Dissertations / Theses on the topic 'Solutions with exponential growth'
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Sani, F. "EXPONENTIAL-TYPE INEQUALITIES IN R^N AND APPLICATIONS TO ELLIPTIC AND BIHARMONIC EQUATIONS." Doctoral thesis, Università degli Studi di Milano, 2012. http://hdl.handle.net/2434/170626.
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Adams' inequality in its original form is nothing but the Trudinger-Moser inequality for Sobolev spaces involving higher order derivatives. In this Thesis we present Adams-type inequalities for unbounded domains in R^n and some applications to existence and multiplicity results for elliptic and biharmonic problems involving nonlinearities with exponential growth.
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Omaba, McSylvester E. "Some properties of a class of stochastic heat equations." Thesis, Loughborough University, 2014. https://dspace.lboro.ac.uk/2134/16338.
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We study stochastic heat equations of the forms $[\partial_t u-\sL u]\d t\d x=\lambda\int_\R\sigma(u,h)\tilde{N}(\d t,\d x,\d h),$ and $[\partial_t u-\sL u]\d t\d x=\lambda\int_{\R^d}\sigma(u,h)N(\d t,\d x,\d h)$. Here, $u(0,x)=u_0(x)$ is a non-random initial function, $N$ a Poisson random measure with its intensity $\d t\d x\nu(\d h)$ and $\nu(\d h)$ a L\'vy measure; $\tilde$ is the compensated Poisson random measure and $\sL$ a generator of a L\'{e}vy process. The function $\sigma:\R\rightarrow\R$ is Lipschitz continuous and $\lambda>0$ the noise level. The above discontinuous noise driven equations are not always easy to handle. They are discontinuous analogues of the equation introduced in \cite{Foondun} and also more general than those considered in \cite{Saint}. We do not only compare the growth moments of the two equations with each other but also compare them with growth moments of the class of equations studied in \cite{Foondun}. Some of our results are significant generalisations of those given in \cite{Saint} while the rest are completely new. Second and first growth moments properties and estimates were obtained under some linear growth conditions on $\sigma$. We also consider $\sL:=-(-\Delta)^{\alpha/2}$, the generator of $\alpha$-stable processes and use some explicit bounds on its corresponding fractional heat kernel to obtain more precise results. We also show that when the solutions satisfy some non-linear growth conditions on $\sigma$, the solutions cease to exist for both compensated and non-compensated noise terms for different conditions on the initial function $u_0(x)$. We consider also fractional heat equations of the form $ \partial_t u(t,x)=-(-\Delta)^{\alpha/2}u(t,x)+\lambda\sigma(u(t,x)\dot{F}(t,x),\,\, \text{for}\,\, x\in\R^d,\,t>0,\,\alpha\in(1,2),$ where $\dot{F}$ denotes the Gaussian coloured noise. Under suitable assumptions, we show that the second moment $\E|u(t,x)|^2$ of the solution grows exponentially with time. In particular we give an affirmative answer to the open problem posed in \cite{Conus3}: given $u_0$ a positive function on a set of positive measure, does $\sup_{x\in\R^d}\E|u(t,x)|^2$ grow exponentially with time? Consequently we give the precise growth rate with respect to the parameter $\lambda$.
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Rakesh, Arora. "Fine properties of solutions for quasi-linear elliptic and parabolic equations with non-local and non-standard growth." Thesis, Pau, 2020. http://www.theses.fr/2020PAUU3021.
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Dans cette thèse, nous étudions les propriétés fines des solutions d'équations elliptiques et paraboliques quasi-linéaires impliquant une croissance non locale et non standard. Nous nous sommes concentrés sur trois différents types d’équations aux dérivées partielles (EDP).Dans un premier temps, nous étudions les propriétés qualitatives des solutions faibles et fortes d’équations d'évolution comportant des termes à croissance non-standard. La motivation de l'étude de ces types d'équations réside dans la modélisation de caractéristiques anisotropes se produisant dans les modèles de fluides électro-rhéologiques, la restauration d'images, le processus de filtration dans les milieux complexes, les problèmes de stratigraphie ou encore les interactions biologiques hétérogènes. Dans cette étude, nous déterminons des conditions suffisantes sur les données initiales pour obtenir l'existence et l'unicité de solution forte. Nous établissons également la régularité de second ordre de la solution forte ainsi que des résultats optimaux d'intégrabilité à l’aide de nouvelles inégalités d'interpolation.Nous étudions en outre les propriétés des solutions faibles de problèmes doublement non-linéaires impliquant premièrement une classe d'opérateurs de type Leray-Lions et une non-linéarité dans la dérivée temporelle. Nous considérons les questions d'existence, d'unicité, de régularité ainsi que de comportement à l’infini des solutions faibles de ces problèmesDans une deuxième étude, nous considérons des systèmes de type Kirchhoff impliquant des opérateurs non-linéaires de type Choquard avec des poids singuliers. Cette classe de problèmes apparaît dans de nombreux phénomènes physiques comme la variation de longueur d’une corde tendue en vibration où le terme de Kirchhoff mesure le changement de tension ou encore la propagation d’ondes électromagnétiques dans le plasma. Motivé par les nombreuses applications physiques, nous étudions cette classe d’équations et nous établissons l'existence et des résultats de non-unicité pour des systèmes impliquant le n-Laplacien et des opérateurs polyharmoniques à l’aide d’inégalités de type Adams, Moser et Trudinger.Enfin, nous étudions des problèmes singuliers impliquant des opérateurs non-locaux comme le p-Laplacien fractionnaire. Nous établissons l'existence et la multiplicité des solutions classiques dans le cas du Laplacien fractionnaire impliquant une non-linéarité exponentielle en utilisant la théorie des bifurcations. Pour caractériser le comportement des grandes solutions, nous étudions en détail les singularités isolées pour l'équation elliptique semi-linéaire singulière. Nous obtenons la symétrie de la solution classique du problème Laplacien fractionnaire grâce à la méthode du plan mobile et d’un principe du maximum. Nous étudions également le problème de p-Laplacian fractionnaire non-linéaire impliquant une non-linéarité singulière et des poids singuliers. Nous montrons l'existence/ non-existence, l'unicité et la régularité holdérienne en exploitant le comportement des solutions proche du bord du domaine et par des méthodes d'approximationIn this thesis, we study the fine properties of solutions to quasilinear elliptic and parabolic equations involving non-local and non-standard growth. We focus on three different types of partial differential equations (PDEs).Firstly, we study the qualitative properties of weak and strong solutions of the evolution equations with non-standard growth. The importance of investigating these kinds of evolutions equations lies in modeling various anisotropic features that occur in electrorheological fluids models, image restoration, filtration process in complex media, stratigraphy problems, and heterogeneous biological interactions. We derive sufficient conditions on the initial data for the existence and uniqueness of a strong solution of the evolution equation with Dirichlet type boundary conditions. We establish the global higher integrability and second-order regularity of the strong solution via proving new interpolation inequalities. We also study the existence, uniqueness, regularity, and stabilization of the weak solution of Doubly nonlinear equation driven by a class of Leray-Lions type operators and non-monotone sub-homogeneous forcing terms. Secondly, we study the Kirchhoff equation and system involving different kinds of non-linear operators with exponential nonlinearity of the Choquard type and singular weights. These type of problems appears in many real-world phenomena starting from the study in the length of the string during the vibration of the stretched string, in the study of the propagation of electromagnetic waves in plasma, Bose-Einstein condensation and many more. Motivating from the abundant physical applications, we prove the existence and multiplicity results for the Kirchhoff equation and system with subcritical and critical exponential non-linearity, that arise out of several inequalities proved by Adams, Moser, and Trudinger. To deal with the system of Kirchhoff equations, we prove new Adams, Moser and Trudinger type inequalities in the Cartesian product of Sobolev spaces.Thirdly, we study the singular problems involving nonlocal operators. We show the existence and multiplicity for the classical solutions of Half Laplacian singular problem involving exponential nonlinearity via bifurcation theory. To characterize the behavior of large solutions, we further study isolated singularities for the singular semi linear elliptic equation. We show the symmetry and monotonicity properties of classical solution of fractional Laplacian problem using moving plane method and narrow maximum principle. We also study the nonlinear fractional Laplacian problem involving singular nonlinearity and singular weights. We prove the existence, uniqueness, non-existence, optimal Sobolev and Holder regularity results via exploiting the C^1,1 regularity of the boundary, barrier arguments and approximation method
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Pereira, Denilson da Silva. "Soluções nodais para problemas elípticos semilineares com crescimento crítico exponencial." Universidade Federal da Paraíba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/7449.
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In this work, we study existence, non-existence and multiplicity results of nodal solutions for the nonlinear Schrödinger equation (P) -u + V (x)u = f(u) in ; where is a smooth domain in R2 which is not necessarily bounded, f is a continuous function which has exponential critical growth and V is a continuous and nonnegative potential. In the first part, we prove the existence of least energy nodal solution in both cases, bounded and unbounded domain. Moreover, we also prove a nonexistence result of least energy nodal solution for the autonomous case in whole R2. In the second part, we establish multiplicity of multi-bump type nodal solutions. Finally, for V - 0, we prove a result of infinitely many nodal solutions on a ball. The main tools used are Variational methods, Lions's Lemma, Penalization methods and a process of anti-symmetric continuation.
