scholarly journals The diffusion time of the connecting orbit around rotation number zero for the monotone twist maps

2000 ◽  
Vol 6 (2) ◽  
pp. 255-274
Author(s):  
Qiudong Wang ◽  
Keyword(s):  
Rotation Number ◽  
Diffusion Time ◽  
Twist Maps ◽  
Connecting Orbit

scholarly journals Regular dependence of invariant curves and Aubry–Mather sets of twist maps of an annulus

1988 ◽  
Vol 8 (4) ◽  
pp. 555-584 ◽  
Author(s):  
Raphaël Douady
Keyword(s):  
Hamiltonian Systems ◽  
Rotation Number ◽  
Positive Measure ◽  
Invariant Curves ◽  
Rotation Numbers ◽  
Twist Maps ◽  
Area Preserving Maps ◽  
Area Preserving

AbstractWe prove that smooth enough invariant curves of monotone twist maps of an annulus with fixed diophantine rotation number depend on the map in a differentiable way. Partial results hold for Aubry-Mather sets.Then we show that invariant curves of the same map with different rotation numbers ω and ω′ cannot approach each other at a distance less than cst. |ω−ω′|. By K.A.M. theory, this implies that, under suitable assumptions, the union of invariant curves has positive measure.Analogous results are due to Zehnder and Herman (for the first part), and to Lazutkin and Pöschel (for the second one), in the case of Hamiltonian systems and area preserving maps.

scholarly journals Boundaries of instability zones for symplectic twist maps

2013 ◽  
Vol 13 (1) ◽  
pp. 19-41 ◽  
Author(s):  
M.-C. Arnaud
Keyword(s):  
Rotation Number ◽  
Irrational Rotation ◽  
Invariant Curve ◽  
Partial Answer ◽  
Twist Map ◽  
Instability Zone ◽  
Counter Example ◽  
Twist Maps ◽  
Irrational Rotation Number ◽  
The One

AbstractVery few things are known about the curves that are at the boundary of the instability zones of symplectic twist maps. It is known that in general they have an irrational rotation number and that they cannot be KAM curves. We address the following questions. Can they be very smooth? Can they be non-${C}^{1} $?Can they have a Diophantine or a Liouville rotation number? We give a partial answer for${C}^{1} $and${C}^{2} $twist maps.In Theorem 1, we construct a${C}^{2} $symplectic twist map$f$of the annulus that has an essential invariant curve$\Gamma $such that$\bullet $ $\Gamma $is not differentiable;$\bullet $the dynamics of${f}_{\vert \Gamma } $is conjugated to the one of a Denjoy counter-example;$\bullet $ $\Gamma $is at the boundary of an instability zone for$f$.Using the Hayashi connecting lemma, we prove in Theroem 2 that any symplectic twist map restricted to an essential invariant curve can be embedded as the dynamics along a boundary of an instability zone for some${C}^{1} $symplectic twist map.

scholarly journals A topological version of a theorem of Mather on twist maps

1984 ◽  
Vol 4 (4) ◽  
pp. 585-603 ◽  
Author(s):  
Glen Richard Hall
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Point ◽  
Rotation Number ◽  
Point Theorem ◽  
Twist Map ◽  
Twist Maps ◽  
Recent Theorem ◽  
Topological Version ◽  
Area Preserving

AbstractIn this report we show that a twist map of an annulus with a periodic point of rotation number p/q must have a Birkhoff periodic point of rotation number p/q. We use topological techniques so no assumption of area-preservation or circle intersection property is needed. If the map is area-preserving then this theorem andthe fixed point theorem of Birkhoff imply a recent theorem of Aubry and Mather. We also show that periodic orbits of (significantly) smallest period for a twist map must be Birkhoff.

