First-order Mathematical Model Research Articles

Influence of flow direction in the performance of anaerobic filters

This work aimed to evaluate the performance of similar anaerobic filters operating with opposite wastewater flows, and compare mathematical models that describe the kinetics of organic matter degradation in both. Two pilot-scale filters were fed with domestic effluent – one filter worked as upflow (UAF) and the other as downflow (DAF). Experimental COD data obtained from samples taken along the length of the filters were used to fit the first-order mathematical model, the model proposed by Leduy and Zajic (1973) and the model proposed by Brasil et al. (2007). The first model showed overestimated reaction constant (k) values when compared to those obtained using the other models. The models proposed by Brasil et al. (2007) and Leduy and Zajic (1973) presented the highest coefficients of determination (R2). The average removal efficiencies of total COD were equal to 68 and 79% for UAF and DAF, respectively. The results revealed no significant differences between the two filters with regard to the variables applied.

Evaluation of oxygen transfer rates in stirred‐tank bioreactors for clinical manufacturing

Several methods are available for determining the volumetric oxygen transfer coefficient in bioreactors, though their application in industrial bioprocess has been limited. To be practically useful, mass transfer measurements made in nonfermenting systems must be consistent with observed microbial respiration rates. This report details a procedure for quantifying the relationship between agitation frequency and oxygen transfer rate that was applied in stirred-tank bioreactors used for clinical biologics manufacturing. The intrinsic delay in dissolved oxygen (DO) measurement was evaluated by shifting the bioreactor pressure and fitting a first-order mathematical model to the DO response. The dynamic method was coupled with the DO lag results to determine the oxygen transfer rate in Water for Injection (WFI) and a complete culture medium. A range of agitation frequencies was investigated at a fixed air sparge flow rate, replicating operating conditions used in Pichia pastoris fermentation. Oxygen transfer rates determined by this method were in excellent agreement with off-gas calculations from cultivation of the organism (P = 0.1). Fermentation of Escherichia coli at different operating parameters also produced respiration rates that agreed with the corresponding dynamic method results in WFI (P = 0.02). The consistency of the dynamic method results with the off-gas data suggests that compensation for the delay in DO measurement can be combined with dynamic gassing to provide a practical, viable model of bioreactor oxygen transfer under conditions of microbial fermentation.

Non-local first-order modelling of crowd dynamics: A multidimensional framework with applications

In this work a physical modelling framework is presented, describing the intelligent, non-local, and anisotropic behaviour of pedestrians. Its phenomenological basics and constitutive elements are detailed, and a qualitative analysis is provided. Within this common framework, two first-order mathematical models, along with related numerical solution techniques, are derived. The models are oriented to specific real world applications: a one-dimensional model of crowd–structure interaction in footbridges and a two-dimensional model of pedestrian flow in an underground station with several obstacles and exits. The noticeable heterogeneity of the applications demonstrates the significance of the physical framework and its versatility in addressing different engineering problems. The results of the simulations point out the key role played by the physiological and psychological features of human perception on the overall crowd dynamics.

Spatial autoregressive structure of meander evolution revisited

Meandering rivers are intrinsically dynamic geomorphic systems that exhibit progressive change in their planforms as they migrate across their floodplains. Recent research in river meandering has focused on the development of linear mathematical models of meander migration. These models, which are based on momentum and mass conservation principles, aim to capture the basic physical mechanisms governing flow-sediment interactions in meandering rivers. A common attribute of the models is that bank erosion is represented as a linear function of near-bank velocity and near-bank velocity is expressed as a spatial convolution of channel curvature. Thus, in all of these process-based models, planform curvature, as mediated through its influence on near-bank velocity, has a strong effect on channel migration. Mathematical details of the curvature–migration relation depend on the number of curvature related convolution terms in the model; the number of such terms increases with increasing model order. Although first- through fourth-order linear models have been developed, few studies have examined rigorously the relation between planform curvature and migration in natural rivers to determine if even the simplest model-based curvature–migration relations correspond to relations derived from empirical data. This paper evaluates empirically the spatial structure of the relation between upstream planform curvature and local channel migration for bends along the Beatton River, British Columbia, Canada. In particular, we compare empirically derived curvature–migration relations to the exponential-decay form of this relation embodied in first-order linear mathematical models of meander migration. For this purpose, we use a refined empirical methodology and recently developed analytical techniques that overcome limitations of a similar analysis of the Beatton River bends conducted by Furbish (1991). The refined methodology examines the influence of upstream lags of planform curvature on migration rates. The new analytical techniques provide data on channel curvature and migration rate at a much finer spatial interval than in the analysis of Furbish (1991). The validity of the approach for revealing the exponential-decay structure of the curvature–migration relation is confirmed by applying it to a synthetic data set generated using a first-order mathematical model. In contrast to the findings of Furbish (1991), our results for the Beatton River bends show that the structure of the spatially distributed upstream curvature effect is more complex than pure exponential decay. The findings suggest that oscillatory components of the relation between curvature and migration rate are important in the planform dynamics of individual complex bends. These findings are consistent with results of recent empirical analysis of the curvature–migration relation based on discrete signal processing and with the structure of the curvature–migration relation in high-order mathematical models of meander migration.

