Liquid-phase adsorption of n-paraffins on type 5A molecular sieves

As a basis for the commercial separation of normal paraffins a detailed study has been made of factors affecting the adsorption of binary liquid mixtures of high molecular weight normal paraffins (C12, C16, and C20) from isooctane on type 5A molecular sieves. The literature relating to molecular sieve properties and applications, and to liquid-phase adsorption of high molecular weight normal paraffin compounds by zeolites, was reviewed. Equilibrium isotherms were determined experimentally for the normal paraffins under investigation at temperatures of 303oK, 323oK and 343oK and showed a non-linear, favourable- type of isotherm. A higher equilibrium amount was adsorbed with lower molecular weight normal paraffins. An increase in adsorption temperature resulted in a decrease in the adsorption value. Kinetics of adsorption were investigated for the three normal paraffins at different temperatures. The effective diffusivity and the rate of adsorption of each normal paraffin increased with an increase in temperature in the range 303 to 343oK. The value of activation energy was between 2 and 4 kcal/mole. The dynamic properties of the three systems were investigated over a range of operating conditions (i.e. temperature, flow rate, feed concentration, and molecular sieve size in the range 0.032 x 10-3 to 2 x 10-3m) with a packed column. The heights of adsorption zones calculated by two independent equations (one based on a constant width, constant velocity and adsorption zone and the second on a solute material balance within the adsorption zone) agreed within 3% which confirmed the validity of using the mass transfer zone concept to provide a simple design procedure for the systems under study. The dynamic capacity of type 5A sieves for n-eicosane was lower than for n-hexadecane and n-dodecane corresponding to a lower equilibrium loading capacity and lower overall mass transfer coefficient. The values of individual external, internal, theoretical and experimental overall mass transfer coefficient were determined. The internal resistance was in all cases rate-controlling. A mathematical model for the prediction of dynamic breakthrough curves was developed analytically and solved from the equilibrium isotherm and the mass transfer rate equation. The experimental breakthrough curves were tested against both the proposed model and a graphical method developed by Treybal. The model produced the best fit with mean relative percent deviations of 26, 22, and 13% for the n-dodecane, n-hexadecane, and n-eicosane systems respectively.

Dynamic simulation of chemical processes

This thesis describes the design and implementation of an interactive dynamic simulator called DASPRII. The starting point of this research has been an existing dynamic simulation package, DASP. DASPII is written in standard FORTRAN 77 and is implemented on universally available IBM-PC or compatible machines. It provides a means for the analysis and design of chemical processes. Industrial interest in dynamic simulation has increased due to the recent increase in concern over plant operability, resiliency and safety. DASPII is an equation oriented simulation package which allows solution of dynamic and steady state equations. The steady state can be used to initialise the dynamic simulation. A robust non linear algebraic equation solver has been implemented for steady state solution. This has increased the general robustness of DASPII, compared to DASP. A graphical front end is used to generate the process flowsheet topology from a user constructed diagram of the process. A conversational interface is used to interrogate the user with the aid of a database, to complete the topological information. An original modelling strategy implemented in DASPII provides a simple mechanism for parameter switching which creates a more flexible simulation environment. The problem description generated is by a further conversational procedure using a data-base. The model format used allows the same model equations to be used for dynamic and steady state solution. All the useful features of DASPI are retained in DASPII. The program has been demonstrated and verified using a number of example problems, Significant improvements using the new NLAE solver have been shown. Topics requiring further research are described. The benefits of variable switching in models has been demonstrated with a literature problem.

An investigation of the dynamic characteristics of a bolted-rotor system

A Jeffcott rotor consists of a disc at the centre of an axle supported at its end by bearings. A bolted Jeffcott rotor is formed by two discs, each with a shaft on one side. The discs are held together by spring loaded bolts near the outer edge. When the rotor turns there is tendency for the discs to separate on one side. This effect is more marked if the rotor is unbalanced, especially at resonance speeds. The equations of motion of the system have been developed with four degrees of freedom to include the rotor and bearing movements in the respective axes. These equations which include non-linear terms caused by the rotor opening, are subjected to external force such from rotor imbalance. A simulation model based on these equations was created using SIMULINK. An experimental test rig was used to characterise the dynamic features. Rotor discs open at a lateral displacement of the rotor of 0.8 mm. This is the threshold value used to show the change of stiffness from high stiffness to low stiffness. The experimental results, which measure the vibration amplitude of the rotor, show the dynamic behaviour of the bolted rotor due to imbalance. Close agreement of the experimental and theoretical results from time histories, waterfall plots, pseudo-phase plots and rotor orbit plot, indicated the validity of the model and existence of the non-linear jump phenomenon.

