Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology

Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37

Nonlinear Time-Fractional Differential Equations in Combustion Science

MSC 2010: 34A08 (main), 34G20, 80A25

Improved response time of laser etched polymer optical fiber Bragg grating humidity sensor

The humidity sensor made of polymer optical fiber Bragg grating (POFBG) responds to the water content change in fiber induced by the change of environmental condition. The response time strongly depends on fiber size as the water change is a diffusion process. The ultra short laser pulses have been providing an effective micro fabrication method to achieve spatial localized modification in materials. In this work we used the excimer laser to create different microstructures (slot, D-shape) in POFBG to improve its performance. A significant improvement in the response time has been achieved in a laser etched D-shaped POFBG humidity sensor.

Variational Markov chain Monte Carlo for Bayesian smoothing of non-linear diffusions

In this paper we develop set of novel Markov Chain Monte Carlo algorithms for Bayesian smoothing of partially observed non-linear diffusion processes. The sampling algorithms developed herein use a deterministic approximation to the posterior distribution over paths as the proposal distribution for a mixture of an independence and a random walk sampler. The approximating distribution is sampled by simulating an optimized time-dependent linear diffusion process derived from the recently developed variational Gaussian process approximation method. The novel diffusion bridge proposal derived from the variational approximation allows the use of a flexible blocking strategy that further improves mixing, and thus the efficiency, of the sampling algorithms. The algorithms are tested on two diffusion processes: one with double-well potential drift and another with SINE drift. The new algorithm's accuracy and efficiency is compared with state-of-the-art hybrid Monte Carlo based path sampling. It is shown that in practical, finite sample applications the algorithm is accurate except in the presence of large observation errors and low to a multi-modal structure in the posterior distribution over paths. More importantly, the variational approximation assisted sampling algorithm outperforms hybrid Monte Carlo in terms of computational efficiency, except when the diffusion process is densely observed with small errors in which case both algorithms are equally efficient. © 2011 Springer-Verlag.

Mechanistic Models of Anti-HIV Microbicide Drug Delivery

A new modality for preventing HIV transmission is emerging in the form of topical microbicides. Some clinical trials have shown some promising results of these methods of protection while other trials have failed to show efficacy. Due to the relatively novel nature of microbicide drug transport, a rigorous, deterministic analysis of that transport can help improve the design of microbicide vehicles and understand results from clinical trials. This type of analysis can aid microbicide product design by helping understand and organize the determinants of drug transport and the potential efficacies of candidate microbicide products.

Microbicide drug transport is modeled as a diffusion process with convection and reaction effects in appropriate compartments. This is applied here to vaginal gels and rings and a rectal enema, all delivering the microbicide drug Tenofovir. Although the focus here is on Tenofovir, the methods established in this dissertation can readily be adapted to other drugs, given knowledge of their physical and chemical properties, such as the diffusion coefficient, partition coefficient, and reaction kinetics. Other dosage forms such as tablets and fiber meshes can also be modeled using the perspective and methods developed here.

The analyses here include convective details of intravaginal flows by both ambient fluid and spreading gels with different rheological properties and applied volumes. These are input to the overall conservation equations for drug mass transport in different compartments. The results are Tenofovir concentration distributions in time and space for a variety of microbicide products and conditions. The Tenofovir concentrations in the vaginal and rectal mucosal stroma are converted, via a coupled reaction equation, to concentrations of Tenofovir diphosphate, which is the active form of the drug that functions as a reverse transcriptase inhibitor against HIV. Key model outputs are related to concentrations measured in experimental pharmacokinetic (PK) studies, e.g. concentrations in biopsies and blood. A new measure of microbicide prophylactic functionality, the Percent Protected, is calculated. This is the time dependent volume of the entire stroma (and thus fraction of host cells therein) in which Tenofovir diphosphate concentrations equal or exceed a target prophylactic value, e.g. an EC50.

Results show the prophylactic potentials of the studied microbicide vehicles against HIV infections. Key design parameters for each are addressed in application of the models. For a vaginal gel, fast spreading at small volume is more effective than slower spreading at high volume. Vaginal rings are shown to be most effective if inserted and retained as close to the fornix as possible. Because of the long half-life of Tenofovir diphosphate, temporary removal of the vaginal ring (after achieving steady state) for up to 24h does not appreciably diminish Percent Protected. However, full steady state (for the entire stromal volume) is not achieved until several days after ring insertion. Delivery of Tenofovir to the rectal mucosa by an enema is dominated by surface area of coated mucosa and whether the interiors of rectal crypts are filled with the enema fluid. For the enema 100% Percent Protected is achieved much more rapidly than for vaginal products, primarily because of the much thinner epithelial layer of the mucosa. For example, 100% Percent Protected can be achieved with a one minute enema application, and 15 minute wait time.

