Experimental study and mathematical modelling of self-oscillation at the electrode-magnetic fluid interface in an electric field

The article describes a mathematical model of self-oscillation in the form of a boundary value problem for a nonlinear system of partial differential equations, with a numerical solution. The numerical results were compared to the experimental data to confirm the adequacy of the model. The model uses the classical system of differential equations of material balance, Nernst-Planck and Poisson equations without simplifications or fitting parameters. The aim of the article was to study the parameters of concentration self-oscillation in a layer of the dispersed phase particles of magnetic fluid at the interface with an electrode in an electric field. For this purpose, we developed a mathematical model, the consistency of which wasconfirmed by the corresponding physical mechanism.As a result of numerical experiments, we found the critical value of the potential jump after which self-oscillation began. We also determined the oscillation growth period and other characteristics of the process. We developed software called AutoWave01 with an intuitive user interface and advanced functionality for the study of self-oscillation in a thin layer of magnetic colloid.

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Approximation of weak solution for the problem of a pH-gradient creation in isoelectrofocusing

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2014.0290 ◽

2014 ◽

Vol 470 (2171) ◽

pp. 20140290

Author(s):

L. V. Sakharova ◽

E. V. Shiryaeva ◽

M. Yu. Zhukov

Keyword(s):

Mathematical Model ◽

Aqueous Solution ◽

Weak Solution ◽

Differential Equations ◽

Electric Field ◽

Small Parameter ◽

General Model ◽

Smooth Functions ◽

Piecewise Continuous ◽

The Mathematical Model

The mathematical model describing the stationary natural pH -gradient arising under the action of an electric field in an aqueous solution of ampholytes is constructed and investigated. The model is a part of a more general model of the isoelectrofocusing process. Investigation is based on the approximation of a weak solution by the piecewise continuous non-smooth functions. The method can be used for solving classes of problems for ordinary differential equations with a small parameter at the highest derivatives and the turning points.

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Glycemia monitoring

Nonlinear Analysis Modelling and Control ◽

10.15388/na.1998.2.0.15282 ◽

1998 ◽

Vol 2 ◽

pp. 23-30

Author(s):

Igor Basov ◽

Donatas Švitra

Keyword(s):

Diabetes Mellitus ◽

Mathematical Model ◽

Numerical Methods ◽

Differential Equations ◽

Blood Sugar ◽

Self Regulation ◽

Physiological System ◽

Non Linear ◽

The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

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Mathematical model to predict the characteristics of polarization in dielectric materials: The concept of piezoelectrcity and electrostriction

10.31221/osf.io/39572 ◽

2019 ◽

Author(s):

Chem Int

Keyword(s):

Mathematical Model ◽

Electric Field ◽

Lead Zirconate Titanate ◽

Dielectric Material ◽

Strain Curve ◽

Dielectric Materials ◽

Lead Zirconate ◽

Simulation Software ◽

Constitutive Law ◽

Basic Material

Model was developed for the prediction of polarization characteristics in a dielectric material exhibiting piezoelectricity and electrostriction based on mathematical equations and MATLAB computer simulation software. The model was developed based on equations of polarization and piezoelectric constitutive law and the functional coefficient of Lead Zirconate Titanate (PZT) crystal material used was 2.3×10-6 m (thickness), the model further allows the input of basic material and calculation of parameters of applied voltage levels, applied stress, pressure, dielectric material properties and so on, to generate the polarization curve, strain curve and the expected deformation change in the material length charts. The mathematical model revealed that an application of 5 volts across the terminals of a 2.3×10-6 m thick dielectric material (PZT) predicted a 1.95×10-9 m change in length of the material, which indicates piezoelectric properties. Both polarization and electric field curve as well as strain and voltage curve were also generated and the result revealed a linear proportionality of the compared parameters, indicating a resultant increase in the electric field yields higher polarization of the dielectric materials atmosphere.

