Using ordinary multiplication to do relativistic velocity addition

Relativistic addition of velocities in one dimension, though a mainstay of introductory physics, contributes much less physical insight than it could. For such calculations, we propose the use of velocity factors (two-way doppler factors). Velocities can easily, often by inspection, be turned into velocity factors, and vice versa. Velocity factors compose by ordinary multiplication. This simple device considerably extends the kinds of questions that can be asked and answered in an introductory course.Comment: 6 page

Microstructural and Isotopic Constraints on WL Rim Formation

Coordinated microanalyses of Wark-Lovering (WL) rims are needed to best understand their origin and to decipher their subsequent evolution both in the nebular and parent body settings. Here we present the mineralogy, petrology, microstructures, O isotopic compositions, and Al-Mg systematics of a WL rim on a Type B CAI, Big Guy, from the reduced CV3 chondrite Vigarano [1]. Our SEM and TEM study reveals seven distinct mineral layers in the WL rim that include: (1) gehlenite with rare grossite, (2) hibonite, (3) spinel with minor hibonite and perovskite, (4) zoned melilite (k(sub ~0-10)), (5) anorthite, (6) zoned diopside grading outwards from Al,Ti-rich to Al,Tipoor, and (7) forsterite intergrown with diopside. We infer a two-stage history in which WL rim formation was initiated by flash melting and extensive evaporation of the original inclusion edge, followed by subsequent condensation under highly dynamic conditions. The outermost edge of the CAI mantle is mineralogically and texturally distinct compared to the underlying mantle that is composed of coarse, zoned melilite (k(sub ~10-60)) grains. The mantle edge contains finegrained gehlenite with hibonite and rare grossite that likely formed by rapid crystallization from a Ca,Al-rich melt produced during a flash vaporization event [2]. These gehlenite and hibonite layers are surrounded by successive layers of spinel, melilite, diopside, and forsterite, indicating their sequential gas-solid reactions onto hibonite. Anorthite occurs as a discontinuous layer that corrodes adjacent melilite and Al-diopside, and appears to have replaced them [3,4], probably even later than the forsterite layer formation. All the WL rim minerals analyzed using the JSC NanoSIMS 50L are 16O-rich (17O 23), indicating their formation in an 16O-rich gas reservoir. Our data are in contrast with many CV CAIs that show heterogeneous 17O values across their WL rims [5]. Our Al-Mg data obtained using the UCLA ims-1290 ion microprobe of the CAI interior and the WL rim define a well-correlated isochron with (26Al/27Al)(sub 0) = 4.94 10(exp 5), indicating their synchronous formation 5 10(exp 4) years after the canonical CAI value. In contrast, no 26Mg excesses are observed in the WL rim anorthite, which suggests its later formation or later isotopic resetting in an 16O-rich gas reservoir, after 26Al had decayed

Evidence for a null entropy of extremal black holes

We present some arguments in support of a {\it zero} entropy for {\it extremal} black holes. These rely on a combination of both quantum, thermodynamic, and statistical physics arguments. This result may shed some light on the nature of these extreme objects. In addition, we show that within a {\it quantum} framework the capture of a particle by an initially extremal black hole always results with a final nonextremal black hole.Comment: 11 page

Attacking Group Protocols by Refuting Incorrect Inductive Conjectures

Automated tools for finding attacks on flawed security protocols often fail to deal adequately with group protocols. This is because the abstractions made to improve performance on fixed 2 or 3 party protocols either preclude the modelling of group protocols all together, or permit modelling only in a fixed scenario, which can prevent attacks from being discovered. This paper describes Coral, a tool for finding counterexamples to incorrect inductive conjectures, which we have used to model protocols for both group key agreement and group key management, without any restrictions on the scenario. We will show how we used Coral to discover 6 previously unknown attacks on 3 group protocols

Local light-ray rotation

We present a sheet structure that rotates the local ray direction through an arbitrary angle around the sheet normal. The sheet structure consists of two parallel Dove-prism sheets, each of which flips one component of the local direction of transmitted light rays. Together, the two sheets rotate transmitted light rays around the sheet normal. We show that the direction under which a point light source is seen is given by a Mobius transform. We illustrate some of the properties with movies calculated by ray-tracing software.Comment: 9 pages, 6 figure