scholarly journals Construction of mathematical modelling of a population of microalgae

2021 ◽  
Vol 939 (1) ◽  
pp. 012054
Author(s):  
Sh Rakhmanov ◽  
D Abdullaeva ◽  
N Azizova ◽  
A Nigmatov
Keyword(s):  
Differential Equation ◽  
Mathematical Modelling ◽  
Technological Process ◽  
Mathematic Model ◽  
System Of Equations ◽  
System Of Differential Equations ◽  
Periodic Mode ◽  
Cultivation Process ◽  
Nutrient Resources ◽  
Effect Of Inhibitors

Abstract This article devoted to the development of the mathematic model of the technological process of the chlorella cultivation process, its features and solving of this mathematic model. The Exponential growth of microalgae population under conditions of unlimited nutrient resources and population space proceeds at a rate proportional to the number of species of predominant cells and is described by the differential equation. In the presence of several inhibitors, specific velocity equations with the number of inhibitors can be used, but, as a rule, there are practically no elements acting as inhibitors in the cultivation of Chlorella microalgae. The modeling of this particular class of objects did not take into account the effect of inhibitors on the growth of microalgae. The consumption of nutrients to support the life of microalgae is described by the differential equation. In the course of this work, the processes of cultivation of microalgae were brought together into a system of equations. As a result, a system of differential equations of the technological process of Chlorella cultivation was obtained. Thus, the obtained system of equations describes the process of cultivation of microalgae and its technological process, implemented in a periodic mode.

scholarly journals Tolerance Modelling of Vibrations and Stability for Periodic Slender Visco-Elastic Beams on a Foundation with Damping. Revisiting

Materials ◽  
2020 ◽  
Vol 13 (18) ◽  
pp. 3939
Author(s):  
Jarosław Jędrysiak
Keyword(s):  
Mathematical Modelling ◽  
System Of Differential Equations ◽  
Governing Equations ◽  
Asymptotic Homogenization ◽  
Elastic Beams ◽  
Oscillating Coefficients ◽  
Constant Coefficients ◽  
Tolerance Modelling ◽  
Tolerance Method ◽  
Modelling Approach

The mathematical modelling of certain problems of vibrations and stability for periodic slender visco-elastic beams is presented in this note. To consider these problems and take into account the effect of the microstructure, the tolerance modelling approach is proposed. Using this technique, the equation with non-continuous, periodic, highly oscillating coefficients is replaced by a system of differential equations with constant coefficients. Moreover, these governing equations describe the effect of the microstructure on the overall behavior of the beams under consideration. The tolerance modelling can lead to equations of two different tolerance models—the standard and the general, under weakened assumptions. This averaging tolerance method was assessed by comparison with the asymptotic homogenization, the governing equations of which omit this effect. My considerations were limited to proposing and presenting only mathematical models describing investigated beams. In a simple analytical example, the application of the presented average models is shown.

scholarly journals Sequential eigenfunction expansion for a problem in combustion theory

2003 ◽  
Vol 45 (1) ◽  
pp. 35-48 ◽  
Author(s):  
M. Al-Refai ◽  
K. K. Tam
Keyword(s):  
Differential Equation ◽  
Eigenfunction Expansion ◽  
Time Dependent ◽  
Linear Parabolic Equation ◽  
System Of Equations ◽  
Multiple Steady State ◽  
Definitive Answer ◽  
Combustion Theory ◽  
The Galerkin Method ◽  
Steady State Solutions

AbstractA method of sequential eigenfunction expansion is developed for a semi-linear parabolic equation. It allows the time-dependent coefficients of the eigenfunctions to be determined sequentially and iterated to reach convergence. At any stage, only a single ordinary differential equation needs to be considered, in contrast to the Galerkin method which requires the consideration of a system of equations. The method is applied to a central problemin combustion theory to provide a definitive answer to the question of the influence of the initial data in determining whether the solution is sub- or super-critical, in the case of multiple steady-state solutions. It is expected this method will prove useful in dealing with similar problems.

scholarly journals Application of Artificial Neural Network to Improve Pleurotus sp. Cultivation Modelling