Kinetics of Peroxides Degradation to Hexenal During Bleaching of High Oleic Safflower Oil

Bleaching is an important step of the vegetal oil refining for the removal of impurities. Some of the reactions that take place during this stage can be explained by the catalytic properties of bleaching clays. The most important reaction is the decomposition of peroxides to secondary oxidation products, mainly trans-2-hexenal. Therefore, in the present study, empirical and mathematical models were applied to predict the kinetic parameters of peroxide reduction and the formation of trans-2-hexenal during bleaching of high oleic safflower oil. For this, neutralized high oleic safflower oil was mixed with bleaching clay (Tonsil Optimum 320 FF) at three different concentrations (0.5%, 1.0%, and 1.5% based on the weight of the oil), in a laboratory reactor with agitation at 90 °C, 100 °C, and 110±1 °C during 60 min. Results showed that the first-order mathematical model is suitable to predict both peroxide reduction and formation of trans-2-hexenal (R2 > 0.90). Kinetics parameters of initial rate (k0) and the decontamination constant (kd) suggest a high correlation between peroxide reduction to trans-2-hexenal and clays used for bleaching high oleic safflower oil. This information may be used to design particular bleaching conditions for high oleic safflower oil.

Effectiveness of Bioremediation Processes of Hydrocarbon Pollutants in Weathered Drill Wastes

The aim of this article is to present the problem of purification of 50-year-old weathered wastes (soil) from waste pits—the result of oil drilling. The soil was deeply contaminated with petroleum hydrocarbons—total petroleum hydrocarbon (TPH) level: 85,654–101,842 mg kg dry mass. This work presents results of waste pit material purification with the use of stage technology: initial reclamation, basic bioremediation, and bioaugmentation (inoculation with indigenous microorganisms). The whole process was controlled with the use of gas chromatography/flame ionization detector. This analytical method enables observation of alternation in n-alkanes content during the consecutive stages of purification. According to this method, estimation of oil hydrocarbon biodegradation degree with the use of n-C17/Pr and n-C18/F indicators can be done. The use of biomarker C30-17α(H)21β(H)-hopane to normalize the TPH concentration in laboratory research enabled the creation of the first-order mathematical model of biodegradation. It is possible to recognize the dynamics of the following purification stages due to the calculated first-order biodegradation constants. Decrease in the TPH content (63.8–65.1%) was a result of laboratory tests led in 130 days of basic bioremediation. The next stage of soil purification (130 days) included inoculation with biopreparation based on indigenous microorganisms—TPH decrease in 80.7–81.7%. Laboratory tests results enabled elaboration of purification methods applied in tested waste pits in industrial conditions (in situ). The technology of the G-44 and G-12 waste pits purification from huge petroleum hydrocarbons content, consisting of stage purification process, enables the TPH decrease to the satisfactory level in 3 years.

First-order model of thermal lensing in a virtual eye

An ABCD beam-propagation method was used to build a first-order mathematical model of a thermal lens effect from a near-infrared laser beam in water and ocular media. The model was found to fit experimental z-scan data best when the thermo-optic coefficient dn/dT of liquid water at 292 K was -4.46x10(-5) K(-1). The physiological parameters of the human eye were simulated in a simple eye model using this fitted dn/dT value. Conservative model simulations for 1150 and 1318 nm laser radiation include parameter sets used in experimental ocular exposures performed by Zuclich et al. [Health Phys.92, 15 (2007)] to illustrate the transient response of the thermal lens approaching the limits of the retinal damage thresholds for equivalent laser radiation sources.

