Water wave propagation and scattering over topographical bottoms

Here I present a general formulation of water wave propagation and scattering over topographical bottoms. A simple equation is found and is compared with existing theories. As an application, the theory is extended to the case of water waves in a column with many cylindrical steps

Square Patterns and Quasi-patterns in Weakly Damped Faraday Waves

Pattern formation in parametric surface waves is studied in the limit of weak viscous dissipation. A set of quasi-potential equations (QPEs) is introduced that admits a closed representation in terms of surface variables alone. A multiscale expansion of the QPEs reveals the importance of triad resonant interactions, and the saturating effect of the driving force leading to a gradient amplitude equation. Minimization of the associated Lyapunov function yields standing wave patterns of square symmetry for capillary waves, and hexagonal patterns and a sequence of quasi-patterns for mixed capillary-gravity waves. Numerical integration of the QPEs reveals a quasi-pattern of eight-fold symmetry in the range of parameters predicted by the multiscale expansion.Comment: RevTeX, 11 pages, 8 figure

Interaction of Nearly-Inviscid, Multi-mode Faraday Waves and Mean Flows

Faraday waves [1] are gravity-capillary waves that are excited on the surface of a fluid when its container is vibrated vertically and the vertical acceleration exceeds a threshold value. These waves have received much attention in the literature both as a basic fluid dynamical problem and as a paradigm of a pattern-forming system [2-4]. Unfortunately, in the low viscosity limit, there are several basic issues that remain unresolved, particularly in connection with the generation of mean flows in the bulk. The viscous part of these flows (also called streaming flow or acoustic streaming) is driven by the oscillatory boundary layers attached to the solid walls and the free surface by well-known mechanisms first uncovered by Schlichting [5] and Longuet-Higgins [6]. This mean flow has been shown recently to affect the dynamics of the primary waves at leading order in a related, laterally vibrated system [7]. This is somewhat similar to the effect of an internal circulation on surface wave dynamics in drops [8]

Impacts of climate change on national biodiversity population trends

Climate change has had well-documented impacts on the distribution and phenology of species across many taxa, but impacts on species’ abundance, which relates closely to extinction risk and ecosystem function, have not been assessed across taxa. In the most comprehensive multi-taxa comparison to date, we modelled variation in national population indices of 501 mammal, bird, aphid, butterfly and moth species as a function of annual variation in weather variables, which through time allowed us to identify a component of species’ population growth that can be associated with post-1970s climate trends. We found evidence that these climate trends have significantly affected population trends of 15.8% of species, including eight with extreme (> 30% decline per decade) negative trends consistent with detrimental impacts of climate change. The modelled effect of climate change could explain 48% of the significant across-species population decline in moths and 63% of the population increase in winged aphids. The other taxa did not have significant across-species population trends or consistent climate change responses. Population declines in species of conservation concern were linked to both climatic and non-climatic factors respectively accounting for 42 and 58% of the decline. Evident differential impacts of climate change between trophic levels may signal the potential for future ecosystem disruption. Climate change has therefore already driven large-scale population changes of some species, had significant impacts on the overall abundance of some key invertebrate groups and may already have altered biological communities and ecosystems in Great Britain

Solar flare prediction using advanced feature extraction, machine learning and feature selection

YesNovel machine-learning and feature-selection algorithms have been developed to study: (i) the flare prediction capability of magnetic feature (MF) properties generated by the recently developed Solar Monitor Active Region Tracker (SMART); (ii) SMART's MF properties that are most significantly related to flare occurrence. Spatio-temporal association algorithms are developed to associate MFs with flares from April 1996 to December 2010 in order to differentiate flaring and non-flaring MFs and enable the application of machine learning and feature selection algorithms. A machine-learning algorithm is applied to the associated datasets to determine the flare prediction capability of all 21 SMART MF properties. The prediction performance is assessed using standard forecast verification measures and compared with the prediction measures of one of the industry's standard technologies for flare prediction that is also based on machine learning - Automated Solar Activity Prediction (ASAP). The comparison shows that the combination of SMART MFs with machine learning has the potential to achieve more accurate flare prediction than ASAP. Feature selection algorithms are then applied to determine the MF properties that are most related to flare occurrence. It is found that a reduced set of 6 MF properties can achieve a similar degree of prediction accuracy as the full set of 21 SMART MF properties

Transverse phase-locking in fully frustrated Josephson junction arrays: a new type of fractional giant steps

We study, analytically and numerically, phase locking of driven vortex lattices in fully-frustrated Josephson junction arrays at zero temperature. We consider the case when an ac current is applied {\it perpendicular} to a dc current. We observe phase locking, steps in the current-voltage characteristics, with a dependence on external ac-drive amplitude and frequency qualitatively different from the Shapiro steps, observed when the ac and dc currents are applied in parallel. Further, the critical current increases with increasing transverse ac-drive amplitude, while it decreases for longitudinal ac-drive. The critical current and the phase-locked current step width, increase quadratically with (small) amplitudes of the ac-drive. For larger amplitudes of the transverse ac-signal, we find windows where the critical current is hysteretic, and windows where phase locking is suppressed due to dynamical instabilities. We characterize the dynamical states around the phase-locking interference condition in the $IV$ curve with voltage noise, Lyapunov exponents and Poincar\'e sections. We find that zero temperature phase-locking behavior in large fully frustrated arrays is well described by an effective four plaquette model.Comment: 12 pages, 11 figure

Quantum Interference in Superconducting Wire Networks and Josephson Junction Arrays: Analytical Approach based on Multiple-Loop Aharonov-Bohm Feynman Path-Integrals

We investigate analytically and numerically the mean-field superconducting-normal phase boundaries of two-dimensional superconducting wire networks and Josephson junction arrays immersed in a transverse magnetic field. The geometries we consider include square, honeycomb, triangular, and kagome' lattices. Our approach is based on an analytical study of multiple-loop Aharonov-Bohm effects: the quantum interference between different electron closed paths where each one of them encloses a net magnetic flux. Specifically, we compute exactly the sums of magnetic phase factors, i.e., the lattice path integrals, on all closed lattice paths of different lengths. A very large number, e.g., up to $10^{81}$ for the square lattice, exact lattice path integrals are obtained. Analytic results of these lattice path integrals then enable us to obtain the resistive transition temperature as a continuous function of the field. In particular, we can analyze measurable effects on the superconducting transition temperature, $T_c(B)$, as a function of the magnetic filed $B$, originating from electron trajectories over loops of various lengths. In addition to systematically deriving previously observed features, and understanding the physical origin of the dips in $T_c(B)$ as a result of multiple-loop quantum interference effects, we also find novel results. In particular, we explicitly derive the self-similarity in the phase diagram of square networks. Our approach allows us to analyze the complex structure present in the phase boundaries from the viewpoint of quantum interference effects due to the electron motion on the underlying lattices.Comment: 18 PRB-type pages, plus 8 large figure