Discontinuous Galerkin methods for the p-biharmonic equation from a discrete variational perspective

We study discontinuous Galerkin approximations of the p-biharmonic equation for p∈(1,∞) from a variational perspective. We propose a discrete variational formulation of the problem based on an appropriate definition of a finite element Hessian and study convergence of the method (without rates) using a semicontinuity argument. We also present numerical experiments aimed at testing the robustness of the method.

Investigation by Combined Solid-State NMR and SAXS Methods of the Morphology and Domain Size in Polystyrene-b-Polyethylene Oxide-b-Polystyrene Triblock Copolymers

The microphase structure of a series of polystyrene-b-polyethylene oxide-b-polystyrene (SEOS) triblock copolymers with different compositions and molecular weights has been studied by solid-state NMR, DSC, wide and small angle X-ray scattering (WAXS and SAXS). WAXS and DSC measurements were used to detect the presence of crystalline domains of polyethyleneoxide (PEO) blocks at room temperature as a function of the copolymer chemical composition. Furthermore, DSC experiments allowed the determination of the melting temperatures of the crystalline part of the PEO blocks. SAXS measurements, performed above and below the melting temperature of the PEO blocks, revealed the formation of periodic structures, but the absence or the weakness of high order reflections peaks did not allow a clear assessment of the morphological structure of the copolymers. This information was inferred by combining the results obtained by SAXS and (1)H NMR spin diffusion experiments, which also provided an estimation of the size of the dispersed phases of the nanostructured copolymers. (C) 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48:55-64,2010

Extraction methods and availability of phosphorus for soybean in soils from Parana State, Brazil

In studies on the evaluation of methodologies for the analysis of soil, phosphorus (P) has been the single most studied aspect, due to the complexity of this dynamic element in soil. However, these studies have been limited regarding soil conditions in Paranaa. The present study aimed to evaluate the efficiency of the Mehlich-1, Mehlich-3 and ion exchange resin methods in the evaluation of available P for soybean (Glycine max) in the soils of Paranaa State. Twelve soil samples collected from the upper 0-20 cm were planted with soybean for a period of 42 days in the greenhouse. The ability to extract soil P followed the order of decreasing average amount of extracted P: Mehlich-3 > resin > Mehlich-1. The correlation coefficients between the content of P extracted by Mehlich-1, Mehlich-3 and resin and the amount of P accumulated in the plants were 0.86, 0.90 and 0.93, respectively. Mehlich-1, Mehlich-3 and resin showed similar efficiency in the evaluation of P availability to plants and, under conditions of natural fertility and in soils that had received no application of poorly natural reactive phosphates, can be used to quantify the concentrations of P in the soils of Parana State.

Methods Used for Assessing Stresses in Buccomaxillary Prostheses: Photoelasticity, Finite Element Technique, and Extensometry

The authors describe a literature revision on assessing stresses in buccomaxillary prostheses photoelasticity, finite element technique, and extensometry. They describe the techniques and the importance for use of each method in buccomaxillary prostheses with implants and the need of accomplishing more studies in this scarce literary area.

Integrable aspects of the scaling q-state Potts models II: finite-size effects

We continue our discussion of the q-state Potts models for q less than or equal to 4, in the scaling regimes close to their critical and tricritical points. In a previous paper, the spectrum and full S-matrix of the models on an infinite line were elucidated; here, we consider finite-size behaviour. TBA equations are proposed for all cases related to phi(21) and phi(12) perturbations of unitary minimal models. These are subjected to a variety of checks in the ultraviolet and infrared limits, and compared with results from a recently-proposed non-linear integral equation. A non-linear integral equation is also used to study the flows from tricritical to critical models, over the full range of q. Our results should also be of relevance to the study of the off-critical dilute A models in regimes 1 and 2. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Discrete generator coordinate: Symmetry restoration in finite-dimensional spaces

Group theoretical-based techniques and fundamental results from number theory are used in order to allow for the construction of exact projectors in finite-dimensional spaces. These operators are shown to make use only of discrete variables, which play the role of discrete generator coordinates, and their application in the number symmetry restoration is carried out in a nuclear BCS wave function which explicitly violates that symmetry. © 1999 Published by Elsevier Science B.V. All rights reserved.

Local dimension and finite time prediction in spatiotemporal chaotic systems

Predictability is related to the uncertainty in the outcome of future events during the evolution of the state of a system. The cluster weighted modeling (CWM) is interpreted as a tool to detect such an uncertainty and used it in spatially distributed systems. As such, the simple prediction algorithm in conjunction with the CWM forms a powerful set of methods to relate predictability and dimension.

