Volume 26: 2013

Peer Reviewed Papers
December 6, 2013

Absolute Magnitudes of Turnoff Stars in Globular Clusters Palomar 13 and Whiting 1
Kathleen Grabowski, Matthew Newby and Heidi Jo Newberg

Particular Solution to a Time-Fractional Heat Equation
Simon P. Kelow and Kevin M. Hayden

Effect of Temperature on Pulse Wave Velocity and Arterial Compliance
Tucker Frawley and T. Brian Bunton
May 7, 2013

High Peak Power VCSELs in Short Range LIDAR Applications
Neil E. Newman, Duncan C. Spaulding, Graham Allen, Mohamed A. Diagne
March 29, 2013

Spacecraft Approaching Technique
Rey Carvajal
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Absolute Magnitudes of Turnoff Stars in Globular Clusters Palomar 13 and Whiting 1

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Kathleen Grabowski, Matthew Newby, Heidi Jo Newberg
Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, NY

We characterize the F-turnoff (FTO) stars in two globular clusters in the halo of the Milky Way. Data for the two clusters, Palomar 13 and Whiting 1, recently became available in Data Release 8 (DR8) of the Sloan Digital Sky Survey (SDSS). Based on a histogram of the absolute magnitude distribution, we find that the peak of the distribution of FTO stars in Palomar 13 is Mg = 4:46 ± 0:26 and in Whiting 1 it is Mg = 4:11 ± 0:30. These measurements are in good agreement with Newby et al. (2011). The widths of the absolute magnitude distributions of Whiting 1 FTO stars are also consistent within 1σ with the results of Newby et al. (2011), even though Whiting 1 is younger and more metal-rich than the previously studied globular clusters. Palomar 13 is marginally inconsistent within 2σ − 3σ because fewer of the fainter stars are observed than expected. Since Palomar 13 is within the range of cluster properties previously studied, it was not expected that this cluster would be an outlier. The discrepancy is likely due to lower than expected completeness in measuring faint stars in the cluster, due to the fact that the seeing in the Palomar 13 images is worse than in other SDSS images of globular clusters. We continue to find that globular clusters in the halo of the Milky Way all have similar absolute magnitude distributions. We also confirm that Whiting 1 is within the Sagittarius dwarf tidal stream, while Palomar 13 is not.

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Particular Solution to a Time-Fractional Heat Equation

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Simon P. Kelow1 and Kevin M. Hayden2
1Department of Astronomy and Physics, Northern Arizona University, Flagstaff, AZ
2Faculty Advisor, Department of Mathematics and Statistics, Northern Arizona University, Flagstaff, AZ


When the derivative of a function is non-integer order, e.g. the 1/2 derivative, one ventures into the subject of fractional calculus. The time-fractional heat equation is a generalization of the standard heat equation as it uses an arbitrary derivative order close to 1 for the time derivative. We present a particular solution to an initial-boundary-value time-fractional heat equation problem and compare the properties of the solutions when the time derivative order is varied. Orders of the time-fractional heat equation which return solutions that display physically impossible characteristics are also considered. One observed property is slightly less exponential decay of heat for the solutions of non-integer order time derivatives greater than one. Another property is solutions with non-integer order time derivatives less than one exhibit slightly greater exponential decay. Both of these comparisions are made with respect to the standard heat equation solution, where the order of the time derivative is one.

fractional calculus, time-fractional heat equation; time-fractional diffusion equation

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Effect of Temperature on Pulse Wave Velocity and Arterial Compliance

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Tucker Frawleya and T. Brian Buntona
Dept. of Chemistry and Physics, Coastal Carolina University, Conway, SC 29528

The compliance of a material is the ability of the material to expand or contract. A low arterial compliance will lead to high blood pressure and, ultimately, cardiovascular disease. The velocity of the pulse wave traveling through an artery is a function of the compliance of the artery that it is traveling through. Therefore, the compliance of an artery can be indirectly observed by measuring several pulse wave velocities in the artery. This experiment investigates the effect, if any, of temperature on arterial compliance. Two electrocardiographs (ECGs) were taken from healthy human subjects at the right wrist to right elbow, before and after an application of a temperature gradient. For one study, the subject's arm was put into water of a significantly higher temperature than the body. For the other study, the subject's arm was put into water of a significantly lower temperature than the body. From the ECGs taken, the relative pulse wave velocities before and after the applications of the local temperature gradients were determined. It was determined that the local heating resulted in an increase in the pulse wave velocity in the artery, and the application of the local cooling resulted in a decrease in the pulse wave velocity in the artery.

compliance, pulse wave velocity, cardiovascular, thermoregulation

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High Peak Power VCSELs in Short Range LIDAR Applications

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Neil E. Newman1, Duncan C. Spaulding1, Graham Allen1, Mohamed A. Diagne1,2
1Department of Physics, Astronomy, and Geophysics, Connecticut College, New London, Connecticut 06320,
2Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts 02420

A technique for short-range LIDAR that monitors high-peak-power pulses rather than uniform square pulses is demonstrated using a commercially available Optek OPV310 VCSEL with a 10μm aperture operating at a wavelength of 850nm for applications in LIDAR-based active defense systems. Using 10ns pulses at a 0.1% duty cycle and 60mW of peak power, a target one meter away exhibiting Lambertian reflectance was detected with a 3:1 minimum signal-to-noise ratio in a narrow-field LIDAR setup using a 28dB amplifier. At 0.75m, using the same target and no signal amplification, a 2:1 minimum signal to noise ratio was achieved in a wide-field setup. These results establish the viability of commercially available low power VCSEL devices for LIDAR.

LIDAR, VCSELs

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Spacecraft Approaching Technique

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Rey Carvajal
Harriet L Wilkes Honors College of Florida Atlantic University,
Department of Physics, Jupiter, FL


Using already established equations of motion for particles under a gravitational force, we analyze the motion of two spacecrafts in the same circular orbit approaching each other if one of the craft were to speed up or slow down. The purpose of this paper is to analyze and develop equations of motion for the transfer of spacecrafts from circular orbits to elliptical orbits with the intention of spacecraft approach. We can come up with a table of velocities that allow for a number of safe approaches for the spacecraft to take. We found that projecting a safe approach requires that we know the new speed of the transfer spacecraft, the desired change in distance between the two spacecrafts, and the magnitude of the radius vector of the perigee for the elliptical transfer.

Spacecraft, Particle Motion, Approach

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