arXiv subjects

Thomas M. Antonsen

Publications and source records attributed to Thomas M. Antonsen.

45 records · Page 3Linked to original sources

arXiv2009

Sensor Based on Extending the Concept of Fidelity to Classical Waves

We propose and demonstrate a remote sensor scheme by applying the quantum mechanical concept of fidelity loss to classical waves. The sensor makes explicit use of time-reversal invariance and spatial reciprocity in a wave chaotic system to sensitively and remotely measure the presence of small perturbations. The loss of fidelity is measured through a classical wave-analog of the Loschmidt echo by employing a single-channel time-reversal mirror to rebroadcast a probe signal into the perturbed system. We also introduce the use of exponential amplification of the probe signal to partially overcome the effects of propagation losses and to vary the sensitivity.

nlin.CD↗

arXiv2009

The effect of short ray trajectories on the scattering statistics of wave chaotic systems

In many situations, the statistical properties of wave systems with chaotic classical limits are well-described by random matrix theory. However, applications of random matrix theory to scattering problems require introduction of system specific information into the statistical model, such as the introduction of the average scattering matrix in the Poisson kernel. Here it is shown that the average impedance matrix, which also characterizes the system-specific properties, can be expressed in terms of classical trajectories that travel between ports and thus can be calculated semiclassically. Theoretical results are compared with numerical solutions for a model wave-chaotic system.

cond-mat.stat-mech↗

arXiv2009

Large coupled oscillator systems with heterogeneous interaction delays

In order to discover generic effects of heterogeneous communication delays on the dynamics of large systems of coupled oscillators, this paper studies a modification of the Kuramoto model incorporating a distribution of interaction delays. By focusing attention on the reduced dynamics on an invariant manifold of the original system, we derive governing equations for the system which we use to study stability of the incoherent states and the dynamical transitional behavior from stable incoherent states to stable coherent states. We find that spread in the distribution function of delays can greatly alter the system dynamics.

nlin.CD↗

arXiv2009

Long Time Evolution of Phase Oscillator Systems

It is shown, under weak conditions, that the dynamical evolution of an important class of large systems of globally coupled, heterogeneous frequency, phase oscillators is, in an appropriate physical sense, time-asymptotically attracted toward a reduced manifold of system states. This manifold, which is invariant under the system evolution, was previously known and used to facilitate the discovery of attractors and bifurcations of such systems. The result of this paper establishes that attractors for the order parameter dynamics obtained by restriction to this reduced manifold are, in fact, the only such attractors of the full system. Thus all long time dynamical behavior of the order parameters of these systems can be obtained by restriction to the reduced manifold.

nlin.CD↗

arXiv2008

Echo Phenomena in Large Systems of Coupled Oscillators

As exemplified by the Kuramoto model, large systems of coupled oscillators may undergo a transition to phase coherence with increasing coupling strength. It is shown that below the critical coupling strength for this transition such systems may be expected to exhibit `echo' phenomena: a stimulation by two successive pulses separated by a time interval tau leads to the spontaneous formation of response pulses at a time tau, 2 tau, 3 tau ..., after the second stimulus pulse. Analysis of this phenomenon, as well as illustrative numerical experiments, are presented. The theoretical significance and potential uses of echoes in such systems are discussed.

nlin.CD↗

arXiv2008

Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators

It is shown that, in the infinite size limit, certain systems of globally coupled phase oscillators display low dimensional dynamics. In particular, we derive an explicit finite set of nonlinear ordinary differential equations for the macroscopic evolution of the systems considered. For example, an exact, closed form solution for the nonlinear time evolution of the Kuramoto problem with a Lorentzian oscillator frequency distribution function is obtained. Low dimensional behavior is also demonstrated for several prototypical extensions of the Kuramoto model, and time-delayed coupling is also considered.

nlin.CD↗

arXiv2005

Intermittency in Two-Dimensional Turbulence with Drag

We consider the enstrophy cascade in forced two-dimensional turbulence with a linear drag force. In the presence of linear drag, the energy wavenumber spectrum drops with a power law faster than in the case without drag, and the vorticity field becomes intermittent, as shown by the anomalous scaling of the vorticity structure functions. Using a previous theory, we compare numerical simulation results with predictions for the power law exponent of the energy wavenumber spectrum and the scaling exponents of the vorticity structure functions $ζ_{2q}$ obtained in terms of the distribution of finite time Lyapunov exponents. We also study, both by numerical experiment and theoretical analysis, the multifractal structure of the viscous enstrophy dissipation in terms of its Rényi dimension spectrum $D_q$ and singularity spectrum $f(α)$. We derive a relation between $D_q$ and $ζ_{2q}$, and discuss its relevance to a version of the refined similarity hypothesis. In addition, we obtain and compare theoretically and numerically derived results for the dependence on separation $r$ of the probability distribution of $δ_{\V{r}}ω$, the difference between the vorticity at two points separated by a distance $r$. Our numerical simulations are done on a $4096 \times 4096$ grid.

cond-mat.soft↗

arXiv2004

Experimental observation and characterization of the magnetorotational instability

Differential rotation occurs in conducting flows in accretion disks and planetary cores. In such systems, the magnetorotational instability can arise from coupling Lorentz and centrifugal forces to cause large radial angular momentum fluxes. We present the first experimental observation of the magnetorotational instability. Our system consists of liquid sodium between differentially rotating spheres, with an imposed coaxial magnetic field. We characterize the observed patterns, dynamics and torque increases, and establish that this instability can occur from a hydrodynamic turbulent background.

physics.flu-dyn↗

arXiv2004

Universal Impedance Fluctuations in Wave Chaotic Systems

We experimentally investigate theoretical predictions of universal impedance fluctuations in wave chaotic systems using a microwave analog of a quantum chaotic infinite square well potential. Our approach emphasizes the use of the radiation impedance to remove the non-universal effects of the particular coupling from the outside world to the scatterer. Specific predictions that we test include the probability distribution functions (PDFs) of the real (related to the local density of states in disordered metals) and imaginary parts of the normalized cavity impedance, the equality of the variances of these PDFs, and the dependence of the universal PDFs on a single control parameter characterizing the level of loss. We find excellent agreement between the statistical data and theoretical predictions.

cond-mat.dis-nn↗