Variable-order Model Research Articles

Grey water treatment and reuse by using RBC: A kinetic approach

Grey water treatment with rotating biological contactor (RBC) was investigated to assess water reuse potential. The study involves influent characterization, setting-up and operation of two RBCs, conformity assessment of the effluent for reuse and determination of the biofilm kinetics. Monod and variable order models were applied. Biofilm characteristics, such as weight per unit area and thickness were measured. Nitrification and mineralization processes took place in the biofilm matrix simultaneously. About 85% CODT and 75% TKN removal efficiencies were achieved. The average effluent BOD5 concentration was 7 mg L−1. The reaction showed typical zero-order, 0° kinetic relation. The 0° rate constant was determined as 5.7 ± 1.5. UV light was used for disinfection of treated grey water. Efficiency, operational ease, reliability, and personnel requirements were compared with the other grey water treatment processes. It is concluded that RBC may be effectively used for grey water treatment and the effluent can be reused for toilet flush purposes after disinfection. However, it is recommended that detached particles from biofilm should be further removed by filtration.

Fractional differential models for anomalous diffusion

In this study, we investigate three kinds of fractional differential models (distributed-order model, variable-order model and random-order model) for characterization of anomalous diffusion. The characteristics, physical advantages and potential applications of each model are highlighted. The numerical simulations also validate our analytical and comparison results. Furthermore, a generalized distributed–variable-order model and a more generalized distributed–variable–random-order model are proposed to combine the advantages of distributed-order model, variable-order model and random-order model.

On mean square displacement behaviors of anomalous diffusions with variable and random orders

Mean square displacement (MSD) is used to characterize anomalous diffusion. Recently, models of anomalous diffusion with variable-order and random-order were proposed, but no MSD analysis has been given so far. The purpose of this Letter is to offer a concise derivation of MSD functions for the variable-order model and the random-order model. Numerical results are presented to illustrate the analytical results. In addition, we show how to establish a variable-random-order model for a given MSD function which has clear application potentials.

Modeling of organic matter removal and nitrification in sewer systems — an approach to wastewater treatment

Investigations were carried out to develop the best sustainable management system for domestic wastewaters. Sewer systems have a crucial significance within the current concept of wastewater management. It is suggested that sewer lines may be used as biological reactors to reduce pollution loads. The concept of emphasizing centralized treatment systems may cause transportation of wastewater for long distances. In this study organic matter removal and nitrification capability of sewer lines were investigated with a special emphasis on kinetic behavior. For this purpose, a sewage circulating reactor was set up and operated to assess the transformations of organic compounds and nutrients during the transport process and to determine the kinetic relations. Packing material was used in the circulating reactor to increase the biofilm area and to enhance removal efficiencies of pollutants. The model was operated by feeding with glucose based synthetic wastewater. Parameters related to organic content and nitrification were monitored. Kinetic constants were determined by using Monod and variable order model kinetics. Around 85–90% COD and TOC removal efficiencies were attained following 7 h circulation of the wastewater in the reactor. TN reduction of 55% was achieved at a 24 h circulation period. Equations representing the organic matter removal and nitrification rates were developed based on variable order and Monod concepts. The modeling results, obtained by using the developed equations at infinitesimal intervals, were compared to the experimental data. The Monod concept model, which takes into account the amount of biological growth, was shown to be slightly more accurate than the variable order model for this study.

Variable Order Modeling of Diffusive-convective Effects on the Oscillatory Flow Past a Sphere

This work advances our understanding of the drag force acting on a particle due to the oscillatory flow of a viscous fluid with finite Reynolds and Strouhal numbers. The drag force is is determined using the novel concept of variable order (VO) calculus, where the order of derivative can vary with the parameters and variables, according to the dynamics of the flow. Using the VO formulation we determine: (i) The region of validity of Tchen's equation for oscillatory flow, (ii) the region where the order of the derivative is fractional but constant, and (iii) the region where the strong non-linearity of the flow requires a variable order derivative to account for the increased complexity of the flow.

RECOGNITION OF CIS-REGULATORY ELEMENTS WITH VOMBAT

Variable order Markov models and variable order Bayesian trees have been proposed for the recognition of cis-regulatory elements, and it has been demonstrated that they outperform traditional models such as position weight matrices, Markov models, and Bayesian trees for the recognition of binding sites in prokaryotes. Here, we study to which degree variable order models can improve the recognition of eukaryotic cis-regulatory elements. We find that variable order models can improve the recognition of binding sites of all the studied transcription factors. To ease a systematic evaluation of different model combinations based on problem-specific data sets and allow genomic scans of cis-regulatory elements based on fixed and variable order Markov models and Bayesian trees, we provide the VOMBATserver to the public community.

Prediction suffix trees for supervised classification of sequences

This paper presents a statistical test and algorithms for patterns extraction and supervised classification of sequential data. First it defines the notion of prediction suffix tree (PST). This type of tree can be used to efficiently describe variable order chain. It performs better than the Markov chain of order L and at a lower storage cost. We propose an improvement of this model, based on a statistical test. This test enables us to control the risk of encountering different patterns in the model of the sequence to classify and in the model of its class. Applications to biological sequences are presented to illustrate this procedure. We compare the results obtained with different models (Markov chain of order L, Variable order model and the statistical test, with or without smoothing). We set out to show how the choice of the parameters of the models influences performance in these applications. Obviously these algorithms can be used in other fields in which the data are naturally ordered.

