Spectral direct numerical simulations of incompressible MHD turbulence at a resolution of up to ${1024}^3$ collocation points are presented for a statistically isotropic system as well as for a setup with an imposed strong mean magnetic field. The spectra of residual energy, $E_k^{\mathrm{R}}=|E_k^{\mathrm{M}}-E_k^{\mathrm{K}}|$, and total energy, $E_k=E_k^{\mathrm{K}}+E_k^{\mathrm{M}}$, are observed to scale self-similarly in the inertial range as $E_k^{\mathrm{R}}\sim k^{-7/3}$, $E_k\sim k^{-5/3}$ (isotropic case) and $E_{k_{\perp }}^{\mathrm{R}}\sim k_{\perp }^{-2}$, $E_{k_{\perp }}\sim k_{\perp }^{-3/2}$ (anisotropic case, perpendicular to the mean field direction). A model of dynamic equilibrium between kinetic and magnetic energy, based on the corresponding evolution equations of the eddy-damped quasinormal Markovian closure approximation, explains the findings. The assumed interplay of turbulent dynamo and Alfvén effect yields $E_k^{\mathrm{R}}\sim k{E}_k^2$, which is confirmed by the simulations.

Level fluctuations in a quantum system have been used to characterize quantum chaos using random matrix models. Recently time series methods were used to relate the level fluctuations to the classical dynamics in the regular and chaotic limit. In this, we show that the spectrum of the system undergoing order to chaos transition displays a characteristic $f^{-\gamma }$ noise and $\gamma$ is correlated with the classical chaos in the system. We demonstrate this using a smooth potential and a time-dependent system modeled by Gaussian and circular ensembles, respectively, of random matrix theory. We show the effect of short periodic orbits on these fluctuation measures.

We clarify the nature of coupling between surface plasmon polaritons (SPP) and transmitted light in metallic nanoslit structures. The coupling strength is found to be the product of the geometric opening ratio, the aperture momentum, and the Fabry-Perot factor. We determine the effective coupling, which includes corrections due to other SPPs, and show that this effective coupling causes enhanced transmission with redshifted or blueshifted transmission peaks. Without coupling, SPP is proven to suppress transmission due to the equipartition of diffraction orders. These results show good agreement with experiment.

We study interface thermal resistance (ITR) in a system consisting of two dissimilar anharmonic lattices exemplified by the Fermi-Pasta-Ulam and Frenkel-Kontorova models. It is found that the ITR is asymmetric; namely, it depends on how the temperature gradient is applied. The dependence of the ITR on the coupling constant, temperature, temperature difference, and system size is studied. Possible applications in nanoscale heat management and control are discussed.

For a two-dimensional fluid in a square domain with no-slip walls, new direct numerical simulations reveal that the transition from steady to chaotic flow occurs through a sequence of various periodic and quasiperiodic flows, similar to the well-known Ruelle-Takens-Newhouse scenario. For all solutions beyond the ground state, the phenomenology is dominated by a domain-filling circulation cell, whereas the associated symmetry is reduced from the full symmetry group of the square to rotational symmetry over an angle $\pi$. The results complement both laboratory experiments in containers with rigid walls and numerical simulations on double-periodic domains.

A one-parameter family of periodic orbits with frequency $\omega$ and energy $E$ of an autonomous Hamiltonian system is degenerate when $E^{\prime }(\omega )=0$. In this paper, new features of the nonlinear bifurcation near this degeneracy are identified. A new normal form is found where the coefficient of the nonlinear term is determined by the curvature of the energy-frequency map. An important property of the bifurcating “homoclinic torus” is the homoclinic angle and a new asymptotic formula for it is derived. The theory is constructive, and so is useful for physical applications and in numerics.