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A mathematical model of the electric field perturbation about an array of conductive wires and its impact on the passing charged particle distribution

Physics of Plasmas ◽

10.1063/5.0042859 ◽

2021 ◽

Vol 28 (3) ◽

pp. 033507

Author(s):

K. Shadman

Keyword(s):

Mathematical Model ◽

Charged Particle ◽

Electric Field ◽

Particle Distribution ◽

Field Perturbation

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Ultrasonic Waves in Bubbly Liquids: An Analytic Approach

Mathematics ◽

10.3390/math9111309 ◽

2021 ◽

Vol 9 (11) ◽

pp. 1309

Author(s):

P. R. Gordoa ◽

A. Pickering

Keyword(s):

Mathematical Model ◽

Partial Differential Equations ◽

Differential Equations ◽

Acoustic Waves ◽

Elliptic Functions ◽

Coupled System ◽

Ultrasonic Waves ◽

Partial Differential ◽

Special Cases ◽

Spherical Bubbles

We consider the problem of the propagation of high-intensity acoustic waves in a bubble layer consisting of spherical bubbles of identical size with a uniform distribution. The mathematical model is a coupled system of partial differential equations for the acoustic pressure and the instantaneous radius of the bubbles consisting of the wave equation coupled with the Rayleigh–Plesset equation. We perform an analytic analysis based on the study of Lie symmetries for this system of equations, concentrating our attention on the traveling wave case. We then consider mappings of the resulting reductions onto equations defining elliptic functions, and special cases thereof, for example, solvable in terms of hyperbolic functions. In this way, we construct exact solutions of the system of partial differential equations under consideration. We believe this to be the first analytic study of this particular mathematical model.

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Mathematical model implementation in conditions of uncertainty and possible risks

Energy and automation ◽

10.31548/energiya2021.04.137 ◽

2021 ◽

pp. 137-145

Author(s):

A. Kravtsov ◽

◽

D. Levkin ◽

O. Makarov ◽

◽

...

Keyword(s):

Thermal Conductivity ◽

Mathematical Model ◽

Differential Equations ◽

Boundary Value Problem ◽

Boundary Value Problems ◽

Layer Structure ◽

Boundary Value ◽

Goal Function ◽

Cauchy Problems ◽

System Of Differential Equations

The article presents the theoretical and methodological principles for forecasting and mathematical modeling of possible risks in technological and biotechnological systems. The authors investigated in details the possible approach to the calculation of the goal function and its parameters. Considerable attention is paid to substantiating the correctness of boundary value problems and Cauchy problems. In mechanics, engineering, and biology, Cauchy problems and boundary value problems of differential equations are used to model physical processes. It is important that differential equations have a single physically sound solution. The authors of this article investigate the specific features of boundary value problems and Cauchy problems with boundary conditions in a two-point medium, and determine the conditions for the correctness of such problems in the spaces of power growth functions. The theory of pseudo-differential operators in the space of generalized functions was used to prove the correctness of boundary value problems. The application of the obtained results will make it possible to guarantee the correctness of mathematical models built in conditions of uncertainty and possible risks. As an example of a computational mathematical model that describes the state of the studied object of non-standard shape, the authors considered the boundary value problem of the system of differential equations of thermal conductivity for the embryo under the action of a laser beam. For such a boundary value problem, it is impossible to guarantee the existence and uniqueness of the solution of the system of differential equations. To be sure of the existence of a single solution, it is necessary either not to take into account the three-layer structure of the microbiological object, or to determine the conditions for the correctness of the boundary value problem. Applying the results obtained by the authors, the correctness of the boundary value problem of systems of differential equations of thermal conductivity for the embryo is proved taking into account the three-layer structure of the microbiological object. This makes it possible to increase the accuracy and speed of its implementation on the computer. Key words: forecasting, risk, correctness, boundary value problems, conditions of uncertainty

