scholarly journals Mathematical modelling and optimization of the electroplating process with a rotating cathode to reduce the non-uniformity of the coating thickness

2019 ◽  
Vol 298 ◽  
pp. 00014
Author(s):  
Denis Solovjev ◽  
Inna Solovjeva ◽  
Viktoriya Konkina
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Coating Thickness ◽  
Cathode Surface ◽  
Stationary Process ◽  
Zinc Plating ◽  
Calculation Results ◽  
Electroplating Process ◽  
Theoretical Electrochemistry ◽  
Modelling And Optimization

The article is devoted to the development of an approach to improving the electroplating uniformity on the cathode surface, rotating around its axis, using a figured anode. A mathematical model of a stationary process with distributed coordinates, based on the equations of theoretical electrochemistry, has been developed for this approach. The problem for optimizing the anode shape according to the criterion for minimizing the non-uniformity of the deposited coating on the rotating cathode is formulated. The results of solving this problem are demonstrated on the example of the Zinc plating. Possible improvements to improve the accuracy of the calculation results for the developed mathematical model are given in the conclusion of the article.

scholarly journals Mathematical model and calculation results of the kerosene aerosol combustion rate

2020 ◽  
Vol 1565 ◽  
pp. 012022
Author(s):  
V A Poryazov ◽  
K M Moiseeva ◽  
A Yu Krainov ◽  
D A Krainov
Keyword(s):  
Mathematical Model ◽  
Combustion Rate ◽  
Calculation Results

Mathematical Modelling the Process of Cup Wheel Precision Grinding of Rotating Concave Paraboloid

2016 ◽  
Vol 693 ◽  
pp. 837-842
Author(s):  
Fu Yi Xia ◽  
Li Ming Xu ◽  
De Jin Hu
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Abrasive Particle ◽  
Influence Factors ◽  
Machining Process ◽  
Quadric Surface ◽  
Precision Grinding ◽  
Cup Wheel ◽  
The Mathematical Model ◽  
Trajectory Equation

A novel principle of cup wheel grinding of rotating concave quadric surface was proposed. The mathematical model of machining process was established to prove the feasibility of precision grinding of rotating concave paraboloid based on the introduced principle. The conditions of non-interference grinding of concave paraboloid were mathematically derived. The processing range and its influence factors were discussed. The trajectory equation of abrasive particle was concluded. Finally, the math expressions of numerical controlled parameters was put forward in the process of grinding of the concave paraboloid.

Mathematical modelling.

2021 ◽  
Author(s):  
Ed Rutgers Durner
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Mathematical Models ◽  
Growth And Development ◽  
Fertilizer Recommendations ◽  
Mathematical Equations

Abstract Plants are studied to understand their growth and development so that their quality and productivity can be optimised. Models are developed that can be simple and descriptive, or quite complex with numerous mathematical equations; their level of complexity is linked to their purpose. This summary serves as an introduction to mathematical models in horticulture. It is not a manual for modelling itself, but rather an overview of how important mathematical models are in horticultural production. Mathematical models are used extensively in horticulture both extrinsically, i.e. when calculating chilling hour accumulations and intrinsically, i.e. when applying fertilizer to a crop. In chilling calculations, developed models are used directly. Fertilizer recommendations were probably developed using a mathematical model. The first part of this article discusses models in general and reviews general characteristics of mathematical models. The second part outlines the major uses of mathematical modelling in modern horticultural production. Presentations of specific models are limited in order to present a general discussion of models with examples that will interest most horticulturists.

scholarly journals ПОБУДОВА МАТЕМАТИЧНОЇ МОДЕЛІ СКЛАДНОГО РУХУ ФЛАКОНІВ НА ЛІНІЯХ РОЗЛИВУ ЛІКІВ ФАРМАЦЕВТИЧНОЇ ПРОМИСЛОВОСТІ

2012 ◽  
Author(s):  
N. О. Kravets
Keyword(s):  
Mathematical Model ◽  
Experimental Evaluation ◽  
Theoretical Dependence ◽  
Complex Product ◽  
Lateral Lines ◽  
Calculation Results ◽  
The Mathematical Model

The  mathematical model of the complex product motion along the lateral lines at the plate conveyers of the bottle lines is presented in the artcle. The experimental evaluation of the gained theoretical dependence is suggested.   The calculation results coordinate well with the modelling and experiment resuls.

scholarly journals MATHEMATICAL MODELLING OF THE UNMANNED AERIAL VEHICLE DYNAMICS

2018 ◽  
pp. 37-44
Author(s):  
V. Y. Stepanov
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Unmanned Aerial Vehicle ◽  
Vehicle Dynamics ◽  
Point Of View ◽  
Dynamics Analysis ◽  
Aerial Vehicle ◽  
Main Components ◽  
Controlled Object

The article gives a classification of the main components of unmanned aerial vehicle (UAV) systems, gives the areas in which the application of UAVs is actual in practice today. Further, the UAV is considered in more detail from the point of view of its flight dynamics analysis, the equation necessary for creating a mathematical model, as well as the model of an ordinary dynamic system as a non-stationary nonlinear controlled object, is given. Next, a description of the developed software for modeling and a description of program algorithm are given. Finally, a conclusion describes the necessary directions for further scientific researches.

