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The spectrum of dynamical systems arising from substitutions of constant length

F. M. Dekking
1978 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete  
A lar ge class of examples of minimal flows are given by those arising from substitutions.  ...  An interesting side result is that if (X,T,y) is a dyna mical system arising from a substitution of constant length then T n is minimal if and only if T n is ergodic.  ...  J>iJ Ui- According to theorem 1 (X(e),T) is topologically isomorphic to a substitution flow of constant length if X 2 = 0 . We conjecture that this condition is also necessary.  ... 
doi:10.1007/bf00534241 fatcat:xbgqpvqwdbe7rje55vctuxj6ga

Mixing properties of substitutions

F. M. Dekking, M. Keane
1978 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete  
We show that the minimal flow (X, T) arising from n is topologically strongly mixing of order two, but not of order three, pro viding the first example of a minimal flow with these properties.  ...  (If minimality is not required, an example can be found in [6] .) It is also proved that no minimal flow arising from a substitution can be topologically strongly mixing of all orders.  ... 
doi:10.1007/bf00534205 fatcat:xzteegizjfh2hdk7b6yahjyaa4

Page 422 of Mathematical Reviews Vol. 44, Issue 2 [page]

1972 Mathematical Reviews  
The authors examine the structure of constant length substitution minimal sets in the bilateral 2-shift (Q, ¢), i.e., minimal sets arising from a substitution of the form 6(0)=aga,, ---, 4,1, (1) =bob,  ...  It is | shown by spectral considerations that minimal sets arising from continuous substitutions are never isomorphic to those from discrete substitutions.  ... 

Page 1689 of Mathematical Reviews Vol. 45, Issue 6 [page]

1973 Mathematical Reviews  
This paper is devoted to an extensive and rather deep study of substitution minimal sets (M,c) of constant length, i.e., minimal sets of the symbolic flow on n symbols that arise from a map of the form  ...  0(i)=2,%,---x,, where 0sisn—-1, 0S2,<Sn-—1, and the length r is constant for each i.  ... 

Substitutions, tiling dynamical systems and minimal self-joinings [article]

Younghwan Son
2014 arXiv   pre-print
We show that the substitution subshifts arising from \theta and \eta have minimal self-joinings and are mildly mixing.  ...  We also give a criterion for 1-dimensional tiling systems arising from \theta or \eta to have minimal self-joinings. We apply this to obtain examples of mildly mixing 1-dimensional tiling systems.  ...  Let ζ be an aperiodic, primitive, constant length substitution on the alphabet A = {0, 1}, where the number of 0s occurring in ζ(0) is different from the number of 0s occurring in ζ(1).  ... 
arXiv:1402.5672v1 fatcat:lnduawthgnegtcqvclsudxz7la

Pure Discrete Spectrum for One-dimensional Substitution Systems of Pisot Type

V. F. Sirvent, B. Solomyak
2002 Canadian mathematical bulletin  
flow.  ...  As a corollary, we prove pure discrete spectrum for every R-action associated with a two-symbol substitution of Pisot type (this is conjectured for an arbitrary number of symbols).  ...  The substitution ζ is said to have constant length if i → |ζ(i)| is constant on A; otherwise, it has non-constant length. Definition.  ... 
doi:10.4153/cmb-2002-062-3 fatcat:vq6nt7hxhnd3zadyw5mnnapopu

A theoretical model of the pressure field arising from asymmetric intraglottal flows applied to a two-mass model of the vocal folds

Byron D. Erath, Sean D. Peterson, Matías Zañartu, George R. Wodicka, Michael W. Plesniak
2011 Journal of the Acoustical Society of America  
A theoretical flow solution is presented for predicting the pressure distribution along the vocal fold walls arising from asymmetric flow that forms during the closing phases of speech.  ...  The method was validated with experimental velocity data from 7.5 times life-size vocal fold models, acquired for varying flow rates and glottal divergence angles.  ...  ACKNOWLEDGMENTS This work was supported by a grant from the National Science Foundation (CBET 0828903).  ... 
doi:10.1121/1.3586785 pmid:21786907 fatcat:ljlxpnlm3ja6tblbmwfkrkb264

Flow views and infinite interval exchange transformations for recognizable substitutions [article]

Natalie Priebe Frank
2021 arXiv   pre-print
As an example of utility, some spectral results for constant-length substitutions are included.  ...  A flow view is the graph of a measurable conjugacy between a substitution or S-adic subshift and an exchange of infinitely many intervals (IIET) in [0,1].  ...  Since µ(E δ ) = m(D δ ), this contradicts the definition of D δ and completes the proof. 5.4. Pictures for the non-constant length case.  ... 
arXiv:2103.07997v3 fatcat:u3vkd22opvbz5ouvf75d3tawve

