The Geometry of Synchronization (Long Version)

We graft synchronization onto Girard's Geometry of Interaction in its most concrete form, namely token machines. This is realized by introducing proof-nets for SMLL, an extension of multiplicative linear logic with a specific construct modeling synchronization points, and of a multi-token abstract machine model for it. Interestingly, the correctness criterion ensures the absence of deadlocks along reduction and in the underlying machine, this way linking logical and operational properties.Comment: 26 page

Synchronization of spin-torque driven nanooscillators for point contacts on a quasi-1D nanowire: Micromagnetic simulations

In this paper we present detailed numerical simulation studies on the synchronization of two spin-torque nanooscillators (STNO) in the quasi-1D geometry: magnetization oscillations are induced in a thin NiFe nanostripe by a spin polarized current injected via square-shaped CoFe nanomagnets on the top of this stripe. In a sufficiently large out-of-plane field, a propagating oscillation mode appears in such a system. Due to the absence of the geometrically caused wave decay in 1D systems, this mode is expected to enable a long-distance synchronization between STNOs. Indeed, our simulations predict that synchronization of two STNOs on a nanowire is possible up to the intercontact distance 3 mkm (for the nanowire width 50 nm). However, we have also found several qualitatively new features of the synchronization behaviour for this system, which make the achievement of a stable synchronization in this geometry to a highly non-trivial task. In particular, there exist a minimal distance between the nanocontacts, below which a synchronization of STNOs can not be achieved. Further, when the current value in the first contact is kept constant, the amplitude of synchronized oscillations depends non-monotonously on the current value in the second contact. Finally, for one and the same currents values through the contacts there might exist several synchronized states (with different frequencies), depending on the initial conditions.Comment: 13 pages with 4 figurews, recently submitted to PR

A three-sphere swimmer for flagellar synchronization

In a recent letter (Friedrich et al., Phys. Rev. Lett. 109:138102, 2012), a minimal model swimmer was proposed that propels itself at low Reynolds numbers by a revolving motion of a pair of spheres. The motion of the two spheres can synchronize by virtue of a hydrodynamic coupling that depends on the motion of the swimmer, but is rather independent of direct hydrodynamic interactions. This novel synchronization mechanism could account for the synchronization of a pair of flagella, e.g. in the green algae Chlamydomonas. Here, we discuss in detail how swimming and synchronization depend on the geometry of the model swimmer and compute the swimmer design for optimal synchronization. Our analysis highlights the role of broken symmetries for swimming and synchronization.Comment: 25 pages, 4 color figures, provisionally accepted for publication in the New Journal of Physic

Synchronization in disordered Josephson junction arrays: Small-world connections and the Kuramoto model

We study synchronization in disordered arrays of Josephson junctions. In the first half of the paper, we consider the relation between the coupled resistively- and capacitively shunted junction (RCSJ) equations for such arrays and effective phase models of the Winfree type. We describe a multiple-time scale analysis of the RCSJ equations for a ladder array of junctions \textit{with non-negligible capacitance} in which we arrive at a second order phase model that captures well the synchronization physics of the RCSJ equations for that geometry. In the second half of the paper, motivated by recent work on small world networks, we study the effect on synchronization of random, long-range connections between pairs of junctions. We consider the effects of such shortcuts on ladder arrays, finding that the shortcuts make it easier for the array of junctions in the nonzero voltage state to synchronize. In 2D arrays we find that the additional shortcut junctions are only marginally effective at inducing synchronization of the active junctions. The differences in the effects of shortcut junctions in 1D and 2D can be partly understood in terms of an effective phase model.Comment: 31 pages, 21 figure

Synchronization of the Frenet-Serret linear system with a chaotic nonlinear system by feedback of states

A synchronization procedure of the generalized type in the sense of Rulkov et al [Phys. Rev. E 51, 980 (1995)] is used to impose a nonlinear Malasoma chaotic motion on the Frenet-Serret system of vectors in the differential geometry of space curves. This could have applications to the mesoscopic motion of biological filamentsComment: 12 pages, 7 figures, accepted at Int. J. Theor. Phy

Synchronization in a ring of pulsating oscillators with bidirectional couplings

We study the dynamical behavior of an ensemble of oscillators interacting through short range bidirectional pulses. The geometry is 1D with periodic boundary conditions. Our interest is twofold. To explore the conditions required to reach fully synchronization and to invewstigate the time needed to get such state. We present both theoretical and numerical results.Comment: Revtex, 4 pages, 2 figures. To appear in Int. J. Bifurc. and Chao