Pub Date : 2024-08-28DOI: 10.1134/s1995080224602595
I. G. Goryacheva, A. A. Yakovenko
Abstract
The combined effect of the asperities density and their height distribution in contact of the rough rigid and smooth elastic half-spaces is investigated, taking into account the mutual influence of contact spots and statistical nature of the height distribution of asperities. The normal and exponential types of the height distribution of asperities with various densities and the dispersions of their height distribution are used in calculations of the contact characteristics at macroscale (the approach of contacting bodies and the relative contact area under given normal pressure) and the microscale (real contact pressure distributions). The obtained results are compared with ones calculated from the simplified models neglecting the mutual influence of individual contact spots. It is shown that neglecting the mutual influence of asperities in contact, which is made in many models of the discrete contact, can lead to significant errors in determining the contact characteristics on both the macro- and microscales. Based on the asymptotic analysis the analytical expressions for the approach of the contacting bodies and the relative contact area were derived and used for analysis of the microgeometry parameters effects on the rigid rough half-space penetration into the elastic half-space at high nominal pressures.
{"title":"The Asperities Density and Height Distribution Combined Effect on Rough Elastic Bodies Contact Characteristics","authors":"I. G. Goryacheva, A. A. Yakovenko","doi":"10.1134/s1995080224602595","DOIUrl":"https://doi.org/10.1134/s1995080224602595","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The combined effect of the asperities density and their height distribution in contact of the rough rigid and smooth elastic half-spaces is investigated, taking into account the mutual influence of contact spots and statistical nature of the height distribution of asperities. The normal and exponential types of the height distribution of asperities with various densities and the dispersions of their height distribution are used in calculations of the contact characteristics at macroscale (the approach of contacting bodies and the relative contact area under given normal pressure) and the microscale (real contact pressure distributions). The obtained results are compared with ones calculated from the simplified models neglecting the mutual influence of individual contact spots. It is shown that neglecting the mutual influence of asperities in contact, which is made in many models of the discrete contact, can lead to significant errors in determining the contact characteristics on both the macro- and microscales. Based on the asymptotic analysis the analytical expressions for the approach of the contacting bodies and the relative contact area were derived and used for analysis of the microgeometry parameters effects on the rigid rough half-space penetration into the elastic half-space at high nominal pressures.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-28DOI: 10.1134/s1995080224602145
A. A. Gubaidullin, O. Yu. Boldyreva, D. N. Dudko
Abstract
The transmission and reflection of a pulse wave in a porous medium with a layer of a fractured porous medium under normal and oblique incidence is numerically investigated. The study was carried out using a two-velocity model of a porous medium and a three-velocity model of a fractured porous medium. ‘‘Opened pores’’ condition was used on the ‘‘porous medium–fractured porous medium’’ interface. The problem is considered in a two-dimensional formulation. The features of this wave process are revealed.
{"title":"Wave Interaction with Fractured Porous Layer in Porous Medium","authors":"A. A. Gubaidullin, O. Yu. Boldyreva, D. N. Dudko","doi":"10.1134/s1995080224602145","DOIUrl":"https://doi.org/10.1134/s1995080224602145","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The transmission and reflection of a pulse wave in a porous medium with a layer of a fractured porous medium under normal and oblique incidence is numerically investigated. The study was carried out using a two-velocity model of a porous medium and a three-velocity model of a fractured porous medium. ‘‘Opened pores’’ condition was used on the ‘‘porous medium–fractured porous medium’’ interface. The problem is considered in a two-dimensional formulation. The features of this wave process are revealed.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-28DOI: 10.1134/s1995080224602340
L. R. Shaidullin, S. A. Fadeev
Abstract
Resonant oscillations of gas in a tube with an end in the form of an inverted cone have been investigated. As the height of the inverted cone inserted into the tube increases, a decrease in the resonant frequency and amplitude of gas pressure oscillations is observed. The dispersion of the resonant frequency is due to the viscosity and thermal conductivity of the gas. It is found that tubes with an inverted cone-shaped end are less efficient resonators compared to uniform tubes with a flat closed end. The decrease in the amplitude of gas pressure oscillations is attributed to the increase in the near-wall losses due to the increase in the total sidewall extent.
