Order 10 4 speedup in global linear instability analysis using matrix formation

A unified solution framework is presented for one-, two- or three-dimensional complex non-symmetric eigenvalue problems, respectively governing linear modal instability of incompressible fluid flows in rectangular domains having two, one or no homogeneous spatial directions. The solution algorithm is based on subspace iteration in which the spatial discretization matrix is formed, stored and inverted serially. Results delivered by spectral collocation based on the Chebyshev-Gauss-Lobatto (CGL) points and a suite of high-order finite-difference methods comprising the previously employed for this type of work Dispersion-Relation-Preserving (DRP) and Padé finite-difference schemes, as well as the Summationby- parts (SBP) and the new high-order finite-difference scheme of order q (FD-q) have been compared from the point of view of accuracy and efficiency in standard validation cases of temporal local and BiGlobal linear instability. The FD-q method has been found to significantly outperform all other finite difference schemes in solving classic linear local, BiGlobal, and TriGlobal eigenvalue problems, as regards both memory and CPU time requirements. Results shown in the present study disprove the paradigm that spectral methods are superior to finite difference methods in terms of computational cost, at equal accuracy, FD-q spatial discretization delivering a speedup of ð (10 4). Consequently, accurate solutions of the three-dimensional (TriGlobal) eigenvalue problems may be solved on typical desktop computers with modest computational effort.

Controlling moisture loss as a tool to reduce bruise susceptibility.

A method to reduce the bruise susceptibility of apples by controlling the moisture loss of the fruit was evaluated. Previous research indicates that reduction of the relative humidity of the storage air leads to an immediate effect on the weight loss and on skin properties and to a lower bruise susceptibility of apples. The diffusion equation is used to determine the waterpotential profile inside the fruit during storage. Characteristics of the waterpotential distribution in the fruit are related to measured bruise volumes. The results indicate how /this model can be used to control bruise susceptibility.

Long wave theory for experimental devices with compressed/expanded surfactant monolayers

Surfactant monolayers are of interest in a variety of phenomena, including thin film dynamics and the formation and dynamics of foams. Measurement of surface properties has received a continuous attention and requires good theoretical models to extract the relevant physico- chemical information from experimental data. A common experimental set up consists in a shallow liquid layer whose free surface is slowly com- pressed/expanded in periodic fashion by moving two slightly immersed solid barriers, which varies the free surface area and thus the surfactant concentration. The simplest theory ignores the fluid dynamics in the bulk fluid, assuming spatially uniform surfactant concentration, which requires quite small forcing frequencies and provides reversible dynamics in the compression/expansion cycles. Sometimes, it is not clear whether depar- ture from reversibility is due to non-equilibrium effects or to the ignored fluid dynamics. Here we present a long wave theory that takes the fluid dynamics and the symmetries of the problem into account. In particular, the validity of the spatially-uniform-surfactant-concentration assumption is established and a nonlinear diffusion equation is derived. This allows for calculating spatially nonuniform monolayer dynamics and uncovering the physical mechanisms involved in the surfactant behavior. Also, this analysis can be considered a good means for extracting more relevant information from each experimental run.

Mejora y optimización de un código de simulación hidrodinámico con transporte de radiación para el estudio de sistemas en condiciones de alta densidad de energía

