Dissertations / Theses: 'Time dependent solution'

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Yang, Feng Wei. "Multigrid solution methods for nonlinear time-dependent systems." Thesis, University of Leeds, 2014. http://etheses.whiterose.ac.uk/7579/.

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An efficient, accurate and reliable numerical solver is essential for solving complex mathematical models and obtaining their computational approximations. The solver presented in this work is built upon nonlinear multigrid with the full approximation scheme (FAS). Its implementation is achieved, in part, using a complex, open source software library PARAMESH, and the resulting numerical solver, Campfire, also combines with adaptive mesh refinement, adaptive time stepping and parallelization through domain decomposition. There are five mathematical models considered in this work, ranging from applications such as binary alloy solidification and fluid dynamics to a multi-phase-field model of tumour growth. These mathematical models consist of nonlinear, time-dependent and coupled partial differential equations (PDEs). Using our adaptive, parallel multigrid solver, together with finite difference method (FDM) and backward differentiation formulas (BDF), we are able to solve all five models in computationally demanding 2-D and/or 3-D situations. Due to the choice of second order central finite difference and second order BDF2 method, we obtain, and demonstrate, solutions with an overall second order convergence rate and optimal multigrid convergence. In the case of the multi-phase-field model of tumour growth, this has not previously been achieved. The novelties of our work also include solving the model of binary alloy solidification with a time-dependent temperature field in 3-D for the first time; implementing non-time-dependent equations alongside the coupled time-dependent partial differential equations (and increasing the range of boundary conditions) to significantly increase the generality and range of applicability of the described multigrid solver; improving the efficiency of the implementation of the solver through multiple developments; and introducing penalty terms to smoothly control the behaviour of phase variables where their range of valid values is constrained.

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McDonald, Eleanor. "All-at-once solution of time-dependent PDE problems." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:60f2985b-6071-47ae-97a9-7813db0194ae.

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In this thesis, we examine the solution to a range of time-dependent Partial Differential Equation (PDE) problems. Throughout, we focus on the development of preconditioners for the all-at-once system, which solves for all time-steps in a single coupled computation. The preconditioners developed are used with existing iterative methods and, due to their specific block structure, could be applied in parallel over time. We first develop solvers for the heat equation and the transient convection-diffusion equation. For both of these forward problems, the all-at-once system is non-symmetric. Despite this, in certain cases, we are able to provide rigorous termination bounds for non-symmetric iterative methods, contrary to what is generally possible for non-symmetric systems. The ideas developed for evolutionary PDEs are extended to develop preconditioners for time-dependent optimal control problems. By incorporating the methods designed for the forward problem, we are able to develop block diagonal Schur complement based preconditioners, which also could be implemented in parallel over time. We provide extensive eigenvalue analysis for each preconditioner and demonstrate their effectiveness through numerical computations for a variety of problems. We are able to describe solvers that are robust to various parameters, including the mesh size and number of time-steps.

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Tråsdahl, Øystein. "Numerical solution of partial differential equations in time-dependent domains." Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2008. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9752.

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Numerical solution of heat transfer and fluid flow problems in two spatial dimensions is studied. An arbitrary Lagrangian-Eulerian (ALE) formulation of the governing equations is applied to handle time-dependent geometries. A Legendre spectral method is used for the spatial discretization, and the temporal discretization is done with a semi-implicit multi-step method. The Stefan problem, a convection-diffusion boundary value problem modeling phase transition, makes for some interesting model problems. One problem is solved numerically to obtain first, second and third order convergence in time, and another numerical example is used to illustrate the difficulties that may arise with distribution of computational grid points in moving boundary problems. Strategies to maintain a favorable grid configuration for some particular geometries are presented. The Navier-Stokes equations are more complex and introduce new challenges not encountered in the convection-diffusion problems. They are studied in detail by considering different simplifications. Some numerical examples in static domains are presented to verify exponential convergence in space and second order convergence in time. A preconditioning technique for the unsteady Stokes problem with Dirichlet boundary conditions is presented and tested numerically. Free surface conditions are then introduced and studied numerically in a model of a droplet. The fluid is modeled first as Stokes flow, then Navier-Stokes flow, and the difference in the models is clearly visible in the numerical results. Finally, an interesting problem with non-constant surface tension is studied numerically.

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Abd, El Aziz Osama Mostafa. "Solution of time dependent problems using the Global Element Method." Thesis, University of Liverpool, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329416.

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Johansson, Karoline. "A counterexample concerning nontangential convergence for the solution to the time-dependent Schrödinger equation." Thesis, Växjö University, School of Mathematics and Systems Engineering, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-1082.

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Abstract: Considering the Schrödinger equation $\Delta_x u = i\partial{u}/\partial{t}$, we have a solution $u$ on the form $$u(x, t)= (2\pi)^{-n} \int_{\RR} {e^{i x\cdot \xi}e^{it|\xi|^2}\widehat{f}(\xi)}\, d \xi, x \in \RR, t \in \mathbf{R}$$ where $f$ belongs to the Sobolev space. It was shown by Sjögren and Sjölin, that assuming $\gamma : \mathbf{R}_+ \rightarrow \mathbf{R}_+ $ being a strictly increasing function, with $\gamma(0) = 0$ and $u$ and $f$ as above, there exists an $f \in H^{n/2} (\RR)$ such that $u$ is continuous in $\{ (x, t); t>0 \}$ and $$\limsup_{(y,t)\rightarrow (x,0),|y-x|<\gamma (t), t>0} |u(y,t)|= + \infty$$ for all $x \in \RR$. This theorem was proved by choosing $$\widehat{f}(\xi )=\widehat{f_a}(\xi )= | \xi | ^{-n} (\log | \xi |)^{-3/4} \sum_{j=1}^{\infty} \chi _j(\xi)e^{- i( x_{n_j} \cdot \xi + t_j | \xi | ^a)}, \, a=2,$$ where $\chi_j$ is the characteristic function of shells $S_j$ with the inner radius rapidly increasing with respect to $j$. The purpose of this essay is to explain the proof given by Sjögren and Sjölin, by first showing that the theorem is true for $\gamma (t)=t$, and to investigate the result when we use $$S^a f_a (x, t)= (2 \pi)^{-n}\int_{\RR} {e^{i x\cdot \xi}e^{it |\xi|^a}\widehat{f_a}(\xi)}\, d \xi$$ instead of $u$.

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Loskutov, Valentin, and Vyacheslav Sevriugin. "Analytical solution for the time dependent self-diffusion coefficient of a liquid in a porous medium." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-194287.

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The purpose of our work is to attempt to find the analytical expression approximating the experimentally obtained D(t) dependence of molecules of liquids or gases, in porous systems. The statement of the problem is based on the most general representations of self-diffusion processes in porous systems.

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Loskutov, Valentin, and Vyacheslav Sevriugin. "Analytical solution for the time dependent self-diffusion coefficient of a liquid in a porous medium." Diffusion fundamentals 5 (2007) 3, S. 1-5, 2007. https://ul.qucosa.de/id/qucosa%3A14267.

