A Comprehensive Method of Estimating Electric Fields from Vector Magnetic Field and Doppler Measurements

Photospheric electric fields, estimated from sequences of vector magnetic field and Doppler measurements, can be used to estimate the flux of magnetic energy (the Poynting flux) into the corona and as time-dependent boundary conditions for dynamic models of the coronal magnetic field. We have modified and extended an existing method to estimate photospheric electric fields that combines a poloidal-toroidal (PTD) decomposition of the evolving magnetic field vector with Doppler and horizontal plasma velocities. Our current, more comprehensive method, which we dub the "{\bf P}TD-{\bf D}oppler-{\bf F}LCT {\bf I}deal" (PDFI) technique, can now incorporate Doppler velocities from non-normal viewing angles. It uses the \texttt{FISHPACK} software package to solve several two-dimensional Poisson equations, a faster and more robust approach than our previous implementations. Here, we describe systematic, quantitative tests of the accuracy and robustness of the PDFI technique using synthetic data from anelastic MHD (\texttt{ANMHD}) simulations, which have been used in similar tests in the past. We find that the PDFI method has less than $1$ error in the total Poynting flux and a $10$ error in the helicity flux rate at a normal viewing angle $(\theta=0$) and less than $25$ and $10$ errors respectively at large viewing angles ($\theta<60^\circ$). We compare our results with other inversion methods at zero viewing angle, and find that our method's estimates of the fluxes of magnetic energy and helicity are comparable to or more accurate than other methods. We also discuss the limitations of the PDFI method and its uncertainties.Comment: 56 pages, 10 figures, ApJ (in press

Photospheric Electric Fields and Energy Fluxes in the Eruptive Active Region NOAA 11158

How much electromagnetic energy crosses the photosphere in evolving solar active regions? With the advent of high-cadence vector magnetic field observations, addressing this fundamental question has become tractable. In this paper, we apply the "PTD-Doppler-FLCT-Ideal" (PDFI) electric field inversion technique of Kazachenko et al. (2014) to a 6-day HMI/SDO vector magnetogram and Doppler velocity sequence, to find the electric field and Poynting flux evolution in active region NOAA 11158, which produced an X2.2 flare early on 2011 February 15. We find photospheric electric fields ranging up to $2$ V/cm. The Poynting fluxes range from $[-0.6$ to $2.3]\times10^{10}$ ergs$\cdot$cm$^{-2}$s$^{-1}$, mostly positive, with the largest contribution to the energy budget in the range of $[10^9$-$10^{10}]$ ergs$\cdot$cm$^{-2}$s$^{-1}$. Integrating the instantaneous energy flux over space and time, we find that the total magnetic energy accumulated above the photosphere from the initial emergence to the moment before the X2.2 flare to be $E=10.6\times10^{32}$ ergs, which is partitioned as $2.0$ and $8.6\times10^{32}$ ergs, respectively, between free and potential energies. Those estimates are consistent with estimates from preflare non-linear force-free field (NLFFF) extrapolations and the Minimum Current Corona estimates (MCC), in spite of our very different approach. This study of photospheric electric fields demonstrates the potential of the PDFI approach for estimating Poynting fluxes and opens the door to more quantitative studies of the solar photosphere and more realistic data-driven simulations of coronal magnetic field evolution.Comment: 51 pages, 10 figures, accepted by ApJ on August 11, 201

Analysis of Economic Depreciation for Multi-Family Property

This paper uses a hedonic pricing model and National Council of Real Estate Investment Fiduciaries data to estimate economic depreciation for multi-family real estate. The findings indicate that investment grade multi-family housing depreciates approximately 2.7% per year in real terms based on total property value. This implies a depreciation rate for just the building of about 3.25% per year. With 2% inflation, this suggests a nominal depreciation rate of about 5.25% per year. Converted into a straight-line depreciation rate that has the same present value, this suggests a depreciable life of 30.5 years - as compared to 27.5 years allowed under the current tax laws. Thus, these laws are slightly favorable to multi-family properties by providing a tax depreciation rate that exceeds economic depreciation, which is in part due to inflation that has been less than expected during the past decade.

On the beta function and the neutrix product of distributions

The Beta function B(x,n) and the related Beta functions B(x ±, n) and B±(x,n) are defined as distributions and a number of neutrix products of distributions are evaluated

A Clinical Masquerader: Squamous Cell Carcinoma of the Eyelid Previously Diagnosed as an Eye Bump

Malignant eyelid tumors are often difficult to diagnose at early stage growth, and can be clinically challenging. Due to the high prevalence of periocular skin cancers, clinicians must be very attentive in their assessment of skin lesions amongst their patients. This case report highlights an early non-healing eyelid lesion transforming into squamous cell carcinoma. An 83-year-old male with no history of malignancy presented with a non-healing and rapidly growing lesion of the left lower eyelid. He first noticed this lesion one-month prior and was treated with oral antibiotics without improvement by his primary care provider. Our slit lamp examination of the left eyelid revealed a large ulcerated mass with white mucoid discharge draining from the center of the lesion. After an oculoplastics referral, the patient was diagnosed with squamous cell carcinoma confirmed by biopsy. Computed tomography(CT) showed no metastasis or invasion to deep layer tissue. The management decision in this case required exenteration of the left eye socket followed by radiation therapy. This case illustrates the clinical course and invasive nature of periocular squamous cell carcinoma. It can present in a variety of different appearances, but are mostly painless, hyperkeratotic lesions that progressively change and ulcerate. An extensive history and careful clinical examination are vital in order to detect malignancy in a timely manner

Pair Analytics: Capturing Reasoning Processes in Collaborative Visual Analytics

Studying how humans interact with abstract, visual representations of massive amounts of data provides knowledge about how cognition works in visual analytics. This knowledge provides guidelines for cognitive-aware design and evaluation of visual analytic tools. Different methods have been used to capture and conceptualize these processes including protocol analysis, experiments, cognitive task analysis, and field studies. In this article, we introduce Pair Analytics: a method for capturing reasoning processes in visual analytics. We claim that Pair Analytics offers two advantages with respect to other methods: (1) a more natural way of making explicit and capturing reasoning processes and (2) an approach to capture social and cognitive processes used to conduct collaborative analysis in real-life settings. We support and illustrate these claims with a pilot study of three phenomena in collaborative visual analytics: coordination of attention, cognitive workload, and navigation of analysis

Calculation of the entropy of binary hard sphere mixtures from pair correlation functions

This is the publisher's version, also available electronically from http://scitation.aip.org/content/aip/journal/jcp/97/3/10.1063/1.463103.We evaluate the entropy of several binary hard sphere fluid mixtures using two approximate expressions that require as input only the pair correlation functions,g αβ(r). An approximation based on the incompressible limit is found to be accurate for medium to high density fluids

Phased Array Feed Calibration, Beamforming and Imaging

Phased array feeds (PAFs) for reflector antennas offer the potential for increased reflector field of view and faster survey speeds. To address some of the development challenges that remain for scientifically useful PAFs, including calibration and beamforming algorithms, sensitivity optimization, and demonstration of wide field of view imaging, we report experimental results from a 19 element room temperature L-band PAF mounted on the Green Bank 20-Meter Telescope. Formed beams achieved an aperture efficiency of 69% and system noise temperature of 66 K. Radio camera images of several sky regions are presented. We investigate the noise performance and sensitivity of the system as a function of elevation angle with statistically optimal beamforming and demonstrate cancelation of radio frequency interference sources with adaptive spatial filtering.Comment: 19 pages, 13 figure