Approximations of attainability sets and of integral funnels of differential inclusions

Ушаков, В. Н.; Матвийчук, Александр Ростиславович; Ушаков, А. В.

doi:10.20537/vm110403

Cited by 13 publications

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“…The processes that accompany the breakdown in liquids are considered in detail in [6]. According to [6], four mechanisms of discharge initiation (ignition) can be recognized: bubble, microexplosive, ionization, and electrothermal.…”

Section: Characteristic Features Of the Initiation And Propagation Ofmentioning

confidence: 99%

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Synthesis and modification of molecular nanoparticles in electrical discharge plasma in liquids

et al. 2015

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A review of studies on the synthesis and modification of nanosized particles by electrical discharges in liquid media is presented. The modern understanding of the mechanisms of initiation and features of discharge evolution in liquids are analyzed. By using of the spectroscopic diagnostics, parameters of the discharge plasma in liquids (water, ethanol) are determined. It is shown that the pulsed electrical discharge between electrodes immersed in a nonconducting or weakly conducting liquid, provides a simple and effective method for the synthesis of nanoparticles of different compositions with the average size ranging from 5 to 50 nm. The morphology, phase structure, and composition of the particles formed are defined by the discharge mode and composition of the liquid medium in which the discharge is produced. The conditions for the synthesis of nanosized metal oxides, carbides, and silicides (for example, copper and zinc oxides, titanium and tungsten carbides, gadolinium silicides) were found. Zinc oxide nanoparticles were produced in pulsed electrical discharge plasma in distilled water, and the possibility of their doping with nitrogen atoms during synthesis was demonstrated. Experimental results on the modification of tungsten and copper powders by spark discharge in ethanol are discussed. The possibility to synthesize copper chalcogenides CuInSe 2 by electrical discharge treatment of a mixture of copper, indium, and selenium powders was demonstrated.wide range of nanomaterials (metals and intermetallics, nitrides, metal oxides and carbides, composite materials).Electrical discharge in liquids is accompanied by a complex of physical and chemical phenomena, including shock wave generation, cavitation processes, formation of a vapor-gas bubble and its pulsation, ionization and decomposition of liquid molecules in the plasma channel and around it, intense UV and sound radiation, and pulsed electric and magnetic fields. These processes generate free radicals, singlet oxygen, ozone, and hydrogen peroxide. Furthermore, electrode erosion results in release into the liquid of atoms and ions of the electrode materials. These excited or ionized particles take part in diverse physicochemical processes that affect the liquid and objects placed in it. A great variety of compounds, including metastable ones, can form in the plasma channel. Nanoparticles are formed by chemical reactions of atoms and ions released from electrodes with the decomposition products of the surrounding liquid.

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Section: Characteristic Features Of the Initiation And Propagation Ofmentioning

confidence: 99%

“…The discharge propagation stage, too, can occur by different mechanisms [6,7]: fast, slow, and electrothermal.…”

Section: Characteristic Features Of the Initiation And Propagation Ofmentioning

confidence: 99%

Synthesis and modification of molecular nanoparticles in electrical discharge plasma in liquids

et al. 2015

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“…Another well-known method is of Euler type (the "pixel method") that is based on grid approximation of sets (see, e.g. [16,19,21,26,34,38]). However, the algorithms derived through the use of this approach usually require a lot of computational effort, and moreover, they render highly inaccurate results at the boundaries.…”

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confidence: 99%

The method of uniform monotonous approximation of the reachable set border for a controllable system

et al. 2015

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A numerical method of a two-dimensional non-linear controllable system reachable set boundary approximation is considered. In order to approximate the boundary right piecewise linear closed contours are used: a set of broken lines on a plane. As an application of the proposed technique a method of finding linear functional global extremum is described, including its use for systems with arbitrary dimensionality.

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Time Optimal Control Problem for the Waste Water Biotreatment Model

2014

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Approximations of attainability sets and of integral funnels of differential inclusions

Cited by 13 publications

References 0 publications

Synthesis and modification of molecular nanoparticles in electrical discharge plasma in liquids

Synthesis and modification of molecular nanoparticles in electrical discharge plasma in liquids

The method of uniform monotonous approximation of the reachable set border for a controllable system

Time Optimal Control Problem for the Waste Water Biotreatment Model

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