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The purpose of our work is to attempt to find the analytical expression approximating the experimentally obtained D(t) dependence of molecules of liquids or gases, in porous systems. The statement of the problem is based on the most general representations of self-diffusion processes in porous systems.

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Stoor, Daniel. "Solution of the Stefan problem with general time-dependent boundary conditions using a random walk method." Thesis, Örebro universitet, Institutionen för naturvetenskap och teknik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-385147.

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This work deals with the one-dimensional Stefan problem with a general time- dependent boundary condition at the fixed boundary. The solution will be obtained using a discrete random walk method and the results will be compared qualitatively with analytical- and finite difference method solutions. A critical part has been to model the moving boundary with the random walk method. The results show that the random walk method is competitive in relation to the finite difference method and has its advantages in generality and low effort to implement. The finite difference method has, on the other hand, higher accuracy for the same computational time with the here chosen step lengths. For the random walk method to increase the accuracy, longer execution times are required, but since the method is generally easily adapted for parallel computing, it is possible to speed up. Regarding applications for the Stefan problem, there are a large range of examples such as climate models, the diffusion of lithium-ions in lithium-ion batteries and modelling steam chambers for oil extraction using steam assisted gravity drainage.

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Schroeder, Gregory C. "Estimates for the rate of convergence of finite element approximations of the solution of a time-dependent variational inequality." Master's thesis, University of Cape Town, 1993. http://hdl.handle.net/11427/17404.

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Bibliography: pages 93-101.
The main aim of this thesis is to analyse two types of general finite element approximations to the solution of a time-dependent variational inequality. The two types of approximations considered are the following: 1. Semi-discrete approximations, in which only the spatial domain is discretised by finite elements; 2. fully discrete approximations, in which the spatial domain is again discretised by finite elements and, in addition, the time domain is discretised and the time-derivatives appearing in the variational inequality are approximated by backward differences. Estimates of the error inherent in the above two types of approximations, in suitable Sobolev norms, are obtained; in particular, these estimates express the rate of convergence of successive finite element approximations to the solution of the variational inequality in terms of element size h and, where appropriate, in terms of the time step size k. In addition, the above analysis is preceded by related results concerning the existence and uniqueness of the solution to the variational inequality and is followed by an application in elastoplasticity theory.

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Bozkaya, Nuray. "Application Of The Boundary Element Method To Parabolic Type Equations." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/3/12612074/index.pdf.

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In this thesis, the two-dimensional initial and boundary value problems governed by unsteady partial differential equations are solved by making use of boundary element techniques. The boundary element method (BEM) with time-dependent fundamental solution is presented as an efficient procedure for the solution of diffusion, wave and convection-diffusion equations. It interpenetrates the equations in such a way that the boundary solution is advanced to all time levels, simultaneously. The solution at a required interior point can then be obtained by using the computed boundary solution. Then, the coupled system of nonlinear reaction-diffusion equations and the magnetohydrodynamic (MHD) flow equations in a duct are solved by using the time-domain BEM. The numerical approach is based on the iteration between the equations of the system. The advantage of time-domain BEM are still made use of utilizing large time increments. Mainly, MHD flow equations in a duct having variable wall conductivities are solved successfully for large values of Hartmann number. Variable conductivity on the walls produces coupled boundary conditions which causes difficulties in numerical treatment of the problem by the usual BEM. Thus, a new time-domain BEM approach is derived in order to solve these equations as a whole despite the coupled boundary conditions, which is one of the main contributions of this thesis. Further, the full MHD equations in stream function-vorticity-magnetic induction-current density form are solved. The dual reciprocity boundary element method (DRBEM), producing only boundary integrals, is used due to the nonlinear convection terms in the equations. In addition, the missing boundary conditions for vorticity and current density are derived with the help of coordinate functions in DRBEM. The resulting ordinary differential equations are discretized in time by using unconditionally stable Gear'
s scheme so that large time increments can be used. The Navier-Stokes equations are solved in a square cavity up to Reynolds number 2000. Then, the solution of full MHD flow in a lid-driven cavity and a backward facing step is obtained for different values of Reynolds, magnetic Reynolds and Hartmann numbers. The solution procedure is quite efficient to capture the well known characteristics of MHD flow.

11

Chung, Pong C. "Time-dependent rheology of polymer solutions /." The Ohio State University, 1985. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487262825077271.

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Carter-Fenk, Kevin D. "Design and Implementation of Quantum Chemistry Methods for the Condensed Phase: Noncovalent Interactions at the Nanoscale and Excited States in Bulk Solution." The Ohio State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu161617640330551.

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Geffroy, Aguilar Enrique Leal L. Gary Leal L. Gary. "Birefringence of polymer solutions in time dependent flows /." Diss., Pasadena, Calif. : California Institute of Technology, 1990. http://resolver.caltech.edu/CaltechETD:etd-02232007-154744.

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Habbireeh, A. A. "The numerical solution of time dependant problems by finite element methods." Thesis, University of Liverpool, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.383495.

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15

Wirth, Jens. "Asymptotic properties of solutions to wave equations with time-dependent dissipation." Doctoral thesis, [S.l.] : [s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=974675024.

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Wirth, Jens. "Asymptotic properties of solutions to wave equations with time-dependent dissipation." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola&quot, 2009. http://nbn-resolving.de/urn:nbn:de:swb:105-9950076.

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Gegenstand der Dissertation ist die Untersuchung der asymptotischen Eigenschaften von Lösungen des Cauchy-Problems für eine Wellengleichung mit zeitabhängiger Dämpfung $b=b(t)$ und das Wechselspiel zwischen dem Verhalten des Koeffizienten $b(t)ge0$ und sich ergebenden Abschätzungen der Energie auf der Basis von $L^q$, $qge2$. Dabei stellt sich heraus, dass zwischen zwei Szenarien, dem der nicht-effektiven und dem der effektiven Dämpfung zu unterscheiden ist. In beiden Fällen werden die Hauptterme der Lösungsdarstellung konstruiert und davon ausgehend erstmalig $L^p$--$L^q$ Abschätzung für die Lösung und ihre Ableitungen angegeben. Ebenso wird die Schärfe der Abschätzungen diskutiert und in Form einer modifizierten Scattering-Theorie beziehungsweise des Diffusionsphänomens konkretisiert.

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Angeli, Cesare. "Analytical solutions for the run-up of long water waves excited by time-independent and time-dependent forcing." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21772/.

