On a comparison method to reaction-diffusion systems and its applications to chemotaxis

In this paper we consider a general system of reaction-diffusion equations and introduce a comparison method to obtain qualitative properties of its solutions. The comparison method is applied to study the stability of homogeneous steady states and the asymptotic behavior of the solutions of different systems with a chemotactic term. The theoretical results obtained are slightly modified to be applied to the problems where the systems are coupled in the differentiated terms and / or contain nonlocal terms. We obtain results concerning the global stability of the steady states by comparison with solutions of Ordinary Differential Equations.

A subgrid viscosity Lagrance-Galerkin method for convection-diffusion problems

We present and analyze a subgrid viscosity Lagrange-Galerk in method that combines the subgrid eddy viscosity method proposed in W. Layton, A connection between subgrid scale eddy viscosity and mixed methods. Appl. Math. Comp., 133: 14 7-157, 2002, and a conventional Lagrange-Galerkin method in the framework of P1⊕ cubic bubble finite elements. This results in an efficient and easy to implement stabilized method for convection dominated convection diffusion reaction problems. Numerical experiments support the numerical analysis results and show that the new method is more accurate than the conventional Lagrange-Galerkin one.

Interface discontinuity factors in the modal eigenspace of the multigroup diffusion matrix

Interface discontinuity factors based on the Generalized Equivalence Theory are commonly used in nodal homogenized diffusion calculations so that diffusion average values approximate heterogeneous higher order solutions. In this paper, an additional form of interface correction factors is presented in the frame of the Analytic Coarse Mesh Finite Difference Method (ACMFD), based on a correction of the modal fluxes instead of the physical fluxes. In the ACMFD formulation, implemented in COBAYA3 code, the coupled multigroup diffusion equations inside a homogenized region are reduced to a set of uncoupled modal equations through diagonalization of the multigroup diffusion matrix. Then, physical fluxes are transformed into modal fluxes in the eigenspace of the diffusion matrix. It is possible to introduce interface flux discontinuity jumps as the difference of heterogeneous and homogeneous modal fluxes instead of introducing interface discontinuity factors as the ratio of heterogeneous and homogeneous physical fluxes. The formulation in the modal space has been implemented in COBAYA3 code and assessed by comparison with solutions using classical interface discontinuity factors in the physical space

On the Extension of the Analytic Nodal Diffusion Solver ANDES to Sodium Fast Reactors

Within the framework of the Collaborative Project for a European Sodium Fast Reactor, the reactor physics group at UPM is working on the extension of its in-house multi-scale advanced deterministic code COBAYA3 to Sodium Fast Reactors (SFR). COBAYA3 is a 3D multigroup neutron kinetics diffusion code that can be used either as a pin-by-pin code or as a stand-alone nodal code by using the analytic nodal diffusion solver ANDES. It is coupled with thermalhydraulics codes such as COBRA-TF and FLICA, allowing transient analysis of LWR at both fine-mesh and coarse-mesh scales. In order to enable also 3D pin-by-pin and nodal coupled NK-TH simulations of SFR, different developments are in progress. This paper presents the first steps towards the application of COBAYA3 to this type of reactors. ANDES solver, already extended to triangular-Z geometry, has been applied to fast reactor steady-state calculations. The required cross section libraries were generated with ERANOS code for several configurations. The limitations encountered in the application of the Analytic Coarse Mesh Finite Difference (ACMFD) method –implemented inside ANDES– to fast reactors are presented and the sensitivity of the method when using a high number of energy groups is studied. ANDES performance is assessed by comparison with the results provided by ERANOS, using a mini-core model in 33 energy groups. Furthermore, a benchmark from the NEA for a small 3D FBR in hexagonal-Z geometry and 4 energy groups is also employed to verify the behavior of the code with few energy groups.