Reactor kinetics for submerged aerobic biofilms

Due to water shortage in cities, small wastewater treatment plants are needed and new technologies are demanded. Pilot plant experiments were made to evaluate the performance of a submerged aerobic biofilm system for the treatment of municipal wastewater. Influent flow rates were varied to adjust organic loading rates from 5.2 to 28.8 gCOD/m2 d. Using COD values, the pilot plant performance was analyzed for kinetics simulation. The Stover–Kincannon and a general variable-order models were used to analyze the data obtained over several months of experimentation. The data showed good correlation with the Stover–Kincannon model but not with the variable-order model. The results lead to a design organic load of 20 gCOD/m2 d to reach an effluent COD under 50 mg/l.

Subsurface flow constructed wetlands treating municipal wastewater for nitrogen transformation and removal

Research was conducted on pilot‐scale, subsurface flow constructed wetland systems treating municipal wastewater. Increasing the hydraulic retention time (HRT) from 1.7 days to 4.3 days reduced the mean effluent NH4 concentration by 2.7 mg N/L. Hydroperiod manipulation caused a 2.9‐mg N/L decrease in effluent NH4. The influent NH4 concentration for the 9‐month study period averaged 21 mg N/L. The lowest average effluent NH4 concentration observed in single‐stage treatment cells was 13 mg N/L. The mean effluent NH4 concentration from the second‐stage cells of two wetland cells in series was 10 mg N/L. During the period from May through September, the second‐stage cells produced an effluent NH4 concentration of 6 mg N/L. A variable‐order kinetic model for sizing the second‐stage cells of a series system yielded a coefficient of determination, r2 of 0.94 for the summer NH4 removal data. The predicted HRT to reduce NH4 from 20 mg N/L to 5 mg N/L was 3.9 days, if the cells were subjected to cyclic draw and fill.

Modeling of Degradation of Solutions Containing Nitrogen and Carbon Compounds in Aerated Submerged Fixed-Film (ASFF) Bioreactors

The biodegradation reaction rates of waste-water solutions containing nitrogen and carbon compounds were studied in an aerated submerged fixed film (ASFF) reactor with four compartments. A solution containing sucrose (carbon source) and ammonium chloride (nitrogen source) was considered in this study. The kinetic models considered in the analysis were the variable order model and the Monod model. Measurements and analysis were performed as a function of organic and hydraulic loading for the reactor. Analysis of the kinetic data was carried out in the first compartment and in the combined section of the reactor which included the second, third, and fourth compartments. The reaction order for carbon removal in the first compartment was found to vary over a range of 1–2 and drops to a range of 0.7–1.2 in the combined section. Lower reaction orders were obtained for nitrogen removal which varied from 0.6–1 in the first compartment and the combined section. Upon application of the Monod model for the two reactions, similar trends to those of the variable order model were obtained for carbon and nitrogen removal in both sections of the reactor. The calculated Monod constants for carbon removal were one to two orders of magnitudes larger than those for nitrogen removal. Measured removal rates of carbon in the first compartment were two orders of magnitudes higher than the nitrogen removal rates in the same compartment. However, the removal rates of both components are comparable in the combined section, especially at high feed flow rates. This behaviour was consistent with literature data on simultaneous removal of carbon and nitrogen compounds, where high concentrations of carbon resulted in severe reduction in the removal rates of nitrogen compounds.

Estimating optical flow in segmented images using variable-order parametric models with local deformations

This paper presents a new model for estimating optical flow based on the motion of planar regions plus local deformations. The approach exploits brightness information to organize and constrain the interpretation of the motion by using segmented regions of piecewise smooth brightness to hypothesize planar regions in the scene. Parametric flow models are estimated in these regions in a two step process which first computes a coarse fit and then estimates the appropriate parametrization of the motion of the region. The initial fit is refined using a generalization of the standard area-based regression approaches. Since the assumption of planarity is likely to be violated, we allow local deformations from the planar assumption in the same spirit as physically-based approaches which model shape using coarse parametric models plus local deformations. This parametric plus deformation model exploits the strong constraints of parametric approaches while retaining the adaptive nature of regularization approaches. Experimental results on a variety of images model produces accurate flow estimates while the incorporation of brightness segmentation boundaries.

Discrete minimum entropy quantization

We present a simple lower bound on the entropy of a quantized signal and a method for determining the minimum entropy quantization, subject to a maximum distortion, for a discrete memoryless random process. This quantization allows more efficient use of variable-order models for compression of images and sound.