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Nello studio fisico e matematico dei maremoti, l'interazione con la costa, o problema del run-up rappresenta ancora oggi una grande sfida. Da un lato, si tratta forse del problema di maggiore urgenza, in quanto è proprio all'arrivo alla terra ferma che il maremoto causa le maggiori perdite umane e materiali. Dall'altro lato, la formulazione matematica del problema è particolarmente complessa ed alcune caratteristiche del fenomeno non sono ancora ben comprese. In questa tesi viene proposto un metodo di calcolo della posizione della linea di costa in problemi bidimensionali, che suppone di poter applicare le equazioni della fluidodinamica in approssimazione di shallow water lineare. Se la prima di queste ipotesi è sempre utilizzata in questo contesto, questo non vale per la seconda. In generale il problema è non lineare e prevede condizioni al contorno mobili. Nonostante ciò, si può notare un fatto sorprendente: i problemi ai valori iniziali in formulazione lineare e non lineare producono soluzioni con gli stessi punti stazionari. Spesso l'informazione fondamentale che si vuole ottenere è l'estensione dell'area inondata, ovvero il valore massimo del run-up, che sarà previsto quindi correttamente anche in approssimazione lineare. Sulla base di queste considerazioni, viene presentato un modello capace di prevedere l'inondazione su una spiaggia lineare dovuta ad una qualsiasi deformazione del fondale che sia piccola rispetto alla profondità locale del mare. Questo modello è quindi applicabile nel caso di terremoti e frane sottomarine in prossimità della costa. I risultati delle applicazioni sono in accordo con i principali studi analoghi presenti in letteratura. Per questo, il modello è utilizzato per alcuni casi nuovi, ovvero uno studio della dipendenza del run-up massimo dalla magnitudo, in cui le caratteristiche della faglia sono dedotte da leggi di scala, e un nuovo semplice modello per una frana di forma Gaussiana con parametri variabili nel tempo.

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Fitzner, Christian [Verfasser], and Michael [Akademischer Betreuer] Thies. "Time dependent solutions of the massless Gross-Neveu model / Christian Fitzner. Gutachter: Michael Thies." Erlangen : Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2013. http://d-nb.info/1075740576/34.

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Celik, Hakan. "Time and Temperature Dependent Surface Tension Measurements of Responsive Protein-based Polymer Surfactant Solutions." Cleveland State University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=csu1440182119.

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Zhang, Ran. "Fundamental solutions of a class of pseudo-differential operators with time-dependent negative definite symbols." Thesis, Swansea University, 2011. https://cronfa.swan.ac.uk/Record/cronfa42643.

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In this thesis, we construct the fundamental solutions of pseudo-differential operators q(x,t,D) with time-dependent negative definite symbols q(x,t,xi) which are discussed as generators of Feller- and L2-sub-Markovian semigroups . The results are based on the Hille-Yosida theorem, the standard results of analytic semigroups of operators and the fundamental solutions of time-dependent parabolic equations.

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Fernandes, Jessica Colnaghi. "Análise do comportamento de sensores EGFET como função do tempo, iluminação, área da superfície e temperatura." Universidade de São Paulo, 2011. http://www.teses.usp.br/teses/disponiveis/59/59135/tde-04042012-103423/.

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O transistor de efeito de campo de porta estendida (EGFET) é um dispositivo composto por uma membrana sensível a íons e um MOSFET comercial, que pode ser aplicado para a medição do teor de íons em uma solução. O filme fino de óxido de estanho dopado com flúor (FTO) foi utilizado como a membrana seletiva do EGFET, e todo o sistema foi utilizado como sensor de pH. Os sensores de pH desenvolvidos a partir de transistores de efeito de campo (FETs) detectam o campo elétrico criado pelos íons da solução. A alteração do pH no organismo afeta a estrutura e a atividade das macromoléculas biológicas, por isso a detecção da alteração do pH no organismo é de grande importância. O objetivo deste trabalho foi o estudo da influência de alguns agentes externos sobre o FTO para ser utilizado como membrana sensível a íons do EGFET como sensor de pH. O sensor padrão apresentou uma resposta linear no escuro por volta de 37 mV/pH, para uma área de membrana de 230 mm2 . Foram estudados o efeito da evolução da medida no tempo, o efeito da iluminação, o efeito da alteração da área de contato do filme fino de FTO com a solução de pH e o efeito da alteração da temperatura da solução de pH. Para as medições feitas no escuro a dependência do tempo foi diferente das medições feitas na presença de luz UV-VIS. Para pHs ácidos a presença da luz faz com que o valor da corrente Ids diminua em relação a mesma medição no escuro enquanto que para pHs básicos, o valor da corrente aumenta. A sensibilidade na presença da luz altera em torno de 10%. Para o estudo do efeito da área foram utilizadas duas formas diferentes de medições, sendo a primeira forma utilizando diferentes áreas da mesma amostra e a segunda forma utilizando áreas diferentes para diferentes amostras. O aumento da temperatura da solução aumenta o valor da corrente do sensor em até 5% e aumenta a sensibilidade em 60%.
The extended gate field effect transistor (EGFET) is a device composed of a conventional ion sensitive electrode and a commercial MOSFET device, which can be applied for the measurement of ion content in a solution. The fluorine-doped tin oxide thin film (FTO) is used as a sensitive membrane of the EGFET, and the whole system was used as a pH sensor. The pH sensor developed from field effect transistors (FTO) detect the electric field created by the ions of the solution. Changing the pH in the body affects the structure and activity of biological macromolecules, and the detection of pH change in the body is of great importance. The aim of this paper was study the influence of some external agents in the FTO for used as ion sensitive membrane EGFET as pH sensor. The standard sensor presented a linear response in the dark about 37 mV/pH, for a membrane area of 230 mm2 . Was studied the effect of the evolution of the measure in time, the illumination effect, the effect of changing the contact area of the FTO thin film with the solution pH and the effect of changing the temperature of the pH solution. For measurements in the dark the time dependence is different than for the case under UV-VIS illumination. For acids solutions the light presence causes a current value decreases over the same measurement in the dark, whereas for basic solution the current values increases. The sensitivity in light presence changes around 10%. To study the area effect two different studies was applied. The first measure was using different areas of the same sample and the second measure was using different areas of different samples. Increasing the solution temperature the current value of the sensor also increases and the sensitivity increase about 60%.

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Fahs, Amin. "Modeling of naturel convection in porous media : development of semi-analytical and spectral numerical solutions of heat transfer problem in special domains." Thesis, Strasbourg, 2021. https://publication-theses.unistra.fr/restreint/theses_doctorat/2021/Fahs_Amin_2021_ED269.pdf.

