950 resultados para Initial Value Problem


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The development of a new set of frost property measurement techniques to be used in the control of frost growth and defrosting processes in refrigeration systems was investigated. Holographic interferometry and infrared thermometry were used to measure the temperature of the frost-air interface, while a beam element load sensor was used to obtain the weight of a deposited frost layer. The proposed measurement techniques were tested for the cases of natural and forced convection, and the characteristic charts were obtained for a set of operational conditions. ^ An improvement of existing frost growth mathematical models was also investigated. The early stage of frost nucleation was commonly not considered in these models and instead an initial value of layer thickness and porosity was regularly assumed. A nucleation model to obtain the droplet diameter and surface porosity at the end of the early frosting period was developed. The drop-wise early condensation in a cold flat plate under natural convection to a hot (room temperature) and humid air was modeled. A nucleation rate was found, and the relation of heat to mass transfer (Lewis number) was obtained. It was found that the Lewis number was much smaller than unity, which is the standard value usually assumed for most frosting numerical models. The nucleation model was validated against available experimental data for the early nucleation and full growth stages of the frosting process. ^ The combination of frost top temperature and weight variation signals can now be used to control the defrosting timing and the developed early nucleation model can now be used to simulate the entire process of frost growth in any surface material. ^

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In this thesis, a numerical program has been developed to simulate the wave-induced ship motions in the time domain. Wave-body interactions have been studied for various ships and floating bodies through forced motion and free motion simulations in a wide range of wave frequencies. A three-dimensional Rankine panel method is applied to solve the boundary value problem for the wave-body interactions. The velocity potentials and normal velocities on the boundaries are obtained in the time domain by solving the mixed boundary integral equations in relation to the source and dipole distributions. The hydrodynamic forces are calculated by the integration of the instantaneous hydrodynamic pressures over the body surface. The equations of ship motion are solved simultaneously with the boundary value problem for each time step. The wave elevation is computed by applying the linear free surface conditions. A numerical damping zone is adopted to absorb the outgoing waves in order to satisfy the radiation condition for the truncated free surface. A numerical filter is applied on the free surface for the smoothing of the wave elevation. Good convergence has been reached for both forced motion simulations and free motion simulations. The computed added-mass and damping coefficients, wave exciting forces, and motion responses for ships and floating bodies are in good agreement with the numerical results from other programs and experimental data.

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Multi-frequency eddy current measurements are employed in estimating pressure tube (PT) to calandria tube (CT) gap in CANDU fuel channels, a critical inspection activity required to ensure fitness for service of fuel channels. In this thesis, a comprehensive characterization of eddy current gap data is laid out, in order to extract further information on fuel channel condition, and to identify generalized applications for multi-frequency eddy current data. A surface profiling technique, generalizable to multiple probe and conductive material configurations has been developed. This technique has allowed for identification of various pressure tube artefacts, has been independently validated (using ultrasonic measurements), and has been deployed and commissioned at Ontario Power Generation. Dodd and Deeds solutions to the electromagnetic boundary value problem associated with the PT to CT gap probe configuration were experimentally validated for amplitude response to changes in gap. Using the validated Dodd and Deeds solutions, principal components analysis (PCA) has been employed to identify independence and redundancies in multi-frequency eddy current data. This has allowed for an enhanced visualization of factors affecting gap measurement. Results of the PCA of simulation data are consistent with the skin depth equation, and are validated against PCA of physical experiments. Finally, compressed data acquisition has been realized, allowing faster data acquisition for multi-frequency eddy current systems with hardware limitations, and is generalizable to other applications where real time acquisition of large data sets is prohibitive.

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We report on the first demonstration of passive all-optical plasma lensing using a two-stage setup. An intense femtosecond laser accelerates electrons in a laser wakefield accelerator (LWFA) to 100 MeVover millimeter length scales. By adding a second gas target behind the initial LWFAstage we introduce a robust and independently tunable plasma lens. We observe a density dependent reduction of the LWFA electron beam divergence from an initial value of 2.3 mrad, down to 1.4 mrad (rms), when the plasma lens is in operation. Such a plasma lens provides a simple and compact approach for divergence reduction well matched to the mm-scale length of the LWFA accelerator. The focusing forces are provided solely by the plasma and driven by the bunch itself only, making this a highly useful and conceptually new approach to electron beam focusing. Possible applications of this lens are not limited to laser plasma accelerators. Since no active driver is needed the passive plasma lens is also suited for high repetition rate focusing of electron bunches. Its understanding is also required for modeling the evolution of the driving particle bunch in particle driven wake field acceleration.

