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.

Analysis of signal impairment and crosstalk penalty induced by different types of optical filters in 100 Gbps PM-DQPSK based systems

Optical filters are crucial elements in optical communication networks. Their influence toward the optical signal will affect the communication quality seriously. In this paper we will study and simulate the optical signal impairment and crosstalk penalty caused by different kinds of filters, which include Butterworth, Bessel, Fiber Bragg Grating (FBG) and Fabry-Perot (F-P). Signal impairment from filter concatenation effect and crosstalk penalty from out-band and in-band are analyzed from Q-penalty, eye opening penalty (EOP) and optical spectrum. The simulation results show that signal impairment and crosstalk penalty induced by the Butterworth filter is the minimum among these four types of filters. Signal impairment caused by filter concatenation effect shows that when center frequency of all filters is aligned perfectly with the laser's frequency, 12 50-GHz Butterworth filters can be cascaded, with 1-dB EOP. This value is reduced to 9 when the center frequency is misaligned with 5 GHz. In the 50-GHz channel spacing DWDM networks, total Q-penalty induced by a pair of Butterworth filters based demultiplexer and multiplexer is lower than 0.5 dB when the filter bandwidth is in the range of 42-46 GHz.

DNA packing in stable lipid complexes designed for gene transfer imitates DNA compaction in bacteriophage

The structure of complexes made from DNA and suitable lipids (lipoplex, Lx) was examined by cryo-electron microscopy (cryoEM). We observed a distinct concentric ring-like pattern with striated shells when using plasmid DNA. These spherical multilamellar particles have a mean diameter of 254 nm with repetitive spacing of 7.5 nm with striation of 5.3 nm width. Small angle x-ray scattering revealed repetitive ordering of 6.9 nm, suggesting a lamellar structure containing at least 12 layers. This concentric and lamellar structure with different packing regimes also was observed by cryoEM when using linear double-stranded DNA, single-stranded DNA, and oligodeoxynucleotides. DNA chains could be visualized in DNA/lipid complexes. Such specific supramolecular organization is the result of thermodynamic forces, which cause compaction to occur through concentric winding of DNA in a liquid crystalline phase. CryoEM examination of T4 phage DNA packed either in T4 capsides or in lipidic particles showed similar patterns. Small angle x-ray scattering suggested an hexagonal phase in Lx-T4 DNA. Our results indicate that both lamellar and hexagonal phases may coexist in the same Lx preparation or particle and that transition between both phases may depend on equilibrium influenced by type and length of the DNA used.

The Role of Preassembled Cytoplasmic Complexes in Assembly of Flagellar Dynein Subunits

Previous work has revealed a cytoplasmic pool of flagellar precursor proteins capable of contributing to the assembly of new flagella, but how and where these components assemble is unknown. We tested Chlamydomonas outer-dynein arm subunit stability and assembly in the cytoplasm of wild-type cells and 11 outer dynein arm assembly mutant strains (oda1-oda11) by Western blotting of cytoplasmic extracts, or immunoprecipitates from these extracts, with five outer-row dynein subunit-specific antibodies. Western blots reveal that at least three oda mutants (oda6, oda7, and oda9) alter the level of a subunit that is not the mutant gene product. Immunoprecipitation shows that large preassembled flagellar complexes containing all five tested subunits (three heavy chains and two intermediate chains) exist within wild-type cytoplasm. When the preassembly of these subunits was examined in oda strains, we observed three patterns: complete coassembly (oda 1, 3, 5, 8, and 10), partial coassembly (oda7 and oda11), and no coassembly (oda2, 6, and 9) of the four tested subunits with HCβ. Our data, together with previous studies, suggest that flagellar outer-dynein arms preassemble into a complete Mr ≃ 2 × 106 dynein arm that resides in a cytoplasmic precursor pool before transport into the flagellar compartment.

Ligand-dependent activation of transcription in vitro by retinoic acid receptor α/retinoid X receptor α heterodimers that mimics transactivation by retinoids in vivo

