Partial mass concentration for fast-diffusions with non-local aggregation terms

We study well-posedness and long-time behaviour of aggregation-diffusion equations of the form $\frac{\partial \rho}{\partial t} = \Delta \rho^m + \nabla \cdot( \rho (\nabla V + \nabla W \ast \rho))$ in the fast-diffusion range, $0<m<1$, and $V$ and $W$ regular enough. We develop a well-posedness theory, first in the ball and then in $\mathbb R^d$, and characterise the long-time asymptotics in the space $W^{-1,1}$ for radial initial data. In the radial setting and for the mass equation, viscosity solutions are used to prove partial mass concentration asymptotically as $t \to \infty$, i.e. the limit as $t \to \infty$ is of the form $\alpha \delta_0 + \widehat \rho \, dx$ with $\alpha \geq 0$ and $\widehat \rho \in L^1$. Finally, we give instances of $W \ne 0$ showing that partial mass concentration does happen in infinite time, i.e. $\alpha > 0$

Determination of Arsenic, Mercury and Barium in herbarium mount paper using dynamic ultrasound-assisted extraction prior to atomic fluorescence and absorption spectrometry

A dynamic ultrasound-assisted extraction method using Atomic Absorption and Atomic Flourescence spectrometers as detectors was developed to analyse mercury, arsenic and barium from herbarium mount paper originating from the herbarium collection of the National Museum of Wales. The variables influencing extraction were optimised by a multivariate approach. The optimal conditions were found to be 1% HNO3 extractant solution used at a flow rate of 1 mL min-1. The duty cycle and amplitude of the ultrasonic probe was found to be 50% in both cases with an ultrasound power of 400 W. The optimal distance between the probe and the top face of the extraction chamber was found to be 0 cm. Under these conditions the time required for complete extraction of the three analytes was 25 min. Cold vapour and hydride generation coupled to atomic fluorescence spectrometry was utilized to determine mercury and arsenic, respectively. The chemical and instrumental conditions were optimized to provide detection limits of 0.01ng g-1 and 1.25 ng g-1 for mercury and arsenic, respectively. Barium was determined by graphite-furnace atomic absorption spectrometry, with a detection limit of 25 ng g-1. By using 0.5 g of sample, the concentrations of the target analytes varied for the different types of paper and ranged between 0.4–2.55 µg g-1 for Ba, 0.035–10.47 µg g-1 for As and 0.0046–2.37 µg g-1 for Hg

Estimación de estado e incertidumbre en un CSTR mediante Observador Asintótico y modos deslizantes de alto orden

En este artículo se propone una estructura de estimación de estado para un Reactor de Tanque Agitado en Continuo (CSTR), mediante un Observador Asintótico, conjuntamente con un estimador de perturbaciones basado en un algoritmo de modos deslizantes de alto orden, tipo Super Twisting Generalizado. El esquema de estimación propuesto permite la reconstrucción asintótica de la concentración en el reactor, con base en la medición de la temperatura al interior del mismo y de la chaqueta, en la presencia de cambios en el coeficiente global de intercambio de calor UA, la constante de frecuencia k_0 de la ecuación de Arrhenius y la energía de activación E. Adicionalmente, la estructura es capaz de estimar UA y el término k_0 e^(-E/RT) de la cinética. Las propiedades del esquema propuesto se demuestran matemáticamente y a través de simulaciones.Universidad Nacional de ColombiaCinvesta

A Soft Sensor for Biomass in a Batch Process with Delayed Measurements

This paper presents a soft sensor to estimate the biomass concentration in a batch bioprocess used in production of δ-endotoxins of Bacillus thuringiensis, subject to delayed measurements. The soft sensor proposed is based on a cascade observer-predictor algorithm. The observer stage is based on a class of second order sliding mode algorithms, allowing a fixed time estimation of the biomass. Additionally, the prediction stage offsets the effect of the delay in measurements. Simulations show the feasibility of the proposed observer.Universidad Nacional de ColombiaCINVESTAV-IPNITESO, A.C

Robust Estimation for a CSTR Using a High Order Sliding Mode Observer and an Observer-Based Estimator

