Dynamical properties of groups of automorphisms on Heisenberg nilmanifolds

Jean-Romain Heu

doi:10.1007/s10711-009-9407-9

From the Oort cloud to Halley-type comets

International Astronomical Union Colloquium ◽

10.1017/s0252921100031638 ◽

1999 ◽

Vol 173 ◽

pp. 327-338 ◽

Cited By ~ 5

Author(s):

J.A. Fernández ◽

T. Gallardo

Keyword(s):

Total Population ◽

Complex Function ◽

Dynamical Evolution ◽

Oort Cloud ◽

Capture Process ◽

Influx Rate ◽

Short Period ◽

Dynamical Properties ◽

Orbital Periods ◽

Probability Of Capture

AbstractThe Oort cloud probably is the source of Halley-type (HT) comets and perhaps of some Jupiter-family (JF) comets. The process of capture of Oort cloud comets into HT comets by planetary perturbations and its efficiency are very important problems in comet ary dynamics. A small fraction of comets coming from the Oort cloud − of about 10−2− are found to become HT comets (orbital periods < 200 yr). The steady-state population of HT comets is a complex function of the influx rate of new comets, the probability of capture and their physical lifetimes. From the discovery rate of active HT comets, their total population can be estimated to be of a few hundreds for perihelion distancesq <2 AU. Randomly-oriented LP comets captured into short-period orbits (orbital periods < 20 yr) show dynamical properties that do not match the observed properties of JF comets, in particular the distribution of their orbital inclinations, so Oort cloud comets can be ruled out as a suitable source for most JF comets. The scope of this presentation is to review the capture process of new comets into HT and short-period orbits, including the possibility that some of them may become sungrazers during their dynamical evolution.

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Dynamical properties of highly entangled polyalkylmethacrylate solutions : A comparative study

Journal de Physique IV (Proceedings) ◽

10.1051/jp4:2000765 ◽

2000 ◽

Vol 10 (PR7) ◽

pp. Pr7-321-Pr7-324

Author(s):

V. Villari ◽

A. Faraone, ◽

S. Magazù, ◽

G. Maisano ◽

R. Ponterio

Keyword(s):

Comparative Study ◽

Dynamical Properties

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Computational studies on the static and dynamical properties of one dimensional integer spin quantum magnets

10.32657/10356/143094 ◽

2020 ◽

Author(s):

◽

Ernest Teng Siang Ong

Keyword(s):

Computational Studies ◽

Quantum Magnets ◽

One Dimensional ◽

Integer Spin ◽

Spin Quantum ◽

Dynamical Properties

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Pseudo-Anosov Theory

10.23943/princeton/9780691147949.003.0015 ◽

2017 ◽

Cited By ~ 1

Author(s):

Benson Farb ◽

Dan Margalit

Keyword(s):

Braid Groups ◽

Intersection Numbers ◽

Branched Covers ◽

Algebraic Integers ◽

Dehn Twists ◽

Mapping Classes ◽

Dynamical Properties

This chapter focuses on the construction as well as the algebraic and dynamical properties of pseudo-Anosov homeomorphisms. It first presents five different constructions of pseudo-Anosov mapping classes: branched covers, constructions via Dehn twists, homological criterion, Kra's construction, and a construction for braid groups. It then proves a few fundamental facts concerning stretch factors of pseudo-Anosov homeomorphisms, focusing on the theorem that pseudo-Anosov stretch factors are algebraic integers. It also considers the spectrum of pseudo-Anosov stretch factors, along with the special properties of those measured foliations that are the stable (or unstable) foliations of some pseudo-Anosov homeomorphism. Finally, it describes the orbits of a pseudo-Anosov homeomorphism as well as lengths of curves and intersection numbers under iteration.

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Statistical mechanics

10.1093/oso/9780198803195.003.0002 ◽

2017 ◽

Author(s):

Michael P. Allen ◽

Dominic J. Tildesley

Keyword(s):

Statistical Mechanics ◽

Potential Model ◽

Quantum Corrections ◽

Inhomogeneous Systems ◽

Hard Constraints ◽

Complex Liquids ◽

Fluid Membranes ◽

Dynamical Properties ◽

Canonical Ensembles ◽

Grand Canonical

This chapter contains the essential statistical mechanics required to understand the inner workings of, and interpretation of results from, computer simulations. The microcanonical, canonical, isothermal–isobaric, semigrand and grand canonical ensembles are defined. Thermodynamic, structural, and dynamical properties of simple and complex liquids are related to appropriate functions of molecular positions and velocities. A number of important thermodynamic properties are defined in terms of fluctuations in these ensembles. The effect of the inclusion of hard constraints in the underlying potential model on the calculated properties is considered, and the addition of long-range and quantum corrections to classical simulations is presented. The extension of statistical mechanics to describe inhomogeneous systems such as the planar gas–liquid interface, fluid membranes, and liquid crystals, and its application in the simulation of these systems, are discussed.

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