{"title":"Effect of a Rigid Cone Inserted in a Tube on Resonant Gas Oscillations","authors":"L. R. Shaidullin, S. A. Fadeev","doi":"10.1134/s1995080224602340","DOIUrl":"https://doi.org/10.1134/s1995080224602340","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Resonant oscillations of gas in a tube with an end in the form of an inverted cone have been investigated. As the height of the inverted cone inserted into the tube increases, a decrease in the resonant frequency and amplitude of gas pressure oscillations is observed. The dispersion of the resonant frequency is due to the viscosity and thermal conductivity of the gas. It is found that tubes with an inverted cone-shaped end are less efficient resonators compared to uniform tubes with a flat closed end. The decrease in the amplitude of gas pressure oscillations is attributed to the increase in the near-wall losses due to the increase in the total sidewall extent.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-28DOI: 10.1134/s1995080224602261
D. Yu. Legostaev, S. P. Rodionov
Abstract
We consider two-dimensional single-phase fluid flow of an incompressible fluid in a fractured porous medium, which is located inside a square computational domain. The fractures had a random position and orientation, and the fracture length distribution follows a power law. Fracture networks are simulated using the discrete-fracture model. Calculations were performed for fracture network realizations created by multiple random generations. Fluid flows between opposite boundaries of the computational domain (line source and sink) and between vertical wells (point source and sink) are considered. The influence of the type of source and sink on the percolation probability is determined. The dependence of the flow rate between production and injection wells on the fracture network structure was investigated. The flow between the opposite boundaries of the computational domain is considered. For this case, the numerical dependence of the equivalent permeability of the fractured porous medium on the percolation parameter was approximated by an analytical piecewise function. This approximation was used to estimate fluid flow rates between vertical wells.
{"title":"Numerical Investigation of the Structure of Fracture Network Impact on Interwell Conductivity","authors":"D. Yu. Legostaev, S. P. Rodionov","doi":"10.1134/s1995080224602261","DOIUrl":"https://doi.org/10.1134/s1995080224602261","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We consider two-dimensional single-phase fluid flow of an incompressible fluid in a fractured porous medium, which is located inside a square computational domain. The fractures had a random position and orientation, and the fracture length distribution follows a power law. Fracture networks are simulated using the discrete-fracture model. Calculations were performed for fracture network realizations created by multiple random generations. Fluid flows between opposite boundaries of the computational domain (line source and sink) and between vertical wells (point source and sink) are considered. The influence of the type of source and sink on the percolation probability is determined. The dependence of the flow rate between production and injection wells on the fracture network structure was investigated. The flow between the opposite boundaries of the computational domain is considered. For this case, the numerical dependence of the equivalent permeability of the fractured porous medium on the percolation parameter was approximated by an analytical piecewise function. This approximation was used to estimate fluid flow rates between vertical wells.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-28DOI: 10.1134/s1995080224602480
E. V. Murashkin, Y. N. Radayev
Abstract
The present paper deals with the triple weights pseudotensor formulation of multivariant thermoelasticity for acentric isotropic micropolar solids. The fundamental concepts of pseudoinvariant volume/area/arc elements of odd integer weights in three-dimensional spaces are discussed. The developed theory of acentric isotropic micropolar thermoelasticity is formulated in terms of contravariant pseudovector of spinor displacements having positive odd algebraic weight and covariant absolute vector of translational displacements. Three energetic forms (H), (E), and (A) of thermoelasticity potential are proposed. The latter is derived from the irreducible system of algebraic invarinats/pseudoinvariants being actually their linear span with coefficients thus allowing us to introduce the conventional thermoelasticity moduli (shear modulus of elasticity, Poisson’s ratio, characteristic nano/microlength, etc.). For others energetic forms thermoelasticity anisotropic micropolar (E) moduli are determined via (A) moduli and then (H) moduli are found in terms of (A) moduli. The triple weights formulation of multivariant constitutive equations for acentric isotropic thermoelastic solid are obtained and analyzed. A comparison of proposed multivariant constitutive equations elucidates the absolute invariance of Poisson’s ratio, i.e., it insensibility to mirror reflections and prohibition of assigning any algebraic weight to this constitutive scalar.
