25,834 research outputs found
Random billiards with wall temperature and associated Markov chains
By a random billiard we mean a billiard system in which the standard specular
reflection rule is replaced with a Markov transition probabilities operator P
that, at each collision of the billiard particle with the boundary of the
billiard domain, gives the probability distribution of the post-collision
velocity for a given pre-collision velocity. A random billiard with
microstructure (RBM) is a random billiard for which P is derived from a choice
of geometric/mechanical structure on the boundary of the billiard domain. RBMs
provide simple and explicit mechanical models of particle-surface interaction
that can incorporate thermal effects and permit a detailed study of
thermostatic action from the perspective of the standard theory of Markov
chains on general state spaces.
We focus on the operator P itself and how it relates to the
mechanical/geometric features of the microstructure, such as mass ratios,
curvatures, and potentials. The main results are as follows: (1) we
characterize the stationary probabilities (equilibrium states) of P and show
how standard equilibrium distributions studied in classical statistical
mechanics, such as the Maxwell-Boltzmann distribution and the Knudsen cosine
law, arise naturally as generalized invariant billiard measures; (2) we obtain
some basic functional theoretic properties of P. Under very general conditions,
we show that P is a self-adjoint operator of norm 1 on an appropriate Hilbert
space. In a simple but illustrative example, we show that P is a compact
(Hilbert-Schmidt) operator. This leads to the issue of relating the spectrum of
eigenvalues of P to the features of the microstructure;(3) we explore the
latter issue both analytically and numerically in a few representative
examples;(4) we present a general algorithm for simulating these Markov chains
based on a geometric description of the invariant volumes of classical
statistical mechanics
Tracking Data Acquisition System (TDAS) for the 1990's. Volume 6: TDAS navigation system architecture
One-way range and Doppler methods for providing user orbit and time determination are examined. Forward link beacon tracking, with on-board processing of independent navigation signals broadcast continuously by TDAS spacecraft; forward link scheduled tracking; with on-board processing of navigation data received during scheduled TDAS forward link service intervals; and return link scheduled tracking; with ground-based processing of user generated navigation data during scheduled TDAS return link service intervals are discussed. A system level definition and requirements assessment for each alternative, an evaluation of potential navigation performance and comparison with TDAS mission model requirements is included. TDAS satellite tracking is also addressed for two alternatives: BRTS and VLBI tracking
New Finishes for Zinc Alloys
Since 1958, the International Lead Zinc Research Organization (ILSRC) has pursued a number of projects which have resulted in new methods of polishing and finishing of zinc alloys. This paper surveys the six important developments which have arisen as a result of ILZRO research in the finishing field
Depletion effects and loop formation in self-avoiding polymers
Langevin dynamics is employed to study the looping kinetics of self-avoiding
polymers both in ideal and crowded solutions. A rich kinetics results from the
competition of two crowding-induced effects: the depletion attraction and the
enhanced viscous friction. For short chains, the enhanced friction slows down
looping, while, for longer chains, the depletion attraction renders it more
frequent and persistent. We discuss the possible relevance of the findings for
chromatin looping in living cells.Comment: 4 pages, 3 figure
Conformal thin-sandwich puncture initial data for boosted black holes
We apply the puncture approach to conformal thin-sandwich black-hole initial
data. We solve numerically the conformal thin-sandwich puncture (CTSP)
equations for a single black hole with non-zero linear momentum. We show that
conformally flat solutions for a boosted black hole have the same maximum
gravitational radiation content as the corresponding Bowen-York solution in the
conformal transverse-traceless decomposition. We find that the physical
properties of these data are independent of the free slicing parameter.Comment: 12 pages, 11 figure
Ill-posedness in the Einstein equations
It is shown that the formulation of the Einstein equations widely in use in
numerical relativity, namely, the standard ADM form, as well as some of its
variations (including the most recent conformally-decomposed version), suffers
from a certain but standard type of ill-posedness. Specifically, the norm of
the solution is not bounded by the norm of the initial data irrespective of the
data. A long-running numerical experiment is performed as well, showing that
the type of ill-posedness observed may not be serious in specific practical
applications, as is known from many numerical simulations.Comment: 13 pages, 3 figures, accepted for publication in Journal of
Mathematical Physics (to appear August 2000
Program logics for homogeneous meta-programming.
A meta-program is a program that generates or manipulates another program; in homogeneous meta-programming, a program may generate new parts of, or manipulate, itself. Meta-programming has been used extensively since macros
were introduced to Lisp, yet we have little idea how formally to reason about metaprograms. This paper provides the first program logics for homogeneous metaprogramming
â using a variant of MiniMLe by Davies and Pfenning as underlying meta-programming language.We show the applicability of our approach by reasoning about example meta-programs from the literature. We also demonstrate that our logics are relatively complete in the sense of Cook, enable the inductive derivation of characteristic formulae, and exactly capture the observational properties induced by the operational semantics
Spectroscopic biomedical imaging with the Medipix2 detector
This study confirms that the Medipix2 x-ray detector enables spectroscopic bio-medical plain radiography. We show that the detector has the potential to provide new, useful information beyond the limited spectroscopic information of modern dual-energy computed tomography (CT) scanners. Full spectroscopic 3D-imaging is likely to be the next major technological advance in computed tomography, moving the modality towards molecular imaging applications. This paper focuses on the enabling technology which allows spectroscopic data collection and why this information is useful. In this preliminary study we acquired the first spectroscopic images of human tissue and other biological samples obtained using the Medipix2 detector. The images presented here include the clear resolution of the 1.4mm long distal phalanx of a 20-week-old miscarried foetus, showing clear energy-dependent variations. The opportunities for further research using the forthcoming Medipix3 detector are discussed and a prototype spectroscopic CT scanner (MARS, Medipix All Resolution System) is briefly describe
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