Formulation of topical non-steroidal anti-inflammatory agents

Reversed-pahse high-performance liquid chromatographic (HPLC) methods were developed for the assay of indomethacin, its decomposition products, ibuprofen and its (tetrahydro-2-furanyl)methyl-, (tetrahydro-2-(2H)pyranyl)methyl- and cyclohexylmethyl esters. The development and application of these HPLC systems were studied. A number of physico-chemical parameters that affect percutaneous absorption were investigated. The pKa values of indomethacin and ibuprofen were determined using the solubility method. Potentiometric titration and the Taft equation were also used for ibuprofen. The incorporation of ethanol or propylene glycol in the solvent resulted in an improvement in the aqueous solubility of these compounds. The partition coefficients were evaluated in order to establish the affinity of these drugs towards the stratum corneum. The stability of indomethacin and of ibuprofen esters were investigated and the effect of temperature and pH on the decomposition rates were studied. The effect of cetyltrimethylammonium bromide on the alkaline degradation of indomethacin was also followed. In the presence of alcohol, indomethacin alcoholysis was observed and the kinetics of decomposition were subjected to non-linear regression analysis and the rate constants for the various pathways were quantified. The non-isothermal, sufactant non-isoconcentration and non-isopH degradation of indomethacin were investigated. The analysis of the data was undertaken using NONISO, a BASIC computer program. The degradation profiles obtained from both non-iso and iso-kinetic studies show that there is close concordance in the results. The metabolic biotransformation of ibuprofen esters was followed using esterases from hog liver and rat skin homogenates. The results showed that the esters were very labile under these conditions. The presence of propylene glycol affected the rates of enzymic hydrolysis of the ester. The hydrolysis is modelled using an equation involving the dielectric constant of the medium. The percutaneous absorption of indomethacin and of ibuprofen and its esters was followed from solutions using an in vitro excised human skin model. The absorption profiles followed first order kinetics. The diffusion process was related to their solubility and to the human skin/solvent partition coefficient. The percutaneous absorption of two ibuprofen esters from suspensions in 20% propylene glycol-water were also followed through rat skin with only ibuprofen being detected in the receiver phase. The sensitivity of ibuprofen esters to enzymic hydrolysis compared to the chemical hydrolysis may prove valuable in the formulation of topical delivery systems.

Bifurcation study for a vertical channel with constant flux and large aspect ratio

Using suitable coupled Navier-Stokes Equations for an incompressible Newtonian fluid we investigate the linear and non-linear steady state solutions for both a homogeneously and a laterally heated fluid with finite Prandtl Number (Pr=7) in the vertical orientation of the channel. Both models are studied within the Large Aspect Ratio narrow-gap and under constant flux conditions with the channel closed. We use direct numerics to identify the linear stability criterion in parametric terms as a function of Grashof Number (Gr) and streamwise infinitesimal perturbation wavenumber (making use of the generalised Squire’s Theorem). We find higher harmonic solutions at lower wavenumbers with a resonance of 1:3exist, for both of the heating models considered. We proceed to identify 2D secondary steady state solutions, which bifurcate from the laminar state. Our studies show that 2D solutions are found not to exist in certain regions of the pure manifold, where we find that 1:3 resonant mode 2D solutions exist, for low wavenumber perturbations. For the homogeneously heated fluid, we notice a jump phenomenon existing between the pure and resonant mode secondary solutions for very specific wavenumbers .We attempt to verify whether mixed mode solutions are present for this model by considering the laterally heated model with the same geometry. We find mixed mode solutions for the laterally heated model showing that a bridge exists between the pure and 1:3 resonant mode 2D solutions, of which some are stationary and some travelling. Further, we show that for the homogeneously heated fluid that the 2D solutions bifurcate in hopf bifurcations and there exists a manifold where the 2D solutions are stable to Eckhaus criterion, within this manifold we proceed to identify 3D tertiary solutions and find that the stability for said 3D bifurcations is not phase locked to the 2D state. For the homogeneously heated model we identify a closed loop within the neutral stability curve for higher perturbation wavenumubers and analyse the nature of the multiple 2D bifurcations around this loop for identical wavenumber and find that a temperature inversion occurs within this loop. We conclude that for a homogeneously heated fluid it is possible to have abrup ttransitions between the pure and resonant 2D solutions, and that for the laterally heated model there exist a transient bifurcation via mixed mode solutions.