2019 ◽  
Vol 255 ◽  
pp. 02010
Author(s):  
Fakharudin Abdul Sahli ◽  
Zainol Norazwina ◽  
Dzulkefli Noor Athirah
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Mathematical Modelling ◽  
Nitrogen Concentration ◽  
Network Modelling ◽  
Connection Weight ◽  
Palm Fruit ◽  
Cultivation Process ◽  
Artificial Neural ◽  
Trained Network

Mathematical modelling for nitrogen concentration in mycelium (N) during Pleurotus sp. cultivation had successfully been produced using multiple linear regression. Two different substrates were used to cultivate the Pleurotus sp. which were empty palm fruit bunch (EFB) and sugarcane bagasse (SB). Both substrates were collected and prepared as the selected factors which were type of substrate (SB - A and EFB - B), size of substrates (0.5 cm and 2.5 cm), mass ratio of spawn to substrate (SP/SS) (1:10 and 1:14), temperature during spawn running (25°C and ambient) and pre-treatment of substrates (steam and non-steam). The response was nitrogen concentration in mycelium (N). This paper presents the application of artificial neural network to improve the modelling process. Artificial neural network is one of the machine learning method which use the cultivation process information and extract the pattern from the data. Neural network ability to learn pattern by changing the connection weight had produced a trained network which represent the Pleurotus sp. cultivation process. Next this trained network was validated using error measurement to determine the modelling accuracy. The results show that the artificial neural network modelling produced better results with higher accuracy and lower error when compared to the mathematical modelling.

scholarly journals Regime of small number of photons in the cavity for a singleemitter laser

2021 ◽  
Vol 2103 (1) ◽  
pp. 012158
Author(s):  
N V Larionov
Keyword(s):  
Differential Equation ◽  
Exact Solutions ◽  
Master Equation ◽  
Cavity Mode ◽  
Photon Number ◽  
System Of Equations ◽  
Equation Approach ◽  
Master Equation Approach ◽  
Single Emitter ◽  
Analytical Expressions

Abstract The model of a single-emitter laser generating in the regime of small number of photons in the cavity mode is theoretically investigated. Based on a system of equations for different moments of the field operators the analytical expressions for mean photon number and photon number variance are obtained. Using the master equation approach the differential equation for the phase-averaged quasi-probability Q is derived. For some limiting cases the exact solutions of this equation are found.

scholarly journals Mathematical modelling of the mass-spring-damper system - A fractional calculus approach

2012 ◽  
Vol 22 (5) ◽  
pp. 5-11 ◽  
Author(s):  
José Francisco Gómez Aguilar ◽  
Juan Rosales García ◽  
Jesus Bernal Alvarado ◽  
Manuel Guía
Keyword(s):  
Differential Equation ◽  
Fractional Calculus ◽  
Mathematical Modelling ◽  
Fractional Differential Equation ◽  
Fractional Order ◽  
Time Derivative ◽  
System A ◽  
Fractional Differential ◽  
Mass Spring ◽  
Derivatives Of

In this paper the fractional differential equation for the mass-spring-damper system in terms of the fractional time derivatives of the Caputo type is considered. In order to be consistent with the physical equation, a new parameter is introduced. This parameter char­acterizes the existence of fractional components in the system. A relation between the fractional order time derivative and the new parameter is found. Different particular cases are analyzed

Theoretical Analysis of Activation Energy Effect on Prandtl–Eyring Nanoliquid Flow Subject to Melting Condition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ikram Ullah ◽  
Rashid Ali ◽  
Hamid Nawab ◽  
Abdussatar ◽  
Iftikhar Uddin ◽  
...  
Keyword(s):  
Differential Equation ◽  
Activation Energy ◽  
Convective Flow ◽  
Skin Friction Coefficient ◽  
System Of Equations ◽  
Energy Effect ◽  
Melting Condition ◽  
Ode System ◽  
Physical Importance ◽  
Controlling Variables

Abstract This study models the convective flow of Prandtl–Eyring nanomaterials driven by a stretched surface. The model incorporates the significant aspects of activation energy, Joule heating and chemical reaction. The thermal impulses of particles with melting condition is addressed. The system of equations is an ordinary differential equation (ODE) system and is tackled numerically by utilizing the Lobatto IIIA computational solver. The physical importance of flow controlling variables to the temperature, velocity and concentration is analyzed using graphical illustrations. The skin friction coefficient and Nusselt number are examined. The results of several scenarios, mesh-point utilization, the number of ODEs and boundary conditions evaluation are provided via tables.