{"title":"Theory of Poisson’s Ratio for a Thermoelastic Micropolar Acentric Isotropic Solid","authors":"E. V. Murashkin, Y. N. Radayev","doi":"10.1134/s1995080224602480","DOIUrl":"https://doi.org/10.1134/s1995080224602480","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The present paper deals with the triple weights pseudotensor formulation of multivariant thermoelasticity for acentric isotropic micropolar solids. The fundamental concepts of pseudoinvariant volume/area/arc elements of odd integer weights in three-dimensional spaces are discussed. The developed theory of acentric isotropic micropolar thermoelasticity is formulated in terms of contravariant pseudovector of spinor displacements having positive odd algebraic weight and covariant absolute vector of translational displacements. Three energetic forms (H), (E), and (A) of thermoelasticity potential are proposed. The latter is derived from the irreducible system of algebraic invarinats/pseudoinvariants being actually their linear span with coefficients thus allowing us to introduce the conventional thermoelasticity moduli (shear modulus of elasticity, Poisson’s ratio, characteristic nano/microlength, etc.). For others energetic forms thermoelasticity anisotropic micropolar (E) moduli are determined via (A) moduli and then (H) moduli are found in terms of (A) moduli. The triple weights formulation of multivariant constitutive equations for acentric isotropic thermoelastic solid are obtained and analyzed. A comparison of proposed multivariant constitutive equations elucidates the absolute invariance of Poisson’s ratio, i.e., it insensibility to mirror reflections and prohibition of assigning any algebraic weight to this constitutive scalar.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-28DOI: 10.1134/s1995080224602297
N. G. Musakaev, S. L. Borodin, D. S. Belskikh
Abstract
A mathematical model of non-isothermal filtration of methane, carbon dioxide and water is constructed based on the methods and equations of multiphase media mechanics considering the replacement of methane in the gas hydrate with carbon dioxide. The equations of the mathematical model and the methodology for their numerical solution are presented. The numerical solutions for one-dimensional plane-parallel approximation are constructed for the problem of injecting carbon dioxide into a reservoir initially saturated with methane and its hydrate. Those solutions describe the distributions in the reservoir of pressure, temperature, mass concentrations of gas phase components and saturations of methane and carbon dioxide hydrates.
{"title":"Methodology for Calculating the Parameters of Non-isothermal Filtration Considering the CO $${}_{mathbf{2}}$$ –CH $${}_{mathbf{4}}$$ Replacement in Methane Hydrate","authors":"N. G. Musakaev, S. L. Borodin, D. S. Belskikh","doi":"10.1134/s1995080224602297","DOIUrl":"https://doi.org/10.1134/s1995080224602297","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A mathematical model of non-isothermal filtration of methane, carbon dioxide and water is constructed based on the methods and equations of multiphase media mechanics considering the replacement of methane in the gas hydrate with carbon dioxide. The equations of the mathematical model and the methodology for their numerical solution are presented. The numerical solutions for one-dimensional plane-parallel approximation are constructed for the problem of injecting carbon dioxide into a reservoir initially saturated with methane and its hydrate. Those solutions describe the distributions in the reservoir of pressure, temperature, mass concentrations of gas phase components and saturations of methane and carbon dioxide hydrates.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-28DOI: 10.1134/s1995080224602212
M. A. Ilgamov
Abstract
Oscillations and waves in a nanofilm in contact with a gaseous medium are considered. It is assumed that the excitation frequencies are in the ultrasonic range. The simplest model is constructed, based on Timoshenko theory of plate bending and on the first approximation of the reaction from the gaseous medium. This takes into account the surface effect caused by the difference in elastic characteristics in the near-surface layer and in the main volume of the material. The derived relations within the Timoshenko model are simplified, which makes it possible to obtain visible results. The contribution of surface effects and reactions from the gaseous medium is assessed. Linear dynamics of a semi-infinite film is studied.