Mathematical Modelling the Power Supply-Load System for Electro-Discharge Polishing Process

2010 ◽  
Vol 159 ◽  
pp. 125-128
Author(s):  
A. Parshuta ◽  
V. Chitanov ◽  
Lilyana Kolaklieva ◽  
Roumen Kakanakov
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Numerical Solution ◽  
Power Supply ◽  
Equation System ◽  
Electrolyte Temperature ◽  
Polishing Process ◽  
The Real ◽  
Quadratic Interpolation ◽  
Runge Kutta

The real electro-discharge polishing (EDP) system has been presented by an equivalent electrical scheme and described by a corresponded equation system. The Runge-Kutta-Merson method with automatically changed step is used for the numerical solution the equation system. The current through the resistor equivalent to the steam gas wrapper is defined with an I-V characteristic obtained by the method of multi-interval quadratic interpolation-approximation. A mathematical model of the power supply-load system has been realized in Basic and Matlab® languages. On the base of the developed modelling conditions limiting the current and voltage overload in the EDP system have been determined depending on the maximum polished area and the electrolyte temperature.

scholarly journals Quantification of plasma cell dynamics using mathematical modelling

2018 ◽  
Vol 5 (1) ◽  
pp. 170759 ◽  
Author(s):  
Marcel Mohr ◽  
Dirk Hose ◽  
Anja Seckinger ◽  
Anna Marciniak-Czochra
Keyword(s):  
Mathematical Model ◽  
Bone Marrow ◽  
Mathematical Modelling ◽  
Plasma Cells ◽  
Cell Dynamics ◽  
Growth And Survival ◽  
Specific Antibodies ◽  
Health And Disease ◽  
Potential Basis ◽  
The Impact

Plasma cells (PCs) are the main antibody-producing cells in humans. They are long-lived so that specific antibodies against either pathogens or vaccines are produced for decades. PC longevity is attributed to specific areas within the bone marrow micro-environment, the so-called ‘niche’, providing the cells with required growth and survival factors. With antigen encounters, e.g. infection or vaccination, new PCs are generated and home to the bone marrow where they compete with resident PCs for the niche. We propose a parametrized mathematical model describing healthy PC dynamics in the bone marrow. The model accounts for competition for the niche between newly produced PCs owing to vaccination and resident PCs. Mathematical analysis and numerical simulations of the model allow explanation of the recovery of PC homoeostasis after a vaccine-induced perturbation, and the fraction of vaccine-specific PCs inside the niche. The model enables quantification of the niche-related dynamics of PCs, i.e. the duration of PC transition into the niche and the impact of different rates for PC transitions into and out of the niche on the observed cell dynamics. Ultimately, it provides a potential basis for further investigations in health and disease.

Simulation of fuel bed ignition by wildland firebrands

2018 ◽  
Vol 27 (8) ◽  
pp. 550 ◽  
Author(s):  
O. V. Matvienko ◽  
D. P. Kasymov ◽  
A. I. Filkov ◽  
O. I. Daneyko ◽  
D. A. Gorbatov
Keyword(s):  
Mathematical Model ◽  
Pinus Sylvestris ◽  
Mathematical Modelling ◽  
Thermal Energy ◽  
Ignition Time ◽  
Pine Bark ◽  
Bark Sample ◽  
Airflow Velocity ◽  
Experimental Conditions ◽  
Series Of Experiments

A 3-D mathematical model of fuel bed (FB) ignition initiated by glowing firebrands originating during wildland fires is proposed. In order to test and verify the model, a series of experiments was conducted to determine the FB ignition time by a single pine bark and twig firebrand (Pinus sylvestris). Irrespective of the pine bark sample sizes and experimental conditions, the ignition of the FB was not observed. Conversely, pine twigs, under certain parameters, ignited the FB in the range of densities (60–105 kg m−3) and with the airflow velocity of ≥2 m s−1. The results of the mathematical modelling have shown that a single pine bark firebrand ≤5 cm long with a temperature of T ≤ 1073 K does not ignite in the flaming mode the FB, and only the thermal energy of larger particles is sufficient for flaming ignition of the adjacent layers of the FB. The analysis of the results has shown that the firebrand length is a major factor in the initiation of ignition. Comparison of the calculated and observed FB ignition times by a single firebrand have shown that our modelling accords well with the experimental results.

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