Neste trabalho, estudamos resultados de existência, não existência e multiplicidade de soluções nodais para a equação de Schrödinger não-linear (P) -u + V (x)u = f(u) em ;onde é um domínio suave em R2 não necessariamente limitado, f é uma função que possui crescimento crítico exponencial e V é um potencial contínuo e não-negativo. Na primeira parte, mostramos a existência de soluções nodais de energia mínima em ambos os casos, domínio limitado e ilimitado. Mostramos ainda um resultado de não existência de solução nodal de energia mínima para o caso autônomo em todo o R2. Na segunda parte, estabelecemos a multiplicidade de soluções do tipo multi-bump nodal. Finalmente, para V - 0, mostramos um resultado de existência de infinitas soluções nodais em uma bola. As principais ferramentas utilizadas são Métodos Variacionais, Lema de Deformação, Lema de Lions, Método de penalização e um processo de continuação anti-simétrica.
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Hagemann, Philipp. "The exponential growth model : does theory confirm evidence?" Master's thesis, Instituto Superior de Economia e Gestão, 2016. http://hdl.handle.net/10400.5/12971.
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Mestrado em EconomiaA dissertação apresentada estuda as origens e o papel dos modelos de crescimento exponencial na teoria do crescimento. O modelo reavalia o conceito das taxas de crescimento constantes, ilustrando o último debate sobre crescimento a longo prazo e as alternativas correspondentes. Após a apresentação dos conceitos de crescimento unificados, uma análise empírica demonstra a capacidade da utilização de modelos de crescimento exponencial para contabilizar os dados do PIB per capita mundial ao longo de diferentes períodos. A dissertação mostra que o modelo exponencial é uma generalização valiosa para uma pequena amostra de países. Este demonstra ainda algumas limitações, assim que certos períodos sejam excedidos.
The presented dissertation studies the origins and role of exponential growth models in growth theory. It reassesses the concept of constant growth rates by illustrating the latest debate on long-run growth and corresponding alternatives. After the presentation of unified growth concepts, an empirical analysis demonstrates the usability of exponential growth models to count for global GDP per capita data over different periods. The dissertation shows that the exponential model is a valuable generalization for a few country samples. It further demonstrates strong limitations as soon as certain periods are exceeded.
info:eu-repo/semantics/publishedVersion
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SOAVE, NICOLA. "Variational and geometric methods for nonlinear differential equations." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2014. http://hdl.handle.net/10281/49889.
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This thesis is devoted to the study of several problems arising in the field of nonlinear analysis. The work is divided in two parts: the first one concerns existence of oscillating solutions, in a suitable sense, for some nonlinear ODEs and PDEs, while the second one regards the study of qualitative properties, such as monotonicity and symmetry, for solutions to some elliptic problems in unbounded domains. Although the topics faced in this work can appear far away one from the other, the techniques employed in different chapters share several common features. In the firts part, the variational structure of the considered problems plays an essential role, and in particular we obtain existence of oscillating solutions by means of non-standard versions of the Nehari's method and of the Seifert's broken geodesics argument. In the second part, classical tools of geometric analysis, such as the moving planes method and the application of Liouville-type theorems, are used to prove 1-dimensional symmetry of solutions in different situations.
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Fischer, Manfred M., and Philipp Piribauer. "Model uncertainty in matrix exponential spatial growth regression models." WU Vienna University of Economics and Business, 2013. http://epub.wu.ac.at/4013/1/wp158.pdf.
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This paper considers the problem of model uncertainty associated with variable selection and specification of the spatial weight matrix in spatial growth regression models in general and growth regression models based on the matrix exponential spatial specification in particular. A natural solution, supported by formal probabilistic reasoning, is the use of Bayesian model averaging which assigns probabilities on the model space and deals with model uncertainty by mixing over models, using the posterior model probabilities as weights. This paper proposes to adopt Bayesian information criterion model weights since they have computational advantages over fully Bayesian model weights. The approach is illustrated for both identifying model covariates and unveiling spatial structures present in pan-European growth data. (authors' abstract)Series: Department of Economics Working Paper Series
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Piribauer, Philipp, and Manfred M. Fischer. "Model uncertainty in matrix exponential spatial growth regression models." Wiley-Blackwell, 2015. http://dx.doi.org/10.1111/gean.12057.
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This paper considers the most important aspects of model uncertainty for spatial regression
models, namely the appropriate spatial weight matrix to be employed and the appropriate explanatory vari-
ables. We focus on the spatial Durbin model (SDM) specification in this study that nests most models used
in the regional growth literature, and develop a simple Bayesian model averaging approach that provides a
unified and formal treatment of these aspects of model uncertainty for SDM growth models. The approach
expands on the work by LeSage and Fischer (2008) by reducing the computational costs through the use
of Bayesian information criterion model weights and a matrix exponential specification of the SDM model.
The spatial Durbin matrix exponential model has theoretical and computational advantages over the spatial
autoregressive specification due to the ease of inversion, differentiation and integration of the matrix expo-
nential. In particular, the matrix exponential has a simple matrix determinant which vanishes for the case of
a spatial weight matrix with a trace of zero (LeSage and Pace 2007). This allows for a larger domain of spatial
growth regression models to be analysed with this approach, including models based on different classes of
spatial weight matrices. The working of the approach is illustrated for the case of 32 potential determinants
and three classes of spatial weight matrices (contiguity-based, k-nearest neighbor and distance-based spatial
weight matrices), using a dataset of income per capita growth for 273 European regions. (authors' abstract)
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Leuyacc, Yony Raúl Santaria. "On Hamiltonian elliptic systems with exponential growth in dimension two." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-02082017-150001/.
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In this work we study the existence of nontrivial weak solutions for some Hamiltonian elliptic systems in dimension two, involving a potential function and nonlinearities which possess maximal growth with respect to a critical curve (hyperbola). We consider four different cases. First, we study Hamiltonian systems in bounded domains with potential function identically zero. The second case deals with systems of equations on the whole space, the potential function is bounded from below for some positive constant and satisfies some integrability conditions, while the nonlinearities involve weight functions containing a singulatity at the origin. In the third case, we consider systems with coercivity potential functions and nonlinearities with weight functions which may have singularity at the origin or decay at infinity. In the last case, we study Hamiltonian systems, where the potential can be unbounded or can vanish at infinity. To establish the existence of solutions, we use variational methods combined with Trudinger-Moser type inequalities for Lorentz-Sobolev spaces and a finite-dimensional approximation.Neste trabalho estudamos a existência de soluções fracas não triviais para sistemas hamiltonianos do tipo elíptico, em dimensão dois, envolvendo uma função potencial e não linearidades tendo crescimento exponencial máximo com respeito a uma curva (hipérbole) crítica. Consideramos quatro casos diferentes. Primeiramente estudamos sistemas de equações em domínios limitados com potencial nulo. No segundo caso, consideramos sistemas de equações em domínio ilimitado, sendo a função potencial limitada inferiormente por alguma constante positiva e satisfazendo algumas de integrabilidade, enquanto as não linearidades contêm funções-peso tendo uma singularidade na origem. A classe seguinte envolve potenciais coercivos e não linearidades com funções peso que podem ter singularidade na origem ou decaimento no infinito. O quarto caso é dedicado ao estudo de sistemas em que o potencial pode ser ilimitado ou decair a zero no infinito. Para estabelecer a existência de soluções, utilizamos métodos variacionais combinados com desigualdades do tipo Trudinger-Moser em espaços de Lorentz-Sobolev e a técnica de aproximação em dimensão finita.
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Harden, Lisa A. Govil N. K. "On the growth of polynomials and entire functions of exponential type." Auburn, Ala., 2004. http://repo.lib.auburn.edu/EtdRoot/2004/FALL/Mathematics/Thesis/hardeli_58_Thesis.pdf.
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Ferrante, Cristian. "Cosmological and static spherically symmetric solutions to Einstein equations with an exponential scalar potential." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2022. http://amslaurea.unibo.it/25606/.
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Exponential potentials can be associated both with expanding and collapsing cos- mologies: whereas power-law inflation can be obtained for a nearly flat exponential potential, a stable contracting cosmology (which, by the way, can solve the hori- zon problem) can be obtained for a negative sufficiently steep exponential potential. Motivated by these results, we study the Einstein equation for a scalar field with an exponential potential in a static and spherically symmetric spacetime. For the same parameters which describe a stable contracting cosmology, we find a non- asymptotically flat black hole and we study its properties.
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Alqahtani, Aisha M. "Exponential time differencing methods and asymptotic behaviour of solutions of problems in ground water flow." Thesis, Heriot-Watt University, 2015. http://hdl.handle.net/10399/2881.
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We start this thesis with a numerical study of the convergence of the exponential time differencing (ETD) schemes and the semi-implicit Euler method for the Allen-Cahn equation and a reaction-convection-diffusion equation and also compare the accuracy and efficiency of these methods. Next, we solve the nonlinear convection-diffusion (green roof) model numerically using the ETD method and central difference approximation. This numerical solution is investigated for three different initial values for the saturation. Finally, we study travelling wave solutions and self-similar solutions for the green roof, in particular, for the two limiting cases of being close to a saturated region and a dry region. Travelling waves, in the form of fronts, are found for most realistic limiting values of saturation; travelling waves are also investigated for some limiting versions of the model. Self-similar solutions, valid for high or for low saturations, are additionally investigated.
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Cyr, David Robert. "Bubble growth behavior in supersaturated liquid solutions." Fogler Library, University of Maine, 2001. http://www.library.umaine.edu/theses/pdf/CyrDR2001.pdf.
