Microscopic chaos and diffusion

We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of models involving a single particle moving in two dimensions and colliding with fixed scatterers. We find that a number of microscopically nonchaotic models exhibit diffusion, and that the standard methods of chaotic time series analysis are ill suited to the problem of distinguishing between chaotic and nonchaotic microscopic dynamics. However, we show that periodic orbits play an important role in our models, in that their different properties in chaotic and nonchaotic systems can be used to distinguish such systems at the level of time series analysis, and in systems with absorbing boundaries. Our findings are relevant to experiments aimed at verifying the existence of chaoticity and related dynamical properties on a microscopic level in diffusive systems.Comment: 28 pages revtex, 14 figures incorporated with epsfig; see also chao-dyn/9904041; revised to clarify the definition of chaos and include discussion of a mixed model with both square and circular scatterer

Microscopic chaos from Brownian motion?

A recent experiment on Brownian motion has been interpreted to exhibit direct evidence for microscopic chaos. In this note we demonstrate that virtually identical results can be obtained numerically using a manifestly microscopically nonchaotic system.Comment: 3 pages, 1 figure, Comment on P. Gaspard et al, Nature vol 394, 865 (1998); rewritten in a more popular styl

An Improved Procedure for Laboratory Rearing of the Corn Earworm, \u3ci\u3eHeliothis Zea\u3c/i\u3e (Lepidoptera: Noctuidae)

An improved method for the laboratory rearing of the corn earworm. Heliothis zea, described. The rearing medium is a modification of the commonly used wheat germ An oviposition chamber, a feeder for adults, and a simple and inexpensive contrnlled humidity chamber are described

Formal proof of the AVM-1 microprocessor using the concept of generic interpreters

A microprocessor designated AVM-1 was designed to demonstrate the use of generic interpreters in verifying hierarchically decomposed microprocessor specifications. This report is intended to document the high-order language (HOL) code verifying AVM-1. The organization of the proof is discussed and some technical details concerning the execution of the proof scripts in HOL are presented. The proof scripts used to verify AVM-1 are also presented

Optimal slit orientation for long multi-object spectroscopic exposures

Historically, long-slit spectroscopic observations were carried out using the parallactic angle for the slit orientation if slit loss was an important consideration (either to maximize the signal-to-noise or to do spectrophotometry). This requires periodic realignment of the slit position angle as the parallactic angle changes. This is not possible for multi-slit observations where one slit position angle must be chosen for the entire exposure. Common wisdom suggests using the parallactic angle at the meridian (HA=0). In this paper, I examine what the best strategy is for long, multi-slit exposures. I find that in extreme cases (very long exposure time) the best choice is to orient the slit \emph{perpendicular} to the parallactic angle at the meridian. There are two effects to consider: the increasing dispersion with increasing airmass and the changing angle between the parallactic angle and the slit. In the case of \emph{traditional} slit orientation, the two effects amplify each other, thus rendering a significant fraction of the observation useless. Using the perpendicular orientation, the two processes work against each other, thus most of the observation remains useful. I will use, as an example, our 8 hour Lockman Hole observations using the Keck telescope, but generic methods are given to evaluate a particular observation. I also make the tools available to the community.Comment: Accepted by A&A (20/06/2005

The formal verification of generic interpreters

The task assignment 3 of the design and validation of digital flight control systems suitable for fly-by-wire applications is studied. Task 3 is associated with formal verification of embedded systems. In particular, results are presented that provide a methodological approach to microprocessor verification. A hierarchical decomposition strategy for specifying microprocessors is also presented. A theory of generic interpreters is presented that can be used to model microprocessor behavior. The generic interpreter theory abstracts away the details of instruction functionality, leaving a general model of what an interpreter does

The Spectra of Main Sequence Stars in Galactic Globular Clusters II. CH and CN Bands in M71

Spectra with a high signal-to-noise ratio of 79 stars which are just below the main sequence turnoff of M71 are presented. They yield indices for the strength of the G band of CH and the ultraviolet CN band at 3885 \AA. These indices are each to first order bimodal and they are anti-correlated. There are approximately equal numbers of CN weak/CH strong and CN strong/CH weak main sequence stars in M71. It is not yet clear whether these star-to-star variations arise from primordial variations or from mixing within a fraction of individual stars as they evolve.Comment: Accepted for publication in the AJ to appear back to back with paper I. 14 pages with 5 figure

Algebraic Properties of Valued Constraint Satisfaction Problem

The paper presents an algebraic framework for optimization problems expressible as Valued Constraint Satisfaction Problems. Our results generalize the algebraic framework for the decision version (CSPs) provided by Bulatov et al. [SICOMP 2005]. We introduce the notions of weighted algebras and varieties and use the Galois connection due to Cohen et al. [SICOMP 2013] to link VCSP languages to weighted algebras. We show that the difficulty of VCSP depends only on the weighted variety generated by the associated weighted algebra. Paralleling the results for CSPs we exhibit a reduction to cores and rigid cores which allows us to focus on idempotent weighted varieties. Further, we propose an analogue of the Algebraic CSP Dichotomy Conjecture; prove the hardness direction and verify that it agrees with known results for VCSPs on two-element sets [Cohen et al. 2006], finite-valued VCSPs [Thapper and Zivny 2013] and conservative VCSPs [Kolmogorov and Zivny 2013].Comment: arXiv admin note: text overlap with arXiv:1207.6692 by other author

Charge Transfer in Partition Theory

The recently proposed Partition Theory (PT) [J.Phys.Chem.A 111, 2229 (2007)] is illustrated on a simple one-dimensional model of a heteronuclear diatomic molecule. It is shown that a sharp definition for the charge of molecular fragments emerges from PT, and that the ensuing population analysis can be used to study how charge redistributes during dissociation and the implications of that redistribution for the dipole moment. Interpreting small differences between the isolated parts' ionization potentials as due to environmental inhomogeneities, we gain insight into how electron localization takes place in H2+ as the molecule dissociates. Furthermore, by studying the preservation of the shapes of the parts as different parameters of the model are varied, we address the issue of transferability of the parts. We find good transferability within the chemically meaningful parameter regime, raising hopes that PT will prove useful in chemical applications.Comment: 12 pages, 16 figure