We demonstrate superresolution imaging of single rare-earth emitting centers, namely, trivalent cerium, in yttrium aluminum garnet crystals by means of stimulated emission depletion (STED) microscopy. The achieved all-optical resolution is $\approx 50\mathrm{nm}$. Similar results were obtained on $H3$ color centers in diamond. In both cases, STED resolution is improving slower than the conventional inverse square-root dependence on the depletion beam intensity. In the proposed model of this effect, the anomalous behavior is caused by excited state absorption and the interaction of the emitter with nonfluorescing crystal defects in its local surrounding.

Particle detachment bursts during the flow of suspensions through porous media are a phenomenon that can severely affect the efficiency of deep bed filters. Despite the relevance in several industrial fields, little is known about the statistical properties and the temporal organization of these events. We present experiments of suspensions of deionized water carrying quartz particles pushed with a peristaltic pump through a filter of glass beads measuring simultaneously the pressure drop, flux, and suspension solid fraction. We find that the burst size distribution scales consistently with a power law, suggesting that we are in the presence of a novel experimental realization of a self-organized critical system. Temporal correlations are present in the time series, like in other phenomena such as earthquakes or neuronal activity bursts, and also an analog to Omori’s law can be shown. The understanding of burst statistics could provide novel insights in different fields, e.g., in the filter and petroleum industries.

We introduce a new method of statistical analysis to characterize the dynamics of turbulent fluids in two dimensions. We establish that, in equilibrium, the vortex distributions can be uniquely connected to the temperature of the vortex gas, and we apply this vortex thermometry to characterize simulations of decaying superfluid turbulence. We confirm the hypothesis of vortex evaporative heating leading to Onsager vortices proposed in Phys. Rev. Lett. 113, 165302 (2014), and we find previously unidentified vortex power-law distributions that emerge from the dynamics.

The formation of iterated structures, such as satellite and subsatellite drops, filaments, and bubbles, is a common feature in interfacial hydrodynamics. Here we undertake a computational and theoretical study of their origin in the case of thin films of viscous fluids that are destabilized by long-range molecular or other forces. We demonstrate that iterated structures appear as a consequence of discrete self-similarity, where certain patterns repeat themselves, subject to rescaling, periodically in a logarithmic time scale. The result is an infinite sequence of ridges and filaments with similarity properties. The character of these discretely self-similar solutions as the result of a Hopf bifurcation from ordinarily self-similar solutions is also described.

Geophysical models approximate classical fluid motion in rotating frames. Even accurate approximations can have profound consequences, such as the loss of inertial frames. If geophysical fluid dynamics are not strictly equivalent to Newtonian hydrodynamics observed in a rotating frame, what kind of dynamics are they? We aim to clarify fundamental similarities and differences between relativistic, Newtonian, and geophysical hydrodynamics, using variational and covariant formulations as tools to shed the necessary light. A space-time variational principle for the motion of a perfect fluid is introduced. The geophysical action is interpreted as a synchronous limit of the relativistic action. The relativistic Levi-Civita connection also has a finite synchronous limit, which provides a connection with which to endow geophysical space-time, generalizing Cartan (1923). A covariant mass-momentum budget is obtained using covariance of the action and metric-preserving properties of the connection. Ultimately, geophysical models are found to differ from the standard compressible Euler model only by a specific choice of a metric-Coriolis-geopotential tensor akin to the relativistic space-time metric. Once this choice is made, the same covariant mass-momentum budget applies to Newtonian and all geophysical hydrodynamics, including those models lacking an inertial frame. Hence, it is argued that this mass-momentum budget provides an appropriate, common fundamental principle of dynamics. The postulate that Euclidean, inertial frames exist can then be regarded as part of the Newtonian theory of gravitation, which some models of geophysical hydrodynamics slightly violate.

