Boundary identification in the domain of a parabolic partial differential equation

Bakgrunden och inspirationen till föreliggande studie är tidigare forskning i tillämpningar på randidentifiering i metallindustrin. Effektiv randidentifiering möjliggör mindre säkerhetsmarginaler och längre serviceintervall för apparaturen i industriella högtemperaturprocesser, utan ökad risk för materielhaverier. I idealfallet vore en metod för randidentifiering baserad på uppföljning av någon indirekt variabel som kan mätas rutinmässigt eller till en ringa kostnad. En dylik variabel för smältugnar är temperaturen i olika positioner i väggen. Denna kan utnyttjas som insignal till en randidentifieringsmetod för att övervaka ugnens väggtjocklek. Vi ger en bakgrund och motivering till valet av den geometriskt endimensionella dynamiska modellen för randidentifiering, som diskuteras i arbetets senare del, framom en flerdimensionell geometrisk beskrivning. I de aktuella industriella tillämpningarna är dynamiken samt fördelarna med en enkel modellstruktur viktigare än exakt geometrisk beskrivning. Lösningsmetoder för den s.k. sidledes värmeledningsekvationen har många saker gemensamt med randidentifiering. Därför studerar vi egenskaper hos lösningarna till denna ekvation, inverkan av mätfel och något som brukar kallas förorening av mätbrus, regularisering och allmännare följder av icke-välställdheten hos sidledes värmeledningsekvationen. Vi studerar en uppsättning av tre olika metoder för randidentifiering, av vilka de två första är utvecklade från en strikt matematisk och den tredje från en mera tillämpad utgångspunkt. Metoderna har olika egenskaper med specifika fördelar och nackdelar. De rent matematiskt baserade metoderna karakteriseras av god noggrannhet och låg numerisk kostnad, dock till priset av låg flexibilitet i formuleringen av den modellbeskrivande partiella differentialekvationen. Den tredje, mera tillämpade, metoden kännetecknas av en sämre noggrannhet förorsakad av en högre grad av icke-välställdhet hos den mera flexibla modellen. För denna gjordes även en ansats till feluppskattning, som senare kunde observeras överensstämma med praktiska beräkningar med metoden. Studien kan anses vara en god startpunkt och matematisk bas för utveckling av industriella tillämpningar av randidentifiering, speciellt mot hantering av olinjära och diskontinuerliga materialegenskaper och plötsliga förändringar orsakade av “nedfallande” väggmaterial. Med de behandlade metoderna förefaller det möjligt att uppnå en robust, snabb och tillräckligt noggrann metod av begränsad komplexitet för randidentifiering.

Estimation of evaporation in the Banabuiú dam, in the state of Ceará, Brazil, by different combined methods, derived from the Penman equation

The state of Ceará, Brazil, has 75% of its area covered by Brazilian semiarid, with its peculiar features. In this state, the dams are constituted in water structure of strategic importance, ensuring, both in time and space, the development and supply of water to population. However, construction of reservoirs results in various impacts that should be carefully observed when deciding on their implementation. One of the impacts identified as negative is the increased evaporation, which constitutes a major component of water balance in reservoirs, especially in arid regions. Several methods for estimating evaporation have been proposed over time, many of them deriving from the Penman equation. This study evaluated six different methods for estimating evaporation in order to determine the most suitable for use in hydrological models for water balance in reservoirs in the state of Ceará. The tested methods were proposed by Penman, Kohler-Nordenson-Fox, Priestley-Taylor, deBruim-Keijman, Brutsaert-Stricker and deBruim. The methods presented good performance when tested for water balance during the dry season, and the Priestley-Taylor was the most appropriate, since the data from de simulated water balance with evaporation estimated by this method were the closest of the water balance data observed from measures of reservoir level and the elevation-volume curve provided by the Company of Management of Water Resources of the state of Ceará - COGERH.

Methodology for spatialization of intense rainfall equation parameters

The aim of this study was to generate maps of intense rainfall equation parameters using interpolated maximum intense rainfall data. The study area comprised Espírito Santo State, Brazil. A total of 59 intense rainfall equations were used to interpolate maximum intense rainfall, with a 1 x 1 km spatial resolution. Maximum intense rainfall was interpolated considering recurrence of 2; 5; 10; 20; 50 and 100 years, and duration of 10; 20; 30; 40; 50; 60; 120; 240; 360; 420; 660; 720; 900; 1,140; 1,380 and 1,440 minutes, resulting in 96 maps of maximum intense rainfall. The used interpolators were inverse distance weighting and ordinary kriging, for which significance level (p-value) and coefficient of determination (R²) were evaluated for the cross-validation data, choosing the method that presented better R² to generate maps. Finally, maps of maximum intense precipitation were used to estimate, cell by cell, the intense rainfall equation parameters. In comparison with literature data, the mean percentage error of estimated intense rainfall equations was 13.8%. Maps of spatialized parameters, obtained in this study, are of simple use; once they are georeferenced, they may be imported into any geographic information system to be used for a specific area of interest.