Thermal cycling experiments for glass moulds surface texture lifetime prediction – Evaluation with the help of statistical techniques

In this study, test specimens consisting of stainless steel that is widely used in manufacturing glass household goods, another stainless steel specimen and the specimen of the latter material that was surface boronized are subjected to glass forming temperature in laboratory conditions, and the changing surface roughness parameters have been monitored with precise measurement techniques. The information obtained from surface texture was not only useful for determining mould surface performance but could also be used as a distinguishing mark about the quality of glassware. The results are informative about the effects of surface texture alterations during thermal cycling operations to the mould’s lifetime. The data that were obtained have been evaluated by using SPSS 13.0 (Statistical Package for Social Science) and a first-order mathematical model that gives R a (arithmetical average roughness) parameter value against cycling number, and last but not the least some material specifications have been established.

Preferential permeability of methanol into water using polysilicone and poly(1-trimethylsilyl-1-propyne) membranes

The permeation of initially pure methanol into >95% relative humidity air has been demonstrated with three membranes, supported poly(1-trimethylsilyl-1-propyne) (PTMSP), supported poly(dimethylsiloxane) (PDMS), and a 125-μm polysilicone film. Although fundamentally similar to pervaporation, the arrangement entailed small scale (∼1 cm 2) membrane dispensing of methanol with water counterdiffusion. Volumetric readings over time, final concentration measurements, and subsequent parameter fitting to a derived first-order mathematical model revealed high selectivities – 8.4, 10.3, and 8.3 for the respective membranes – for delivery of methanol versus uptake of water. These selectivities represented factors of 1.5, 1.9, and 1.5 beyond the relative saturation vapor pressures of methanol and water, perhaps, as a result of a favorable inhibition of water counterdiffusion by methanol permeation. Initial methanol permeation rates of 380, 730, and 260 g/h m 2 were also estimated. A transport mechanism adjustment is suspected with PTMSP because of a slightly more rapid permeation rate decrease than indicated by the model. The experimental arrangement and mathematical model provide a new general framework for evaluation of membranes and designs for potential dispensing applications.

Measurements and models of radio frequency impulsive noise for indoor wireless communications

The authors present the results of average and impulsive noise measurements inside several office buildings and retail stores. The noise measurement system operated at 918 MHz, 2.44 GHz, and 4 GHz with a nominal 40-MHz, 3-dB RF bandwidth. Omnidirectional and directional antennas were used to investigate the characteristics and sources of RF noise in indoor channels. Statistical analyses of the measurements are presented in the form of peak amplitude probability distributions, pulse duration distributions, and interarrival time distributions. Simple first-order mathematical models for these statistical characterizations are also presented. These analyses indicate that photocopiers, printers (both line printers and cash register receipt printers), elevators, and microwave ovens are significant sources of impulse noise in office and retail environments.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Computer models of albumin and haemoglobin glycation

Two first-order mathematical models were developed to mimic the glycation of haemoglobin ( H) and albumin ( A). The total concentrations of A and H were assumed to be constant. The responses of the two models to varying blood glucose level were compared. The parameters of the haemoglobin model were not numerically estimated, only an informal fit was performed using clinical and published data. Nonlinear regression analysis was used to estimate the parameters of the albumin model. The level of glycated A ( G A ) was derived from the measured fructosamine level. Three diabetics were monitored daily for the level of fructosamine and blood glucose profile over a period of 10, 16 and 21 days, respectively. Conclusions: (1) The difference between G A and glycated H ( G H ) resulting from different elimination rates is decreased by the stratification of erythrocyte population. (2) Both G A and G H seem to have higher elimination rates than their nonglycated equivalents.

Dispersion in electrochemical cells with radial flow between parallel electrodes. I. A dispersive plug flow mathematical model

The conventional relations for dispersion in tubes and ducts are inappropriate for radial flows such as are found in the disc-stack and pump cells. A first-order mathematical model is therefore developed for radial flow between infinite parallel planes. The shapes of the predicted responses to pulses of injected material are shown to be in qualitative agreement with experimental curves, however the form of the mathematical expression is inappropriate for routine data analysis. Nevertheless simple relationships are derived which enable the dispersion coefficient and mean residence time of an electrogenerated species to be determined from the first and second moments of the response and a knowledge of the geometry of the system. In Part II experimental data are analysed in detail with the aid of the model; however, it is clear that an improved model is of a three-phase flow, a slow phase creeping along either plane with a faster ‘core’ flow in between.