Discontinuous solutions and boundary value problems for non-linearly elastic fibre-reinforced materials

En este trabajo se han analizado varios problemas en el contexto de la elasticidad no lineal basándose en modelos constitutivos representativos. En particular, se han analizado problemas relacionados con el fenómeno de perdida de estabilidad asociada con condiciones de contorno en el caso de material reforzados con fibras. Cada problema se ha formulado y se ha analizado por separado en diferentes capítulos. En primer lugar se ha mostrado el análisis del gradiente de deformación discontinuo para un material transversalmente isótropo, en particular, el modelo del material considerado consiste de una base neo-Hookeana isótropa incrustada con fibras de refuerzo direccional caracterizadas con un solo parámetro. La solución de este problema se vincula con instabilidades que dan lugar al mecanismo de fallo conocido como banda de cortante. La perdida de elipticidad de las ecuaciones diferenciales de equilibrio es una condición necesaria para que aparezca este tipo de soluciones y por tanto las inestabilidades asociadas. En segundo lugar se ha analizado una deformación combinada de extensión, inación y torsión de un tubo cilíndrico grueso donde se ha encontrado que la deformación citada anteriormente puede ser controlada solo para determinadas direcciones de las fibras refuerzo. Para entender el comportamiento elástico del tubo considerado se ha ilustrado numéricamente los resultados obtenidos para las direcciones admisibles de las fibras de refuerzo bajo la deformación considerada. En tercer lugar se ha estudiado el caso de un tubo cilíndrico grueso reforzado con dos familias de fibras sometido a cortante en la dirección azimutal para un modelo de refuerzo especial. En este problema se ha encontrado que las inestabilidades que aparecen en el material considerado están asociadas con lo que se llama soluciones múltiples de la ecuación diferencial de equilibrio. Se ha encontrado que el fenómeno de instabilidad ocurre en un estado de deformación previo al estado de deformación donde se pierde la elipticidad de la ecuación diferencial de equilibrio. También se ha demostrado que la condición de perdida de elipticidad y ^W=2 = 0 (la segunda derivada de la función de energía con respecto a la deformación) son dos condiciones necesarias para la existencia de soluciones múltiples. Finalmente, se ha analizado detalladamente en el contexto de elipticidad un problema de un tubo cilíndrico grueso sometido a una deformación combinada en las direcciones helicoidal, axial y radial para distintas geotermias de las fibras de refuerzo . In the present work four main problems have been addressed within the framework of non-linear elasticity based on representative constitutive models. Namely, problems related to the loss of stability phenomena associated with boundary value problems for fibre-reinforced materials. Each of the considered problems is formulated and analysed separately in different chapters. We first start with the analysis of discontinuous deformation gradients for a transversely isotropic material under plane deformation. In particular, the material model is an augmented neo-Hookean base with a simple unidirectional reinforcement characterised by a single parameter. The solution of this problem is related to material instabilities and it is associated with a shear band-type failure mode. The loss of ellipticity of the governing differential equations is a necessary condition for the existence of these material instabilities. The second problem involves a detailed analysis of the combined non-linear extension, inflation and torsion of a thick-walled circular cylindrical tube where it has been found that the aforementioned deformation is controllable only for certain preferred directions of transverse isotropy. Numerical results have been illustrated to understand the elastic behaviour of the tube for the admissible preferred directions under the considered deformation. The third problem deals with the analysis of a doubly fibre-reinforced thickwalled circular cylindrical tube undergoing pure azimuthal shear for a special class of the reinforcing model where multiple non-smooth solutions emerge. The associated instability phenomena are found to occur prior to the point where the nominal stress tensor changes monotonicity in a particular direction. It has been also shown that the loss of ellipticity condition that arises from the equilibrium equation and ^W=2 = 0 (the second derivative of the strain-energy function with respect to the deformation) are equivalent necessary conditions for the emergence of multiple solutions for the considered material. Finally, a detailed analysis in the basis of the loss of ellipticity of the governing differential equations for a combined helical, axial and radial elastic deformations of a fibre-reinforced circular cylindrical tube is carried out.

