Coupled Dipole Method Determination of the Electromagnetic Force on a Particle over a Flat Dielectric Substrate

We present a theory to compute the force due to light upon a particle on a dielectric plane by the Coupled Dipole Method (CDM). We show that, with this procedure, two equivalent ways of analysis are possible, both based on Maxwell's stress tensor. The interest in using this method is that the nature and size or shape of the object, can be arbitrary. Even more, the presence of a substrate can be incorporated. To validate our theory, we present an analytical expression of the force due to the light acting on a particle either in presence, or not, of a surface. The plane wave illuminating the sphere can be either propagating or evanescent. Both two and three dimensional calculations are studied.Comment: 10 pages, 8 figures and 3 table

A global spectral library to characterize the world's soil

Soil provides ecosystem services, supports human health and habitation, stores carbon and regulates emissions of greenhouse gases. Unprecedented pressures on soil from degradation and urbanization are threatening agro-ecological balances and food security. It is important that we learn more about soil to sustainably manage and preserve it for future generations. To this end, we developed and analyzed a global soil visible-near infrared (vis-NIR) spectral library. It is currently the largest and most diverse database of its kind. We show that the information encoded in the spectra can describe soil composition and be associated to land cover and its global geographic distribution, which acts as a surrogate for global climate variability. We also show the usefulness of the global spectra for predicting soil attributes such as soil organic and inorganic carbon, clay, silt, sand and iron contents, cation exchange capacity, and pH. Using wavelets to treat the spectra, which were recorded in different laboratories using different spectrometers and methods, helped to improve the spectroscopic modelling. We found that modelling a diverse set of spectra with a machine learning algorithm can find the local relationships in the data to produce accurate predictions of soil properties. The spectroscopic models that we derived are parsimonious and robust, and using them we derived a harmonized global soil attribute dataset, which might serve to facilitate research on soil at the global scale. This spectroscopic approach should help to deal with the shortage of data on soil to better understand it and to meet the growing demand for information to assess and monitor soil at scales ranging from regional to global. New contributions to the library are encouraged so that this work and our collaboration might progress to develop a dynamic and easily updatable database with better global coverage. We hope that this work will reinvigorate our community's discussion towards larger, more coordinated collaborations. We also hope that use of the database will deepen our understanding of soil so that we might sustainably manage it and extend the research outcomes of the soil, earth and environmental sciences towards applications that we have not yet dreamed of

Hopf algebras and Markov chains: Two examples and a theory

The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied methods of card shuffling, a natural "rock-breaking" process, and Markov chains on simplicial complexes. Many of these chains can be explictly diagonalized using the primitive elements of the algebra and the combinatorics of the free Lie algebra. For card shuffling, this gives an explicit description of the eigenvectors. For rock-breaking, an explicit description of the quasi-stationary distribution and sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes will only appear on the version on Amy Pang's website, the arXiv version will not be updated.

Photonic molecules and spectral engineering

This chapter reviews the fundamental optical properties and applications of pho-tonic molecules (PMs) - photonic structures formed by electromagnetic coupling of two or more optical microcavities (photonic atoms). Controllable interaction between light and matter in photonic atoms can be further modified and en-hanced by the manipulation of their mutual coupling. Mechanical and optical tunability of PMs not only adds new functionalities to microcavity-based optical components but also paves the way for their use as testbeds for the exploration of novel physical regimes in atomic physics and quantum optics. Theoretical studies carried on for over a decade yielded novel PM designs that make possible lowering thresholds of semiconductor microlasers, producing directional light emission, achieving optically-induced transparency, and enhancing sensitivity of microcavity-based bio-, stress- and rotation-sensors. Recent advances in material science and nano-fabrication techniques make possible the realization of optimally-tuned PMs for cavity quantum electrodynamic experiments, classical and quantum information processing, and sensing.Comment: A review book chapter: 29 pages, 19 figure

A global spectral library to characterize the world's soil

Soil provides ecosystem services, supports human health and habitation, stores carbon and regulates emissions of greenhouse gases. Unprecedented pressures on soil from degradation and urbanization are threatening agro-ecological balances and food security. It is important that we learn more about soil to sustainably manage and preserve it for future generations. To this end, we developed and analyzed a global soil visible-near infrared (vis-NIR) spectral library. It is currently the largest and most diverse database of its kind. We show that the information encoded in the spectra can describe soil composition and be associated to land cover and its global geographic distribution, which acts as a surrogate for global climate variability. We also show the usefulness of the global spectra for predicting soil attributes such as soil organic and inorganic carbon, clay, silt, sand and iron contents, cation exchange capacity, and pH. Using wavelets to treat the spectra, which were recorded in different laboratories using different spectrometers and methods, helped to improve the spectroscopic modelling. We found that modelling a diverse set of spectra with a machine learning algorithm can find the local relationships in the data to produce accurate predictions of soil properties. The spectroscopic models that we derived are parsimonious and robust, and using them we derived a harmonized global soil attribute dataset, which might serve to facilitate research on soil at the global scale. This spectroscopic approach should help to deal with the shortage of data on soil to better understand it and to meet the growing demand for information to assess and monitor soil at scales ranging from regional to global. New contributions to the library are encouraged so that this work and our collaboration might progress to develop a dynamic and easily updatable database with better global coverage. We hope that this work will reinvigorate our community's discussion towards larger, more coordinated collaborations. We also hope that use of the database will deepen our understanding of soil so that we might sustainably manage it and extend the research outcomes of the soil, earth and environmental sciences towards applications that we have not yet dreamed of