A variation of the excite-and-probe technique is used to measure the picosecond evolution of laser-induced transient gratings that are produced in germanium by the direct absorption of 40 psec optical pulses at 1.06-μm. Grating lifetimes are determined for free carrier densities between 10¹⁸ cm⁻³ and 10²¹ cm⁻³ . For carrier densities less than 10¹⁹ cm⁻³ , a linear diffusion-recombination model for the grating provides a good fit to the experimental data and allows the extraction of the diffusion coefficient and an estimation of the linear recombination lifetime. Above carrier densities of approximately 10²⁰ cm⁻³ , the density dependence of the diffusion coefficient and nonlinear recombination processes must be considered. Numerical solutions to the resulting nonlinear partial differential equation are obtained that allow extraction of information concerning the high density diffusion coefficient and the nonlinear recombination rates.

No description available.

No description available.

No description available.

In this study we are interested on the following 4-dimensional system of stochastic differential equations.dS=(-βSI+μ(K-S)+αI+ζR)dt-σ_1 SIF_1 (S,E,I,R)dW_1+σ_4 RF_4 (S,E,I,R)dW_4 dE=(βSI-(μ+η)E)dt+σ_1 SIF_1 (S,E,I,R)dW_1-σ_2 EF_2 (S,E,I,R)dW_2 dI=(ηE-(α+γ+μ)I)dt+σ_2 EF_2 (S,E,I,R)dW_2-σ_3 IF_3 (S,E,I,R)dW_3 dR=(γI-(μ+ζ)R)dt+σ_3 IF_3 (S,E,I,R)dW_3-σ_4 RF_4 (S,E,I,R)dW_4 with variance parameters σ_i≥0 and constants α,β,η,γ,μ ζ≥0. This system may be used to model the dynamics of susceptible, exposed, infected and recovering individuals subject to a present virus with state-dependent random transitions. Our main goal is to prove the existence of a bounded, unique, strong (pathwise), global solution to this system, and to discuss asymptotic stochastic and moment stability of the two equilibrium points, namely the disease free and the endemic equilibria. In this model, as suggested by our advisor, diffusion coefficients can be any local Lipschitz continuous functions on bounded domain D={(S,E,I,R)∈R_+^4:00 of maximum carrying capacity and W_i are independent and identical Wiener processes defined on a complete probability space (Ω,F,{F_t }_(t≥0),P). At the end we carry out some simulations to illustrate our results.

The stochastic SEIR(S) model with random total population is given by the system of stochastic differential equations:dS=(-βSI+μ(K-S)+αI+ζR)dt-σ_1 SIF_1 (S,E,I,R)dW_1+σ_4 RF_4 (S,E,I,R)dW_4+σ_5 S(K-N)dW_5\\ dE=(βSI-(μ+η)E)dt+σ_1 SIF_1 (S,E,I,R)dW_1-σ_2 EF_2 (S,E,I,R)dW_2+σ_5 E(K-N)dW_5 \\ dI=(ηE-(α+γ+μ)I)dt+σ_2 EF_2 (S,E,I,R)dW_2-σ_3 IF_3 (S,E,I,R)dW_3+σ_5 I(K-N)dW_5 \\ dR=(γI-(μ+ζ)R)dt+σ_3 IF_3 (S,E,I,R)dW_3-σ_4 RF_4 (S,E,I,R)dW_4+σ_5 R(K-N)dW_5, where σ_i>0 and constants α, β, η, γ, ζ, μ≥0. K represents the maximum carrying capacity for the total population and W_k=(W_k (t))_(t≥0) are independent, standard Wiener processes on a complete probability space (Ω,F,(F_t )_(t≥0),P). The SDE for the total population N=S+E+I+R has the form dN(t)=μ(K-N)dt+σ_5 N(K-N)dW_5 on D_0=(0,K). The goal of our study is to prove the existence of unique, Markovian, continuous time solutions on the 4D prism D={(S,E,I,R)∈R_+^4:0≤S, E,I,R≤K, S+E+I+R≤K}. Then using the method of Lyapunov functions we prove the asymptotic stochastic and moment stability of disease-free and endemic equilibria. Finally, we use numerical simulations to illustrate our results.

