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Finite current stationary states of random walks on one-dimensional lattices with aperiodic disorder

Hiroshi Miki
2016 Physica A: Statistical Mechanics and its Applications  
Three aperiodic sequences, the Thue-Morse (TM), the paperfolding (PF), and the Rudin-Shapiro (RS) sequences, are used to construct the aperiodic disorder.  ...  These are binary sequences, composed of two symbols A and B, and the ratio of the number of As to that of Bs converges to unity in the infinite sequence length limit, but their effects on diffusional behavior  ...  research was supported by the initiative-based project E-05 "Creation and Sustainable Governance of New Commons through Foundation of Integrated Local Environmental Knowledge (ILEK)", Research Institute for  ... 
doi:10.1016/j.physa.2016.05.057 fatcat:lwcby2wgl5azrg3gboweawdelm

Quasiperiodic music

Darren C. Ong
2020 Journal of Mathematics and the Arts  
We also discuss connections between quasiperiodic music and other works of music theory and composition that make use of aperiodic order or periodic order with large periods, such as Lindenmayer systems  ...  The author also wishes to thank Jake and Jamie Fillman for many helpful discussions, Maria Mannone for creating that delightful design for the graphical abstract, as well as the anonymous reviewers for  ...  By the Morse-Hedlund Theorem (Baake & Grimm, 2013, Proposition 4.11) , for any aperiodic infinite string σ (n) ≥ n + 1.  ... 
doi:10.1080/17513472.2020.1766339 fatcat:pgorbm76ajexha3ftpdmkl3reu

On mixing in infinite measure spaces

U. Krengel, L. Sucheston
1968 Bulletin of the American Mathematical Society  
Examples of exact endomorphisms are provided by unilateral shifts on stochastic processes with infinite invariant measure and trivial remote c-algebra; e.g., null-recurrent aperiodic Markov chains or aperiodic  ...  measure, is that for each c>0 and for each FGSS p(A n r\F)-»0 uniformly in the class of all sequences (A n ) with A n E.Q>n and ix(A n ) <c.  ...  As applied to null-recurrent irreducible aperiodic Markov chains, Theorem 7 is a strengthening of a theorem of Orey (cf. [l]), which assumes that ƒ is one-dimensional (defined on integers).  ... 
doi:10.1090/s0002-9904-1968-12090-7 fatcat:cirn5nwu7nfznidqg6tjpohiwy

Aperiodic order and spectral properties [article]

Michael Baake, David Damanik, Uwe Grimm
2015 arXiv   pre-print
This article presents a very gentle introduction to the field of aperiodic order, aimed at a general audience.  ...  the letter (r or b) at position n in the bi-infinite sequence W .  ...  The surprising result is that the infinite sequence v you obtain in this way will exactly reproduce the sequence of colours in P , starting with the red point at position n = 0.  ... 
arXiv:1506.04978v1 fatcat:jekptg7dmrclriqfvyzjbiruvy

Note on the Merit Factors of Sequences [article]

N.A. Carella
2013 arXiv   pre-print
A method for estimating the merit factors of sequences will be provided.  ...  The result is also effective in determining the nonexistence of certain infinite collections of cyclic difference sets and cyclic matrices and associated binary sequences.  ...  The existence of an infinite collection sequences of bounded aperiodic autocorrelations | ρ(t) | ≤ c, for t ≢ 0 mod n, implies that the merit factors of orders o(n), using Proposition 11.  ... 
arXiv:math/0506048v4 fatcat:xuvlukc52fdztfvyt7d4s7ken4

Recognizability for sequences of morphisms [article]

Valérie Berthé, Wolfgang Steiner, Jörg Thuswaldner, Reem Yassawi
2017 arXiv   pre-print
As an application, for a recognizable sequence of morphisms, we obtain an almost everywhere bijective correspondence between the S-adic shift it generates, and the measurable Bratteli-Vershik dynamical  ...  We prove that a sequence of morphisms on alphabets of bounded size, such that compositions of consecutive morphisms are growing on all letters, is eventually recognizable for aperiodic points.  ...  on left infinite sequences.  ... 
arXiv:1705.00167v1 fatcat:xygk5nu6nzgohco5xtnf4qxwle

Furstenberg systems of bounded multiplicative functions and applications [article]

Nikos Frantzikinakis, Bernard Host
2019 arXiv   pre-print
We prove a structural result for measure preserving systems naturally associated with any finite collection of multiplicative functions that take values on the complex unit disc.  ...  One consequence of our structural result is that strongly aperiodic multiplicative functions satisfy the logarithmically averaged variant of the disjointness conjecture of Sarnak for a wide class of zero  ...  We say that f ∈ M is aperiodic (or non-pretentious using terminology from [18] ) if it averages to 0 on every infinite arithmetic progression, meaning, if E n∈N f (an + b) = 0, for all a, b ∈ N.  ... 
arXiv:1804.08556v3 fatcat:4hreex3jpvds7jpqrwgh2arpsq