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Two-third of the terrestrial C is stored in soils, and more than 50% of soil organic C (SOC) is stored in subsoils from 30 – 100 cm. Hence, subsoil is important as a source or sink for CO2 in the global carbon cycle. Especially the stable organic carbon (OC) is stored in subsoil, as several studies have shown that subsoil OC is of a higher average age than topsoil OC. However, there is still a lack of knowledge regarding the mechanisms of C sequestration and C turnover in subsoil. Three main factors are discussed, which possibly reduce carbon turnover rates in subsoil: Resource limitation, changes in the microbial community, and changes in gas conditions. The experiments conducted in this study, which aimed to elucidate the importance of the mentioned factors, focused on two neighbouring arable sites, with depth profiles differing in SOC stocks: One Colluvic Cambisol (Cam) with high SOC contents (8-12 g kg-1) throughout the profile and one Haplic Luvisol (Luv) with low SOC contents (3-4 g kg-1) below 30 cm depth. The first experiment was designed to gain more knowledge regarding the microbial community and its influence on carbon sequestration in subsoil. Soil samples were taken at four different depths on the two sites. Microbial biomass C (MBC) was determined to identify depth gradients in relation to the natural C availability. Bacterial and fungal residues as well as ergosterol were determined to quantify changes in the in the microbial community composition. Multi-substrate-induced-respiration (MSIR) was used to identify shifts in functional diversity of the microbial community. The MSIR revealed that substrate use in subsoil differed significantly from that in topsoil and also differed highly between the two subsoils, indicating a strong influence of resource limitations on microbial substrate use. Amino sugar analysis and the ratio of ergosterol to microbial biomass C showed that fungal dominance decreased with depth. The results clearly demonstrated that microbial parameters changed with depth according to substrate availability. The second experiment was an incubation experiment using subsoil gas conditions with and without the addition of C4 plant residues. Soil samples were taken from topsoil and subsoil of the two sites. SOC losses during the incubation, were not influenced by the subsoil gas conditions. Plant-derived C losses were generally stronger in the Cam (7.5 mg g-1), especially at subsoil gas conditions, than in the Luv (7.0 mg g-1). Subsoil gas conditions had no general effects on microbial measures with and without plant residue addition. However, the contribution of plant-derived MBC to total MBC was significantly reduced at subsoil gas conditions. This lead to the conclusion that subsoil gas conditions alter the metabolism of microorganisms but not the degradation of added plant residues is general. The third experiment was a field experiment carried out for two years. Mesh bags containing original soil material and maize root residues (C4 plant) were buried at three different depths at the two sites. The recovery of the soilbags took place 12, 18, and 24 months after burial. We determined the effects of these treatments on SOC, density fractions, and MBC. The mean residence time for maize-derived C was similar at all depths and both sites (403 d). MBC increased to a similar extent (2.5 fold) from the initial value to maximum value. This increase relied largely on the added maize root residues. However, there were clear differences visible in terms of the substrate use efficiency, which decreased with depth and was lower in the Luv than in the Cam. Hence freshly added plant material is highly accessible to microorganisms in subsoil and therefore equally degraded at both sites and depths, but its metabolic use was determined by the legacy of soil properties. These findings provide strong evidence that resource availability from autochthonous SOM as well as from added plant residues have a strong influence on the microbial community and its use of different substrates. However, under all of the applied conditions there was no evidence that complex substrates, i.e. plant residues, were less degraded in subsoil than in topsoil.

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We present an analytical solution of a mixed boundary value problem for an unbounded 2D doubly periodic domain which is a model of a composite material with mixed imperfect interface conditions. We find the effective conductivity of the composite material with mixed imperfect interface conditions, and also give numerical analysis of several of their properties such as temperature and flux.

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Thesis (Ph.D.)--University of Washington, 2016-08

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In this paper, we focus on a Riemann–Hilbert boundary value problem (BVP) with a constant coefficients for the poly-Hardy space on the real unit ball in higher dimensions. We first discuss the boundary behaviour of functions in the poly-Hardy class. Then we construct the Schwarz kernel and the higher order Schwarz operator to study Riemann–Hilbert BVPs over the unit ball for the poly- Hardy class. Finally, we obtain explicit integral expressions for their solutions. As a special case, monogenic signals as elements in the Hardy space over the unit sphere will be reconstructed in the case of boundary data given in terms of functions having values in a Clifford subalgebra. Such monogenic signals represent the generalization of analytic signals as elements of the Hardy space over the unit circle of the complex plane.