This paper presents an estimation structure for a continuous stirred-tank reactor, which is comprised of a sliding mode observer-based estimator coupled with a high-order sliding-mode observer. The whole scheme allows the robust estimation of the state and some parameters, specifically the concentration of the reactive mass, the heat of reaction and the global coefficient of heat transfer, by measuring the temperature inside the reactor and the temperature inside the jacket. In order to verify the results, the convergence proof of the proposed structure is done, and numerical simulations are presented with noiseless and noisy measurements, suggesting the applicability of the posed approach.ITESO, A.C.Universidad Nacional de Colombi

Robust Estimation for a CSTR Using a High Order Sliding Mode Observer and an Observer-Based Estimator

This paper presents an estimation structure for a continuous stirred-tank reactor, which is comprised of a sliding mode observer-based estimator coupled with a high-order sliding-mode observer. The whole scheme allows the robust estimation of the state and some parameters, specifically the concentration of the reactive mass, the heat of reaction and the global coefficient of heat transfer, by measuring the temperature inside the reactor and the temperature inside the jacket. In order to verify the results, the convergence proof of the proposed structure is done, and numerical simulations are presented with noiseless and noisy measurements, suggesting the applicability of the posed approach.ITESO, A.C.Universidad Nacional de Colombi

An Equivalent Control Based Observer for Biomass in a Batch Process

In this paper a sliding-mode observer for a batch bioprocess, the d-endotoxins production of bacillus thuringiensis (BT), is presented. The proposed observer is based on the equivalent control method and a class of second-order sliding mode operators. The use of these operators in the observer design allows the fixed-time convergence of the measured variables, while the unmeasured variables converge exponentially. This structure allows to estimate the biomass in the d-endotoxins production of BT, even, under noisy measurement conditions. Simulations show the feasibility of the proposed observer. Convergence proofs are also presented

A Robust Extended State Observer for the Estimation of Concentration and Kinetics in a CSTR

This paper presents a state estimation structure for a Continuous Stirred Tank Reactor (CSTR), by means of an Asymptotic Observer jointly with a disturbance high order sliding mode-based estimator. The proposed estimation scheme allows the asymptotic reconstruction of the concentration inside the reactor based on the measures of the temperature inside the reactor and the temperature inside the jacket, in presence of changes in the global coefficient of heat transfer UA, the Arrhenius constant k0 and the activation energy E. Additionally, the structure is able to estimate UA and the kinetics term k0e−ERT. The properties of the proposed scheme are proved mathematically and verified through numerical simulations.ITESO, A.C.CINVESTAV-IP

Changes in compliance with school-based physical activity recommendations in Spanish youth: The UP&DOWN longitudinal study

The study aimed (a) to examine changes in physical activity (PA) during the whole day, school hours, recess, and physical education classes (PEC) during a 2-year period in primary and secondary students; (b) to identify changes in the proportion of compliance with specific PA recommendations for these periods; and (c) to examine whether PA levels at baseline are associated with PA levels 2 years later. Eight hundred and fourteen (51.8% boys) children and 658 (50.1% boys) adolescents from 41 Spanish schools participated in the study. Hip-worn accelerometers were used to assess PA during different time periods. Light PA (LPA) declined during the whole day, school hours, recess (all P < 0.001, except child girls for recess), and PEC (all, P < 0.05) in children and adolescents. Moderate-to-vigorous PA (MVPA) during the whole day and recess declined in child boys (P < 0.01 and P < 0.001, respectively) and adolescent boys (P < 0.001 and P < 0.05, respectively). MVPA during PEC declined in adolescent boys (P < 0.001) and adolescent girls (all P < 0.05). The proportion of compliance with the specific PA recommendations for these periods declined (P < 0.05), except for PEC in adolescent girls. PA during the whole day at baseline was moderately associated with PA during the whole day years later (ICCs = 0.210-0.544, with one exception), but this association was lower for the school-based PA. In conclusion, time spent in MVPA and LPA during the whole day and recess declined over time in child and adolescent boys and during PEC in adolescents. These findings highlight the need to promote PA interventions in these settings