NLSE-based model of a random distributed feedback fiber laser

In this work we propose a NLSE-based model of power and spectral properties of the random distributed feedback (DFB) fiber laser. The model is based on coupled set of non-linear Schrödinger equations for pump and Stokes waves with the distributed feedback due to Rayleigh scattering. The model considers random backscattering via its average strength, i.e. we assume that the feedback is incoherent. In addition, this allows us to speed up simulations sufficiently (up to several orders of magnitude). We found that the model of the incoherent feedback predicts the smooth and narrow (comparing with the gain spectral profile) generation spectrum in the random DFB fiber laser. The model allows one to optimize the random laser generation spectrum width varying the dispersion and nonlinearity values: we found, that the high dispersion and low nonlinearity results in narrower spectrum that could be interpreted as four-wave mixing between different spectral components in the quasi-mode-less spectrum of the random laser under study could play an important role in the spectrum formation. Note that the physical mechanism of the random DFB fiber laser formation and broadening is not identified yet. We investigate temporal and statistical properties of the random DFB fiber laser dynamics. Interestingly, we found that the intensity statistics is not Gaussian. The intensity auto-correlation function also reveals that correlations do exist. The possibility to optimize the system parameters to enhance the observed intrinsic spectral correlations to further potentially achieved pulsed (mode-locked) operation of the mode-less random distributed feedback fiber laser is discussed.

Solving Differential Equations by Parallel Laplace Method with Assured Accuracy

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Linear dispersive pre-defined peak amplitude modulation of spectrally modulated airy-based pulses

Spectrally modulated Airy-based pulses peak amplitude modulation (PAM) in linear dispersive media is investigated, designed, and numerically simulated. As it is shown here, it is possible to design the spectral modulation of the initial Airy-based pulses to obtain a pre-defined PAM profile as the pulse propagates. Although optical pulses self-amplitude modulation is a well-known effect under non-linear propagation, the designed Airy-based pulses exhibit PAM under linear dispersive propagation. This extraordinary linear propagation property can be applied in many kinds of dispersive media, enabling its use in a broad range of experiments and applications. © 2013 Optical Society of America.

Quasi-Monte Carlo Methods for some Linear Algebra Problems. Convergence and Complexity

We present quasi-Monte Carlo analogs of Monte Carlo methods for some linear algebra problems: solving systems of linear equations, computing extreme eigenvalues, and matrix inversion. Reformulating the problems as solving integral equations with a special kernels and domains permits us to analyze the quasi-Monte Carlo methods with bounds from numerical integration. Standard Monte Carlo methods for integration provide a convergence rate of O(N^(−1/2)) using N samples. Quasi-Monte Carlo methods use quasirandom sequences with the resulting convergence rate for numerical integration as good as O((logN)^k)N^(−1)). We have shown theoretically and through numerical tests that the use of quasirandom sequences improves both the magnitude of the error and the convergence rate of the considered Monte Carlo methods. We also analyze the complexity of considered quasi-Monte Carlo algorithms and compare them to the complexity of the analogous Monte Carlo and deterministic algorithms.

N–Dimensional Orthogonal Tile Sizing Problem

AMS subject classification: 68Q22, 90C90

Parameterized Link Functions in Generalized Linear Random Effect Models: a Case Study on Breast Cancer Treatment

In non-linear random effects some attention has been very recently devoted to the analysis ofsuitable transformation of the response variables separately (Taylor 1996) or not (Oberg and Davidian 2000) from the transformations of the covariates and, as far as we know, no investigation has been carried out on the choice of link function in such models. In our study we consider the use of a random effect model when a parameterized family of links (Aranda-Ordaz 1981, Prentice 1996, Pregibon 1980, Stukel 1988 and Czado 1997) is introduced. We point out the advantages and the drawbacks associated with the choice of this data-driven kind of modeling. Difficulties in the interpretation of regression parameters, and therefore in understanding the influence of covariates, as well as problems related to loss of efficiency of estimates and overfitting, are discussed. A case study on radiotherapy usage in breast cancer treatment is discussed.