Multifractal or multiaffine analysis is a promising new branch of methods in nonlinear physics for the study of turbulent flows and turbulentlike systems. In this Letter we present a new method based on the multifractal singularity extraction technique, the maximum singular stream-function method (MSSM), which provides a first order approximation to the stream function from experimental data in 2D turbulent systems. The essence of MSSM relies in relating statistical properties associated with the energy cascade in flows with geometrical properties. MSSM is a valuable tool to process sparse collections of data and to obtain instant estimates of the velocity field. We show an application of MSSM to oceanography as a way to obtain the current field from sea surface temperature satellite images; we validate the result with independent dynamical information obtained from sea level measurements.

We show that a single rectangular hole in a metallic film exhibits transmission resonances that appear near the cutoff wavelength of the hole waveguide. For light polarized with the electric field pointing along the hole’s short axis, it is shown that the normalized-to-area transmittance at resonance is proportional to the ratio between the long and short sides, and to the dielectric constant inside the hole. Importantly, this resonant transmission process is accompanied by a huge enhancement of the electric field at both entrance and exit interfaces of the hole.

We report experiments on spontaneous imbibition of a viscous fluid by a model porous medium in the absence of gravity. The average position of the interface satisfies Washburn’s law. Scaling of the interface fluctuations suggests a dynamic exponent $z\simeq 3$, indicative of global dynamics driven by capillary forces. The complete set of exponents clearly shows that interfaces are not self-affine, exhibiting distinct local and global scaling, both for time ($\beta =0.64\pm 0.02$, ${\beta }^{*}=0.33\pm 0.03$) and space ($\alpha =1.94\pm 0.20$, ${\alpha }_{\mathrm{loc}}=0.94\pm 0.10$). These values are compatible with an intrinsic anomalous scaling scenario.

We study Poincaré recurrence of chaotic attractors for regions of finite size. Contrary to the standard case, where the size of the recurrent regions tends to zero, the measure is no longer supported solely by unstable periodic orbits of finite length inside it, but also by other special recurrent trajectories, located outside that region. The presence of the latter leads to a deviation of the distribution of the Poincaré first return times from a Poissonian. Consequently, by taking into account the contribution of these special recurrent trajectories, a corrected estimate of the measure is obtained. This has wide experimental implications, as in the laboratory all returns can exclusively be observed for regions of finite size, and only unstable periodic orbits of finite length can be detected.

We study the problem of heat conduction in a mass-disordered two-dimensional harmonic crystal. Using two different stochastic heat baths, we perform simulations to determine the system size ($L$) dependence of the heat current ($J$). For white noise heat baths we find that $J\sim 1/L^{\alpha }$ with $\alpha \approx 0.59$, while correlated noise heat baths give $\alpha \approx 0.51$. A special case with correlated disorder is studied analytically and gives $\alpha =3/2$, which agrees also with results from exact numerics.

We theoretically predict and experimentally demonstrate chaotic behaviors in a system comprising of three-level atoms inside an optical ring cavity. This electromagnetically induced transparency (EIT) system is driven to chaos through period-doubling route by reducing the frequency detuning of the coupling laser beam. The chaos occurs in a different parametric regime as previously predicted and is believed to be caused by the enhanced dispersion and nonlinearity due to induced atomic coherence in such EIT system.

We propose and analyze a scheme for ultrafast spectroscopy with nanometer spatial and femtosecond temporal resolution. The interaction of polarization-shaped laser pulses with a nanostructure allows us to control the spatial and temporal evolution of the optical near field. Employing a learning algorithm, the field is tailored such that pump and probe excitation occur at different positions and at different times. Both excitations can be restricted to subdiffraction extensions and are separable on a nanometer length scale. This enables the direct spatial probing of nanoscale energy transfer or charge transfer processes.

We study the pattern formation in a lattice of locally coupled phase oscillators with quenched disorder. In the synchronized regime quasiregular concentric waves can arise which are induced by the disorder of the system. Maximal regularity is found at the edge of the synchronization regime. The emergence of the concentric waves is related to the symmetry breaking of the interaction function. An explanation of the numerically observed phenomena is given in a one-dimensional chain of coupled phase oscillators. Scaling properties, describing the target patterns are obtained.