Meridional Circulation, Turbulence, and Diffusion Processes in Stars

1976 ◽  
Vol 32 ◽  
pp. 109-116 ◽  
Author(s):  
S. Vauclair
Keyword(s):  
Convection Zone ◽  
Diffusion Processes ◽  
Meridional Circulation ◽  
Diffusion Time ◽  
Work In Progress ◽  
First Results ◽  
Stellar Envelopes ◽  
And Diffusion ◽  
Turbulence And Diffusion ◽  
Hr Diagram

This paper gives the first results of a work in progress, in collaboration with G. Michaud and G. Vauclair. It is a first attempt to compute the effects of meridional circulation and turbulence on diffusion processes in stellar envelopes. Computations have been made for a 2 Mʘstar, which lies in the Am - δ Scuti region of the HR diagram.Let us recall that in Am stars diffusion cannot occur between the two outer convection zones, contrary to what was assumed by Watson (1970, 1971) and Smith (1971), since they are linked by overshooting (Latour, 1972; Toomre et al., 1975). But diffusion may occur at the bottom of the second convection zone. According to Vauclair et al. (1974), the second convection zone, due to He II ionization, disappears after a time equal to the helium diffusion time, and then diffusion may happen at the bottom of the first convection zone, so that the arguments by Watson and Smith are preserved.

scholarly journals Gas Damping in Capacitive MEMS Transducers in the Free Molecular Flow Regime

Sensors ◽  
2021 ◽  
Vol 21 (7) ◽  
pp. 2566
Author(s):  
Boris A. Boom ◽  
Alessandro Bertolini ◽  
Eric Hennes ◽  
Johannes F. J. van den Brand
Keyword(s):  
Flow Regime ◽  
Gas Diffusion ◽  
Diffusion Time ◽  
Molecular Flow ◽  
Free Molecular Flow ◽  
Simple Analytical Model ◽  
Gas Damping ◽  
Wide Range ◽  
Capacitive Mems ◽  
Insight Into

We present a novel analysis of gas damping in capacitive MEMS transducers that is based on a simple analytical model, assisted by Monte-Carlo simulations performed in Molflow+ to obtain an estimate for the geometry dependent gas diffusion time. This combination provides results with minimal computational expense and through freely available software, as well as insight into how the gas damping depends on the transducer geometry in the molecular flow regime. The results can be used to predict damping for arbitrary gas mixtures. The analysis was verified by experimental results for both air and helium atmospheres and matches these data to within 15% over a wide range of pressures.

scholarly journals Processes controlling the initial mass function: interstellar turbulence and magnetic fields

1991 ◽  
Vol 147 ◽  
pp. 407-408
Author(s):  
R. C. Fleck
Keyword(s):  
Magnetic Fields ◽  
Mass Function ◽  
Diffusion Time ◽  
Interstellar Cloud ◽  
Initial Mass Function ◽  
Mass Scaling ◽  
Interstellar Turbulence ◽  
Time Scaling ◽  
Turbulent Pressure ◽  
Low Mass

The observed flattening of the initial stellar mass function at low mass can be accounted for in terms of the different interstellar cloud size-mass scaling and different ambipolar diffusion time scaling for small, thermally-supported clouds and larger clouds supported primarily by turbulent pressure.

scholarly journals Interpretation and diversity of exoplanetary material orbiting white dwarfs

2019 ◽  
Vol 490 (1) ◽  
pp. 202-218 ◽  
Author(s):  
Andrew Swan ◽  
Jay Farihi ◽  
Detlev Koester ◽  
Mark Hollands ◽  
Steven Parsons ◽  
...  
Keyword(s):  
White Dwarfs ◽  
Diffusion Time ◽  
Source Material ◽  
Consensus Model ◽  
Improved Method ◽  
Core Component ◽  
Accretion Process ◽  
Medium Resolution ◽  
Solar System Objects ◽  
Formation Conditions

