Variational techniques are used to develop a theory for the time evolution of a thin strand of viscous fluid suspended from two points. The shape of the strand is approximated to be a parabola and energy conservation is used to derive a differential equation modeling the change in height over time. Data is collected with a high resolution camera and a strobe light to obtain the position and shape of the strand over multiple intervals of time. Three very different and unexpected types of behaviors are observed depending on the initial thickness and shape of the filament. The approximation fits well with one type of behavior but variations in the thickness of the strand, and consequently in the center of mass, need to be factored in to predict the others.

In this study, the theoretical performance of a concentrating solar thermal electric system (CSTES) using a field of parabolic trough collectors (PTC) is investigated. The commercial software TRNSYS and the Solar Thermal Electric Components (STEC) library are used to model the overall system design and for simulations. The model was constructed using data from the literature for an existing 30-MW solar electric generating system (SEGS VI) using PTC&rsquo / s in Kramer Junction, California. The CSTES consists of a PTC loop that drives a Rankine cycle with superheat and reheat, 2-stage high and 5-stage low pressure turbines, 5-feedwater heaters and a dearator. As a first approximation, the model did not include significant storage or back-up heating. The model&rsquo / s predictions were benchmarked against published data for the system in California for a summer day. Good agreement between the model&rsquo / s predictions and published data were found, with errors usually less than 10%. Annual simulations were run using weather data for both California and Antalya, Turkey. The monthly outputs for the system in California and Antalya are compared both in terms of absolute monthly outputs and in terms of ratios of minimum to maximum monthly outputs. The system in Antalya is found to produce30 % less energy annually than the system in California. The ratio of the minimum (December) to maximum (July) monthly energy produced in Antalya is 0.04.

This thesis uses a method called "parabolic equation approach." This method can treat both the variations of the terrain and the refractive index simultaneously. This method makes it possible to predict the radio propagation more precisely. We can discuss the effects of the variations of the refractive index to radio signal and demo effects by using parabolic equation method. The Effective Earth Radius Factor is 4/3 suggested by CCIR so-called "Standard Atmosphere Model". But we try to find more suitable K in the Southern Taiwan area. We adopt Parabolic Equation Propagation Model to simulate real situation of radio propagation in the Southern Taiwan area and the prediction is compared with the measurement obtained previously. We can get the best K in the Southern Taiwan area is 1.8 and 1.9. The best K is greater than the value of 4/3 suggested by CCIR. Recently the government on Taiwan release more radio broadcasting licenses to the general public. As the number of radio stations increases, the interference between stations becomes more likely. There have been reports about the poor quality of broadcasting from stations. In this paper, we will study the interference using FM radio stations as an example. Given the characteristics of the transmitting antenna including location, frequency, pattern, height and power, the field strength can be computed with the equivalent earth radius factor K as a parameter. The difference in interference level is obtained under the standard atmosphere (K=4/3) and a case of K=1.55 which has been reported to be more suitable in Taiwan. Finally an extreme case that a ducting exists will be studied. Our results can be used to find more suitable separation distances free from interferences between co-channel and adjacent channel stations. By including a realistic tropospheric term, the more accurate field strength predictions can give the Spectrum Authority a better spectrum assignment tool. This has the potential to increase the number of available stations that can be made available or to reduce the interference stations may experience.

A class of parametric optimal control problems for semilinear parabolic equations is considered. Using recent regularity results for solutions of such equations, sufficient conditions are derived under which the solutions to optimal control problems are locally Lipschitz continuous functions of the parameter in the L1-norm. It is shown that these conditions are also necessary, provided that the dependence of data on the parameter is sufficiently strong.

An optimal control problem governed by the heat equation with nonlinear boundary conditions is considered. The objective functional consists of a quadratic terminal part and a quadratic regularization term. It is known, that an SQP method converges quadratically to the optimal solution of the problem. To handle the quadratic optimal control subproblems with high precision, very large scale mathematical programming problems have to be treated. The constrained problem is reduced to an unconstrained one by a method due to Bertsekas. A multigrid approach developed by Hackbusch is applied to solve the unconstrained problems. Some numerical examples illustrate the behaviour of the method.

Thesis (M.S.)--University of North Carolina at Wilmington, 2003. / Includes bibliographical references (leaf : [37]).