Truncation error estimation in the Discontinuous Galerkin Spectral Element Method

En esta tesis, el método de estimación de error de truncación conocido como restimation ha sido extendido de esquemas de bajo orden a esquemas de alto orden. La mayoría de los trabajos en la bibliografía utilizan soluciones convergidas en mallas de distinto refinamiento para realizar la estimación. En este trabajo se utiliza una solución en una única malla con distintos órdenes polinómicos. Además, no se requiere que esta solución esté completamente convergida, resultando en el método conocido como quasi-a priori T-estimation. La aproximación quasi-a priori estima el error mientras el residuo del método iterativo no es despreciable. En este trabajo se demuestra que algunas de las hipótesis fundamentales sobre el comportamiento del error, establecidas para métodos de bajo orden, dejan de ser válidas en esquemas de alto orden, haciendo necesaria una revisión completa del comportamiento del error antes de redefinir el algoritmo. Para facilitar esta tarea, en una primera etapa se considera el método conocido como Chebyshev Collocation, limitando la aplicación a geometrías simples. La extensión al método Discontinuouos Galerkin Spectral Element Method presenta dificultades adicionales para la definición precisa y la estimación del error, debidos a la formulación débil, la discretización multidominio y la formulación discontinua. En primer lugar, el análisis se enfoca en leyes de conservación escalares para examinar la precisión de la estimación del error de truncación. Después, la validez del análisis se demuestra para las ecuaciones incompresibles y compresibles de Euler y Navier Stokes. El método de aproximación quasi-a priori r-estimation permite desacoplar las contribuciones superficiales y volumétricas del error de truncación, proveyendo información sobre la anisotropía de las soluciones así como su ratio de convergencia con el orden polinómico. Se demuestra que esta aproximación quasi-a priori produce estimaciones del error de truncación con precisión espectral. ABSTRACT In this thesis, the τ-estimation method to estimate the truncation error is extended from low order to spectral methods. While most works in the literature rely on fully time-converged solutions on grids with different spacing to perform the estimation, only one grid with different polynomial orders is used in this work. Furthermore, a non timeconverged solution is used resulting in the quasi-a priori τ-estimation method. The quasi-a priori approach estimates the error when the residual of the time-iterative method is not negligible. It is shown in this work that some of the fundamental assumptions about error tendency, well established for low order methods, are no longer valid in high order schemes, making necessary a complete revision of the error behavior before redefining the algorithm. To facilitate this task, the Chebyshev Collocation Method is considered as a first step, limiting their application to simple geometries. The extension to the Discontinuous Galerkin Spectral Element Method introduces additional features to the accurate definition and estimation of the error due to the weak formulation, multidomain discretization and the discontinuous formulation. First, the analysis focuses on scalar conservation laws to examine the accuracy of the estimation of the truncation error. Then, the validity of the analysis is shown for the incompressible and compressible Euler and Navier Stokes equations. The developed quasi-a priori τ-estimation method permits one to decouple the interfacial and the interior contributions of the truncation error in the Discontinuous Galerkin Spectral Element Method, and provides information about the anisotropy of the solution, as well as its rate of convergence in polynomial order. It is demonstrated here that this quasi-a priori approach yields a spectrally accurate estimate of the truncation error.

Type-I intermittency with discontinuous reinjection probability density in a truncation model of the derivative nonlinear Schrödinger equation

In previous papers, the type-I intermittent phenomenon with continuous reinjection probability density (RPD) has been extensively studied. However, in this paper type-I intermittency considering discontinuous RPD function in one-dimensional maps is analyzed. To carry out the present study the analytic approximation presented by del Río and Elaskar (Int. J. Bifurc. Chaos 20:1185-1191, 2010) and Elaskar et al. (Physica A. 390:2759-2768, 2011) is extended to consider discontinuous RPD functions. The results of this analysis show that the characteristic relation only depends on the position of the lower bound of reinjection (LBR), therefore for the LBR below the tangent point the relation {Mathematical expression}, where {Mathematical expression} is the control parameter, remains robust regardless the form of the RPD, although the average of the laminar phases {Mathematical expression} can change. Finally, the study of discontinuous RPD for type-I intermittency which occurs in a three-wave truncation model for the derivative nonlinear Schrodinger equation is presented. In all tests the theoretical results properly verify the numerical data

