A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.

Secretion of five extracellular enzymes by strains of chromoblastomycosis agents

The gelatinase, urease, lipase, phospholipase and DNase activities of 11 chromoblastomycosis agents constituted by strains of Fonsecaea pedrosoi, F. compacta, Phialophora verrucosa, Cladosporium carrionii, Cladophialophora bantiana and Exophiala jeanselmei were analyzed and compared. All strains presented urease, gelatinase and lipase activity. Phospholipase activity was detected only on five of six strains of F. pedrosoi. DNase activity was not detected on the strains studied. Our results indicate that only phospholipase production, induced by egg yolk substrate, was useful for the differentiation of the taxonomically related species studied, based on their enzymatic profile.

Characterization of sol-gel matrices with entrapped cutinase

Dissertação para obtenção do Grau de Doutor em Engenharia Química e Bioquímica

Mind the gap: characterization of periplasmic cytochromes from Shewanella oneidensis involved in extracellular electron transfer

Dissertation presented to obtain the Ph.D degree in Biochemistry

Analysis of metabolic flux distributions in relation to the extracellular environment in Avian cells

Continuous cell lines that proliferate in chemically defined and simple media have been highly regarded as suitable alternatives for vaccine production. One such cell line is the AG1.CR.pIX avian cell line developed by PROBIOGEN. This cell line can be cultivated in a fully scalable suspension culture and adapted to grow in chemically defined, calf serum free, medium [1]–[5]. The medium composition and cultivation strategy are important factors for reaching high virus titers. In this project, a series of computational methods was used to simulate the cell’s response to different environments. The study is based on the metabolic model of the central metabolism proposed in [1]. In a first step, Metabolic Flux Analysis (MFA) was used along with measured uptake and secretion fluxes to estimate intracellular flux values. The network and data were found to be consistent. In a second step, Flux Balance Analysis (FBA) was performed to access the cell’s biological objective. The objective that resulted in the best predicted results fit to the experimental data was the minimization of oxidative phosphorylation. Employing this objective, in the next step Flux Variability Analysis (FVA) was used to characterize the flux solution space. Furthermore, various scenarios, where a reaction deletion (elimination of the compound from the media) was simulated, were performed and the flux solution space for each scenario was calculated. Growth restrictions caused by essential and non-essential amino acids were accurately predicted. Fluxes related to the essential amino acids uptake and catabolism, the lipid synthesis and ATP production via TCA were found to be essential to exponential growth. Finally, the data gathered during the previous steps were analyzed using principal component analysis (PCA), in order to assess potential changes in the physiological state of the cell. Three metabolic states were found, which correspond to zero, partial and maximum biomass growth rate. Elimination of non-essential amino acids or pyruvate from the media showed no impact on the cell’s assumed normal metabolic state.

Modeling and optimization of extracellular polysaccharides production by Enterobacter A47

Polysaccharides are gaining increasing attention as potential environmental friendly and sustainable building blocks in many fields of the (bio)chemical industry. The microbial production of polysaccharides is envisioned as a promising path, since higher biomass growth rates are possible and therefore higher productivities may be achieved compared to vegetable or animal polysaccharides sources. This Ph.D. thesis focuses on the modeling and optimization of a particular microbial polysaccharide, namely the production of extracellular polysaccharides (EPS) by the bacterial strain Enterobacter A47. Enterobacter A47 was found to be a metabolically versatile organism in terms of its adaptability to complex media, notably capable of achieving high growth rates in media containing glycerol byproduct from the biodiesel industry. However, the industrial implementation of this production process is still hampered due to a largely unoptimized process. Kinetic rates from the bioreactor operation are heavily dependent on operational parameters such as temperature, pH, stirring and aeration rate. The increase of culture broth viscosity is a common feature of this culture and has a major impact on the overall performance. This fact complicates the mathematical modeling of the process, limiting the possibility to understand, control and optimize productivity. In order to tackle this difficulty, data-driven mathematical methodologies such as Artificial Neural Networks can be employed to incorporate additional process data to complement the known mathematical description of the fermentation kinetics. In this Ph.D. thesis, we have adopted such an hybrid modeling framework that enabled the incorporation of temperature, pH and viscosity effects on the fermentation kinetics in order to improve the dynamical modeling and optimization of the process. A model-based optimization method was implemented that enabled to design bioreactor optimal control strategies in the sense of EPS productivity maximization. It is also critical to understand EPS synthesis at the level of the bacterial metabolism, since the production of EPS is a tightly regulated process. Methods of pathway analysis provide a means to unravel the fundamental pathways and their controls in bioprocesses. In the present Ph.D. thesis, a novel methodology called Principal Elementary Mode Analysis (PEMA) was developed and implemented that enabled to identify which cellular fluxes are activated under different conditions of temperature and pH. It is shown that differences in these two parameters affect the chemical composition of EPS, hence they are critical for the regulation of the product synthesis. In future studies, the knowledge provided by PEMA could foster the development of metabolically meaningful control strategies that target the EPS sugar content and oder product quality parameters.

