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While bouncing walking silicone oil droplets (walkers) do show many quantumlike phenomena, the original, most intriguing, double-slit experiment with walkers has been shown to be an overinterpretation of data. Several experiments and numerical simulations have proven that for at least some parameter region there is no randomness. Still, true randomness was claimed to be observed in an experiment on chaotically bouncing walkers. Also, most of the available phase space has not been investigated. The main goal of this paper is therefore to look for true interference and chaos in the entire phase space. Recently, we made an extensive investigation of drops interacting with slits, but still in a limited range. However, the outcome was always deterministic and only incidentally mimicked the statistics of the corresponding quantum case. We also showed that the extra interference, already seen by others, in the double-slit case was caused by reflection of waves from the outlet of the unused slit after passage and thus was not a true double-slit effect. A new theoretical treatment of bouncing drop dynamics has since given analytic relations for the associated wave field, leading to a proposal for criteria for the possible occurrence of true interference in the double-slit experiment. Satisfying these criteria, requires working close to the onset of the Faraday instability, with two spatial conditions favoring slow walkers, and a temporal condition favoring fast walkers. The regions of high velocity, where the walkers bounce periodically, and of very low velocity, with chaotically bouncing walkers, have not been comprehensively investigated so far. We have therefore looked at these regions, probing the limits for interaction with slits. Furthermore, noting that a short transit time is essential to fulfill the criteria, experiments were done using double-slit barriers only 0.5 and 2 mm broad. Nowhere was true interference or a chaotic response found. As the theory has implications for many of the observed quantumlike phenomena involving walkers as, e.g., tunneling and interaction between drops, we have measured the spatial and temporal decay of the wave field. A comparison with the theory shows very good agreement but leads to a reformulation of the above-mentioned criteria.

Just over a decade ago Couder and Fort [Phys. Rev. Lett. 97, 154101 (2006)PRLTAO0031-900710.1103/PhysRevLett.97.154101] published a provocative paper suggesting that a classical system might be able to simulate the truly fundamental quantum mechanical single- and double-slit experiment. The system they investigated was that of an oil droplet walking on a vibrated oil surface. Their results have since been challenged by Andersen et al. [Phys. Rev. E 92, 013006 (2015)PLEEE81539-375510.1103/PhysRevE.92.013006] by pointing to insufficient statistical support and a lack of experimental control over critical parameters. Here we show that the randomness in the original experiment is an artifact of lack of control. We present experimental data from an extensive scan of the parameter space of the system including the use of different size slits and tight control of critical parameters. For the single-slit we find very diverse samples of interference-like patterns but all causal by nature. This also holds for the double-slit. However, an extra interference effect appears here. The origin of this is investigated by blocking either the inlet or the outlet of one slit. Hereby we show that the extra interference is solely due to back-scatter of the associated wave field from the outlet of the slit not passed by the droplet. Recently Pucci et al. [J. Fluid Mech. 835, 1136 (2018)JFLSA70022-112010.1017/jfm.2017.790] using a much broader slit also showed that the classical system is basically causal. They, too, observed the extra interference effect for the double-slit. However, the reason behind was not determined. Moreover they claimed the existence of a chaotic regime just below the cri- tical acceleration for spontaneous generation of Faraday surface waves. Our measurements do not support the validity of this claim. However, the drop dynamics turns out to have an interesting multifaceted interaction with the slit structure.

In a thought-provoking paper, Couder and Fort [Phys. Rev. Lett. 97, 154101 (2006)] describe a version of the famous double-slit experiment performed with droplets bouncing on a vertically vibrated fluid surface. In the experiment, an interference pattern in the single-particle statistics is found even though it is possible to determine unambiguously which slit the walking droplet passes. Here we argue, however, that the single-particle statistics in such an experiment will be fundamentally different from the single-particle statistics of quantum mechanics. Quantum mechanical interference takes place between different classical paths with precise amplitude and phase relations. In the double-slit experiment with walking droplets, these relations are lost since one of the paths is singled out by the droplet. To support our conclusions, we have carried out our own double-slit experiment, and our results, in particular the long and variable slit passage times of the droplets, cast strong doubt on the feasibility of the interference claimed by Couder and Fort. To understand theoretically the limitations of wave-driven particle systems as analogs to quantum mechanics, we introduce a Schrödinger equation with a source term originating from a localized particle that generates a wave while being simultaneously guided by it. We show that the ensuing particle-wave dynamics can capture some characteristics of quantum mechanics such as orbital quantization. However, the particle-wave dynamics can not reproduce quantum mechanics in general, and we show that the single-particle statistics for our model in a double-slit experiment with an additional splitter plate differs qualitatively from that of quantum mechanics.

