Search results for "Statistical and Nonlinear Physics"
showing 10 items of 896 documents
Bifurcations of links of periodic orbits in non-singular Morse - Smale systems on
1997
The set of periodic orbits of a non-singular Morse - Smale (NMS) flow on defines a link; a characterization of all possible links of NMS flows on has been developed by Wada. In the frame of codimension-one bifurcations, this characterization allows us to study the restrictions a link requires for suffering a given bifurcation. We also derive the topological description of the new link and the possibility of relating links by a chain of this type of bifurcation.
Visible parts and dimensions
2003
We study the visible parts of subsets of n-dimensional Euclidean space: a point a of a compact set A is visible from an affine subspace K of n, if the line segment joining PK(a) to a only intersects A at a (here PK denotes projection onto K). The set of all such points visible from a given subspace K is called the visible part of A from K. We prove that if the Hausdorff dimension of a compact set is at most n−1, then the Hausdorff dimension of a visible part is almost surely equal to the Hausdorff dimension of the set. On the other hand, provided that the set has Hausdorff dimension larger than n−1, we have the almost sure lower bound n−1 for the Hausdorff dimensions of visible parts. We al…
One-dimensional families of projections
2008
Let m and n be integers with 0 < m < n. We consider the question of how much the Hausdorff dimension of a measure may decrease under typical orthogonal projections from onto m-planes provided that the dimension of the parameter space is one. We verify the best possible lower bound for the dimension drop and illustrate the sharpness of our results by examples. The question stems naturally from the study of measures which are invariant under the geodesic flow.
Comparison of discretization strategies for the model-free information-theoretic assessment of short-term physiological interactions
2023
This work presents a comparison between different approaches for the model-free estimation of information-theoretic measures of the dynamic coupling between short realizations of random processes. The measures considered are the mutual information rate (MIR) between two random processes [Formula: see text] and [Formula: see text] and the terms of its decomposition evidencing either the individual entropy rates of [Formula: see text] and [Formula: see text] and their joint entropy rate, or the transfer entropies from [Formula: see text] to [Formula: see text] and from [Formula: see text] to [Formula: see text] and the instantaneous information shared by [Formula: see text] and [Formula: see…
Convergence of KAM iterations for counterterm problems
1998
Abstract We analyse two iterative KAM methods for counterterm problems for finite-dimensional matrices. The starting point for these methods is the KAM iteration for Hamiltonians linear in the action variable in classical mechanics. We compare their convergence properties when a perturbation parameter is varied. The first method has no fixed points beyond a critical value of the perturbation parameter. The second one has fixed points for arbitrarily large perturbations. We observe different domains of attraction separated by Julia sets.
Filter approach to the stochastic analysis of MDOF wind-excited structures
1999
Abstract In this paper, an approach useful for stochastic analysis of the Gaussian and non-Gaussian behavior of the response of multi-degree-of-freedom (MDOF) wind-excited structures is presented. This approach is based on a particular model of the multivariate stochastic wind field based upon a particular diagonalization of the power spectral density (PSD) matrix of the fluctuating part of wind velocity. This diagonalization is performed in the space of eigenvectors and eigenvalues that are called here wind-eigenvalues and wind-eigenvectors, respectively. From the examination of these quantities it can be recognized that the wind-eigenvectors change slowly with frequency while the first wi…
Multiplicity results for systems of asymptotically linear second order equations
2002
Abstract We prove the existence and multiplicity of solutions, with prescribed nodal properties, for a BVP associated with a system of asymptotically linear second order equations. The applicability of an abstract continuation theorem is ensured by upper and lower bounds on the number of zeros of each component of a solution.
High-order harmonic generation via bound-bound transitions in an elliptically polarized laser field
2016
We use a simplified five-level system to investigate the high-order harmonic generation (HHG) spectrum emitted by an atom driven by a linearly or elliptically polarized laser field. For this model, the Schrödinger equation is exactly analytically reduced to the system of ordinary differential equations, which is solved numerically. Studying the intensity and polarization of the emitted radiation, we find that under high laser ellipticity the harmonic emission is suppressed. However, the harmonic intensity typically depends nonmonotonously on the laser ellipticity. Such anomalous behavior is very pronounced for the resonant harmonic. We offer an explanation of this behavior based on the incr…
Phase separation of symmetrical polymer mixtures in thin-film geometry
1995
Monte Carlo simulations of the bond fluctuation model of symmetrical polymer blends confined between two “neutral” repulsive walls are presented for chain lengthNA=NB=32 and a wide range of film thicknessD (fromD=8 toD=48 in units of the lattice spacing). The critical temperaturesTc(D) of unmixing are located by finite-size scaling methods, and it is shown that\(T_c (\infty ) - T_c (D) \propto D^{ - {1 \mathord{\left/ {\vphantom {1 {v_3 }}} \right. \kern-\nulldelimiterspace} {v_3 }}} \), wherev3≈0.63 is the correlation length exponent of the three-dimensional Ising model universality class. Contrary to this result, it is argued that the critical behavior of the films is ruled by two-dimensi…
Host–virus evolutionary dynamics with specialist and generalist infection strategies: Bifurcations, bistability, and chaos
2019
In this work, we have investigated the evolutionary dynamics of a generalist pathogen, e.g., a virus population, that evolves toward specialization in an environment with multiple host types. We have particularly explored under which conditions generalist viral strains may rise in frequency and coexist with specialist strains or even dominate the population. By means of a nonlinear mathematical model and bifurcation analysis, we have determined the theoretical conditions for stability of nine identified equilibria and provided biological interpretation in terms of the infection rates for the viral specialist and generalist strains. By means of a stability diagram, we identified stable fixed…