Se presentan las mejoras introducidas en un código de transporte de radiación acoplada a la hidrodinámica llamado ARWEN para el estudio de sistemas en el rango de física de alta densidad de energía (High Energy Density Physics). Los desarrollos introducidos se basan en las siguientes áreas: ít>,~ Ecuaciones de estado: se desarrolla una nueva metodología mediante la cual es posible ajustar los resultados de un modelo simple de ecuaciones de estado como QEOS a datos experimentales y resultados de AIMD. Esta metodología tiene carácter general para poder ser aplicada en gran cantidad de materuales de interés y amplia la flexibilidad de ajuste de los métodos de los que ha partido como base este trabajo. En segundo lugar, se ha desarrollado una librería para la gestión de tablas de datos de ecuaciones de estado que también incluye la gestión de tablas con datos de opacidades y de ionización. Esta nueva librería extiende las capacidades de la anterior al tener llamadas más específicas que aceleran los cálculos, y posibilidad de uso de varias tablas a la vez. Solver de difusión: se ha desarrollado un nuevo paquete para resolver la ecuación de difusión que se aplicará a la conducción de calor dentro del plasma. El método anterior no podía ser ejecutado en paralelo y producía resultados dependientes de la resolución de la malla, mientras que este método es paralelizable y además obtiene una solución con mejor convergencia, lo que supone una solución que no depende del refinamiento del mallado. Revisión del paquete de radiación: en primer lugar se ha realizado una revisión de la implementación del modelo de radiación descubriendo varios errores que han sido depurados. También se ha incluido la nueva librería de gestión de tablas de opacidades que permiten la obtención de las propiedades ópticas del plasma en multigrupos de energía. Por otra parte se ha extendido el cálculo de los coeficientes de transporte al esquema multimaterial que ha introducido David Portillo García en el paquete hidrodinámico del código de simulación. Por último se ha revisado el esquema de resolución del transporte y se ha modificado para hacerlo paralelizable. • Se ha implementado un paquete de trazado de rayos para deposición láser que extiende la utilidad del anterior al ser en 3D y poder utilizar entonces diferentes configuraciones. • Una vez realizadas todas estas tareas se ha aplicado el código ARWEN al estudio de la astrofísica de laboratorio simulando los experimentos llevados a cabo en la instalación PALS por Chantal Stehlé acerca de ondas de choque radiativas. Se han comparado los resultados experimentales frente a las predicciones del código ARWEN obteniéndose una gran concordancia en la velocidad de la onda de choque generada y en las dimensiones del precursor. El código de simulación sobre el que se ha trabajado, junto con los desarrollos aportados por otros investigadores durante la realización de esta tesis, ha permitido participar en colaboraciones con laboratorios de Francia o Japón y se han producido resultados científicos publicados basados en el trabajo descrito en esta tesis. ABSTRACT Improvements in radiation hydrodynamic code ARWEN for the study of systems in the range of physics high energy density (High Energy Density Physics) are presented. The developments introduced are based on the following áreas: • Equations of state: a new methodology was developed to adjust the results of a simple Equation of State model like QEOS to experimental data and results of AIMD. This methodology can be applied to a large amount of materials and it increases the flexibility and range of the previous methods used as basis for this work. Also a new computer library has been developed to manage data tables of thermodynamic properties as well as includes the management of opacity and ionization data tables. This new library extends the capabilities of the previous one with more specific routines, and the possibility of using múltiple tables for several materials. • Diffusion solver: a new package has been developed to solve the diffusion equation applied to the heat conduction of the plasma. The previous method is not parallelizable and it produced mesh dependent results, while this new package can be executed in parallel and achieves a more converged solution that does not depend on the refinement of the mesh. • Radiation package: the check of the radiation model rose several bugs in the implementation that had been removed. The new computer library for EOS managing includes capabilities to store opacity tables for multigroups of energy. Moreover the transport coefficients calculations have been extended for the new multimaterial hydrodynamic package developed by David Portillo García. Also the solving methodology for the transport equation has been modified to make the code run in parallel. • A new ray tracing package has been introduced to extend the previous one to 3D. Once all these tasks has been implemented, the ARWEN code has been applied to study laboratory astrophysics systems. Simulations have been done in order to reproduce the results of the experiments carried out in PALS facility by Chantal Stehlé in radiative shock production. Experimental results are in cióse agreement to the ARWEN estimations of the speed of the shock wave and the length of the precursor. The simulation code used in this thesis, including the work done in ARWEN by other colleagues at the time of this research, allowed the collaboration with other research institution in France and Japan and some of the results presented in this thesis have been published in scientific journals.

