New Directions in Simulation, Control and Analysis for Interfaces and Free Boundaries

The field of mathematical and numerical analysis of systems of nonlinear partial differential equations involving interfaces and free boundaries is a flourishing area of research. Many such systems arise from mathematical models in material science, fluid dynamics and biology, for example phase separation in alloys, epitaxial growth, dynamics of multiphase fluids, evolution of cell membranes and in industrial processes such as crystal growth. The governing equations for the dynamics of the interfaces in many of these applications involve surface tension expressed in terms of the mean curvature and a driving force. Here the forcing terms depend on variables that are solutions of additional partial differential equations which hold either on the interface itself or in the surrounding bulk regions. Often in applications of these mathematical models, suitable performance indices and appropriate control actions have to be specified. Mathematically this leads to optimization problems with partial differential equation constraints including free boundaries. Because of the maturity of the field of computational free boundary problems it is now timely to consider such control problems

Idaho National Laboratory LDRD Annual Report FY 2012

This report provides a glimpse into our diverse research and development portfolio, wwhich encompasses both advanced nuclear science and technology and underlying technologies. IN keeping with the mission, INL's LDRD program fosters technical capabilities necessary to support current and future DOE-Office of Nuclear Energy research and development needs

Mathematical Theory and Modelling in Atmosphere-Ocean Science

Mathematical theory and modelling in atmosphere-ocean science combines a broad range of advanced mathematical and numerical techniques and research directions. This includes the asymptotic analysis of multiscale systems, the deterministic and stochastic modelling of sub-grid-scale processes, and the numerical analysis of nonlinear PDEs over a broad range of spatial and temporal scales. This workshop brought together applied mathematicians and experts in the disciplinary fields of meteorology and oceanography for a wide-ranging exchange of ideas and results in this area with the aim of fostering fundamental interdisciplinary work in this important science area

Modulation of transglutaminase 2 activity in H9c2 cells by protein kinase A and protein kinase C signalling

Transglutaminase 2 (TG2; EC 2.3.2.13) has been shown to protect cardiomyocytes against ischaemia and reperfusion-induced cell death and to mediate cell survival in many cell types. Given the prominent role of PKA and PKC in cardioprotection, this study investigated whether TG2 was involved in the cytoprotection induced by activation of these two kinases in cardiomyocyte-like H9c2 cells. Cultured H9c2 cells were extracted following stimulation with activators of PKC (phorbol-12-myristate-13-acetate; PMA) and PKA (forskolin; FK). Transglutaminase 2 activity was determined using an amine incorporating (in vitro and in situ) and a protein crosslinking assays. Different protein kinase inhibitors were used to determine the involvement of PKC and PKA in the activation of TG2 in H9c2 cells. To confirm the involvement of TG2 activity via PKC and PKA, TG2 specific (Z-DON and R283) inhibitors were used. Western blot analysis revealed the presence of TG2 and TG1 (TG2 >> TG1) protein, but not TG3. Since the H2O2, a major contributor to reactive oxygen species following damage was used to induce oxidative stress. The role of TG2 in PMA- and forskolin-induced cytoprotection was investigated by monitoring H2O2-induced oxidative stress in H9c2 cells. The identification of TG2 substrates in H9c2 cells was investigated using pull down assay coupled with proteomic analysis techniques. The PMA and FK-induced time and concentration-dependent increases in TG2 catalysed biotin cadaverine incorporation in H9c2 cells. Forskolin but not PMA also increased TG2 catalysed protein crosslinking. The PKC (Ro-31 8220) and PKA (KT 5720 and Rp-8-Cl-cAMPS) inhibitors, blocked PMA and FK-induced TG2 activity. Immunocytochemistry using ExtrAvidin®-FITC revealed in situ TG2-mediated biotin cadaverine incorporation into protein substrates following stimulation of PMA, FK and their receptor agonists. The TG2 inhibitors Z-DON and R283 attenuated the PMA- and FK-induced increases in TG2 activity. Pre-treatment with PMA and FK reversed H2O2-induced cell death as judged by a MTT reduction assay and the release of cellular LDH. The TG2 inhibitors R283 and Z-DON blocked PMA and FK-induced cytoprotection. Proteomic analysis identified more than 25 proteins that serve as intracellular substrates for TG2 following PMA and FK stimulation. Some of these identified proteins have already been reported as TG2 substrates, but not in H9c2 cells e.g. tubulin while others e.g. α-actinin have not been identified before. In summary, these data have shown TG2 activity to be stimulated via PKA and PKC-dependent signalling pathways in H9c2 cells and suggest a role for TG2 in cytoprotection-induced via these two protein kinases