Method adjustment and equation set of maximum rainfall intensity, duration and frequency in the Mato Grosso do Sul State

Due to the lack of information concerning maximum rainfall equations for most locations in Mato Grosso do Sul State, the alternative for carrying out hydraulic work projects has been information from meteorological stations closest to the location in which the project is carried out. Alternative methods, such as 24 hours rain disaggregation method from rainfall data due to greater availability of stations and longer observations can work. Based on this approach, the objective of this study was to estimate maximum rainfall equations for Mato Grosso do Sul State by adjusting the 24 hours rain disaggregation method, depending on data obtained from rain gauge stations from Dourado and Campo Grande. For this purpose, data consisting of 105 rainfall stations were used, which are available in the ANA (Water Resources Management National Agency) database. Based on the results we concluded: the intense rainfall equations obtained by pluviogram analysis showed determination coefficient above 99%; and the performance of 24 hours rain disaggregation method was classified as excellent, based on relative average error WILMOTT concordance index (1982).

The bifurcational behaviour of the spatially distributed Rayleigh equation

At the present work the bifurcational behaviour of the solutions of Rayleigh equation and corresponding spatially distributed system is being analysed. The conditions of oscillatory and monotonic loss of stability are obtained. In the case of oscillatory loss of stability, the analysis of linear spectral problem is being performed. For nonlinear problem, recurrent formulas for the general term of the asymptotic approximation of the self-oscillations are found, the stability of the periodic mode is analysed. Lyapunov-Schmidt method is being used for asymptotic approximation. The correlation between periodic solutions of ODE and PDE is being investigated. The influence of the diffusion on the frequency of self-oscillations is being analysed. Several numerical experiments are being performed in order to support theoretical findings.

Use of the Wasserman equation in optimization of the duration of the power ramp in a cardiopulmonary exercise test: a study of Brazilian men

This study aimed to analyze the agreement between measurements of unloaded oxygen uptake and peak oxygen uptake based on equations proposed by Wasserman and on real measurements directly obtained with the ergospirometry system. We performed an incremental cardiopulmonary exercise test (CPET), which was applied to two groups of sedentary male subjects: one apparently healthy group (HG, n=12) and the other had stable coronary artery disease (n=16). The mean age in the HG was 47±4 years and that in the coronary artery disease group (CG) was 57±8 years. Both groups performed CPET on a cycle ergometer with a ramp-type protocol at an intensity that was calculated according to the Wasserman equation. In the HG, there was no significant difference between measurements predicted by the formula and real measurements obtained in CPET in the unloaded condition. However, at peak effort, a significant difference was observed between oxygen uptake (V˙O2)peak(predicted)and V˙O2peak(real)(nonparametric Wilcoxon test). In the CG, there was a significant difference of 116.26 mL/min between the predicted values by the formula and the real values obtained in the unloaded condition. A significant difference in peak effort was found, where V˙O2peak(real)was 40% lower than V˙O2peak(predicted)(nonparametric Wilcoxon test). There was no agreement between the real and predicted measurements as analyzed by Lin’s coefficient or the Bland and Altman model. The Wasserman formula does not appear to be appropriate for prediction of functional capacity of volunteers. Therefore, this formula cannot precisely predict the increase in power in incremental CPET on a cycle ergometer.

An analysis of decoupling procedures in generating thermal Green's functions of O([lambda]â ´) by the Zubarev equation of motion method

The Zubarev equation of motion method has been applied to an anharmonic crystal of O( ,,4). All possible decoupling schemes have been interpreted in order to determine finite temperature expressions for the one phonon Green's function (and self energy) to 0()\4) for a crystal in which every atom is on a site of inversion symmetry. In order to provide a check of these results, the Helmholtz free energy expressions derived from the self energy expressions, have been shown to agree in the high temperature limit with the results obtained from the diagrammatic method. Expressions for the correlation functions that are related to the mean square displacement have been derived to 0(1\4) in the high temperature limit.