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DIFFERENTIAL EQUATIONS FOR TRAIN STARTING WITH ELASTIC CONNECTIONS

Fundamental and Applied Problems of Engineering and Technology ◽

10.33979/2073-7408-2021-346-2-18-26 ◽

2021 ◽

Vol 2 ◽

pp. 18-26

Author(s):

I.P. POPOV

Keyword(s):

Mathematical Model ◽

Differential Equations ◽

Friction Force ◽

Static Friction ◽

Longitudinal Vibrations ◽

Maximum Tension ◽

Inert Mass ◽

The Moment ◽

Elastic Couplings ◽

Selection Of

The starting mode for the train is the most difficult. An effective method of pulling is the selection of coupling clearances. In this case, the cars are set in motion sequentially and the inert mass, as well as the static friction force immediately at the moment of starting, are minimal. This method has two significant drawbacks - a small fixed value of the gaps in the couplings and the shock nature of the impulse transfer. These disadvantages can be avoided by using elastically deformable couplings. The aim of this work is to construct a mathematical model of "easy" starting of a train with elastic couplings. The softening of the train start-off mode is essentially due to the replacement of the simultaneous start-off of the sections with alternate ones. To exclude longitudinal vibrations of the composition, after reaching the maximum tension of the coupling, the possibility of its harmonic compression should be mechanically blocked.

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A Piezoelectric Screw Dislocation Interacting with a Dielectric Crack in a Hexagonal Piezoelectric Material

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.9.183 ◽

2005 ◽

Vol 9 ◽

pp. 183-190

Author(s):

Jin Xi Liu ◽

X.L. Liu

Keyword(s):

Electric Field ◽

Screw Dislocation ◽

Electric Displacement ◽

Image Force ◽

Mapping Method ◽

Piezoelectric Medium ◽

Intensity Factors ◽

Potential Jump ◽

Piezoelectric Screw Dislocation ◽

Dielectric Crack

This paper is concerned with the interaction of a piezoelectric screw dislocation with a semi-infinite dielectric crack in a piezoelectric medium with hexagonal symmetry. The solution of the considered problem is obtained from the dislocation solution of a piezoelectric half-plane adjoining a gas medium of dielectric constant ε0 by using the conformal mapping method. The intensity factors of stress, electric displacement and electric field and the image force on the dislocation are given explicitly. The effect of electric boundary conditions on the dislocation-crack interaction is analyzed and discussed in detail. The results show that ε0 only influences the electric displacement and electric field intensity factors and the image force produced by the electric potential jump.

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CALCULATION OF TEMPERATURE OF ROUTINE WATER COOLED IN IRRIGATED LAYERS

Technical science and innovation ◽

10.51346/tstu-01.19.3.-77-0036 ◽

2019 ◽

Vol 2019 (3) ◽

pp. 249-255

Author(s):

N Usmonov ◽

◽

Sh Sanayev ◽

Z Yusupov

Keyword(s):

Mathematical Model ◽

Cooling System ◽

Material Balance ◽

Polymeric Materials ◽

Water Supply Systems ◽

Evaporative Water ◽

Circulating Water ◽

Industrial Enterprises ◽

Air Cooler ◽

Air Conditioning Systems

The article describes the developed mathematical model, algorithm and program for calculating the process of cooling the water leaving the evaporative cooler and the final temperature of humid air. The compilation of a mathematical model is based on the analysis of literature data. Practically at all industrial enterprises, technological equipment is cooled by means of circulating water supply systems equipped with evaporative coolers. The article made a choice of a cooling system for air conditioning systems of residential premises. The developed basic design scheme of the evaporative water and air cooler with the irrigated layer is presented, as well as the estimated thermal and material balance. One of the main elements of these devices is a heat-mass transfer nozzle - sprinkler. This article presents the results of mathematical modeling of processes occurring in the volume of the sprinkler evaporator chamber, Raschig rings composed of vertical polymeric materials. Expressions are obtained for determining the values of air temperature based on the calculation of thermal modeling of the process of cooling circulating water in evaporative coolers of the type in question.

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