Microgravity Science and Applications: Program Tasks and Bibliography for Fiscal Year 1996

NASA's Microgravity Science and Applications Division (MSAD) sponsors a program that expands the use of space as a laboratory for the study of important physical, chemical, and biochemical processes. The primary objective of the program is to broaden the value and capabilities of human presence in space by exploiting the unique characteristics of the space environment for research. However, since flight opportunities are rare and flight research development is expensive, a vigorous ground-based research program, from which only the best experiments evolve, is critical to the continuing strength of the program. The microgravity environment affords unique characteristics that allow the investigation of phenomena and processes that are difficult or impossible to study an Earth. The ability to control gravitational effects such as buoyancy driven convection, sedimentation, and hydrostatic pressures make it possible to isolate phenomena and make measurements that have significantly greater accuracy than can be achieved in normal gravity. Space flight gives scientists the opportunity to study the fundamental states of physical matter-solids, liquids and gasses-and the forces that affect those states. Because the orbital environment allows the treatment of gravity as a variable, research in microgravity leads to a greater fundamental understanding of the influence of gravity on the world around us. With appropriate emphasis, the results of space experiments lead to both knowledge and technological advances that have direct applications on Earth. Microgravity research also provides the practical knowledge essential to the development of future space systems. The Office of Life and Microgravity Sciences and Applications (OLMSA) is responsible for planning and executing research stimulated by the Agency's broad scientific goals. OLMSA's Microgravity Science and Applications Division (MSAD) is responsible for guiding and focusing a comprehensive program, and currently manages its research and development tasks through five major scientific areas: biotechnology, combustion science, fluid physics, fundamental physics, and materials science. FY 1996 was an important year for MSAD. NASA continued to build a solid research community for the coming space station era. During FY 1996, the NASA Microgravity Research Program continued investigations selected from the 1994 combustion science, fluid physics, and materials science NRAS. MSAD also released a NASA Research Announcement in microgravity biotechnology, with more than 130 proposals received in response. Selection of research for funding is expected in early 1997. The principal investigators chosen from these NRAs will form the core of the MSAD research program at the beginning of the space station era. The third United States Microgravity Payload (USMP-3) and the Life and Microgravity Spacelab (LMS) missions yielded a wealth of microgravity data in FY 1996. The USMP-3 mission included a fluids facility and three solidification furnaces, each designed to examine a different type of crystal growth

Instabilities in geophysical fluid dynamics: the influence of symmetry and temperature dependent viscosity in convection