Stochastic models describing how interacting individuals give rise to collective behaviour have become a widely used tool across disciplines—ranging from biology to physics to social sciences. Continuum population-level models based on partial differential equations for the population density can be a very useful tool (when, for large systems, particle-based models become computationally intractable), but the challenge is to predict the correct macroscopic description of the key attributes at the particle level (such as interactions between individuals and evolution rules). In this thesis we consider the simple class of models consisting of diffusive particles with short-range interactions. It is relevant to many applications, such as colloidal systems and granular gases, and also for more complex systems such as diffusion through ion channels, biological cell populations and animal swarms. To derive the macroscopic model of such systems, previous studies have used ad hoc closure approximations, often generating errors. Instead, we provide a new systematic method based on matched asymptotic expansions to establish the link between the individual- and the population-level models. We begin by deriving the population-level model of a system of identical Brownian hard spheres. The result is a nonlinear diffusion equation for the one-particle density function with excluded-volume effects enhancing the overall collective diffusion rate. We then expand this core problem in several directions. First, for a system with two types of particles (two species) we obtain a nonlinear cross-diffusion model. This model captures both alternative notions of diffusion, the collective diffusion and the self-diffusion, and can be used to study diffusion through obstacles. Second, we study the diffusion of finite-size particles through confined domains such as a narrow channel or a Hele–Shaw cell. In this case the macroscopic model depends on a confinement parameter and interpolates between severe confinement (e.g., a single- file diffusion in the narrow channel case) and an unconfined situation. Finally, the analysis for diffusive soft spheres, particles with soft-core repulsive potentials, yields an interaction-dependent non-linear term in the diffusion equation.

Solid state lithium ion electrolytes are important to the development of next generation safer and high power density lithium ion batteries. Perovskite-structured LLT is a promising solid electrolyte with high lithium ion conductivity. LLT also serves as a good model system to understand lithium ion diffusion behaviors in solids. In this thesis, molecular dynamics and related atomistic computer simulations were used to study the diffusion behavior and diffusion mechanism in bulk crystal and grain boundary in lithium lanthanum titanate (LLT) solid state electrolytes. The effects of defect concentration on the structure and lithium ion diffusion behaviors in LLT were systematically studied and the lithium ion self-diffusion and diffusion energy barrier were investigated by both dynamic simulations and static calculations using the nudged elastic band (NEB) method. The simulation results show that there exist an optimal vacancy concentration at around x=0.067 at which lithium ions have the highest diffusion coefficient and the lowest diffusion energy barrier. The lowest energy barrier from dynamics simulations was found to be around 0.22 eV, which compared favorably with 0.19 eV from static NEB calculations. It was also found that lithium ions diffuse through bottleneck structures made of oxygen ions, which expand in dimension by 8-10% when lithium ions pass through. By designing perovskite structures with large bottleneck sizes can lead to materials with higher lithium ion conductivities. The structure and diffusion behavior of lithium silicate glasses and their interfaces, due to their importance as a grain boundary phase, with LLT crystals were also investigated by using molecular dynamics simulations. The short and medium range structures of the lithium silicate glasses were characterized and the ceramic/glass interface models were obtained using MD simulations. Lithium ion diffusion behaviors in the glass and across the glass/ceramic interfaces were investigated. It was found that there existed a minor segregation of lithium ions at the glass/crystal interface. Lithium ion diffusion energy barrier at the interface was found to be dominated by the glass phase.