On generalized low-rate denial-of-quality attack against Internet services

Yajuan Tang, Xiapu Luo, Qing Hui, Rocky K. C. Chang
2009 2009 17th International Workshop on Quality of Service  
As a result, we obtain for the first time optimal attack patterns for both periodic and aperiodic attacks. Extensive simulation results also agree with the analytical results.  ...  Second, we investigate the worst impacts of a DoQ attack by optimizing a utility function for the attacks.  ...  Moreover, if the attack sequence is an infinite sequence, then this subsequence is infinite as well.  ... 
doi:10.1109/iwqos.2009.5201419 dblp:conf/iwqos/TangLHC09 fatcat:537iz7znongr7nsmrgdijhi2gm

Aperiodicity in equilibrium systems: Between order and disorder [article]

Aernout C.D.van Enter
2013 arXiv   pre-print
Here we discuss some issues related to the notion and occurrence of aperiodic order in equilibrium statistical mechanics.  ...  Spatial aperiodicity occurs in various models and material s. Although today the most well-known examples occur in the area of quasicrystals, other applications might also be of interest.  ...  Acknowledgements: I wish to thank the conference organisers of ICQ12 for inviting me, and my coauthors for all they taught me.  ... 
arXiv:1310.0267v2 fatcat:ybbgczo3e5dzxd52c36pfesnxa

Catching and missing finite sets

Martin H. Ellis
1978 Canadian mathematical bulletin  
If T is a 1-1 bimeasurable measure-preserving aperiodic transformation on a probability space X which is a Lebesgue space, then {A:A<=^X and for almost every pair of finite sets F and G there is an neN  ...  satisfying F^T'A and GHTM.^} is dense in the cr-algebra of measurable sets.  ...  Let T be a 1-1 bimeasurable measure-preserving aperiodic transformation on a measure space X whose total measure is finite (by aperiodic we mean {x :3n G N + with 7^(x) = x} has measure zero).  ... 
doi:10.4153/cmb-1978-074-9 fatcat:zhzgu5lyundmze6cx2afmfsm34

Aperiodic Tilings and Entropy [chapter]

Bruno Durand, Guilhem Gamard, Anaël Grandjean
2014 Lecture Notes in Computer Science  
In this paper we present a construction of Kari-Culik aperiodic tile set - the smallest known until now. With the help of this construction, we prove that this tileset has positive entropy.  ...  Consider a bi-infinite sequence x n of positive real numbers, such that either x n+1 = 2x n or x n+1 = x n /3 for every n. It is easy to see that every such sequences are aperiodic.  ...  Imagine you are on an infinite, measured line, and you are making jumps of length x along the line.  ... 
doi:10.1007/978-3-319-09698-8_15 fatcat:joqxmsoujjdx3blcvxznuyo32m

Bratteli diagrams: structure, measures, dynamics [article]

S. Bezuglyi, O. Karpel
2015 arXiv   pre-print
This paper is a survey on general (simple and non-simple) Bratteli diagrams which focuses on the following topics: finite and infinite tail invariant measures on the path space X_B of a Bratteli diagram  ...  We also discuss the structure of Bratteli diagrams, orbit equivalence and full groups, homeomorphic measures.  ...  S.B. would like to thank the University of Iowa for the warm hospitality where the paper was finished.  ... 
arXiv:1503.03360v1 fatcat:r7o5jn4c6ffcdnballlki7zutu

Infinite Words with Well Distributed Occurrences [chapter]

Ĺubomíra Balková, Michelangelo Bucci, Alessandro De Luca, Svetlana Puzynina
2013 Lecture Notes in Computer Science  
In this paper we introduce the well distributed occurrences (WDO) combinatorial property for infinite words, which guarantees good behavior (no lattice structure) in some related pseudorandom number generators  ...  An infinite word u on a d-ary alphabet has the WDO property if, for each factor w of u, positive integer m, and vector v ∈ Z d m , there is an occurrence of w such that the Parikh vector of the prefix  ...  Acknowledgements The first author was supported by the Czech Science Foundation grant GAČR 13-03538S, and thanks L'Oréal Czech Republic for the Fellowship Women in Science.  ... 
doi:10.1007/978-3-642-40579-2_8 fatcat:o243vwtqgrdtxgd3cutiubdhbi

WHAT IS...Aperiodic Order?

Michael Baake, David Damanik, Uwe Grimm
2016 Notices of the American Mathematical Society  
This article provides a brief introductory account of the theory of aperiodic order.  ...  in which a sequence of measures { } converges to if and only if ( ) → ( ) for all continuous functions with compact support.  ...  As an example, consider the bi-infinite sequence … 0110100110010110|0110100110010110 … and notice that it is invariant under the square of the Thue-Morse substitution 0 ↦ 01, 1 ↦ 10.  ... 
doi:10.1090/noti1394 fatcat:hgn5ketkbjc7dinfdpoptv5jce

Emergent dimerization and localization in disordered quantum chains

André P. Vieira, José A. Hoyos
2018 Physical review B  
We uncover a novel mechanism for inducing a gapful phase in interacting many-body quantum chains.  ...  The mechanism is nonperturbative, being triggered only in the presence of both strong interactions and strong aperiodic (disordered) modulation.  ...  JAH also acknowledges the hospitality of the Aspen Center for Physics, and the financial support of the NSF and the Simons Foundation. We thank Thomas Vojta for useful discussions.  ... 
doi:10.1103/physrevb.98.104203 fatcat:g4nb275fz5a6fmy4tdcamycmci
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