Radial basis functions (RBFs) are probably best known for their applications to scattered data problems. Until the 1990s, RBF theory only involved functions that were scalar-valued. Matrix-valued RBFs were subsequently introduced by Narcowich and Ward in 1994, when they constructed divergence-free vector-valued functions that interpolate data at scattered points. In 2002, Lowitzsch gave the first error estimates for divergence-free interpolants. However, these estimates are only valid when the target function resides in the native space of the RBF. In this paper we develop Sobolev-type error estimates for cases where the target function is less smooth than functions in the native space. In the process of doing this, we give an alternate characterization of the native space, derive improved stability estimates for the interpolation matrix, and give divergence-free interpolation and approximation results for band-limited functions. Furthermore, we introduce a new class of matrix-valued RBFs that can be used to produce curl-free interpolants.

In this dissertation, we consider various aspects of the boundary behavior of holomorphic functions of several complex variables. In dimension one, a characterization of the radial limit zero sets of nonconstant holomorphic functions on the disc has been given by Lusin, Privalov, McMillan, and Berman. In higher dimensions, no such characterization is known for holomorphic functions on the unit ball B. Rudin posed the question as to the existence of nonconstant holomorphic functions on the ball with radial limit zero almost everywhere. Hakim, Sibony, and Dupain showed that such functions exist. Because the characterization in dimension one involves both Lebesgue measure and Baire category, it is natural to also ask whether there exist nonconstant holomorphic functions on the ball having residual radial limit zero sets. We show here that such functions exist. We also prove a higher dimensional version of the Lusin-Privalov Radial Uniqueness Theorem, but we show that, in contrast to what is the case in dimension one, the converse does not hold. We show that any characterization of radial limit zero sets on the ball must take into account the "complex structure" on the ball by giving an example that shows that the family of these sets is not closed under orthogonal transformations of the underlying real coordinates. In dimension one, using the theorem of McMillan and Berman, it is easy to see that radial limit zero sets are not closed under unions (even finite unions). Since there is no analogous result in higher dimensions of the McMillan and Berman result, it is not obvious whether the radial limit zero sets in higher dimensions are closed under finite unions. However, we show that, as is the case in dimension one, these sets are not closed under finite unions. Finally, we show that there are smooth curves of finite length in S that are non-tangential limit uniqueness sets for holomorphic functions on B. This strengthens a result of M. Tsuji.

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Submitted by Ricardo Kalid (kalid@ufba.br) on 2012-10-10T16:32:49Z No. of bitstreams: 1 DISSERTAÇÃO DE MESTRADO PROF. KALID- Modelagem e Simulação de Reatores catalíticos de Leito Fixo e Fluxo Radial.pdf: 78544584 bytes, checksum: dd345cf472a6a585df946d8bd1517236 (MD5) / Made available in DSpace on 2012-10-10T16:32:49Z (GMT). No. of bitstreams: 1 DISSERTAÇÃO DE MESTRADO PROF. KALID- Modelagem e Simulação de Reatores catalíticos de Leito Fixo e Fluxo Radial.pdf: 78544584 bytes, checksum: dd345cf472a6a585df946d8bd1517236 (MD5) Previous issue date: 1991-05-02

Memoria para optar al título de Periodista / El autor no autoriza el acceso a texto completo de su documento / La radio queda en ‘desventaja’ ante la televisión, cuyo auge se debe a que cuenta con dos vías por las que entrega información: la visual y la auditiva, lo que la hace más atractiva para los espectadores. Al contar el medio elegido para este proyecto sólo con el canal de audio, hemos propuesto complementar su ‘falencia’ a través del uso de la semiótica musical, llamando la atención del público a través de su imaginación con una propuesta experimental del uso del sonido.