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Matemáticas. Fecha de lectura: 25-04-2014Spectral numerical methods are proposed to solve the time evolution of a convection problem in a 2D domain with viscosity strongly dependent on temperature. We have considered periodic boundary conditions along the horizontal coordinate which introduce the O(2) symmetry into the setting. This motivates the use of spectral methods as an approach to the problem. The analysis is assisted by bifurcation techniques such as branch continuation, which has proven to be a useful, and systematic method for gaining insight into the possible stationary solutions satis ed by the basic equations. Several viscosity laws which correspond to di erent dependences of the viscosity with the temperature are investigated. Numerous examples are found along the branching diagrams, in which stable stationary solutions become unstable through a Hopf bifurcation. In the neighborhood of these bifurcation points, the scope of our techniques is examined by exploring transitions from stationary regimes towards time dependent regimes. Our study is mainly focused on viscosity laws that model an abrupt transition of viscosity with temperature. In particular, both a smooth and a sharp transition are explored. Regarding the stationary solutions, the way in which di erent parameters in the viscosity laws a ect the formation and morphology of thermal plumes is discussed. A variety of shapes ranging from spout to mushroom shaped are found. Some stationary stable patterns that break the plume symmetry along their vertical axis are detected, as well as others that correspond to non-uniformly distributed plumes. The main di erence between the solutions observed for the smooth and sharp transition laws is the presence in the latter case of a stagnant lid, which is absent in the rst law. In both cases, we report time-dependent solutions that are greatly in uenced by the presence of the symmetry and which have not previously been described in the context of temperature-dependent viscosities, such as travelling waves, heteroclinic connections and chaotic regimes. Notable solutions are found for the sharp transition viscosity law in which time-dependent solutions alternate an upper stagnant lid with plate-like behaviors that move either towards the right or towards the left. This introduces temporary asymmetries on the convecting styles. This kind of solutions are also related to the presence of the O(2) symmetry and constitute an example of a plate-like convective style which is not linked to a subduction process. These ndings provide an innovative approach to the understanding of convection styles in planetary interiors and suggest that symmetry may play a role in describing how planets work. Finally, the centrifugal and viscosity e ects in a rotating cylinder with large Prandtl number are numerically studied in a regime where the Coriolis force is relatively large. Our focus is on aqueous mixtures of glycerine with mass concentration in the range of 60%-90%, and Rayleigh number values that extend from the onset, where thermal convection is in the so-called wall modes regime, in which pairs of hot and cold thermal plumes ascend and descend in the sidewall boundary layer, to values in which the bulk uid region is also convecting. The mean viscosity, which varies faster than exponentially with variations in the percentage of glycerine, leads to a faster than exponential increase in the Froude number for a xed Coriolis force, and hence an enhancement of the centrifugal buoyancy e ects with signi cant dynamical consequences are described.En esta tesis proponemos métodos numéricos espectrales, para resolver la evolución temporal de un problema de convección en un dominio 2D con viscosidad fuertemente dependiente de la temperatura. Las condiciones de contorno periódicas a lo largo de la coordenada horizontal introducen la simetría O(2) en el problema lo que motiva el uso de métodos espectrales en este contexto. Realizamos un análisis de las soluciones mediante técnicas propias de la teoría de bifurcaciones, y constatamos que son un método útil y sistemático para describir el panorama de las soluciones estacionarias que satisfacen las ecuaciones básicas. Investigamos varias leyes de viscosidad que corresponden a diferentes dependencias de ésta con la temperatura. A lo largo de los diagramas de bifurcación se encuentran numerosos ejemplos en los que la solución estacionaria estable se vuelve inestable a través de una bifurcación Hopf. En las proximidades de esos puntos examinamos el alcance de nuestras técnicas, explorando la transición desde regímenes estacionarios a regímenes dependientes del tiempo. Nuestro estudio se centra principalmente en las leyes de la viscosidad que modelan una transición abrupta de la viscosidad con la temperatura. En particular, se exploran tanto una transición suave como una brusca. En cuanto a las soluciones estacionarias, se discute como los diferentes pará metros en las leyes de viscosidad afectan a la formación y la morfología de las plumas térmicas. Se encuentran una variedad de la formas que van desde forma de protuberancia (\spout") a la forma de seta. Se detectan algunos patrones de soluciones estacionarias estables que rompen la simetría de la pluma a lo largo de su eje vertical y otros que se corresponden con plumas distribuidas de manera no uniforme. La principal diferencia entre las soluciones observadas para las leyes de transición suave y brusca es la presencia, con esta última ley, de una capa estancada que no está presente con la primera. En ambos casos mostramos soluciones dependientes del tiempo que están muy influenciadas por la presencia de la simetría y que no se han descrito previamente en el contexto de convección con viscosidad dependiente de la temperatura. Estas soluciones son por ejemplo ondas viajeras, conexiones heteroclínicas y regímenes caótico. Para transiciones bruscas de la ley de viscosidad destacan soluciones dependientes del tiempo, en las que se alternan una capa superior estancada, con una capa o placa que se mueve rígidamente hacia la derecha o la izquierda. Esto introduce estilos de convección que son asimétricos en el tiempo. Este tipo de soluciones también están relacionadas con la presencia de la simetría O(2) y constituyen un ejemplo de convección en forma de placa que no est a vinculada a un proceso de subducción. Estos resultados aportan un enfoque innovador para la comprensión de estilos de convección en el interior de planetas y sugieren que la simetría puede desempeñar un papel importante en la descripción de como funcionan. Por último, se estudian numéricamente los efectos centrífugos en un cilindro que rota, en un régimen en el que la fuerza de Coriolis es relativamente grande y en el que el fluido tiene un número de Prandtl alto. Nuestra atención se centra en mezclas acuosas de glicerina con concentraciones de masa en el intervalo de 60 %-90% y valores de número de Rayleigh que se extienden desde el inicio de la convección térmica; que son el denominado régimen de modos de pared, donde pares de plumas calientes y frías ascienden y descienden en la capa límite de la pared lateral; hasta valores en los que la convección está completamente desarrollada en toda la celda. El aumento de la viscosidad media, que varía con el porcentaje de glicerina considerado, conduce, para una fuerza de Coriolis ja, a un aumento en el n mero de Froude y por lo tanto, a un incremento de los efectos centrífugos para los que describimos su impacto en la dinámica