Background: Recommendations for antibiotic treatment of acute otitis media (AOM) have changed over the years, and today many experts recommend initial observation. However, antibiotic prescribing should be considered in children aged <2 years or if AOM is accompanied by discharging ear., Objectives: To investigate the quality of treatment of AOM in general practice and to explore the influence of selected GP and patient characteristics on antibiotic prescribing., Methods: During the winter 2008, a prospective registration of patients diagnosed with AOM was conducted in general practice in Lithuania, Kaliningrad, Spain, Argentina, Sweden and Denmark. Some 1175 patients diagnosed with AOM were registered. Information about age and sex of the patient, duration of symptoms (days), temperature >38.5°C, ear discharge and the antibiotic treatment given was recorded., Results: Danish GPs had the lowest antibiotic prescription rate for AOM [72.7% (95% confidence interval (CI) = 67.0-77.8)] and GPs in Kaliningrad had the highest [97.1% (95% CI = 89.8-99.6)]. Narrow-spectrum penicillin was almost exclusively prescribed in the two Nordic countries, while broad-spectrum penicillins, often in combination with clavulanic acid, were prescribed in the other four countries. Macrolides comprised 5-10% of prescriptions. Antibiotic prescribing was associated with the following characteristics of the patients: symptoms for >3 days, ear discharge and fever., Conclusion: The majority of patients with AOM were treated with antibiotics in all six countries, but considerable variations in both prescribing rate and choice of antibiotics were identified.

We measure elastomechanical spectra for a family of thin shells. We show that these spectra can be described by a "semiclassical" trace formula comprising periodic orbits on geodesics, with the periods of these orbits consistent with those extracted from experiment. The influence of periodic orbits on spectra in the case of two-dimensional curved geometries is thereby demonstrated, where the parameter corresponding to Planck's constant in quantum systems involves the wave number and the curvature radius. We use these findings to explain the marked clustering of levels when the shell is hemispherical.

It is shown that the deviations of the experimental statistics of six chaotic acoustic resonators from Wigner-Dyson random matrix theory predictions are explained by a recent model of random missing levels. In these resonatorsa made of aluminum plates a the larger deviations occur in the spectral rigidity (SRs) while the nearest-neighbor distributions (NNDs) are still close to the Wigner surmise. Good fits to the experimental NNDs and SRs are obtained by adjusting only one parameter, which is the fraction of remaining levels of the complete spectra. For two Sinai stadiums, one Sinai stadium without planar symmetry, two triangles, and a sixth of the three-leaf clover shapes, was found that 7%, 4%, 7%, and 2%, respectively, of eigenfrequencies were not detected.

We present an amplitude equation for sand ripples under oscillatory flow in a situation where the sand is moving in a narrow channel and the height profile is practically one dimensional. The equation has the form ht = - epsilon(h-h)+((hx)2-1)hxx-hxxxx+delta((hx)2)xx which, due to the first term, is neither completely local (it has long-range coupling through the average height h) nor has local sand conservation. We argue that this is reasonable and show that the equation compares well with experimental observations in narrow channels. We focus in particular on the so-called doubling transition, a secondary instability caused by the sudden decrease in the amplitude of the water motion, leading to the appearance of a new ripple in each trough. This transition is well reproduced for sufficiently large delta (asymmetry between trough and crest). We finally present surprising experimental results showing that long-range coupling is indeed seen in the initial details of the doubling transition, where in fact two small ripples are initially formed, followed by global symmetry breaking removing one of them.

Experiments studying ripple formation under water have usually used sinusoidal driving force. Here an experiment is presented where the driving force can be an arbitrary wave form, thus trying to mimic the realistic wave motion in shallow water coastal zones. We study a simple modulated sine wave and more complicated wave forms with several superposed harmonics. In particular we demonstrate how a small higher order harmonic can have a dramatic effect on the wavelength of the ripple pattern.

We applied a recently proposed rescaling of curvatures of eigenvalues of parameter-dependent random matrices to experimental data from acoustic systems and to a theoretical result. It is found that the data from four different experiments, ranging from isotropic plates to anisotropic three-dimensional objects, and the theoretical result always agree with the universal curvature distribution, if only the curvatures are rescaled such that the average of their absolute values is unity.

