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  • 1
    Electronic Resource
    Electronic Resource
    The dynamics of spatiotemporal modulations (1995)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 5 (1995), S. 578-588 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The modulational instability of traveling waves is often thought to be a crucial point in the mechanism of transition to space–time disorder and turbulence. The aim of this paper is to study the effect of spatiotemporal modulations on some dynamics u0(x,t), which may occur as an instability process when a control parameter varies, for instance. We analyze the properties of the modulated dynamics of the form g1(x)g2(t)u0(x,t) compared to those of the reference dynamics u0(x,t), using operator theory. We show that, if the reference dynamics is invariant under some space–time symmetry in the sense of Ref. [J. Nonlinear Sci. 2, 183 (1992)], the modulation has the effect of either deforming this symmetry or breaking it, depending on whether the corresponding operator remains unitary or not. We also demonstrate that the smallest Euclidean space containing the modulated dynamics has a dimension smaller than or equal to the smallest Euclidean space containing u0(x,t). The previous results are then applied to the case of modulated uniformly traveling waves. While the spatiotemporal translation invariance of the wave never persists in the presence of a modulation, the existence of a spatiotemporal symmetry depends on the resonance of the Fourier sidebands due to the modulation. In case of nonresonance, a spatiotemporal symmetry exists and is explicitly determined. In this situation, the modulated wave and the carrier wave have the same spectrum (up to a normalization factor), the same entropy, and the spatial (resp., temporal) two-point correlation is deformed only by the spatial (resp., temporal) modulation. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166127
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  • 2
    Electronic Resource
    Electronic Resource
    Describing the dynamics with a bi-orthogonal decomposition (1992)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 2 (1992), S. 315-321 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A space–time decomposition of a signal into orthogonal temporal modes (chronos) and orthogonal spatial modes (topos) for the analysis of the dynamics of CML closed to a Hopf bifurcation are used. Global energy and entropy as a tool to distinguish different kinds of dynamics in CML are introduced.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.165923
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  • 3
    Electronic Resource
    Electronic Resource
    Hemodynamic Effects of Elevation and Stabilization of the Heart During Off-Pump Coronary Surgery (2000)
    Oxford, UK : Blackwell Publishing Ltd
    Journal of cardiac surgery 15 (2000), S. 0 
    Details
    ISSN: 1540-8191
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Medicine
    Notes: Abstract  Background: Coronary artery bypass grafting (CABG) surgery is now being performed without the use of cardiopulmonary bypass (CPB). To achieve complete myocardial revascularization off-CPB, a technique has been developed to expose target coronary arteries while hemodynamics are maintained. Methods: Complete myocardial revascularization was performed in 18 consecutive patients. Exposure of target coronary arteries was achieved by a “single-suture” technique, placed in the oblique sinus of the pericardium. Traction on the suture elevates and rotates the heart, thereby exposing all target coronary arteries. Cardiac index (CI) and intracardiac pressures were measured with a Swan-Ganz catheter during the different phases of the operation. Results: All patients were successfully operated on without CPB. There were no postoperative complications or deaths. There were no major hemodynamic changes during the different stages of the operation; in other words, CI was unchanged during elevation of the heart and snaring of the main coronary branches. Pulmonary artery wedge pressure (PAWP) increased markedly during occlusion and stabilization of the circumflex coronary artery (p 〈 0.05). A marked increase in CI and cardiac output (CO) from baseline values was also recorded before chest closure (p 〈 0.05). Conclusion: Complete myocardial revascularization can be achieved safely without CPB. The single-suture technique allows for exposure of all target coronary arteries without hemodynamic compromise.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1540-8191.2000.tb01298.x
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  • 4
    Electronic Resource
    Electronic Resource
    Spatiotemporal and statistical symmetries (1995)
    Springer
    Journal of statistical physics 81 (1995), S. 793-828 
    Details
    ISSN: 1572-9613
    Keywords: Spatiotemporal complexity ; spatiotemporal symmetries ; statistical symmetries ; two-point correlations ; biorthogonal decomposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The notion of symmetries, either statistical or deterministic, can be useful for the characterization of complex systems and their bifurcations. In this paper, we investigate the connection between the (microscopic) spatiotemporal symmetries of a space-time functionu(x, t), on the one hand, and the (macroscopic) symmetries of statistical quantities such as the spatial (resp. temporal) two-point correlations and the spatial (resp. temporal) average, on the other hand. We show, how, under certain conditions, these symmetries are related to the symmetries of the orbits described byu(x, t) in the characteristic (phase) spaces. We also determine the largest group of spatiotemporal symmetries (in the sense introduced in our earlier work) satisfied by a given space-time functionu(x, t) and indicate how to extract the subgroups of point symmetries, namely those directly implemented on the space and time variables. Conversely, we determine all the functions invariant by a given space-time symmetry group. Finally, we illustrate all the previous points with specific examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02179258
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  • 5
    Electronic Resource