The stress generation on pore walls due to the growth of a sodium chloride crystal in a confined aqueous solution is studied from evaporation experiments in microfluidic channels in conjunction with numerical computations of crystal growth. The study indicates that the stress buildup on the pore walls is a highly transient process taking place over a very short period of time (in less than 1 s in our experiments). The analysis makes clear that what matters for the stress generation is not the maximum supersaturation at the onset of the crystal growth but the supersaturation at the interface between the solution and the crystal when the latter is about to be confined between the pore walls. The stress generation is summarized in a simple stress diagram involving the pore aspect ratio and the Damkhöler number characterizing the competition between the precipitation reaction kinetics and the ion transport towards the growing crystal. This opens up the route for a better understanding of the damage of porous materials induced by salt crystallization, an important issue in Earth sciences, reservoir engineering, and civil engineering.

Based on fundamental properties of the light scattering by a particle under a plane, linearly polarized wave illumination, we rigorously prove the existence of the ultimate upper limit for the light absorption by any partial mode and calculate this limit explicitly. The limit is a certain simple universal function of the incident light wave number, and the multipolarity of the corresponding partial mode solely. It does not depend on the optical constants of the scatterer, its size, or even its shape. First, we obtain this result for the scattering by a spherical particle. Then, we generalize it to an arbitrary finite obstacle. The results are valid for any polarization of the incident wave, any angle of its incidence, and any type of the scatterer (homogeneous, stratified, or with smoothly variable refractive index). We also prove that the maximal partial absorption cross section for any finite scatterer cannot exceed the corresponding value for a homogeneous sphere in 3D and circular cylinder in 2D. As an example, the results are applied to maximize the absorption cross section of a spherical core-shell structure.

The system of cavity polaritons driven by a plane electromagnetic wave is found to undergo the spontaneous breaking of spatial symmetry, which results in a lifted phase locking with respect to the driving field and, consequently, in the possibility of internal ordering. In particular, periodic spin and intensity patterns arise in polariton wires; they exhibit strong long-range order and can serve as media for signal transmission. Such patterns have the properties of dynamical chimeras: they are formed spontaneously in perfectly homogeneous media and can be partially chaotic. The reported new mechanism of chimera formation requires neither time-delayed feedback loops nor nonlocal interactions.

By tracking the divergence of two initially close trajectories in phase space in an Eulerian approach to forced turbulence, the relation between the maximal Lyapunov exponent $\lambda$ and the Reynolds number Re is measured using direct numerical simulations, performed on up to $2048^3$ collocation points. The Lyapunov exponent is found to solely depend on the Reynolds number with $\lambda \propto {\mathrm{Re}}^{0.53}$ and that after a transient period the divergence of trajectories grows at the same rate at all scales. Finally a linear divergence is seen that is dependent on the energy forcing rate. Links are made with other chaotic systems.

We demonstrate the effectiveness of using machine learning for model-free prediction of spatiotemporally chaotic systems of arbitrarily large spatial extent and attractor dimension purely from observations of the system’s past evolution. We present a parallel scheme with an example implementation based on the reservoir computing paradigm and demonstrate the scalability of our scheme using the Kuramoto-Sivashinsky equation as an example of a spatiotemporally chaotic system.

We have conducted experimental measurements and numerical simulations of a precession-driven flow in a cylindrical cavity. The study is dedicated to the precession dynamo experiment currently under construction at Helmholtz-Zentrum Dresden-Rossendorf and aims at the evaluation of the hydrodynamic flow with respect to its ability to drive a dynamo. We focus on the strongly nonlinear regime in which the flow is essentially composed of the directly forced primary Kelvin mode and higher modes in terms of standing inertial waves arising from nonlinear self-interactions. We obtain an excellent agreement between experiment and simulation with regard to both flow amplitudes and flow geometry. A peculiarity is the resonance-like emergence of an axisymmetric mode that represents a double roll structure in the meridional plane. Kinematic simulations of the magnetic field evolution induced by the time-averaged flow yield dynamo action at critical magnetic Reynolds numbers around ${\mathrm{Rm}}^{\mathrm{c}}\approx 430$, which is well within the range of the planned liquid sodium experiment.