Large-scale tree-based unfitted finite elements for metal additive manufacturing

This thesis addresses large-scale numerical simulations of partial differential equations posed on evolving geometries. Our target application is the simulation of metal additive manufacturing (or 3D printing) with powder-bed fusion methods, such as Selective Laser Melting (SLM), Direct Metal Laser Sintering (DMLS) or Electron-Beam Melting (EBM). The simulation of metal additive manufacturing processes is a remarkable computational challenge, because processes are characterised by multiple scales in space and time and multiple complex physics that occur in intricate three-dimensional growing-in-time geometries. Only the synergy of advanced numerical algorithms and high-performance scientific computing tools can fully resolve, in the short run, the simulation needs in the area. The main goal of this Thesis is to design a a novel highly-scalable numerical framework with multi-resolution capability in arbitrarily complex evolving geometries. To this end, the framework is built by combining three computational tools: (1) parallel mesh generation and adaptation with forest-of-trees meshes, (2) robust unfitted finite element methods and (3) parallel finite element modelling of the geometry evolution in time. Our numerical research is driven by several limitations and open questions in the state-of-the-art of the three aforementioned areas, which are vital to achieve our main objective. All our developments are deployed with high-end distributed-memory implementations in the large-scale open-source software project FEMPAR. In considering our target application, (4) temporal and spatial model reduction strategies for thermal finite element models are investigated. They are coupled to our new large-scale computational framework to simplify optimisation of the manufacturing process. The contributions of this Thesis span the four ingredients above. Current understanding of (1) is substantially improved with rigorous proofs of the computational benefits of the 2:1 k-balance (ease of parallel implementation and high-scalability) and the minimum requirements a parallel tree-based mesh must fulfil to yield correct parallel finite element solvers atop them. Concerning (2), a robust, optimal and scalable formulation of the aggregated unfitted finite element method is proposed on parallel tree-based meshes for elliptic problems with unfitted external contour or unfitted interfaces. To the author’s best knowledge, this marks the first time techniques (1) and (2) are brought together. After enhancing (1)+(2) with a novel parallel approach for (3), the resulting framework is able to mitigate a major performance bottleneck in large-scale simulations of metal additive manufacturing processes by powder-bed fusion: scalable adaptive (re)meshing in arbitrarily complex geometries that grow in time. Along the development of this Thesis, our application problem (4) is investigated in two joint collaborations with the Monash Centre for Additive Manufacturing and Monash University in Melbourne, Australia. The first contribution is an experimentally-supported thorough numerical assessment of time-lumping methods, the second one is a novel experimentally-validated formulation of a new physics-based thermal contact model, accounting for thermal inertia and suitable for model localisation, the so-called virtual domain approximation. By efficiently exploiting high-performance computing resources, our new computational framework enables large-scale finite element analysis of metal additive manufacturing processes, with increased fidelity of predictions and dramatical reductions of computing times. It can also be combined with the proposed model reductions for fast thermal optimisation of the manufacturing process. These tools open the path to accelerate the understanding of the process-to-performance link