O objetivo principal desta tese de doutorado foi a valorização da casca da amêndoa de cacau através do estudo da viabilidade técnica do emprego de tecnologias de extração a pressão atmosférica (ATME) e com líquido pressurizado (PLE) para extração da gordura e biocompostos deste material, utilizando etanol e isopropanol como solventes, os quais são solventes GRAS com aplicação potencial como substitutos do hexano na extração de lipídeos. Para que a sua viabilidade na aplicação de processos de extração fosse atestada, inicialmente, a casca da amêndoa de cacau seca (CS) foi caracterizada. A CS mostrou ser um material nutricionalmente interessante, com teor intermediário de lipídeos (entre 18 a 22% b.s.), elevado teor de fibras, flavanóis e alcaloides e alta solubilidade proteica (47 - 54%), além de não apresentar contaminação por micotoxinas e cádmio. Sua gordura se destacou por ter perfil lipídico semelhante ao da manteiga de cacau com teor superior de ácido linoleico e teores de tocoferóis totais bastante elevados os quais variaram entre 1016 a 1273 mg/kg de gordura, sendo os isômeros majoritários o (γ+β) tocoferois. Assim, a cinética de extração por PLE de lipídios e flavanóis totais (FLA) para sistemas contendo CS e etanol em grau absoluto (Et0) foi estudada nas temperaturas de 60, 75 e 90 °C em tempos estáticos variando de 3 a 50 minutos e razão mássica sólido:solvente de 1:3. A partir destes experimentos determinou-se 30 minutos como o tempo adequado para que a condição de equilíbrio fosse alcançada para as três temperaturas avaliadas; à partir deste intervalo de tempo a extração de lipídeos está estabilizada e o rendimento de extração de FLA é máximo. Os extratos, as gorduras e os sólidos desengordurados oriundos da PLE foram avaliados levando a concluir que esta técnica foi extremamente viável para extração de lipídeos, flavanóis, alcaloides e tocoferóis da CS, fornecendo rendimentos de extração bastante elevados, em curto período de tempo, em um único estágio de contato. Os dados experimentais da cinética por PLE foram modelados e os coeficientes de difusão para a gordura foram estimados. Além disso, pode-se verificar que a PLE não afetou a solubilidade das proteínas presentes no material das extrações conduzidas a 60 e 75 °C, o que permite a obtenção de um sólido desengordurado com elevado valor. A investigação do processo de extração por ATME iniciou-se com sistemas contendo CS e solventes etanol e isopropanol, em grau absoluto e azeotrópico, nas temperaturas de 60, 75 e 90 °C com razão mássica sólido:solvente de 1:3 e tempo de extração de 1 hora. Pode-se observar que, nessas condições, os experimentos de extração forneceram resultados de rendimento de extração de gordura aquém do esperado. Apesar disso, foi possível avaliar o efeito dos parâmetros de processo, temperatura e tipo de solvente, sobre o processo de extração; pode-se concluir que temperaturas mais elevadas levam a maiores rendimentos de extração de todas as classes de compostos avaliadas, para os lipídeos, em geral, o solvente isopropanol em grau absoluto foi o mais eficiente, entretanto, na extração de compostos fenólicos, FLA e tocoferóis o solvente etanol em grau azeotrópico apresentou melhor desempenho. Para uma investigação mais aprofundada, realizou-se o estudo da cinética de extração de lipídeos por ATME com os solventes etanol em grau absoluto e azeotrópico nas temperaturas de 75 e 90 °C. Com estes experimentos pode-se observar que, para garantir que a condição de equilíbrio fosse alcançada, seria necessário tempo de extração de pelo menos 3 horas para os solventes avaliados, com este tempo de extração os rendimentos aumentaram consideravelmente, bem como o teor de flavanóis totais nos extratos; por outro lado, a solubilidade proteica da fase rafinado diminuiu consideravelmente. Os dados experimentais de cinética por ATME foram modelados e os coeficientes de difusão para a gordura foram também estimados, sendo aproximadamente 5 vezes menores que os estimados para a PLE. Com base na determinação do tempo necessário para se atingir a condição de equilíbrio, realizou-se os experimentos para determinação dos coeficientes de partição (k) da gordura da casca da amêndoa de cacau, o qual permite estimar o número de estágios de extração para máxima exaustão dos sólidos em termos de teor de lipídeos. Estes experimentos mostraram que o solvente Et0 a temperaturas mais elevadas fornece coeficientes de partição maiores. Os valores de kgordura maiores obtidos para o Et0, se comparado com o solvente etanol em grau azeotrópico, indicam que seu emprego em processos de extração exigiria um número menor de estágios de contato para o esgotamento do sólido. Analisando os processos de extração empregados, pode-se concluir que a PLE apresenta eficiência superior na extração simultânea de flavanóis e compostos lipídicos da casca da