{"title":"Oscillations of Nanofilms in a Fluid","authors":"M. A. Ilgamov","doi":"10.1134/s1995080224602212","DOIUrl":"https://doi.org/10.1134/s1995080224602212","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Oscillations and waves in a nanofilm in contact with a gaseous medium are considered. It is assumed that the excitation frequencies are in the ultrasonic range. The simplest model is constructed, based on Timoshenko theory of plate bending and on the first approximation of the reaction from the gaseous medium. This takes into account the surface effect caused by the difference in elastic characteristics in the near-surface layer and in the main volume of the material. The derived relations within the Timoshenko model are simplified, which makes it possible to obtain visible results. The contribution of surface effects and reactions from the gaseous medium is assessed. Linear dynamics of a semi-infinite film is studied.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-28DOI: 10.1134/s1995080224602315
A. D. Nizamova, V. N. Kireev, S. F. Urmancheev
Abstract
Issues related to transient regimes of fluid flow in channels with different cross sections are a priority when solving problems of hydrodynamics. Currently, research related to the influence of heat exchange on the stability of fluid flow in processes in which the change in viscosity with temperature cannot be neglected has become particularly relevant. This article examines some features of the loss of stability of a laminar fluid flow with an exponential dependence of viscosity on temperature in an annular channel with a given temperature regime on its walls. For this purpose, the generalized Orr–Sommerfeld equation was derived, which was eventually written in relation to the stream function. A numerical study of the corresponding boundary value problem was carried out using the spectral method based on Chebyshev polynomials. It was shown that taking into account the effect of temperature on the viscosity of the liquid, which implies its non-uniform distribution over the cross section of the channel, leads to a decrease in the critical Reynolds number, which is consistent with the results of previous studies. In particular, as previously noted, for a narrow channel and a small thermoviscosity parameter, the spectrum of eigenvalues is identical to the spectrum for an isothermal flow in a flat channel. A change in the relative channel width and an increase in the thermoviscosity parameter leads to a significant restructuring of the structure of the eigenvalue spectra of the generalized Orr–Sommerfeld equation. As a result of the studies carried out in the presented work, the dependencies of the critical Reynolds number on the exponential factor or, in other words, the thermoviscosity parameter, which characterizes the intensity of the change in viscosity with increasing temperature, and on the parameter determining the ratio of the width of the annular channel to the radius of the inner cylindrical surface were constructed. It has been established that with increasing parameter of the relative channel width, the value of the critical Reynolds number changes non-monotonically, and its minimum value depends on the specific liquid. The latter circumstance can serve as a theoretical justification for carrying out optimization calculations when modeling technological processes. The dependence of the critical Reynolds number on the thermoviscosity parameter has a form close to a decreasing exponential function for all sizes of annular channels.
