scholarly journals Expansive flows on uniform spaces

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Se-Hyun Ku
Keyword(s):  
Topological Equivalence ◽  
Uniform Spaces ◽  
Dynamical Properties ◽  
Expansive Flows

<p style='text-indent:20px;'>In this paper we study several dynamical properties on uniform spaces. We define expansive flows on uniform spaces and provide some equivalent ways of defining expansivity. We also define the concept of expansive measures for flows on uniform spaces. We prove for flows on compact uniform spaces that every expansive measure vanishes along the orbits and has no singularities in the support. We also prove that every expansive measure for flows on uniform spaces is aperiodic and is expansive with respect to time-<inline-formula><tex-math id="M1">\begin{document}$ T $\end{document}</tex-math></inline-formula> map. Furthermore we show that every expansive measure for flows on compact uniform spaces maintains expansive under topological equivalence.</p>

scholarly journals Bimeron clusters in chiral antiferromagnets

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Xiaoguang Li ◽  
Laichuan Shen ◽  
Yuhao Bai ◽  
Junlin Wang ◽  
Xichao Zhang ◽  
...  
Keyword(s):  
Topological Equivalence ◽  
Material System ◽  
High Current ◽  
Relativistic Dynamics ◽  
Spintronic Devices ◽  
Wide Range ◽  
Out Of Plane ◽  
Statics And Dynamics ◽  
Dynamical Properties ◽  
Moriya Interaction

Abstract A magnetic bimeron is an in-plane topological counterpart of a magnetic skyrmion. Despite the topological equivalence, their statics and dynamics could be distinct, making them attractive from the perspectives of both physics and spintronic applications. In this work, we demonstrate the stabilization of bimeron solitons and clusters in the antiferromagnetic (AFM) thin film with interfacial Dzyaloshinskii–Moriya interaction (DMI). Bimerons demonstrate high current-driven mobility as generic AFM solitons, while featuring anisotropic and relativistic dynamics excited by currents with in-plane and out-of-plane polarizations, respectively. Moreover, these spin textures can absorb other bimeron solitons or clusters along the translational direction to acquire a wide range of Néel topological numbers. The clustering involves the rearrangement of topological structures, and gives rise to remarkable changes in static and dynamical properties. The merits of AFM bimeron clusters reveal a potential path to unify multibit data creation, transmission, storage, and even topology-based computation within the same material system, and may stimulate spintronic devices enabling innovative paradigms of data manipulations.

From the Oort cloud to Halley-type comets

1999 ◽  
Vol 173 ◽  
pp. 327-338 ◽  
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 &lt; 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 &lt;2 AU. Randomly-oriented LP comets captured into short-period orbits (orbital periods &lt; 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.

Dynamical properties of highly entangled polyalkylmethacrylate solutions : A comparative study

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

ON THE QUANTIFICATION OF UNIFORM PROPERTIES.PART 2

2001 ◽  
Vol 37 (1-2) ◽  
pp. 169-184
Author(s):  
B. Windels
Keyword(s):  
Metric Spaces ◽  
Uniform Spaces ◽  
Complete Metric Spaces ◽  
The Subject

In 1930 Kuratowski introduced the measure of non-compactness for complete metric spaces in order to measure the discrepancy a set may have from being compact.Since then several variants and generalizations concerning quanti .cation of topological and uniform properties have been studied.The introduction of approach uniform spaces,establishes a unifying setting which allows for a canonical quanti .cation of uniform concepts,such as completeness,which is the subject of this article.

Pseudo-Anosov Theory

2017 ◽  
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.

LIFTING THE FUNCTOR ITO THE CATEGORY OF UNIFORM SPACES

2020 ◽  
Vol 4 (1) ◽  
pp. 29-39
Author(s):  
Dilrabo Eshkobilova ◽  
Keyword(s):  
Compact Support ◽  
Probability Measures ◽  
Uniform Spaces ◽  
Continuous Maps ◽  
Uniformly Continuous

Uniform properties of the functor Iof idempotent probability measures with compact support are studied. It is proved that this functor can be lifted to the category Unif of uniform spaces and uniformly continuous maps

A NOTE ON COVERING L−LOCALLY UNIFORM SPACES

2020 ◽  
Vol 9 (9) ◽  
pp. 7137-7148
Author(s):  
J. Moshahary ◽  
D. Kr. Mitra
Keyword(s):  
Uniform Spaces

Statistical mechanics

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.

On ARU-Resolutions of Uniform Spaces

2003 ◽  
Vol 10 (2) ◽  
pp. 201-207
Author(s):  
V. Baladze
Keyword(s):  
Uniform Space ◽  
Uniform Spaces

Abstract In this paper theorems which give conditions for a uniform space to have an ARU-resolution are proved. In particular, a finitistic uniform space admits an ARU-resolution if and only if it has trivial uniform shape or it is an absolute uniform shape retract.

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