Improved Directional Local Extrema Patterns

The article investigates some issues of complex systems analysis and synthesis that contain local, discrete sources of temperature fields. The emphasis of the author's research lies in the calculation and optimization of the parameters of the laser action on the embryo. The biotechnological process is described by the boundary value problem of a non-stationary, multidimensional differential equation of thermal conductivity which satisfies the boundary conditions of heat flux, beginning and end of the laser action process. The author proposes an algorithm for calculation and optimization of the control parameters of laser action on multilayer microbiological material. The object of the study is the embryo under the action of a laser beam for fission. As a first approximation, at the stage of calculation and optimization of the parameters of the biotechnological process, the embryo is considered as a homogeneous body. The values of thermophysical characteristics are calculated by the method of expert evaluation of the parameters of the emitters. The correctness of the boundary value problem of the process of laser action on the embryo is proved by the author using the method of pseudodifferential operators. Seeking the solution of the boundary value problem in the form of the series, the analytical function of the temperature field distribution is obtained using the Fourier method of the separated variables in the article. Using the method of indeterminate coefficients, the author found the temperature of the laser action on the embryo. Using the approximate gradient method of finding local extrema and the method of directed search of local extrema, it is possible to obtain rational values of optimized parameters of the biotechnological process. The author outlines possible approaches for optimization of technical parameters of laser emitters. In his opinion, the results of research can be considered fundamental for the calculation and optimization of the parameters of the laser action on the embryo, taking into account the multilayer structure of the latter.

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Magnetohydrodynamic spectrum of gravitating plane plasmas with flow

Journal of Plasma Physics ◽

10.1017/s0022377898007454 ◽

1999 ◽

Vol 61 (2) ◽

pp. 221-240 ◽

Cited By ~ 11

Author(s):

B. van der HOLST ◽

R. J. NIJBOER ◽

J. P. GOEDBLOED

Keyword(s):

Shear Flow ◽

Spectral Problem ◽

Critical Values ◽

Equilibrium Flow ◽

Local Extrema ◽

Ideal Magnetohydrodynamic ◽

The Ideal

The ideal magnetohydrodynamic spectrum of gravitating plane plasmas with equilibrium flow is investigated. Flow makes the spectral problem non-self-adjoint, so that the spectrum can become overstable. The criteria for cluster spectra to appear are derived analytically and both stable and unstable sides of the spectrum are examined numerically. Above certain critical values of the shear flow at the resonant surface, the gravitating interchange modes disappear. However, the local extrema of the continua can then take over the cluster spectrum.

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Many continuous functions have many proper local extrema

Journal of Mathematical Analysis and Applications ◽

10.1016/0022-247x(91)90058-8 ◽

1991 ◽

Vol 154 (2) ◽

pp. 558-571 ◽

Cited By ~ 1

Author(s):

Angelo Bella ◽

Janusz J Charatonik ◽

Alfonso Villani

Keyword(s):

Continuous Functions ◽

Local Extrema

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Модель поведения гранулярного ВТСП во внешнем магнитном поле: температурная эволюция гистерезиса магнитосопротивления

Физика твердого тела ◽

10.21883/ftt.2020.07.49464.029 ◽

2020 ◽

Vol 62 (7) ◽

pp. 1008

Author(s):

С.В. Семенов ◽

Д.А. Балаев

Keyword(s):

High Temperature ◽

External Field ◽

High Temperature Superconductor ◽

Magnetic Moments ◽

Local Maximum ◽

Effective Field ◽

Temperature Range ◽

Flux Compression ◽

Local Extrema ◽

Extraordinary Form

Abstract A model for describing the magnetoresistance behavior in a granular high-temperature superconductor (HTS) that has been developed in the last decade explains a fairly extraordinary form of the hysteretic R ( H ) dependences at T = const and their hysteretic features, including the local maximum, the negative magnetoresistance region, and the local minimum. In the framework of this model, the effective field B _eff in the intergrain medium has been considered, which represents a superposition of the external field and the field induced by the magnetic moments of HTS grains. This field can be written in the form B _eff( H ) = H + 4πα M ( H ), where M ( H ) is the experimental field dependence of the magnetization and α is the parameter of crowding of the magnetic induction lines in the intergrain medium. Therefore, the magnetoresistance is a function of not simply an external field, but also the “internal” effective field R ( H ) = f ( B _eff( H )). The magnetoresistance of the granular YBa_2Cu_3O_7 – δ HTS has been investigated in a wide temperature range. The experimental hysteretic R ( H ) dependences obtained in the high -temperature range (77–90 K) are well explained using the developed model and the parameter α is 20–25. However, at a temperature of 4.2 K, no local extrema are observed, although the expression for B _eff( H ) predicts them and the parameter α somewhat increases (~30–35) at this temperature. An additional factor that must be taken into account in this model can be the redistribution of the microscopic current trajectories, which also affects the dissipation in the intergrain medium. At low temperatures under the strong magnetic flux compression (α ~ 30–35), the microscopic trajectories of the current I _ m can change and tunneling through the neighboring grain is preferred, but the angle between I _ m and B _eff will be noticeably smaller than 90°, although the external (and effective) field direction is perpendicular to the macroscopic current direction.

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Optimization of automatic control of the speed of rotation of a marine diesel engine

Automation of ship technical facilities ◽

10.31653/1819-3293-2021-1-27-03-21 ◽

2021 ◽

Vol 27 (1) ◽

pp. 03-21

Author(s):

Сергей Иванович Горб ◽

◽

Екатерина Яцык

Keyword(s):

Diesel Engine ◽

Rotational Speed ◽

Optimality Criterion ◽

Factor Space ◽

Established Method ◽

Tuning Parameters ◽

Local Extrema ◽

Marine Engines ◽

Marine Diesel ◽

Speed Stability

Annotation – The well-established method of tuning the speed governors (SG) of diesel engines during their operation under conditions of step disturbances, which are characteristic of diesel-generators, cannot be used for the main marine engines, the dynamic modes of which are associated, first of all, with heavy seas, because disturbances cannot change stepwise both along the channel for setting the rotational speed and along the load channel. In this regard, the practical need for the development of a method for tuning the SG of the main engines, which takes into account the peculiarities of their operation in heavy seas, has been determined. The study simulates the automatic speed control system (ASC) of the main marine engine HYUNDAI – MAN B&W 6G70ME-C9.2 of the large crude carrier "GOLDWAY" with the AutoChief 600 electronic SG. The minimum of instability of the controlled parameter was used as an optimality criterion, i.e. the amplitude of the oscillations of the rotational speed of the diesel engine shaft, with the most probable values of the amplitude and period of oscillations (rolling) of the disturbing effect. The study has established that changing the tuning parameters of the governor may lead to local extrema of the optimality criterion when using an electronic governor in the ACS in the factor space of disturbances on a diesel engine, which are typical for heavy seas. It means that the task, requiring finding local extrema using specialized methods, can be set when using an electronic governor in the ACS. However, a significant decrease in the instability of the rotational speed was achieved by carrying out a simple enumeration of the tuning parameters of the SG. It was also found that with a "heavy" propeller, the rotational speed stability can be increased by decreasing the proportional gain, as well as increasing the integrator time.

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