Finite element simulation of dispersion in the Bay of Santander

Two mathematical models are used to simulate pollution in the Bay of Santander. The first is the hydrodynamic model that provides the velocity field and height of the water. The second gives the pollutant concentration field as a resultant. Both models are formulated in two-dimensional equations. Linear triangular finite elements are used in the Galerkin procedure for spatial discretization. A finite difference scheme is used for the time integration. At each time step the calculated results of the first model are input to the second model as field data. The efficiency and accuracy of the models are tested by their application to a simple illustrative example. Finally a case study in simulation of pollution evolution in the Bay of Santander is presented

Neuropeptide release by efficient recruitment of diffusing cytoplasmic secretory vesicles

Neuropeptides are slowly released from a limited pool of secretory vesicles. Despite decades of research, the composition of this pool has remained unknown. Endocrine cell studies support the hypothesis that a population of docked vesicles supports the first minutes of hormone release. However, it has been proposed that mobile cytoplasmic vesicles dominate the releasable neuropeptide pool. Here, to determine the cellular basis of the releasable pool, single green fluorescent protein-labeled secretory vesicles were visualized in neuronal growth cones with the use of an inducible construct or total internal reflection fluorescence microscopy. We report that vesicle movement follows the diffusion equation. Furthermore, rapidly moving secretory vesicles are used more efficiently than stationary vesicles near the plasma membrane to support stimulated release. Thus, randomly moving cytoplasmic vesicles participate in the first minutes of neuropeptide release. Importantly, the preferential recruitment of diffusing cytoplasmic secretory vesicles contributes to the characteristic slow kinetics and limited extent of sustained neuropeptide release.

Endoplasmic Reticulum Stress-induced mRNA Splicing Permits Synthesis of Transcription Factor Hac1p/Ern4p That Activates the Unfolded Protein Response

An intracellular signaling from the endoplasmic reticulum (ER) to the nucleus, called the unfolded protein response (UPR), is activated when unfolded proteins are accumulated in the ER under a variety of stress conditions (“ER stress”). We and others recently identified Hac1p/Ern4p as a transcription factor responsible for the UPR in Saccharomyces cerevisiae. It was further reported that Hac1p (238 aa) is detected only in ER-stressed cells, and its expression is mediated by unconventional splicing of HAC1 precursor mRNA. The splicing replaces the C-terminal portion of Hac1p; it was proposed that precursor mRNA is also translated but the putative product of 230 aa is rapidly degraded by the ubiquitin–proteasome pathway. We have identified and characterized the same regulated splicing and confirmed its essential features. Contrary to the above proposal, however, we find that the 238-aa product of mature mRNA and the 230-aa-type protein tested are highly unstable with little or no difference in stability. Furthermore, we demonstrate that the absence of Hac1p in unstressed cells is due to the lack of translation of precursor mRNA. We conclude that Hac1p is synthesized as the result of ER stress-induced mRNA splicing, leading to activation of the UPR.

A quantitative method for evaluating the stabilities of nucleic acids

We report a general method for screening, in solution, the impact of deviations from canonical Watson-Crick composition on the thermodynamic stability of nucleic acid duplexes. We demonstrate how fluorescence resonance energy transfer (FRET) can be used to detect directly free energy differences between an initially formed “reference” duplex (usually a Watson-Crick duplex) and a related “test” duplex containing a lesion/alteration of interest (e.g., a mismatch, a modified, a deleted, or a bulged base, etc.). In one application, one titrates into a solution containing a fluorescently labeled, FRET-active, reference duplex, an unlabeled, single-stranded nucleic acid (test strand), which may or may not compete successfully to form a new duplex. When a new duplex forms by strand displacement, it will not exhibit FRET. The resultant titration curve (normalized fluorescence intensity vs. logarithm of test strand concentration) yields a value for the difference in stability (free energy) between the newly formed, test strand-containing duplex and the initial reference duplex. The use of competitive equilibria in this assay allows the measurement of equilibrium association constants that far exceed the magnitudes accessible by conventional titrimetric techniques. Additionally, because of the sensitivity of fluorescence, the method requires several orders of magnitude less material than most other solution methods. We discuss the advantages of this method for detecting and characterizing any modification that alters duplex stability, including, but not limited to, mutagenic lesions. We underscore the wide range of accessible free energy values that can be defined by this method, the applicability of the method in probing for a myriad of nucleic acid variations, such as single nucleotide polymorphisms, and the potential of the method for high throughput screening.