All-trans and 9-cis retinoic acids (RA) signals are transduced by retinoic acid receptor/retinoid X receptor (RAR/RXR) heterodimers that act as functional units controlling the transcription of RA-responsive genes. With the aim of elucidating the underlying molecular mechanisms, we have developed an in vitro transcription system using a chromatin template made up of a minimal promoter and a direct repeat with 5-spacing-based RA response element. RARα and RXRα were expressed in and purified from baculovirus-infected Sf9 cells, and transcription was carried out by using naked DNA or chromatin templates. Transcription from naked templates was not affected by the presence of RA and/or RAR/RXR heterodimers. In contrast, very little transcription occurred from chromatin templates in the absence of RA or RAR/RXR heterodimers whereas their addition resulted in a dosage-dependent stimulation of transcription that never exceeded that occurring on naked DNA templates. Most importantly, the addition of synthetic agonistic or antagonistic retinoids to the chromatin transcription system mimicked their stimulatory or inhibitory action in vivo, and activation by a RXR-specific retinoid was subordinated to the binding of an agonist ligand to the RAR partner. Moreover, the addition of the p300 coactivator generated a synergistic enhancement of transcription. Thus, the dissection of this transcription system ultimately should lead to the elucidation of the molecular mechanisms by which RAR/RXR heterodimers control transcription in a ligand-dependent manner.

NOMAD: a versatile strategy for in vitro DNA manipulation applied to promoter analysis and vector design.

Molecular analysis of complex modular structures, such as promoter regions or multi-domain proteins, often requires the creation of families of experimental DNA constructs having altered composition, order, or spacing of individual modules. Generally, creation of every individual construct of such a family uses a specific combination of restriction sites. However, convenient sites are not always available and the alternatives, such as chemical resynthesis of the experimental constructs or engineering of different restriction sites onto the ends of DNA fragments, are costly and time consuming. A general cloning strategy (nucleic acid ordered assembly with directionality, NOMAD; WWW resource locator http:@Lmb1.bios.uic.edu/NOMAD/NOMAD.htm l) is proposed that overcomes these limitations. Use of NOMAD ensures that the production of experimental constructs is no longer the rate-limiting step in applications that require combinatorial rearrangement of DNA fragments. NOMAD manipulates DNA fragments in the form of "modules" having a standardized cohesive end structure. Specially designed "assembly vectors" allow for sequential and directional insertion of any number of modules in an arbitrary predetermined order, using the ability of type IIS restriction enzymes to cut DNA outside of their recognition sequences. Studies of regulatory regions in DNA, such as promoters, replication origins, and RNA processing signals, construction of chimeric proteins, and creation of new cloning vehicles, are among the applications that will benefit from using NOMAD.

The sigma subunit of Escherichia coli RNA polymerase senses promoter spacing.

The promoters recognized by sigma 70, the primary sigma of Escherichia coli, consist of two highly conserved hexamers located at -10 and -35 bp from the start point of transcription, separated by a preferred spacing of 17 bp. sigma factors have two distinct DNA binding domains that recognize the two hexamer sequences. However, the component of RNA polymerase recognizing the length of the spacing between hexamers has not been determined. Using an equilibrium DNA binding competition assay, we demonstrate that a polypeptide of sigma 70 carrying both DNA binding domains is very sensitive to promoter spacing, whereas a sigma 70 polypeptide with only one DNA binding domain is not. Furthermore, a mutant sigma, selected for increasing transcription of the minimal lac promoter (18-bp spacer), has an altered response to promoter spacing in vivo and in vitro. Our data support the idea that sigma makes simultaneous, productive contacts at both the -10 and the -35 regions of the promoter and discerns the spacing between these conserved regions.

Periodic variation in side-chain polarities of T-cell antigenic peptides correlates with their structure and activity.

We present an analysis that synthesizes information on the sequence, structure, and motifs of antigenic peptides, which previously appeared to be in conflict. Fourier analysis of T-cell antigenic peptides indicates a periodic variation in amino acid polarities of 3-3.6 residues per period, suggesting an amphipathic alpha-helical structure. However, the diffraction patterns of major histocompatibility complex (MHC) molecules indicate that their ligands are in an extended non-alpha-helical conformation. We present two mutually consistent structural explanations for the source of the alpha-helical periodicity, based on an observation that the side chains of MHC-bound peptides generally partition with hydrophobic (hydrophilic) side chains pointing into (out of) the cleft. First, an analysis of haplotype-dependent peptide motifs indicates that the locations of their defining residues tend to force a period 3-4 variation in hydrophobicity along the peptide sequence, in a manner consistent with the spacing of pockets in the MHC. Second, recent crystallographic determination of the structure of a peptide bound to a class II MHC molecule reveals an extended but regularly twisted peptide with a rotation angle of about 130 degrees. We show that similar structures with rotation angles of 100-130 degrees are energetically acceptable and also span the length of the MHC cleft. These results provide a sound physical chemical and structural basis for the existence of a haplotype-independent antigenic motif which can be particularly important in limiting the search time for antigenic peptides.

