Vortex ring refraction at large Froude numbers

We have experimentally studied the impact of an initially planar axisymmetric vortex ring, incident at an oblique angle, upon a gravity-induced interface separating two fluids of differing densities. After impact, the vortex ring was found to exhibit a variety of subsequent trajectories, which we organize according to both the incidence angle, $\theta_i$, and the interface strength, defined as the ratio of the Atwood and Froude numbers, $A/F$. For grazing incidence angles ($\theta_i \gtrsim 70$ deg.) vortices either penetrate or reflect from the interface, depending on whether the interface is weak or strong. In some cases, reflected vortices execute damped oscillations before finally disintegrating. For smaller incidence angles ($\theta_i \lesssim 70$ deg.) vortices penetrate the interface. When there is a strong interface, these vortices are observed to curve back up toward the interface. When there is a weak interface, these vortices are observed to refract downward, away from the interface. The critical interface strength below which vortex ring refraction is observed is given by $\log_{10}{(A/F)}= -2.38 \pm 0.05$.Comment: 26 pages, 11 figures; Submitted to Physical Review

NMR implementation of Quantum Delayed-Choice Experiment

We report the first experimental demonstration of quantum delayed-choice experiment via nuclear magnetic resonance techniques. An ensemble of molecules each with two spin-1/2 nuclei are used as target and the ancilla qubits to perform the quantum circuit corresponding the delayed-choice setup. As expected in theory, our experiments clearly demonstrate the continuous morphing of the target qubit between particle-like and wave-like behaviors. The experimental visibility of the interference patterns shows good agreement with the theory.Comment: Revised text, more figures adde

Discretely guided electromagnetic effective medium

A material comprised of an array of subwavelength coaxial waveguides decomposes incident electromagnetic waves into spatially discrete wave components, propagates these components without frequency cut-off, and reassembles them on the far side of the material. The propagation of these wave components is fully controlled by the physical properties of the waveguides and their geometrical distribution in the array. This allows for an exceptional degree of control over the electromagnetic response of this effective medium, with numerous potential applications. With the development of nanoscale subwavelength coaxial waveguides, these applications (including metamaterial functionality) can be enabled in the visible frequency range

The time resolution of the St. Petersburg paradox

A resolution of the St. Petersburg paradox is presented. In contrast to the standard resolution, utility is not required. Instead, the time-average performance of the lottery is computed. The final result can be phrased mathematically identically to Daniel Bernoulli's resolution, which uses logarithmic utility, but is derived using a conceptually different argument. The advantage of the time resolution is the elimination of arbitrary utility functions.Comment: 20 pages, 1 figur

Measuring and modelling the energy cost of reconfiguration in sensor networks [forthcoming]

As Wireless Sensor Networks (WSN) must operate for long periods on a limited power budget, estimating the energy cost of software operations is critical. Contemporary reconfiguration approaches for WSN allow for software evolution at various granularities; from reflashing of a complete software image, through replacement of complete applications, to the reconfiguration of individual software components. This paper contributes a generic model for measuring and modelling the energy cost of reconfiguration in WSN. We validate that this model is accurate in the face of different hardware platforms, software stacks and software encapsulation approaches. We have embedded this model in the LooCI middleware, resulting in the first energy aware reconfigurable component model for sensor networks. We evaluate our approach using two real-world WSN applications and demonstrate that our model predicts the energy cost of reconfiguration with 93% accuracy. Using this model we demonstrate that selecting the most appropriate software modularisation approach is key to minimising energy consumption

Infrared spectroscopy of diatomic molecules - a fractional calculus approach

The eigenvalue spectrum of the fractional quantum harmonic oscillator is calculated numerically solving the fractional Schr\"odinger equation based on the Riemann and Caputo definition of a fractional derivative. The fractional approach allows a smooth transition between vibrational and rotational type spectra, which is shown to be an appropriate tool to analyze IR spectra of diatomic molecules.Comment: revised + extended version, 9 pages, 6 figure

Methodological perspectives on the application of compound-specific stable isotope fingerprinting for sediment source apportionment