Theoretical prediction of a crystal structure.

The diffusion equation method of global minimization is applied to compute the crystal structure of S6, with no a priori knowledge about the system. The experimental lattice parameters and positions and orientations of the molecules in the unit cell are predicted correctly.

Well posedness of an integrodifferential kinetic model of Fokker-Planck type for angiogenesis.

Tumor induced angiogenesis processes including the effect of stochastic motion and branching of blood vessels can be described coupling a (nonlocal in time) integrodifferential kinetic equation of Fokker–Planck type with a diffusion equation for the tumor induced ingiogenic factor. The chemotactic force field depends on the flux of blood vessels through the angiogenic factor. We develop an existence and uniqueness theory for this system under natural assumptions on the initial data. The proof combines the construction of fundamental solutions for associated linearized problems with comparison principles, sharp estimates of the velocity integrals and compactness results for this type of kinetic and parabolic operators

Exact Numerical Processing

Paper submitted to Euromicro Symposium on Digital Systems Design (DSD), Belek-Antalya, Turkey, 2003.

Numerical evaluation of the fields induced by body motion in or near high-field MRI scanners

In modern magnetic resonance imaging, both patients and health care workers are exposed to strong. non-uniform static magnetic fields inside and outside of the scanner. In which body movement may be able to induce electric currents in tissues which could be potentially harmful. This paper presents theoretical investigations into the spatial distribution of induced E-fields in a tissue-equivalent human model when moving at various positions around the magnet. The numerical calculations are based on an efficient. quasi-static, finite-difference scheme. Three-dimensional field profiles from an actively shielded 4 T magnet system are used and the body model projected through the field profile with normalized velocity. The simulation shows that it is possible to induce E-fields/currents near the level of physiological significance under some circumstances and provides insight into the spatial characteristics of the induced fields. The methodology presented herein can be extrapolated to very high field strengths for the evaluation of the effects of motion at a variety of field strengths and velocities. (C) 2004 Elsevier Ltd. All rights reserved.

Numerical evaluation of e-fields induced by body motion near high-field MRI scanner

In modern magnetic resonance imaging (MRI), both patients and radiologists are exposed to strong, nonuniform static magnetic fields inside or outside of the scanner, in which the body movement may be able to induce electric currents in tissues which could be possibly harmful. This paper presents theoretical investigations into the spatial distribution of induced E-fields in the human model when moving at various positions around the magnet. The numerical calculations are based on an efficient, quasistatic, finite-difference scheme and an anatomically realistic, full-body, male model. 3D field profiles from an actively-shielded 4 T magnet system are used and the body model projected through the field profile with normalized velocity. The simulation shows that it is possible to induce E-fields/currents near the level of physiological significance under some circumstances and provides insight into the spatial characteristics of the induced fields. The results are easy to extrapolate to very high field strengths for the safety evaluation at a variety of field strengths and motion velocities.

Renewal Processes of Mittag-Leffler and Wright Type

2000 MSC: 26A33, 33E12, 33E20, 44A10, 44A35, 60G50, 60J05, 60K05.

Theorem for Series in Three-Parameter Mittag-Leffler Function

Mathematics Subject Classification 2010: 26A33, 33E12.