Finite element evaluation of three methods of stable fixation of condyle base fractures

The surgical treatment of mandibular condyle fractures currently offers several possibilities for stable internal fixation. In this study, a finite element model evaluation was performed of three different methods for osteosynthesis of low subcondylar fractures: (1) two four-hole straight plates, (2) one seven-hole lambda plate, and (3) one four-hole trapezoidal plate. The finite element model evaluation considered a load applied to the first molar on the contralateral side to the fracture. Results showed that, although the three methods are capable of withstanding functional loading, the lambda plate displayed a more homogeneous stress distribution for both osteosynthesis material and bone and may be a better method when single-plate fixation is the option.

Computer graphics applied to anatomy: a study of two bio-cad modeling methods on finite element analysis of human edentulous hemi-mandible

Modeling is a step to perform a finite element analysis. Different methods of model construction are reported in literature, as the Bio-CAD modeling. The purpose of this study was to perform a model evaluation and application using two methods of Bio-CAD modeling from human edentulous hemi-mandible on the finite element analysis. From CT scans of dried human skull was reconstructed a stereolithographic model. Two methods of modeling were performed: STL conversion approach (Model 1) associated to STL simplification and reverse engineering approach (Model 2). For finite element analysis was used the action of lateral pterygoid muscle as loading condition to assess total displacement (D), equivalent von-Mises stress (VM) and maximum principal stress (MP). Two models presented differences on the geometry regarding surface number (1834 (model 1); 282 (model 2)). Were observed differences in finite element mesh regarding element number (30428 nodes/16683 elements (model 1); 15801 nodes/8410 elements (model 2). D, VM and MP stress areas presented similar distribution in two models. The values were different regarding maximum and minimum values of D (ranging 0-0.511 mm (model 1) and 0-0.544 mm (model 2), VM stress (6.36E-04-11.4 MPa (model 1) and 2.15E-04-14.7 MPa (model 2) and MP stress (-1.43-9.14 MPa (model 1) and -1.2-11.6 MPa (model 2). From two methods of Bio-CAD modeling, the reverse engineering presented better anatomical representation compared to the STL conversion approach. The models presented differences in the finite element mesh, total displacement and stress distribution.

Yang-Lee zeros of the two- and three-state Potts model defined on π3 Feynman diagrams

We present both analytical and numerical results on the position of partition function zeros on the complex magnetic field plane of the q=2 state (Ising) and the q=3 state Potts model defined on phi(3) Feynman diagrams (thin random graphs). Our analytic results are based on the ideas of destructive interference of coexisting phases and low temperature expansions. For the case of the Ising model, an argument based on a symmetry of the saddle point equations leads us to a nonperturbative proof that the Yang-Lee zeros are located on the unit circle, although no circle theorem is known in this case of random graphs. For the q=3 state Potts model, our perturbative results indicate that the Yang-Lee zeros lie outside the unit circle. Both analytic results are confirmed by finite lattice numerical calculations.

Perfomance of methods for estimating reference evapotranspiration in the municipalities of Frederico Westphalen and Palmeira das Missoes, State of Rio Grande do Sul, Brazil

The estimation of reference evapotranspiration (ETo), used in water balance, allows to determine soil water content, assisting on irrigation management. The present study aimed to compare simple ETo estimating methods with the Penman-Monteith (FAO), in the folowing time scales: daily, 5, 10, 15 and 30 days and monthly in the counties of Frederico Westphalen and Palmeira das Missoes, in the Rio Grande do Sul state, Brazil. The methods tested had their efficiency improved by increasing the time scale of analysis, keeping the same performance for both locations. The highest and lowest ETo values occurred in December and June, respectively. Most methods underestimated ETo. For any of the time scales Makking and Radiaton FAO24 methods can replace the Penman-Monteith for estimating ETo.