Adaptation strategies for high order discontinuous Galerkin methods based on Tau-estimation

In this paper three p-adaptation strategies based on the minimization of the truncation error are presented for high order discontinuous Galerkin methods. The truncation error is approximated by means of a ? -estimation procedure and enables the identification of mesh regions that require adaptation. Three adaptation strategies are developed and termed a posteriori, quasi-a priori and quasi-a priori corrected. All strategies require fine solutions, which are obtained by enriching the polynomial order, but while the former needs time converged solutions, the last two rely on non-converged solutions, which lead to faster computations. In addition, the high order method permits the spatial decoupling for the estimated errors and enables anisotropic p-adaptation. These strategies are verified and compared in terms of accuracy and computational cost for the Euler and the compressible Navier?Stokes equations. It is shown that the two quasi- a priori methods achieve a significant reduction in computational cost when compared to a uniform polynomial enrichment. Namely, for a viscous boundary layer flow, we obtain a speedup of 6.6 and 7.6 for the quasi-a priori and quasi-a priori corrected approaches, respectively.

Adaptation Strategies for Discontinuous Galerkin Spectral Element Methods by means of Truncation Error Estimations

In this work a p-adaptation (modification of the polynomial order) strategy based on the minimization of the truncation error is developed for high order discontinuous Galerkin methods. The truncation error is approximated by means of a truncation error estimation procedure and enables the identification of mesh regions that require adaptation. Three truncation error estimation approaches are developed and termed a posteriori, quasi-a priori and quasi-a priori corrected. Fine solutions, which are obtained by enriching the polynomial order, are required to solve the numerical problem with adequate accuracy. For the three truncation error estimation methods the former needs time converged solutions, while the last two rely on non-converged solutions, which lead to faster computations. Based on these truncation error estimation methods, algorithms for mesh adaptation were designed and tested. Firstly, an isotropic adaptation approach is presented, which leads to equally distributed polynomial orders in different coordinate directions. This first implementation is improved by incorporating a method to extrapolate the truncation error. This results in a significant reduction of computational cost. Secondly, the employed high order method permits the spatial decoupling of the estimated errors and enables anisotropic p-adaptation. The incorporation of anisotropic features leads to meshes with different polynomial orders in the different coordinate directions such that flow-features related to the geometry are resolved in a better manner. These adaptations result in a significant reduction of degrees of freedom and computational cost, while the amount of improvement depends on the test-case. Finally, this anisotropic approach is extended by using error extrapolation which leads to an even higher reduction in computational cost. These strategies are verified and compared in terms of accuracy and computational cost for the Euler and the compressible Navier-Stokes equations. The main result is that the two quasi-a priori methods achieve a significant reduction in computational cost when compared to a uniform polynomial enrichment. Namely, for a viscous boundary layer flow, we obtain a speedup of a factor of 6.6 and 7.6 for the quasi-a priori and quasi-a priori corrected approaches, respectively. RESUMEN En este trabajo se ha desarrollado una estrategia de adaptación-p (modificación del orden polinómico) para métodos Galerkin discontinuo de alto orden basada en la minimización del error de truncación. El error de truncación se estima utilizando el método tau-estimation. El estimador permite la identificación de zonas de la malla que requieren adaptación. Se distinguen tres técnicas de estimación: a posteriori, quasi a priori y quasi a priori con correción. Todas las estrategias requieren una solución obtenida en una malla fina, la cual es obtenida aumentando de manera uniforme el orden polinómico. Sin embargo, mientras que el primero requiere que esta solución esté convergida temporalmente, el resto utiliza soluciones no convergidas, lo que se traduce en un menor coste computacional. En este trabajo se han diseñado y probado algoritmos de adaptación de malla basados en métodos tau-estimation. En primer lugar, se presenta un algoritmo de adaptacin isótropo, que conduce a discretizaciones con el mismo orden polinómico en todas las direcciones espaciales. Esta primera implementación se mejora incluyendo un método para extrapolar el error de truncación. Esto resulta en una reducción significativa del coste computacional. En segundo lugar, el método de alto orden permite el desacoplamiento espacial de los errores estimados, permitiendo la adaptación anisotropica. Las mallas obtenidas mediante esta técnica tienen distintos órdenes polinómicos en cada una de las direcciones espaciales. La malla final tiene una distribución óptima de órdenes polinómicos, los cuales guardan relación con las características del flujo que, a su vez, depenen de la geometría. Estas técnicas de adaptación reducen de manera significativa los grados de libertad y el coste computacional. Por último, esta aproximación anisotropica se extiende usando extrapolación del error de truncación, lo que conlleva un coste computational aún menor. Las estrategias se verifican y se comparan en téminors de precisión y coste computacional utilizando las ecuaciones de Euler y Navier Stokes. Los dos métodos quasi a priori consiguen una reducción significativa del coste computacional en comparación con aumento uniforme del orden polinómico. En concreto, para una capa límite viscosa, obtenemos una mejora en tiempo de computación de 6.6 y 7.6 respectivamente, para las aproximaciones quasi-a priori y quasi-a priori con corrección.

