Numerical solution of parabolic Cauchy problems in planar corner domains

An iterative method for the parabolic Cauchy problem in planar domains having a finite number of corners is implemented based on boundary integral equations. At each iteration, mixed well-posed problems are solved for the same parabolic operator. The presence of corner points renders singularities of the solutions to these mixed problems, and this is handled with the use of weight functions together with, in the numerical implementation, mesh grading near the corners. The mixed problems are reformulated in terms of boundary integrals obtained via discretization of the time-derivative to obtain an elliptic system of partial differential equations. To numerically solve these integral equations a Nyström method with super-algebraic convergence order is employed. Numerical results are presented showing the feasibility of the proposed approach. © 2014 IMACS.

Low Volatility Options and Numerical Diffusion of Finite Difference Schemes

2000 Mathematics Subject Classification: 65M06, 65M12.

An R-package for the Estimation and Testing of Multiple Covariates and Biomarker Interactions for Survival Data Based on Local Partial Likelihood

When we study the variables that a ffect survival time, we usually estimate their eff ects by the Cox regression model. In biomedical research, e ffects of the covariates are often modi ed by a biomarker variable. This leads to covariates-biomarker interactions. Here biomarker is an objective measurement of the patient characteristics at baseline. Liu et al. (2015) has built up a local partial likelihood bootstrap model to estimate and test this interaction e ffect of covariates and biomarker, but the R code developed by Liu et al. (2015) can only handle one variable and one interaction term and can not t the model with adjustment to nuisance variables. In this project, we expand the model to allow adjustment to nuisance variables, expand the R code to take any chosen interaction terms, and we set up many parameters for users to customize their research. We also build up an R package called "lplb" to integrate the complex computations into a simple interface. We conduct numerical simulation to show that the new method has excellent fi nite sample properties under both the null and alternative hypothesis. We also applied the method to analyze data from a prostate cancer clinical trial with acid phosphatase (AP) biomarker.

A posteriori error estimation for discontinuous Galerkin discretizations of H(curl)-elliptic partial differential equations

We develop the a posteriori error estimation of interior penalty discontinuous Galerkin discretizations for H(curl)-elliptic problems that arise in eddy current models. Computable upper and lower bounds on the error measured in terms of a natural (mesh-dependent) energy norm are derived. The proposed a posteriori error estimator is validated by numerical experiments, illustrating its reliability and efficiency for a range of test problems.

Experimental and Numerical Analysis of Gas Flows in Microchannels and Micro Heat Exchanger

Due to increased interest in miniaturization, great attention has been given in the recent decade to the micro heat exchanging systems. Literature survey suggests that there is still a limited understanding of gas flows in micro heat exchanging systems. The aim of the current thesis is to further the understanding of fluid flow and heat transfer phenomenon inside such geometries when a compressible working fluid is utilized. A combined experimental and numerical approach has been utilized in order to overcome the lack of employable sensors for micro dimensional channels. After conducting a detailed comparison between various data reduction methodologies employed in the literature, the best suited methodology for gas microflow experimentalists is proposed. A transitional turbulence model is extensively validated against the experimental results of the microtubes and microchannels under adiabatic wall conditions. Heat transfer analysis of single microtubes showed that when the compressible working fluid is used, Nusselt number results are in partial disagreement with the conventional theory at highly turbulent flow regime for microtubes having a hydraulic diameter less than 250 microns. Experimental and numerical analysis on a prototype double layer microchannel heat exchanger showed that compressibility is detrimental to the thermal performance. It has been found that compressibility effects for micro heat exchangers are significant when the average Mach number at the outlet of the microchannel is greater than 0.1 compared to the adiabatic limit of 0.3. Lastly, to avoid a staggering amount of the computational power needed to simulate the micro heat exchanging systems with hundreds of microchannels, a reduced order model based on the porous medium has been developed that considers the compressibility of the gas inside microchannels. The validation of the proposed model against experimental results of average thermal effectiveness and the pressure loss showed an excellent match between the two.

Experimental and numerical investigation on short and long term performance of macro-synthetic fibre reinforced concrete materials