Application of [Lambda] to the fourth perturbation theory in calculating the equation of state of rare gas solids and fcc metals

We have calculated the thermodynamic properties of monatomic fcc crystals from the high temperature limit of the Helmholtz free energy. This equation of state included the static and vibrational energy components. The latter contribution was calculated to order A4 of perturbation theory, for a range of crystal volumes, in which a nearest neighbour central force model was used. We have calculated the lattice constant, the coefficient of volume expansion, the specific heat at constant volume and at constant pressure, the adiabatic and the isothermal bulk modulus, and the Gruneisen parameter, for two of the rare gas solids, Xe and Kr, and for the fcc metals Cu, Ag, Au, Al, and Pb. The LennardJones and the Morse potential were each used to represent the atomic interactions for the rare gas solids, and only the Morse potential was used for the fcc metals. The thermodynamic properties obtained from the A4 equation of state with the Lennard-Jones potential, seem to be in reasonable agreement with experiment for temperatures up to about threequarters of the melting temperature. However, for the higher temperatures, the results are less than satisfactory. For Xe and Kr, the thermodynamic properties calculated from the A2 equation of state with the Morse potential, are qualitatively similar to the A 2 results obtained with the Lennard-Jones potential, however, the properties obtained from the A4 equation of state are in good agreement with experiment, since the contribution from the A4 terms seem to be small. The lattice contribution to the thermal properties of the fcc metals was calculated from the A4 equation of state, and these results produced a slight improvement over the properties calculated from the A2 equation of state. In order to compare the calculated specific heats and bulk moduli results with experiment~ the electronic contribution to thermal properties was taken into account~ by using the free electron model. We found that the results varied significantly with the value chosen for the number of free electrons per atom.

On the equation of state and atomic mean square displacement of crystals

We have presented a Green's function method for the calculation of the atomic mean square displacement (MSD) for an anharmonic Hamil toni an . This method effectively sums a whole class of anharmonic contributions to MSD in the perturbation expansion in the high temperature limit. Using this formalism we have calculated the MSD for a nearest neighbour fcc Lennard Jones solid. The results show an improvement over the lowest order perturbation theory results, the difference with Monte Carlo calculations at temperatures close to melting is reduced from 11% to 3%. We also calculated the MSD for the Alkali metals Nat K/ Cs where a sixth neighbour interaction potential derived from the pseudopotential theory was employed in the calculations. The MSD by this method increases by 2.5% to 3.5% over the respective perturbation theory results. The MSD was calculated for Aluminum where different pseudopotential functions and a phenomenological Morse potential were used. The results show that the pseudopotentials provide better agreement with experimental data than the Morse potential. An excellent agreement with experiment over the whole temperature range is achieved with the Harrison modified point-ion pseudopotential with Hubbard-Sham screening function. We have calculated the thermodynamic properties of solid Kr by minimizing the total energy consisting of static and vibrational components, employing different schemes: The quasiharmonic theory (QH), ).2 and).4 perturbation theory, all terms up to 0 ().4) of the improved self consistent phonon theory (ISC), the ring diagrams up to o ().4) (RING), the iteration scheme (ITER) derived from the Greens's function method and a scheme consisting of ITER plus the remaining contributions of 0 ().4) which are not included in ITER which we call E(FULL). We have calculated the lattice constant, the volume expansion, the isothermal and adiabatic bulk modulus, the specific heat at constant volume and at constant pressure, and the Gruneisen parameter from two different potential functions: Lennard-Jones and Aziz. The Aziz potential gives generally a better agreement with experimental data than the LJ potential for the QH, ).2, ).4 and E(FULL) schemes. When only a partial sum of the).4 diagrams is used in the calculations (e.g. RING and ISC) the LJ results are in better agreement with experiment. The iteration scheme brings a definitive improvement over the).2 PT for both potentials.

Some Travelling Wave Solutions of KdV-Burgers Equation

In this paper we study the extended Tanh method to obtain some exact solutions of KdV-Burgers equation. The principle of the Tanh method has been explained and then apply to the nonlinear KdV- Burgers evolution equation. A finnite power series in tanh is considered as an ansatz and the symbolic computational system is used to obtain solution of that nonlinear evolution equation. The obtained solutions are all travelling wave solutions.

The Wage Rate and the Profit Rate in the Price of Production Equation: a New Solution to an Old Problem

The aim of this paper is to demonstrate that, even if Marx's solution to the transformation problem can be modified, his basic concusions remain valid.

Closure of the Monte Carlo dynamical equation in the spherical Sherrington-Kirkpatrick model

We study the analytical solution of the Monte Carlo dynamics in the spherical Sherrington-Kirkpatrick model using the technique of the generating function. Explicit solutions for one-time observables (like the energy) and two-time observables (like the correlation and response function) are obtained. We show that the crucial quantity which governs the dynamics is the acceptance rate. At zero temperature, an adiabatic approximation reveals that the relaxational behavior of the model corresponds to that of a single harmonic oscillator with an effective renormalized mass.

A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it

In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type s(x)y"n(x) + t(x)y'n(x) - lnyn(x) = 0 and show that all the three classical orthogonal polynomial families as well as three finite orthogonal polynomial families, extracted from this equation, can be identified as special cases of this derived polynomial sequence. Some general properties of this sequence are also given.