Neighborhood-corrected interface discontinuity factors for multi-group pin-by-pin diffusion calculations for LWR

Performing three-dimensional pin-by-pin full core calculations based on an improved solution of the multi-group diffusion equation is an affordable option nowadays to compute accurate local safety parameters for light water reactors. Since a transport approximation is solved, appropriate correction factors, such as interface discontinuity factors, are required to nearly reproduce the fully heterogeneous transport solution. Calculating exact pin-by-pin discontinuity factors requires the knowledge of the heterogeneous neutron flux distribution, which depends on the boundary conditions of the pin-cell as well as the local variables along the nuclear reactor operation. As a consequence, it is impractical to compute them for each possible configuration; however, inaccurate correction factors are one major source of error in core analysis when using multi-group diffusion theory. An alternative to generate accurate pin-by-pin interface discontinuity factors is to build a functional-fitting that allows incorporating the environment dependence in the computed values. This paper suggests a methodology to consider the neighborhood effect based on the Analytic Coarse-Mesh Finite Difference method for the multi-group diffusion equation. It has been applied to both definitions of interface discontinuity factors, the one based on the Generalized Equivalence Theory and the one based on Black-Box Homogenization, and for different few energy groups structures. Conclusions are drawn over the optimal functional-fitting and demonstrative results are obtained with the multi-group pin-by-pin diffusion code COBAYA3 for representative PWR configurations.

Rapid microbiological detection method based on ultrasonic instrumentation

Los métodos de detección rápida de microorganismos se están convirtiendo en una herramienta esencial para el control de calidad en el área de la biotecnología, como es el caso de las industrias de alimentos y productos farmacéuticos y bioquímicos. En este escenario, el objetivo de esta tesis doctoral es desarrollar una técnica de inspección rápida de microoganismos basada en ultrasonidos. La hipótesis propuesta es que la combinación de un dispositivo ultrasónico de medida y un medio líquido diseñado específicamente para producir y atrapar burbujas, pueden constituir la base de un método sensible y rápido de detección de contaminaciones microbianas. La técnica presentada es efectiva para bacterias catalasa-positivas y se basa en la hidrólisis del peróxido de hidrógeno inducida por la catalasa. El resultado de esta reacción es un medio con una creciente concentración de burbujas. Tal medio ha sido estudiado y modelado desde el punto de vista de la propagación ultrasónica. Las propiedades deducidas a partir del análisis cinemático de la enzima se han utilizado para evaluar el método como técnica de inspección microbiana. En esta tesis, se han investigado aspectos teóricos y experimentales de la hidrólisis del peróxido de hidrógeno. Ello ha permitido describir cuantitativamente y comprender el fenómeno de la detección de microorganismos catalasa-positivos mediante la medida de parámetros ultrasónicos. Más concretamente, los experimentos realizados muestran cómo el oxígeno que aparece en forma de burbujas queda atrapado mediante el uso de un gel sobre base de agar. Este gel fue diseñado y preparado especialmente para esta aplicación. A lo largo del proceso de hidrólisis del peróxido de hidrógeno, se midió la atenuación de la onda y el “backscattering” producidos por las burbujas, utilizando una técnica de pulso-eco. Ha sido posible detectar una actividad de la catalasa de hasta 0.001 unidades/ml. Por otra parte, este estudio muestra que por medio del método propuesto, se puede lograr una detección microbiana para concentraciones de 105 células/ml en un periodo de tiempo corto, del orden de unos pocos minutos. Estos resultados suponen una mejora significativa de tres órdenes de magnitud en comparación con otros métodos de detección por ultrasonidos. Además, la sensibilidad es competitiva con modernos y rápidos métodos microbiológicos como la detección de ATP por bioluminiscencia. Pero sobre todo, este trabajo muestra una metodología para el desarrollo de nuevas técnicas de detección rápida de bacterias basadas en ultrasonidos. ABSTRACT In an industrial scenario where rapid microbiological methods are becoming essential tools for quality control in the biotechnological area such as food, pharmaceutical and biochemical; the objective of the work presented in this doctoral thesis is to develop a rapid microorganism inspection technique based on ultrasounds. It is proposed that the combination of an ultrasonic measuring device with a specially designed liquid medium, able to produce and trap bubbles could constitute the basis of a sensitive and rapid detection method for microbial contaminations. The proposed technique is effective on catalase positive microorganisms. Well-known catalase induced hydrogen peroxide hydrolysis is the fundamental of the developed method. The physical consequence of the catalase induced hydrogen peroxide hydrolysis is an increasingly bubbly liquid medium. Such medium has been studied and modeled from the point of view of ultrasonic propagation. Properties deduced from enzyme kinematics analysis have been extrapolated to investigate the method as a microbial inspection technique. In this thesis, theoretical and experimental aspects of the hydrogen peroxide hydrolysis were analyzed in order to quantitatively describe and understand the catalase positive microorganism detection by means of ultrasonic measurements. More concretely, experiments performed show how the produced oxygen in form of bubbles is trapped using the new gel medium based on agar, which was specially designed for this application. Ultrasonic attenuation and backscattering is measured in this medium using a pulse-echo technique along the hydrogen peroxide hydrolysis process. Catalase enzymatic activity was detected down to 0.001 units/ml. Moreover, this study shows that by means of the proposed method, microbial detection can be achieved down to 105 cells/ml in a short time period of the order of few minutes. These results suppose a significant improvement of three orders of magnitude compared to other ultrasonic detection methods for microorganisms. In addition, the sensitivity reached is competitive with modern rapid microbiological methods such as ATP detection by bioluminescence. But above all, this work points out a way to proceed for developing new rapid microbial detection techniques based on ultrasound.