This thesis provides an analytical and two numerical methods for solving a parabolic equation of two-dimensional mean curvature flow with some applications. In analytical method, this equation is solved by Lie group analysis method, and in numerical method, two algorithms are implemented in MATLAB for solving this equation. A geometric algorithm and a step-wise algorithm; both are based on a deterministic game theoretic representation for parabolic partial differential equations, originally proposed in the genial work of Kohn-Serfaty [1]. / +46-767165881

Thin films that are functionally gradient improve the mechanical properties of film-substrate layered materials. Mechanical properties of such materials are found by using indentation tests. In this study, finite element models are developed to simulate the indentation test. The models are based on an axisymmetric half space of a specimen subjected to spherical indentation. The film layer through the thickness is modeled to have either homogeneous material properties or nonhomogeneous material properties that vary linearly. Maximum indenter displacement, and maximum normal and shear stresses at the interface are compared between the homogeneous model and the nonhomogeneous model for pragmatic contact length to film thickness ratios of 0.2 to 0.4, and film to substrate moduli ratios of 1 to 200 to 1. Additionally, a coefficient is derived from regression of the stress data produced by these models and compared to that used to define the pressure field in the axisymmetric Hertzian contact model. The results of this study suggest that a displacement boundary condition to an indenter produces the same results as a pressure distribution boundary condition. The critical normal stresses that occur between modeling a film as a nonhomogeneous and as a homogeneous material vary from 19% for a modulus ratio of 2.5:1 to as high as 66% for a modulus ratio of 200:1 indicating that the modeling techniques produced very different maximum normal stresses. The difference in the maximum shear stress between the nonhomogeneous and the homogeneous models varied from 19% for a 2.5:1 modulus ratio to 57% for the 200:1 modulus ratio but reached values as low as 6% for the 50:1 modulus ratio. The maximum contact depth between the nonhomogeneous and the homogeneous models varied from 14% for the 2.5:1 case to as much as 75% in the 200:1 case. The results from the reapplication of the pressure field derived from the regression coefficients and the R2 values from these regression models indicate the correctness of the regression model used as well as its ability to replicate the normal stresses in the contact area and maximum indenter displacements in a FEA model for both the homogeneous and the nonhomogeneous models for modulus ratios ranging from 2.5:1 to 200:1. The agreement between the regression based coefficients and the force based coefficients suggests the validity for the use of the theoretical axisymmetric Hertzian contact model for defining the pressure field in the contact area and displacements for both the homogeneous case and the nonhomogeneous case for the considered film to substrate moduli ratios and contact length to film thickness ratios.

We study the Hitchin component in the space of representations of the fundamental group of a Riemann surface into a split real Lie group in the rank 2 case. We prove that such representations are described by a conformal structure and class of Higgs bundle we call cyclic and we show cyclic Higgs bundles correspond to a form of the affine Toda equations. We also relate various real forms of the Toda equations to minimal surfaces in quadrics of arbitrary signature. In the case of the Hitchin component for PSL(3,R) we provide a new proof of the relation to convex RP²-structures and hyperbolic affine spheres. For PSp(4,R) we prove such representations are the monodromy for a special class of projective structure on the unit tangent bundle of the surface. We prove these are isomorphic to the convex-foliated projective structures of Guichard and Wienhard. We elucidate the geometry of generic 2-plane distributions in 5 dimensions, work which traces back to Cartan. Nurowski showed that there is an associated signature (2,3) conformal structure. We clarify this as a relationship between a parabolic geometry associated to the split real form of G₂ and a conformal geometry with holonomy in G₂. Moreover in terms of the conformal geometry we prove this distribution is the bundle of maximal isotropics corresponding to the annihilator of a spinor satisfying the twistor-spinor equation. The moduli space of deformations of a compact coassociative submanifold L in a G₂ manifold is shown to have a natural local embedding as a submanifold of H2(L,R). We consider G2-manifolds with a T^4-action of isomorphisms such that the orbits are coassociative tori and prove a local equivalence to minimal 3-manifolds in R^{3,3} = H²(T⁴,R) with positive induced metric. By studying minimal surfaces in quadrics we show how to construct minimal 3-manifold cones in R^{3,3} and hence G₂-metrics from equations that are a set of affine Toda equations. The relation to semi-flat special Lagrangian fibrations and the Monge-Ampere equation is explained.

Darbe yra išbandytas naujai pasiūlytas atsitiktinių skaičių generavimo algoritmas, kuris sudarytas iš netiesinių rekurentinių sekų generavimo tolygiai pasiskirsčiusio intervale [0,1], bei išbandyta jo kokybė modeliuojant konkrečius tikimybinius pasiskirstymus. / The paper has tested the newly proposed random number generation algorithm, which consists of a linear recurrent sequence of generating uniformly distributed in the interval [0,1], and its quality is tested by modeling the specific probability distribution.