scholarly journals Estimation of parameters characterizing a steady-state synthesis process with nonlinear microorganism growth kinetics

2022 ◽  
Vol 11 (4) ◽  
pp. 561-569
Author(s):  
Yu. L. Gordeeva ◽  
B. A. Ul’yanov ◽  
E. L. Gordeeva
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Numerical Experiment ◽  
Dilution Rate ◽  
Growth Kinetics ◽  
Technology Implementation ◽  
Theoretical Basis ◽  
Lactic Acid Production ◽  
Synthesis Process ◽  
Estimation Of Parameters

The paper describes a theoretical basis developed for estimating the parameters of a steady-state biotechnological process characterized by nonlinear microorganism growth kinetics. This study aimed to obtain a common methodological basis for estimating input parameters that determine actual technology implementation, taking into account all possible restrictions on the concentration of incoming substrate Sf (g/l) and dilution rate D (h-1 ). The theory development was based on a mathematical model describing one of the most common processes of lactic acid production. This mathematical model includes three mass balance equations (for biomass, substrate, and product), as well as an equation of microorganism growth kinetics. The study established relations for calculating the ultimate value of the dilution rate D ult at a given Sf , relations for the maximum and minimum values of Sf , as well as Sf and D providing the maximum productivity value QP, g/(l·h), where QP = PD (P – product concentration, g/l). These relations were designed to calculate the parameters of possible process implementation for two options at the same value of QP: two values of D calculated for a given Sf and two values of Sf calculated for a given D. A numerical experiment is described using the constants of the mathematical model confirmed by foreign studies. This numerical experiment is illustrated using an Sf-D dependence pattern determining an acceptable value range for Sf and D, with the separate calculation of parameters according to Sf sections. For each of these sections, calculation formulas are provided. It is concluded that the developed theoretical basis is sufficiently general in nature to be applied to biotechnological processes that involve other kinetic relations, as well as microorganism strains creating by-products and using raw materials that are employed to reproduce the substrate in the process of synthesis.

scholarly journals Steady Modeling for an Ammonia Synthesis Reactor Based on a Novel CDEAS-LS-SVM Model

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Zhuoqian Liu ◽  
Lingbo Zhang ◽  
Wei Xu ◽  
Xingsheng Gu
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Differential Evolution ◽  
Ammonia Synthesis ◽  
Fast Convergence ◽  
Operating Conditions ◽  
Synthesis Process ◽  
Plant Behavior ◽  
Svm Model ◽  
Simulation Results

A steady-state mathematical model is built in order to represent plant behavior under stationary operating conditions. A novel modeling using LS-SVR based on Cultural Differential Evolution with Ant Search is proposed. LS-SVM is adopted to establish the model of the net value of ammonia. The modeling method has fast convergence speed and good global adaptability for identification of the ammonia synthesis process. The LS-SVR model was established using the above-mentioned method. Simulation results verify the validity of the method.

scholarly journals Temporal Evolution of Immunity Distributions in a Population with Waning and Boosting

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
M. V. Barbarossa ◽  
M. Polner ◽  
G. Röst
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Temporal Evolution ◽  
Disease Outbreaks ◽  
Population Level ◽  
Coupled System ◽  
Disease Outbreak ◽  
Periodic Disease ◽  
Evolution Of Immunity

We investigate the temporal evolution of the distribution of immunities in a population, which is determined by various epidemiological, immunological, and demographical phenomena: after a disease outbreak, recovered individuals constitute a large immune population; however, their immunity is waning in the long term and they may become susceptible again. Meanwhile, their immunity can be boosted by repeated exposure to the pathogen, which is linked to the density of infected individuals present in the population. This prolongs the length of their immunity. We consider a mathematical model formulated as a coupled system of ordinary and partial differential equations that connects all these processes and systematically compare a number of boosting assumptions proposed in the literature, showing that different boosting mechanisms lead to very different stationary distributions of the immunity at the endemic steady state. In the situation of periodic disease outbreaks, the waveforms of immunity distributions are studied and visualized. Our results show that there is a possibility to infer the boosting mechanism from the population level immune dynamics.

scholarly journals The mathematical stability study for the system of the CoO(OH) – overoxidized polypyrrole composite synthesis in the presence of fluor ions

2016 ◽  
Vol 16 ◽  
pp. 13-17
Author(s):  
V. Tkach ◽  
S.C. De Oliveira ◽  
R. Ojani ◽  
P.I. Yagodynets ◽  
U. Páramo-García
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Bifurcation Analysis ◽  
Stability Theory ◽  
Stability Study ◽  
Linear Stability Theory ◽  
Monotonic Instability ◽  
Overoxidized Polypyrrole ◽  
Polypyrrole Composite ◽  
Steady State Stability

