Abstract:In this paper we describe a recently developed algorithm called Topological

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During megavoltage photon and electron beam radiotherapy treatment involving the eye, patients commonly report visual sensations; "nerve stimulation" is the conventional explanation. We propose that the phenomenon can be attributed to Cherenkov radiation inside the eye. The threshold electron energy for Cherenkov radiation in water is 260 keV. The human retina is able to perceive approximately 5-14 visible photons in 0.001 s. A single 500 keV electron traversing 1 mm of water will induce nearly 15 Cherenkov visible range photons. We propose that a portal image involving the eye will produce sufficient Cherenkov radiation to be detected by the retina.

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Abstract:We report on the optical observations and analysis of the high-energy peaked BL Lac object (HBL), Mrk 501, at redshift z = 0.033. We can confirm microvariable behavior over the course of minutes on several occasions per night. As an alternative to the commonly understood dynamical model of random variations in intensity of the AGN, we develop a relativistic beaming model with a minimum of free parameters, which allows us to infer changes in the line of sight angles for the motion of the different relativistic components. We hope our methods can be used in future studies of beamed emission in other active microvariable sources, similar to the one we explored.

In radiation shielding design, one is usually faced with a set of conflicting goals that are navigated by an experienced physicist. If one has abundant space, the task is simplified because concrete is relatively inexpensive and will provide adequate shielding for high energy photons and neutrons, when applicable. However, if space is constrained (which is usually the case), the design becomes more difficult since one will likely have to employ combinations of steel, lead, and concrete, or other new materials--each with different properties and costs. Very experienced shielding designers can draw upon previous plans, but they do not know if their design is optimal in any sense. We have constructed a linear program that minimizes the cost of the shielding materials and minimizes the dose at the protection point or the shielding thickness subject to space constraints and to Federal or State regulations regarding the allowable exposure to individuals adjacent to the radiotherapy vault. In spite of what appears to be a simple model, the solution may require iterations of the optimization to arrive at the optimal solution.

A glance at Bessel functions shows they behave similar to the damped sinusoidal function. In this paper two physical examples (pendulum and spring-mass system with linearly increasing length and mass respectively) have been used as evidence for this observation. It is shown in this paper how Bessel functions can be approximated by the damped sinusoidal function. The numerical method that is introduced works very well in adiabatic condition (slow change) or in small time (independent variable) intervals. The results are also compared with the Lagrange polynomial.