Public Provision of Private Goods, Self-Selection and Income Tax Avoidance

Redistributive taxation should benefit those with low earnings capacity rather than those who choose a lower income to obtain tax savings. Several contributions have highlighted how public provision of work complements can discourage people from lowering labour supply to diminish taxable income. We show how tax avoidance, previously neglected, can alter the conclusions regarding public provision. Tax avoidance breaks the link between labour supply and reported income. An agent reducing his reported income to escape taxes may no longer forego a publicly provided labour complement because he may now lower his income by avoiding more rather than working less

Whispering gallery modes in open quantum billiards

The poles of the S-matrix and the wave functions of open 2D quantum billiards with convex boundary of different shape are calculated by the method of complex scaling. Two leads are attached to the cavities. The conductance of the cavities is calculated at energies with one, two and three open channels in each lead. Bands of overlapping resonance states appear which are localized along the convex boundary of the cavities and contribute coherently to the conductance. These bands correspond to the whispering gallery modes appearing in the classical calculations.Comment: 9 pages, 3 figures in jpg and gif forma

Improved microscopic-macroscopic approach incorporating the effects of continuum states

The Woods-Saxon-Strutinsky method (the microscopic-macroscopic method) combined with Kruppa's prescription for positive energy levels, which is necessary to treat neutron rich nuclei, is studied to clarify the reason for its success and to propose improvements for its shortcomings. The reason why the plateau condition is met for the Nilsson model but not for the Woods-Saxon model is understood in a new interpretation of the Strutinsky smoothing procedure as a low-pass filter. Essential features of Kruppa's level density is extracted in terms of the Thomas-Fermi approximation modified to describe spectra obtained from diagonalization in truncated oscillator bases. A method is proposed which weakens the dependence on the smoothing width by applying the Strutinsky smoothing only to the deviations from a reference level density. The BCS equations are modified for the Kruppa's spectrum, which is necessary to treat the pairing correlation properly in the presence of continuum. The potential depth is adjusted for the consistency between the microscopic and macroscopic Fermi energies. It is shown, with these improvements, that the microscopic-macroscopic method is now capable to reliably calculate binding energies of nuclei far from stability.Comment: 66 pages, 29 figures, 1 tabl

Analysis of active optics correction for a large honeycomb mirror

In the development of space-based large telescope systems, having the capability to perform active optics correction allows correcting wavefront aberrations caused by thermal perturbations so as to achieve diffraction-limited performance with relaxed stability requirements. We present a method of active optics correction used for current ground-based telescopes and simulate its effectiveness for a large honeycomb primary mirror in space. We use a finite-element model of the telescope to predict misalignments of the optics and primary mirror surface errors due to thermal gradients. These predicted surface error data are plugged into a Zemax ray trace analysis to produce wavefront error maps at the image plane. For our analysis, we assume that tilt, focus and coma in the wavefront error are corrected by adjusting the pointing of the telescope and moving the secondary mirror. Remaining mid- to high-order errors are corrected through physically bending the primary mirror with actuators. The influences of individual actuators are combined to form bending modes that increase in stiffness from low-order to high-order correction. The number of modes used is a variable that determines the accuracy of correction and magnitude of forces. We explore the degree of correction that can be made within limits on actuator force capacity and stress in the mirror. While remaining within these physical limits, we are able to demonstrate sub-25 nm RMS surface error over 30 hours of simulated data. The results from this simulation will be part of an end-to-end simulation of telescope optical performance that includes dynamic perturbations, wavefront sensing, and active control of alignment and mirror shape with realistic actuator performance.Comment: 8 pages, 6 figures, presented at SPIE Optics + Photonics 202

Approaches to developing tolerance and error budget for active three mirror anastigmat space telescopes

The size of the optics used in observatories is often limited by fabrication, metrology, and handling technology, but having a large primary mirror provides significant benefits for scientific research. The evolution of rocket launch options enables heavy payload carrying on orbit and outstretching the telescope's form-factor choices. Moreover, cost per launch is lower than the traditional flight method, which is obviously advantageous for various novel space observatory concepts. The University of Arizona has successfully fabricated many large-scale primary optics for ground-based observatories including the Large Binocular Telescope (LBT, 8.4 meter diameter two primary mirrors), Large Synoptic Survey Telescope (now renamed to Vera C. Rubin Observatory, 8.4 meter diameter monolithic primary and tertiary mirror), and the Giant Magellan Telescope (GMT, 8.4 meter diameter primary mirror seven segments). Launching a monolithic primary mirror into space could bypass many of the difficulties encountered during the assembly and deployment of the segmented primary mirrors. However, it might bring up unprecedented challenges and hurdles, also. We explore and foresee the expected challenges and evaluate them. To estimate the tolerance and optical error budget of a large optical system in space such as three mirror anastigmat telescope, we have developed a methodology that considers various errors from design, fabrication, assembly, and environmental factors.Comment: 6 pages, presented August 2023 at SPIE Optics+Photonics, San Diego, CA, US