Finite element methods for multicomponent convection-diffusion

We develop finite element methods for coupling the steady-state Onsager--Stefan--Maxwell equations to compressible Stokes flow. These equations describe multicomponent flow at low Reynolds number, where a mixture of different chemical species within a common thermodynamic phase is transported by convection and molecular diffusion. Developing a variational formulation for discretizing these equations is challenging: the formulation must balance physical relevance of the variables and boundary data, regularity assumptions, tractability of the analysis, enforcement of thermodynamic constraints, ease of discretization, and extensibility to the transient, anisothermal, and non-ideal settings. To resolve these competing goals, we employ two augmentations: the first enforces the mass-average constraint in the Onsager--Stefan--Maxwell equations, while its dual modifies the Stokes momentum equation to enforce symmetry. Remarkably, with these augmentations we achieve a Picard linearization of symmetric saddle point type, despite the equations not possessing a Lagrangian structure. Exploiting the structure of linear irreversible thermodynamics, we prove the inf-sup condition for this linearization, and identify finite element function spaces that automatically inherit well-posedness. We verify our error estimates with a numerical example, and illustrate the application of the method to non-ideal fluids with a simulation of the microfluidic mixing of hydrocarbons

Sequential and Spontaneous Star Formation Around the Mid-Infrared Halo HII Region KR 140

We use 2MASS and MSX infrared observations, along with new molecular line (CO) observations, to examine the distribution of young stellar objects (YSOs) in the molecular cloud surrounding the halo HII region KR 140 in order to determine if the ongoing star-formation activity in this region is dominated by sequential star formation within the photodissociation region (PDR) surrounding the HII region. We find that KR 140 has an extensive population of YSOs that have spontaneously formed due to processes not related to the expansion of the HII region. Much of the YSO population in the molecular cloud is concentrated along a dense filamentary molecular structure, traced by C18O, that has not been erased by the formation of the exciting O star. Some of the previously observed submillimetre clumps surrounding the HII region are shown to be sites of recent intermediate and low-mass star formation while other massive starless clumps clearly associated with the PDR may be the next sites of sequential star formation.Comment: Accepted for publication in MNRAS, 8 pages, 10 figure

Photodetachment study of He^- quartet resonances below the He(n=3) thresholds

The photodetachment cross section of He^- has been measured in the photon energy range 2.9 eV to 3.3 eV in order to investigate doubly excited states. Measurements were made channel specific by selectively detecting the residual He atoms left in a particular excited state following detachment. Three Feshbach resonances were found in the He(1s2p ^3P)+e^-(epsilon p) partial cross section: a ^4S resonance below the He(1s3s ^3S) threshold and two ^4P resonances below the He(1s3p ^3P) threshold. The measured energies of these doubly excited states are 2.959260(6) eV, 3.072(7) eV and 3.26487(4) eV. The corresponding widths are found to be 0.20(2) meV, 50(5) meV and 0.61(5) meV. The measured energies agree well with recent theoretical predictions for the 1s3s4s ^4S, 1s3p^2 ^4P and 1s3p4p ^4P states, respectively, but the widths deviate noticeably from calculations for 1s3p^2 ^4P and 1s3p4p ^4P states.Comment: 10 pages, 3 figures, LaTeX2e scrartcl, amsmath. Accepted by Journal of Physics B; minor changes after referee repor

Euler-Lagrange equations for composition functionals in calculus of variations on time scales

In this paper we consider the problem of the calculus of variations for a functional which is the composition of a certain scalar function $H$ with the delta integral of a vector valued field $f$, i.e., of the form $H(\int_{a}^{b}f(t,x^{\sigma}(t),x^{\Delta}(t))\Delta t)$. Euler-Lagrange equations, natural boundary conditions for such problems as well as a necessary optimality condition for isoperimetric problems, on a general time scale, are given. A number of corollaries are obtained, and several examples illustrating the new results are discussed in detail.Comment: Submitted 10-May-2009 to Discrete and Continuous Dynamical Systems (DCDS-B); revised 10-March-2010; accepted 04-July-201

Dynamic orifice area variations in functional mitral regurgitation: In vivoreproduction and mechanistic insights

