scholarly journals Nonlinear Concave Spiral Waves in Active Media Transferring Energy

2019 ◽  
Vol 224 ◽  
pp. 02011
Author(s):  
Mikhail Mazurov
Keyword(s):  
Mathematical Model ◽  
Breaking Waves ◽  
Spiral Waves ◽  
Computational Experiments ◽  
Active Media ◽  
Nagumo Equation

Spiral concave autowaves are widely implemented in physics, chemistry, hydrodynamics, meteorology and other fields. A mathematical model of spiral concave autowaves based on the Fitzhugh-Nagumo equation and modified axiomatic models are presented. The existence of spiral concave autowaves transferring energy was predicted via computational experiments. Applications of spiral concave autowaves carrying energy in hydrodynamics, generation of tornadoes, breaking waves, and tsunamis and examples of such autowaves in biology and medicine are reviewed and the importance of concave spiral autowaves transferring energy is emphasized.

scholarly journals Computation of the response functions of spiral waves in active media

2009 ◽  
Vol 79 (5) ◽  
Author(s):  
I. V. Biktasheva ◽  
D. Barkley ◽  
V. N. Biktashev ◽  
G. V. Bordyugov ◽  
A. J. Foulkes
Keyword(s):  
Spiral Waves ◽  
Response Functions ◽  
Active Media

Kinematical Description of Meandering Spiral Waves in Active Media

2002 ◽  
Vol 216 (5) ◽  
Author(s):  
M. Braune ◽  
H. Engel
Keyword(s):  
Boundary Condition ◽  
Spiral Waves ◽  
Rigid Rotation ◽  
Active Media ◽  
Curvature Effects ◽  
Kinematical Approach

Under certain conditions the dynamics of spiral waves in active media can be described within a kinematical approach. We discuss the importance of curvature effects for the transition from rigidly rotating to outward meandering spirals. To include these effects into the kinematical description we propose a modified boundary condition for the curvature at the tip. This allows to recover a variety of rotation regimes with hypocycloid-like trajectories of the spiral tip corresponding to outward meandering spiral waves which are frequently observed experimentally in active media of quite different nature beyond the instability of rigid rotation.

scholarly journals Energy Justification of the Number of Tractors for Agricultural Operations

2021 ◽  
Vol 37 ◽  
pp. 00136
Author(s):  
Camill A. Khafizov ◽  
Ramil N. Khafizov ◽  
Azat A. Nurmiev ◽  
Ilgiz G. Galiev
Keyword(s):  
Mathematical Model ◽  
Total Energy ◽  
System Analysis ◽  
Optimal Number ◽  
Computational Experiments ◽  
Energy Costs ◽  
Total Energy Consumption ◽  
Agricultural Producers ◽  
Main Research ◽  
Minimum Total Energy

The relevance of the problem under study is due to the need to substantiate the sufficient number of tractors used for various technological operations, depending on the volume of works performed, and taking into account their influence on the crop yield. The purpose is to develop the mathematical model of machine and tractor units used in technological operations by formalizing the vague concept of optimal agrotechnical timing of technological operations and calculating the optimal number of tractors to perform works by the total energy costs. The main research method is mathematical modeling of operations performed by machine-tractor units based on the system analysis and computational experiments and using the energy mathematical model. The article describes a criterion for optimizing the tractor parameters, dependences of the energy mathematical model of the unit. The results of computational experiments showed that for each operation there is an optimal number of tractors and tractor units minimizing the minimum total energy costs. Calculations were carried out when treating 1000 hectares with various tractors. It was revealed that the total energy consumption differs by 2 or more times. The required number of tractors depends on their main parameters, propeller parameters and other factors. It was revealed that with an increase in the volume of works, the required optimal number of tractors increases. The method for substantiating the required optimal number of tractors in technological operations will improve operations of tractors used by large agricultural producers, reduce the total energy costs for cultivating up to 12–16 thousand MJ/ha.

scholarly journals Nonlinear Concave Spiral Autowaves in Active Media, Transferring Energy, Their Application in Biology and Medicine

2018 ◽  
Vol 13 (1) ◽  
pp. 187-207 ◽  
Author(s):  
M.E. Mazurov
Keyword(s):  
Computational Experiments ◽  
Self Organization ◽  
Medical Applications ◽  
Detailed Review ◽  
Active Media ◽  
New Type ◽  
Biological And Medical Applications

The paper reviews the works devoted to convex spiral autowaves, which are widely known. Recently a new type of autowaves has been discovered - concave autowaves, they propagate from the periphery of active media to the center and are capable of transfering energy. It is proved that concave spiral autowaves can exist in specific inhomogeneous active media. Their existence is confirmed by computational experiments. It is established that concave autowaves are widespread in nature. The article gives a more detailed review of the biological and medical applications of spiral concave autowaves, it is also known that there are many of them in physics, chemistry, hydrodynamics, meteorology, and space. Concave spiral autowaves, carrying energy, are one of the essential tools of self-organization.

scholarly journals MATHEMATICAL AND COMPUTER SIMULATION OF THE PROCESSES OF TWO-PHASE JOINT GAS FILTRATION AND WATER IN A POROUS ENVIRONMENT

2019 ◽  
pp. 14-23
Keyword(s):  
Mathematical Model ◽  
Porous Medium ◽  
Porous Media ◽  
Numerical Solution ◽  
Difference Equations ◽  
Nonlinear Differential Equations ◽  
Computational Experiments ◽  
Water Filtration ◽  
Graphical Form ◽  
Gas Filtration

A mathematical model, methods and algorithms for the numerical solution of problems of joint gas-water filtration in porous media are considered. The mathematical model of the process of non-stationary joint gas-water filtration in a porous medium is described by a system of nonlinear differential equations of parabolic type. In the numerical solution of the boundary value problem of gas displacement by water in a porous medium, the differential sweeping method is used for systems of differential-difference equations. The system of differential-difference equations with respect to the gas pressure function is nonlinear, therefore, an iterative method is used for it, based on the method of quasilinearization of nonlinear terms. Computational algorithms and software have been developed for conducting computational experiments to study unsteady processes of gas filtration in porous media. The results of the developed software, as well as the results of computational experiments in a graphical form in visual form are given.

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