Behavior of the Escape Rate Function in Hyperbolic Dynamical Systems

For a fixed initial reference measure, we study the dependence of the escape rate on the hole for a smooth or piecewise smooth hyperbolic map. First, we prove the existence and Holder continuity of the escape rate for systems with small holes admitting Young towers. Then we consider general holes for Anosov diffeomorphisms, without size or Markovian restrictions. We prove bounds on the upper and lower escape rates using the notion of pressure on the survivor set and show that a variational principle holds under generic conditions. However, we also show that the escape rate function forms a devil's staircase with jumps along sequences of regular holes and present examples to elucidate some of the difficulties involved in formulating a general theory.Comment: 21 pages. v2 differs from v1 only by additions to the acknowledgment

Kinematic design of a finger abduction mechanism for an anthropomorphic robotic hand

This paper presents the kinematic design of an abduction mechanism for the fingers of an underactuated anthropomorphic robotic hand. This mechanism will enhance the range of feasible grasps of the underactuated hand without significantly increasing its complexity. The analysis of the link between the index finger and the third finger is first assessed, where the parameters are studied in order to follow the amplitude constraint and to minimize the coordination error. Then, the study of the mechanism joining the third finger and the little finger is summarized. Finally, a prototype of the finger's abduction system is presented. <br><br> <i>This paper was presented at the IFToMM/ASME International Workshop on Underactuated Grasping (UG2010), 19 August 2010, Montréal, Canada.</i&gt

Peeping at chaos: Nondestructive monitoring of chaotic systems by measuring long-time escape rates

One or more small holes provide non-destructive windows to observe corresponding closed systems, for example by measuring long time escape rates of particles as a function of hole sizes and positions. To leading order the escape rate of chaotic systems is proportional to the hole size and independent of position. Here we give exact formulas for the subsequent terms, as sums of correlation functions; these depend on hole size and position, hence yield information on the closed system dynamics. Conversely, the theory can be readily applied to experimental design, for example to control escape rates.Comment: Originally 4 pages and 2 eps figures incorporated into the text; v2 has more numerical results and discussion: now 6 pages, 4 figure

Magellanic Cloud Periphery Carbon Stars IV: The SMC

The kinematics of 150 carbon stars observed at moderate dispersion on the periphery of the Small Magellanic Cloud are compared with the motions of neutral hydrogen and early type stars in the Inter-Cloud region. The distribution of radial velocities implies a configuration of these stars as a sheet inclined at 73+/-4 degrees to the plane of the sky. The near side, to the South, is dominated by a stellar component; to the North, the far side contains fewer carbon stars, and is dominated by the neutral gas. The upper velocity envelope of the stars is closely the same as that of the gas. This configuration is shown to be consistent with the known extension of the SMC along the line of sight, and is attributed to a tidally induced disruption of the SMC that originated in a close encounter with the LMC some 0.3 to 0.4 Gyr ago. The dearth of gas on the near side of the sheet is attributed to ablation processes akin to those inferred by Weiner & Williams (1996) to collisional excitation of the leading edges of Magellanic Stream clouds. Comparison with pre LMC/SMC encounter kinematic data of Hardy, Suntzeff, & Azzopardi (1989) of carbon stars, with data of stars formed after the encounter, of Maurice et al. (1989), and Mathewson et al. (a986, 1988) leaves little doubt that forces other than gravity play a role in the dynamics of the H I.Comment: 30 pages; 7 figures, latex compiled, 1 table; to appear in AJ (June 2000

The Antisocial Effects of Social Media and How Colleges and Universities Can Manage Related Litigation Risks

Rapid advancements in information technology have transformed day-to-day university operations and, in doing so, have altered the landscape of risk management. Authors Gregory L. Demers, J. William Piereson, Mark A. Cianci, and Peter L. Welsh provide an overview of some of the most significant social-media-related risks faced by colleges and universities, before considering ways to mitigate these risks through a broad insurance coverage plan. The article explains how, given the relative novelty of this field, the coverage afforded by insurance policies inevitably will vary, often significantly, from insurer to insurer