ABSTRACT Nine metal-polluted white dwarfs are observed with medium-resolution optical spectroscopy, where photospheric abundances are determined and interpreted by comparison with Solar system objects. An improved method for making such comparisons is presented, which overcomes potential weaknesses of prior analyses, with numerous sources of error considered to highlight the limitations on interpretation. The stars are inferred to be accreting rocky, volatile-poor asteroidal materials with origins in differentiated bodies, in line with the consensus model. The most heavily polluted star in the sample has 14 metals detected, and appears to be accreting material from a rocky planetesimal, whose composition is mantle-like with a small Fe–Ni core component. Some unusual abundances are present. One star is strongly depleted in Ca, while two others show Na abundances elevated above bulk-Earth abundances; it is speculated that either the latter reflect diversity in the formation conditions of the source material, or they are traces of past accretion events. Another star shows clear signs that accretion ceased around 5 Myr ago, causing Mg to dominate the photospheric abundances, as it has the longest diffusion time of the observed elements. Observing such post-accretion systems allows constraints to be placed on models of the accretion process.

scholarly journals DTI at long diffusion time improves fiber tracking

2010 ◽  
Vol 23 (5) ◽  
pp. 459-465 ◽  
Author(s):  
Swati Rane ◽  
Govind Nair ◽  
Timothy Q. Duong
Keyword(s):  
Fiber Tracking ◽  
Diffusion Time

Effects of Rotation on Heat Transfer for a Single Row Jet Impingement Array With Crossflow

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Justin A. Lamont ◽  
Srinath V. Ekkad ◽  
Mary Anne Alvin
Keyword(s):  
Heat Transfer ◽  
Liquid Crystal ◽  
Rotation Number ◽  
Coriolis Force ◽  
Room Temperature ◽  
Turbine Blades ◽  
Target Surface ◽  
Channel Height ◽  
Potential Core ◽  
Single Row

The effects of the Coriolis force are investigated in rotating internal serpentine coolant channels in turbine blades. For complex flow in rotating channels, detailed measurements of the heat transfer over the channel surface will greatly enhance the blade designers’ ability to predict hot spots so coolant may be distributed more effectively. The present study uses a novel transient liquid crystal technique to measure heat transfer in a rotating, radially outward channel with impingement jets. A simple case with a single row of constant pitch impinging jets with the crossflow effect is presented to demonstrate the novel liquid crystal technique and document the baseline effects for this type of geometry. The present study examines the differences in heat transfer distributions due to variations in jet Rotation number, Roj, and jet orifice-to-target surface distance (H/dj = 1,2, and 3). Colder air, below room temperature, is passed through a room temperature test section to cause a color change in the liquid crystals. This ensures that buoyancy is acting in a similar direction as in actual turbine blades where walls are hotter than the coolant fluid. Three parameters were controlled in the testing: jet coolant-to-wall temperature ratio, average jet Reynolds number, Rej, and average jet Rotation number, Roj. Results show, such as serpentine channels, the trailing side experiences an increase in heat transfer and the leading side experiences a decrease for all jet channel height-to-jet diameter ratios (H/dj). At a jet channel height-to-jet diameter ratio of 1, the crossflow from upstream spent jets greatly affects impingement heat transfer behavior in the channel. For H/dj = 2 and 3, the effects of the crossflow are not as prevalent as H/dj = 1: however, it still plays a detrimental role. The stationary case shows that heat transfer increases with higher H/dj values, so that H/dj = 3 has the highest results of the three examined. However, during rotation the H/dj = 2 case shows the highest heat transfer values for both the leading and trailing sides. The Coriolis force may have a considerable effect on the developing length of the potential core, affecting the resulting heat transfer on the target surface.

Invariant curves for area-preserving twist maps far from integrable

1991 ◽  
Vol 65 (3-4) ◽  
pp. 617-643 ◽  
Author(s):  
Alessandra Celletti ◽  
Luigi Chierchia
Keyword(s):  
Invariant Curves ◽  
Twist Maps ◽  
Area Preserving
Sign in / Sign up

Export Citation Format

Share Document