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Le problème de la cavité poreuse carrée est largement utilisé comme cas de référence courant pour les problèmes de Convection Naturelle (CN) en milieux poreux. Il peut être utilisé pour plusieurs applications numériques, théoriques et pratiques. Par ailleurs, toutes les solutions de haute précision existantes dans la littérature scientifique sont développées dans des conditions de régime permanent. Cependant, il est bien connu que les processus de CN dans les milieux poreux se produisent naturellement dans un régime dépendant du temps, car les conditions aux limites peuvent être variables dans le temps. Pour surmonter cette difficulté, la solution en régime permanent est souvent simulée comme une solution transitoire qui évolue jusqu'à atteindre l'état d'équilibre. Ces régimes dépendant du temps sont très efficaces pour détecter les effets des variations de paramètres sur le processus physique de CN, en particulier pour les sujets d'intérêt de cette thèse: la variation du niveau d'inclinaison du domaine et la prise en compte des variations de température de la paroi chaude dans le temps. À cet effet, trois objectifs sont identifiés dans cette thèse: 1. Développer une solution de convection naturelle en fonction du temps dans des milieux poreux en utilisant le Modèle Darcy en deux modes: transitoire et instable. 2. Étudier le comportement en fonction du temps de la convection naturelle dans des milieux poreux ayant le niveau d'inclinaison du domaine comme paramètre variable dans deux modes: transitoire et instable. 3. Développer une solution de convection naturelle en fonction du temps dans des milieux poreux en utilisant le Modèle Darcy-Lapwood-Brinkman en deux modes: transitoire et instable. Pour ce faire, du fait de la grande précision dans les domaines simplement connectés, une méthode spectrale de résidus pondérés de type Galerkin est choisie pour développer une solution au problème de CN dans une cavité carrée poreuse. L’application de la procédure de Fourier-Galerkin (FG), deux configurations traitant des régimes instables sont considérées où chaque solution est dérivée pour une large gamme des nombres de Rayleigh (Ra) avec d'autres conditions spéciales. Ce travail de thèse est subdivisé en cinq chapitres. Dans le premier chapitre, nous avons présenté un aperçu physique du processus de convection naturelle en milieux poreux. Dans le deuxième chapitre, le développement mathématique des équations, la méthode de résolution et la procédure de résolution sont décrits en détails. Dans le chapitre trois, la première étude de cas de cette thèse, la solution dépendante du temps de la convection naturelle dans une cavité carrée remplie de milieux poreux saturé utilisant le modèle de Darcy est développé. Dans le chapitre quatre, le problème de variation temporelle de Darcy-Lapwood- Brinkman de CN dans une enceinte poreuse saturée carrée est étudié. Dans le chapitre cinq, les solutions dépendant du temps sont développées pour le problème de convection naturelle utilisant la loi de Darcy dans une cavité poreuse inclinée et considéré comme une étude complète sur les effets de l'inclinaison du domaine sur le processus physique du problème de convection libre. Pour tous les cas, les régimes transitoires et instables sont considérés
The problem of the porous square cavity is extensively used as a common benchmark case for Natural convection (NC) problem in porous media. It can be used for several numerical, theoretical, and practical purposes. All the existing high accurate solutions are developed under steady-state conditions. However, it is well known that the processes of NC in porous media occurs naturally in a time-dependent procedure, as boundary conditions can be variable in time. Also, the convergence of the steady-state solution is known to be difficult. To overcome this difficulty, the steady-state solution is often simulated as a transient solution that evolves until reaching the steady-state condition. These time-dependent modes are very efficient to detect the effects of the parameter variations on the physical process of NC, especially for the subject of interest in this thesis: the domain inclination level and hot wall temperature variation in time. For this purpose, three goals are identified in this Thesis: 1. Developing a time-dependent solution of natural convection in porous media using the Darcy model in two modes: Transient and unsteady. 2. Investigating the time-dependent behavior of natural convection in porous media having the domain inclination level as a variable parameter in two modes: Transient and unsteady. 3. Developing a time-dependent solution of natural convection in porous media using the Darcy-Lapwood-Brinkman model in two modes: Transient and unsteady. To do so, according to the high accuracy in the simply connected domains, one of the Galerkin spectral weighted residual method is chosen to develop a space-time dependent solution for NC problem in a square porous cavity. Applying the Fourier-Galerkin (FG) procedure, two configurations dealing with transient and unsteady regimes are considered where each solution is derived for a wide range of Rayleigh numbers with other special conditions. This work of thesis is explained in details as five chapters.The NC physical process with the time-dependent variations is described in the transient mode to reach the steady-state solution and for the unsteady mode during a one period using periodic sinusoidal boundary conditions on the cavity hot wall. Finally, the work of this thesis is described in details in five chapters; while the sixth and last chapter is devoted to the summary and conclusion.The results in this thesis work provide a set of high-accurate data that are published in three papers to be used for testing numerical codes of heat transfer in time-dependent configurations

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Cheng, Danling. "Integrated System Model Reliability Evaluation and Prediction for Electrical Power Systems: Graph Trace Analysis Based Solutions." Diss., Virginia Tech, 2009. http://hdl.handle.net/10919/28944.

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A new approach to the evaluation of the reliability of electrical systems is presented. In this approach a Graph Trace Analysis based approach is applied to integrated system models and reliability analysis. The analysis zones are extended from the traditional power system functional zones. The systems are modeled using containers with iterators, where the iterators manage graph edges and are used to process through the topology of the graph. The analysis provides a means of computationally handling dependent outages and cascading failures. The effects of adverse weather, time-varying loads, equipment age, installation environment, operation conditions are considered. Sequential Monte Carlo simulation is used to evaluate the reliability changes for different system configurations, including distributed generation and transmission lines. Historical weather records and loading are used to update the component failure rates on-the-fly. Simulation results are compared against historical reliability field measurements. Given a large and complex plant to operate, a real-time understanding of the networks and their situational reliability is important to operational decision support. This dissertation also introduces using an Integrated System Model in helping operators to minimize real-time problems. A real-time simulation architecture is described, which predicts where problems may occur, how serious they may be, and what is the possible root cause.
Ph. D.

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Hunter, Brandon. "Channel Probing for an Indoor Wireless Communications Channel." BYU ScholarsArchive, 2003. https://scholarsarchive.byu.edu/etd/64.

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The statistics of the amplitude, time and angle of arrival of multipaths in an indoor environment are all necessary components of multipath models used to simulate the performance of spatial diversity in receive antenna configurations. The model presented by Saleh and Valenzuela, was added to by Spencer et. al., and included all three of these parameters for a 7 GHz channel. A system was built to measure these multipath parameters at 2.4 GHz for multiple locations in an indoor environment. Another system was built to measure the angle of transmission for a 6 GHz channel. The addition of this parameter allows spatial diversity at the transmitter along with the receiver to be simulated. The process of going from raw measurement data to discrete arrivals and then to clustered arrivals is analyzed. Many possible errors associated with discrete arrival processing are discussed along with possible solutions. Four clustering methods are compared and their relative strengths and weaknesses are pointed out. The effects that errors in the clustering process have on parameter estimation and model performance are also simulated.

25

Tsung-WenHuang and 黃聰文. "Analytical Solution and Inverse Analysis of Heat Conduction Problems with Time-Dependent Boundary Conditions." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/70599390857410079734.