The potentiostatic synthesis of CoO(OH) – Overoxidized polypyrrole composite in the presence of fluor ions has been investigated mathematically. The corresponding mathematical model was described and analyzed by means of linear stability theory and bifurcation analysis. The steady-state stability requirements, like also oscillatory and monotonic instability conditions are derived.Mongolian Journal of Chemistry 16 (42), 2015, 13-17

scholarly journals The Analytical Study of the Value of Adhesion of Cement Gel between Reinforcement and Concrete

2020 ◽  
Vol 26 (3) ◽  
pp. 483-495
Author(s):  
A. N. Nikolyukin ◽  
◽  
V. P. Yartsev ◽  
S. A. Mamontov ◽  
I. I. Kolomnikova ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Numerical Modeling ◽  
Numerical Experiment ◽  
Bearing Capacity ◽  
Analytical Study ◽  
Bonding Process ◽  
Periodic Profile

Disruption of the adhesion of reinforcement to concrete causes significant deformation of the structure, which can subsequently lead to the loss of its bearing capacity. There is a need to study the bonding process between concrete and reinforcement under various influences. The results of a numerical experiment on pulling out reinforcement of periodic profile from concrete are presented. A mathematical model to study the processes taking place in the field of embedding reinforcement in concrete has been built. The results of numerical modeling are described.

Relationship between the Steady-Handling Characteristics of Automobiles and Their Stability

1973 ◽  
Vol 15 (5) ◽  
pp. 326-328 ◽  
Author(s):  
R. S. Sharp
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Degree Of Freedom ◽  
Nonlinear Region ◽  
Handling Characteristics ◽  
Yield Information ◽  
Turning Motion ◽  
The Stability ◽  
Three Degree Of Freedom

Analyses of the steady-state handling behaviour of an automobile and the stability of its steady-turning motion, based on a three degree of freedom mathematical model, are used to show that the steady behaviour and the stability are related similarly in the nonlinear region as in the well documented linear one. It is concluded that analysis and measurement of the steady behaviour will yield information on the stability of automobiles.

Dynamics of Dual-Cell Series Miura-Ori Structures With Different Types of Inter-Cell Connections

2021 ◽  
Author(s):  
Hai Zhou ◽  
Haiping Wu ◽  
Jian Xu ◽  
Hongbin Fang
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Theoretical Basis ◽  
Initial Conditions ◽  
Cell Structure ◽  
Dynamic Responses ◽  
Complex Environment ◽  
Current State ◽  
Different Types ◽  
Cell Series

Abstract Origami-inspired structures and materials have shown remarkable properties and performances originating from the intricate geometries of folding. Origami folding could be a dynamic process and origami structures could possess rich dynamic characteristics under external excitations. However, the current state of dynamics of origami has mostly focused on the dynamics of a single cell. This research has performed numerical simulations on multi-stable dual-cell series Miura-Ori structures with different types of inter-cell connections based on a dynamic model that does not neglect in-plane mass. We introduce a concept of equivalent constraint stiffness k* to distinguish different types of inter-cell connections. Results of numerical simulations reveal the multi-stable dual-cell structure will exhibit a variety of complex nonlinear dynamic responses with the increasing of connection stiffness because of the deeper energy well it has. The connection stiffness has a strong effect on the steady-state dynamic responses under different excitation amplitudes and a variety of initial conditions. This effect makes us able to adjust the dynamic behaviors of dual-cell series Miura-Ori structure to our needs in a complex environment. Furthermore, the results of this research could provide us a theoretical basis for the dynamics of origami folding and serve as guidelines for designing dynamic applications of origami metastructures and metamaterials.

A mathematical model of a brushed DC motor system

2021 ◽  
Vol 2 (2) ◽  
pp. 60-68
Author(s):  
N. N. A. Rahman ◽  
N. M. Yahya
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Motor System ◽  
Dc Motor ◽  
Positioning System ◽  
Pd Controller ◽  
Trial And Error ◽  
Trial And Error Method ◽  
Low Torque ◽  
Error Method

Mathematical model has been proposed for some system that involves a brushed DC motor and it is widely used in industry. Brushed DC motor ideals for applications with a low- torque, manage to change pace or speed and it is widely used in many applications such as x-y table positioning system, conveyor systems and other system that required to use the features that brushed DC motor have. Mathematical model of brushed DC motor in order to verify the performance of the DC motor. In this paper, mathematical model of brushed DC motor will be derived from a brushed DC motor circuit that consist of two parts that are electrical and mechanical part. To validate the functionality of mathematical model, the performance of the brushed DC motor without any controller will be compared with the brushed DC motor with the presence of PI-PD controller that will be tuned by trial-and-error method. Performances of both brushed DC motor with and without controller will be compared in terms of transient response which are, rise time, Tr, settling time, Ts, steady state error, ess and lastly percentage overshoot. At the end of the study, the brushed DC motor with PI-PD controller show a better performance compared to the brushed DC motor without any controller.

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