Evidence for protein X binding to a discontinuous epitope on the cellular prion protein during scrapie prion propagation

Studies on the transmission of human (Hu) prions to transgenic (Tg) mice suggested that another molecule provisionally designated protein X participates in the formation of nascent scrapie isoform of prion protein (PrPSc). We report the identification of the site at which protein X binds to the cellular isoform of PrP (PrPC) using scrapie-infected mouse (Mo) neuroblastoma cells transfected with chimeric Hu/MoPrP genes even though protein X has not yet been isolated. Substitution of a Hu residue at position 214 or 218 prevented PrPSc formation. The side chains of these residues protrude from the same surface of the C-terminal α-helix and form a discontinuous epitope with residues 167 and 171 in an adjacent loop. Substitution of a basic residue at positions 167, 171, or 218 also prevented PrPSc formation: at a mechanistic level, these mutant PrPs appear to act as “dominant negatives” by binding protein X and rendering it unavailable for prion propagation. Our findings seem to explain the protective effects of basic polymorphic residues in PrP of humans and sheep and suggest therapeutic and prophylactic approaches to prion diseases.

The heme oxygenase gene (pbsA) in the red alga Rhodella violacea is discontinuous and transcriptionally activated during iron limitation

Heme oxygenase (HO) catalyzes the opening of the heme ring with the release of iron in both plants and animals. In cyanobacteria, red algae, and cryptophyceae, HO is a key enzyme in the synthesis of the chromophoric part of the photosynthetic antennae. In an attempt to study the regulation of this key metabolic step, we cloned and sequenced the pbsA gene encoding this enzyme from the red alga Rhodella violacea. The gene is located on the chloroplast genome, split into three distant exons, and is presumably expressed by a trans-splicing mechanism. The deduced polypeptide sequence is homologous to other reported HOs from organisms containing phycobilisomes (Porphyra purpurea and Synechocystis sp. strain PCC 6803) and, to a lesser extent, to vertebrate enzymes. The expression is transcriptionally activated under iron deprivation, a stress condition frequently encountered by algae, suggesting a second role for HO as an iron-mobilizing agent in photosynthetic organisms.

OliI, a unique restriction endonuclease that recognizes the discontinuous sequence 5′-CACNN↓NNGTG-3′

A new type II restriction endonuclease designated OliI has been partially purified from the halophilic bacterium Oceanospirillum linum 4-5D. OliI recognizes the interrupted hexanucleotide palindrome 5′-CACNN↓NNGTG-3′ and cleaves it in the center generating blunt-ended DNA fragments.

