scholarly journals Mathematical modeling of the process of ferrum removal in a biological reactor by bacteria Gallionella and Leptothrix

2020 ◽  
pp. 51-54
Author(s):  
Olena Prysiazhniuk ◽  
Igor Prysіazhnіuk ◽  
Alexander Kvartenko
Keyword(s):  
Nonlinear Boundary ◽  
Bacterial Biomass ◽  
Computer Experiments ◽  
Inhomogeneous System ◽  
Cleaning Efficiency ◽  
Computer Prediction ◽  
Proposed Model ◽  
Filter Loading ◽  
Numerical Analytical Method ◽  
Derivatives Of

This paper proposes a mathematical model for computer prediction of the process of biological deironing of groundwater in a bioreactor, taking into account the presence of two types of iron bacteria Leptothrix and Gallionella in groundwater while maintaining a constant filtration rate. An algorithm for a numerical-analytical method for solving the corresponding nonlinear boundary value problem for an inhomogeneous system of differential equations in partial derivatives of the first order has been developed. The developed model allows to use computer experiments to predict the change in time on the depth of contact loading of cleaning efficiency, distribution of bacterial biomass values ​​in both filtered water and in filter loading, mass of stationary and mobile matrix structures. Also, the proposed model allows to predict the duration of effective operation of the biological reactor of iron deironing between its washing.

scholarly journals COMPUTER PREDICTION OF INCREASING EFFICIENCY OF WORK OF RAPID MULTILAYER FILTERS FOR ADSORPTION PURIFICATION OF WATER

2020 ◽  
pp. 5-17
Author(s):  
Andrij Bomba ◽  
Jurij Klimjuk
Keyword(s):  
Filtration Rate ◽  
Computer Experiments ◽  
Filtration Flow ◽  
Chemical Adsorption ◽  
Computer Prediction ◽  
Proposed Model ◽  
Adsorption Temperature ◽  
Multilayer Filters ◽  
Physical And Chemical ◽  
Purification Of Water

A model of the adsorption purification of water from impurities in rapid multilayer cone-shaped filters with piecewisehomogeneous porous loads with a constant filtration rate taking into account the removal of part of the heat on the surfaces of division of layers is formulated. The proposed model provides an opportunity to conduct computer experiments to study the change in the concentrations of impurities in the filtration flow and adsorbed on the surface of the adsorbent load during physical and chemical adsorption, temperature, characteristics of piecewise-homogeneous porous loads along the filter height and based on their prediction of optimal adsorbent use and increasing the duration of filters.

scholarly journals Computer Prediction of Adsorption Water Purification Process in Rapid Cone-Shaped Filters

2019 ◽  
pp. 13-16
Author(s):  
Andrii Bomba ◽  
Yurii Klymyuk ◽  
Igor Prysіazhnіuk
Keyword(s):  
Filtration Rate ◽  
Computer Experiments ◽  
Surface Flow ◽  
Filtration Flow ◽  
Purification Process ◽  
Computer Prediction ◽  
Proposed Model ◽  
Equipotential Surfaces ◽  
Model Region ◽  
Purification Of Water

In the paper a mathematical model for computer predicting the process of adsorption purification of water from impurities in rapid filters taking into account changes in the temperature of the filtration flow along the height of the filter while observing the constant filtration rate is formulated. Analgorithm for numerically-asymptotic approximation of solution of the corresponding nonlinear singularly perturbed boundary value problem for a model region of a conical shape, bounded two equipotential surfaces and a surface flow, is developed. The proposed model allows through computer experiments to investigate changes in the characteristics of porous loads (filtration coefficients, active porosity), to predict the optimal variants for using adsorbents, and increasing the duration of the filters operation due to the choice of their shape, taking into account the effect on the process of adsorption purification ofwater not only changes in the filtration rate flow along the height of the filter, but also the temperature.

scholarly journals Analytical Algorithm for Oxygen Concentration of Aircraft Fuel Tank in Various Inerting Stages

2021 ◽  
Vol 11 (16) ◽  
pp. 7698
Author(s):  
Yuhao Wei ◽  
Yang Pei ◽  
Yuxue Ge
Keyword(s):  
Differential Equations ◽  
Oxygen Concentration ◽  
Fuel Tank ◽  
Conventional Model ◽  
Aircraft Fuel ◽  
Proposed Model ◽  
Fuel Tanks ◽  
Analytical Algorithm ◽  
Fire And Explosion ◽  
Derivatives Of

