scholarly journals Zero-dimensional and symbolic extensions of topological flows

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
David Burguet ◽  
Ruxi Shi
Keyword(s):  
Suspension Flow ◽  
Dimensional System ◽  
Orbit Equivalence ◽  
Suspension Flows ◽  
Dimensional Flow ◽  
Symbolic Extension ◽  
Zero Sequence ◽  
Full Shift ◽  
Symbolic Flow ◽  
Roof Function

<p style='text-indent:20px;'>A zero-dimensional (resp. symbolic) flow is a suspension flow over a zero-dimensional system (resp. a subshift). We show that any topological flow admits a principal extension by a zero-dimensional flow. Following [<xref ref-type="bibr" rid="b6">6</xref>] we deduce that any topological flow admits an extension by a symbolic flow if and only if its time-<inline-formula><tex-math id="M1">\begin{document}$ t $\end{document}</tex-math></inline-formula> map admits an extension by a subshift for any <inline-formula><tex-math id="M2">\begin{document}$ t\neq 0 $\end{document}</tex-math></inline-formula>. Moreover the existence of such an extension is preserved under orbit equivalence for regular topological flows, but this property does not hold for singular flows. Finally we investigate symbolic extensions for singular suspension flows. In particular, the suspension flow over the full shift on <inline-formula><tex-math id="M3">\begin{document}$ \{0,1\}^{\mathbb Z} $\end{document}</tex-math></inline-formula> with a roof function <inline-formula><tex-math id="M4">\begin{document}$ f $\end{document}</tex-math></inline-formula> vanishing at the zero sequence <inline-formula><tex-math id="M5">\begin{document}$ 0^\infty $\end{document}</tex-math></inline-formula> admits a principal symbolic extension or not depending on the smoothness of <inline-formula><tex-math id="M6">\begin{document}$ f $\end{document}</tex-math></inline-formula> at <inline-formula><tex-math id="M7">\begin{document}$ 0^\infty $\end{document}</tex-math></inline-formula>.</p>

scholarly journals On Sinaĭ Billiards on Flat Surfaces with Horns

2021 ◽  
Vol 183 (2) ◽  
Author(s):  
Henk Bruin
Keyword(s):  
Exponential Decay ◽  
Height Function ◽  
Suspension Flow ◽  
Limit Laws ◽  
Suspension Flows ◽  
Flat Surfaces ◽  
Exponential Tails ◽  
Exponential Decay Of Correlations ◽  
Sinai Billiards ◽  
Young Towers

AbstractWe show that certain billiard flows on planar billiard tables with horns can be modeled as suspension flows over Young towers (Ann. Math. 147:585–650, 1998) with exponential tails. This implies exponential decay of correlations for the billiard map. Because the height function of the suspension flow itself is polynomial when the horns are Torricelli-like trumpets, one can derive Limit Laws for the billiard flow, including Stable Limits if the parameter of the Torricelli trumpet is chosen in (1, 2).

Chaotic mixing in a bounded three-dimensional flow

2000 ◽  
Vol 417 ◽  
pp. 265-301 ◽  
Author(s):  
G. O. FOUNTAIN ◽  
D. V. KHAKHAR ◽  
I. MEZIĆ ◽  
J. M. OTTINO
Keyword(s):  
Laser Sheet ◽  
Three Dimensional ◽  
Vertical Axis ◽  
Operating Conditions ◽  
Chaotic Advection ◽  
Base Case ◽  
Dimensional System ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Moderate Reynolds Number