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Lin, Qun. "The well-posedness and solutions of Boussinesq-type equations." Thesis, Curtin University, 2009. http://hdl.handle.net/20.500.11937/2247.
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We develop well-posedness theory and analytical and numerical solution techniques for Boussinesq-type equations. Firstly, we consider the Cauchy problem for a generalized Boussinesq equation. We show that under suitable conditions, a global solution for this problem exists. In addition, we derive sufficient conditions for solution blow-up in finite time.Secondly, a generalized Jacobi/exponential expansion method for finding exact solutions of non-linear partial differential equations is discussed. We use the proposed expansion method to construct many new, previously undiscovered exact solutions for the Boussinesq and modified Korteweg-de Vries equations. We also apply it to the shallow water long wave approximate equations. New solutions are deduced for this system of partial differential equations.Finally, we develop and validate a numerical procedure for solving a class of initial boundary value problems for the improved Boussinesq equation. The finite element method with linear B-spline basis functions is used to discretize the equation in space and derive a second order system involving only ordinary derivatives. It is shown that the coefficient matrix for the second order term in this system is invertible. Consequently, for the first time, the initial boundary value problem can be reduced to an explicit initial value problem, which can be solved using many accurate numerical methods. Various examples are presented to validate this technique and demonstrate its capacity to simulate wave splitting, wave interaction and blow-up behavior.
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MOTHEY, DEEPA. "EFFECT OF MUCIN ON EXPONENTIAL GROWTH, STATIONARY PHASE SURVIVAL AND BIOFILM FORMATION IN STREPTOCOCCUS MUTANS." Diss., Temple University Libraries, 2012. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/184609.
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Microbiology and ImmunologyPh.D.
Streptococcus mutans is a member of the dental plaque and is the principal causative agent of dental caries. It can metabolize a wide array of sugars which results in the production of acid that causes demineralization of the tooth surface. S. mutans can also persist for extended periods of starvation, which may occur in different niches within the oral cavity. Previous studies have shown that mucin prolonged the survival of S. mutans in batch cultures and biofilms. Our laboratory has shown that the pyruvate dehydrogenase (pdh) operon is upregulated in stationary phase and is important for prolonged survival during nutrient starvation in chemically defined medium (CDM). In this study, I found that mucin enabled S. mutans to grow in a minimal chemically defined medium (MCDM) containing glucose and lacking all amino acids. A pdh mutant was found to be impaired in survival in CDM or MCDM supplemented with mucin. Additionally, I have shown that a galactose utilization mutant was impaired in survival in CDM with mucin and no exogenous glucose; galactose is the most abundant utilizable sugar residue in mucin. Mucin, supplemented in minimal medium with sucrose, also enabled S. mutans to form biofilms. Survival of the biofilms was pdh independent. Although biofilm formation was not seen in the absence of sucrose, cells did adhere to the glass coverslip; their survival was found to be pdh dependent. Using a previously constructed reporter strain, pdh expression was observed in a majority of cells in this condition. The expression of the pdh operon was also monitored in batch cultures. The starting inoculum size affected the percentage of fluorescent cells and the outcome of survival in media (CDM or MCDM) supplemented with mucin and no sugar. Greater than 50% of the stationary phase population expressed pdh in CDM with galactose. Less than 1% expressed pdh in CDM with glucose. However, galactose was unable to prolong survival of S. mutans in batch cultures in contrast to the effect of mucin. These results show that mucin may have a metabolic role in promoting long term survival of S. mutans. However it is possible that different components of mucin can be utilized in different conditions.
Temple University--Theses
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Lin, Qun. "The well-posedness and solutions of Boussinesq-type equations." Curtin University of Technology, Department of Mathematics and Statistics, 2009. http://espace.library.curtin.edu.au:80/R/?func=dbin-jump-full&object_id=129030.
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We develop well-posedness theory and analytical and numerical solution techniques for Boussinesq-type equations. Firstly, we consider the Cauchy problem for a generalized Boussinesq equation. We show that under suitable conditions, a global solution for this problem exists. In addition, we derive sufficient conditions for solution blow-up in finite time.Secondly, a generalized Jacobi/exponential expansion method for finding exact solutions of non-linear partial differential equations is discussed. We use the proposed expansion method to construct many new, previously undiscovered exact solutions for the Boussinesq and modified Korteweg-de Vries equations. We also apply it to the shallow water long wave approximate equations. New solutions are deduced for this system of partial differential equations.
Finally, we develop and validate a numerical procedure for solving a class of initial boundary value problems for the improved Boussinesq equation. The finite element method with linear B-spline basis functions is used to discretize the equation in space and derive a second order system involving only ordinary derivatives. It is shown that the coefficient matrix for the second order term in this system is invertible. Consequently, for the first time, the initial boundary value problem can be reduced to an explicit initial value problem, which can be solved using many accurate numerical methods. Various examples are presented to validate this technique and demonstrate its capacity to simulate wave splitting, wave interaction and blow-up behavior.
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Yu, Dong-Sheng. "Asymptotic solutions of dendritic crystal growth in external flow." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ64702.pdf.
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Yu, Dong-Sheng 1963. "Asymptotic solutions of dendritic crystal growth in external flow." Thesis, McGill University, 1999. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=36740.
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The present thesis is concerned with the effect of external fluid flow on steady axisymmetric dendrtic growth from a undercooled pure melt with zero surface tension. We consider two limiting cases: (1) the weak flow case, where the velocity of the forced external floe is much less than dendrite tip growth velocity; (2) the strong flow case, where the velocity of the forced external flow is much larger than dendrite tip growth velocity, and obtain uniformly valid asymptotic expansion solutions in terms of the generalized Laguerre series representation. For the case of weak external flow, we have a regular perturbation problem. The solution is obtained by using the regular perturbation expansion method. For the case of strong external flow, we have a singular boundary problem. The solution is found by using matched asymptotic expansion technique.
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Hodgson, Ian. "Growth, inhibition and pathogenicity of microorganisms in enteral nutrient solutions." Thesis, Open University, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.287009.
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Pötschke, Markus. "Simulation of electric field-assisted nanowire growth from aqueous solutions." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-194735.
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The present work is aimed at investigating the mechanisms of nanowire growth from aqueous solutions through a physical and chemical modeling. Based on this modeling, deriving an optimized process control is intended. The work considers two methods of nanowire growth. The first is the dielectrophoretic nanowire assembly from neutral molecules or metal clusters. Secondly, in the directed electrochemical nanowire assembly metal-containing ions are reduced in an AC electric field in the vicinity of the nanowire tip and afterwards deposited at the nanowire surface. To describe the transport and growth processes, continuum models are employed. Furthermore, it has been necessary to consider electro-kinetic fluid flows to match the experimental observations. The occurring partial differential equations are solved numerically by means of finite element method (FEM). The effect of the process parameters on the nanowire growth are analyzed by comparing experimental results to a parameter study. The evaluation has yielded that an AC electro-osmotic fluid flow has a major influence on the dielectrophoretic nanowire assembly regarding the growth velocity and morphology. In the case of directed electrochemical nanowire assembly, the nanowire morphology can be controlled by the applied AC signal shape. Based on the nanowire growth model, an optimized AC signal has been designed, whose parametrization allows to adjust to the chemical precursor and the desired nanowire diameterZiel der vorliegenden Arbeit ist es, mittels physikalischer und chemischer Modelle die Mechanismen des Nanodrahtwachstums aus wässrigen Lösungen zu erforschen und daraus eine optimierte Prozesskontrolle abzuleiten. Dabei werden zwei Verfahren des Nanodrahtwachstums näher betrachtet: Dies sind die dielektrophoretische Assemblierung von neutralen Molekülen oder Metallclustern sowie die gerichtete elektrochemische Nanodrahtabscheidung (engl. directed electrochemical nanowire assembly), bei der metallhaltige Ionen im elektrischen Wechselfeld an der Nanodrahtspitze zunächst reduziert und anschließend als Metallatome abgeschieden werden. Zur Beschreibung der Transport- und Wachstumsprozesse werden Kontinuumsmodelle eingesetzt. Darüber hinaus hat es sich als notwendig erwiesen, elektrokinetische Fluidströmungen zu berücksichtigen, um die experimentellen Beobachtungen zu reproduzieren. Die auftretenden partiellen Differenzialgleichungen werden mittels der Finiten Elemente Methode (FEM) numerisch gelöst. Die Auswirkungen der Prozessparameter auf das Nanodrahtwachstum werden durch den Vergleich von experimentellen Ergebnissen mit Parameterstudien analysiert. Die Auswertung hat ergeben, dass für das dielektrophoretische Wachstum ein durch Wechselfeldelektroosmose (engl. AC electro-osmosis) angetriebener Fluidstrom die Drahtwachstumsgeschwindigkeit und -morphologie maßgeblich beeinflusst. Im Falle der gerichteten elektrochemischen Nanodrahtabscheidung lässt sich die Drahtmorphologie über das angelegte elektrische Wechselsignal steuern. Unter Verwendung des Wachstumsmodells ist ein optimiertes Signal generiert worden, dessen Parametrisierung eine gezielte Anpassung auf den chemischen Ausgangsstoff und den gewünschten Drahtdurchmesser erlaubt
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Seaman, Callie. "Investigation of nutrient solutions for the hydroponic growth of plants." Thesis, Sheffield Hallam University, 2017. http://shura.shu.ac.uk/18141/.
