On the Assouad dimension of self-similar sets with overlaps

It is known that, unlike the Hausdorff dimension, the Assouad dimension of a self-similar set can exceed the similarity dimension if there are overlaps in the construction. Our main result is the following precise dichotomy for self-similar sets in the line: either the \emph{weak separation property} is satisfied, in which case the Hausdorff and Assouad dimensions coincide; or the \emph{weak separation property} is not satisfied, in which case the Assouad dimension is maximal (equal to one). In the first case we prove that the self-similar set is Ahlfors regular, and in the second case we use the fact that if the \emph{weak separation property} is not satisfied, one can approximate the identity arbitrarily well in the group generated by the similarity mappings, and this allows us to build a \emph{weak tangent} that contains an interval. We also obtain results in higher dimensions and provide illustrative examples showing that the `equality/maximal' dichotomy does not extend to this setting.Comment: 24 pages, 2 figure

An Evolving Role for Cancer Rehabilitation in the Era of Low‐Dose Lung Computed Tomography Screening

Lung cancer is the number one cause of cancer‐related death worldwide, and is often detected in the later stages. Use of low‐dose chest computed tomography in at‐risk patients provides earlier detection and is being adopted as the standard screening tool, replacing less precise methods of radiography and sputum cytology. In the past, late detection of disease meant that rehabilitation interventions attempted to salvage function and to improve aerobic capacity to the point where patients could tolerate the sometimes‐extensive oncologic treatment, including lobectomy or pneumonectomy. Earlier detection may shift this toward more often addressing specific neuromusculoskeletal impairments, such as postthoracotomy pain or peripheral neuropathy, as patients with early‐stage disease may not be as debilitated by chronic disease or metastases as those with late‐stage lung cancer. Patients with advanced disease, however, will still require rehabilitation interventions, and this fragile population creates unique challenges. Rehabilitation professionals should look for ways to expand care to lung cancer patients, as both the number of those treated and the 5‐year survival rate are expected to increase.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/147113/1/pmr2s407.pd

100-LBF LO2/LCH4 - Reaction Control Engine Technology Development for Future Space Vehicles

The National Aeronautics and Space Administration (NASA) has identified liquid oxygen (LO2)/liquid methane (LCH4) propulsion systems as promising options for some future space vehicles. NASA issued a contract to Aerojet to develop a 100-lbf (445 N) LO2/LCH4 Reaction Control Engine (RCE) aimed at reducing the risk of utilizing a cryogenic reaction control system (RCS) on a space vehicle. Aerojet utilized innovative design solutions to develop an RCE that can ignite reliably over a broad range of inlet temperatures, perform short minimum impulse bits (MIB) at small electrical pulse widths (EPW), and produce excellent specific impulse (Isp) across a range of engine mixture ratios (MR). These design innovations also provide a start transient with a benign MR, ensuring good thrust chamber compatibility and long life. In addition, this RCE can successfully operate at MRs associated with main engines, enabling the RCE to provide emergency backup propulsion to minimize vehicle propellant load and overall system mass

Crystalline optical cavity at 4 K with thermal noise limited instability and ultralow drift

Crystalline optical cavities are the foundation of today's state-of-the-art ultrastable lasers. Building on our previous silicon cavity effort, we now achieve the fundamental thermal noise-limited stability for a 6 cm long silicon cavity cooled to 4 Kelvin, reaching $6.5\times10^{-17}$ from 0.8 to 80 seconds. We also report for the first time a clear linear dependence of the cavity frequency drift on the incident optical power. The lowest fractional frequency drift of $-3\times10^{-19}$/s is attained at a transmitted power of 40 nW, with an extrapolated drift approaching zero in the absence of optical power. These demonstrations provide a promising direction to reach a new performance domain for stable lasers, with stability better than $1\times10^{-17}$ and fractional linear drift below $1\times10^{-19}$/s

Test Results for a Non-toxic, Dual Thrust Reaction Control Engine

A non-toxic, dual thrust reaction control engine (RCE) was successfully tested over a broad range of operating conditions at the Aerojet Sacramento facility. The RCE utilized LOX/Ethanol propellants; and was tested in steady state and pulsing modes at 25-lbf thrust (vernier) and at 870-lbf thrust (primary). Steady state vernier tests vaned chamber pressure (Pc) from 0.78 to 5.96 psia, and mixture ratio (MR) from 0.73 to 1.82, while primary steady state tests vaned Pc from 103 to 179 psia and MR from 1.33 to 1.76. Pulsing tests explored EPW from 0.080 to 10 seconds and DC from 5 to 50 percent at both thrust levels. Vernier testing accumulated a total of 6,670 seconds of firing time, and 7,215 pulses, and primary testing accumulated a total of 2,060 seconds of firing time and 3,646 pulses

Ignition Characterization Test Results for the LO2/Ethanol Propellant Combination