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博士
國立成功大學
機械工程學系
102
This paper discusses the analytical solution and inverse analysis of heat conduction problems with time-dependent boundary conditions. First, the non-uniform medium heat conduction problem is studied. A new analytic solution method is developed, without integral transform, to find the exact solution for the transient heat conduction in non-uniform medium with general time-dependent boundary conditions. By introducing suitable shifting functions, the governing second-order differential equation with variable coefficients and time-dependent boundary conditions is transformed into a differential equation with homogenous boundary conditions. If the physic properties of the medium are in polynomial forms, the exact solution of the system can be developed. Then, examples are given to illustrate the analysis. Limiting cases are studied and compared with those in the existing literature. The influence of physic parameters on the temperature distribution of the system is revealed. Secondly, a hybrid inverse scheme involving the shifting functions, eigenfunction expansion and least-square methods in conjunction with experimental data inside the test material, without integral transform, is proposed to estimate the unknown surface conditions for the linear inverse heat conduction problems with uniform medium. The functional form of the surface conditions is unknown a priori. We can analyze the whole time domain or divide it into several sub-time intervals for analysis and then estimates the unknown surface conditions on each sub-time interval. In order to show the accuracy and reliability of the present inverse scheme, comparisons among the present estimates, exact solution, previous results and experimental data are made. The effects of the measurement locations on the estimated results are also investigated. The results show that good estimation of the surface conditions can be obtained.

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Kundrat, Matthew David. "Time dependent density functional theory modeling of chiroptical properties of amino acids in solution." 2008. http://proquest.umi.com/pqdweb?did=1594481531&sid=2&Fmt=2&clientId=39334&RQT=309&VName=PQD.

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Thesis (Ph.D.)--State University of New York at Buffalo, 2008.
Title from PDF title page (viewed on Jan. 22, 2009) Available through UMI ProQuest Digital Dissertations. Thesis adviser: Autschbach, Jochen Includes bibliographical references.

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Zia, Haider. "Time-dependent Photomodulation of a Single Atom Tungsten Tip Tunnelling Barrier." Thesis, 2010. http://hdl.handle.net/1807/25733.

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There has been much work on electron emission. It has lead to the concept of the photon and new electron sources for imaging such as electron microscopes and the rst formulation of holographic reconstructions [1-6]. Analytical derivations are important to gain physical insight into the problem of developing better electron sources. However, to date, such formulations have su ered by a number of approximations that have masked important physics. In this thesis, a new approach is provided that solves the Schrodinger wave equation for photoemission from a single atom tungsten tip barrier or more generally, for photoemission from a Schottky triangular barrier potential, with or without image potential e ects. We describe the system, then introduce the mathematical derivation. We conclude with the applications of the theory.

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Nyirenda, Edwin. "A time-dependent green element formulation for solution of potential flow problems in 3 dimensional domains." Thesis, 2011. http://hdl.handle.net/10539/9724.

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In this work we develop a generalised methodology for the solution of the timedependent second order parabolic differential equation of potential flow in heterogeneous media using the Green element method. Parabolic differential equations are one class of differential equations, the others being elliptic partial differential equations and hyperbolic differential equations. Since elliptic differential equations generally arise from a diffusion process that has reached equilibrium, they can also be solved using the methodology developed, and represent a simplification because of the steady state situation. Potential flow problems are of great interest in many engineering applications such as flow in aquifers, heat transfer processes, electro-magnetic field problems, etc. Traditionally, the finite difference method and the finite element method have proved to be powerful techniques to solve such potential flow problems, but each has limitations and challenges which have led to continued research in numerical methods. The finite difference method is more applicable to domains with regular boundary, and the finite element method, though extremely versatile, exhibits unacceptable inaccuracies with coarse meshes, thus requiring fine meshes with the associated high computation costs. In view of some of the limitations with these earlier methods, several numerical schemes are now being developed as viable alternatives to these conventional methods. Among such methods are the boundary element method, the finite volume method, and the analytic element method. The boundary element method has been particularly promising because of its domain-reduction feature and the second order accuracy that can generally be achieved. The domain-reduction feature of the boundary element method, though achieved for restricted class of problems, lends it to efficient grid generation algorithm, while its second-order accuracy ensures reliability and consistency of the numerical solutions. -v- The boundary element method in its original formulation is unable to deal with heterogeneities in the domain. For physical problems, especially in groundwater flow, heterogeneities and anisotropy are a natural and frequent occurrence, and this has fuelled research into boundary element techniques that are capable of accommodating these features. The Green element method is one technique which is based on the boundary element theory and which has been proven to be very effective in handling heterogeneities and anisotropy in 1D and 2D domains. However, development of techniques to implement the Green element method in 3D domains has remained largely unexplored. This work represents an effort in this direction. We have investigated the adoption of the general tetrahedral and hexahedra elements for use with the Green element method, and found that the large number of degrees of freedom generated precludes retention of the internal normal direction as in 1D and 2D formulations. Furthermore, some of the complicated surface and domain integrations with these elements can only be addressed with quadrature methods. The compatibility issues that arise between element faces, which present considerable challenges to multi-domain boundary element techniques, are innovatively addressed in the computer code that has been developed in this work. The Green element method is implemented for steady and time-dependent problems using regular hexahedra elements, and the results show that the performance is slightly better than the results obtained using FEMWATER. FEMWATER is an established finite element method software. No attempt is made to compare the computation efficiencies of the 3D GEM code and FEMWATER because the two codes were not developed on a common platform.

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Tseng, Jeng-Wei, and 曾政偉. "Solution by Genetic Algorithm In Regard to Sequence-Dependent Setup Time for Unrelated Parallel Machines Scheduling Problems." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/61545397683774752374.

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碩士
國立勤益科技大學
工業工程與管理系
95
Some of the factory machines in these research cases are to be upgraded with new equipments, therefore, in certain work assignment, the machine configuration changes, i.e. new and old machines coexist together in particular production process. Some of the work machines are definitely performing faster than others. And certain manufacturing process is restricted to be carried out on certain machines. Accordingly, this research focuses on unrelated parallel machine scheduling problems and takes into considerations to minimize the overall delay for processing orders and the total production time. Another individual case needed to be considered is that, since the production materials are varied in nature, and the molds replaced must be cleaned prior production line change. As a consequence, the preparation time for every production line must be included as such. Subsequently, a parallel machine scheduling system configured on genetic algorithms can be used to find solutions according the superior search capabilities of the former. The parameter settings in genetic algorithm are critical to solution’s efficiency and effectiveness. Hence, Taguchi method is used to determine the parameter design and fine-tuning in the process of executing genetic algorithm, and eventually the most optimum parameter combination can be located. During this study, a case of manufacturer for lamps and lanterns was adopted to prove the effectiveness and stability of Taguchi method. And further comparisons were made against other frequently used traditional work scheduling methods. The final findings prove that, the configuration system proposed by this research can acquire fairly good scheduling results under the production environment from companies adopted as study case.

30

Sýkora, Petr. "Pohyb stlačitelné tekutiny v časově proměnných oblastech." Master's thesis, 2012. http://www.nusl.cz/ntk/nusl-305087.