Full textAbstract:
Hydroponics is used extensively in food production and plant research, allowing optimal control over the supply of elements to the plant. In hydroponics, nutrient can be delivered via a solution that is supplied to the growing plant or as a seed coat or treatment that is applied to the seed before sowing and germination. The form in which the nutrients are supplied to the plant influences their bioavailability, up-take, and distribution within the plant. Commercially produced hydroponic nutrients are typically supplied as two separate concentrated solutions. If these are mixed before being diluted then precipitates are formed which limit the bioavailability of certain elements in the nutrient solution. The chemical nature of the precipitate has been investigated by XRD, XRF, ion-chromatography and IR and Raman spectroscopies, with the aim of understanding its composition. Mass spectrometry is a highly sensitive analytical technique which has been applied to the monitoring of uptake and distribution of elements and compounds in plant tissue. Techniques including MALDI-MS, LA-ICP-MS and HPLC-ICP-MS have been utilized in the work presented here to demonstrate the distribution and accumulation of elements and compounds within plant material that has been grown hydroponically. The use of a zinc based seed coating as a nutrient source for barley seeds in a hydroponic fodder production system has been investigated. The effect of the zinc on the yield and dry mass of the fodder was determined. The total zinc content in the fodder has been determined using ICP mass spectrometry. A method to map the location and distribution of zinc and other metallic elements in seeds and the fodder plants using Laser-Ablation ICP Mass Spectrometry LA-ICP-MS has been developed. Selenium is an essential element for human health. Broccoli is known to be a hyper-accumulator of selenium and the use of selenium-containing hydroponic nutrients for the biofortification of broccoli with selenium is presented. Laser-Ablation ICP Mass Spectrometry LA-ICP-MS has been used to monitor the accumulation and distribution of selenium in the broccoli plants. Imaging MALDI-MS has allowed the demonstration of the nitrogen cycle in plants and to show pictorially that atoms and molecules from dead plants are incorporated into new life. Radish plants were grown hydroponically using a nutrient solution system containing isotopically-enriched nitrogen-15 KNO3 (98% labelled) as the only source of nitrogen. Plants were cropped and left to ferment in water for 2 weeks to create a radish "tea", which was used as a source of nitrogen for radish grown in a second hydroponics experiment. After 5 weeks of growth, the radish plants were harvested and cryosectioned, and sections were imaged by positive-ion MALDI imaging. The presence of labelled species in the plants grown using 15N KNO3 as nutrient and those grown from the radish "tea" was readily discernible. The uptake of 15N into several identifiable metabolites has been studied by MALDI-MS imaging.
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Campbell, Joseph Patrick. "Toward Macromolecular Shape And Size Control: Novel Enantioselective Nitrations And Iterative Exponential Growth Methods For Polymer Synthesis." ScholarWorks @ UVM, 2019. https://scholarworks.uvm.edu/graddis/1090.
Full textAbstract:
Chirality is a key principle in organic chemistry. All chiral compounds are non-superimposable mirror images of each other and therefore lack an improper axis of rotation (Sn). These mirror images often have identical properties in an achiral environment, however when two chiral molecules interact, they produce different shapes and properties. Nature, to this extent takes advantage of this aspect through unique formation of shape defined biological macromolecules that are tailored to carry out various life processes. This level of shape control is only made possible because of natural chiral monomers such as amino acids or glycosides that make up such macromolecules. Under new methods such as Chirality Assisted Synthesis (CAS), shape and size-controlled polymers and macromolecules can be realized through the use of chiral monomers to make well defined macromolecules. Because chirality dictates shape, and shape defines function in reference to macromolecules, controlling the chirality of monomers, while concurrently dictating shape and size can lead to the potential of biomimetic methodologies and cage like structures.
Accessing shape defined monomers can be difficult especially when in reference to chiral compounds. The unique structure of enantiopure tribenzotriquinacenes show promise in the formation of well-defined cage like structures through utilization of CAS methodology. Synthesis of functionalized tribenzotriquinacenes along with development of an enantioselective electrophilic aromatic nitration method was attempted. Further exploration into the effectiveness of through-space enantioselective nitrations found a dependence on solvent temperature, and the auxiliary that is used. Synthetic difficulties, results, modifications and processes toward a generalized method are presented herein.
In addition, controlling the size of polymers has always been a difficult synthetic challenge. Overall selectivity toward one product over another is determined via a variety of chemical properties. However, the formation of sequence and size defined polymers are a prominent aspect of natural polymers. The size selective synthesis, of unique ABAB sequenced polymers was attempted using an iterative exponential growth method. The ability to scale up these processes and create monodisperse oligoethers is also presented and described herein.
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Jemtå, Emilia, and Björklund Matilda Kvist. "Values over value? : Pension beneficiaries' willingness to pay for socially responsible investments and their perception of exponential growth." Thesis, Jönköping University, Internationella Handelshögskolan, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:hj:diva-52610.
Full textAbstract:
Background: As more individuals continuously become more conscious of the external influences of their decisions, integrating social and ethical criteria and perceived non-monetary value in their investment decisions, the interest in socially responsible investments (SRI) has escalated in the past decade. Reflecting this shift, the Swedish Pension Agency continuously increases the requirements and sustainability demands for the funds available in the premium pension selection. To investigate the underlying variables affecting the decision to invest socially responsibly, the authors of this thesis studied Swedish pension beneficiaries’ demographics, attitudes and beliefs. Purpose: The purpose of this thesis is to examine the socio-demographic and psychological determinants of pension beneficiaries' and the influence of these variables on the willingness to pay for socially responsible investments. The study will additionally explore the tendency to underestimate exponential growth in one’s pension savings. Method: The study is conducted by collecting primary data in the form of quantitative research through an online questionnaire. Based on previous research, six hypotheses are developed. This in order to investigate the relationship between willingness to pay for socially responsible investments and several socio-demographic and psychographic variables. Additionally, to examine Swedish pension beneficiaries’ tendency to underestimate exponential growth. The data collected is analysed through a multiple linear regression model and other descriptive statistics to examine if the hypotheses are rejected or not. Conclusion: The majority of the subjects in the study are willing to pay for SRI. Gender significantly impacts the willingness to pay for SRI, as men demonstrate a lower willingness to pay than women. Furthermore, altruistic values, concern for one’s pension savings, concern for ESG-related issues (environmental, social and governance) and perceived consumer effectiveness proves to have a significant impact on the willingness to pay for SRI. Further, the sample demonstrated a definite tendency to underestimate exponential growth.
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Soler, Bru Laia. "Liquid-assisted ultrafast growth of superconducting films derived from chemical solutions." Doctoral thesis, Universitat Autònoma de Barcelona, 2019. http://hdl.handle.net/10803/667208.
Full textAbstract:
L'ús generalitzat de superconductors d'alta temperatura (HTS) en aplicacions a gran escala està, en part, encara limitat per l’elevat cost de fabricació de cintes recobertes (CCs). Amb la intenció d'aconseguir un avanç important per assolir un major rendiment, en aquesta tesi hem desenvolupat una tècnica innovadora que combina els beneficis de Deposició de Solucions Químiques (CSD) a baix cost amb les altes velocitats del creixement cristal·lí a partir de fases líquides. Es basa en la formació d'un líquid transitori derivat de solucions de carboxilats, aprofitant els obstacles cinètics per la cristal·lització de la fase d'equilibri.
En aquesta tesi doctoral, primer expliquem els fonaments del procés que condueix a la cristal·lització de YBa2Cu3O7-δ assistida per un líquid transitori; i després portem a terme una investigació detallada sobre aquesta tècnica. El "proof-of-principle" de la viabilitat d'aquesta nova aproximació es va aconseguir amb la disponibilitat dels forns tipus RTA que permeten rampes fins a 80ºC/s.
Les reaccions implicades en el procés s'observen amb mesures in situ i de microscòpia, entre altres. Primer, la piròlisi resultant de la barreja de propionats de Ba, Cu i Y a baixes temperatures (500ºC) és observada amb espectroscòpia in situ d’infraroig. A continuació, s’utilitza difracció de rajos-X amb llum de sincrotró per revelar les reaccions que tenen lloc per convertir el BaCO3, CuO i Y2O3 en la fase final, així com analitzar la nucleació i el creixement del YBa2Cu3O7-δ des del líquid transitori (TLAG).
Per dur a terme el procés, el pas de deposició es realitza amb mètodes d'impressió d'injecció de tinta o revestiment per rotació. Les característiques de les solucions s'han adaptat a la tècnica de deposició i es correlacionen amb la morfologia de la capa resultant.
A continuació s'han investigat diversos paràmetres per controlar la velocitat de la reacció limitant per l'eliminació del carbonat de bari amb l’objectiu d’evitar la retenció de carboni a les capes gruixudes epitaxials.
Posteriorment, s'estableixen els conceptes bàsics per a la comprensió dels mecanismes de nucleació i creixement del YBCO a partir de TLAG. Amb l'objectiu d'obtenir capes epitaxials de YBCO orientades en l’eix-c, es presenten diverses estratègies per controlar la força de cristal·lització. Els paràmetres rellevants són: la composició de la solució, la pressió d'oxigen, les rampes d’escalfament i les temperatures de creixement. Finalment, les condicions de cristal·lització es correlacionen amb les microestructures i propietats superconductores de les capes resultants.