amêndoa de cacau em relação a ATME, e também impacta menos a solubilidade proteica dos sólidos desengordurados oriundos do processo de extração, fato que demonstra sua elevada viabilidade técnica. / The main objective of this Ph.D. thesis was the valorization of the cocoa bean shell through the study of the technical feasibility of the use of atmospheric pressure extraction (ATME) and pressurized liquid extraction (PLE) technologies for the extraction of fat and biocompounds of this material, using ethanol and isopropanol as solvents, which are GRAS solvents with potential application as substitutes for hexane in lipid extraction. In order for its viability in the application of extraction processes to be attested, initially, the dried cocoa bean shell (CS) was characterized. CS showed to be a nutritionally interesting material, with an intermediate content of lipids (between 18 to 22% d.b.), high fiber content, flavanols and alkaloids and high protein solubility (47-54%), besides not being contaminated by mycotoxins and cadmium. Its fat was remarkable for having a lipid profile similar to that of cocoa butter with a higher content of linoleic acid and quite high total tocopherols, which ranged from 1016 to 1273 mg / kg of fat, with the major isomers being (γ + β) tocopherols. Thus the PLE extraction kinetics of lipids and total flavanols (FLA) for systems containing CS and absolute ethanol (Et0) were studied at 60, 75 and 90 ° C in static times ranging from 3 to 50 minutes and mass ratio solid:solvent of 1: 3. From these experiments, 30 minutes were determined as the adequate time for the equilibrium condition to be reached for the three temperatures evaluated; from this time interval the lipid extraction is stabilized and the extraction yield of FLA is maximal. The raffinate phases, extract phases and fats from PLE were evaluated leading to the conclusion that this technique was extremely viable for extracting lipids, flavanols, alkaloids and tocopherols, providing very high extraction yields in a short period of time with a single stage of contact. Experimental data of PLE kinetics were modeled and the diffusion coefficients for fat were estimated. In addition, PLE did not affect the solubility of the proteins present in the material from extractions conducted at 60 and 75 °C, which allows obtaining a high value defatted meal. The investigation of the extraction process by ATME started with systems containing CS and solvents ethanol and isopropanol, in absolute and azeotrope degree, at 60, 75 and 90 ° C with mass ratio solid:solvent of 1:3 and time of extraction time of 1 hour. Under these conditions, the extraction experiments gave results of fat extraction yields less than expected. Despite this, it was possible to evaluate the effect of process parameters, temperature and type of solvent on the extraction process; it can be concluded that higher temperatures lead to higher extraction yields of all classes of compounds evaluated. For lipids, in general, the absolute isopropanol was the most efficient solvent, however, in the extraction of phenolic compounds, FLA and tocopherols the ethanol azeotropic showed better performance. For a more in-depth investigation, the kinetics of lipid extraction by ATME with ethanol in absolute and azeotropic degree at 75 and 90 °C were carried out. With these experiments it can be observed that, in order to guarantee that the equilibrium condition was reached, extraction time of at least 3 hours was required for the solvents evaluated, with this time of extraction the yields increased considerably, as well as the content of flavanols totals in extracts; on the other hand, the protein solubility of the raffinate phase decreased considerably. Experimental kinetic data by ATME were modeled and the diffusion coefficients for fat were also estimated, being approximately 5 times smaller than those estimated for PLE. Based on the determination of the time required to reach the equilibrium condition, the experiments were carried out to determine the partition coefficients (k) of the cocoa bean shell fat, which allows estimating the number of extraction stages to maximum depletion in terms of lipid content. These experiments showed that the solvent Et0 at higher temperatures provides larger partition coefficients. The higher kfat values obtained for Et0, when compared to ethanol solvent in azeotropic grade, indicate that their use in extraction processes would require a lower number of contact stages for the depletion of the solid. Analyzing the extraction processes applyed, it can be concluded that PLE has superior efficiency in the simultaneous extraction of flavanols and lipid compounds from the cocoa bean shell in relation to ATME, and has less impact on the protein solubility of the defatted meal, a fact that demonstrates its high technical feasibility.