Fibre Reinforced Concretes are innovative composite materials whose applications are growing considerably nowadays. Being composite materials, their performance depends on the mechanical properties of both components, fibre and matrix and, above all, on the interface. The variables to account for the mechanical characterization of the material, could be proper of the material itself, i.e. fibre and concrete type, or external factors, i.e. environmental conditions. The first part of the research presented is focused on the experimental and numerical characterization of the interface properties and short term response of fibre reinforced concretes with macro-synthetic fibers. The experimental database produced represents the starting point for numerical models calibration and validation with two principal purposes: the calibration of a local constitutive law and calibration and validation of a model predictive of the whole material response. In the perspective of the design of sustainable admixtures, the optimization of the matrix of cement-based fibre reinforced composites is realized with partial substitution of the cement amount. In the second part of the research, the effect of time dependent phenomena on MSFRCs response is studied. An extended experimental campaign of creep tests is performed analysing the effect of time and temperature variations in different loading conditions. On the results achieved, a numerical model able to account for the viscoelastic nature of both concrete and reinforcement, together with the environmental conditions, is calibrated with the LDPM theory. Different type of regression models are also elaborated correlating the mechanical properties investigated, bond strength and residual flexural behaviour, regarding the short term analysis and creep coefficient on time, for the time dependent behaviour, with the variable investigated. The experimental studies carried out emphasize the several aspects influencing the material mechanical performance allowing also the identification of those properties that the numerical approach should consider in order to be reliable.

Numerical Analysis and Redesign of a High Speed Linear Cascade Wind Tunnel for Aircraft Gas Turbine Engines Testing

Linear cascade testing serves a fundamental role in the research, development, and design of turbomachines as it is a simple yet very effective way to compute the performance of a generic blade geometry. These kinds of experiments are usually carried out in specialized wind tunnel facilities. This thesis deals with the numerical characterization and subsequent partial redesign of the S-1/C Continuous High Speed Wind Tunnel of the Von Karman Institute for Fluid Dynamics. The current facility is powered by a 13-stage axial compressor that is not powerful enough to balance the energy loss experienced when testing low turning airfoils. In order to address this issue a performance assessment of the wind tunnel was performed under several flow regimes via numerical simulations. After that, a redesign proposal aimed at reducing the pressure loss was investigated. This consists of a linear cascade of turning blades to be placed downstream of the test section and designed specifically for the type of linear cascade being tested. An automatic design procedure was created taking as input parameters those measured at the outlet of the cascade. The parametrization method employed Bézier curves to produce an airfoil geometry that could be imported into a CAD software so that a cascade could be designed. The proposal was simulated via CFD analysis and proved to be effective in reducing pressure losses up to 41%. The same tool developed in this thesis could be adopted to design similar apparatuses and could also be optimized and specialized for the design of turbomachines components.

Petroleomics By Electrospray Ionization Ft-icr Mass Spectrometry Coupled To Partial Least Squares With Variable Selection Methods: Prediction Of The Total Acid Number Of Crude Oils.

Negative-ion mode electrospray ionization, ESI(-), with Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) was coupled to a Partial Least Squares (PLS) regression and variable selection methods to estimate the total acid number (TAN) of Brazilian crude oil samples. Generally, ESI(-)-FT-ICR mass spectra present a power of resolution of ca. 500,000 and a mass accuracy less than 1 ppm, producing a data matrix containing over 5700 variables per sample. These variables correspond to heteroatom-containing species detected as deprotonated molecules, [M - H](-) ions, which are identified primarily as naphthenic acids, phenols and carbazole analog species. The TAN values for all samples ranged from 0.06 to 3.61 mg of KOH g(-1). To facilitate the spectral interpretation, three methods of variable selection were studied: variable importance in the projection (VIP), interval partial least squares (iPLS) and elimination of uninformative variables (UVE). The UVE method seems to be more appropriate for selecting important variables, reducing the dimension of the variables to 183 and producing a root mean square error of prediction of 0.32 mg of KOH g(-1). By reducing the size of the data, it was possible to relate the selected variables with their corresponding molecular formulas, thus identifying the main chemical species responsible for the TAN values.

Effects Of Partial Inhibition Of Respiratory Complex I On H2o 2 Production By Isolated Brain Mitochondria In Different Respiratory States.

The aim of this work was to characterize the effects of partial inhibition of respiratory complex I by rotenone on H2O2 production by isolated rat brain mitochondria in different respiratory states. Flow cytometric analysis of membrane potential in isolated mitochondria indicated that rotenone leads to uniform respiratory inhibition when added to a suspension of mitochondria. When mitochondria were incubated in the presence of a low concentration of rotenone (10 nm) and NADH-linked substrates, oxygen consumption was reduced from 45.9 ± 1.0 to 26.4 ± 2.6 nmol O2 mg(-1) min(-1) and from 7.8 ± 0.3 to 6.3 ± 0.3 nmol O2 mg(-1) min(-1) in respiratory states 3 (ADP-stimulated respiration) and 4 (resting respiration), respectively. Under these conditions, mitochondrial H2O2 production was stimulated from 12.2 ± 1.1 to 21.0 ± 1.2 pmol H2O2 mg(-1) min(-1) and 56.5 ± 4.7 to 95.0 ± 11.1 pmol H2O2 mg(-1) min(-1) in respiratory states 3 and 4, respectively. Similar results were observed when comparing mitochondrial preparations enriched with synaptic or nonsynaptic mitochondria or when 1-methyl-4-phenylpyridinium ion (MPP(+)) was used as a respiratory complex I inhibitor. Rotenone-stimulated H2O2 production in respiratory states 3 and 4 was associated with a high reduction state of endogenous nicotinamide nucleotides. In succinate-supported mitochondrial respiration, where most of the mitochondrial H2O2 production relies on electron backflow from complex II to complex I, low rotenone concentrations inhibited H2O2 production. Rotenone had no effect on mitochondrial elimination of micromolar concentrations of H2O2. The present results support the conclusion that partial complex I inhibition may result in mitochondrial energy crisis and oxidative stress, the former being predominant under oxidative phosphorylation and the latter under resting respiration conditions.