Es presenten dos camins diferents per dur a terme el creixement mitjançant la formació de líquid. Un és a través d’un augment de temperatura a pressió d'oxígen constant (ruta-Temperatura). L’altre procés consisteix en dos passos (ruta-pO2). Per aquest últim, l'eliminació de BaCO3 es desvincula del creixement de YBCO mitjançant un salt en pO2.
Cal abordar diversos reptes en funció de la ruta. Alguns d’ells són: la reactivitat del líquid amb els substrats degut a la seva naturalesa altament corrosiva, o una mullabilitat inadequada.
Finalment, hem tingut èxit en obtenir pel·lícules fines de YBCO epitaxials d’entre 90-500 nm amb propietats superconductores molt elevades (Tc 90-92K, Jc fins a 5MA/cm2 a 77K), i velocitats de creixement fins a 100 nm/s, augmentat així en un factor 100 la velocitat de creixement de la metodologia de CSD convencional. Aquesta metodologia podria ser traslladada a altres materials.The widespread use of High Temperature Superconductors (HTS) into large scale applications is, in part, still limited by the high costs of coated conductors manufacturing. Aiming for a breakthrough to achieve high throughput, in this thesis we have developed a novel technique that combines the low cost benefits of Chemical Solution Deposition (CSD) with the very high growth rates of crystallization from liquid phases. It relies on the formation of a transient liquid derived from carboxylate solutions, taking advantage of the kinetic hindrances on crystallization to reach the equilibrium phase. In this dissertation, we first explain the basics of the process that leads to YBa2Cu3O7-δ crystallization assisted by a transient liquid and then we elaborate on the results of our investigation about this technique. The “proof-of-principle” of this new approximation viability has been achieved with the use of rapid thermal annealing furnaces, allowing heating rates up to 80ºC/s. The reactions involved in the process are observed with in situ measurements and microscopic analyses, among others. First, the pyrolysis of the Ba, Cu and Y propionates mixture at low temperatures (500ºC) is observed with in situ infrared spectroscopy. Then, time resolved X-ray diffraction with synchrotron light is used to reveal the reaction paths to convert the resulting BaCO3, CuO and Y2O3 to the final phase, as well as nucleation and growth of the YBa2Cu3O7-δ film from the transient liquid. To do so, the deposition step is performed with spin coating or Ink Jet printing methodologies. The solutions characteristics have been adapted to the deposition technique and correlated to the resulting film morphology. Then, several parameters have been investigated to control the rate limiting BaCO3, elimination reaction in order to avoid carbon retention in the final thick epitaxial films. Afterwards, the basic concepts for understanding the nucleation and growth mechanisms of YBCO with TLAG are set. With the aim of obtaining c-axis epitaxial YBa2Cu3O7-δ films, several strategies are presented to control the driving force for crystallization. The relevant parameters are solution composition, oxygen pressure, heating ramps and growth temperatures. Finally, the crystallization conditions are correlated to the resulting films microstructure and superconducting performances. Two different paths are presented to reach TLAG. A direct temperature raise at constant oxygen pressure (Temperature-route), or a two step process (pO2-route). For the latter, BaCO3 elimination is disentangled from YBa2Cu3O7-δ growth by a jump on pO2. Additionally, several challenges needed to be addressed depending on the route: liquid reactivity with the substrates due to its highly corrosive nature or improper wettability, are some of them. Finally, we have succeeded in obtaining highly epitaxial YBCO thin films of 90-500nm with very high superconducting performances (Tc 90-92K, Jc up to 5MA/cm2 at self-field and 77K), at growth rates up to 100nm/s, increased by a factor 100 from those reported with conventional CSD. This methodology could be applied to other materials.
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Weeks, Mark E. "An investigation into the global cellular responses of Listeria monocytogenes during the transition from exponential to stationary growth phase." Thesis, University of Kent, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.268322.
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Queraltó, López Albert. "Growth of functional oxide heterostructures from chemical solutions using advanced processing methodologies." Doctoral thesis, Universitat Autònoma de Barcelona, 2015. http://hdl.handle.net/10803/286006.
Full textAbstract:
En aquesta tesi doctoral, hem explorat innovadores tècniques de processat basades en el dipòsit de solucions químiques per tal de produir heteroestructures d’òxids, mitjançant processos d’autoassemblatge i autoorganització. Essencialment, s’ha dut a terme una profunda investigació dels mecanismes termodinàmics i cinètics involucrats en la nucleació i cristal·lització de diferents heteroestructures d’òxids (nanoilles i capes primes) amb materials com CeO2, LaNiO3, Ba0.8Sr0.2TiO3 i La0.7Sr0.3MnO3 sobre substrats monocristal·lins (Y2O3:ZrO2, LaAlO3, SrTiO3) i tecnològics com silici o cintes metàl·liques recoberts amb capes d’òxids.
Tractaments tèrmics usant rampes d’escalfament ràpides (∼20 ºC/s) han permès separar la nucleació del creixement. En primer lloc, hem reportat que es possible aconseguir cristal·litzar, fins i tot epitaxialment, a baixes temperatures (<500 ºC). També hem determinat el paper que juguen diferents paràmetres de processat (temperatura, rampa d’escalfament i atmosfera), i el tipus i orientació del substrat en les velocitats de nucleació i creixement, com també en la morfologia final del sistema. Anàlisis termodinàmics indiquen que la tensió creada entre capa i substrat té una contribució important en la nucleació i creixement. A més, s’ha pogut veure que la situació de tensió del sistema està altament influenciada per les diferències en l’expansió tèrmica soferta entre capa i substrat.
També hem demostrat que el creixement dels grans segueix un comportament auto-limitat està en gran mesura influenciat per un procés de difusió atòmica activat tèrmicament. Curiosament, la transformació des de material policristal·lí a epitaxial segueix el mateix comportament, i està impulsat per una reducció en les frontes de gra policristal·lines. Les velocitats de creixement del procés (0.01-0.1 nm/s) depenen en gran mesura de com ràpid el material epitaxial creix respecte el policristal·lí. En aquest sentit, hem pogut calcular que els coeficients de difusió atòmica epitaxials són un ordre de magnitud més grans que els policristal·lins, 10-19 i 10-20 m2/s respectivament. S’ha determinat que el gruix de la capa pot influenciar negativament en la velocitat de creixement epitaxial, dificultant la obtenció de capes epitaxials a gruixos grans.
En la mateixa línea, hem implementat i utilizat una metodologia innovadora com és la irradiació làser en condicions atmosfèriques per al creixement d’heteroestructures d’òxids, com a alternativa als tractaments tèrmics. La influència dels mecanismes tèrmics fotoinduïts s’ha avaluat mitjançant simulacions numèriques, usant els paràmetres òptics i termofísics dels diferents materials. Així doncs, hem demostrat la capacitat d’assolir la descomposició de capes metal·lorgàniques precursores, en particular propionats de Ce-Zr, amb temps de processat significativament inferiors i amb resultats equivalents als tractaments tèrmics convencionals. El disseny de patrons micromètrics ha estat possible gràcies al confinament espacial del feix làser. Altrament, també s’ha aconseguit la cristal·lització epitaxial de capes d’òxids sobre substrats monocristal·lins i tecnològics després d’una optimització en les condicions experimentals (fluència, nombre de polsos, temperatura del substrat, etc). S’ha observat que aquest creixement epitaxial és significativament més ràpid comparat amb els tractaments tèrmics (poques mil·lèsimes de segon comparat amb desenes de minuts). La raó d’aquest creixement tant ràpid s’ha atribuït principalment a les temperatures més elevades assolides amb els tractaments làser que tenen una influència rellevant en la difusió atòmica. Tanmateix, hem proposat que altres fenòmens com els grans gradients tèrmics dins les capes (1010 ºC/m), com també efectes fotoquímics derivats del trencament directe dels enllaços químics pels fotons làser poden tenir també una contribució important. Finalment, hem vist que les propietats funcionals de les capes crescudes amb làser són bastant similars a aquelles obtingudes amb tractaments tèrmics.
