A uniqueness and regularity criterion for Q-tensor models with Neumann boundary conditions

We give a regularity criterion for a $Q$-tensor system modeling a nematic Liquid Crystal, under homogeneous Neumann boundary conditions for the tensor $Q$. Starting of a criterion only imposed on the velocity field ${\bf u}$ two results are proved; the uniqueness of weak solutions and the global in time weak regularity for the time derivative $(\partial_t {\bf u},\partial_t Q)$. This paper extends the work done in [F. Guill\'en-Gonz\'alez, M.A. Rodr\'iguez-Bellido \& M.A. Rojas-Medar, Sufficient conditions for regularity and uniqueness of a 3D nematic liquid crystal model, Math. Nachr. 282 (2009), no. 6, 846-867] for a nematic Liquid Crystal model formulated in $({\bf u},{\bf d})$, where ${\bf d}$ denotes the orientation vector of the liquid crystal molecules.Comment: 13 page

Optimal bilinear control problem related to a chemo-repulsion system in 2D domains

In this paper we study a bilinear optimal control problem associated to a chemo-repulsion model with linear production term. We analyze the existence, uniqueness and regularity of pointwise strong solutions in a bidimensional domain. We prove the existence of an optimal solution and, using a Lagrange multipliers theorem, we derive first-order optimality conditions

Real-time quantitative sonoelastography in an ultrasound research system

Quantitative Sono-Elastographie ist eine neue Technologie für die Ultraschall Bildgebung, die Radiologen maligne Tumoren ohne Risiko der strahlungsinduzierten Krebs (d.h. Mammographie) zu erfassen können. Aufgrund gefunden Rechenkomplexität in der aktuellen Algorithmen, Implementierung von Echtzeit-Anwendungen, die Prüfungsverfahren profitieren wurde jedoch noch nicht berichtet. Zusätzlich, aktuelle Schätzer für die Darstellung eine Elastizität Bilder vorhanden Artefakte der hohen Schätzung Varianz, die die Techniker in die Gegenwart steifer Massen irreführen könnten und zwar, falsch-positive Diagnose zu erzeugen. In dieser Arbeit wird eine GPU-basierte Elastographie-System entwickelt und an einem Forschungsultraschallgeräten implementiert. Quantitative Elastizität in Echtzeit bei 2 FPS mit einer Verbesserung Rechenzeitfaktor aus 26 wird gezeigt. Validierung der Systemgenauigkeit Anzeige wurde, auf Gelatinebasis Gewebe Phantome durchgeführt., waren niedrige Vorspannung der Elastizitätswerte berichtet wurde (4,7 %) bei geringe Anregungsfrequenzen nachahmt. Ausserdem wird eine neue Elastizität Schätzer auf quantitative Sono-Elastographie basiert eingeführt. Ein lineares Problem wurde entlang der seitlichen Abmessung modelliert und eine Regularisierung Methode wurde implementieren. Elastizität Bilder mit niedriger Vorspannung wurde darstellen (1,48 %) sowie seine Leistung in einer Brust kalibrierte Phantom mit verbesserter CNR (47,3 dB) im Vergleich mit anderen Schätzer ausgewertet sowie die Verringerung Seiten Artefakte bereits erwähnt in der Literatur (PD: 22,7 dB, 1DH 28,7 dB) gefunden. Diese zwei Beitrag profitieren, die Umsetzung und Entwicklung weiterer Elastographie Techniken, die eine verbesserte Qualität der Elastizität Bilder liefern könnten und somit eine verbesserte Genauigkeit der Diagnose.Quantitative sonoelastography is an alternative technology for ultrasound imaging that helps radiologist to diagnose malignant tumors with no risk of radiation-induced cancer (i.e. mammography). However, due to the high computational complexity found in the current algorithms, implementation of real-time systems that could benefit examination procedures has not been yet reported. Additionally, elasticity maps depicted from current estimators feature artifacts of high estimation variance that could mislead the technician into the presence of stiffer masses, generating false positive diagnosis. In this thesis, a GPU-based elastography system was designed and implemented on a research ultrasound equipment, displaying quantitative elasticity in real-time at 2 FPS with an improvement computational time factor of 26. Validation of the system accuracy was conducted on gelatin-based tissue mimicking phantoms, where low bias of elasticity values were reported (4.7%) at low excitation frequencies. Additionally, a new elasticity estimator based on quantitative sonoelastography was developed. A linear problem was modeled from the acquired sonolastography data along the lateral dimension and a regularization method was implemented. The resulting elasticity images presented low bias (1.48%), enhanced CNR and reduced lateral artifacts when evaluating the algorithm’s performance in a breast calibrated phantom and comparing it with other estimators found in the literature. These two contribution benefit the implementation and development of further elastography techniques that could provide enhanced quality of elasticity images and thus, improved accuracy of diagnosis.Tesi