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In this work we study the existence of weak solutions for compressible Navier-Stokes equations in unbounded time dependent domains. Using the methods introduced in Feireisl E. Dynamics of Viscous Compressible Fluids we extend the results of article Feireisl E. Neustupa J. Stebel J., Convergence of a Brinkman-type penalization for compressible fluid flows, which studies the flow with a "no-slip" boundary condition on bounded domains. Next, we extend results of article Feireisl E. Kreml O. Nečasová Š. Neustupa J. Stebel J., Weak solutions to the barotropic Navier- Stokes system with slip boundary conditions in time dependent domains, which studies flow with compete Navier boundary condition. Finally, we discuss solutions for rotating fluid system. In this case, there are new members in momentum equation, representing the Coriolis and centrifugal force, which cause problems.

31

Nguyen, Khanh Phuong. "Meta-heuristic Solution Methods for Rich Vehicle Routing Problems." Thèse, 2014. http://hdl.handle.net/1866/11200.

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Le problème de tournées de véhicules (VRP), introduit par Dantzig and Ramser en 1959, est devenu l'un des problèmes les plus étudiés en recherche opérationnelle, et ce, en raison de son intérêt méthodologique et de ses retombées pratiques dans de nombreux domaines tels que le transport, la logistique, les télécommunications et la production. L'objectif général du VRP est d'optimiser l'utilisation des ressources de transport afin de répondre aux besoins des clients tout en respectant les contraintes découlant des exigences du contexte d’application. Les applications réelles du VRP doivent tenir compte d’une grande variété de contraintes et plus ces contraintes sont nombreuse, plus le problème est difficile à résoudre. Les VRPs qui tiennent compte de l’ensemble de ces contraintes rencontrées en pratique et qui se rapprochent des applications réelles forment la classe des problèmes ‘riches’ de tournées de véhicules. Résoudre ces problèmes de manière efficiente pose des défis considérables pour la communauté de chercheurs qui se penchent sur les VRPs. Cette thèse, composée de deux parties, explore certaines extensions du VRP vers ces problèmes. La première partie de cette thèse porte sur le VRP périodique avec des contraintes de fenêtres de temps (PVRPTW). Celui-ci est une extension du VRP classique avec fenêtres de temps (VRPTW) puisqu’il considère un horizon de planification de plusieurs jours pendant lesquels les clients n'ont généralement pas besoin d’être desservi à tous les jours, mais plutôt peuvent être visités selon un certain nombre de combinaisons possibles de jours de livraison. Cette généralisation étend l'éventail d'applications de ce problème à diverses activités de distributions commerciales, telle la collecte des déchets, le balayage des rues, la distribution de produits alimentaires, la livraison du courrier, etc. La principale contribution scientifique de la première partie de cette thèse est le développement d'une méta-heuristique hybride dans la quelle un ensemble de procédures de recherche locales et de méta-heuristiques basées sur les principes de voisinages coopèrent avec un algorithme génétique afin d’améliorer la qualité des solutions et de promouvoir la diversité de la population. Les résultats obtenus montrent que la méthode proposée est très performante et donne de nouvelles meilleures solutions pour certains grands exemplaires du problème. La deuxième partie de cette étude a pour but de présenter, modéliser et résoudre deux problèmes riches de tournées de véhicules, qui sont des extensions du VRPTW en ce sens qu'ils incluent des demandes dépendantes du temps de ramassage et de livraison avec des restrictions au niveau de la synchronization temporelle. Ces problèmes sont connus respectivement sous le nom de Time-dependent Multi-zone Multi-Trip Vehicle Routing Problem with Time Windows (TMZT-VRPTW) et de Multi-zone Mult-Trip Pickup and Delivery Problem with Time Windows and Synchronization (MZT-PDTWS). Ces deux problèmes proviennent de la planification des opérations de systèmes logistiques urbains à deux niveaux. La difficulté de ces problèmes réside dans la manipulation de deux ensembles entrelacés de décisions: la composante des tournées de véhicules qui vise à déterminer les séquences de clients visités par chaque véhicule, et la composante de planification qui vise à faciliter l'arrivée des véhicules selon des restrictions au niveau de la synchronisation temporelle. Auparavant, ces questions ont été abordées séparément. La combinaison de ces types de décisions dans une seule formulation mathématique et dans une même méthode de résolution devrait donc donner de meilleurs résultats que de considérer ces décisions séparément. Dans cette étude, nous proposons des solutions heuristiques qui tiennent compte de ces deux types de décisions simultanément, et ce, d'une manière complète et efficace. Les résultats de tests expérimentaux confirment la performance de la méthode proposée lorsqu’on la compare aux autres méthodes présentées dans la littérature. En effet, la méthode développée propose des solutions nécessitant moins de véhicules et engendrant de moindres frais de déplacement pour effectuer efficacement la même quantité de travail. Dans le contexte des systèmes logistiques urbains, nos résultats impliquent une réduction de la présence de véhicules dans les rues de la ville et, par conséquent, de leur impact négatif sur la congestion et sur l’environnement.
For more than half of century, since the paper of Dantzig and Ramser (1959) was introduced, the Vehicle Routing Problem (VRP) has been one of the most extensively studied problems in operations research due to its methodological interest and practical relevance in many fields such as transportation, logistics, telecommunications, and production. The general goal of the VRP is to optimize the use of transportation resources to service customers with respect to side-constraints deriving from real-world applications. The practical applications of the VRP may have a variety of constraints, and obviously, the larger the set of constraints that need to be considered, i.e., corresponding to `richer' VRPs, the more difficult the task of problem solving. The needs to study closer representations of actual applications and methodologies producing high-quality solutions quickly to larger-sized application problems have increased steadily, providing significant challenges for the VRP research community. This dissertation explores these extensional issues of the VRP. The first part of the dissertation addresses the Periodic Vehicle Routing Problem with Time Windows (PVRPTW) which generalizes the classical Vehicle Routing Problem with Time Windows (VRPTW) by extending the planning horizon to several days where customers generally do not require delivery on every day, but rather according to one of a limited number of possible combinations of visit days. This generalization extends the scope of applications to many commercial distribution activities such as waste collection, street sweeping, grocery distribution, mail delivery, etc. The major contribution of this part is the development of a population-based hybrid meta-heuristic in which a set of local search procedures and neighborhood-based meta-heuristics cooperate with the genetic algorithm population evolution mechanism to enhance the solution quality as well as to promote diversity of the genetic algorithm population. The results show that the proposed methodology is highly competitive, providing new best solutions in some large instances. The second part of the dissertation aims to present, model and solve two rich vehicle routing problems which further extend the VRPTW with time-dependent demands of pickup and delivery, and hard time synchronization restrictions. They are called Time-dependent Multi-zone Multi-Trip Vehicle Routing Problem with Time Windows (TMZT-VRPTW), and Multi-zone Mult-Trip Pickup and Delivery Problem with Time Windows and Synchronization (MZT-PDTWS), respectively. These two problems originate from planning the operations of two-tiered City Logistics systems. The difficulty of these problems lies in handling two intertwined sets of decisions: the routing component which aims to determine the sequences of customers visited by each vehicle, and the scheduling component which consists in planning arrivals of vehicles at facilities within hard time synchronization restrictions. Previously, these issues have been addressed separately. Combining these decisions into one formulation and solution method should yield better results. In this dissertation we propose meta-heuristics that address the two decisions simultaneously, in a comprehensive and efficient way. Experiments confirm the good performance of the proposed methodology compared to the literature, providing system managers with solution requiring less vehicles and travel costs to perform efficiently the same amount of work. In the context of City Logistics systems, our results indicate a reduction in the presence of vehicles on the streets of the city and, thus, in their negative impact on congestion and environment.