Even though the first theoretical example of chaotic advection was a three-dimensional flow (Hénon 1966), the number of theoretical studies addressing chaos and mixing in three-dimensional flows is small. One problem is that an experimentally tractable three-dimensional system that allows detailed experimental and computational investigation had not been available. A prototypical, bounded, three-dimensional, moderate-Reynolds-number flow is presented; this system lends itself to detailed experimental observation and allows high-precision computational inspection of geometrical and dynamical effects. The flow structure, captured by means of cuts with a laser sheet (experimental Poincaré section), is visualized via continuously injected fluorescent dye streams, and reveals detailed chaotic structures and chains of high-period islands. Numerical experiments are performed and compared with particle image velocimetry (PIV) and flow visualization results. Predictions of existing theories for chaotic advection in three-dimensional volume-preserving flows are tested. The ratio of two frequencies of particle motion – the frequency of motion around the vertical axis and the frequency of recirculation in the plane containing the axis – is identified as the crucial parameter. Using this parameter, the number of islands in the chain can be predicted. The same parameter – using as a base-case the integrable motion – allows the identification of operating conditions where small perturbations lead to nearly complete mixing.

scholarly journals Electrical Tomography: A Review of Configurations, and Application to Fibre Flow Suspensions Characterisation

2020 ◽  
Vol 10 (7) ◽  
pp. 2355 ◽  
Author(s):  
Pedro Faia ◽  
Rui Silva ◽  
Maria G. Rasteiro ◽  
Fernando Garcia
Keyword(s):  
Flow Characteristics ◽  
Suspension Flow ◽  
Electrical Tomography ◽  
Suspension Flows ◽  
Flow Monitoring ◽  
Non Invasive ◽  
Long Time ◽  
Invasive Techniques ◽  
Solid Liquid ◽  
Industrial Relevance

Understanding the behaviour of suspension flows continues to be a subject of great interest considering its industrial relevance, regardless of the long time and effort dedicated to it by the scientific and industrial communities. Information about several flow characteristics, such as flow regimen, relative velocity between phases, and spatial distribution of the phases, are essential for the development of exact models for description of processes involving pulp suspension. Among the diverse non-invasive techniques for flow characterisation that have been reported in the literature for obtaining experimental data about suspension flow in different processes, Electrical Tomography is one of the most interesting, since it presents perhaps the best compromise among cost, portability, and, above all, safety of handling (indeed there is no need to use radiation, which requires special care when using it). In this paper, a brief review and comparison between existing technologies for pulp suspension flow monitoring will be presented, together with their strengths and weaknesses. Emphasis is given to Electrical Tomography, because it offers the above-mentioned compromise and thus was the strategy adopted by the authors to characterise different flow processes (solid–liquid, liquid–liquid, fibres, etc.). The produced portable EIT system is described, and examples of results of its use for pulp suspension flow characterisation are reported and discussed.

Three Dimensional Simulation of Suspension Flow in a Mold Cavity

2010 ◽  
Author(s):  
Ahmed N. Oumer ◽  
Ahmed M. S. Ali ◽  
Othman B. Mamat
Keyword(s):  
Fourth Order ◽  
Fiber Orientation ◽  
Three Dimensional ◽  
Fiber Suspension ◽  
Suspension Flow ◽  
Cross Model ◽  
Suspension Flows ◽  
Orientation Tensor ◽  
Fiber Orientation Distribution ◽  
Dimensional Simulation

This paper presents three-dimensional simulation of fiber suspension flows in a cavity using the Finite Volume Method (FVM). The numerical simulation model described makes it possible to predict the propagation of the fiber-polymer solution and fiber orientation during the filling phase. Therefore, the objective of the work is to develop a Computational Fluid Dynamics (CFD) model to simulate and characterize the fiber suspension flow in three dimensional cavities. The model is intended to describe the fiber orientation distribution in three dimensional mold cavities. The continuity, momentum, energy and the fiber orientation equations are solved using the FVM. The flow is considered to be incompressible, non-isothermal, transient, and to behave as non-Newtonian fluid. A numerical analysis is presented to illustrate the application of the FVM to dilute suspension flows in injection molding processes. The volume-of-fluid method is employed to describe the flow of the two incompressible, immiscible phases, i.e., liquid suspension and air. Since the flow is a non-Newtonian, the Cross model is used to describe the shear-thinning behavior of the suspension. The governing equations of the flow and the fiber are implemented and solved by means of the open source code OpenFOAM. The evolution equation of the fiber orientation contains a fourth order orientation tensor which is approximated in terms of second order tensor through the use of appropriate closure rules. In this study the Hybrid closure model of Advani and Tucker is used to approximate the fourth order orientation tensor. To validate the numerical algorithm, test cases of suspension flow in a rectangular cavity are modeled for different fiber-polymer matrices. The numerical results are compared with available experimental findings and with those of Newtonian flows.

