Mass transfer and chemical reaction on a distillation plate

A multistage distillation column in which mass transfer and a reversible chemical reaction occurred simultaneously, has been investigated to formulate a technique by which this process can be analysed or predicted. A transesterification reaction between ethyl alcohol and butyl acetate, catalysed by concentrated sulphuric acid, was selected for the investigation and all the components were analysed on a gas liquid chromatograph. The transesterification reaction kinetics have been studied in a batch reactor for catalyst concentrations of 0.1 - 1.0 weight percent and temperatures between 21.4 and 85.0 °C. The reaction was found to be second order and dependent on the catalyst concentration at a given temperature. The vapour liquid equilibrium data for six binary, four ternary and one quaternary systems are measured at atmospheric pressure using a modified Cathala dynamic equilibrium still. The systems with the exception of ethyl alcohol - butyl alcohol mixtures, were found to be non-ideal. Multicomponent vapour liquid equilibrium compositions were predicted by a computer programme which utilised the Van Laar constants obtained from the binary data sets. Good agreement was obtained between the predicted and experimental quaternary equilibrium vapour compositions. Continuous transesterification experiments were carried out in a six stage sieve plate distillation column. The column was 3" in internal diameter and of unit construction in glass. The plates were 8" apart and had a free area of 7.7%. Both the liquid and vapour streams were analysed. The component conversion was dependent on the boilup rate and the reflux ratio. Because of the presence of the reaction, the concentration of one of the lighter components increased below the feed plate. In the same region a highly developed foam was formed due to the presence of the catalyst. The experimental results were analysed by the solution of a series of simultaneous enthalpy and mass equations. Good agreement was obtained between the experimental and calculated results.

Transmission comparison of ultra-long Raman fibre laser based amplification with first and dual order Raman amplification using 10×118 Gbit/s DP-QPSK

Experimental investigations of 10×118 Gbit/s DP-QPSK WDM transmission using three types of distributed Raman amplification techniques are presented. Novel ultra-long Raman fibre laser based amplification with second order counter-propagated pumping is compared with conventional first order and dual order counter-pumped Raman amplification. We demonstrate that URFL based amplification can extend the transmission reach up to a distance of 7520 km in comparison with 5010 km and 6180 km using first order and dual order Raman amplification respectively. © 2014 IEEE.

Analytical characterization of a quasi-lossless Raman-amplified fibre transmission scheme

In this paper, we explore theoretically a novel amplifier scheme, that combines second order bidirectional pumping and fiber Bragg grating reflectors to achieve quasi-lossless transmission over long spans. The scheme is shown to significantly reduce the signal power variation over the span as compared to commonly used schemes with the same number of pump sources. It is concluded that it can be practical to analyze a simplified system of three equations, obtained by neglecting noise terms, that would allow us to better understand the physical mechanisms and to find analytical estimates for the required pump power or the power variations along the fibre span

Performance of the Bayesian online algorithm for the perceptron

In this letter, we derive continuum equations for the generalization error of the Bayesian online algorithm (BOnA) for the one-layer perceptron with a spherical covariance matrix using the Rosenblatt potential and show, by numerical calculations, that the asymptotic performance of the algorithm is the same as the one for the optimal algorithm found by means of variational methods with the added advantage that the BOnA does not use any inaccessible information during learning. © 2007 IEEE.

Polynomial Expansions for Solutions of Higher-Order Bessel Heat Equation in Quantum Calculus

Mathematics Subject Class.: 33C10,33D60,26D15,33D05,33D15,33D90

Viability Kernels of Higher Order

AMS subject classification: Primary 34A60, Secondary 49K24.