Development of technique for determining of stamping hammer blow efficiency

2021 ◽  
pp. 491-498
Author(s):  
A.M. Zolotov ◽  
M.O. Smirnov
Keyword(s):  
Mathematical Modelling ◽  
Turbine Blade ◽  
Technological Process ◽  
Stamping Process ◽  
Die Forging ◽  
Stage Process ◽  
Force Displacement ◽  
Hammer Blow

The multiple-stage process of large-sized turbine blade blanks on steam-air die-forging hammer is considered. Mathematical modelling of the stamping process of large-sized turbine blade on falling parts 25 t mass stamping hammer is carried out. Measurements of the number of hammer blows and the under-stamping of blade blanks at each stage of the technological process are performed. Method for determining of the hammer blow efficiency is developed. Diagram of the force—displacement of falling parts 25 t mass hammer is constructed. The dependence of the blow efficiency of falling parts 25 t mass hammer is obtained, with can be used in mathematical modelling of the stamping processes of large-sized forgings on this hammer.

Computational Study of Inclusion Burst via the Proton Sponge Hypothesis

2010 ◽  
Author(s):  
Eric Freeman ◽  
Lisa Mauck Weiland ◽  
Wilson S. Meng
Keyword(s):  
Computational Study ◽  
Burst Release ◽  
System Of Equations ◽  
Biological Applications ◽  
Proton Sponge ◽  
System Of Differential Equations ◽  
Governing Equations ◽  
Stiff System ◽  
Broad Array ◽  
Insight Into

Biological proteins embedded in either a biological or an engineered membrane will actively maintain electrochemical balance across that membrane through transport of fluid and charge. While membrane studies are often planar, in nature they typically take the form of inclusions (∼spherical). Study and ultimately manipulation of the protein transporter types and density, and interior/exterior states of these inclusions lend insight into burst mechanisms appropriate to a broad array of engineering and biological applications, such as intracellular burst release of a vaccine. To explore these phenomena the governing equations of each transporter, as well as the membrane state are established. The result is a model requiring the simultaneous solution of a stiff system of differential equations. Presented is the computational solution of this system of equations for a specific burst scenario — the hypothesis that a proton sponge may be employed to expedite intracellular burst release of a DNA vaccine is explored.

Numerical Simulation of 2D Flow in a Curved Channel

2011 ◽  
Vol 374-377 ◽  
pp. 378-381
Author(s):  
Ming Qin Liu ◽  
Yu Ling Liu ◽  
Wen Li Wei
Keyword(s):  
Explicit Scheme ◽  
System Of Equations ◽  
System Of Differential Equations ◽  
Curved Channel ◽  
Order Accuracy ◽  
Governing System ◽  
2D Flow ◽  
Two Dimensional Flow ◽  
Flow Boundaries

This paper is concerned with a new numerical method of two-dimensional flow. The governing system of differential equations is transformed into an equivalent system applied over a square-grid network in order to overcome the difficulties and inaccuracies associated with the determination of characteristics near the flow boundaries. The MacCormack two-step explicit scheme with second-order accuracy is used for the solution of the transformed system of equations. The present numerical model has been used to numerically compute flow in sharply curved channel.

An evaluation of a dynamic model of the secondary clarifier

1996 ◽  
Vol 34 (5-6) ◽  
pp. 19-26 ◽  
Author(s):  
Ulf Jeppsson ◽  
Stefan Diehl
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytical Solution ◽  
Mathematical Modelling ◽  
Dynamic Behaviour ◽  
Linear Partial Differential Equation ◽  
Layer Model ◽  
Important Conclusion ◽  
Secondary Clarifier ◽  
Theoretical Results

The main objective of the paper is to support and illustrate recent theoretical results on the mathematical modelling of the secondary clarifier. A new settler model is compared with a traditional layer model by means of numerical simulations. Emphasis is put on the numerical solution's ability to approximate the analytical solution of the conservation law written as a non-linear partial differential equation. The new settler model is consistent in this respect. Another important conclusion is that a layer model dividing the settler into only ten layers (normally used in settler models) is too crude an approximation to capture the detailed dynamic behaviour of the settler. All simulations presented are performed with the settler models coupled to the IAWQ Activated Sludge Model No. 1.

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