The classical connection between symmetry breaking and the onset of chaos in dynamical systems harks back to the seminal theory of Noether [Transp. Theory Statist. Phys. 1, 186 (1918)]. We study the Lagrangian kinematics of steady 3D Stokes flow through simple cubic and body-centered cubic (bcc) crystalline lattices of close-packed spheres, and uncover an important exception. While breaking of point-group symmetries is a necessary condition for chaotic mixing in both lattices, a further space-group (glide) symmetry of the bcc lattice generates a transition from globally regular to globally chaotic dynamics. This finding provides new insights into chaotic mixing in porous media and has significant implications for understanding the impact of symmetries upon generic dynamical systems.

Almost twenty years ago, light was slowed down to less than ${10}^{-7}$ of its vacuum speed in a cloud of ultracold atoms of sodium. Upon a sudden turn-off of the coupling laser, a slow light pulse can be imprinted on cold atoms such that it can be read out and converted into a photon again. In this process, the light is stopped by absorbing it and storing its shape within the atomic ensemble. Alternatively, the light can be stopped at the band edge in photonic-crystal waveguides, where the group speed vanishes. Here, we extend the phenomenon of stopped light to the new field of parity-time ($PT$) symmetric systems. We show that zero group speed in $PT$ symmetric optical waveguides can be achieved if the system is prepared at an exceptional point, where two optical modes coalesce. This effect can be tuned for optical pulses in a wide range of frequencies and bandwidths, as we demonstrate in a system of coupled waveguides with gain and loss.

Since its discovery in 2002, the chimera state has frequently been described as a counterintuitive, puzzling phenomenon. The Kuramoto model, in contrast, has become a celebrated paradigm useful for understanding a range of phenomena related to phase transitions, synchronization, and network effects. Here we show that the chimera state can be understood as emerging naturally through a symmetry-breaking bifurcation from the Kuramoto model’s partially synchronized state. Our analysis sheds light on recent observations of chimera states in laser arrays, chemical oscillators, and mechanical pendula.

We show that smaller gas bubbles grow at the expense of larger bubbles and all bubbles approach the same surface curvature after long times in porous media. This anticoarsening effect is contrary to typical Ostwald ripening and leads to uniformly sized bubbles in a homogeneous medium. Evolution dynamics of bubble populations were measured, and mathematical models were developed that fit the experimental data well. Ostwald ripening is shown to be the driving mechanism in this anticoarsening phenomenon; however, the relationship between surface curvature and bubble size determined by the pore-throat geometric confinement reverses the ripening direction.

We predict a new class of three-dimensional (3D) topological dissipative optical one-component solitons in homogeneous laser media with fast saturable absorption. Their skeletons formed by vortex lines where the field vanishes are tangles, i.e., $N_c$ knotted or unknotted, linked or unlinked closed lines and $M$ unclosed lines that thread all the closed lines and end at the infinitely far soliton periphery. They are generated by embedding two-dimensional laser solitons or their complexes in 3D space after their rotation around an unclosed, infinite vortex line with topological charge $M_0$ ($N_c$, $M$, and $M_0$ are integers). With such structure propagation, the “hula-hoop” solitons form; their stability is confirmed numerically. For the solitons found, all vortex lines have unit topological charge: the number of closed lines $N_c=1$ and 2 (unknots, trefoils, and Solomon knots links); unclosed vortex lines are unknotted and unlinked, their number $M=1$, 2, and 3.

We experimentally study steady Marangoni-driven surfactant transport on the interface of a deep water layer. Using hydrodynamic measurements, and without using any knowledge of the surfactant physicochemical properties, we show that sodium dodecyl sulphate and Tergitol 15-S-9 introduced in low concentrations result in a flow driven by adsorbed surfactant. At higher surfactant concentration, the flow is dominated by the dissolved surfactant. Using camphoric acid, whose properties are a priori unknown, we demonstrate this method’s efficacy by showing its spreading is adsorption dominated.