Spontaneous creation of macroscopic flow and metachronal waves in an array of cilia

Cells or bacteria carrying cilia on their surface show many striking features : alignment of cilia in an array, two-phase asymmetric beating for each cilium, coordination between cilia and existence of metachronal waves with a constant phase difference between two adjacent cilia. We give simple theoretical arguments based on hydrodynamic coupling and an internal mechanism of the cilium derived from the behavior of a collection of molecular motors, to account qualitatively for these cooperative features. Hydrodynamic interactions can lead to the alignment of an array of cilia. We study the effect of a transverse external flow and obtain a two-phase asymmetrical beating, faster along the flow and slower against the flow, proceeding around an average curved position. We show that an aligned array of cilia is able to spontaneously break the left-right symmetry and to create a global average flow. Metachronism arises as a local minimum of the beating threshold and leads to a rather constant flow

Topological entropy and periods of self–maps on compact manifolds

Let (M; f) be a discrete dynamical system induced by a self{map f defined on a smooth compact connected n{dimensional manifold M. We provide sufficient conditions in terms of the Lefschetz zeta function in order that: (1) f has positive topological entropy when f is C1, and (2) f has infinitely many periodic points when f is C1 and f(M) ⊆ Int(M). Moreover, for the particular manifolds Sn, Sn x Sm, CPn and HPn we improve the previous sufficient conditions.The first author of this work was partially supported by MINECO grant number MTM2014-51891-P and Fundación Séneca de la Región de Murcia grant number 19219/PI/14. The second author is partially supported by a MINECO grant MTM2013-40998-P, an AGAUR grant number 2014SGR-568, and the grants FP7-PEOPLE-2012-IRSES 318999 and 316338

The implicit theory of historical change in the work of Alan S. Milward

Alan S. Milward was an economic historian who developed an implicit theory of historical change. His interpretation which was neither liberal nor Marxist posited that social, political, and economic change, for it to be sustainable, had to be a gradual process rather than one resulting from a sudden, cataclysmic revolutionary event occurring in one sector of the economy or society. Benign change depended much less on natural resource endowment or technological developments than on the ability of state institutions to respond to changing political demands from within each society. State bureaucracies were fundamental to formulating those political demands and advising politicians of ways to meet them. Since each society was different there was no single model of development to be adopted or which could be imposed successfully by one nation-state on others, either through force or through foreign aid programs. Nor could development be promoted simply by copying the model of a more successful economy. Each nation-state had to find its own response to the political demands arising from within its society. Integration occurred when a number of nation– states shared similar political objectives which they could not meet individually but could meet collectively. It was not simply the result of their increasing interdependence. It was how and whether nation-states responded to these domestic demands which determined the nature of historical change.historical change,development,World Wars,Third Reich,Blitzkrieg,New Order,Vichy,Fascism,Grossraumwirtschaft,German question,reconstruction,golden age,integration,supranationality,Bretton Woods

Topological entropy of continuous self–maps on a graph

Let G be a graph and f be a continuous self–map on G. We provide sufficient conditions based on the Lefschetz zeta function in order that f has positive topological entropy. Moreover, for the particular graphs: p–flower graph, n-lips graph and (p+r1L1+:::+rsLs)–graph we are able to go further and state more precise conditions for having positive topological entropy.The second author is partially supported by the Ministerio de Economía, Industria y Competitividad, Agencia Estatal de Investigación grants MTM-2016-77278-P (FEDER) and MDM-2014-0445, the Agència de Gestió d’Ajuts Universitaris i de Recerca grant 2017SGR1617, and the H2020 European Research Council grant MSCA-RISE-2017-777911

Civilizaciondigital.org: la civilización digital

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