Results of these models have good agreement with experimental pharmacokinetic data, in animals and clinical trials. They also improve upon traditional, empirical PK modeling, and this is illustrated here. Our deterministic approach can inform design of sampling in clinical trials by indicating time periods during which significant changes in drug concentrations occur in different compartments. More fundamentally, the work here helps delineate the determinants of microbicide drug delivery. This information can be the key to improved, rational design of microbicide products and their dosage regimens.

INVESTIGATION OF MAGNESIUM ION CHARGE STORAGE MECHANISM IN MANGANESE DIOXIDE

Magnesium (Mg) battery is considered as a promising candidate for the next generation battery technology that could potentially replace the current lithium (Li)-ion batteries due to the following factors. Magnesium possesses a higher volumetric capacity than commercialized Li-ion battery anode materials. Additionally, the low cost and high abundance of Mg compared to Li makes Mg batteries even more attractive. Moreover, unlike metallic Li anodes which have a tendency to develop a dendritic structure on the surface upon the cycling of the battery, Mg metal is known to be free from such a hazardous phenomenon. Due to these merits of Mg as an anode, the topic of rechargea¬ble Mg batteries has attracted considerable attention among researchers in the last few decades. However, the aforementioned advantages of Mg batteries have not been fully utilized due to the serious kinetic limitation of Mg2+ diffusion process in many hosting compounds which is believed to be due to a strong electrostatic interaction between divalent Mg2+ ions and hosting matrix. This serious kinetic hindrance is directly related to the lack of cathode materials for Mg battery that provide comparable electrochemical performances to that of Li-based system. Manganese oxide (MnO2) is one of the most well studied electrode materials due to its excellent electrochemical properties, including high Li+ ion capacity and relatively high operating voltage (i.e., ~ 4 V vs. Li/Li+ for LiMn2O4 and ~ 3.2 V vs. Mg/Mg2+). However, unlike the good electrochemical properties of MnO2 realized in Li-based systems, rather poor electrochemical performances have been reported in Mg based systems, particularly with low capacity and poor cycling performances. While the origin of the observed poor performances is believed to be due to the aforementioned strong ionic interaction between the Mg2+ ions and MnO2 lattice resulting in a limited diffusion of Mg2+ ions in MnO2, very little has been explored regarding the charge storage mechanism of MnO2 with divalent Mg2+ ions. This dissertation investigates the charge storage mechanism of MnO2, focusing on the insertion behaviors of divalent Mg2+ ions and exploring the origins of the limited Mg2+ insertion behavior in MnO2. It is found that the limited Mg2+ capacity in MnO2 can be significantly improved by introducing water molecules in the Mg electrolyte system, where the water molecules effectively mitigated the kinetic hindrance of Mg2+ insertion process. The combination of nanostructured MnO2 electrode and water effect provides a synergic effect demonstrating further enhanced Mg2+ insertion capability. Furthermore, it is demonstrated in this study that pre-cycling MnO2 electrodes in water-containing electrolyte activates MnO2 electrode, after which improved Mg2+ capacity is maintained in dry Mg electrolyte. Based on a series of XPS analysis, a conversion mechanism is proposed where magnesiated MnO2 undergoes a conversion reaction to Mg(OH)2 and MnOx and Mn(OH)y species in the presence of water molecules. This conversion process is believed to be the driving force that generates the improved Mg2+ capacity in MnO2 along with the water molecule’s charge screening effect. Finally, it is discussed that upon a consecutive cycling of MnO2 in the water-containing Mg electrolyte, structural water is generated within the MnO2 lattice, which is thought to be the origin of the observed activation phenomenon. The results provided in this dissertation highlight that the divalency of Mg2+ ions result in very different electrochemical behaviors than those of the well-studied monovalent Li+ ions towards MnO2.

A simulação do real organizacional: O método dos casos como ponte entre o conhecimento tácito e o académico

O desenvolvimento da ciência organizacional tem sido marcado pelo desdobramento de modas e modelos nas mais diversas áreas. O presente artigo reflecte sobre o seu papel, particularmente, por via dos estudos de caso. Sendo as escolas de negócios e de gestão um dos actores importantes na difusão destes modismos, o método dos casos, enquanto estratégia pedagógica, é entendido aqui como um importante veículo de coordenação entre a investigação científica organizacional e a sua realidade. Contribui para a aproximação entre os vários intervenientes neste processo (professores, alunos, gestores, líderes e empresários). Advoga-se a sua importância por estabelecer uma ponte entre a academia e a o mundo organizacional, entre o conhecimento teórico dos académicos e o conhecimento tácito dos agentes empresariais.

