Biomedical subjects

Michael A Zaks

Publications and source records attributed to Michael A Zaks.

6 recordsLinked to original sources

PubMed2006

Ferrofluidic torsional pendulum driven by oscillating magnetic field.

A thin disk-shaped container filled with a ferrofluid and suspended in a horizontal linearly polarized ac magnetic field can perform torsional vibrations around its vertical diameter. In contrast to a recently studied spherical pendulum, the cell is sensitive to the field direction: It exposes its edge to the stationary or slowly oscillating magnetic field, and its broad side to the field of a high frequency. When the amplitude of the latter field is increased, the state of rest gets destabilized, yielding to oscillations near the equilibrium. Further growth of the field strength results in the onset of the cell rotation. We describe sequences of local and global bifurcations which accompany those transitions.

Journal Article↗

PubMed2004

Nonlinear dynamics of a ferrofluid pendulum.

A ferrofluid torsion pendulum in an oscillating magnetic field exhibits a rich variety of nonlinear self-oscillatory regimes. The dynamics is governed by the system of coupled differential equations for the in- and off-axis components of the fluid magnetization and the pendulum angular deflection. In the limiting case of high driving frequency, the system reduces to the sole Rayleigh-type equation. Much more complicated temporal patterns arise when the field frequency and the pendulum eigen frequency are of the same order.

Journal Article↗

PubMed2003

Role of unstable periodic orbits in phase and lag synchronization between coupled chaotic oscillators.

An increase of the coupling strength in the system of two coupled Rössler oscillators leads from a nonsynchronized state through phase synchronization to the regime of lag synchronization. The role of unstable periodic orbits in these transitions is investigated. Changes in the structure of attracting sets are discussed. We demonstrate that the onset of phase synchronization is related to phase-lockings on the surfaces of unstable tori, whereas transition from phase to lag synchronization is preceded by a decrease in the number of unstable periodic orbits.

Models, Theoretical↗

PubMed2002

Steady stokes flow with long-range correlations, fractal fourier spectrum, and anomalous transport.

We consider viscous two-dimensional steady flows of incompressible fluids past doubly periodic arrays of solid obstacles. In a class of such flows, the autocorrelations for the Lagrangian observables decay in accordance with the power law, and the Fourier spectrum is neither discrete nor absolutely continuous. We demonstrate that spreading of the droplet of tracers in such flows is anomalously fast. Since the flow is equivalent to the integrable Hamiltonian system with 1 degree of freedom, this provides an example of integrable dynamics with long-range correlations, fractal power spectrum, and anomalous transport properties.

Journal Article↗

PubMed2002

Self-induced slow-fast dynamics and swept bifurcation diagrams in weakly desynchronized systems.

In systems close to the state of phase synchronization, the fast timescale of oscillations interacts with the slow timescale of the phase drift. As a result, "fast" dynamics is subjected to a slow modulation, due to which an autonomous system under fixed parameter values can imitate repeated bifurcational transitions. We demonstrate the action of this general mechanism for a set of two coupled autonomous chaotic oscillators and for a chaotic system perturbed by a periodic external force. In both cases, the Poincaré sections of phase portraits resemble bifurcation diagram of a logistic mapping with time-dependent parameter.

Journal Article↗

PubMed2001

Multifractal Fourier spectra and power-law decay of correlations in random substitution sequences.

Binary symbolic sequences produced by randomly alternating substitution rules are considered. Exact expressions for the characteristics of autocorrelations and power spectra are derived. The decay of autocorrelation function obeys the power law. The Fourier spectral measure is either absolutely continuous or a mixture of the absolutely continuous and singular continuous components. For the latter case, the multifractal characteristics of this measure are computed.

Journal Article↗