A series of contracts were issued by the Marshall Space Flight Center (MSFC) of the National Aeronautics and Space Administration (NASA) under the auspices of the Exploration Systems Mission Directorate to develop and expand the maturity of candidate technologies considered to be important for future space exploration. One such technology was to determine the viability of incorporating non-toxic propellants for Reaction Control Subsystems (RCS). Contract NAS8-01109 was issued to Aerojet to develop a dual thrust Reaction Control Engine (RCE) that utilized liquid oxygen and ethanol as the propellants. The dual thrust RCE incorporated a primary thrust level of 870 lbf, and a vernier thrust level of 10 - 30 lbf. The preferred RCS approach for the dual thrust RCE was to utilize pressure-fed liquid oxygen (LOX) and ethanol propellants; however, previous dual thrust feasibility testing incorporated GOX/Ethanol igniters as opposed to LOX/Ethanol igniters in the design. GOX/Ethanol was easier to ignite, but this combination had system design implications of providing GOX for the igniters. A LOX/Ethanol igniter was desired; however, extensive LOX/Ethanol ignition data over the anticipated operating range for the dual thrust RCE did not exist. Therefore, Aerojet designed and tested a workhorse LOX igniter to determine LOX/Ethanol ignition characteristics as part of a risk mitigation effort for the dual thrust RCE design. LOX, encompassing potential two-phase flow conditions anticipated being present in real mission applications. A workhorse igniter was designed to accommodate the hll LOX design flowrate, as well as a reduced GOX flowrate. It was reasoned that the initial LOX flow through the igniter would flash to GOX due to the latent heat stored in the hardware, causing a reduced oxygen flowrate because of a choked, or sonic, flow condition through the injection elements. As LOX flow continued, the hardware would chill-in, with the injected oxygen flow transitioning from cold GOX through two-phase flow to subcooled LOX. permitted oxygen state points to be determined in the igniter oxidizer manifold, and gas-side igniter chamber thermocouples provided chamber thermal profile characteristics. The cold flow chamber pressure (P(sub c)) for each test was determined and coupled with the igniter chamber diameter (D(sub c)) to calculate the characteristic quench parameter (P(sub c) x D(sub c)), which was plotted as a function of core mixture ratio, m. Ignition limits were determined over a broad range of valve inlet conditions, and ignition was demonstrated with oxygen inlet conditions that ranged from subcooled 210 R LOX to 486 R GOX. Once ignited at cold GOX conditions, combustion was continuous as the hardware chilled in and the core mixture ratio transitioned from values near 1.0 to over 12.5. Pulsing is required in typical RCS engines; therefore, the workhorse igniter was pulse tested to verify the ability to provide the required ignition for a pulsing RCE. The minimum electrical pulse width (EPW) of the dual thrust RCE was 0.080 seconds

Contribution of Extragalactic Infrared Sources to CMB Foreground Anisotropy

We estimate the level of confusion to Cosmic Microwave Background anisotropy measurements caused by extragalactic infrared sources. CMB anisotropy observations at high resolution and high frequencies are especially sensitive to this foreground. We use data from the COBE satellite to generate a Galactic emission spectrum covering mm and sub-mm wavelengths. Using this spectrum as a template, we predict the microwave emission of the 5319 brightest infrared galaxies seen by IRAS. We simulate skymaps over the relevant range of frequencies (30-900 GHz) and instrument resolutions (10'-10 degrees Full Width Half Max). Analysis of the temperature anisotropy of these skymaps shows that a reasonable observational window is available for CMB anisotropy measurements.Comment: 14 pages (LaTex source), 3 PostScript figures. Final version, to appear in ApJLetters May 1. Expanded discussion of systematic error

Metapopulation Viability of Swamp Rabbits in Southern Illinois: Potential Impacts of Habitat Change

Swamp rabbits (Sylvilagus aquaticus) in southern Illinois exist as a metapopulation due to fragmentation of the bottomland hardwood forests in which they live. This fragmentation makes their persistence in Illinois uncertain. We used population viability analysis (PVA) to estimate the probability of persistence of the swamp rabbit metapopulation in Illinois, using a habitat suitability map we created and life history parameters drawn from the literature. We varied the parameters used in our PVA from 50% to 150% of the initial value to compare their effects on extinction risk and to direct future management and research. We tested the effects of potential habitat loss and fragmentation by 1) removing patches individually and in groups from the analysis and by 2) adding 60, 120, and 180 m to the edge of all patches. We also tested the potential effect of dispersal corridors by increasing dispersal between connected patches. Under baseline conditions, the model suggests a 0% chance of quasiextinction (90% metapopulation decline) of swamp rabbits within 25 (or even 50) years. Changes in fecundity values and the effects of catastrophic flooding had the greatest effect on extinction risk, and changes in no other parameter yielded any appreciable impact. Removing the largest patches from the population increased the 25- year risk of extinction to 4%, whereas any other modifications to the habitat did not change the extinction risk. We suggest that managers focus on sustaining habitat quality, particularly upland habitats adjacent to occupied bottomland hardwood forests to improve the likelihood of swamp rabbit persistence in Illinois