Dysprosium transport in Nd-Fe-B pellets

The addition of heavy rare earth (RE) elements to Nd2Fe14B based magnets to form (Nd,Dy)2Fe14B is known to increase the coercivity and high temperature performance required for hybrid vehicle electric motors and other extreme temperature applications. Attempts to conserve heavy rare earth elements for high temperature (RE)2Fe14B based magnets have led to the development of a grain boundary diffusion process for bulk magnets. This process relies on transport of a heavy rare earth, such as Dy, into a bulk Nd2Fe14B magnet along pores, a low volume fraction of eutectic liquid along grain boundary grain triple junctions and grain boundaries. This enriches the grain surfaces in Dy through the thickness of the bulk magnet, leading to larger increases coercivity with a smaller Dy concentration than can be achieved with homogeneous alloys. Attempts to carry out the same process during sintering require significant control of Dy transport efficiency. The macroscopic transport of Dy in Nd2.7Fe14B1.4 based powder packs is studied using a 'layered' pellet, where Nd2.7Fe14B1.4powder is an interlayer and Dy source as a center layer. The sintering of this layered pellet provided evidence for very large effective diffusion lengths aided by Dy rich liquid flow through connected porosity. Approaches to controlling Dy transportation include decreasing the liquid phase transport capability of the powder pack by increasing the melting point of the Dy source and the decreasing amount of RE rich liquid in the powder packs. The solid-liquid reaction is studied in which melt spun Nd2.7Fe14B1.4 ribbons are PVD coated with Dy-Fe eutectic composition and then thermally treated. The resulting microstructure from the reaction between Dy-Fe eutectic coating and Nd2.7Fe14B1.4 ribbon is interpreted as support for a proposed dissolution/reprecipitation process between solid and liquid phases. The estimate the diffusion coefficient and the effective diffusion length of Dy sources in Nd2.7Fe14B1.4 layered pellets and melt spun ribbons were obtained from the calculation of Fick's second law combined with EDS results from the experiment. The results indicate that the effective diffusion coefficient of Dy in the layered pellets is higher than the diffusion in ribbons due to its higher porosity than ribbons.

El efecto de la definición regulatoria de banda ancha sobre la difusión y la competencia del mercado de servicios de Internet fijo en Colombia

A partir de la dinámica evolutiva de la economía de las Tecnologías de la Información y las Comunicaciones y el establecimiento de estándares mínimos de velocidad en distintos contextos regulatorios a nivel mundial, en particular en Colombia, en el presente artículo se presentan diversas aproximaciones empíricas para evaluar los efectos reales que conlleva el establecimiento de definiciones de servicios de banda ancha en el mercado de Internet fijo. Con base en los datos disponibles para Colombia sobre los planes de servicios de Internet fijo ofrecidos durante el periodo 2006-2012, se estima para los segmentos residencial y corporativo el proceso de difusión logístico modificado y el modelo de interacción estratégica para identificar los impactos generados sobre la masificación del servicio a nivel municipal y sobre las decisiones estratégicas que adoptan los operadores, respectivamente. Respecto a los resultados, se encuentra, por una parte, que las dos medidas regulatorias establecidas en Colombia en 2008 y 2010 presentan efectos significativos y positivos sobre el desplazamiento y el crecimiento de los procesos de difusión a nivel municipal. Por otra parte, se observa sustituibilidad estratégica en las decisiones de oferta de velocidad de descarga por parte de los operadores corporativos mientras que, a partir del análisis de distanciamiento de la velocidad ofrecida respecto al estándar mínimo de banda ancha, se demuestra que los proveedores de servicios residenciales tienden a agrupar sus decisiones de velocidad alrededor de los niveles establecidos por regulación.

Flow injection analysis of ethyl xanthate by gas diffusion and UV detection as CS(2) for process monitoring of sulfide ore flotation

A sensitive and robust analytical method for spectrophotometric determination of ethyl xanthate, CH(3)CH(2)OCS(2)(-) at trace concentrations in pulp solutions from froth flotation process is proposed. The analytical method is based on the decomposition of ethyl xanthate. EtX(-), with 2.0 mol L(-1) HCl generating ethanol and carbon disulfide. CS(2). A gas diffusion cell assures that only the volatile compounds diffuse through a PTFE membrane towards an acceptor stream of deionized water, thus avoiding the interferences of non-volatile compounds and suspended particles. The CS(2) is selectively detected by UV absorbance at 206 nm (epsilon = 65,000 L mol(-1) cm(-1)). The measured absorbance is directly proportional to EtX(-) concentration present in the sample solutions. The Beer`s law is obeyed in a 1 x 10(-6) to 2 x 10(-4) mol L(-1) concentration range of ethyl xanthate in the pulp with an excellent correlation coefficient (r = 0.999) and a detection limit of 3.1 x 10(-7) mol L(-1), corresponding to 38 mu g L. At flow rates of 200 mu L min(-1) of the donor stream and 100 mu L min(-1) of the acceptor channel a sampling rate of 15 injections per hour could be achieved with RSD < 2.3% (n = 10, 300 mu L injections of 1 x 10(-5) mol L(-1) EtX(-)). Two practical applications demonstrate the versatility of the FIA method: (i) evaluation the free EtX(-) concentration during a laboratory study of the EtX(-) adsorption capacity on pulverized sulfide ore (pyrite) and (ii) monitoring of EtX(-) at different stages (from starting load to washing effluents) of a flotation pilot plant processing a Cu-Zn sulfide ore. (C) 2010 Elsevier By. All rights reserved.