Theoretical Investigation of Intra- and Inter-cellular Spatiotemporal Calcium Patterns in Microcirculation

Microcirculatory vessels are lined by endothelial cells (ECs) which are surrounded by a single or multiple layer of smooth muscle cells (SMCs). Spontaneous and agonist induced spatiotemporal calcium (Ca2+) events are generated in ECs and SMCs, and regulated by complex bi-directional signaling between the two layers which ultimately determines the vessel tone. The contractile state of microcirculatory vessels is an important factor in the determination of vascular resistance, blood flow and blood pressure. This dissertation presents theoretical insights into some of the important and currently unresolved phenomena in microvascular tone regulation. Compartmental and continuum models of isolated EC and SMC, coupled EC-SMC and a multi-cellular vessel segment with deterministic and stochastic descriptions of the cellular components were developed, and the intra- and inter-cellular spatiotemporal Ca2+ mobilization was examined. Coupled EC-SMC model simulations captured the experimentally observed localized subcellular EC Ca2+ events arising from the opening of EC transient receptor vanilloid 4 (TRPV4) channels and inositol triphosphate receptors (IP3Rs). These localized EC Ca2+ events result in endothelium-derived hyperpolarization (EDH) and Nitric Oxide (NO) production which transmit to the adjacent SMCs to ultimately result in vasodilation. The model examined the effect of heterogeneous distribution of cellular components and channel gating kinetics in determination of the amplitude and spread of the Ca2+ events. The simulations suggested the necessity of co-localization of certain cellular components for modulation of EDH and NO responses. Isolated EC and SMC models captured intracellular Ca2+ wave like activity and predicted the necessity of non-uniform distribution of cellular components for the generation of Ca2+ waves. The simulations also suggested the role of membrane potential dynamics in regulating Ca2+ wave velocity. The multi-cellular vessel segment model examined the underlying mechanisms for the intercellular synchronization of spontaneous oscillatory Ca2+ waves in individual SMC. From local subcellular events to integrated macro-scale behavior at the vessel level, the developed multi-scale models captured basic features of vascular Ca2+ signaling and provide insights for their physiological relevance. The models provide a theoretical framework for assisting investigations on the regulation of vascular tone in health and disease.

Fibonacci Series, Golden Proportions, and the Human Biology

Pythagoras, Plato and Euclid’s paved the way for Classical Geometry. The idea of shapes that can be mathematically defined by equations led to the creation of great structures of modern and ancient civilizations, and milestones in mathematics and science. However, classical geometry fails to explain the complexity of non-linear shapes replete in nature such as the curvature of a flower or the wings of a Butterfly. Such non-linearity can be explained by fractal geometry which creates shapes that emulate those found in nature with remarkable accuracy. Such phenomenon begs the question of architectural origin for biological existence within the universe. While the concept of a unifying equation of life has yet to be discovered, the Fibonacci sequence may establish an origin for such a development. The observation of the Fibonacci sequence is existent in almost all aspects of life ranging from the leaves of a fern tree, architecture, and even paintings, makes it highly unlikely to be a stochastic phenomenon. Despite its wide-spread occurrence and existence, the Fibonacci series and the Rule of Golden Proportions has not been widely documented in the human body. This paper serves to review the observed documentation of the Fibonacci sequence in the human body.

Análise não-linear do campo de temperaturas desenvolvidas durante a soldagem do tipo TIG contínuo em placas delgadas

This study offers an analytical approach in order to provide a determination of the temperature field developed during the DC TIG welding of a thin plate of aluminum. The non-linear characteristics of the phenomenon, such as the dependence of the thermophysical and mechanical properties with temperature were considered in this study. In addition to the conductive heat exchange process, were taken into account the exchange by natural convection and radiation. A transient analysis is performed in order to obtain the temperature field as a function of time. It is also discussed a three-dimensional modeling of the heat source. The results obtained from the analytical model were be compared with the experimental ones and those available in the literature. The analytical results show a good correlation with the experimental ones available in the literature, thus proving the feasibility and efficiency of the analytical method for the simulation of the heat cycle for this welding process.

Active suspension development based on energy analysis

This research focuses on developing active suspension optimal controllers for two linear and non-linear half-car models. A detailed comparison between quarter-car and half-car active suspension approaches is provided for improving two important scenarios in vehicle dynamics, i.e. ride quality and road holding. Having used a half-car vehicle model, heave and pitch motion are analyzed for those scenarios, with cargo mass as a variable. The governing equations of the system are analysed in a multi-energy domain package, i.e., 20-Sim. System equations are presented in the bond-graph language to facilitate calculation of energy usage. The results present optimum set of gains for both ride quality and road holding scenarios are the gains which has derived when maximum allowable cargo mass is considered for the vehicle. The energy implications of substituting passive suspension units with active ones are studied by considering not only the energy used by the actuator, but also the reduction in energy lost through the passive damper. Energy analysis showed less energy was dissipated in shock absorbers when either quarter-car or half-car controllers were used instead of passive suspension. It was seen that more energy could be saved by using half-car active controllers than the quarter-car ones. Results also proved that using active suspension units, whether quarter-car or half-car based, under those realistic limitations is energy-efficient and suggested.