Image processing methods for human brain connectivity analysis from in-vivo diffusion MRI

The structural connectivity of the brain is considered to encode species-wise and subject-wise patterns that will unlock large areas of understanding of the human brain. Currently, diffusion MRI of the living brain enables to map the microstructure of tissue, allowing to track the pathways of fiber bundles connecting the cortical regions across the brain. These bundles are summarized in a network representation called connectome that is analyzed using graph theory. The extraction of the connectome from diffusion MRI requires a large processing flow including image enhancement, reconstruction, segmentation, registration, diffusion tracking, etc. Although a concerted effort has been devoted to the definition of standard pipelines for the connectome extraction, it is still crucial to define quality assessment protocols of these workflows. The definition of quality control protocols is hindered by the complexity of the pipelines under test and the absolute lack of gold-standards for diffusion MRI data. Here we characterize the impact on structural connectivity workflows of the geometrical deformation typically shown by diffusion MRI data due to the inhomogeneity of magnetic susceptibility across the imaged object. We propose an evaluation framework to compare the existing methodologies to correct for these artifacts including whole-brain realistic phantoms. Additionally, we design and implement an image segmentation and registration method to avoid performing the correction task and to enable processing in the native space of diffusion data. We release PySDCev, an evaluation framework for the quality control of connectivity pipelines, specialized in the study of susceptibility-derived distortions. In this context, we propose Diffantom, a whole-brain phantom that provides a solution to the lack of gold-standard data. The three correction methodologies under comparison performed reasonably, and it is difficult to determine which method is more advisable. We demonstrate that susceptibility-derived correction is necessary to increase the sensitivity of connectivity pipelines, at the cost of specificity. Finally, with the registration and segmentation tool called regseg we demonstrate how the problem of susceptibility-derived distortion can be overcome allowing data to be used in their original coordinates. This is crucial to increase the sensitivity of the whole pipeline without any loss in specificity.

Design of a Semi-analytical Method to Describe Plasma-Wall Interactions

Electric probes are objects immersed in the plasma with sharp boundaries which collect of emit charged particles. Consequently, the nearby plasma evolves under abrupt imposed and/or naturally emerging conditions. There could be localized currents, different time scales for plasma species evolution, charge separation and absorbing-emitting walls. The traditional numerical schemes based on differences often transform these disparate boundary conditions into computational singularities. This is the case of models using advection-diffusion differential equations with source-sink terms (also called Fokker-Planck equations). These equations are used in both, fluid and kinetic descriptions, to obtain the distribution functions or the density for each plasma species close to the boundaries. We present a resolution method grounded on an integral advancing scheme by using approximate Green's functions, also called short-time propagators. All the integrals, as a path integration process, are numerically calculated, what states a robust grid-free computational integral method, which is unconditionally stable for any time step. Hence, the sharp boundary conditions, as the current emission from a wall, can be treated during the short-time regime providing solutions that works as if they were known for each time step analytically. The form of the propagator (typically a multivariate Gaussian) is not unique and it can be adjusted during the advancing scheme to preserve the conserved quantities of the problem. The effects of the electric or magnetic fields can be incorporated into the iterative algorithm. The method allows smooth transitions of the evolving solutions even when abrupt discontinuities are present. In this work it is proposed a procedure to incorporate, for the very first time, the boundary conditions in the numerical integral scheme. This numerical scheme is applied to model the plasma bulk interaction with a charge-emitting electrode, dealing with fluid diffusion equations combined with Poisson equation self-consistently. It has been checked the stability of this computational method under any number of iterations, even for advancing in time electrons and ions having different time scales. This work establishes the basis to deal in future work with problems related to plasma thrusters or emissive probes in electromagnetic fields.