Convection-diffusion-reaction models of sedimentation : Numerical approximation, analysis of solutions and inverse problems

The core of this Doctoral thesis is mainly based in the studies of one-dimensional initial-boundary value problems, which are given by a single non-linear hyperbolic partial differential equation (PDE) with non-convex flux function, or by a system of strongly degenerate parabolic PDEs, for the simulation of sedimentation processes of solid particles immersed in a fluid. Particular attention is paid to the case of settling in vessels with varying cross-sectional area. Sedimentation processes are widely used in wastewater treatment (WWT) and mineral processing, where accurate model calibration and reliable simulators are needed. Among the topics covered in the research presented in this thesis are the construction of entropy solutions, the development and implementation of reliable numerical schemes for hyperbolic PDEs (and systems of PDEs), the solution of inverse problems of flux identification, and the disseminationof results to the applied sciences.The outputs of this thesis can be divided into three parts. The first part (Papers I to III) contains the construction of the entropy solutions for the PDE modeling the batch sedimentation in vessels with non-constant cross-sectional area(Paper I and II) and for the PDE modeling centrifugal sedimentation (Paper III). The problem is in both cases solved by the method of characteristics and the types of solutions are distinguished mainly depending on the initial value.Paper II contains the description and solution of the inverse problem of flux identification for the model of sedimentation in conical vessels due to gravity, and Paper III the inverse problem for the model of centrifugal settling. In bothcases, the solution of the inverse problem has the advantage that almost the entire flux function can be identified from only one experiment. These identification methods mean a significant advantage in comparison with the classic one, made by standard tests in cylindrical vessels, in terms of the portion of flux identified. An algorithm necessary for the identification from discrete data is also presented in each problem (Papers II and III).The second part (Papers IV to VI) includes the development of numerical methods for the simulation of sedimentation in WWT. In Paper IV, a numerical scheme for the case of continuous and batch sedimentation in vessels withvarying cross-sectional area is studied. An advantageous CFL condition is derived as an improvement over other numerical methods for the same kind of application. Simulations of continuous and batch settling are also included.Papers V and VI consider reactive settling, where the unknown is a vector of solid and liquid components, and each model is described by a coupled system of convection-diffusion-reaction PDEs. In Paper V, a method-of-lines formulation for the approximation of the model equations is introduced. This formulation has the advantage that it can be solved by any time stepping solver, such as those commonly used in the WWT community where ordinary differentialequations (ODEs) should be solved simultaneously with the PDE system. Additionally, an invariant-region property is proved for the scheme and simulations of interesting scenarios are presented. In Paper VI, sequencing batch reactors (SBRs) are studied. The model equations for the SBRs are derived following Paper V, but with the addition that in this case, the extraction and filling of mixture lead to a moving-boundary problem. The movement of the boundary is described by an ODE which can be precomputed. A reliable numerical scheme that preserves the mass is proposed and numerical simulations for the case of denitrification are shown.The third part (Papers VII and VIII) is related to applications and dissemination of the flux identification methods to the applied sciences. The validation of the inverse problem for batch settling in conical vessels is presented in Pa-per VII. The validation was carried out with data taken from activated sludge collected from the WWT plant in Västerås, Sweden. Paper VIII contains a review of flux identification methods related to PDE models for sedimentation processes. Advantages and disadvantages are discussed, and simulations of identified fluxes with the methods under study are presented.In Chapter 4 the numerical simulation of multidimensional batch sedimentation is discussed and two-dimensional simulations are presented

The pluripotency factor NANOG controls primitive hematopoiesis and directly regulates Tal1

Progenitors of the first hematopoietic cells in the mouse arise in the early embryo from Brachyury-positive multipotent cells in the posterior-proximal region of the epiblast, but the mechanisms that specify primitive blood cells are still largely unknown. Pluripotency factors maintain uncommitted cells of the blastocyst and embryonic stem cells in the pluripotent state. However, little is known about the role played by these factors during later development, despite being expressed in the postimplantation epiblast. Using a dual transgene system for controlled expression at postimplantation stages, we found that Nanog blocks primitive hematopoiesis in the gastrulating embryo, resulting in a loss of red blood cells and downregulation of erythropoietic genes. Accordingly, Nanog-deficient embryonic stem cells are prone to erythropoietic differentiation. Moreover, Nanog expression in adults prevents the maturation of erythroid cells. By analysis of previous data for NANOG binding during stem cell differentiation and CRISPR/Cas9 genome editing, we found that Tal1 is a direct NANOG target. Our results show that Nanog regulates primitive hematopoiesis by directly repressing critical erythroid lineage specifiers.This work was supported by the Spanish government (grant BFU2014-54608-P and BFU2017-84914-P to MM; grants RYC-2011-09209 and BFU-2012-35892 to JI). The Gottgens and Nichols laboratories are supported by core funding from the Wellcome Trust and MRC to the Wellcome and MRC Cambridge Stem Cell Institute. The CNIC is supported by the Spanish Ministry of Science, Innovation and Universities (MINECO) and the Pro CNIC Foundation, and is a Severo Ochoa Center of Excellence (SEV-2015-0505)S