Compound-specific stable isotope (CSSI) fingerprinting of sediment sources is a recently introduced tool to overcome some limitations of conventional approaches for sediment source apportionment. The technique uses the C-13 CSSI signature of plant-derived fatty acids (delta C-13-fatty acids) associated with soil minerals as a tracer. This paper provides methodological perspectives to advance the use of CSSI fingerprinting in combination with stable isotope mixing models (SIMMs) to apportion the relative contributions of different sediment sources (i.e. land uses) to sediments. CSSI fingerprinting allows quantitative estimation of the relative contribution of sediment sources within a catchment at a spatio-temporal resolution, taking into account the following approaches. First, application of CSSI fingerprinting techniques to complex catchments presents particular challenges and calls for well-designed sampling strategies and data handling. Hereby, it is essential to balance the effort required for representative sample collection and analyses against the need to accurately quantify the variability within the system. Second, robustness of the CSSI approach depends on the specificity and conservativeness of the delta C-13-FA fingerprint. Therefore, saturated long-chain (> 20 carbon atoms) FAs, which are biosynthesised exclusively by higher plants and are more stable than the more commonly used short-chain FAs, should be used. Third, given that FA concentrations can vary largely between sources, concentration-dependent SIMMs that are also able to incorporate delta C-13-FA variability should be standard operation procedures to correctly assess the contribution of sediment sources via SIMMs. This paper reflects on the use of delta C-13-FAs in erosion studies and provides recommendations for its application. We strongly advise the use of saturated long-chain (> 20 carbon atoms) FAs as tracers and concentration-dependent Bayesian SIMMs. We anticipate progress in CSSI sediment fingerprinting from two current developments: (i) development of hierarchical Bayesian SIMMs to better address catchment complexity and (ii) incorporation of dual isotope approaches (delta C-13- and delta H-2-FA) to improve estimates of sediment sources

The soil N cycle: new insights and key challenges

The study of soil N cycling processes has been, is, and will be at the centre of attention in soil science research. The importance of N as a nutrient for all biota; the ever-increasing rates of its anthropogenic input in terrestrial (agro)ecosystems; its resultant losses to the environment; and the complexity of the biological, physical, and chemical factors that regulate N cycling processes all contribute to the necessity of further understanding, measuring, and altering the soil N cycle. Here, we review important insights with respect to the soil N cycle that have been made over the last decade, and present a personal view on the key challenges of future research. We identify three key challenges with respect to basic N cycling processes producing gaseous emissions: 1. quantifying the importance of nitrifier denitrification and its main controlling factors; 2. characterizing the greenhouse gas mitigation potential and microbiological basis for N2O consumption; 3. characterizing hotspots and hot moments of denitrification Furthermore, we identified a key challenge with respect to modelling: 1. disentangling gross N transformation rates using advanced 15N / 18O tracing models Finally, we propose four key challenges related to how ecological interactions control N cycling processes: 1. linking functional diversity of soil fauna to N cycling processes beyond mineralization; 2. determining the functional relationship between root traits and soil N cycling; 3. characterizing the control that different types of mycorrhizal symbioses exert on N cycling; 4. quantifying the contribution of non-symbiotic pathways to total N fixation fluxes in natural systems We postulate that addressing these challenges will constitute a comprehensive research agenda with respect to the N cycle for the next decade. Such an agenda would help us to meet future challenges on food and energy security, biodiversity conservation, water and air quality, and climate stability

Energy aware software evolution for wireless sensor networks

Wireless Sensor Networks (WSNs) are subject to high levels of dynamism arising from changing environmental conditions and application requirements. Reconfiguration allows software functionality to be optimized for current environmental conditions and supports software evolution to meet variable application requirements. Contemporary software modularization approaches for WSNs allow for software evolution at various granularities; from monolithic re-flashing of OS and application functionality, through replacement of complete applications, to the reconfiguration of individual software components. As the nodes that compose a WSN must typically operate for long periods on a single battery charge, estimating the energy cost of software evolution is critical. This paper contributes a generic model for calculating the energy cost of the reconfiguration in WSN. We have embedded this model in the LooCI middleware, resulting in the first energy aware reconfigurable component model for sensor networks. We evaluate our approach using two real-world WSN applications and find that (i.) our model accurately predicts the energy cost of reconfiguration and (ii.) component-based reconfiguration has a high initial cost, but provides energy savings during software evolution

Ten Misconceptions from the History of Analysis and Their Debunking

The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d'Alembert, Cauchy, and others.Comment: 46 pages, 4 figures; Foundations of Science (2012). arXiv admin note: text overlap with arXiv:1108.2885 and arXiv:1110.545