Probabilistic Approach to the Neumann Problem for a Symmetric Operator

2000 Mathematics Subject Classification: Primary 60J45, 60J50, 35Cxx; Secondary 31Cxx.

Methyl chloride purification for the silicone industry

This study experimentally investigated methyl chloride (MeCl) purification method using an inhouse designed and built volumetric adsorption/desorption rig. MeCl is an essential raw material in the manufacture of silicone however all technical grades of MeCl contain concentrations (0.2 - 1.0 % wt) of dimethyl ether (DME) which poison the process. The project industrial partner had previously exhausted numerous separation methods, which all have been deemed not suitable for various reasons. Therefore, adsorption/desorption separation was proposed in this study as a potential solution with less economic and environmental impact. Pure component adsorption/desorption was carried out for DME and MeCl on six different adsorbents namely: zeolite molecular sieves (types 4 Å and 5 Å); silica gels (35-70 mesh, amorphous precipitated, and 35-60 mesh) and granular activated carbon (type 8-12 mesh). Subsequent binary gas mixture adsorption in batch and continuous mode was carried out on both zeolites and all three silica gels following thermal pre-treatment in vacuum. The adsorbents were tested as received and after being subjected to different thermal and vacuum pre-treatment conditions. The various adsorption studies were carried out at low pressure and temperature ranges of 0.5 - 3.5 atm and 20 - 100 °C. All adsorbents were characterised using Brunauer Emmett Teller (BET), thermogravimetric analysis (TGA), scanning electron microscopy (SEM) and energy dispersive x-ray analysis (EDXA) to investigate their physical and chemical properties. The well-known helium (He) expansion method was used to determine the empty manifold and adsorption cell (AC) regions and respective void volumes for the different adsorbents. The amounts adsorbed were determined using Ideal gas laws via the differential pressure method. The heat of adsorption for the various adsorbate-adsorbent (A-S) interactions was calculated using a new calorimetric method based on direct temperature measurements inside the AC. Further adsorption analysis included use of various empirical and kinetic models to determine and understand the behaviour of the respective interactions. The gas purification behaviour was investigated using gas chromatography and mass spectroscopy (GC-MC) analysis. Binary gas mixture samples were syringed from the manifold iii and AC outlet before and after adsorption/desorption analysis through manual sample injections into the GC-MS to detect and quantify the presence of DME and ultimately observe for methyl chloride purification. Convincing gas purification behaviour was confirmed using two different GC columns, thus giving more confidence on the measurement reliability. From the single pure component adsorption of DME and MeCl on the as received zeolite 4A subjected to 1 h vacuum pre-treatment, both gases exhibited pseudo second order adsorption kinetics with DME exhibiting a rate constant nearly double that of MeCl thus suggesting a faster rate of adsorption. From the adsorption isotherm classification both DME and MeCl exhibited Type II and I adsorption isotherm classifications, respectively. The strength of bonding was confirmed by the differential heat of adsorption measurement, which was found to be 23.30 and 10.21 kJ mol-1 for DME and MeCl, respectively. The former is believed to adsorb heterogeneously through hydrogen bonding whilst MeCl adsorbs homogenously via van der Waal’s (VDW) forces. Single pure component adsorption on as received zeolite 5A, silica gels (35-70, amorphous precipitated and 35-60) resulted in similar adsorption/desorption behaviour in similar quantities (mol kg-1). The adsorption isotherms for DME and MeCl on zeolite 5A, silica gels (35-70, amorphous precipitated and 35-60) and activated carbon 8-12 exhibited Type I classifications, respectively. Experiments on zeolite 5A indicated that DME adsorbed stronger, faster and with a slightly stronger strength of interaction than MeCl but in lesser quantities. On the silica gels adsorbents, DME exhibited a slightly greater adsorption capacity whilst adsorbing at a similar rate and strength of interaction compared to MeCl. On the activated carbon adsorbent, MeCl exhibited the greater adsorption capacity at a faster rate but with similar heats of adsorption. The effect of prolonged vacuum (15 h), thermal pre-treatment (150 °C) and extended equilibrium time (15 min) were investigated for the adsorption behaviour of DME and MeCl on both zeolites 4A and 5A, respectively. Compared to adsorption on as received adsorbents subjected to 1 h vacuum the adsorption capacities for DME and MeCl were found to increase by 1.95 % and 20.37 % on zeolite 4A and by 4.52 % and 6.69 % on zeolite 5A, respectively. In addition the empirical and kinetic models and differential heats of adsorption resulted in more definitive fitting curves and trends due to the true equilibrium position of the adsorbate with the adsorbent. Batch binary mixture adsorption on thermally and vacuum pre-treated zeolite 4A demonstrated purification behaviour of all adsorbents used for MeCl streams containing DME impurities, with a concentration as low as 0.66 vol. %. The GC-MS analysis showed no DME detection for the tested concentration mixtures at the AC outlet after 15 or 30 min, whereas MeCl was detectable in measurable amounts. Similar behaviour was also observed when carrying out adsorption in continuous mode. On the other hand, similar studies on the other adsorbents did not show such favourable MeCl purification behaviour. Overall this study investigated a wide range of adsorbents (zeolites, silica gels and activated carbon) and demonstrated for the first time potential to purify MeCl streams containing DME impurities using adsorption/desorption separation under different adsorbent pre-treatment and adsorption operating conditions. The study also revealed for the first time the adsorption isotherms, empirical and kinetic models and heats of adsorption for the respective adsorbentsurface (A-S) interactions. In conclusion, this study has shown strong evidence to propose zeolite 4A for adsorptive purification of MeCl. It is believed that with a technical grade MeCl stream competitive yet simultaneous co-adsorption of DME and MeCl occurs with evidence of molecular sieiving effects whereby the larger DME molecules are unable to penetrate through the adsorbent bed whereas the smaller MeCl molecules diffuse through resulting in a purified MeCl stream at the AC outlet. Ultimately, further studies are recommended for increased adsorption capacities by considering wider operating conditions, e.g. different adsorbent thermal and vacuum pre-treatment and adsorbing at temperatures closer to the boiling point of the gases and different conditions of pressure and temperature.