Ideación suicida en Estudiantes de Medicina de la Universidad Nacional de Asunción: Suicidal ideation in Medical Students of the National University of Asunción

Introducción: Los estudiantes de Medicina forman parte de uno de los grupos con más alto riesgo de suicidio. Objetivo: Determinar la frecuencia de ideación suicida en estudiantes de Medicina de la Universidad Nacional de Asunción. Metodología: Estudio observacional descriptivo, de corte transversal, con muestreo no probabilístico por conveniencia. Se utilizó la Escala de Ideación Suicida de Beck, adaptada al español por la Universidad Complutense de Madrid, en 288 estudiantes de Medicina de la Universidad Nacional de Asunción. Resultados: Se encontró que la frecuencia de ideación suicida fue del 54,9%. Entre los estudiantes con ideación suicida, la intensidad del deseo de vivir fue en su mayoría de moderada a intensa (77,2%). La intensidad del deseo de morir fue mayoritariamente débil con un 51,9%. La mayoría de los pensamientos/comportamientos suicidas se presentaron de forma ocasional, rara (62,02%) y por períodos breves y pasajeros (81,6%). La razón más frecuente del proyecto de intento suicida fue la de escapar, acabar y resolver problemas (87,34%). El factor disuasorio de intento de suicidio más frecuente (47%) estuvo representado por la familia del estudiante. Discusión: La ideación suicida es un fenómeno de frecuente ocurrencia en estudiantes de Medicina. Es necesario que las Universidades establezcan programas de detección e intervención temprana que permitan disminuir la probabilidad de ocurrencia de desenlaces negativos.   Palabras clave: Ideación suicida; Suicidio; Intento de suicidio; Estudiantes de Medicina

Pluripotency factors regulate the onset of Hox cluster activation in the early embryo

Pluripotent cells are a transient population of the mammalian embryo dependent on transcription factors, such as OCT4 and NANOG, which maintain pluripotency while suppressing lineage specification. However, these factors are also expressed during early phases of differentiation, and their role in the transition from pluripotency to lineage specification is largely unknown. We found that pluripotency factors play a dual role in regulating key lineage specifiers, initially repressing their expression and later being required for their proper activation. We show that Oct4 is necessary for activation of HoxB genes during differentiation of embryonic stem cells and in the embryo. In addition, we show that the HoxB cluster is coordinately regulated by OCT4 binding sites located at the 3′ end of the cluster. Our results show that core pluripotency factors are not limited to maintaining the precommitted epiblast but are also necessary for the proper deployment of subsequent developmental programs.This work was funded by the Spanish government (grants BFU2017-84914-P and PID2020-115755GB-I00 to M.M.; BFU2016-74961-P and BFU2016-81887-REDT to J.L.G.-S.), the Andalusian government (grant BIO-396 to J.L.G.-S.), and the European Research Council (ERC; grant agreement 740041 to J.L.G.-S.). M.T. held Juan de la Cierva fellowships from the Spanish government (FJCI-2017-31791 and IJC2019-038897-I), R.R. and R.D.A. held FPU fellowships from the government, and J.V. was the recipient of a “La Caixa” fellowship. Work in the laboratory of J.L.G.-S. was supported by a María de Maetzu Unit of Excellence Grant (MDM-2016-0687) to the Department of Gene Regulation and Morphogenesis of the CABD. The CBMSO is supported by an institutional grant from the Fundación Ramon Areces, and the CNIC is supported by the Instituto de Salud Carlos III (ISCIII), the Ministerio de Ciencia e Innovación (MCIN), and the Pro CNIC Foundation, and is a Severo Ochoa Center of Excellence (grant CEX2020-001041-S funded by MICIN/AEI/10.13039/501100011033). : With funding from the Spanish government through the ‘Severo Ochoa Centre of Excellence’ accreditation (CEX2020-001041-S)

Pluripotency factors regulate the onset of Hox cluster activation in the early embryo

Pluripotent cells are a transient population of the mammalian embryo dependent on transcription factors, such as OCT4 and NANOG, which maintain pluripotency while suppressing lineage specification. However, these factors are also expressed during early phases of differentiation, and their role in the transition from pluripotency to lineage specification is largely unknown. We found that pluripotency factors play a dual role in regulating key lineage specifiers, initially repressing their expression and later being required for their proper activation. We show that Oct4 is necessary for activation of HoxB genes during differentiation of embryonic stem cells and in the embryo. In addition, we show that the HoxB cluster is coordinately regulated by OCT4 binding sites located at the 3′ end of the cluster. Our results show that core pluripotency factors are not limited to maintaining the precommitted epiblast but are also necessary for the proper deployment of subsequent developmental programs

Nanog regulates Pou3f1 expression at the exit from pluripotency during gastrulation.