    Electronic Resource
    Scaling laws for all Liapunov exponents: Models and measurements (1988)
    Springer
    Journal of statistical physics 52 (1988), S. 259-265 
    Details
    ISSN: 1572-9613
    Keywords: Random matrices ; Liapunov exponents ; symplectic maps ; diamond model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We introduce simple diamond models of random symplectic matrices in order to study the scaling laws of all Liapunov exponents. These universal properties appear in physical problems that are modeled by transfer matrices: dynamical systems, random potentials, random fields, etc. Numerical experiments for the general case are in agreement with the results derived from the models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01016413
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  • 6
    Electronic Resource
    Electronic Resource
    Turbulence spectra (1992)
    Springer
    Journal of statistical physics 67 (1992), S. 203-228 
    Details
    ISSN: 1572-9613
    Keywords: Turbulence ; biorthogonal decomposition ; self-similarity ; fractals ; multifractals ; wavelets
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The scaling invariance of the Navier-Stokes equations in the limit of infinite Reynolds number is used to derive laws for the inertial range of the turbulence spectrum. Whether the flow is homogeneous or not, the spectrum is chosen to be that given by a well-chosen biorthogonal decomposition. If the flow is hoogeneous, this spectrum coincides with the classical Fourier (energy) spectrum which exhibits Kolmogorov's k−5/3 power law if the scaling exponent is assumed to be 1/3. In the more general case where the homogeneity assumption is relaxed, the spectrum is discrete and decays exponentially fast under the assumption that the flow is invariant (in a deterministic or statistical sense) under only one subgroup of the scaling coefficientλ of one scaling group of the equations (corresponding to one value of the scaling exponent). If the flow is invariant under two subgroups of scaling coefficientsλ andλ′, the spectrum becomes maximal, equal toR +. Finally, when a full symmetry, namely an invariance under a whole group, is assumed and the spectrum becomes continuous, the decaying law for the spectral density is derived and found to be independent of the specific value ofh These ideas are then applied to locally self-similar flows with multiple dilation centers (localized in space and time) and multiple scaling exponents, extending the concept of multifractals to space and time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01049031
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  • 7
    Electronic Resource
    Electronic Resource
    Wave propagation phenomena from a spatiotemporal viewpoint: Resonances and bifurcations (1994)
    Springer
    Journal of statistical physics 76 (1994), S. 1005-1043 
    Details
    ISSN: 1572-9613
    Keywords: Wave propagation ; spatiotemporal bifurcation theory ; biorthogonal decomposition ; Fourier analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract By using biorthogonal decompositions, we show how uniformly propagating waves, togehter with their velocity, shape, and amplitude, can be extracted from a spatiotemporal signal consisting of the superposition of various traveling waves. The interaction between the different waves manifests itself in space-time resonances in case of a discrete biorthogonal spectrum and in resonant wavepackets in case of a continuous biorthogonal spectrum. Resonances appear as invariant subspaces under the biorthogonal operator, which leads to closed sets of algebraic equations. The analysis is then extended to superpositions of dispersive waves for which the (Fourier) dispersion relation is no longer linear. We then show how a space-time bifurcation, namely a qualitative change in the spatiotemporal nature of the solution, occurs when the biorthogonal operator is a nonholomorphic function of a parameter. This takes place when two eigenvalues are degenerate in the biorthogonal spectrum and when the spatial and temporal eigenvectors rotate within each eigenspace. Such a scenario applied to the superposition of traveling waves leads to the generation of additional waves propagating at new velocities, which can be computed from the spatial and temporal eigenmodes involved in the process (namely the shape of the propagating waves slightly before the bifurcation). An eigenvalue degeneracy, however, does not necessarily lead to a bifurcation, a situation we refer to as being self-avoiding. We illustrate our theoretical predictions by giving examples of bifurcating and self-avoiding events in propagating phenomena.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02188696
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  • 8
    Electronic Resource
    Electronic Resource
    Spatiotemporal analysis of complex signals: Theory and applications (1991)
    Springer
    Journal of statistical physics 64 (1991), S. 683-739 
    Details
    ISSN: 1572-9613
    Keywords: Spatiotemporal complexity ; spatiotemporal chaos ; signal analysis ; Liapunov exponents ; coupled map lattices ; turbulence ; transition to turbulence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present a space-time description of regular and complex phenomena which consists of a decomposition of a spatiotemporal signal into orthogonal temporal modes that we call chronos and orthogonal spatial modes that we call topos. This permits the introduction of several characteristics of the signal, three characteristic energies and entropies (one temporal, one spatial, and one global), and a characteristic dimension. Although the technique is general, we concentrate on its applications to hydrodynamic problems, specifically the transition to turbulence. We consider two cases of application: a coupled map lattice as a dynamical system model for spatiotemporal complexity and the open flow instability on a rotating disk. In the latter, we show a direct relation between the global entropy and the different instabilities that the flow undergoes as Reynolds number increases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01048312
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