Aims: The spinocerebellar ataxia type 2 (SCA2), type 3 (SCA3) and type 7 (SCA7) are clinically characterized by progressive and severe ataxic symptoms, dysarthria, dysphagia, oculomotor impairments, pyramidal and extrapyramidal manifestations and sensory deficits. Although recent clinical studies reported additional disease signs suggesting involvement of the brainstem auditory system, this has never been studied in detail in SCA2, SCA3 or SCA7. Methods: We performed a detailed pathoanatomical investigation of unconventionally thick tissue sections through the auditory brainstem nuclei (that is, nucleus of the inferior colliculus, nuclei of the lateral lemniscus, superior olive, cochlear nuclei) and auditory brainstem fibre tracts (that is, lateral lemniscus, trapezoid body, dorsal acoustic stria, cochlear portion of the vestibulocochlear nerve) of clinically diagnosed and genetically confirmed SCA2, SCA3 and SCA7 patients. Results: Examination of unconventionally thick serial brainstem sections stained for lipofuscin pigment and Nissl material revealed a consistent and widespread involvement of the auditory brainstem nuclei in the SCA2, SCA3 and SCA7 patients studied. Serial brainstem tissue sections stained for myelin showed loss of myelinated fibres in two of the auditory brainstem fibre tracts (that is, lateral lemniscus, trapezoid body) in a subset of patients. Conclusions: The involvement of the auditory brainstem system offers plausible explanations for the auditory impairments detected in some of our and other SCA2, SCA3 and SCA7 patients upon bedside examination or neurophysiological investigation. However, further clinical studies are required to resolve the striking discrepancy between the consistent involvement of the brainstem auditory system observed in this study and the comparatively low frequency of reported auditory impairments in SCA2, SCA3 and SCA7 patients

Direct and Inverse Variational Problems on Time Scales: A Survey

We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to attain a local minimum at a given point of the vector space. Furthermore, we provide a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation (Helmholtz's problem of the calculus of variations on time scales). New and interesting results for the discrete and quantum settings are obtained as particular cases. Finally, we consider very general problems of the calculus of variations given by the composition of a certain scalar function with delta and nabla integrals of a vector valued field.Comment: This is a preprint of a paper whose final and definite form will be published in the Springer Volume 'Modeling, Dynamics, Optimization and Bioeconomics II', Edited by A. A. Pinto and D. Zilberman (Eds.), Springer Proceedings in Mathematics & Statistics. Submitted 03/Sept/2014; Accepted, after a revision, 19/Jan/201

Prediction of Evapotranspiration in a Mediterranean Region Using Basic Meteorological Variables

A critical need for farmers, particularly those in arid and semiarid areas is to have a reliable, accurate and reasonably accessible means of estimating the evapotranspiration rates of their crops to optimize their irrigation requirements. Evapotranspiration is a crucial process because of its influence on the precipitation that is returned to the atmosphere. The calculation of this variable often starts from the estimation of reference evapotranspiration, for which a variety of methods have been developed. However, these methods are very complex either theoretically and/or because of the large amount of parameters on which they are based, which makes the development of a simple and reliable methodology for the prediction of this variable important. This research combined three concepts such as cluster analysis, multiple linear regression (MLR), and Voronoi diagrams to achieve that end. Cluster analysis divided the study area into groups based on its weather characteristics, whose locations were then delimited by drawing the Voronoi regions associated with them. Regression equations were built to predict daily reference evapotranspiration in each cluster using basic climate variables produced in forecasts made by meteorological agencies. Finally, the Voronoi diagrams were used again to regionalize the crop coefficients and calculate evapotranspiration from the values of reference evapotranspiration derived from the regression models. These operations were applied to the Valencian region (Spain), a Mediterranean area which is partly semiarid and for which evapotranspiration is a critical issue. The results demonstrated the usefulness and accuracy of the methodology to predict the water demands of crops and hence enable farmers to plan their irrigation needs.This paper was possible thanks to the research project RHIVU (Ref. BIA2012-32463), financed by the Spanish Ministry of Economy and Competitiveness with funds from the State General Budget (PGE) and the European Regional Development Fund (ERDF). The authors also wish to express their gratitude to the Spanish Ministry of Agriculture, Food and Environment (MAGRAMA) for providing the data necessary to develop this study

Study of the p p -> p p pi+ pi- Reaction in the Low-Energy Tail of the Roper Resonance

Exclusive measurements of the p p -> p p pi+ pi- reaction have been carried out at Tp = 775 MeV at CELSIUS using the PROMICE/WASA setup. Together with data obtained at lower energy they point to a dominance of the Roper excitation in this process. From the observed interference of its decay routes N* -> N sigma and N* -> Delta pi -> N sigma their energy-dependent relative branching ratio is determined

On a (\beta,q)-generalized Fisher information and inequalities involving q-Gaussian distributions

In the present paper, we would like to draw attention to a possible generalized Fisher information that fits well in the formalism of nonextensive thermostatistics. This generalized Fisher information is defined for densities on $\mathbb{R}^{n}.$ Just as the maximum R\'enyi or Tsallis entropy subject to an elliptic moment constraint is a generalized q-Gaussian, we show that the minimization of the generalized Fisher information also leads a generalized q-Gaussian. This yields a generalized Cram\'er-Rao inequality. In addition, we show that the generalized Fisher information naturally pops up in a simple inequality that links the generalized entropies, the generalized Fisher information and an elliptic moment. Finally, we give an extended Stam inequality. In this series of results, the extremal functions are the generalized q-Gaussians. Thus, these results complement the classical characterization of the generalized q-Gaussian and introduce a generalized Fisher information as a new information measure in nonextensive thermostatistics.Comment: v2: corrected equation (A5