RIN transfer in 2nd-order distributed amplification with ultralong fiber lasers

We investigate numerically the effect of ultralong Raman laser fiber amplifier design parameters, such as span length, pumping distribution and grating reflectivity, on the RIN transfer from the pump to the transmitted signal. Comparison is provided to the performance of traditional second-order Raman amplified schemes, showing a relative performance penalty for ultralong laser systems that gets smaller as span length increases. We show that careful choice of system parameters can be used to partially offset such penalty. © 2010 Optical Society of America.

Incomplete pairwise comparison matrices and weighting methods

A special class of preferences, given by a directed acyclic graph, is considered. They are represented by incomplete pairwise comparison matrices as only partial information is available: for some pairs no comparison is given in the graph. A weighting method satisfies the property linear order preservation if it always results in a ranking such that an alternative directly preferred to another does not have a lower rank. We study whether two procedures, the Eigenvector Method and the Logarithmic Least Squares Method meet this axiom. Both weighting methods break linear order preservation, moreover, the ranking according to the Eigenvector Method depends on the incomplete pairwise comparison representation chosen.

Lattice Boltzmann method for flow and heat transfer in microgeometries

Recent technological developments have made it possible to design various microdevices where fluid flow and heat transfer are involved. For the proper design of such systems, the governing physics needs to be investigated. Due to the difficulty to study complex geometries in micro scales using experimental techniques, computational tools are developed to analyze and simulate flow and heat transfer in microgeometries. However, conventional numerical methods using the Navier-Stokes equations fail to predict some aspects of microflows such as nonlinear pressure distribution, increase mass flow rate, slip flow and temperature jump at the solid boundaries. This necessitates the development of new computational methods which depend on the kinetic theory that are both accurate and computationally efficient. In this study, lattice Boltzmann method (LBM) was used to investigate the flow and heat transfer in micro sized geometries. The LBM depends on the Boltzmann equation which is valid in the whole rarefaction regime that can be observed in micro flows. Results were obtained for isothermal channel flows at Knudsen numbers higher than 0.01 at different pressure ratios. LBM solutions for micro-Couette and micro-Poiseuille flow were found to be in good agreement with the analytical solutions valid in the slip flow regime (0.01 < Kn < 0.1) and direct simulation Monte Carlo solutions that are valid in the transition regime (0.1 < Kn < 10) for pressure distribution and velocity field. The isothermal LBM was further extended to simulate flows including heat transfer. The method was first validated for continuum channel flows with and without constrictions by comparing the thermal LBM results against accurate solutions obtained from analytical equations and finite element method. Finally, the capability of thermal LBM was improved by adding the effect of rarefaction and the method was used to analyze the behavior of gas flow in microchannels. The major finding of this research is that, the newly developed particle-based method described here can be used as an alternative numerical tool in order to study non-continuum effects observed in micro-electro-mechanical-systems (MEMS).