By molecular dynamics simulations, the boundary condition for the Boltzmann equation at a vapor-liquid interface is found to be the product of three one-dimensional Maxwellian distributions for the three velocity components of vapor molecules and a factor including a well-defined condensation coefficient. The Maxwellian distribution for the velocity component normal to the interface is characterized by the liquid temperature, as in a conventional model boundary condition, while those for the tangential components are prescribed by a different temperature, which is a linear function of energy flux across the interface. The condensation coefficient is found to be constant and equal to the evaporation coefficient determined by the liquid temperature only.

A procedure is presented for computing the phase space volume of initial conditions for trajectories that escape or “react” from a multidimensional potential well. The procedure combines a phase space transition state theory, which allows one to construct dividing surfaces that are free of local recrossing and that minimize the directional flux, and a classical spectral theorem. The procedure gives the volume of reactive initial conditions in terms of a sum over each entrance channel of the well of the product of the phase space flux across the dividing surface associated with the channel and the mean residence time in the well of trajectories which enter through the channel. This approach is illustrated for HCN isomerization in three dimensions, for which the method is several orders of magnitude more efficient than standard Monte Carlo sampling.

The phenomenon of irregular cessation and subsequent reversal of the large-scale circulation in turbulent Rayleigh-Bénard convection is theoretically analyzed. The force and thermal balance on a single plume detached from the thermal boundary layer yields a set of coupled nonlinear equations, whose dynamics is related to the Lorenz equations. For Prandtl and Rayleigh numbers in the range ${10}^{-2}\le \mathrm{Pr}\le {10}^3$ and ${10}^7\le \mathrm{Ra}\le {10}^{12}$, the model has the following features: (i) chaotic reversals may be exhibited at $\mathrm{Ra}\ge {10}^7$; (ii) the Reynolds number based on the root mean square velocity scales as ${\mathrm{Re}}_{\mathrm{rms}}\sim {\mathrm{Ra}}^{[0.41\cdots 0.47]}$ (depending on Pr), and as ${\mathrm{Re}}_{\mathrm{rms}}\sim {\mathrm{Pr}}^{-[0.66\cdots 0.76]}$ (depending on Ra); and (iii) the mean reversal frequency follows an effective scaling law $\omega /(\nu L^{-2})\sim {\mathrm{Pr}}^{-(0.64\pm 0.01)}{\mathrm{Ra}}^{0.44\pm 0.01}$. The phase diagram of the model is sketched, and the observed transitions are discussed.

We present measurements of the orientation ${\theta }_0(t)$ of the large-scale circulation (LSC) of turbulent Rayleigh-Bénard convection in cylindrical cells of aspect ratio 1. ${\theta }_0(t)$ undergoes irregular reorientations. It contains reorientation events by rotation through angles $\Delta \theta$ with a monotonically decreasing probability distribution $p(\Delta \theta )$, and by cessations (where the LSC stops temporarily) with a uniform $p(\Delta \theta )$. Reorientations have Poissonian statistics in time. The amplitude of the LSC and the magnitude of the azimuthal rotation rate have a negative correlation.

Perturbative dynamics of spiral and scroll waves involves the “response functions,” i.e., critical eigenvectors of the adjoint linearized operator, dual to the Goldstone modes. A well known method of calculating the Goldstone modes is time integration of the linearized equation. We suggest that backward-time integration of the adjoint linearized equation, which we call causodynamics, can be used to calculate the response functions. This new method is more robust and easier to implement than existing methods. We illustrate how it works for propagating and rotating autowaves in reaction-diffusion systems. The method reveals unexpected qualitative difference between similarly looking regimes.

A new type of modulational instability for coherent as well as partially coherent light in systems with integrating nonlinearity caused by an irreversible process is investigated both experimentally and theoretically. In such systems plane waves never reach the stationary limit and exhibit a nontrivial time dependence resulting in new features of the modulational instability. For example, the modulational frequency of the nonexponentially increasing perturbation with maximum gain decreases while the wave is propagating. The threshold for vanishing modulational instability due to a finite degree of spatial coherence depends only on system parameters and not on the light intensity.