Data assimilation using adaptive, non-conservative, moving mesh models

Numerical models solved on adaptive moving meshes have become increasingly prevalent in recent years. Motivating problems include the study of fluids in a Lagrangian frame and the presence of highly localized structures such as shock waves or interfaces. In the former case, Lagrangian solvers move the nodes of the mesh with the dynamical flow; in the latter, mesh resolution is increased in the proximity of the localized structure. Mesh adaptation can include remeshing, a procedure that adds or removes mesh nodes according to specific rules reflecting constraints in the numerical solver. In this case, the number of mesh nodes will change during the integration and, as a result, the dimension of the model's state vector will not be conserved. This work presents a novel approach to the formulation of ensemble data assimilation (DA) for models with this underlying computational structure. The challenge lies in the fact that remeshing entails a different state space dimension across members of the ensemble, thus impeding the usual computation of consistent ensemble-based statistics. Our methodology adds one forward and one backward mapping step before and after the ensemble Kalman filter (EnKF) analysis, respectively. This mapping takes all the ensemble members onto a fixed, uniform reference mesh where the EnKF analysis can be performed. We consider a high-resolution (HR) and a low-resolution (LR) fixed uniform reference mesh, whose resolutions are determined by the remeshing tolerances. This way the reference meshes embed the model numerical constraints and are also upper and lower uniform meshes bounding the resolutions of the individual ensemble meshes. Numerical experiments are carried out using 1-D prototypical models: Burgers and Kuramoto-Sivashinsky equations and both Eulerian and Lagrangian synthetic observations. While the HR strategy generally outperforms that of LR, their skill difference can be reduced substantially by an optimal tuning of the data assimilation parameters. The LR case is appealing in high dimensions because of its lower computational burden. Lagrangian observations are shown to be very effective in that fewer of them are able to keep the analysis error at a level comparable to the more numerous observers for the Eulerian case. This study is motivated by the development of suitable EnKF strategies for 2-D models of the sea ice that are numerically solved on a Lagrangian mesh with remeshing

Coupled-resonator-induced-transparency concept for wavelength routing applications

The presence of coupled resonators induced transparency (CRIT) effects in side-coupled integrated spaced sequence of resonators (SCISSOR) of different radii has been studied. By controlling the rings radii and their center to center distance, it is possible to form transmission channels within the SCISSOR stop-band. Two different methods to exploit the CRIT effect in add/drop filters are proposed. Their performances, e. g. linewidth, crosstalk and losses, are examined also for random variations in the structural parameters. Finally, few examples of high performances mux/demux structures and 2 × 2 routers based on these modified SCISSOR are presented. CRIT based SCISSOR optical devices are particularly promising for ultra-dense wavelength division multiplexing applications

Data assimilation using adaptive, non-conservative, moving mesh models

Numerical models solved on adaptive moving meshes have become increasingly prevalent in recent years. Motivating problems include the study of fluids in a Lagrangian frame and the presence of highly localized structures such as shock waves or interfaces. In the former case, Lagrangian solvers move the nodes of the mesh with the dynamical flow; in the latter, mesh resolution is increased in the proximity of the localized structure. Mesh adaptation can include remeshing, a procedure that adds or removes mesh nodes according to specific rules reflecting constraints in the numerical solver. In this case, the number of mesh nodes will change during the integration and, as a result, the dimension of the model's state vector will not be conserved. This work presents a novel approach to the formulation of ensemble data assimilation (DA) for models with this underlying computational structure. The challenge lies in the fact that remeshing entails a different state space dimension across members of the ensemble, thus impeding the usual computation of consistent ensemble-based statistics. Our methodology adds one forward and one backward mapping step before and after the ensemble Kalman filter (EnKF) analysis, respectively. This mapping takes all the ensemble members onto a fixed, uniform reference mesh where the EnKF analysis can be performed. We consider a high-resolution (HR) and a low-resolution (LR) fixed uniform reference mesh, whose resolutions are determined by the remeshing tolerances. This way the reference meshes embed the model numerical constraints and are also upper and lower uniform meshes bounding the resolutions of the individual ensemble meshes. Numerical experiments are carried out using 1-D prototypical models: Burgers and Kuramoto–Sivashinsky equations and both Eulerian and Lagrangian synthetic observations. While the HR strategy generally outperforms that of LR, their skill difference can be reduced substantially by an optimal tuning of the data assimilation parameters. The LR case is appealing in high dimensions because of its lower computational burden. Lagrangian observations are shown to be very effective in that fewer of them are able to keep the analysis error at a level comparable to the more numerous observers for the Eulerian case. This study is motivated by the development of suitable EnKF strategies for 2-D models of the sea ice that are numerically solved on a Lagrangian mesh with remeshing

Optical characterization of a SCISSOR device.