Les diferents metodologies de creixement combinades amb tècniques de caracterització avançades (microscòpies de força atòmica i electròniques, difracció de raig X, espectroscòpies infraroja-visible-ultravioleta, el·lipsometria) han permès aquest detallat estudi i una millor comprensió dels mecanismes de nucleació i creixement de heteroestructures d’òxids a partir del dipòsit de solucions químiques. Les metodologies i anàlisis desenvolupats han estat fonamentals per al desenvolupament d’aquesta tesi i el seu ús pot ésser traslladat a altres sistemes.In this thesis, we have explored innovative processing methodologies based on the deposition of chemical solutions to produce oxide heterostructures through self-assembling and self-organization processes. Essentially, we performed an in-depth investigation of the thermodynamic and kinetic mechanisms involved in nucleation and crystallization of different oxide heterostructures (nanoislands and thin-films) involving doped-CeO2, LaNiO3, Ba0.8Sr0.2TiO3 and La0.7Sr0.3MnO3 on single crystals (Y2O3:ZrO2 (YSZ), LaAlO3, SrTiO3) and technical substrates like silicon wafers or oxide-buffered stainless steel metallic tapes. Rapid Thermal Annealing (RTA) furnaces were successfully employed to separate nucleation and coarsening through the use of very fast heating ramps (∼20 ºC/s). First of all, we reported that crystallization and even epitaxial growth can be achieved at very low temperatures (<500 ºC). We also determined the role of the different processing parameters (temperature, heating ramp and atmosphere), substrate type and orientation on nucleation and growth rates of nanoislands and films, and the final morphology. Thermodynamic analyses indicated that strain has an important contribution in nucleation, as well as the final morphology of the system. The strain state of the different heterostructures was found to strongly depend on thermal expansion coefficients of film and substrate. We also demonstrated that grain coarsening follows a self-limited behavior, and it is highly influenced by a thermally-activated atomic diffusion. Interestingly, we also determined that the transformation from random to epitaxially-oriented material follows the same growth behavior, and it is driven by the reduction of polycrystalline grain boundaries. The growth rate of the process (0.01-0.1 nm/s) highly depends on how fast the epitaxial material grows as compared to the coarsening of polycrystalline grains. We calculated that the epitaxial atomic diffusion coefficients are one order of magnitude larger than polycrystalline coefficients, 10-19 and 10-20 m2/s, respectively. Additionally, we determined that the epitaxial growth rate depends on precursor layer thickness, and this might be a drawback for reaching high epitaxial thick films. A very new strategy such as Pulsed Laser Annealing at atmospheric conditions has been implemented and employed as an alternative to thermal treatments for the growth of oxide heterostructures. The influence of photo-induced thermal mechanisms has been evaluated through numerical simulations, employing optical and thermo-physical properties of different materials. We have demonstrated the capability to achieve decomposition of CSD precursor films with shorter processing times than in thermal treatments with equivalent results, particularly for the case of Ce-Zr propionates. The spatially-confined nature of the laser beam has also permitted to design micrometric patterned structures. Epitaxial crystallization of oxide films has also been achieved on single crystal and technical substrates after optimization of experimental conditions (fluence, number of pulses, substrate temperature, etc). A significantly faster epitaxial growth compared to thermal treatments has been achieved, i.e. few milliseconds vs tens of minutes. This rapid growth is mostly caused by the higher temperatures developed by laser annealing and influencing atomic diffusion. Additionally, we proposed that other mechanisms should be considered such as temperature gradients developed inside films (1010 ºC/m), as well as photochemical effects caused by direct bond dissociation by the laser photons. The functional properties of laser-grown films have been evaluated and compared with equivalent samples produced using thermal treatments, showing quite similar results. The different growth methodologies employed combined with advanced characterization techniques (atomic force and scanning transmission electron microscopies, advanced x-ray diffraction measurements, infrared-visible-ultraviolet spectroscopies, ellipsometry) allowed me to perform the profound study undertaken and provided us with a better understanding of nucleation and growth mechanisms of oxide heterostructures from chemical solution deposition. The methodologies and analyses developed have been fundamental for the development of this thesis and their application can be made extensive to other systems.
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Ali, Zakaria Idriss. "Stochastic quasilinear parabolic equations with non standard growth : weak and strong solutions." Thesis, University of Pretoria, 2015. http://hdl.handle.net/2263/53502.
Full textAbstract:
This thesis consists of two main parts.
The rst part concerns the existence of weak probabilistic solutions (called elsewhere
martingale solutions) for a stochastic quasilinear parabolic equation of generalized
polytropic ltration, characterized by the presence of a nonlinear elliptic part admitting
nonstandard growth.
The deterministic version of the equation was rst introduced and studied by Samokhin
in [178] as a generalized model for polytropic ltration. Our objective is to investigate
the corresponding stochastic counterpart in the functional setting of generalized
Lebesgue and Sobolev spaces. We establish an existence result of weak probabilistic
solutions when the forcing terms do not satisfy Lipschitz conditions and the noise
involves cylindrical Wiener processes.
The second part is devoted to the existence and uniqueness results for a class of
strongly nonlinear stochastic parabolic partial di erential equations.
This part aims to treat an important class of higher-order stochastic quasilinear
parabolic equations involving unbounded perturbation of zeroth order. The deterministic
case was studied by Brezis and Browder (Proc. Natl. Acad. Sci. USA,
76(1): 38-40, 1979). Our main goal is to provide a detailed study of the corresponding
stochastic problem. We establish the existence of a probabilistic weak solution
and a unique strong probabilistic solution. The main tools used in this part of the
thesis are a regularization through a truncation procedure which enables us to adapt
the work of Krylov and Rozosvkii (Journal of Soviet Mathematics, 14: 1233-1277,
1981), combined with analytic and probabilistic compactness results (Prokhorov and
Skorokhod Theorems), the theory of pseudomonotone operators, and a Banach space
version of Yamada-Watanabe's theorem due to R ockner, Schmuland and Zhang.
The study undertaken in this thesis is in some sense pioneering since both classes
of stochastic partial di erential equations have not been the object of previous investigation,
to the best of our knowledge.
The results obtained are therefore original and constitute in our view signi cant
contribution to the nonlinear theory of stochastic parabolic equations.Thesis (PhD)--University of Pretoria, 2015.
Mathematics and Applied Mathematics
PhD
Unrestricted
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FREY, BIRGIT Y. "Crescimento de cristais de KHsub2POsub4 por metodos a partir de solucao aquosa." reponame:Repositório Institucional do IPEN, 1991. http://repositorio.ipen.br:8080/xmlui/handle/123456789/10262.
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Made available in DSpace on 2014-10-09T12:36:40Z (GMT). No. of bitstreams: 0Made available in DSpace on 2014-10-09T13:59:09Z (GMT). No. of bitstreams: 1 04225.pdf: 3657624 bytes, checksum: 1c1f3312aa7ca8c7b185e9209815c228 (MD5)
Dissertacao (Mestrado)
IPEN/D
Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP
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Jiang, Yivan. "The synthesis of unimolecular polymers through iterative exponential growth and their applications in block copolymer phase segregation and biological systems." Thesis, Massachusetts Institute of Technology, 2019. https://hdl.handle.net/1721.1/123073.
Full textAbstract:
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Chemistry, 2019Cataloged from PDF version of thesis.
Includes bibliographical references.
Absolute structural control over polymers - in terms of sequence, length, and stereochemistry - is a Holy Grail of polymer science. Inspired by Nature, polymer chemists over the last century have sought new methods and strategies to control these parameters. An inverse relationship exists, however, between the ability to control the primary structure of a macromolecule and the ability to scale the production of the same macromolecule. In this thesis, we describe the application of iterative exponential growth (IEG) toward the scalable synthesis of sequence-defined, unimolecular, chiral polymers. Using this strategy, we have created a wide array of functional molecularly precise polymers of up to 12.1k kDa in molar mass with various side chains for applications in block copolymer phase segregation, lectin binding, and nanoparticle formulations.
by Yivan Jiang.
Ph. D.
Ph.D. Massachusetts Institute of Technology, Department of Chemistry
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Hilton, Anne Marie. "The formation and growth of COâ†2 gas bubbles from supersaturated aqueous solutions." Thesis, University of Nottingham, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.334502.
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Valentini, Francesca <1990>. "Growth of high-tech Born Global startups: US market entry challenges and solutions." Master's Degree Thesis, Università Ca' Foscari Venezia, 2014. http://hdl.handle.net/10579/5246.
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Over the course of the last 20 years, the world has seen a rising number of small and medium enterprises accelerating their internationalization process and becoming global players from their early days, basically from inception. These firms enter many different new markets simultaneously and incur in entry challenges that larger and established firms don’t face when internationalizing. Few qualitative research has been done on Born global firms’ life cycle associated with internationalization challenges and solutions. However it permitted the creation of an hypothetical general market entry challenges framework. This study aims to identify early-establishment internationalization challenges and possible solutions that international Internet-based high-tech startups face entering the US market. To analyze in depth this topic, in collaboration with FireMatter LLC, a Silicon Valley business development services firm, we created “FireMatter Views 2014” global online survey. Our findings show that internationalization challenges of international Internet-based born global startups fit the general pattern proposed from the analysis of previous research. Managing sales opportunities from afar, lacking of US funding and partners are the top challenges, while seeking funding, partners and transferring the team to the US are the top solutions implemented. However results also show that high costs and product localization and/or adaptation are important obstacles to US market entry, adding new issues to the general framework. This research is of great interest for the different Governments, various institutions and public and private associations or firms, as well as incubators/accelerators and future entrepreneurs.
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Valente, Maria Serra. "Stability of non-trivial solutions of stochastic differential equations driven by the fractional Brownian motion." Master's thesis, Instituto Superior de Economia e Gestão, 2019. http://hdl.handle.net/10400.5/18993.
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Mestrado em Mathematical FinanceO objectivo desta dissertação é o de generalizar um resultado sobre a estabilidade exponencial de soluções triviais de equações diferenciais estocásticas com movimento Browniano fraccionário, desenvolvido por Garrido-Atienza et al., para soluções não-triviais. São apresentadas noções de cálculo fraccionário, assim como a definição e principias propriedades do movimento Browniano fraccionário. De seguida, um framework para equações diferenciais estocásticas com movimento Browniano fraccionário é definido juntamente com resultados de existência e unicidade de soluções. O resultado, original desta dissertação, é aplicado a um modelo Vasicek fraccionário de taxas de juro.
This dissertation aims to generalize a result on the exponential stability of trivial solutions of stochastic differential equations driven by the fractional Brownian motion by Garrido-Atienza et al. to non-trivial solutions in the scalar case. Notions on fractional calculus are presented, as well as the definition and main properties of the fractional Brownian motion. Subsequently the framework for SDEs driven by fractional Brownian motion with a pathwise approach is characterized along with some existence and uniqueness results. The result on stability is then applied to the fractional Vasicek model for interest rates.
info:eu-repo/semantics/publishedVersion
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Thomas, Sydney. "Measurement and modelling of long chain branching in chain growth polymerization." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0001/NQ42769.pdf.
