A Quasi-Hamiltonian Discretization of the Thermal Shallow Water Equations

International audienceThe rotating shallow water (RSW) equations are the usual testbed for the development of numerical methods for three-dimensional atmospheric and oceanic models. However, an arguably more useful set of equations are the thermal shallow water equations (TSW), which introduce an additional thermodynamic scalar but retain the single layer, two-dimensional structure of the RSW. As a stepping stone towards a three-dimensional atmospheric dynamical core, this work presents a quasi-Hamiltonian discretization of the thermal shallow water equations using compatible Galerkin methods, building on previous work done for the shallow water equations. Structure-preserving or quasi-Hamiltonian discretizations methods, that discretize the Hamiltonian structure of the equations of motion rather than the equations of motion themselves, have proven to be a powerful tool for the development of models with discrete conservation properties. By combining these ideas with an energy-conserving Poisson time integrator and a careful choice of Galerkin spaces, a large set of desirable properties can be achieved. In particular, for the first time total mass, buoyancy and energy are conserved to machine precision in the fully discrete model

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions

Electromagnetic Waves

This book is dedicated to various aspects of electromagnetic wave theory and its applications in science and technology. The covered topics include the fundamental physics of electromagnetic waves, theory of electromagnetic wave propagation and scattering, methods of computational analysis, material characterization, electromagnetic properties of plasma, analysis and applications of periodic structures and waveguide components, and finally, the biological effects and medical applications of electromagnetic fields

Understanding and engineering interfacial charge transfer of carbon nanotubes and graphene for energy and sensing applications

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2013.Cataloged from PDF version of thesis.Includes bibliographical references.Graphene is a one-atom thick planar monolayer of sp2 -bonded carbon atoms organized in a hexagonal crystal lattice. A single walled carbon nanotube (SWCNT) can be thought of as a graphene sheet rolled up into a seamless hollow cylinder with extremely high length-to-diameter ratio. Their large surface area, and exceptional optical, mechanical and electronic properties make these low-dimensional carbon materials ideal candidates for (opto-)electronic and sensing applications. In this thesis I studied the charge transfer processes that occur at their interface, and developed applications based on the discovered properties. When light is incident on a semiconducting SWCNT, it can excite an electron from the valence band to the conduction band, thereby creating a Coulombically bound electron-hole pair, also known as an exciton. Excitons can decay via radiative or non-radiative recombination or by colliding with other excitons. They can diffuse along the length of a SWCNT or hop from larger band gap SWCNTs to smaller band gap SWCNTs, a process known as exciton energy transfer (EET). We studied their behavior as a function of temperature in SWCNT fibers and showed that at room temperature the rate constant for EET is more than two orders of magnitude larger than that of each of the different recombination processes. This led us to construct a core-shell SWCNT fiber, which consists of a core of smaller band gap SWCNTs, surrounded by a shell of larger band gap SWCNTs, essentially forming what is known as a type I heterojunction. In agreement with a model that describes exciton behavior in the SWCNT fibers, we found that upon illumination all the energy (in the form of excitons) was quickly transferred from the shell to the core, faster than the excitons would otherwise recombine. The SWCNT fiber proved to be an efficient optical and energetic concentrator. We showed that SWCNTs and poly(3-hexylthiophene) (P3HT) form a type II heterojunction, which implies that excitons generated in the P3HT can easily dissociate into free charge carriers at the interface with the SWCNTs. Despite this, the efficiency of a P3HT/SWCNT bulk heterojunction (BHJ) photovoltaic is subpar. We developed a P3HT/SWCNT planar heterojunction (PHJ) and achieved efficiencies that were 30 times higher, which showed that the formation of bundled aggregates in BHJs was the cause: metallic SWCNTs can quench the excitons in an entire bundle. Another interesting feature of our SWCNT/P3HT PHJ is that a maximum efficiency was reached when -60 nm of P3HT was used, which is surprising since in a planar photovoltaic a maximum is expected for ~8.5 nm of P3HT, the value of the exciton diffusion length. A Kinetic Monte Carlo simulation revealed that bulk exciton dissociation was responsible for the lower efficiencies observed in devices with low P3HT thickness. Next we created and studied a junction between SWCNTs and a monolayer of graphene, an ideal one-dimensional/two-dimensional carbon interface. We used Raman spectroscopy to probe the degree of charge transfer at the interface and based on a shift in the G peak position of the graphene Raman signal at the junction deduced that a typical metallic (semiconducting) SWCNT dopes the graphene with 1.12 x 1013 cm-2 (0.325 x 101 cm-2) electrons upon contact, in agreement with the fact that the Fermi level of the SWCNTs is more shallow than that of the graphene. A molecular dynamics simulation ruled out that the observed Raman peak shifts are due to strain, although it did show that SWCNTs are being compressed radially by the graphene sheet, resulting in a widening of their Raman peaks. We studied charge transfer between diazonium molecules and graphene, to better inform transistor and sensor design. The reaction rate depends on the degree of overlap between the filled energy levels in graphene and the unoccupied ones in the diazonium molecule. We showed that with increasing degree of functionalization the charge transfer characteristics of a graphene field effect transistor (FET) alter in the following ways: the minimum conductivity decreases, the Dirac point upshifts, the conductivity plateau at high carrier density decreases and the electronhole conduction asymmetry increases. We developed a theoretical model of charge transport in graphene FETs that takes into account the effect of both short-range and long-range scatterers. Fitting it to the charge-transport data reveals quantitative information about the number of impurities in the substrate supporting the graphene, about the number of defects created as a result of the reaction, and about the degree of electron-hole conduction asymmetry. Graphene functionalization also affects the graphene Raman signal. After reaction, the D to G intensity ratio to increases, which is a sign of covalent modification of the graphene lattice. Additionally, the G peak and 2D peak positions increase while the 2D/G intensity ratio decreases, which are signs of hole-doping. Based on a Raman analysis, we were also able to show that the end group of the diazonium salt can affect both the degree of chemisorption (covalent modification) as well as the degree of physisorption (doping). Finally, we studied the effects of charge transfer between graphene and biological cells on the graphene Raman signal and designed a fundamentally new type of biosensor. Graphene can be thought of as a continuous array of information units (sensor units). The Raman signal collected in each unit can report on its local environment. In contrast to graphene FET biosensors, the graphene Raman biosensor offers subcellular spatial resolution. The graphene Raman signal was shown to display a strong dependence on pH. Metabolically active cells acidify their local environment; therefore, pH is a proxy for cellular metabolism. We placed both human embryonic kidney (HEK) cells that were genetically engineered to produce mouse antibodies and control HEK cells that were not genetically modified onto the graphene. Based on the change in the graphene Raman signal we deduced the former have a metabolic rate that is four times higher than that of the control cells. Increased cellular adhesion allows the cells to interact more closely with the graphene monolayer and intensifies the observed Raman effects.by Geraldine L.C. Paulus.Ph.D