Here, we report on the design, fabrication and characterization of single-channel (SC-) and dual-channel (DC-) side-coupled integrated spaced sequences of optical resonators (SCISSOR) with a finite number (eight) of microring resonators using submicron silicon photonic wires on a silicon-on-insulator (SOI) wafer. We present results on the observation of multiple resonances in the through and the drop port signals of DC-SCISSOR. These result from the coupled resonator induced transparency (CRIT) which appears when the resonator band (RB) and the Bragg band (BB) are nearly coincident. We also observe the formation of high-Q (> 23000) quasi-localized modes in the RB of the drop transmission which appear when the RB and BB are well separated from each other. These multiple resonances and quasi-localized modes are induced by nanometer-scale structural disorders in the dimension of one or more rings. Finally, we demonstrate the tunability of RB (and BB) and localized modes in the DC-SCISSOR by thermo-optical or free-carrier refraction

Oscillatory coupling between a monolithic whispering-gallery resonator and a buried bus waveguide

We report on a combined theoretical and experimental study of the optical coupling between a microdisk resonator and a waveguide laying on different planes. While the lateral coupling between a planar resonator and a waveguide is characterized by a unique distance at which the resonant waveguide transmission vanishes because of destructive interference, the vertical coupling geometry exhibits an oscillatory behavior in the coupling amplitude as a function of the vertical gap. This effect manifests experimentally as oscillations in both the waveguide transmission and the mode quality factor. An analytical description based on coupled-mode theory and a two-port beam-splitter model of the waveguide-resonator coupling is developed, which compares successfully both to experimental data and numerical simulations.Comment: 5 pages, 3 figure

Estimating the sea ice floe size distribution using satellite altimetry: Theory, climatology, and model comparison

In sea-ice-covered areas, the sea ice floe size distribution (FSD) plays an important role in many processes affecting the coupled sea-ice-ocean-atmosphere system. Observations of the FSD are sparse - traditionally taken via a painstaking analysis of ice surface photography - and the seasonal and inter-annual evolution of floe size regionally and globally is largely unknown. Frequently, measured FSDs are assessed using a single number, the scaling exponent of the closest power-law fit to the observed floe size data, although in the absence of adequate datasets there have been limited tests of this "power-law hypothesis". Here we derive and explain a mathematical technique for deriving statistics of the sea ice FSD from polar-orbiting altimeters, satellites with sub-daily return times to polar regions with high along-track resolutions. Applied to the CryoSat-2 radar altimetric record, covering the period from 2010 to 2018, and incorporating 11 million individual floe samples, we produce the first pan-Arctic climatology and seasonal cycle of sea ice floe size statistics. We then perform the first pan-Arctic test of the power-law hypothesis, finding limited support in the range of floe sizes typically analyzed in photographic observational studies. We compare the seasonal variability in observed floe size to fully coupled climate model simulations including a prognostic floe size and thickness distribution and coupled wave model, finding good agreement in regions where modeled ocean surface waves cause sea ice fracture

Ultrafast all-optical switching in a silicon-nanocrystal-based silicon slot waveguide at telecom wavelengths

This document is the Accepted Manuscript version of a Published Work that appeared in final form in Nano Letters, copyright © American Chemical Society after peer review and technica editing by the publisher. To access the final edited and published work see http://pubs.acs.org/page/policy/articlesonrequest/index.htmlWe demonstrate experimentally all-optical switching on a silicon chip at telecom wavelengths. The switching device comprises a compact ring resonator formed by horizontal silicon slot waveguides filled with highly nonlinear silicon nanocrystals in silica. When pumping at power levels about 100 mW using 10 ps pulses, more than 50% modulation depth is observed at the switch output. The switch performs about I order of magnitude faster than previous approaches on silicon and is fully fabricated using complementary metal oxide semiconductor technologies.The work was financially supported by the EU through project PHOLOGIC (FP6-IST-NMP-017158).Martínez Abietar, AJ.; Blasco Solbes, J.; Sanchis Kilders, P.; Galan Conejos, JV.; García-Rupérez, J.; Jordana, E.; Gautier, P.... (2010). Ultrafast all-optical switching in a silicon-nanocrystal-based silicon slot waveguide at telecom wavelengths. Nano Letters. 10(4):1506-1511. doi:10.1021/nl9041017S1506151110

The making of an entertainment revolution: How the TV format trade became a global industry

From its humble origins in the 1950s, the TV format industry has become a global trade worth billions of Euros per year. Few viewers are aware that their favourite shows may be local adaptations but formats represent a significant percentage of European broadcasting schedules in access prime time and prime time. Formatted brands exist in all TV genres and reach almost every country in the world. This article defends the thesis that the format business turned into a global industry in the late 1990s. Before this turning point, the few formatted programmes were most likely American game shows that travelled slowly and to a limited number of territories. Following an overview of this early period, this article examines the convergence of factors that created a world format market. These include the emergence of four exceptional formats (Who Wants to Be a Millionaire?, Survivor, Big Brother and Idols), the formation of a programming market, the rise of the independent production sector, and the globalization of information flows within the TV industry

Optimizing Sisal Programs: a Formal Approach

We formally describe optimization techniques for the com pilation of the language Sisal 2.0. More precisely, we translate Sisal programs into data-flow IF1 graphs and optimize these graphs. An in teractive visualization environment for IF1 graphs is also provided