segments spanning 850 G at 1.9 GHz. These spectra, however, are not directly useful since nitrogen superhyperfine couplings are barely visible. Application of the moving difference (MDIFF) algorithm to the digitized NARS pure absorption spectrum is used to produce spectra that are analogous to the first harmonic EPR. The signal intensity is about four times higher than when using conventional 100 kHz field modulation, depending on line shape. MDIFF not only filters the spectrum, but also the noise, resulting in further improvement of the SNR for the same signal acquisition time. The MDIFF amplitude can be optimized retrospectively, different spectral regions can be examined at different amplitudes, and an amplitude can be used that is substantially greater than the upper limit of the field modulation amplitude of a conventional EPR spectrometer, which improves the signal-to-noise ratio of broad lines

Bumper: A Tool for Analyzing Spacecraft Micrometeoroid and Orbital Debris Risk

Bumper is NASAs computer program for analyzing spacecraft micrometeoroid and orbital debris (MMOD) risk. Bumper was developed in the late-1980s and has been continuously used and maintained since. The user base has grown from a few government entities to now include numerous commercial entities as well. The NASA Johnson Space Center (JSC) Hypervelocity Impact Technology (HVIT) Team is responsible for all aspects of the Bumper software. Bumper has been used to characterize MMOD risk on hundreds of spacecraft. All of the International Space Station (ISS) modules, visiting vehicles and numerous external components and systems have been analyzed. Bumper was used to analyze each of the Space Shuttle missions since STS-50. The Orion Multi-Purpose Crew Vehicle (MPCV) MMOD shielding is being developed using Bumper as well. Bumper has also been used on numerous telescopes (Hubble, James Webb, and Fermi Gamma-ray Space Telescopes), scientific probes (Stardust, New Horizons, Parker Solar Probe), and Earth observation satellites (Landsat, Joint Polar Satellite System). Bumper is also being used to analyze the micrometeoroid risk and support design of the Deep Space Gateway (DSG) and Mars Sample Return (MSR) missions. The HVIT Bumper Configuration Control Board (CCB) ensures that all changes to the code are approved, reviewed, and documented. Most of the changes are made to add new MMOD damage ballistic limit equations (BLEs). BLEs are typically added in response to completion of a hypervelocity impact (HVI) test series and development of an associated BLE. Other less frequent changes include updates of the debris or meteoroid environment models, feature enhancements, and feature retirement. Some BLEs are commercially sensitive and/or proprietary, so the CCB also manages code user-version control and software distribution. The current version Bumper 3 is a FORTRAN executable that utilizes a 64-bit architecture. Bumper 3 has numerous features that make it a powerful tool for analyzing spacecraft MMOD risk. Bumper uses the latest orbital debris and micrometeoroid environment models. Bumper also easily processes large spacecraft geometry models, recognizes hidden surfaces, permits BLE assignment by name or number, and conducts quality checks of the spacecraft geometry model. Bumper 3 can also be used to estimate the effects of particle penetration through thin, high-standoff distance hardware components such as solar arrays and radiators. This is done using a special HVIT-developed technique know as the 3-Part Analysis. The paper introduces the Bumper 3 MMOD risk analysis code and provides an example MMOD risk assessment showing Bumpers role in the overall MMOD protection design process