Photoelastic Analysis Of Fixed Partial Prosthesis Crown Height And Implant Length On Distribution Of Stress In Two Dental Implant Systems.

The aim of this study was to evaluate by photoelastic analysis stress distribution on short and long implants of two dental implant systems with 2-unit implant-supported fixed partial prostheses of 8 mm and 13 mm heights. Sixteen photoelastic models were divided into 4 groups: I: long implant (5 × 11 mm) (Neodent), II: long implant (5 × 11 mm) (Bicon), III: short implant (5 × 6 mm) (Neodent), and IV: short implants (5 × 6 mm) (Bicon). The models were positioned in a circular polariscope associated with a cell load and static axial (0.5 Kgf) and nonaxial load (15°, 0.5 Kgf) were applied to each group for both prosthetic crown heights. Three-way ANOVA was used to compare the factors implant length, crown height, and implant system (α = 0.05). The results showed that implant length was a statistically significant factor for both axial and nonaxial loading. The 13 mm prosthetic crown did not result in statistically significant differences in stress distribution between the implant systems and implant lengths studied, regardless of load type (P > 0.05). It can be concluded that short implants showed higher stress levels than long implants. Implant system and length was not relevant factors when prosthetic crown height were increased.

Long-term Follow-up Of Patients With 46,xy Partial Gonadal Dysgenesis Reared As Males.

Background/Aims. Studies on 46,XY partial gonadal dysgenesis (PGD) have focused on molecular, gonadal, genital, and hormone features; little is known about follow-up. Our aim was to analyze long-term outcomes of PGD. Methods. Retrospective longitudinal study conducted at a reference service in Brazil. Ten patients were first evaluated in the 1990s and followed up until the 2010s; follow-up ranged from 13.5 to 19.7 years. All were reared as males and had at least one scrotal testis; two bore NR5A1 mutations. Main outcomes were: associated conditions, pubertal development, and growth. Results. All patients had normal motor development but three presented cognitive impairment; five had various associated conditions. At the end of the prepubertal period, FSH was high or high-normal in 3/6 patients; LH was normal in all. At the last evaluation, FSH was high or high-normal in 8/10; LH was high or high-normal in 5/10; testosterone was decreased in one. Final height in nine cases ranged from -1.57 to 0.80 SDS. All had spontaneous puberty; only one needed androgen therapy. Conclusions. There is good prognosis for growth and spontaneous pubertal development but not for fertility. Though additional studies are required, screening for learning disabilities is advisable.

Partial-hepatectomized (70%) Model Shows A Correlation Between Hepatocyte Growth Factor Levels And Beta-cell Mass.

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Novel DMRT1 3'UTR+11insT mutation associated to XY partial gonadal dysgenesis

The Y-chromosome-located SRY gene encodes a small testis-specific protein containing a DNA-binding motif known as the HMG (high mobility group) box. However, mutations in SRY are not frequent especially in cases of 46,XY partial gonadal dysgenesis. Several sex-determining genes direct the fate of the bipotential gonad to either testis or ovary. In addition, heterozygous small deletions in 9p can cause complete and partial XY gonadal dysgenesis without other symptoms. Human DMRT1 gene, which is located at 9p24.3, is expressed in testis and ovary and has been considered, among others, a candidate autosomal gene responsible for gonadal dysgenesis. In this report we describe a nucleotide insertion in DMRT1 3'UTR in a patient of XY partial gonadal dygenesis. The 3'UTR+11insT is located within a conserved motif important for mRNA stabilization.

Wavelets And Adaptive Grids For The Discontinuous Galerkin Method

In this paper, space adaptivity is introduced to control the error in the numerical solution of hyperbolic systems of conservation laws. The reference numerical scheme is a new version of the discontinuous Galerkin method, which uses an implicit diffusive term in the direction of the streamlines, for stability purposes. The decision whether to refine or to unrefine the grid in a certain location is taken according to the magnitude of wavelet coefficients, which are indicators of local smoothness of the numerical solution. Numerical solutions of the nonlinear Euler equations illustrate the efficiency of the method. © Springer 2005.