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Dynamical origin of complex motor patterns (Vol. 41, No. 6)
The average activity of a large set of forced, globally coupled excitable units fits the subtleties of the air pressure patterns used by domestic canaries during their song. Each excitable unit is the dynamical caricature of excitatory and inhibitory neural subpopulations in the neural song pathway. Upper panels show different experimental gestures. Lower panels display the simulations.
Many motor patterns in biology are surprisingly simple, particularly taking into account that they are generated by complex neural networks. During song, for example, some songbirds have to generate periodic fluctuations in their air sac pressure and syringeal muscle tension in order to achieve sounds with the adequate acoustic properties. For the case of domestic canaries, the different respiratory patterns used during song were found to be sub-harmonic solutions of a simple, low dimensional dynamical system. Yet, these gestures are generated by thousands of neurons operating in a non-synchronous regime. How can the average activity present the precise, non-trivial features of the solutions of a low dimensional nonlinear dynamical system?
Inspired by this example, we address the general issue of the emergence of low dimensional, non-trivial dynamics out of large, complex interacting units.
In the spirit of classical statistical mechanics, the equations obeyed by the order parameter of a population of globally coupled nonlinear units are derived. The analysis allows showing that non-trivial yet low-dimensional dynamics is possible in average, even in a non-synchronic regime, providing a new mechanism for dimensionality reduction in the dynamics of complex systems.
Dynamical origin of complex motor patterns
L.M. Alonso, J.A. Alliende and G.B. Mindlin, Eur. Phys. J. D 60, 361-367 (2010)
[Abstract] | [PDF]
Bose condensation gives new insight into turbulent advection (Vol. 41, No. 6)
Passive scalar turbulence describes the advection and diffusion of a scalar quantity (such as temperature or pollutant concentration) in a turbulent flow. It was rigorously proven in the 1990’s that the Kraichnan model, now widely hailed as the “Ising model of turbulence”, leads to statistical intermittency and anomalous scaling of the advected field, which means power law behaviour of the structure functions of the scalar with scaling exponents ζN depending in a nonlinear way on their order N. The emergence of anomalous scaling was traced to the existence of statistical integrals of motion showing up in the evolution of Lagrangian fluid particles and exponents ζN identified with the highest scaling dimension or degree of the corresponding so-called “zero modes” (homogeneous functions of interparticle distances, whose average in the N-particle configurational space is left invariant by the dynamics).
Analytical computations of zero modes and their degrees were, up to now, mostly done using perturbative methods around limiting values of parameters for which anomalous scaling disappears. It is shown in this paper that scaling dimensions of zero modes can be recast as eigenvalues of a many-body pseudo-Hamiltonian describing the dynamics of the Lagrangian particles in an appropriate comoving frame. A variational estimate for ζN is then obtained by using techniques borrowed from condensed matter physics and assuming Bose condensation of particles. A connection of zero modes with the extremal events leading to the formation of fronts of the scalar, as caught by the instanton formalism, is also established.
By bridging up the gap between the two most powerful tools (zero modes and instantons) introduced these last years in the study of the inertial range intermittency in turbulent systems, this works revives the hope that they might help us to unravel, once, the whole complexity of incompressible 3D Navier-Stokes turbulence.
Bose-like condensation of Lagrangian particles and higher-order statistics in passive scalar turbulent advection
T. Dombre, EPL, 91, 54002 (2010)
[Abstract]
Long-time behaviour of macroscopic quantum systems (Vol. 41, No. 6)
The renewed interest in the foundations of quantum statistical mechanics in recent years has led us to study John von Neumann's 1929 article on the quantum ergodic theorem (QET). We have found this almost forgotten article, which until now has been available only in German, to be a treasure chest, to be much misunderstood and very relevant to the recent discussion on the general and abstract reasons why, and the exact sense in which, an isolated macroscopic quantum system will approach thermal equilibrium from (more or less) any initial state. In his paper, von Neumann studied the long-time behaviour of macroscopic quantum systems. His main result, the QET, expresses so-called "normal typicality": for a typical finite family of commuting macroscopic observables, every initial wave function ψ(0) from a micro-canonical energy shell so evolves that for most times t in the long run, the joint probability distribution of these observables obtained from ψ(t) is close to their micro-canonical distribution.
In our commentary, we provide a gentle introduction to the QET and discuss its relevance to the approach to thermal equilibrium. There is, in fact, no consensus about the definition of thermal equilibrium for a quantum (or even a classical) system in microscopic terms; the main divide in the literature lies between the "ensemblists" who regard thermal equilibrium as a property of an ensemble (or a mixed state) and the "individualists" who regard thermal equilibrium as a property of an individual system (in a pure state). As we explain, von Neumann's concept of equilibrium is influenced by both views but mainly based on the individualist view, a view that has gained ground recently.
Long-time behaviour of macroscopic quantum systems - Commentary accompanying the English translation of John von Neumann’s 1929 article on the quantum ergodic theorem
S. Goldstein, J.L. Lebowitz, R. Tumulka and N. Zanghì, Eur. Phys. J. H 35, 173 (2010)
[Abstract]
Electrical breakdown in space-borne microwave equipment (Vol. 41, No. 6)
Example of a comparison between theoretical and experimental results for the distribution of impact energy of discharge electrons at the outer wave guide electrode. Lines 1 and 2 correspond to different theoretical predictions and are superimposed on the experimental results.
Electrical breakdown (multipactor) constitutes a severe problem in many modern microwave systems, e.g space borne communication equipment. The breakdown discharge tends to generate noise, change the device impedance, heat the device walls and may permanently damage the devices. The basic physics involved in the multipactor breakdown phenomenon is well known. However, new applications give rise to situations where previous results concerning breakdown are not applicable. The concomitant uncertainties in predicted breakdown power levels makes it necessary to allow for large safety margins in device specifications and/or to use expensive test procedures.
To improve the situation, a strong effort has been made within a close collaboration between Centre National d’Etudes Spatiales in Toulouse, France, Chalmers University of Technology, Gothenburg, Sweden, Institute of Applied Physics, Nizhny Novgorod, Russia and General Physics Institute, Moscow, Russia. The present paper reports on recent results obtained for coaxial waveguides, which are commonly used for transmission of microwaves. A comprehensive analysis is made of multipactor breakdown thresholds in such structures using theoretical modelling and numerical simulations, which are corroborated with results of detailed experiments.
The results provide new knowledge and prediction capability concerning multipactor breakdown in microwave systems involving coaxial waveguides and should be an important input for an upgrading of the document for European Cooperation for Space Standardization.
Experimental and numerical investigation of multipactor discharges in a coaxial waveguide
I.A. Kossyi, G.S. Luk’yanchikov, V.E. Semenov, N.A. Zharova, D. Anderson, M. Lisak and J. Puech, J. Phys. D: Appl. Phys. 43, 345206 (2010)
[Abstract]