O objetivo principal desta tese de doutorado foi a valorização da casca da amêndoa de cacau através do estudo da viabilidade técnica do emprego de tecnologias de extração a pressão atmosférica (ATME) e com líquido pressurizado (PLE) para extração da gordura e biocompostos deste material, utilizando etanol e isopropanol como solventes, os quais são solventes GRAS com aplicação potencial como substitutos do hexano na extração de lipídeos. Para que a sua viabilidade na aplicação de processos de extração fosse atestada, inicialmente, a casca da amêndoa de cacau seca (CS) foi caracterizada. A CS mostrou ser um material nutricionalmente interessante, com teor intermediário de lipídeos (entre 18 a 22% b.s.), elevado teor de fibras, flavanóis e alcaloides e alta solubilidade proteica (47 - 54%), além de não apresentar contaminação por micotoxinas e cádmio. Sua gordura se destacou por ter perfil lipídico semelhante ao da manteiga de cacau com teor superior de ácido linoleico e teores de tocoferóis totais bastante elevados os quais variaram entre 1016 a 1273 mg/kg de gordura, sendo os isômeros majoritários o (γ+β) tocoferois. Assim, a cinética de extração por PLE de lipídios e flavanóis totais (FLA) para sistemas contendo CS e etanol em grau absoluto (Et0) foi estudada nas temperaturas de 60, 75 e 90 °C em tempos estáticos variando de 3 a 50 minutos e razão mássica sólido:solvente de 1:3. A partir destes experimentos determinou-se 30 minutos como o tempo adequado para que a condição de equilíbrio fosse alcançada para as três temperaturas avaliadas; à partir deste intervalo de tempo a extração de lipídeos está estabilizada e o rendimento de extração de FLA é máximo. Os extratos, as gorduras e os sólidos desengordurados oriundos da PLE foram avaliados levando a concluir que esta técnica foi extremamente viável para extração de lipídeos, flavanóis, alcaloides e tocoferóis da CS, fornecendo rendimentos de extração bastante elevados, em curto período de tempo, em um único estágio de contato. Os dados experimentais da cinética por PLE foram modelados e os coeficientes de difusão para a gordura foram estimados. Além disso, pode-se verificar que a PLE não afetou a solubilidade das proteínas presentes no material das extrações conduzidas a 60 e 75 °C, o que permite a obtenção de um sólido desengordurado com elevado valor. A investigação do processo de extração por ATME iniciou-se com sistemas contendo CS e solventes etanol e isopropanol, em grau absoluto e azeotrópico, nas temperaturas de 60, 75 e 90 °C com razão mássica sólido:solvente de 1:3 e tempo de extração de 1 hora. Pode-se observar que, nessas condições, os experimentos de extração forneceram resultados de rendimento de extração de gordura aquém do esperado. Apesar disso, foi possível avaliar o efeito dos parâmetros de processo, temperatura e tipo de solvente, sobre o processo de extração; pode-se concluir que temperaturas mais elevadas levam a maiores rendimentos de extração de todas as classes de compostos avaliadas, para os lipídeos, em geral, o solvente isopropanol em grau absoluto foi o mais eficiente, entretanto, na extração de compostos fenólicos, FLA e tocoferóis o solvente etanol em grau azeotrópico apresentou melhor desempenho. Para uma investigação mais aprofundada, realizou-se o estudo da cinética de extração de lipídeos por ATME com os solventes etanol em grau absoluto e azeotrópico nas temperaturas de 75 e 90 °C. Com estes experimentos pode-se observar que, para garantir que a condição de equilíbrio fosse alcançada, seria necessário tempo de extração de pelo menos 3 horas para os solventes avaliados, com este tempo de extração os rendimentos aumentaram consideravelmente, bem como o teor de flavanóis totais nos extratos; por outro lado, a solubilidade proteica da fase rafinado diminuiu consideravelmente. Os dados experimentais de cinética por ATME foram modelados e os coeficientes de difusão para a gordura foram também estimados, sendo aproximadamente 5 vezes menores que os estimados para a PLE. Com base na determinação do tempo necessário para se atingir a condição de equilíbrio, realizou-se os experimentos para determinação dos coeficientes de partição (k) da gordura da casca da amêndoa de cacau, o qual permite estimar o número de estágios de extração para máxima exaustão dos sólidos em termos de teor de lipídeos. Estes experimentos mostraram que o solvente Et0 a temperaturas mais elevadas fornece coeficientes de partição maiores. Os valores de kgordura maiores obtidos para o Et0, se comparado com o solvente etanol em grau azeotrópico, indicam que seu emprego em processos de extração exigiria um número menor de estágios de contato para o esgotamento do sólido. Analisando os processos de extração empregados, pode-se concluir que a PLE apresenta eficiência superior na extração simultânea de flavanóis e compostos lipídicos da casca da