1,721,001 research outputs found
Deterministic Transport: From Normal to Anomalous Diffusion
Full text linkThe way in which macroscopic transport results from microscopic dynamics is one of the important questions in statistical physics. Dynamical systems theory play a key role in a resent advance in this direction. Offering relatively simple models which are easy to study, dynamical systems theory became a standard branch of modern nonequilibrium statistical physics. In the present work the deterministic diffusion generated by simple dynamical systems is considered. The deterministic nature of these systems is more clearly expressed through the dependencies of the transport quantities as functions of systems parameters. For fully hyperbolic dynamical systems these dependencies were found to be highly irregular and, in fact, fractal. The main focus in this work is on nonhyperbolic and on intermittent dynamical systems. First, the climbing sine map is considered which is a nonhyperbolic system with many physical applications. Then we treat anomalous dynamics generated by a paradigmatic subdiffusive map. In both cases these systems display deterministic transport which, under variation of control parameters, is fractal. For both systems we give an explanation of the observed phenomena. The third part of the thesis is devoted to the relation between chaotic and transport properties of dynamical systems. This question lies at the heart of dynamical systems theory. For closed hyperbolic dynamical systems the Pesin theorem links the sum of positive Lyapunov exponents to the Kolmogorov-Sinai entropy. For open hyperbolic systems the escape rate formula is valid. In this work we have formulated generalizations of these formulas for a class of intermittent dynamical systems where the chaotic properties are weaker
Vortices Termination in the Cardiac Muscle
No full textMethods for termination of three-dimensional electrical vortices in the heart are needed for development of patient-friendly cardiac defibrillation techniques (Nature 475, 235, 2011). The defibrillation technique used today is the delivery of a high-energy electric shock (360 J, 1 kV, 30 A, 12 ms, when applied externally) often associated with severe side effects. Developing low-energy defibrillation methods are hampered by two problems: the unknown locations of the cores of the vortices, and the unpredictable phases of the vortex waves rotating around these cores. The first problem has been resolved through the use of electric field pulses to excite the cores of all pinned vortices simultaneously. Approaches to solve the second problem are being developed. One of them is based on the phase scanning of all pinned vortices in parallel to hit the critical time window (“Vulnerable Window”, VW) of every pinned vortex. We investigate the related physical mechanisms and describe problems created by scanning. We describe also a mechanism by which a 3-dim scroll vortex may be terminated with a VW of the full 2π radians. It makes knowledge of the wave phase no longer required. We describe a mechanism terminating also a free (not pinned) vortex, when the vortex’s core passes not very far from a defect. About 500 experiments with termination of vortices during ventricular fibrillation in pig isolated hearts confirm that pinned vortices, hidden from direct observation, are significant in fibrillation. These results form a physical basis needed for creation of new effective methods for termination vortices underlying fibrillation
Deterministic active particles in the overactive limit
Full text linkWe consider two models of deterministic active particles in an external potential. In the limit where the speed of a particle is fixed, both models coincide and can be formulated as a Hamiltonian system, but only if the potential is time-independent. If the particles are identical, their interaction via a potential force leads to conservative dynamics with a conserved phase volume. In contrast, the phase volume is shown to shrink for non-identical particles
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Impact of local network characteristics on network reconstruction
No full textWhen a network is inferred from data, two types of errors can occur: false positive and false negative conclusions about the presence of links. We focus on the influence of local network characteristics on the probability α of false positive conclusions, and on the probability β of false negative conclusions, in the case of networks of coupled oscillators. We demonstrate that false conclusion probabilities are influenced by local connectivity measures such as the shortest path length and the detour degree, which can also be estimated from the inferred network when the true underlying network is not known a priori. These measures can then be used for quantification of the confidence level of link conclusions, and for improving the network reconstruction via advanced concepts of link weights thresholding.</p
A unified quantification of synchrony in globally coupled populations with the Wiener order parameter
Full text linkWe tackle the quantification of synchrony in globally coupled populations.
Furthermore, we treat the problem of incomplete observations when the
population mean field is unavailable, but only a small subset of units is
observed. We introduce a new order parameter and demonstrate its efficiency for
quantifying synchrony via monitoring general observables, regardless of whether
the oscillations can be characterized in terms of the phases. Under condition
of a significant irregularity in the dynamics of the coupled units, this order
parameter provides a unified description of synchrony in populations of units
of various complexity. The main examples include noise-induced oscillations,
coupled strongly chaotic systems, and noisy periodic oscillations. Furthermore,
we explore how this parameter works for the standard Kuramoto model of coupled
regular phase oscillators. The most significant advantage of our approach is
its ability to infer and quantify synchrony from the observation of a small
percentage of the units and even from a single unit, provided the observations
are sufficiently long
Dynamics of oscillator populations with disorder in the coupling phase shifts
Full text linkWe study populations of oscillators, all-to-all coupled by means of quenched disordered phase shifts. While there is no traditional synchronization transition with a nonvanishing Kuramoto order parameter, the system demonstrates a specific order as the coupling strength increases. This order is characterized by partial phase locking, which is put into evidence by the introduced correlation order parameter and via frequency entrainment. Simulations with phase oscillators, Stuart-Landau oscillators, and chaotic Roessler oscillators demonstrate similar scaling of the correlation order parameter with the coupling and the system size and also similar behavior of the frequencies with maximal entrainment at some finite coupling
Stochastic bursting in networks of excitable units with delayed coupling
No full textWe investigate the phenomenon of stochastic bursting in a noisy excitable unit with multiple weak delay feedbacks, by virtue of a directed tree lattice model. We find statistical properties of the appearing sequence of spikes and expressions for the power spectral density. This simple model is extended to a network of three units with delayed coupling of a star type. We find the power spectral density of each unit and the cross-spectral density between any two units. The basic assumptions behind the analytical approach are the separation of timescales, allowing for a description of the spike train as a point process, and weakness of coupling, allowing for a representation of the action of overlapped spikes via the sum of the one-spike excitation probabilities
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