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In this article we address the question of efficiently solving the algebraic linear system of equations arising from the discretization of a symmetric, elliptic boundary value problem using hp-version discontinuous Galerkin finite element methods. In particular, we introduce a class of domain decomposition preconditioners based on the Schwarz framework, and prove bounds on the condition number of the resulting iteration operators. Numerical results confirming the theoretical estimates are also presented.

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Mestrado em Finanças

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Dissertação de mest. em Estudos Marinhos e Costeiros, especialização em Aquacultura, Unidade de Ciências e Tecnologias dos Recursos Aquáticos, Univ. do Algarve, 1994

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In this work we study an Hammerstein generalized integral equation u(t)=∫_{-∞}^{+∞}k(t,s) f(s,u(s),u′(s),...,u^{(m)}(s))ds, where k:ℝ²→ℝ is a W^{m,∞}(ℝ²), m∈ℕ, kernel function and f:ℝ^{m+2}→ℝ is a L¹-Carathéodory function. To the best of our knowledge, this paper is the first one to consider discontinuous nonlinearities with derivatives dependence, without monotone or asymptotic assumptions, on the whole real line. Our method is applied to a fourth order nonlinear boundary value problem, which models moderately large deflections of infinite nonlinear beams resting on elastic foundations under localized external loads.

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A new spectral method for solving initial boundary value problems for linear and integrable nonlinear partial differential equations in two independent variables is applied to the nonlinear Schrödinger equation and to its linearized version in the domain {x≥l(t), t≥0}. We show that there exist two cases: (a) if l″(t)<0, then the solution of the linear or nonlinear equations can be obtained by solving the respective scalar or matrix Riemann-Hilbert problem, which is defined on a time-dependent contour; (b) if l″(t)>0, then the Riemann-Hilbert problem is replaced by a respective scalar or matrix problem on a time-independent domain. In both cases, the solution is expressed in a spectrally decomposed form.

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The objectives of the study were to evaluate the performance of sentinel lymph node biopsy (SLNB) in detecting occult metastases in papillary thyroid carcinoma (PTC) and to correlate their presence to tumor and patient characteristics. Twenty-three clinically node-negative PTC patients (21 females, mean age 48.4 years) were prospectively enrolled. Patients were submitted to sentinel lymph node (SLN) lymphoscintigraphy prior to total thyroidectomy. Ultrasound-guided peritumoral injections of (99m)Tc-phytate (7.4 MBq) were performed. Cervical single-photon emission computed tomography and computed tomography (SPECT/CT) images were acquired 15 min after radiotracer injection and 2 h prior to surgery. Intra-operatively, SLNs were located with a gamma probe and removed along with non-SLNs located in the same neck compartment. Papillary thyroid carcinoma, SLNs and non-SLNs were submitted to histopathology analysis. Sentinel lymph nodes were located in levels: II in 34.7 % of patients; III in 26 %; IV in 30.4 %; V in 4.3 %; VI in 82.6 % and VII in 4.3 %. Metastases in the SLN were noted in seven patients (30.4 %), in non-SLN in three patients (13.1 %), and in the lateral compartments in 20 % of patients. There were significant associations between lymph node (LN) metastases and the presence of angio-lymphatic invasion (p = 0.04), extra-thyroid extension (p = 0.03) and tumor size (p = 0.003). No correlations were noted among LN metastases and patient age, gender, stimulated thyroglobulin levels, positive surgical margins, aggressive histology and multifocal lesions. Sentinel lymph node biopsy can detect occult metastases in PTC. The risk of a metastatic SLN was associated with extra-thyroid extension, larger tumors and angio-lymphatic invasion. This may help guide future neck dissection, patient surveillance and radioiodine therapy doses.

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We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The sharing problem is formulated in the preferences-endowments space. The solution is defined in a recursive manner incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists, and refer to it as an Ordinal Shapley value (OSV). The OSV associates with each problem an allocation as well as a matrix of concessions ``measuring'' the gains each agent foregoes in favor of the other agents. We analyze the structure of the concessions, and show they are unique and symmetric. Next we characterize the OSV using the notion of coalitional dividends, and furthermore show it is monotone in an agent's initial endowments and satisfies anonymity. Finally, similarly to the weighted Shapley value for TU games, we construct a weighted OSV as well.