Quantifying epistemic actions in human-computer interaction

As digital systems move away from traditional desktop setups, new interaction paradigms are emerging that better integrate with users’ realworld surroundings, and better support users’ individual needs. While promising, these modern interaction paradigms also present new challenges, such as a lack of paradigm-specific tools to systematically evaluate and fully understand their use. This dissertation tackles this issue by framing empirical studies of three novel digital systems in embodied cognition – an exciting new perspective in cognitive science where the body and its interactions with the physical world take a central role in human cognition. This is achieved by first, focusing the design of all these systems on a contemporary interaction paradigm that emphasizes physical interaction on tangible interaction, a contemporary interaction paradigm; and second, by comprehensively studying user performance in these systems through a set of novel performance metrics grounded on epistemic actions, a relatively well established and studied construct in the literature on embodied cognition. The first system presented in this dissertation is an augmented Four-in-a-row board game. Three different versions of the game were developed, based on three different interaction paradigms (tangible, touch and mouse), and a repeated measures study involving 36 participants measured the occurrence of three simple epistemic actions across these three interfaces. The results highlight the relevance of epistemic actions in such a task and suggest that the different interaction paradigms afford instantiation of these actions in different ways. Additionally, the tangible version of the system supports the most rapid execution of these actions, providing novel quantitative insights into the real benefits of tangible systems. The second system presented in this dissertation is a tangible tabletop scheduling application. Two studies with single and paired users provide several insights into the impact of epistemic actions on the user experience when these are performed outside of a system’s sensing boundaries. These insights are clustered by the form, size and location of ideal interface areas for such offline epistemic actions to occur, as well as how can physical tokens be designed to better support them. Finally, and based on the results obtained to this point, the last study presented in this dissertation directly addresses the lack of empirical tools to formally evaluate tangible interaction. It presents a video-coding framework grounded on a systematic literature review of 78 papers, and evaluates its value as metric through a 60 participant study performed across three different research laboratories. The results highlight the usefulness and power of epistemic actions as a performance metric for tangible systems. In sum, through the use of such novel metrics in each of the three studies presented, this dissertation provides a better understanding of the real impact and benefits of designing and developing systems that feature tangible interaction.

Fault development and interaction in distributed strike-slip shear zones: an experimental approach

Analogue model experiments using both brittle and viscous materials were performed to investigate the development and interaction of strike-slip faults in zones of distributed shear deformation. At low strain, bulk dextral shear deformation of an initial rectangular model is dominantly accommodated by left-stepping, en echelon strike-slip faults (Riedel shears, R) that form in response to the regional (bulk) stress field. Push-up zones form in the area of interaction between adjacent left-stepping Riedel shears. In cross sections, faults bounding push-up zones have an arcuate shape or merge at depth. Adjacent left-stepping R shears merge by sideways propagation or link by short synthetic shears that strike subparallel to the bulk shear direction. Coalescence of en echelon R shears results in major, through-going faults zones (master faults). Several parallel master faults develop due to the distributed nature of deformation. Spacing between master faults is related to the thickness of the brittle layers overlying the basal viscous layer. Master faults control to a large extent the subsequent fault pattern. With increasing strain, relatively short antithetic and synthetic faults develop mostly between old, but still active master faults. The orientation and evolution of the new faults indicate local modifications of the stress field. In experiments lacking lateral borders, closely spaced parallel antithetic faults (cross faults) define blocks that undergo clockwise rotation about a vertical axis with continuing deformation. Fault development and fault interaction at different stages of shear strain in our models show similarities with natural examples that have undergone distributed shear.

Sample descriptions, d-spacing and geochemistry at DSDP Holes 68-501 and 69-504B

Mössbauer analyses were conducted on a sample of saponite selected from DSDP Leg 69 basalt core. The sample was initially placed within a nitrogen-purged container on-board Glomar Challenger approximately three hours after recovery, where it remained until analysis. The Mössbauer data revealed an original, in situ Fe2O3/FeO ratio of 0.46, with both Fe**2+ and Fe**3+ in octahedral coordination. With controlled exposure to air under ambient laboratory storage conditions, the proportion of Fe**3+ increased from an original 30% to 51% over a period of about 11.5 months. The Fe**3+ thus produced remained in octahedral coordination, and no observable changes occurred in the physical appearance of the sample.

Remarks on the life and death of the fam'd Mr. Blood : giving an account [brace]of his plot in Ireland, to surprize Dublin Castle; several transactions in his head-quarters in the city; rescue of Captain Mason at Doncaster; attempt on the person of his Grace the Duke of Ormond; seizing on the crown and scepter in the Tower; coming into favour with his Prince; concern about his Grace the Duke of Buckingham; sickness, death, and twice interment : published for publick information.

Leaf A₂ mis-signed as A₁.