Pluripotency is regulated by a network of transcription factors that maintain early embryonic cells in an undifferentiated state while allowing them to proliferate. NANOG is a critical factor for maintaining pluripotency and its role in primordial germ cell differentiation has been well described. However, Nanog is expressed during gastrulation across all the posterior epiblast, and only later in development is its expression restricted to primordial germ cells. In this work, we unveiled a previously unknown mechanism by which Nanog specifically represses genes involved in anterior epiblast lineage. Analysis of transcriptional data from both embryonic stem cells and gastrulating mouse embryos revealed Pou3f1 expression to be negatively correlated with that of Nanog during the early stages of differentiation. We have functionally demonstrated Pou3f1 to be a direct target of NANOG by using a dual transgene system for the controlled expression of Nanog Use of Nanog null ES cells further demonstrated a role for Nanog in repressing a subset of anterior neural genes. Deletion of a NANOG binding site (BS) located nine kilobases downstream of the transcription start site of Pou3f1 revealed this BS to have a specific role in the regionalization of the expression of this gene in the embryo. Our results indicate an active role of Nanog inhibiting neural regulatory networks by repressing Pou3f1 at the onset of gastrulation.This article has an associated First Person interview with the joint first authors of the paper.This work was funded by the Spanish government [grant BFU2017-84914-P to M.M.]. The Gottgens laboratory is supported by core funding from the Wellcome Trust and Medical Research Council to the Wellcome and Medical Research Council Cambridge Stem Cell Institute. The CNIC is supported by the Instituto de Salud Carlos III (ISCIII), the Ministerio de Ciencia, Innovación y Universidades (MCNU) and the Pro CNIC Foundation, and is a Severo Ochoa Center of Excellence [SEV-2015-0505]

Entropy solutions and flux identification of a scalar conservation law modelling centrifugal sedimentation

Centrifugal sedimentation of an ideal suspension in a rotating tube or basket can be modelled by an initial-boundary-value problem for a scalar conservation law with a nonconvex flux function. The sought unknown is the volume fraction of solids as function of radial distance and time for constant initial data. The method of characteristics is used to construct entropy solutions. The qualitatively different solutions, which depend on the initial value and the vessel radial coordinates, are presented in detail along with numerical simulations. Based on the entropy solutions, a new method of flux identification, which does not require any prescribed functional expression, is presented and illustrated with synthetic data

Coupled mixed finite element and finite volume methods for a solid velocity-based model of multidimensional sedimentation

In this paper we introduce and analyze a model of sedimentation based on a solid velocity formulation. A particular feature of the governing equations is given by the fact that the velocity field is non-divergence free. We introduce extra variables such as the pseudostress tensor relating the velocity gradient with the pressure, thus leading to a mixed variational formulation consisting of two systems of equations coupled through their source terms. A result of existence and uniqueness of solutions is shown by means of a fixed-point strategy and the help of the Babuška–Brezzi theory and Banach theorem. Additionally, we employ suitable finite dimensional subspaces to approximate both systems of equations via associated mixed finite element methods. The well-posedness of the resulting coupled scheme is also treated via a fixed-point approach, and hence the discrete version of the existence and uniqueness result is derived analogously to the continuous case. The above is then combined with a finite volume method for the transport equation. Finally, several numerical results illustrating the performance of the proposed model and the full numerical scheme, and confirming the theoretical rates of convergence, are presented

Entropy solutions of a scalar conservation law modeling sedimentation in vessels with varying cross-sectional area

The sedimentation of an ideal suspension in a vessel with variable cross-sectional area can be described by an initial-boundary value problem for a scalar nonlinear hyperbolic conservation law with a nonconvex flux function and a weight function that depends on spatial position. The sought unknown is the local solids' volume fraction. For the most important cases of vessels with downward-decreasing cross-sectional area and flux functions with at most one infection point, entropy solutions of this problem are constructed by the method of characteristics. Solutions exhibit discontinuities that mostly travel at variable speed, i.e., they are curved in the space-time plane. These trajectories are given by ordinary differential equations that arise from the jump condition. It is shown that three qualitatively different solutions may occur in dependence of the initial concentration. The potential application of the findings is a new method of flux identification via settling tests in a suitably shaped vessel. Related models also arise in flows of vehicular traffic, pedestrians, in pipes with varying cross-sectional area, and on curved surfaces

Flux identification methods of sedimentation

Any reasonable model of sedimentation contains the nonlinear hindered-settling flux function. If one assumes ideal conditions and no compression, then there exist several theoretically possible ways of identifying a large part of the flux function from only one experiment by means of formulas derived from the theory of partial differential equations. Such identification methods, including new results on centrifugal settling, are reviewed and compared with synthetic data (simulated experiments)