Analysis of a chemo-repulsion model with nonlinear production: The continuous problem and unconditionally energy stable fully discrete schemes

We consider the following repulsive-productive chemotaxis model: Let $p\in (1,2)$, find $u \geq 0$, the cell density, and $v \geq 0$, the chemical concentration, satisfying \begin{equation}\label{C5:Am} \left\{ \begin{array} [c]{lll} \partial_t u - \Delta u - \nabla\cdot (u\nabla v)=0 \ \ \mbox{in}\ \Omega,\ t>0,\\ \partial_t v - \Delta v + v = u^p \ \ \mbox{in}\ \Omega,\ t>0, \end{array} \right. \end{equation} in a bounded domain $\Omega\subseteq \mathbb{R}^d$, $d=2,3$. By using a regularization technique, we prove the existence of solutions of this problem. Moreover, we propose three fully discrete Finite Element (FE) nonlinear approximations, where the first one is defined in the variables $(u,v)$, and the second and third ones by introducing ${\boldsymbol\sigma}=\nabla v$ as an auxiliary variable. We prove some unconditional properties such as mass-conservation, energy-stability and solvability of the schemes. Finally, we compare the behavior of the schemes throughout several numerical simulations and give some conclusions.Comment: arXiv admin note: substantial text overlap with arXiv:1807.0111

Toenail zinc as a biomarker: Relationship with sources of environmental exposure and with genetic variability in MCC-Spain study

Background: Toenails are commonly used as biomarkers of exposure to zinc (Zn), but there is scarce information about their relationship with sources of exposure to Zn. Objectives: To investigate the main determinants of toenail Zn, including selected sources of environmental exposure to Zn and individual genetic variability in Zn metabolism. Methods: We determined toenail Zn by inductively coupled plasma mass spectrometry in 3,448 general population controls from the MultiCase-Control study MCC-Spain. We assessed dietary and supplement Zn intake using food frequency questionnaires, residential proximity to Zn-emitting industries and residential topsoil Zn levels through interpolation methods. We constructed a polygenic score of genetic variability based on 81 single nucleotide polymorphisms in genes involved in Zn metabolism. Geometric mean ratios of toenail Zn across categories of each determinant were estimated from multivariate linear regression models on log-transformed toenail Zn. Results: Geometric mean toenail Zn was 104.1 μg/g in men and 100.3 μg/g in women. Geometric mean toenail Zn levels were 7 % lower (95 % confidence interval 1–13 %) in men older than 69 years and those in the upper tertile of fibre intake, and 9 % higher (3–16 %) in smoking men. Women residing within 3 km from Zn-emitting industries had 4 % higher geometric mean toenail Zn levels (0–9 %). Dietary Zn intake and polygenic score were unrelated to toenail Zn. Overall, the available determinants only explained 9.3 % of toenail Zn variability in men and 4.8 % in women. Discussion: Sociodemographic factors, lifestyle, diet, and environmental exposure explained little of the individual variability of toenail Zn in the study population. The available genetic variants related to Zn metabolism were not associated with toenail Zn.Instituto de Salud Carlos IIIConsortium for Biomedical Research in Epidemiology and Public Health (CIBERESP)FEDER funds-a way to build Europe PI08/1770 PI09/0773 PI12/00715 PI09/1903 PI09/2078 PI09/1662 PI11/01403 PI12/00150 PI12/00488 PI15/00914 PI17CIII_00034Fundacion Marques de Valdecilla grant API 10/09Junta de Andalucia 2009-S0143Conselleria de Sanitat of the Generalitat Valenciana AP061/10Regional Government of the Basque CountryPrincipality of AsturiasUniversity of OviedoSpanish Ministry of Economy and Competitiveness Juan de la Cierva de Incorporacion IJCI-2014-20900 Instituto de Salud Carlos II