Behavior of a Biological Fixed-Film System Treating Toxic and Nontoxic Organic Wastes

The treatment of industrial wastes containing both toxic and nontoxic organic compounds is often accomplished by biological processes. Despite its success in many instances, the complex nature of the effects of toxic substances on process performance and kinetics is not well understood. This study was conducted to examine the behavior of an aerated submerged fixed-film (ASFF) biological system receiving a mixture of toxic (phenol) and nontoxic (sucrose) bisubstrate and evaluate its kinetic parameters. Laboratory experiments were carried out using a 50-litre ASFF reactor composed of four equal compartments. Heterogeneous biomass acclimated to a bisubstrate (phenol/sucrose) system demonstrated the preference of microorganisms to utilize sucrose with a slower concomitant utilization of phenol. However, the removal in a bisubstrate system is slightly higher than that in a single substrate system which may be attributed to the extra biomass accumulated from the utilization of the other substrate. A steady-state approach to process kinetics indicates that substrate removal in the first compartment follows the Monod model for both sucrose and phenol where no mhibition (Haldane rate expression) appears over the studied range of phenol concentrations up to 800 mg/l. Meanwhile, substrate removal in the second through fourth compartments is better described by a variable order model which is likely to be a function of the hydraulic loading.

Aerobic submerged biofilm reactors for wastewater treatment

Abstract Treatment of wastewater from the campus of the National University of Mexico in a four-stage aerobic submerged biofilm reactor containing Pall-rings resulted in effluent with BOD values of less than 10 mg/l. The nitrification started in the first compartment and the reactor nearly achieved complete nitrification. The resulting biomass was filamentous and had good settling characteristics. Analysis of data indicated that the Stover-Kincannon and the variable order models can be used for the description and design of the process.

Kinetic response of an oxygen-selective electrode evaluated for the quantification of oxygen

An evaluation of the transient response of a membrane-based amperometric electrode for the quantification of oxygen in aqueous and gaseous phases is described. Data collected during the early part of the responses are used to compute the steady-state signals that would be measured if the responses were monitored to steady state. Both first-order and variable-order models were used successfully to fit data for aqueous samples; only the variable-order model worked successfully with data for gaseous samples. Because the shapes of response curves did not permit steady-state signals to be measured, comparisons are based on measured values of current at fixed times in each response. The slopes of computed vs. measured signals varied from 0.90 to 1.03 for fits of data over 3–5 half-lives with both models. Calibration graphs of computed current vs. concentrations were linear for similar fitting ranges and the least-squares parameters were similar to those for current measured at different fixed points in time.

Optimal pruning with applications to tree-structured source coding and modeling

An algorithm introduced by L. Breiman et al. (1984) in the context of classification and regression trees is reinterpreted and extended to cover a variety of applications in source coding and modeling in which trees are involved. These include variable-rate and minimum-entropy tree-structured vector quantization, minimum expected cost decision trees, variable-order Markov modeling, optimum bit allocation, and computer graphics and image processing using quadtrees. A concentration on the first of these and a detailed analysis of variable-rate tree-structured vector quantization are provided. It is found that variable-rate tree-structured vector quantization outperforms not only the fixed-rate variety but also full-search vector quantization. The successive approximation character of variable-rate tree-structured vector quantization permits it to degrade gracefully if the rate is reduced at the encoder. This has applications to the problem of buffer overflow.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The preparation of actions and parameters of action: A fixed or variable process?

Some information processing models consider the selection of an action plan (deciding what to do) and the parameterization of the action (deciding how to do it) as separate stages in movement preparation. Further, these models consider the stages to occur in a fixed order, whereby the selection of an action precedes the parameterization of the action. Five experiments are reported that tested this position. The first four experiments adopted a variation of Rosenbaum's (1980) precuing technique such that, under varying conditions, different amounts and types of advance information were provided to the subject, leaving only the unspecified action or parameter to be supplied following the imperative signal. The critical finding from each study was that the time to specify an action and the time to specify a parameter were equivalent. In experiment 5, similar results were obtained using a response priming paradigm (Rosenbaum and Kornblum 1982). The results of all five studies failed to support a fixed-order model of movement preparation and are more consistent with a variable-order model. The implications of these findings for other models of movement preparation are discussed.

Decoupled boundary layer model of induction machines

A partially decomposed variable-order model of the double-cage induction machine is presented and validated. The model exhibits improved computational efficiency in simulating full machine behaviour including stator transients. A state variable transformation is used to separate the electrical steady-state from the transient part of flux linkage response. The transient flux-linkage response is next decomposed into fast and slow sub-systems which constitute the boundary layers of the overall model. The fast subsystem is then reduced by neglecting the heavily damped fast transients caused by the starting cage. Each of the two decoupled boundary layer equations may be computed using different time steps and even ignored during periods when the corresponding mode is not excited, thereby effectively reducing model order and greatly decreasing computational requirements while retaining simulation accuracy.

Variable-Order Model of Bacterial-Film Kinetics

A variable-order model provides a closely approximate, explicit solution for the flux of a limiting substrate into a “deep” fixed bacterial film. The model incorporates concepts of liquid-layer mass transport, Monod kinetics, and molecular diffusion. The derived equation provides an explicit solution for the flux into a bacterial film, and for this reason, it should aid in the application of fundamental, fixed-film kinetics to practical reactor problems. Examples are given to illustrate use of the model.