Evaluation of the role of heterogeneous nuclear ribonucleoprotein A1 as a host factor in murine coronavirus discontinuous transcription and genome replication

Viruses with RNA genomes often capture and redirect host cell components to assist in mechanisms particular to RNA-dependent RNA synthesis. The nidoviruses are an order of positive-stranded RNA viruses, comprising coronaviruses and arteriviruses, that employ a unique strategy of discontinuous transcription, producing a series of subgenomic mRNAs linking a 5′ leader to distal portions of the genome. For the prototype coronavirus mouse hepatitis virus (MHV), heterogeneous nuclear ribonucleoprotein (hnRNP) A1 has been shown to be able to bind in vitro to the negative strand of the intergenic sequence, a cis-acting element found in the leader RNA and preceding each downstream ORF in the genome. hnRNP A1 thus has been proposed as a host factor in MHV transcription. To test this hypothesis genetically, we initially constructed MHV mutants with a very high-affinity hnRNP A1 binding site inserted in place of, or adjacent to, an intergenic sequence in the MHV genome. This inserted hnRNP A1 binding site was not able to functionally replace, or enhance transcription from, the intergenic sequence. This finding led us to test more directly the role of hnRNP A1 by analysis of MHV replication and RNA synthesis in a murine cell line that does not express this protein. The cellular absence of hnRNP A1 had no detectable effect on the production of infectious virus, the synthesis of genomic RNA, or the quantity or quality of subgenomic mRNAs. These results strongly suggest that hnRNP A1 is not a required host factor for MHV discontinuous transcription or genome replication.

Discontinuous epitopes of hepatitis B surface antigen derived from a filamentous phage peptide library.

The structure of the small hepatitis B virus surface antigen (HBsAg) was investigated by epitope mapping of four anti-HBsAg monoclonal antibodies (mAbs). Amino acid sequences of epitopes were derived from affinity-enrichment experiments (biopanning) using a filamentous phage peptide library. The library consists of 10(9) different clones bearing a 30-residue peptide fused to gene III. Sequence homologies between peptides obtained from panning the library against the antibodies and the native HBsAg sequence allowed for precise description of the binding regions. Three of four mAbs were found to bind to distinct discontinuous epitopes between amino acid residues 101 and 207 of HBsAg. The fourth mAb was demonstrated to bind to residues 121-124. The sequence data are supported by ELISA assays demonstrating the binding of the HBsAg-specific peptides on filamentous phage to mAbs. The sequence data were used to map the surface of HBsAg and to derive a topological model for the alpha-carbon trace of the 101-207 region of HBsAg. The approach should be useful for other proteins for which the crystal structure is not available but a representative set of mAbs can be obtained.

French-frying quality of potatoes : as influenced by cooking methods, storage conditions, and specific gravity of tubers /

Caption title.

Modeling collisional processes in plasmas using discontinuous numerical methods

Thesis (Ph.D.)--University of Washington, 2016-06

A Kinetic Vlasov Model for Plasma Simulation Using Discontinuous Galerkin Method on Many-Core Architectures

Thesis (Ph.D.)--University of Washington, 2016-03

The drying of sewage sludge by immersion frying

The objective of this work was to dry sewage sludge using a fry-drying process. The frying experiments were carried out in commercial fryers modified by adding thermocouples to the setup. During frying, typical drying curves were obtained and it was verified that, in relation to the parameters: oil temperature, oil type and shape of the sample, the shape factor the most effect on the drying rate, at least within the range chosen for the variables studied. Oil uptake and calorific value were also analyzed. The calorific value of the samples increased with frying time, reaching values around 24MJ/kg after 600s of frying (comparable to biocombustibles such as wood and sugarcane bagasse). The process of immersion frying showed great potential for drying materials, especially sewage sludge, obtaining a product with a high energy content, thereby increasing its value as a combustible.