Heteronuclear recoupling methods in solid-state NMR

This thesis is focused on the development of heteronuclear correlation methods in solid-state NMR spectroscopy, where the spatial dependence of the dipolar coupling is exploited to obtain structural and dynamical information in solids. Quantitative results on dipolar coupling constants are extracted by means of spinning sideband analysis in the indirect dimension of the two-dimensional experiments. The principles of sideband analysis were established and are currently widely used in the group of Prof. Spiess for the special case of homonuclear 1H double-quantum spectroscopy. The generalization of these principles to the heteronuclear case is presented, with special emphasis on naturally abundant 13C-1H systems. For proton spectroscopy in the solid state, line-narrowing is of particular importance, and is here achieved by very-fast sample rotation at the magic angle (MAS), with frequencies up to 35 kHz. Therefore, the heteronuclear dipolar couplings are suppressed and have to be recoupled in order to achieve an efficient excitation of the observed multiple-quantum modes. Heteronuclear recoupling is most straightforwardly accomplished by performing the known REDOR experiment, where pi-pulses are applied every half rotor period. This experiment was modified by the insertion of an additional spectroscopic dimension, such that heteronuclear multiple-quantum experiments can be carried out, which, as shown experimentally and theoretically, closely resemble homonuclear double-quantum experiments. Variants are presented which are well-suited for the recording of high-resolution 13C-1H shift correlation and spinning-sideband spectra, by means of which spatial proximities and quantitative dipolar coupling constants, respectively, of heteronuclear spin pairs can be determined. Spectral editing of 13C spectra is shown to be feasible with these techniques. Moreover, order phenomena and dynamics in columnar mesophases with 13C in natural abundance were investigated. Two further modifications of the REDOR concept allow the correlation of 13C with quadrupolar nuclei, such as 2H. The spectroscopic handling of these nuclei is challenging in that they cover large frequency ranges, and with the new experiments it is shown how the excitation problem can be tackled or circumvented altogether, respectively. As an example, one of the techniques is used for the identification of a yet unknown motional process of the H-bonded protons in the crystalline parts of poly(vinyl alcohol).

Supramolecular order and dynamics of discotic materials studied by solid-state NMR recoupling methods

The topic of this thesis is the investigation of structure,order and dynamics in discotic mesogens by advancedsolid-state NMR spectroscopy. Most of the discotic mesogensunder investigation are hexa-peri-hexabenzocoronene (HBC)derivatives which are of particular interest for potentialdevice applications due to their high one-dimensional chargecarrier mobilities. The supramolecular stacking arrangement of the discoticcores was investigated by 2D 1H-1H double-quantum (DQ)methods, which were modified by incorporating the WATERGATEsuppression technique into the experiments in order toovercome severe phase problems arising from the strongsignal of the long alkyl sidechains. Molecular dynamics and sample orientation was probed throughthe generation of sideband patterns by reconversion rotorencoding in 2D recoupling experiments. These experimentswere extended by new recoupling schemes to enable thedistinction of motion and orientation effects. The solid-state NMR studies presented in this work aim tothe understanding of structure-property relationships in theinvestigated discotic materials, while the experimentsapplied to these materials include new recoupling schemeswhich make the desired information on molecular orientationand dynamics accessible without isotope labelling.

Characterisation of supramolecular structures by novel recoupling methods in solid-state NMR

In this work, solid-state NMR methods suitable for the investigation of supramolecular systems were developed and improved. In this context, special interest was focussed on non-covalent interactions responsible for the formation of supramolecular structures, such as pi-pi interacions and hydrogen-bonds. In the first part of this work, solid-state NMR methods were presented that provide information on molecular structure and motion via the investigation of anisotropic interactions, namely quadrupole and dipole-dipole couplings, under magic-angle spinning conditions. A two-dimensional 2H double quantum experiment was developed, which is performed under off magic-angle conditions and correlates 2H isotropic chemical shifts with quasistatic DQ-filtered line shapes. From the latter, the quadrupole coupling parameters of samples deuterated at multiple sites can be extracted in a site-selective fashion. Furthermore, 7Li quadrupole parameters of lithium intercalated into TiO2 were determined by NMR experiments performed under static and MAS conditions, and could provide information on the crystal geometry. For the determination of 7Li-7Li dipole-dipole couplings, multiple-quantum NMR experiments were performed. The 1H-13C REREDOR experiment was found to be capable of determining strong proton-carbon dipole-dipole couplings with an accuracy of 500~Hz, corresponding to a determination of proton-carbon chemical-bond lengths with picometer accuracy In the second part of this work, solid-state NMR experiments were combined with quantum-chemical calculations in order to aid and optimise the interpretation of experimental results. The investigations on Calix[4]hydroquinone nanotubes have shown that this combined approach can provide information on the presence of disordered and/or mobile species in supramolecular structures. As a second example, C3-symmetric discs arranging in helical columnar stacks were investigated. In these systems, 1H chemical shifts experience large pi-shifts due to packing effects, which were found to be long-ranged. Moreover, quantum-chemical calculations revealed that helicity in these systems is induced by the propeller-like conformation of the core of the molecules.