Lattice Boltzmann Method for Flow and Heat Transfer in Microgeometries

Recent technological developments have made it possible to design various microdevices where fluid flow and heat transfer are involved. For the proper design of such systems, the governing physics needs to be investigated. Due to the difficulty to study complex geometries in micro scales using experimental techniques, computational tools are developed to analyze and simulate flow and heat transfer in microgeometries. However, conventional numerical methods using the Navier-Stokes equations fail to predict some aspects of microflows such as nonlinear pressure distribution, increase mass flow rate, slip flow and temperature jump at the solid boundaries. This necessitates the development of new computational methods which depend on the kinetic theory that are both accurate and computationally efficient. In this study, lattice Boltzmann method (LBM) was used to investigate the flow and heat transfer in micro sized geometries. The LBM depends on the Boltzmann equation which is valid in the whole rarefaction regime that can be observed in micro flows. Results were obtained for isothermal channel flows at Knudsen numbers higher than 0.01 at different pressure ratios. LBM solutions for micro-Couette and micro-Poiseuille flow were found to be in good agreement with the analytical solutions valid in the slip flow regime (0.01 < Kn < 0.1) and direct simulation Monte Carlo solutions that are valid in the transition regime (0.1 < Kn < 10) for pressure distribution and velocity field. The isothermal LBM was further extended to simulate flows including heat transfer. The method was first validated for continuum channel flows with and without constrictions by comparing the thermal LBM results against accurate solutions obtained from analytical equations and finite element method. Finally, the capability of thermal LBM was improved by adding the effect of rarefaction and the method was used to analyze the behavior of gas flow in microchannels. The major finding of this research is that, the newly developed particle-based method described here can be used as an alternative numerical tool in order to study non-continuum effects observed in micro-electro-mechanical-systems (MEMS).

Uso de correntropia na generalização de funções cicloestacionárias e aplicações para a extração de características de sinais modulados

Information extraction is a frequent and relevant problem in digital signal processing. In the past few years, different methods have been utilized for the parameterization of signals and the achievement of efficient descriptors. When the signals possess statistical cyclostationary properties, the Cyclic Autocorrelation Function (CAF) and the Spectral Cyclic Density (SCD) can be used to extract second-order cyclostationary information. However, second-order cyclostationary information is poor in nongaussian signals, as the cyclostationary analysis in this case should comprise higher-order statistical information. This paper proposes a new mathematical tool for the higher-order cyclostationary analysis based on the correntropy function. Specifically, the cyclostationary analysis is revisited focusing on the information theory, while the Cyclic Correntropy Function (CCF) and Cyclic Correntropy Spectral Density (CCSD) are also defined. Besides, it is analytically proven that the CCF contains information regarding second- and higher-order cyclostationary moments, being a generalization of the CAF. The performance of the aforementioned new functions in the extraction of higher-order cyclostationary characteristics is analyzed in a wireless communication system where nongaussian noise exists.

Estimação e previsão no processo INARCH(2)

In the last decades the study of integer-valued time series has gained notoriety due to its broad applicability (modeling the number of car accidents in a given highway, or the number of people infected by a virus are two examples). One of the main interests of this area of study is to make forecasts, and for this reason it is very important to propose methods to make such forecasts, which consist of nonnegative integer values, due to the discrete nature of the data. In this work, we focus on the study and proposal of forecasts one, two and h steps ahead for integer-valued second-order autoregressive conditional heteroskedasticity processes [INARCH (2)], and in determining some theoretical properties of this model, such as the ordinary moments of its marginal distribution and the asymptotic distribution of its conditional least squares estimators. In addition, we study, via Monte Carlo simulation, the behavior of the estimators for the parameters of INARCH(2) processes obtained using three di erent methods (Yule- Walker, conditional least squares, and conditional maximum likelihood), in terms of mean squared error, mean absolute error and bias. We present some forecast proposals for INARCH(2) processes, which are compared again via Monte Carlo simulation. As an application of this proposed theory, we model a dataset related to the number of live male births of mothers living at Riachuelo city, in the state of Rio Grande do Norte, Brazil.

Estimação e previsão no processo INARCH(2)

In the last decades the study of integer-valued time series has gained notoriety due to its broad applicability (modeling the number of car accidents in a given highway, or the number of people infected by a virus are two examples). One of the main interests of this area of study is to make forecasts, and for this reason it is very important to propose methods to make such forecasts, which consist of nonnegative integer values, due to the discrete nature of the data. In this work, we focus on the study and proposal of forecasts one, two and h steps ahead for integer-valued second-order autoregressive conditional heteroskedasticity processes [INARCH (2)], and in determining some theoretical properties of this model, such as the ordinary moments of its marginal distribution and the asymptotic distribution of its conditional least squares estimators. In addition, we study, via Monte Carlo simulation, the behavior of the estimators for the parameters of INARCH(2) processes obtained using three di erent methods (Yule- Walker, conditional least squares, and conditional maximum likelihood), in terms of mean squared error, mean absolute error and bias. We present some forecast proposals for INARCH(2) processes, which are compared again via Monte Carlo simulation. As an application of this proposed theory, we model a dataset related to the number of live male births of mothers living at Riachuelo city, in the state of Rio Grande do Norte, Brazil.