Deficient performances of turbocharger compressors inside turbo-charged engines limit the behaviour of the drive train. This problem has shifted the design space for compressors towards their performance at part-speed and low-flow conditions. The most dominant feature of these flow conditions is inlet recirculation. It causes a large portion of flow to be expelled through the rotor inlet, creating a blockage ring on the casing. While on the one hand, inlet recirculation is the main loss-source at low-speed and low-flow within centrifugal compressors, on the other hand, it also keeps the compressors functioning because it reduces incidence. This thesis aimed towards increasing the understanding of inlet recirculation, with the scope on improving the part-speed, low-flow performance of automotive turbocharger compressors. The phenomenon was investigated regarding its key features, the conditions at which it occurs and its impact on performance. Furthermore, a reduced order model was derived and the influence of the tip gap size as a design parameter was analysed. The research was carried out on an automotive turbocharger compressor which was investigated experimentally and numerically. Inlet recirculation is a phenomenon which takes place in the tip region of the rotor, extending far downstream and far upstream of the leading edge. The flow within the recirculation bubble features a strong positive swirl component, affecting the work input into the machine. The phenomenon is non-periodic in a time-averaged sense. An investigation of the rotor flow-field regarding inlet recirculation, carried out for the first time, revealed that the starting point of inlet recirculation is located far inside the rotor passage. An analysis based on mass, momentum and energy allowed the derivation of a low-order model to account for inlet recirculation in preliminary design. In the compressor map, inlet recirculation was present over 40% of the map width at low speeds. It maintained its presence with increasing rotor speed beyond the point where the inlet flow became transonic. The losses in the inlet recirculation zone were shown to be up to 35% of the total compressor loss at low speed. A loss analysis showed that inlet recirculation was the main loss source at low-flow conditions. The tip clearance study showed that the size and intensity of inlet recirculation was independent of the tip gap size. Efficiency gains due to reduced tip leakage were marginalised by the presence of inlet recirculation but the rotor maintained enhanced pressure rise capabilities for reduced tip gap sizes.

Statistics based models have been developed previously to predict a priori the performance of new radial flow compressors and pumps and to model test data of previously designed and tested machines. Unfortunately, critical dynamics in the inlet region of the machines were neglected. Consequently, room for improvement in the previous modeling exists. Historical practice has placed a static pressure tap on the shroud just upstream of the impeller leading edge for experimental characterization. The previously developed statistics based models rely on this measured data. However, the location of the tap may be vulnerable to high gradients which would decrease the dependability of the developed models. Full Computational Fluid Dynamics (CFD) and Multi-Stream Tube (MST) analysis were performed to test the appropriateness of the historically placed static pressure tap location and to characterize the inlet flow of typical radial flow turbomachines. All designs and test data were provided by ConceptsNREC and have been collected for over 40 years. Eleven machines were chosen for investigation to provide a wide variety of inlet geometric and flow conditions. The results derived from the Computational Fluid Dynamics and Multi-Stream Tube analysis suggest that the historically placed static pressure tap location is an inappropriate anchor point for model development. Steep gradients in the static pressure indicate that a relatively minor movement of the static pressure tap would significantly alter the experimental results and generate noise in statistical modeling. While large variations in the pressure field are apparent near the impeller leading edge for all machines considered, the study results show that the flow field is uniform and very predictable when well upstream of the impeller leading edge. Specifically, a point 3 blade height upstream from the impeller leading edge appears to be a sound location to anchor model development. The model is highly dependent upon the flow parameters in the inlet passage. Thus it is important to ensure that the model is anchored at a location where the flow conditions are known to be stable and good. Future anchoring of the model upstream of the impeller leading edge will lead to a more accurate prediction and modeling of the design performance for radial flow turbomachines.

The properties of electrostatic quadrupole lenses are investigated both theoretically and experimentally. A method for measuring the effective lens length is developed and used. Previously reported (6) focusing equations for the two lens system provide an implicit solution involving trigonometric and hyperbolic functions. A nomograph was designed as an aid in carrying out this solution numerically. The two lens system was evaluated for various combinations of object distance, lens separation and image distance. Measured values of focal strengths were compared to theoretical values. Finally, measurements were made on the effective focal strength as a function of radial displacement from the central axis. / Thesis / Master of Science (MSc)

We prove the existence and nonexistence of radial solutions of singular semilinear equations Δu + k(x)f(u)=0 with boundary condition on the exterior of the ball with radius R>0 in ℝ^N such that lim r →∞ u(r)=0, where f: ℝ \ {0} →ℝ is an odd and locally Lipschitz continuous nonlinear function such that there exists a β >0 with f <0 on (0, β), f >0 on (β, ∞), and K(r) ~ r^-α for some α >0.

No description available.