Electrokinetic treatment of environmental matrices. Contaminants removal and phosphorus recovery

There is a need to develop viable techniques for removal and recovery organic and inorganic compounds from environmental matrices, due to their ecotoxicity, regulatory obligations or potential supplies as secondary materials. In this dissertation, electro –removal and –recovery techniques were applied to five different contaminated environmental matrices aiming phosphorus (P) recovery and/or contaminants removal. In a first phase, the electrokinetic process (EK) was carried out in soils for (i) metalloids and (ii) organic contaminants (OCs) removal. In the case of As and Sb mine contaminated soil, the EK process was additionally coupled with phytotechnologies. In a second phase, the electrodialytic process (ED) was applied to wastes aiming P recovery and simultaneous removal of (iii) toxins from membrane concentrate, (iv) heavy metals from sewage sludge ash (SSA), and (v) OCs from sewage sludge (SS). EK enhanced phytoremediation showed to be viable for the remediation of soils contaminated with metalloids, as although remediation was low, it combines advantages of both technologies while allowing site management. EK also proved to be an effective remediation technology for the removal and degradation of emerging OCs from two types of soil. Aiming P recovery and contaminants removal, different ED cell set-ups were tested. For the membrane concentrates, the best P recovery was achieved in a three compartment (3c) cell, but the highest toxin removal was obtained in a two compartment (2c) cell, placing the matrix in the cathode end. In the case of SSA the best approach for simultaneous P recovery and heavy metals removal was to use a 2c-cell placing the matrix in the anode end. However, for simultaneous P recovery and OCs removal, SS should be placed in the cathode end, in a 2c-cell. Overall, the data support that the selection of the cell design should be done case-by-case.

Tensile and bond characterization of natural fibers embeeded in inorganic matrices

Innovative composite materials made of continuous fibers embedded in mortar matrices have been recently received attention for externally bonded reinforcement of masonry structures. In this regards, application of natural fibers for strengthening of the repair mortars is attractive due to their low specific weight, sustainability and recycability. This paper presents experimental characterization of tensile and pull-out behavior of natural fibers embedded in two different mortar-based matrices. A lime-based and a geopolymeric-based mortar are used as sustainable and innovative matrices. The obtained experimental results and observations are presented and discussed.

Dispersion of fillers in viscoelastic polymer matrices using Eulerian-Lagrangian approaches

Understanding the behavior of c omplex composite materials using mixing procedures is fundamental in several industrial processes. For instance, polymer composites are usually manufactured using dispersion of fillers in polymer melt matrices. The success of the filler dispersion depends both on the complex flow patterns generated and on the polymer melt rheological behavior. Consequently, the availability of a numerical tool that allow to model both fluid and particle would be very useful to increase the process insight. Nowadays there ar e computational tools that allow modeling the behavior of filled systems, taking into account both the behavior of the fluid (Computational Rheology) and the particles (Discrete Element Method). One example is the DPMFoam solver of the OpenFOAM ® framework where the averaged volume fraction momentum and mass conservation equations are used to describe the fluid (continuous phase) rheology, and the Newton’s second law of motion is used to compute the particles (discrete phase) movement. In this work the refer red solver is extended to take into account the elasticity of the polymer melts for the continuous phase. The solver capabilities will be illustrated by studying the effect of the fluid rheology on the filler dispersion, taking into account different fluid types (generalized Newtonian or viscoelastic) and particles volume fraction and size. The results obtained are used to evaluate the relevance of considering the fluid complex rheology for the prediction of the composites morphology