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Stechlinski, Peter. "A Study of Infectious Disease Models with Switching." Thesis, 2009. http://hdl.handle.net/10012/4424.

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Infectious disease models with switching are constructed and investigated in detail. Modelling infectious diseases as switched systems, which are systems that combine continuous dynamics with discrete logic, allows for the use of methods from switched systems theory. These methods are used to analyze the stability and long-term behaviour of the proposed switched epidemiological models. Switching is first incorporated into epidemiological models by assuming the contact rate to be time-dependent and better approximated by a piecewise constant. Epidemiological models with switched incidence rates are also investigated. Threshold criteria are established that are sufficient for the eradication of the disease, and, hence, the stability of the disease-free solution. In the case of an endemic disease, some criteria are developed that establish the persistence of the disease. Lyapunov function techniques, as well as techniques for stability of impulsive or non-impulsive switched systems with both stable and unstable modes are used. These methods are first applied to switched epidemiological models which are intrinsically one-dimensional. Multi-dimensional disease models with switching are then investigated in detail. An important part of studying epidemiology is to construct control strategies in order to eradicate a disease, which would otherwise be persistent. Hence, the application of controls schemes to switched epidemiological models are investigated. Finally, epidemiological models with switched general nonlinear incidence rates are considered. Simulations are given throughout to illustrate our results, as well as to make some conjectures. Some conclusions are made and future directions are given.

33

Wang, Shangying. "Quantifying Gene Regulatory Networks." Diss., 2014. http://hdl.handle.net/10161/8676.

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\abstract

Transcription and translation describe the flow of genetic information from DNA to mRNA to protein. Recent studies show that at a single cell level, these processes are stochastic, which results in the variation of the number of mRNA and proteins even under identical environmental conditions. Because the number of mRNA and protein in each single cell are actually very small, these variations can be crucial for cellular function in diverse contexts, such as development, stress response, immunological and nervous system function. Most studies examine the origin and effects of stochastic gene expression using computer simulations. My goal is to develop a theoretical framework to study activity-dependent gene expression using simplified models that capture essential features.

I have examined the dynamics of stochastic gene regulation in three contexts. First, I examine how fluctuations in promoter accessibility lead to "bursty" transcription, during which genes are turned "on" or "off" stochastically. I describe a mathematical formalism to represent bursty gene expression in a coarse-grained manner as a Markov process and derive a master equation for the time evolution of the probability distribution of the number of mRNA molecules. This allows us to examine how transcript number responds to time varying stimuli. This model forms a basic building block for understanding the signal transmission and noise of the transcription process to time varying inputs as would be sensed by cells in dynamic environments. In addition to synthesis, gene expression is subject to additional modes of regulation. One such mechanism that controls transcript numbers is by microRNAs (miRNAs), which pair with target mRNAs to repress protein production following transcription. Although hundreds of miRNAs have been identified in mammalian genomes, the function of miRNA-based repression in the context of gene regulation networks still remains unclear. I explore the functional roles of feedback regulation by miRNAs and show that protein fluctuations strongly depend on the mode of miRNA-mediated repression. I discuss the functional implications of protein fluctuations arising from miRNA-mediated repression on gene regulatory networks. Finally, I examine the impact of fluctuations on alternative splicing, which is a major source for proteomic complexity in higher eukaryotes. Although the proteins regulating alternative splicing have been extensively studied, little is known about how noise arising from the stochastic nature of alternative splicing contributes to the entire gene expression process. I explore the functional roles and noise properties of alternative splicing, focusing on the case of exon skipping and intron retention. I show that while the overall counts of the mRNAs of the two isoforms are independent and Poisson distributed, diffusion and binding of the splicing factors contributes to the variance in the abundance of the isoforms.

Noise in gene expression may be of particular relevance in the nervous system. Environmental stimuli drive the rapid remodeling of neural circuitry in part by inducing the activation of genes to make proteins that modify neuronal excitability and connectivity, ultimately influencing higher order brain function. Finally, I examine the implications of our studies for activity dependent gene expression in the nervous system.

Dissertation

34

Geffroy, Aguilar Enrique. "Birefringence of polymer solutions in time dependent flows." Thesis, 1990. https://thesis.library.caltech.edu/722/1/Aguilar_eg_1990.pdf.

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This is a study of changes of conformation of macromolecules in polymeric solutions which are subjected to time-dependent extensional flows generated by a two-roll mill flow device. The flows produced by the two-roll mill are linear, and two-dimensional. It has a stagnation point at the center of the flow field where the magnitudes of the strain-rates are greater than the vorticity. This study of conformational changes is based on data around the vicinity of the stagnation point, I for steady state flows, and several transient flow histories such as startup, cessation, and double-step flows. We also present an analytical solution for the creeping flow generated by an infinitely long two-roll mill embedded in an unbounded fluid. This solution is used as a benchmark to compare the behavior of the polymer solutions when subjected to flows with different values for the ratio of rate-of-strain to vorticity. The conformational changes are determined experimentally using the Two-color Flow-Birefringence which provides an instantaneous and point-wise measure of the anisotropy of the fluid, together with the relative orientation of the anisotropy with respect to the principal axes of the flow field. Based on relaxation of the fluid anisotropy the characteristic time-scales of the polymer have been evaluated as a function of the flow field properties and the degree of conformational change of the macromolecules. Data for two polymeric solution is presented. The first polymer system is the so-called test-fluid Ml. This polymeric solution is shown to degrade significantly, even for small values of the velocity gradient, as measured by the changes in the macroscopic relaxation time-scales. The second solution is a concentrated polystyrene solution that presents overshoots and undershoots of the polymer conformation dependent of the ratio of vorticity to rate-of-strain. When subjected to large deformations, this polystyrene solution shows not only the possibility of a reduced number of entanglements, but also a significant deformation of the macromolecule segments associated to a shorter relaxation time-scale for the dynamics of concentrated solutions, which corresponds to that predicted by the intermediate relaxation time-scale of Doi-Edwards model.

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Chun-JungHung and 洪浚榮. "Analytical Solutions for Heat Conduction of Plates with Time Dependent Boundary Conditions." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/vrndaz.