In this paper we present an experimental study of the dynamics of underwater sand ripples when a regular pattern of ripples is subjected to a skewed oscillatory flow, i.e., one not perpendicular to the direction of the ripple crests. Striking patterns with new, superposed ripples on top of the original ones occur very quickly with a characteristic angle, which is, in general, not perpendicular to the flow. A slower, more complex transition then follows, leading to the final state where the ripples are again perpendicular to the flow. We investigate the variation of the superposed pattern as a function of the direction, amplitude, and frequency of the drive, and as a function of the viscosity (by changing the temperature). We quantify the dynamics of the entire transition process and finally study the grain motion around idealized (solid) skewed ripples. This leads to a characteristic mean path of a single particle. The path has a shape close to a parallelogram, with no apparent connection to the pattern of real, superposed ripples. On the other hand, a thin layer of sand sprinkled on the solid ripples leads to qualitatively similar patterns.

We calculate the leading Weyl term of the counting function for a monocrystalline quartz sphere. In contrast to other studies of counting functions, the anisotropy of quartz is a crucial element in our investigation. Hence we do not obtain a simple analytical form, but we carry out a numerical evaluation. To this end we employ the Radon transform representation of the Green's function. We compare our result to a previously measured unique data set of several tens of thousands of resonances.

We measure the amplitude of the elastomechanical displacement at a fine grid of points on a free plate having the shape of a Sinai stadium. The obtained displacement field formally corresponds to a wave function in a quantum system. While the distribution of the squared amplitudes agrees with the prediction of random matrix theory (RMT), there is a strong deviation of the spatial correlator from the standard prediction for quantum chaotic systems. We show that this is due to the presence of two modes, leading to a beating phenomenon. We construct a proper extension of the spatial correlator within the framework of RMT.

The European Water Framework Directive (WFD) requires the definition of reference conditions, i.e. pristine conditions, for all surface waters. As the present state of Danish coastal waters cannot be referred to as pristine, reference conditions have to be assessed by analysis of historical data or by the use of models. Using Randers Fjord as an example, the aim of this work was i) to demonstrate possibilities and restrictions of assessing reference conditions by historical data and by modelling; and ii) to demonstrate how ecological conditions have changed along with eutrophication. The ample historical data from Randers Fjord allowed us to assess reference conditions with respect to benthic macrophytes and benthic fauna. Models of varying complexity enabled us to assess reference conditions for nutrients, chlorophyll a, Secchi depth, and eelgrass. We conclude that models can be a useful supplement to assess reference conditions, though they are presently restricted by the lack of quantitative links between eutrophication and species composition.

We present experimental results for the ultrasound transmission spectra and standing wave patterns of a rectangular block of fused quartz. A comparison is made between our data and an approximation of the theoretical staircase function for three-dimensional isotropic elasticity. The main emphasis of our study is on the role of mode conversion in regular ray-splitting billiards. We present the fluctuation statistics and find that these are described by the Gaussian orthogonal ensemble of random matrix theory, despite the fact that the system is not classically chaotic, as demonstrated with numerical simulation. Using temperature perturbation, we find that the vast majority of the resonances are mixtures of transverse and longitudinal wave motion, yet a small number of special resonances remain pure. We further illuminate this by presenting standing wave patterns measured on one face of the block.

Vortex ripples in sand are studied experimentally in a one-dimensional setup with periodic boundary conditions. The nonlinear evolution, far from the onset of instability, is analyzed in the framework of a simple model developed for homogeneous patterns. The interaction function describing the mass transport between neighboring ripples is extracted from experimental runs using a recently proposed method for data analysis, and the predictions of the model are compared to the experiment. An analytic explanation of the wavelength selection mechanism in the model is provided, and the width of the stable band of ripples is measured.

Patterns of vortex ripples form when a sand bed is subjected to an oscillatory fluid flow. Here we describe experiments on the response of regular vortex ripple patterns to sudden changes of the driving amplitude a or frequency f. A sufficient decrease of f leads to a "freezing" of the pattern, while a sufficient increase of f leads to a supercritical secondary "pearling" instability. Sufficient changes in the amplitude a lead to subcritical secondary "doubling" and "bulging" instabilities. Our findings are summarized in a "stability balloon" for vortex ripple pattern formation.

We discuss a random matrix model of systems with an approximate symmetry and present the spectral fluctuation statistics and eigenvector characteristics for the model. An acoustic resonator like, e.g., an aluminum plate may have an approximate symmetry. We have measured the frequency spectrum and the widths for acoustic resonances in thin aluminum plates, cut in the shape of the so-called three-leaf clover. Due to the mirror symmetry through the middle plane of the plate, each resonance of the plate belongs to one of two mode classes and we show how to separate the modes into these two classes using their measured widths. We compare the spectral statistics of each mode class with results for the Gaussian orthogonal ensemble. By cutting a slit of increasing depth on one face of the plate, we gradually break the mirror symmetry and study the transition that takes place as the two classes are mixed. Presenting the spectral fluctuation statistics and the distribution of widths for the resonances, we find that this transition is well described by the random matrix model.