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# mathematical modeling Articles

• ## Mathematical modelling of electrorheological nanofluids

This paper provides a review of theoretical and experimental advancements in electrorheological (ER) fluids. Experimental results and theoretical models for these novel fluids and their impact in the field of nanotechnology are discussed. This paper reviews their development since the ER phenomenon was first described in the 1940s as well as some recent theoretical results of the authors. These ...

• ## Mathematical modeling for solute transport in aquifer

Groundwater pollution may occur due to human activities, industrial effluents, cemeteries, mine spoils, etc. This paper deals with one-dimensional mathematical modeling of solute transport in finite aquifers. The governing equation for solute transport by unsteady groundwater flow is solved analytically by the Laplace transform technique. Initially, the aquifer is subjected to the spatially ...

• ## The Basics of Evapotranspiration

Evapotranspiration (ET) represents the loss of water from the Earth’s surface from the combination of direct evaporation and plant transpiration. ET is usually expressed as a rate such as inches per day. Knowledge of ET is important for irrigation scheduling but it is also an important factor for other land use applications such as septic tank drain fields, watershed level budgeting, and ...

• ## Mathematical modelling of a linkage-based robotic finger

This paper presents the mathematical dynamic model development of a linkage-based robotic finger with fingertip pinching and self-adaptive grasping functions during non-contact mode. The finger's structure is made of a seven-bar linkage mechanism with a slider in the middle phalanx to adjust its effective length in accomplishing these two tasks. This study extends the dynamic models of the ...

• ## Investigation of an LPG accident with different mathematical model applications

An LPG (liquefied petroleum gas) storage accident was reconstructed through several simulation models, with the aims of the reported and filmed effects and damage. The accident happened in Paese, near Treviso (Italy) in March 1996 and was characterised by complex phenomena due to a choked release of LPG from a tanker. There was a dispersion of light winds and, after about 40 minutes, a flash-fire ...

• ## Mathematical modelling of biofilms and biofilm reactors for engineering design

Mathematical models are critical to modern environmental biotechnology—both in research and in the engineering practice. Wastewater treatment plant (WWTP) simulators are used by consulting engineers and WWTP operators when planning, designing, optimizing, and evaluating the unit processes that comprise municipal and industrial WWTPs. Many WWTP simulators have been expanded to include a submerged ...

• ## Mathematical model of biofilm induced calcite precipitation

Microbially modulated carbonate precipitation is a fundamentally important phenomenon of both engineered and natural environments. In this paper, we propose a mixture model for biofilm induced calcite precipitation. The model consists of three phases – calcite, biofilm and solvent – which satisfy conservation of mass and momentum laws with addition of a free energy of mixing. The model also ...

• ## Mathematical model predicting arsenic bioleaching in groundwater treatment

In the Southeast Asia region, arsenic contamination of groundwater has been reported in several countries and a large number of arsenic treatment units were installed in many regions. Microbial activity can greatly affect the mobilization of arsenic under anaerobic conditions when coupled with the oxidation of organic matter. In this study, a mathematical model was developed to predict the ...

• ## Mathematical modelling of a hydraulic controller for PRV flow modulation

This paper describes the development of mathematical models, which represent static and dynamic properties of the AQUAI-MOD® hydraulic controller coupled with a standard pressure reducing valve (PRV) as well as a new experimental set-up for testing the controller and calibrating and validating the models. The purpose of the AQUAI-MOD® controller is to modulate the PRV outlet pressure according to ...

• ## A mathematical model to predict nickel concentration in karaj river sediments

The contamination of surface waters through human activities has been increased over the past years as population density has increased. To fully understand the anthropogenic impact on an ecosystem, long-term data from chemical, physical and biological indicators are needed. To many people, heavy metal pollution is a problem associated with areas of intensive industry. Metals, such as nickel and ...

• ## Mathematical model of water quality rehabilitation with rainwater utilisation: a case study at Haigang

This paper presents a mathematical model of water quality rehabilitation by utilising rainwater, which is separated into initial polluted rainwater and later unpolluted rainwater. The planned Haigang city, belonging to Shanghai metropolis in China, is taken as a case example. An analysis is made on how to utilise rainwater and appraise its function in a water quality rehabilitation scheme. It is ...

• ## A mathematical modelling of the intensity of contaminants (CO2) on occupancy level of a space in continuous use

This study investigates the Indoor Air Quality (IAQ) of a room apartment and focused on the number of occupants that a space or an apartment can accommodate as a result of increase in the concentration level of the CO2 contaminant present within the space. The law of mass action was applied to generate a relation between the concentration of CO2 produced and the concentration of the reactants ...

• ## Mathematical models validation of aluminium electrolysis process using exergy method

A new method of validation of the mathematical model of the processes taking place inside the aluminium electrolysis cell has been proposed. The method is based on the comparison of the calculation results of the entropy generation rates obtained in theoretical way with the exergy losses estimated from global exergy balance equation. The following irreversible processes have been analysed - ...

• ## A study on some standard mathematical modelling on automobiles and environmental pollution in the city of Kolkata

This study examines the global environmental pollution caused by so many anthropogenic activities. In particular, emphasis is laid on the recent experience of the increasing numbers of automobiles on insufficient and damaged roads, particularly in Indian cities, causing severe pollution effects. As far as the numbers are concerned, a standard mathematical model was developed, similar to Malthus' ...

• ## A methodology for a quantitative interpretation of DGGE with the help of mathematical modelling: application in biohydrogen production

Molecular biology techniques provide valuable insights in the investigation of microbial dynamics and evolution. Denaturing gradient gel electrophoresis (DGGE) analysis is one of the most popular methods which have been used in bioprocess assessment. Most of the anaerobic digestion models consider several microbial populations as state variables. However, the difficulty of measuring individual ...

• ## Mathematical models for biomass in membrane-BNR process for wastewater treatment

The equation of biomass is related to the mass-balance equation of substrate. This equation of substrate is expressed according to a model using the Monod equation, which indicates some limits for calculating the amounts of VSS in the MBR process. Some degradation of biomass which is caused by long SRT might result in the generation of substrate based on COD. Research was conducted by lab-scale ...

• ## A mathematical programming model for achieving total emission control in the petroleum refining industry

This paper addresses the planning and optimisation of a petroleum refinery with consideration to multiple pollutants and greenhouse gases reduction alternatives. The study provides a tool that can be utilised for optimum pollution and greenhouse gases control strategy to achieve a given reduction level. The proposed method is based on a mathematical programming model whose performance is ...

• ## Virus elimination in activated sludge systems: from batch tests to mathematical modeling

A virus tool based on Activated Sludge Model No. 3 for modeling virus elimination in activated sludge systems was developed and calibrated with the results from laboratory-scale batch tests and from measurements in a municipal wastewater treatment plant (WWTP). The somatic coliphages were used as an indicator for human pathogenic enteric viruses. The extended model was used to simulate the virus ...

• ## A mathematical model to estimate errors associated with closed flux chambers

Errors associated with the closed flux chamber technique, used to measure surface emissions from landfills, were investigated by using a combination of numerical modeling and laboratory studies. A transient-state, advective–dispersive–reactive model was developed and used in conjunction with its steady-state version to quantify the errors associated with closed flux chambers. In developing the ...

By Springer

• ## Dynamic Mathematical Modeling of Membrane Fouling in Submerged Membrane Bioreactors

ABSTRACTA mathematical model is developed that accounts for internal fouling of membranes due to soluble microbial products during subcritical flux operation, and for supercritical flux fouling due to cake formation and compression.. The model takes into account the filtration effect generated by the cake. A set of differential equations is derived and solved numerically to obtain a description ...

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