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碩士
國立成功大學
機械工程學系
105
This thesis discusses the analytical solution for heat conduction of the two-dimensional plate with time dependent boundary conditions. Reducing the two-dimensional problem into two one-dimensional subsystems by means of the principle of superposition and generalized Fourier coefficient. With help of shifting function method, the non-homogeneous boundary conditions problem can be converted into the transformed function associated with homogeneous boundary conditions. Eventually, the transformed function can be determined by the method of eigenfunction expansion. For Dirichlet boundary conditions, this thesis has developed the solution method which does not require any integral transformation and is easy to solve. The analytical solution is expressed in product and summation form. To illustrate the accuracy, examples are given to compared to the existing literature. Finally, some Dirichlet boundary conditions are studied by the proposed solution method.

36

Chen, Jiann-Mou, and 陳建謀. "Analytical Solutions of 1,2,3-Dimensional Infiltration with Arbitrary Time and Space Dependent Surface Fluxes." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/91001943128648949396.

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博士
國立臺灣大學
農業工程學研究所
89
This study solves the linearized multi-dimensional Richards’ equation with the assumption of constant diffusivity and exponential relationship of hydraulic conductivity and pressure head K=ksExp(αΨ) which satisfies k*=dk/dθ=ks/(θs-θr). Techniques of transformation, Fourier Integral Transformation and Green’s Function Theory are applied to obtain the analytical solutions in this study, that results can provide prediction of the ponding time, and can obtain the arbitrary initial water content distribution and the volumetric water content distribution when time and space are under the conditions of time dependent and non-uniform distribution of surface fluxes. This study also derives multi-dimensional analytical solutions of unsaturated infiltration problems completely. In addition, one dimensional infiltration problems consider finite regions with water table and semi-infinite regions without water table, and obtain the solutions of the volumetric water content profile with variable rainfall intensity before and after ponding, and the ponding time. Two and three dimensional infiltration problems consider finite region with water table, and obtain the analytical solutions of volumetric water content profile with variable rainfall intensity before ponding, and the ponding time. Moreover, the analytical solutions can be applied to the situation of variable evaporation rate. The analytical solutions with the advantage of easy calculation, which are useful tools for verifying accuracy of many numerical models, are often subjected to convergence and mass balance problems.

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Pen-Yuan, Hsu. "Blow up solutions of coupled systems of Nonlinear Schrodinger Equations with a Time-Dependent Nonlinearity." 2006. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0001-1807200616243000.

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Hsu, Pen-Yuan, and 許本源. "Blow up solutions of coupled systems of Nonlinear Schrodinger Equations with a Time-Dependent Nonlinearity." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/98024933911965918728.

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碩士
國立臺灣大學
數學研究所
94
Here we study finite-time blow-up solutions of two-component system of nonlinear Schr¨odinger equations with a time-dependent nonlinearity. From main theorem in this paper, the system may have a solution (Φ,Ψ) such that both ∥▽Φ∥L2(Ω) and ∥▽Ψ∥L2(Ω) blow up at the same time but we don’t know whether ∥Φ∥L∞(Ω) and ∥Ψ∥L∞(Ω) blow up simultaneously.

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Wirth, Jens [Verfasser]. "Asymptotic properties of solutions to wave equations with time-dependent dissipation / vorgelegt von Jens Wirth." 2004. http://d-nb.info/974675024/34.

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王仕宇. "Exploring the Adsorption Kinetics of CV and R6G in Silver and Gold Colloidal Solutions Using Time-Dependent SERS Spectra." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/02215568747297754321.

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碩士
國立嘉義大學
應用化學系研究所
98
R6G and CV have been used as the probe molecules extensively in the studies of surface enhanced Raman scattering (SERS). However, there were few reports about comparing the enhancement factors of R6G with CV in the same silver nanoparticle colloidal solution simultaneously. In this study, the time-dependent SERS spectra of probe molecules in silver nanoprism, spherical silver nanoparticle, and spherical gold nanoparticle colloids, respectively, were recorded at 632.8 nm excitation in the presence of halide ions. The results showed that the silver nanoprisms exhibit a better affinity to CV than R6G by a factor of over 10. Furthermore, we found that CV in the silver nanoprism colloids had a better SERS intensity in the presence than in the absence of R6G. Although this observation successfully demonstrated for the first time that the existence of a non-salt molecule can be helpful to increase the SERS signals of the other molecules, we still lacked a reasonable explanation.

41

Yeh, Chiao-wen, and 葉巧雯. "Search for appropriate photosensitizer for photodynamics therapy applacations---Study of concentration dependence of specturm characteristic and liifetimemeasured by time-correlated single photon counting system in organic solutions." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/81796391788481748548.

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碩士
國立中正大學
物理所
94
Photodynamic therapy (PDT) is a treatment for malignant tumors. It uses an ideal photo sensitive drug, referred to as photosensitizer or photosensitizing agent, to absorb the light and promote the surrounding oxygen molecules from the ground state (triplet) to the excited singlet state via the annihilation process. On the excited singlet state, the oxygen molecules can inactivate viruses in biological fluids. The efficiency of PDT can be determined by monitoring the phosphorescence emitted by the oxygen molecules on the excited singlet state via the singlet®triplet relaxation. Since the phosphorescence wavelength is around 1270 nm and can not be detected by our visible avalanched photo detector available presently, we instead start with the measurement of the visible fluorescence emitted by the photosensitizing agent. Once after we get familiar with the detection technique and the infrared detector becomes available, we will switch to the measurement of 1270 nm phosphorescence by excited singlet oxygen molecules. In this thesis, we measured the absorption and emission spectra of several organic solution including phthalocyanine dissoveld in toluene (H2PC/toluene), zinc phthalocyanine dissolved in 1-Chloranaphthalene (ZnPC/1-Chloranaphthalene), aluminum phthalocyanine chloride dissolved in ethanol (CAP/ethanol) and Silicon 2,3-naphthalocyanine bis(trihexylsilyloxide) dissolved in trtrahydrofuran (SiNC/THF) with different concentrations. Our measurements indicate that the absorption peaks at the same wavelengths with concentration; however, the absorbance increases as the concentration increases. Besides, the former two solutions show much lower absorbance than the latter two solutions of the same concentrations. The emission spectra of the former two solutions, H2PC and ZnPC, also peak at the same wavelength with concentration, similar to the absorption peaks of all the four solutions. However, the emission spectra of the latter two solutions, CAP and SiNC, show that the peak wavelengths vary with their concentration. The peak wavelengths of these two solutions shift to the long wavelength range as the concentrations increase. Beside the absorption and emission spectra measurements, we also measured the lifetime of emission at the peak wavelengths with TCSPC system and found that the lifetimes of the former two solutions decrease as the concentrations increase; however, the lifetimes of the latter two solutions increase as the concentrations increase. We explain this different trends in terms of reabsorption of CAP and SiNC emission.

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Klimanis, Nils. "Generic Programming and Algebraic Multigrid for Stabilized Finite Element Methods." Doctoral thesis, 2006. http://hdl.handle.net/11858/00-1735-0000-0006-B38C-5.

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Dissertations / Theses on the topic 'Time dependent solution'

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