{"title":"The Influence of the Annular Gap Thickness on the Critical Reynolds Number During the Flow of Thermoviscous Liquids","authors":"A. D. Nizamova, V. N. Kireev, S. F. Urmancheev","doi":"10.1134/s1995080224602315","DOIUrl":"https://doi.org/10.1134/s1995080224602315","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Issues related to transient regimes of fluid flow in channels with different cross sections are a priority when solving problems of hydrodynamics. Currently, research related to the influence of heat exchange on the stability of fluid flow in processes in which the change in viscosity with temperature cannot be neglected has become particularly relevant. This article examines some features of the loss of stability of a laminar fluid flow with an exponential dependence of viscosity on temperature in an annular channel with a given temperature regime on its walls. For this purpose, the generalized Orr–Sommerfeld equation was derived, which was eventually written in relation to the stream function. A numerical study of the corresponding boundary value problem was carried out using the spectral method based on Chebyshev polynomials. It was shown that taking into account the effect of temperature on the viscosity of the liquid, which implies its non-uniform distribution over the cross section of the channel, leads to a decrease in the critical Reynolds number, which is consistent with the results of previous studies. In particular, as previously noted, for a narrow channel and a small thermoviscosity parameter, the spectrum of eigenvalues is identical to the spectrum for an isothermal flow in a flat channel. A change in the relative channel width and an increase in the thermoviscosity parameter leads to a significant restructuring of the structure of the eigenvalue spectra of the generalized Orr–Sommerfeld equation. As a result of the studies carried out in the presented work, the dependencies of the critical Reynolds number on the exponential factor or, in other words, the thermoviscosity parameter, which characterizes the intensity of the change in viscosity with increasing temperature, and on the parameter determining the ratio of the width of the annular channel to the radius of the inner cylindrical surface were constructed. It has been established that with increasing parameter of the relative channel width, the value of the critical Reynolds number changes non-monotonically, and its minimum value depends on the specific liquid. The latter circumstance can serve as a theoretical justification for carrying out optimization calculations when modeling technological processes. The dependence of the critical Reynolds number on the thermoviscosity parameter has a form close to a decreasing exponential function for all sizes of annular channels.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-28DOI: 10.1134/s1995080224602194
T. S. Guseva
Abstract
The jet impact process during the nonspherical bubble collapse near a local bump on a solid wall has been studied in detail using the CIP-CUP method to solve the Euler equations. Three scenarios were considered, the first of which corresponds to a nearly plane wall compared to the bubble size, and the other two correspond to the bubble-sized local bump. In all cases, the distance from the impact location to the wall and the jet tip diameter are close, the jet velocity is about 100 m/s. The main difference between the considered scenarios is the initial zone of contact of the jet with the opposite bubble side. Namely, it is a single point in the first case, and in the other two cases it is a bowl-shaped area and an annular area with the formation of a tip bubble. The latter two scenarios have been found to result in significantly higher wall pressure, as well as larger loaded area and load duration.
{"title":"Jet Impact During Bubble Collapse Near a Local Bump on a Solid Wall","authors":"T. S. Guseva","doi":"10.1134/s1995080224602194","DOIUrl":"https://doi.org/10.1134/s1995080224602194","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The jet impact process during the nonspherical bubble collapse near a local bump on a solid wall has been studied in detail using the CIP-CUP method to solve the Euler equations. Three scenarios were considered, the first of which corresponds to a nearly plane wall compared to the bubble size, and the other two correspond to the bubble-sized local bump. In all cases, the distance from the impact location to the wall and the jet tip diameter are close, the jet velocity is about 100 m/s. The main difference between the considered scenarios is the initial zone of contact of the jet with the opposite bubble side. Namely, it is a single point in the first case, and in the other two cases it is a bowl-shaped area and an annular area with the formation of a tip bubble. The latter two scenarios have been found to result in significantly higher wall pressure, as well as larger loaded area and load duration.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-28DOI: 10.1134/s1995080224602546
V. I. Zubov
Abstract
The work analyzes one optimal control problem that arises in nanoelectronics. It is shown that the use of an approximate expression for the variation of electron density leads to an incorrect value for the gradient of the cost functional. It is demonstrated that the formulated optimal control problem is incorrect. For the correct formulation of the optimal control problem, other cost functions should be used.
{"title":"On One Optimization Problem in Nanoelectronics","authors":"V. I. Zubov","doi":"10.1134/s1995080224602546","DOIUrl":"https://doi.org/10.1134/s1995080224602546","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The work analyzes one optimal control problem that arises in nanoelectronics. It is shown that the use of an approximate expression for the variation of electron density leads to an incorrect value for the gradient of the cost functional. It is demonstrated that the formulated optimal control problem is incorrect. For the correct formulation of the optimal control problem, other cost functions should be used.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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