Ullage washing is an efficient inerting method to keep the ullage oxygen concentration under the safe value, thus reducing the hazard and loss of fire and explosion of aircraft fuel tanks. In the conventional model of ullage washing, the initial derivatives of oxygen concentration that are used to solve the differential equations are selected subjectively by researchers and the empirical select influences the accuracy of the result. Therefore, this paper proposes an analytical algorithm that can calculate the ullage oxygen concentration without selecting any initial derivative value. The algorithm is based on a fuel tank ullage washing model regarding various inerting stages. It has been experimentally validated with an average relative error of 5.781%. Moreover, sensitive analyses carried out on the proposed model show that ground-based inerting can effectively reduce the ullage oxygen, concentration in the climb phase. Increasing 5 min of pre-takeoff inerting duration can shorten the time of decreasing the ullage oxygen concentration to 9% after takeoff by 2.1 min.

scholarly journals Simulating of the admixture spreading in a steady 2D lengthy stream of the viscous fluid

2013 ◽  
Vol 2 (1) ◽  
pp. 91-97
Keyword(s):  
Viscous Fluid ◽  
Small Parameter ◽  
Stokes Equations ◽  
Numerical Study ◽  
Computer Experiments ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Convection Diffusion ◽  
Proposed Model ◽  
And Diffusion

The problem of the passive contaminant spreading in a steady viscous fluid stream is discussed while the admixture's dissipation and diffusion are taken into account. The channel is assumed to be a horizontal plane, curvilinear and quite lengthy, so that the ratio of the stream width to its length can be regarded as a small parameter. A mathematical model of the process derived by the small parameter technique from the 2D steady Navier-Stokes equations for incompressible viscous fluid and non-steady convection-diffusion equation of a substance in the moving medium is introduced. A finite element method is applied for numerical study of the proposed model and results of computer experiments are presented.

An EOQ Model for Reuse and Recycling Considering the Balance of Supply and Demand

2015 ◽  
Vol 9 (3) ◽  
pp. 303-311 ◽  
Author(s):  
Tomomi Nonaka ◽  
◽  
Nobutada Fujii ◽  
Keyword(s):  
Inventory Management ◽  
Reverse Logistics ◽  
Supply And Demand ◽  
Computer Experiments ◽  
Demand And Supply ◽  
Product Demand ◽  
Eoq Model ◽  
Proposed Model ◽  
Using Data

Inventory management in reverse logistics is more complex than that in conventional logistics because of uncontrollable factors such as inventory levels increasing from reverse logistics, greater-than-expected disposal, and balance of supply and demand with changing market trends. This paper proposes a new economic order quantity (EOQ) model for reuse and recycling by expanding the EOQ model proposed by Dobos and Richter, 2004. The proposed model introduces a sequentially accumulated marginal reuse rate as a parameter in considering the balance of product demand and supply. The marginal reuse rate is calculated by using data on production distribution and disposal distribution of products for every discretized period. This model considers the sequence among recovery options: reuse, recycle and disposal. Parts are reused after having been inspected to determine whether they are reusable or not. Remaining nonreusable parts are recycled and any remaining nonrecycled parts disposed of. The extended EOQ model is applied to a case study using different scenarios for length of use and multiple generations of products. Results of computer experiments confirmed the effectiveness of the proposed method.

scholarly journals Brainstorming the cryoplane layout by using the iterative AHP-QFD-AHP approach

Aviation ◽  
2018 ◽  
Vol 21 (2) ◽  
pp. 55-63 ◽  
Author(s):  
Caglar UCLER
Keyword(s):  
Creative Thinking ◽  
Incremental Innovation ◽  
Design Management ◽  
Management Tools ◽  
Proposed Model ◽  
Engineering Environment ◽  
Definition Of ◽  
Derivatives Of ◽  
Product Definition

Most of commercial civil aircraft are derivatives of each other. They start with an aero-structural design based on the mission profile, and what remains is the integration of existing subsystems. This only leaves room for incremental innovation. When a totally new concept has to be worked out, an innovative brainstorming procedure has to be facilitated, leading to a new product definition. This collaborative creative thinking is not an easy task, and analytical design management tools are required. Therefore, an iterative AHP-QFD-AHP approach for brainstorming is implemented into a concurrent engineering environment in the early phases of layout conception. In the case study, the proposed model delivered the product definition of the cryoplane concept successfully, which promises clean operation.

