Mixing compositions and other scales

Theory of compositional data analysis is often focused on the composition only. However in practical applications we often treat a composition together with covariables with some other scale. This contribution systematically gathers and develop statistical tools for this situation. For instance, for the graphical display of the dependence of a composition with a categorical variable, a colored set of ternary diagrams might be a good idea for a first look at the data, but it will fast hide important aspects if the composition has many parts, or it takes extreme values. On the other hand colored scatterplots of ilr components could not be very instructive for the analyst, if the conventional, black-box ilr is used. Thinking on terms of the Euclidean structure of the simplex, we suggest to set up appropriate projections, which on one side show the compositional geometry and on the other side are still comprehensible by a non-expert analyst, readable for all locations and scales of the data. This is e.g. done by defining special balance displays with carefully- selected axes. Following this idea, we need to systematically ask how to display, explore, describe, and test the relation to complementary or explanatory data of categorical, real, ratio or again compositional scales. This contribution shows that it is sufficient to use some basic concepts and very few advanced tools from multivariate statistics (principal covariances, multivariate linear models, trellis or parallel plots, etc.) to build appropriate procedures for all these combinations of scales. This has some fundamental implications in their software implementation, and how might they be taught to analysts not already experts in multivariate analysis

Simple finite field nuclear relaxation method for calculating vibrational contribution to degenerate four-wave mixing

A simple extended finite field nuclear relaxation procedure for calculating vibrational contributions to degenerate four-wave mixing (also known as the intensity-dependent refractive index) is presented. As a by-product one also obtains the static vibrationally averaged linear polarizability, as well as the first and second hyperpolarizability. The methodology is validated by illustrative calculations on the water molecule. Further possible extensions are suggested

Nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties by means of electrical property expansions: Application to HF, CH4, CF4, and SF6

Electrical property derivative expressions are presented for the nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties. For CF4 and SF6, as opposed to HF and CH4, a term that is quadratic in the vibrational anharmonicity (and not previously evaluated for any molecule) makes an important contribution to the static second vibrational hyperpolarizability of CF4 and SF6. A comparison between calculated and experimental values for the difference between the (anisotropic) Kerr effect and electric field induced second-harmonic generation shows that, at the Hartree-Fock level, the nuclear relaxation/infinite frequency approximation gives the correct trend (in the series CH4, CF4, SF6) but is of the order of 50% too small

Dynamics and mixing in the Upper Ocean Layer

S'estudia la resposta de la capa de barreja oceànica al forçament atmosfèric considerant dades obtingudes durant 12 dies d'abril del 2001 a 42 estacions a través de l'Atlàntic nord seguint aproximadament la latitud de 53ºN. Aquestes dades inclouen, a més de variables atmosfèriques, mesures de CTD, velocitats amb ADCP i dades de microestructura obtingudes amb un perfilador de caiguda lliure. En aquest últim cas, s'han desenvolupat tècniques de processament de les dades que també es presenten aquí. El transsecte estudiat segueix la posició climatològica del rotacional mitjà anual del vent igual a zero i travessa el corrent del Labrador i algunes branques i meandres del Corrent Atlàntic Nord. El forçament atmosfèric es va caracteritzar per vents intensos i fluxos superficials de calor negatius, tot i que, tal com es dedueix de la comparació del gruix de la capa de barreja amb la longitud de Monin-Obukov, la barreja induïda pel vent va dominar sobre la convectiva durant tot el transsecte.