Understanding the dispersion of fillers in polymer matrices

Understanding the mixing process of complex composite materials is fundamental in several industrial processes. For instance, the dispersion of fillers in polymer melt matrices is commonly employed to manufacture polymer composites, using a twin-screw extruder. The effectiveness of the filler dispersion depends not only on the complex flow patterns generated, but also on the polymer melt rheological behavior. Therefore, the availability of a numerical tool able to predict mixing, taking into account both fluid and particles phases would be very useful to increase the process insight, and thus provide useful guidelines for its optimization. In this work, a new Eulerian-Lagrangian numerical solver is developed OpenFOAM® computational library, and used to better understand the mechanisms determining the dispersion of fillers in polymer matrices. Particular attention will be given to the effect of the rheological model used to represent the fluid behavior, on the level of dispersion obtained. For the Eulerian phase the averaged volume fraction governing equations (conservation of mass and linear momentum) are used to describe the fluid behavior. In the case of the Lagrangian phase, Newton’s second law of motion is used to compute the particles trajectories and velocity. To study the effect of fluid behavior on the filler dispersion, several systems are modeled considering different fluid types (generalized Newtonian or viscoelastic) and particles volume fraction and size. The results obtained are used to correlate the fluid and particle characteristics on the effectiveness of mixing and morphology obtained.

Mechanism of extracellular silver nanoparticles synthesis by Stereum hirsutum and Fusarium oxysporum

The increasing interest for greener and biological methods of synthesis has led to the development of non-toxic and comparatively more bioactive nanoparticles. Unlike physical and chemical methods of nanoparticle synthesis, microbial synthesis in general and mycosynthesis in particular is cost-effective and environment-friendly. However, different aspects, such as the rate of synthesis, monodispersity and downstream processing, need to be improved. Many fungal-based mechanisms have been proposed for the formation of silver nanoparticles (AgNPs), mainly those involving the presence of nitrate reductase, which has been detected in filtered fungus cell used for AgNPs production. There is a general acceptance that nitrate reductase is the main responsible for the reduction of Ag ions for the formation of AgNPs. However, this generally accepted mechanism for fungal AgNPs production is not totally understood. In order to elucidate the molecules participating in the mechanistic formation of metal nanoparticles, the current study is focused on the enzymes and other organic compounds involved in the biosynthesis of AgNPs. The use of each free fungal mycelium of both Stereum hirsutum and Fusarium oxysporum will be assessed. In order to identify defective mutants on the nitrate reductase structural gene niaD, fungal cultures of S.hirsutum and F.oxysporum will be selected by chlorate resistance. In addition, in order to verify if each compound identified as key-molecule influenced on the production of nanoparticles, an in vitro assay using different nitrogen sources will be developed. Lately, fungal extracellular enzymes will be measured and an in vitro assay will be done. Finally, The nanoparticle formation and its characterization will be evaluated by UV-visible spectroscopy, electron microscopy (TEM), X-ray diffraction analysis (XRD), Fourier transforms infrared spectroscopy (FTIR), and LC-MS/MS.

On simple bounds for eigenvalues of symmetric tridiagonal matrices

How much can be said about the location of the eigenvalues of a symmetric tridiagonal matrix just by looking at its diagonal entries? We use classical results on the eigenvalues of symmetric matrices to show that the diagonal entries are bounds for some of the eigenvalues regardless of the size of the off-diagonal entries. Numerical examples are given to illustrate that our arithmetic-free technique delivers useful information on the location of the eigenvalues.

TP perturbation of TN matrices and totally positive directions

Here, we define and consider (linear) TP-directions and TP-paths for a totally nonnegative matrix, in an effort to more deeply understand perturbation of a TN matrix to a TP matrix. We give circumstances in which a TP-direction exists and an example to show that they do not always exist. A strategy to give (nonlinear) TP-paths is given (and applied to this example). A long term goal is to understand the sparsest TP-perturbation for application to completion problems.

Development of hyaluronic acid, dextrin and extracellular matrix hydrogels for cell expansion

Dissertação de mestrado integrado em Engenharia Biomédica (área de especialização em Engenharia Clínica)