E. Ott

External periodic driving of large systems of globally coupled phase oscillators

Large systems of coupled oscillators subjected to a periodic external drive occur in many situations in physics and biology. Here the simple paradigmatic case of equal strength, all-to-all sine coupling of phase oscillators subject to a sinusoidal external drive, is considered. The stationary states and their stability are determined. Using the stability information and numerical experiments, parameter space phase diagrams showing when different types of system behavior apply are constructed, and the bifurcations marking transitions between different types of behavior are delineated. The analysis is supported by results of direct numerical simulation of an ensemble of oscillators.

Coupling of external radiation to circuitry inside complex EM environments

In this paper, we present a hybrid statistical model for confined electromagnetic environments with arbitrary geometry, coupled by electrically wide apertures, in presence of spatially localized sources and sinks. An external (oblique) plane wave is supposed to illuminate the aperture, which radiates inside a wave-chaotic cavity with distributed losses. The dependence of couple voltages on the external radiation is found to take place through a transfer-impedance that is a functional of the hybrid random coupling model. We compute this impedance numerically by the Montecarlo technique.

External radiation of complex cavities described by the random coupling model

This paper considers the problem of coupling of an external radiation to the field of a cavity with irregular shape. In particular, the connections of a statistical model based on random matrix theory, called random coupling model, to deterministic models is explored. The canonical expansion of cavity fields in eigenmodes is preserved, and the coupling of an incoming plane-wave is supposed to take place through a narrow aperture radiating inside the cavity. The fluctuation of the aperture radiation admittance is investigated in various cavity loss conditions. Obtained results constitute the basis for understanding the energy propagation through tightly coupled environments.

Uncovering interference paths in complex environments with the random coupling model

The electromagnetic stress onto circuitry inside enclosures is a complicated process made of several coupling paths originated by multiple sources. Those sources are treated as equivalent apertures, and the cavity is assumed to have irregular boundaries. Then, a statistical description relying on wave-chaos theory is more appropriate to describe the coupling process. The Gibbs maximum entropy principle is adopted to derive the probability density function of the single aperture power stressing onto a port arbitrarily located inside the enclosure. Achieved results can be used to estimate the number of coupling paths between interconnected environments.

Fractal Patterns of Tracers Advected by Smooth Temporally Irregular Fluid Flows and their Analysis by Use of Random Maps

Temporally irregular, large spatial scale, fluid advection of passive tracers occurs in a wide variety of situations. Our main point is that these situations can be conveniently conceptualized as resulting from successive application of a sequence of random maps. This viewpoint is numerically convenient and also provides a useful theoretical framework for dynamical-systems-based analyses of the resulting fractal patterns. Examples of three different situations are discussed: (i) the fractal distribution of passive scalar gradients, (ii) the fractal pattern formed by a scum floating on the surface of a moving fluid, and (iii) the pattern of particles entrained as they flow past an obstacle in an open flow.

Spectral statistics for systems with ray splitting

A finite reverberant system having a discontinuity in some physical parameter will exhibit the splitting of ray trajectories in the high‐frequency limit. It is known that this ray splitting can increase the amount of chaos in the ray trajectories [Couchman et al., Phys. Rev. A 46, 6193 (1992)]. This increase of chaos is expected to reveal itself in the eigenfrequency spectrum as a shift away from Poisson statistics and toward the Gaussian orthogonal ensemble (GOE) statistics of random matrix theory. Numerical results are presented that confirm the predicted shift in the spectral statistics. [Work supported by ONR and DOE.]

Feasibility of steady-state spheromak operation by ECRH current drive

The feasibility of steady-state spheromak operation using ECRH current drive is studied numerically. The model used comprises ray tracing and a linear relativistic treatment of current generation. It is assumed that the RF-generated current distribution will relax to that of the spheromak equilibrium. A reactor grade plasma with an average temperature of 18 keV, a density of 0.8 × 1020 m−3, a maximum magnetic field of 4 T and a fusion power of 2100 MW can be sustained by launching less than 100 MW of ECRH power near the plasma surface.