amêndoa de cacau em relação a ATME, e também impacta menos a solubilidade proteica dos sólidos desengordurados oriundos do processo de extração, fato que demonstra sua elevada viabilidade técnica. / The main objective of this Ph.D. thesis was the valorization of the cocoa bean shell through the study of the technical feasibility of the use of atmospheric pressure extraction (ATME) and pressurized liquid extraction (PLE) technologies for the extraction of fat and biocompounds of this material, using ethanol and isopropanol as solvents, which are GRAS solvents with potential application as substitutes for hexane in lipid extraction. In order for its viability in the application of extraction processes to be attested, initially, the dried cocoa bean shell (CS) was characterized. CS showed to be a nutritionally interesting material, with an intermediate content of lipids (between 18 to 22% d.b.), high fiber content, flavanols and alkaloids and high protein solubility (47-54%), besides not being contaminated by mycotoxins and cadmium. Its fat was remarkable for having a lipid profile similar to that of cocoa butter with a higher content of linoleic acid and quite high total tocopherols, which ranged from 1016 to 1273 mg / kg of fat, with the major isomers being (γ + β) tocopherols. Thus the PLE extraction kinetics of lipids and total flavanols (FLA) for systems containing CS and absolute ethanol (Et0) were studied at 60, 75 and 90 ° C in static times ranging from 3 to 50 minutes and mass ratio solid:solvent of 1: 3. From these experiments, 30 minutes were determined as the adequate time for the equilibrium condition to be reached for the three temperatures evaluated; from this time interval the lipid extraction is stabilized and the extraction yield of FLA is maximal. The raffinate phases, extract phases and fats from PLE were evaluated leading to the conclusion that this technique was extremely viable for extracting lipids, flavanols, alkaloids and tocopherols, providing very high extraction yields in a short period of time with a single stage of contact. Experimental data of PLE kinetics were modeled and the diffusion coefficients for fat were estimated. In addition, PLE did not affect the solubility of the proteins present in the material from extractions conducted at 60 and 75 °C, which allows obtaining a high value defatted meal. The investigation of the extraction process by ATME started with systems containing CS and solvents ethanol and isopropanol, in absolute and azeotrope degree, at 60, 75 and 90 ° C with mass ratio solid:solvent of 1:3 and time of extraction time of 1 hour. Under these conditions, the extraction experiments gave results of fat extraction yields less than expected. Despite this, it was possible to evaluate the effect of process parameters, temperature and type of solvent on the extraction process; it can be concluded that higher temperatures lead to higher extraction yields of all classes of compounds evaluated. For lipids, in general, the absolute isopropanol was the most efficient solvent, however, in the extraction of phenolic compounds, FLA and tocopherols the ethanol azeotropic showed better performance. For a more in-depth investigation, the kinetics of lipid extraction by ATME with ethanol in absolute and azeotropic degree at 75 and 90 °C were carried out. With these experiments it can be observed that, in order to guarantee that the equilibrium condition was reached, extraction time of at least 3 hours was required for the solvents evaluated, with this time of extraction the yields increased considerably, as well as the content of flavanols totals in extracts; on the other hand, the protein solubility of the raffinate phase decreased considerably. Experimental kinetic data by ATME were modeled and the diffusion coefficients for fat were also estimated, being approximately 5 times smaller than those estimated for PLE. Based on the determination of the time required to reach the equilibrium condition, the experiments were carried out to determine the partition coefficients (k) of the cocoa bean shell fat, which allows estimating the number of extraction stages to maximum depletion in terms of lipid content. These experiments showed that the solvent Et0 at higher temperatures provides larger partition coefficients. The higher kfat values obtained for Et0, when compared to ethanol solvent in azeotropic grade, indicate that their use in extraction processes would require a lower number of contact stages for the depletion of the solid. Analyzing the extraction processes applyed, it can be concluded that PLE has superior efficiency in the simultaneous extraction of flavanols and lipid compounds from the cocoa bean shell in relation to ATME, and has less impact on the protein solubility of the defatted meal, a fact that demonstrates its high technical feasibility.