Thin-sectioning and microanalysis of individual extraterrestrial particles

A long standing constraint on the study of micrometeorites has centered on difficulties in preparing them for analysis. This is due largely to their small dimensions and consequent practical limitations on sample manipulation. Chondritic micrometeorites provide a good example; although much has been learned about their chemistry and mineralogy almost nothing was known about such basic properties as texture and petrographic associations. The only way to assess such properties is to examine microstructure indigenous to the particles. Unfortunately, almost all micrometeorites, out of necessity, have been crushed and dispersed onto appropriate substances prior to analysis, and most information about texture and petrography was lost. Recently, thin-sections of individual extraterrestrial particles have been prepared using an ultramicrotome equipped with a diamond knife. This procedure has been applied to stratospheric micrometeorites and Solar Max impact debris. In both cases the sections have enabled observation of a variety of internal particle features, including textures, porosity, and petrographic associations. The sectioning procedure is described and analysis results for chondritic micrometeoroids and select particles from Solar Max are presented

Mumford dendrograms and discrete p-adic symmetries

In this article, we present an effective encoding of dendrograms by embedding them into the Bruhat-Tits trees associated to $p$-adic number fields. As an application, we show how strings over a finite alphabet can be encoded in cyclotomic extensions of $\mathbb{Q}_p$ and discuss $p$-adic DNA encoding. The application leads to fast $p$-adic agglomerative hierarchic algorithms similar to the ones recently used e.g. by A. Khrennikov and others. From the viewpoint of $p$-adic geometry, to encode a dendrogram $X$ in a $p$-adic field $K$ means to fix a set $S$ of $K$-rational punctures on the $p$-adic projective line $\mathbb{P}^1$. To $\mathbb{P}^1\setminus S$ is associated in a natural way a subtree inside the Bruhat-Tits tree which recovers $X$, a method first used by F. Kato in 1999 in the classification of discrete subgroups of $\textrm{PGL}_2(K)$. Next, we show how the $p$-adic moduli space $\mathfrak{M}_{0,n}$ of $\mathbb{P}^1$ with $n$ punctures can be applied to the study of time series of dendrograms and those symmetries arising from hyperbolic actions on $\mathbb{P}^1$. In this way, we can associate to certain classes of dynamical systems a Mumford curve, i.e. a $p$-adic algebraic curve with totally degenerate reduction modulo $p$. Finally, we indicate some of our results in the study of general discrete actions on $\mathbb{P}^1$, and their relation to $p$-adic Hurwitz spaces.Comment: 14 pages, 6 figure

A contribution to laser range imaging technology

The goal of the project was to develop a methodology for fusion of a Laser Range Imaging Device (LRID) and camera data. Our initial work in the project led to the conclusion that none of the LRID's that were available were sufficiently adequate for this purpose. Thus we spent the time and effort on the development of the new LRID with several novel features which elicit the desired fusion objectives. In what follows, we describe the device developed and built under contract. The Laser Range Imaging Device (LRID) is an instrument which scans a scene using a laser and returns range and reflection intensity data. Such a system would be extremely useful in scene analysis in industry and space applications. The LRID will be eventually implemented on board a mobile robot. The current system has several advantages over some commercially available systems. One improvement is the use of X-Y galvonometer scanning mirrors instead of polygonal mirrors present in some systems. The advantage of the X-Y scanning mirrors is that the mirror system can be programmed to provide adjustable scanning regions. For each mirror there are two controls accessible by the computer. The first is the mirror position and the second is a zoom factor which modifies the amplitude of the position of the parameter. Another advantage of the LRID is the use of a visible low power laser. Some of the commercial systems use a higher intensity invisible laser which causes safety concerns. By using a low power visible laser, not only can one see the beam and avoid direct eye contact, but also the lower intensity reduces the risk of damage to the eye, and no protective eyeware is required

Vibration limiting of rotors by feedback control

Experimental findings of a three mass rotor with four channels of feedback control are reported. The channels are independently controllable with force being proportional to the velocity and/or instantaneous displacement from equilibrium of the shaft at the noncontacting probe locations (arranged in the vertical and horizontal attitudes near the support bearings). The findings suggest that automatic feedback control of rotors is feasible for limiting certain vibration levels. Control of one end of a rotor does afford some predictable vibration limiting of the rotor at the other end

A pp-adic RanSaC algorithm for stereo vision using Hensel lifting

A $p$-adic variation of the Ran(dom) Sa(mple) C(onsensus) method for solving the relative pose problem in stereo vision is developped. From two 2-adically encoded images a random sample of five pairs of corresponding points is taken, and the equations for the essential matrix are solved by lifting solutions modulo 2 to the 2-adic integers. A recently devised $p$-adic hierarchical classification algorithm imitating the known LBG quantisation method classifies the solutions for all the samples after having determined the number of clusters using the known intra-inter validity of clusterings. In the successful case, a cluster ranking will determine the cluster containing a 2-adic approximation to the "true" solution of the problem.Comment: 15 pages; typos removed, abstract changed, computation error remove

Ground-State Properties of a Rotating Bose-Einstein Condensate with Attractive Interaction

The ground state of a rotating Bose-Einstein condensate with attractive interaction in a quasi-one-dimensional torus is studied in terms of the ratio $\gamma$ of the mean-field interaction energy per particle to the single-particle energy-level spacing. The plateaus of quantized circulation are found to appear if and only if $\gamma<1$ with the lengths of the plateaus reduced due to hybridization of the condensate over different angular-momentum states.Comment: 4 pages, 2 figures, Accepted for publication in Physical Reveiw Letter

Federal Programs Available to Unemployed Workers

[Excerpt] Four groups of federal programs target unemployed workers: unemployment insurance, health care assistance, job search assistance, and training. This report presents information on federal programs targeted to unemployed workers specifically, but does not attempt to discuss means-tested programs (such as Medicaid or SSI) that are available regardless of employment status. This report will be updated with major new legislation

Solving the Jitter Problem in Microwave Compressed Ultrafast Electron Diffraction Instruments: Robust Sub-50 fs Cavity-Laser Phase Stabilization

We demonstrate the compression of electron pulses in a high-brightness ultrafast electron diffraction (UED) instrument using phase-locked microwave signals directly generated from a mode-locked femtosecond oscillator. Additionally, a continuous-wave phase stabilization system that accurately corrects for phase fluctuations arising in the compression cavity from both power amplification and thermal drift induced detuning was designed and implemented. An improvement in the microwave timing stability from 100 fs to 5 fs RMS is measured electronically and the long-term arrival time stability ($>$10 hours) of the electron pulses improves to below our measurement resolution of 50 fs. These results demonstrate sub-relativistic ultrafast electron diffraction with compressed pulses that is no longer limited by laser-microwave synchronization.Comment: Accepted for publication in Structural Dynamic