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Sun, Yuhua [Verfasser]. "Volume growth and uniqueness of nonnegative solutions of differential inequalities on manifolds / Yuhua Sun." Bielefeld : Universitätsbibliothek Bielefeld, 2014. http://d-nb.info/1054135061/34.
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Nana, Sandjo Albert [Verfasser]. "Solutions for fourth-order parabolic equation modeling epitaxial thin film growth / Albert Nana Sandjo." Aachen : Hochschulbibliothek der Rheinisch-Westfälischen Technischen Hochschule Aachen, 2012. http://d-nb.info/1025882253/34.
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Sohinger, Vedran. "Bounds on the growth of high Sobolev norms of solutions to nonlinear Schrödinger equations." Thesis, Massachusetts Institute of Technology, 2011. http://hdl.handle.net/1721.1/67815.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.Cataloged from PDF version of thesis.
Includes bibliographical references (p. 265-273).
In this thesis, we study the growth of Sobolev norms of global solutions of solutions to nonlinear Schrödinger type equations which we can't bound from above by energy conservation. The growth of such norms gives a quantitative estimate on the low-to high frequency cascade which can occur due to the nonlinear evolution. In our work, we present two possible frequency decomposition methods which allow us to obtain polynomial bounds on the high Sobolev norms of the solutions to the equations we are considering. The first method is a high regularity version of the I-method previously used by Colliander, Keel, Staffilani, Takaoka, and Tao and it allows us to treat a wide range of equations, including the power type NLS equation and the Hartree equation with sufficiently regular convolution potential, as well as the Gross-Pitaevskii equation for dipolar quantum gases in the physically relevant 3D setting. The other method is based on a rough cut-off in frequency and it allows us to bound the growth of fractional Sobolev norms of the completely integrable defocusing cubic NLS on the real line.
by Vedran Sohinger.
Ph.D.
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Kapembwa, Michael. "Heat and mass transfer effects of ice growth mechanisms in water and aqueous solutions." Master's thesis, University of Cape Town, 2013. http://hdl.handle.net/11427/11180.
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Includes bibliographical references.Research into ice crystallization processes is an important area of study. The desire to improve product quality and efficiency of processes involving ice crystallization in industries such as desalination by freezing, freeze drying, freeze concentration and freeze crystallization for food processing, requires insight into the ice growth mechanisms. More so, a novel technology called Eutectic Freeze Crystallization, where water is recovered in the form of ice, requires that ice crystals are of high purity as this directly determines the quality of the water obtained. During ice crystallization, ice growth mechanisms play an important role in determining the structure, size and morphology of ice which have an effect on separation processes and product purity. Heat and mass transfer play a fundamental role in ice growth processes as they affect the thermodynamics and kinetics of the crystallization process. Ice growth experiments were carried out in pure water, in 8.4 wt% and 16.8 wt% magnesium sulphate and in 8.4 wt% sodium nitrate using a 10x5x31 mm test cell made of Plexi-glass®. The Colour Schlieren optical technique was used to conduct the experiments. This is because of its capability to map refractive index gradients related to either temperature or/and concentration gradients of the solution during crystal growth.
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Bramley, Allan Sidney. "A study of the growth and aggregation of calcium oxalate monohydrate /." Title page, contents and summary only, 1994. http://web4.library.adelaide.edu.au/theses/09PH/09phb815.pdf.
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Wasson, Samantha Rae. "Increasing Introductory Biology Students' Modeling Mastery Through Visualizing Population Growth Models." BYU ScholarsArchive, 2021. https://scholarsarchive.byu.edu/etd/9181.
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In introductory biology, college students are taught to predict how populations will grow and change over time by using population growth models. These models are commonly represented as mathematical equations. However, students consistently struggle when math and biology concepts intersect in the classroom, and these struggles lead to suboptimal understanding of how mathematical population models are designed and used. Education literature suggests that students may struggle with population modeling because of math anxiety, the high cognitive load of the task, and the lack of scaffolding for abstract concepts. In our study, we sought to improve student mastery modeling exponential growth, logistic growth, and Lotka-Volterra predator-prey interactions through using pictorial diagrams in modeling pedagogy. We predicted that these diagrams would reduce the amount of triggered math anxiety, lower the cognitive load of the task through reducing element interactivity, and allow for a more scaffolding for abstract symbols through a pictorial representation bridge. To test the effectiveness of population diagrams, we created two versions of a population modeling lesson plan: one version taught using diagrams then equations, while the other taught using purely equations. We also designed practice and assessment questions that tested calculation and model-building ability. We assessed math anxiety, scientific reasoning ability, and math ability at the beginning of the semester and state anxiety, effort of tasks, and difficulty of tasks during each lesson. Over 200 students from a non-major biology course were randomly assigned to each group, and all were given a pre-assessment, four lessons, a practice test, and a unit test on population modeling. Our findings show that while the addition of pictorial models to the traditional pedagogy did not have a significant effect on exponential and logistic growth model mastery, students that were exposed to predator-prey diagrams were more able to create a new model for a three-level predator-prey interaction than students that were only given traditional pedagogy. In addition, students who were exposed to predator-prey interaction diagrams before they derived equations reported a lower cognitive load than students who were only exposed to equations. Although diagrams were not a more helpful calculation tool for students than traditional equations, using population diagrams before to equation derivation may help improve student mastery of growth model creation.
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MAZZOLA, MARCO. "Properties of solutions to variational problems." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2010. http://hdl.handle.net/10281/18339.
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In the context of the variational problems related to integral functionals, we study some necessary conditions for a solution u without standard growth assumptions and strong differentiability conditions on the Lagrangian L. In particular, we investigate the validity of the Euler-Lagrange equation, in its classical and non-classical form, in the cases of functionals with non-differentiable convex Lagrangian or with super-exponential growth for L. Moreover, we investigate the regularity properties for minimizers, concerning higher integrability of the gradient as well as higher differentiability under general growth conditions and mild differentiability assumptions on L.
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Carale, Maria Teresa Reyes. "Salt effects on micellization, micellar growth, and phase behavior of aqueous solutions of nonionic surfactants." Thesis, Massachusetts Institute of Technology, 1993. http://hdl.handle.net/1721.1/82744.
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Deodhar, Anirudh M. "Computational Study of Adiabatic Bubble Growth Dynamics from Submerged Orifices in Aqueous Solutions of Surfactants." University of Cincinnati / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1337100942.
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Uwaha, Makio, and Katsunobu Koyama. "Transition from nucleation to ripening in the classical nucleation model." Elsevier, 2010. http://hdl.handle.net/2237/13867.
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Gao, Angela X. (Angela Xiaodi). "Development of novel polymeric architectures for applications in drug delivery and studies towards the synthesis of perfect polymers by iterative exponential growth "Plus" (IEG+)." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/91119.
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Thesis: S.M., Massachusetts Institute of Technology, Department of Chemistry, 2014.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 86-87).
Polymeric materials are ubiquitous in numerous facets of everyday life, and their applications will only become increasingly prevalent as the field of polymer science advances. The first chapter of this thesis describes the use of polymeric nanoparticles to overcome challenges in traditional drug delivery. Specifically, a series of novel acid-cleavable bisnorbornene crosslinkers were synthesized and evaluated as building blocks for the formation of acid-degradable brush-arm star polymers (BASPs) via the brush-first ring-opening metathesis polymerization (ROMP) method. A bis-norbornene acetal structure was identified that, when employed in conjunction with a poly(ethylene glycol) (PEG) macromonomer, provided highly controlled BASP formation reactions. Combination of this new crosslinker with a novel acid-labile doxorubicin (DOX)-branch-PEG macromonomer provided BASPs that simultaneously degrade and release DOX in cell culture. In vitro cell viability studies using HeLa cells confirmed that these constructs are cytotoxic. Even though polymeric materials have found widespread use in current times, polymer science must overcome certain challenges to contend with the needs of next-generation technologies. In particular, newer polymer applications require the use of macromolecules with precisely defined structure and degree of polymerization--challenges that synthetic polymer chemistry has yet to conquer. The second chapter of this thesis describes a novel synthetic methodology (IEG+) that gives polymers with defined molar mass and sequence using synthetic procedures that are precise, scalable, and amenable to diversification. The IEG+ method utilized monomers equipped with orthogonal protecting groups: epoxides and alkynyl silanes. The epoxide functionality served both as a protecting group and as a masked synthon for alcohols, which allowed for side-chain functionalization of the IEG+ scaffold. Combing R- and Smonomers afforded complete stereochemical control of the IEG backbone. Oligomers of unimolecular molar mass and precise chemical structure were successfully prepared.
by Angela X. Gao.
S.M.
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Li, Ziliang. "Growth and Characterization of Nanocomposite YBa2Cu3O7-δ – BaMO3 (M = Zr, Hf) Thin Films from Colloidal Solutions." Doctoral thesis, Universitat Autònoma de Barcelona, 2018. http://hdl.handle.net/10803/663979.