scholarly journals Mixing for suspension flows over skew-translations and time-changes of quasi-abelian filiform nilflows

2018 ◽  
Vol 39 (12) ◽  
pp. 3407-3436 ◽  
Author(s):  
DAVIDE RAVOTTI
Keyword(s):  
Fourier Coefficients ◽  
Continuous Functions ◽  
Dense Subspace ◽  
Dimensional Torus ◽  
Smooth Functions ◽  
Suspension Flows ◽  
Time Changes ◽  
Uniquely Ergodic ◽  
Dense Set ◽  
Roof Function

We consider suspension flows over uniquely ergodic skew-translations on a $d$-dimensional torus $\mathbb{T}^{d}$ for $d\geq 2$. We prove that there exists a set $\mathscr{R}$ of smooth functions, which is dense in the space $\mathscr{C}(\mathbb{T}^{d})$ of continuous functions, such that every roof function in $\mathscr{R}$ which is not cohomologous to a constant induces a mixing suspension flow. We also construct a dense set of mixing examples which is explicitly described in terms of their Fourier coefficients. In the language of nilflows on nilmanifolds, our result implies that, for every uniquely ergodic nilflow on a quasi-abelian filiform nilmanifold, there exists a dense subspace of smooth time-changes in which mixing occurs if and only if the time-change is not cohomologous to a constant. This generalizes a theorem by Avila, Forni and Ulcigrai [Mixing for time-changes of Heisenberg nilflows. J. Differential Geom.89(3) (2011), 369–410] for the classical Heisenberg group.

scholarly journals Measures of maximal entropy for suspension flows over the full shift

2019 ◽  
Vol 294 (1-2) ◽  
pp. 769-781 ◽  
Author(s):  
Tamara Kucherenko ◽  
Daniel J. Thompson
Keyword(s):  
Maximal Entropy ◽  
Suspension Flows ◽  
Full Shift ◽  
Measures Of Maximal Entropy

Human Platelets Exposed to Mechanical Stresses Express a Potent Lipoxygenase Product

1992 ◽  
Vol 68 (05) ◽  
pp. 589-594 ◽  
Author(s):  
Alon Margalit ◽  
Avinoam A Livne
Keyword(s):  
Regulatory Volume Decrease ◽  
Human Platelets ◽  
Mechanical Stresses ◽  
Arterial Stenosis ◽  
Platelet Suspension ◽  
Suspension Flows ◽  
Lipoxygenase Product ◽  
Pathological Conditions ◽  
K Permeability ◽  
Volume Decrease

SummaryHuman platelets exposed to hypotonicity undergo regulatory volume decrease (RVD), controlled by a potent, yet labile, lipoxygenase product (LP). LP is synthesized and excreted during RVD affecting selectively K+ permeability. LP is assayed by its capacity to reconstitute RVD when lipoxygenase is blocked. Centrifugation for preparing washed platelets (1,550 × g, 10 min) is sufficient to express LP activity, with declining potency in repeated centrifugations, indicating that it is not readily replenish-able. When platelet suspension flows in a vinyl tubing (1 mm i.d.), at physiological velocity, controlled at 90–254 cm/s, LP formation increases as a function of velocity but declines as result of increasing the tubing length. Stirring the platelets in an aggregometer cuvette for 30 s, yields no LP unless the stirring is intermittent. No associated platelet lysis or aggregation are observed following the mechanical stress applications. These results demonstrate that although mechanical stresses result in LP production, the mode of its application plays a major role. These results may indicate that LP is synthesized under pathological conditions and could be of relevance to platelets behavior related to arterial stenosis.

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