A general model for metabolic scaling in self-similar asymmetric networks

Alexander Byers Brummer, Van M. Savage, Brian J. Enquist, Kiran Raosaheb Patil
2017 PLoS Computational Biology  
Biological allometries, such as metabolic scaling, have been hypothesized to result from selection to maximize how vascular networks fill space yet minimize internal transport distances and resistances  ...  Our work shows how space-filling and fluid flow principles constrain allowed branching morphologies within the context of our model.  ...  Acknowledgments The authors wish to thank Alex Cronin, Drew Milsom, and Elif Tekin for their assistance in editing early versions of the manuscript, the Santa Fe Institute for hosting the authors, and  ... 
doi:10.1371/journal.pcbi.1005394 pmid:28319153 pmcid:PMC5378416 fatcat:e3nc4yorare5fpu3in7n4q2yku

On an integrable magnetic geodesic flow on the two-torus [article]

I.A. Taimanov
2016 arXiv   pre-print
We completely integrate the magnetic geodesic flow on a flat two-torus with the magnetic field F = cos (x) dx ∧ dy and describe all contractible periodic magnetic geodesics.  ...  However the lengths of noncontractible contours are at least √ 2E 2π, i.e., the length of γ +− and of γ −+ which are minimal non-contractible geodesics on T 2 .  ...  Theorems 2 and 3 say that the flow in study supplies an explicit example of such a situation. Actually this article arises as an answer to the question by A.  ... 
arXiv:1508.03745v2 fatcat:bg22lobzb5fszp5icdvuv6sydu

The effect of confining boundaries on viscous gravity currents

2007 Journal of Fluid Mechanics  
Similarity solutions are obtained from the governing mathematical equations and compared with closely matching data from laboratory experiments in which the propagation of glycerine along different channels  ...  Geological applications of the results are discussed briefly.  ...  These results are only valid for the instantaneous release of a fixed volume of viscous fluid. Additional relationships will arise if the discharge rate is not constant.  ... 
doi:10.1017/s0022112007005174 fatcat:daeossho65c7tmapujq342ugzm

Self-similarity and spectral theory: on the spectrum of substitutions [article]

Alexander I. Bufetov, Boris Solomyak
2021 arXiv   pre-print
In this survey of the spectral properties of substitution dynamical systems we consider primitive aperiodic substitutions and associated dynamical systems: ℤ-actions and ℝ-actions, the latter viewed as  ...  tiling flows.  ...  Substitutions of non-constant length.  ... 
arXiv:2111.01109v2 fatcat:apzci5lcrfhf3o3z2qctmqcchu

Induced airflow in flying insects I. A theoretical model of the induced flow

S. P. Sane
2006 Journal of Experimental Biology  
In this analysis, I adopt Ellington's method and represent c(r) using Beta functions appropriately rescaled with a constant non-dimensional parameter B i , the ratio of maximum non-dimensional chord length  ...  List of symbols A area of actuator disk AR aspect ratio B i chord rescale ratio c mean chord length c(r) chord length as a function of radial position c(r) non-dimensional chord length C L lift coefficient  ... 
doi:10.1242/jeb.01957 pmid:16354776 fatcat:dbnwvvxpcfdlbf6j2bl5wahdm4

Page 197 of Mathematical Reviews Vol. 57, Issue 1 [page]

1979 Mathematical Reviews  
Japan ily of 24 (1972), 285-306; MR 45 #2688] with certain restrictions on 0.) r such The author also considers substitutions of non-constant length. on of | For such a substitution @ on r symbols {0,  ...  The author shows that if (/,, ---,/,_,) is a right eigenvector of the no. 5, | matrix (/,,), then (X(4), T) is topologically isomorphic to a mini- rnaul) mal set arising from a substitution of constant  ... 

Optical flow: a curve evolution approach

A. Kumar, A.R. Tannenbaum, G.J. Balas
1996 IEEE Transactions on Image Processing  
A novel approach for the computation of optical flow based on an L1 type minimization is presented.  ...  A numerical approach based on computation of evolving curves is proposed for computing the optical flow field and results of experiments are presented.  ...  The level set is given as fIf(x(s), y(s)) = IC = constant. (2.10) Differentiating twice, solving for the various derivatives w.r.t the arc-length and then simply substituting in: ( 2.11) we may write  ... 
doi:10.1109/83.491336 pmid:18285148 fatcat:5w5gdfxh3baxjngntejxzhj77i
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