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El YBa2Cu3O7-δ es el superconductor de alta temperatura con mayor potencial tecnológico para aplicaciones de potencia e imanes que trabajan bajo campos magnéticos elevados. Sin embargo, todavía es un reto mejorar sus prestaciones en forma de película delgada epitaxial con un coste bajo de fabricación. La deposición de soluciones químicas ha surgido como una técnica muy competitiva para obtener láminas delgadas epitaxiales y multicapas de alta calidad con nanoestructuras controladas.
Hemos desarrollado un proceso novedoso de crecimiento mediante Calentamiento Flash que muestra un excelente potencial para la producción industrial en continuo de conductores epitaxiales de YBa2Cu3O7-δ. En esta tesis hemos establecido, por primera vez, una imagen completa que describe las fases intermedias y la evolución de la microestructura durante el calentamiento. Hemos extendido la ventana de la temperatura de crecimiento sin ninguna degradación de las propiedades superconductoras, por lo que la deposición de conductores epitaxiales de YBa2Cu3O7-δ es compatible con el uso de sustratos de cinta metálica con capas tampón de CeO2. Además, también hemos encontrado que este proceso de crecimiento promueve la formación de una alta concentración de defectos de apilamiento y, por lo tanto, de tensiones a escala nanométrica.
Las láminas ultrafinas de YBa2Cu3O7-δ y nanocompuestos, en el rango de 5-50 nm, se prepararon después de una optimización de los parámetros de crecimiento. La reducción de la energía interfacial induce una alta densidad de defectos de apilamiento, lo que conduce a una matriz de YBa2Cu3O7-δ altamente distorsionada. Esta modificación microestructural se vuelve extremadamente grave cuando el grosor de la lámina delgada disminuye por debajo de 25 nm, degradando significativamente las propiedades superconductoras. También hemos estudiado la evolución de las características de las nanopartículas segregadas espontáneamente con el espesor de las láminas delgadas y su influencia en la eficiencia del anclaje de vórtices.
La preparación de nanocompuestos de YBa2Cu3O7-δ a partir de nanopartículas de óxido preformadas y no reactivas que forman soluciones coloidales ha demostrado ser una estrategia muy exitosa para lograr un estricto control de las características de las nanopartículas y la optimización de la nanoestructura de las láminas delgadas superconductoras. Las perovskitas BaMO3 (M = Zr, Hf) son las composiciones más prometedoras de nanopartículas preformadas que hasta ahora han conducido a láminas delgadas de nanocompuestos de alta calidad con altas concentraciones de nanopartículas (20-25% molar). La composición y el tamaño de las nanopartículas han demostrado ser factores cruciales para adaptar el rendimiento del anclaje de vórtices bajo campos magnéticos aplicados. La aplicación del proceso de crecimiento de calentamiento flash al crecimiento de láminas delgadas nanocompuestas permite la preservación del tamaño de las nanopartículas y la generación de una alta densidad de defectos de apilamiento de pequeña longitud, que desempeñan un efecto sinérgico para aumentar la eficiencia de los centros de anclaje de vórtices artificiales y mejorar así las propiedades de los conductores. La técnica de multideposición es efectiva para aumentar aún más el espesor de la lámina delgada, mientras que la eficacia del anclaje de vórtices se conserva y la capacidad de transporte de corriente eléctrica de las láminas delgadas nanocompuestas aumenta.YBa2Cu3O7-δ (YBCO) is the best material choice to address the performances required in power applications and magnets working under high magnetic fields. However, it is still challenging to achieve low manufacturing costs and high superconducting performances of coated conductors (CCs) for large scale power applications. Chemical Solution Deposition has emerged as a very competitive technique to obtain epitaxial films and multi-layers of high quality with controlled nanostructures. We have developed a novel Flash Heating growth process that shows high potential to be compatible with the industrial reel-to-reel production of YBCO CCs. Here we have set up, for the first time, a full image describing the intermediate phase and microstructure evolution during this heating process. We extend the growth temperature window down to 750 ºC without any degradation of superconducting properties, making it being compatible with the deposition of YBCO CCs on CeO2-caped metallic tape substrates. In addition, we have also found that this growth process promotes the formation of a high concentration of stacking faults and so of nanostrain. YBCO and nanocomposite ultrathin films, in the range of 5-50 nm, have been prepared after a series optimization of growth parameters. The relief of the interfacial energy induces a high density of stacking faults, leading to a highly distorted YBCO matrix. Such microstructural disorder becomes extremely serious when the film thicknesses decrease below 25 nm, significantly degrading the superconductivity. We have also studied the evolution of the characteristics of spontaneous segregated nanoparticles with nanocomposite film thicknesses and their influence on the vortex pinning efficiency. The preparation of YBCO nanocomposites from non-reactive preformed oxide nanoparticles forming colloidal solutions has demonstrated to be a very successful strategy to achieve a tight control of the nanoparticle characteristics and the optimized nanostructural landscape on the superconducting films. BaMO3 (M=Zr, Hf) perovskites are shown to be the most promising compositions of preformed nanoparticles up to now that led to high quality nanocomposite films at high nanoparticle concentrations (20-25 mol%). The composition and size of nanoparticles have demonstrated to be crucial factors for tailoring vortex pinning performance in applied magnetic field. The application of the Flash Heating growth process in the growth of nanocomposite films allows both the preservation of nanoparticle size and the generation of a high density of short stacking faults, which play a synergistic effect to increase the artificial pinning centers and enhance the strong pinning contribution. Multi-deposition technique is proved effective to further enhance the film thickness while vortex pinning efficiency is preserved and current-carrying capacity of the nanocomposite films is increased.
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Hardy, Eric M. "Policy drought: water resource management, urban growth, and technological solutions in post-world war II Atlanta." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/50109.
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By the dawn of the twenty-first century the City of Atlanta was facing a crisis of water quantity and water quality. It was involved in two-decades worth of litigation with the states of Alabama and Florida over access to surface waters that originate within Georgia, a legal dispute that threatened to severely reduce the city’ ability to provide water to its growing metropolitan population. In addition, city officials were in the beginning stages of a four-billion dollar, court-ordered program of improvements to its wastewater infrastructure that was intended to reduce the amount of pollution that spewed into its local rivers and streams. This dissertation examines the origins of these water-related problems by exploring the challenges that Atlanta’s public officials, engineers, and activists faced in planning and implementing an effective environmental policy, with particular emphasis placed on the era of post-World War II metropolitan development. Specifically, it focuses on the city’s historical efforts to achieve the comprehensive management of the area’s water resources, the technological systems adopted and solutions proposed, and the political and social milieu that facilitated or hampered these endeavors. Comprehensive water resources management was a neglected and delayed policy approach that was undertaken in the City of Atlanta only after overt threats of federal intervention. This study argues that although the area’s mid-century regional planners advocated for intergovernmental cooperation in order to manage Atlanta’s limited water supplies, their recommendations were undermined by fragmented local governance, timid political leadership, and public indifference. It further suggests that Atlanta’s water supply managers, through increases in the scale and scope of their operations and a reluctance to increase customer rates, facilitated and encouraged greater water consumption, which, in turn, placed intense burdens on both the natural hydraulic cycle and the city’s wastewater facilities. Lastly, it argues the citizen activists as well as state and federal regulators have utilized the federal court system as a blunt planning instrument when Atlanta’s leaders displayed their seeming incapacity to handle the environmental strains of uncoordinated metropolitan development.
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Magnitskiy, Stanislav V. "Controlling seedling height by treating seeds with plant growth regulators." Connect to this title online, 2004. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1101741472.
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Thesis (Ph. D.)--Ohio State University, 2004.Title from first page of PDF file. Document formatted into pages; contains xix, 157 p.; also includes graphics. Includes bibliographical references (p. 147-157).
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Romanchuk, Bradley J. "Computational Modeling of Bubble Growth Dynamics in Nucleate Pool Boiling for Pure Water and Aqueous Surfactant Solutions." University of Cincinnati / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1406809980.
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Sande, Olow. "Boundary Estimates for Solutions to Parabolic Equations." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-281451.
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This thesis concerns the boundary behavior of solutions to parabolic equations. It consists of a comprehensive summary and four scientific papers. The equations concerned are different generalizations of the heat equation. Paper I concerns the solutions to non-linear parabolic equations with linear growth. For non-negative solutions that vanish continuously on the lateral boundary of an NTA cylinder the following main results are established: a backward Harnack inequality, the doubling property for the Riesz measure associated with such solutions, and the Hölder continuityof the quotient of two such solutions up to the boundary. Paper 2 concerns the solutions to linear degenerate parabolic equations, where the degeneracy is controlled by a Muckenhoupt weight of class 1+2/n. For non-negative solutions that vanish continuously on the lateral boundary of an NTA cylinder the following main results are established: a backward Harnack inequality, the doubling property for the parabolic measure, and the Hölder continuity of the quotient of two such solutions up to the boundary. Paper 3 concerns a fractional heat equation. The first main result is that a solution to the fractional heat equation in Euclidean space of dimension n can be extended as a solution to a certain linear degenerate parabolic equation in the upper half space of dimension n+1. The second main result is the Hölder continuity of quotients of two non-negative solutions that vanish continuously on the latteral boundary of a Lipschitz domain. Paper 4 concerns the solutions to uniformly parabolic linear equations with complex coefficients. The first main result is that under certain assumptions on the opperator the bounds for the single layer potentials associated to the opperator are bounded. The second main result is that these bounds always hold if the opperator is realvalued and symmetric.
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Wees, David. "The effects of carbon dioxide enrichment and aeration of hydroponic nutrient solutions on the growth and yield of lettuce /." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66169.
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