A review on the improved regularity for the primitive equations

In this work we will study, some types of regularity properties of solutions for the geophysical model of hydrostatic Navier-Stokes equations, so-called the Primitive Equations (P E). Also, we will present some results about uniqueness and asymptotic behavior in time.Ministerio de Ciencia y Tecnologí

On the singular times of fluids with nonlinear viscosity

Comisión Interministerial de Ciencia y TecnologíaPatronato de la Fundación Cámara de la Universidad de Sevill

Convergence and error estimates of two iterative methods for the strong solution of the incompressible korteweg model

We show the existence of strong solutions for a fluid model with Korteweg tensor, which is obtained as limit of two iterative linear schemes. The different unknowns are sequentially decoupled in the first scheme and in parallel form in the second one. In both cases, the whole sequences are bounded in strong norms and convergent towards the strong solution of the system, by using a generalization of the Banach’s Fixed Point Theorem. Moreover, we explicit a priori and a posteriori error estimates (respect to the weak norms), which let us to compare both schemes.Dirección General de Investigación (Ministerio de Educación y Ciencia)Junta de Andalucí

Analysis of a questionnaire to assess materials produced by teachers in a collaborative space for educational innovation

En este trabajo se han elaborado nuevos materiales de innovación educativa (http://www.uv.es/innovamide). El objetivo del proyecto es el establecimiento de un espacio colaborativo, en el que los profesores puedan implementar materiales, esquemas y otros elementos de apoyo visual al proceso de aprendizaje que hayan sido previamente evaluados y verificados. Para ello, se ha elaborado un cuestionario de evaluación de los materiales, al que se ha aplicado un análisis de jueces para asegurar la validez de contenido y de constructo. Posteriormente, se aplicó a alumnos de varias titulaciones. Los resultados muestran un elevado nivel de satisfacción y utilidad con los materiales elaborados. Son una parte importante de la metodología docente y al ser evaluados por el alumnado presentan un indicador de la satisfacción de los estudiantes con el proceso y los resultados de la docencia.New materials of educational innovation (http://www.uv.es/innovamide) have been developed in this work. The objective of the project is the establishment of a collaborative space, where teachers wishing to participate can implement materials, diagrams, etc. that have been previously evaluated and verified. To do so, has been developed a questionnaire for evaluation of materials, to which has been applied an analysis of judges to ensure the content and construct validity. Subsequently, it was applied to students of various degrees. The results show a high level of satisfaction and usefulness of the processed materials. Materials produced by teachers are an important part of the teaching methodology and to be evaluated by the students are an indicator of satisfaction with teaching students and their results

Weak solutions for an initial-boundary Q-Tensor problem related to liquid crystals

The coupled Navier-Stokes and Q-Tensor system is considered in a bounded three-dimensional domain under homogeneous Dirichlet boundary conditions for the velocity u and either nonhomogeneous Dirichlet or homogeneous Neumann boundary conditions for the tensor Q. The corresponding initial-value problem in the whole space R3 was analyzed in [Paicu & Zarnescu, 2012]. In this paper, three main results concerning weak solutions will be proved; the existence of global in time weak solutions (bounded up to infinite time), a uniqueness criteria and a maximum principle for Q. Moreover, we identify how to modify the system to deduce symmetry and traceless for Q, for any weak solution. The presence of a stretching term in the Q-system plays a crucial role in all the analysis.Ministerio de Economía y Competitivida