Nonlinear Dynamic Battery Model With Boundary and Scanning Hysteresis

2009 ◽  
Author(s):  
Yang Bin ◽  
Yaoyu Li ◽  
Nenglian Feng
Keyword(s):  
Power Management ◽  
Electric Vehicles ◽  
Nonlinear Dynamic ◽  
Nonlinear Boundary ◽  
Hybrid Electric Vehicles ◽  
Sustainable Mobility ◽  
Battery Model ◽  
Nonlinear Hysteresis ◽  
Proposed Model ◽  
Nonlinear State

Battery has drawn much more attention due to the accelerating development of Electric Vehicle (EV) and Plugin Hybrid Electric Vehicles (PHEV) for sustainable mobility. It is worthwhile to study the dynamic model of battery in order to achieve better performance in power management. This paper proposes a nonlinear dynamic battery model for PHEV power management. First, an existing RC equivalent circuit is used to simulate the dynamics of the battery states with respect to the input current. Then, a concept of nonlinear hysteresis degree is introduced, and is adopted to implement the mathematical description of the battery nonlinear boundary and scanning hysteresis. Finally, the dynamics and the nonlinear boundary (scanning) hysteresis are integrated into a comprehensive battery model with an affine nonlinear state-space equation. The effectiveness of the proposed model is verified using some simulation tests.

Quintessence compact stars satisfying Karmarkar condition

2019 ◽  
Vol 97 (4) ◽  
pp. 374-381 ◽  
Author(s):  
G. Abbas ◽  
Shahid Qaisar ◽  
Wajiha Javed ◽  
W. Ibrahim
Keyword(s):  
Radial Pressure ◽  
Compact Stars ◽  
Field Equations ◽  
Anisotropic Parameter ◽  
Proposed Model ◽  
Second Derivatives ◽  
Metric Functions ◽  
The Stability ◽  
Quintessence Field ◽  
Derivatives Of

In this research article, the authors have presented the modelling of quintessence compact stars, which satisfies the Karmarkar conditions. For this purpose, we have formulated the set of Einstein field equations with the static metric, anisotropic perfect fluid, and quintessence field. The equation of state pr= αρ and Karmarkar condition have been used to solve the set of field equations. The unknown constant in the metric functions (appearing due to the Karmarkar conditions) have been found by matching the interior metric with the Schwarzschild exterior metric. The observed value of mass and radius of some well-known classes of stars has been used. The fluid variables density, radial and transverse pressures, and anisotropic parameter have been plotted graphically. The first and second derivatives of density and radial pressure have been evaluated to discuss the regularity of the model. The speed of sound for the radial and transverse directions determines the stability of the proposed model. Moreover, the redshift for the proposed model of the star has been discussed.

FAST INTEGRATION OF ONE-DIMENSIONAL BOUNDARY VALUE PROBLEMS

2013 ◽  
Vol 24 (11) ◽  
pp. 1350082 ◽  
Author(s):  
RAFAEL G. CAMPOS ◽  
RAFAEL GARCÍA RUIZ
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Kdv Equation ◽  
Boundary Value ◽  
Soliton Solutions ◽  
Nonlinear Boundary Value Problems ◽  
One Dimensional ◽  
Dimensional Boundary ◽  
The Fourier Transform ◽  
Derivatives Of

Two-point nonlinear boundary value problems (BVPs) in both unbounded and bounded domains are solved in this paper using fast numerical antiderivatives and derivatives of functions of L2(-∞, ∞). This differintegral scheme uses a new algorithm to compute the Fourier transform. As examples we solve a fourth-order two-point boundary value problem (BVP) and compute the shape of the soliton solutions of a one-dimensional generalized Korteweg–de Vries (KdV) equation.

scholarly journals A Study of Ising Formulations for Minimizing Setup Cost in the Two-Dimensional Cutting Stock Problem

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 182
Author(s):  
Hiroshi Arai ◽  
Harumi Haraguchi
Keyword(s):  
Ising Model ◽  
Optimal Solution ◽  
Computer Experiments ◽  
Error Rates ◽  
Cutting Stock ◽  
Two Dimensional ◽  
Setup Cost ◽  
Proposed Model ◽  
Acceptance Rates ◽  
Future Work

We proposed the method that translates the two-dimensional CSP for minimizing the number of cuts to the Ising model. After that, we conducted computer experiments of the proposed model using the benchmark problem. From the above, the following results are obtained. (1) The proposed Ising model adequately represents the target problem. (2) Acceptance rates were as low as 0.2% to 9.8% and from 21.8% to 49.4%. (3) Error rates from optimal solution were as broad as 0% to 25.9%. For future work, we propose the following changes: (1) Improve the Hamiltonian for constraints. (2) Improve the proposed model to adjust more complex two-dimensional CSP and reduce the number of spins when it deals with large materials and components. (3) Conduct experiments using a quantum annealer.

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