and digital product design and certification in metal additive manufacturing, two milestones that are vital to exploit the technology for mass-production.Aquesta tesi tracta la simulació a gran escala d'equacions en derivades parcials sobre geometries variables. L'aplicació principal és la simulació de procesos de fabricació additiva (o impressió 3D) amb metalls i per mètodes de fusió de llit de pols, com ara Selective Laser Melting (SLM), Direct Metal Laser Sintering (DMLS) o Electron-Beam Melting (EBM). La simulació d'aquests processos és un repte computacional excepcional, perquè els processos estan caracteritzats per múltiples escales espaitemporals i múltiples físiques que tenen lloc sobre geometries tridimensionals complicades que creixen en el temps. La sinèrgia entre algorismes numèrics avançats i eines de computació científica d'alt rendiment és la única via per resoldre completament i a curt termini les necessitats en simulació d'aquesta àrea. El principal objectiu d'aquesta tesi és dissenyar un nou marc numèric escalable de simulació amb capacitat de multiresolució en geometries complexes i variables. El nou marc es construeix unint tres eines computacionals: (1) mallat paral·lel i adaptatiu amb malles de boscs d'arbre, (2) mètodes d'elements finits immersos robustos i (3) modelització en paral·lel amb elements finits de geometries que creixen en el temps. Algunes limitacions i problemes oberts en l'estat de l'art, que són claus per aconseguir el nostre objectiu, guien la nostra recerca. Tots els desenvolupaments s'implementen en arquitectures de memòria distribuïda amb el programari d'accés obert FEMPAR. Quant al problema d'aplicació, (4) s'investiguen models reduïts en espai i temps per models tèrmics del procés. Aquests models reduïts s'acoplen al nostre marc computacional per simplificar l'optimització del procés. Les contribucions d'aquesta tesi abasten els quatre punts de dalt. L'estat de l'art de (1) es millora substancialment amb proves riguroses dels beneficis computacionals del 2:1 balancejat (fàcil paral·lelització i alta escalabilitat), així com dels requisits mínims que aquest tipus de mallat han de complir per garantir que els espais d'elements finits que s'hi defineixin estiguin ben posats. Quant a (2), s'ha formulat un mètode robust, òptim i escalable per agregació per problemes el·líptics amb contorn o interface immerses. Després d'augmentar (1)+(2) amb un nova estratègia paral·lela per (3), el marc de simulació resultant mitiga de manera efectiva el principal coll d'ampolla en la simulació de processos de fabricació additiva en llits de pols de metall: adaptivitat i remallat escalable en geometries complexes que creixen en el temps. Durant el desenvolupament de la tesi, es col·labora amb el Monash Centre for Additive Manufacturing i la Universitat de Monash de Melbourne, Austràlia, per investigar el problema d'aplicació. En primer lloc, es fa una anàlisi experimental i numèrica exhaustiva dels mètodes d'aggregació temporal. En segon lloc, es proposa i valida experimental una nova formulació de contacte tèrmic que té en compte la inèrcia tèrmica i és adequat per a localitzar el model, l'anomenada aproximació per dominis virtuals. Mitjançant l'ús eficient de recursos computacionals d'alt rendiment, el nostre nou marc computacional fa possible l'anàlisi d'elements finits a gran escala dels processos de fabricació additiva amb metalls, amb augment de la fidelitat de les prediccions i reduccions significatives de temps de computació. Així mateix, es pot combinar amb els models reduïts que es proposen per l'optimització tèrmica del procés de fabricació. Aquestes eines contribueixen a accelerar la comprensió del lligam procés-rendiment i la digitalització del disseny i certificació de productes en fabricació additiva per metalls, dues fites crucials per explotar la tecnologia en producció en massa.Postprint (published version