Stationary solutions to a hybrid viscous hydrodynamic model with classical boundaries
In this paper we present a quantum-classical hybrid model based on the hydrodynamic equations in steady state form. The approach presented here, which has already been proposed in previous works, consists in considering an intrinsically hybrid version of the Bohm potential, which acts only in the re...
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AIMS Press
2024-09-01
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| Series: | Mathematics in Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mine.2024027 |
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| author | Federica Di Michele Bruno Rubino Rosella Sampalmieri Kateryna Stiepanova |
| author_facet | Federica Di Michele Bruno Rubino Rosella Sampalmieri Kateryna Stiepanova |
| author_sort | Federica Di Michele |
| collection | DOAJ |
| description | In this paper we present a quantum-classical hybrid model based on the hydrodynamic equations in steady state form. The approach presented here, which has already been proposed in previous works, consists in considering an intrinsically hybrid version of the Bohm potential, which acts only in the region of the domain where quantum effects play an important role, while it disappears where the quantum contribution is essentially negligible and the operation of the device can be well described by using a classical model. Compared to previous results from the same line of research, here we assume that the device at the boundaries of the domain behaves classically, while quantum effects are localised in the central part of it. This is the case of greatest scientific interest, since, in real devices, quantum effects are generally localized in a small area within the device itself. The well posedness of the problem is ensured by adding a viscous term necessary for the convergence of the hybrid limit to an appropriate weak solution. Some numerical tests are also performed for different values of the viscous coefficient, in order to evaluate the effects of the viscosity, especially on the boundaries of the device. |
| format | Article |
| id | doaj-art-fc1fb444cd054916b5ed00c37de157c9 |
| institution | Kabale University |
| issn | 2640-3501 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj-art-fc1fb444cd054916b5ed00c37de157c92025-01-24T01:08:21ZengAIMS PressMathematics in Engineering2640-35012024-09-016570572510.3934/mine.2024027Stationary solutions to a hybrid viscous hydrodynamic model with classical boundariesFederica Di Michele0Bruno Rubino1Rosella Sampalmieri2Kateryna Stiepanova3Istituto Nazionale di Geofisica e Vulcanologia, via Alfonso Corti 12, Milan, ItalyDepartment of Information Engineering, Computer Science and Mathematics, University of L'Aquila via Vetoio, L'Aquila, ItalyDepartment of Information Engineering, Computer Science and Mathematics, University of L'Aquila via Vetoio, L'Aquila, ItalyV. N. Karazin Kharkiv National University, Kharkiv, UkraineIn this paper we present a quantum-classical hybrid model based on the hydrodynamic equations in steady state form. The approach presented here, which has already been proposed in previous works, consists in considering an intrinsically hybrid version of the Bohm potential, which acts only in the region of the domain where quantum effects play an important role, while it disappears where the quantum contribution is essentially negligible and the operation of the device can be well described by using a classical model. Compared to previous results from the same line of research, here we assume that the device at the boundaries of the domain behaves classically, while quantum effects are localised in the central part of it. This is the case of greatest scientific interest, since, in real devices, quantum effects are generally localized in a small area within the device itself. The well posedness of the problem is ensured by adding a viscous term necessary for the convergence of the hybrid limit to an appropriate weak solution. Some numerical tests are also performed for different values of the viscous coefficient, in order to evaluate the effects of the viscosity, especially on the boundaries of the device.https://www.aimspress.com/article/doi/10.3934/mine.2024027hybrid modelquantum modelshydrodynamicviscous termsquantum devices |
| spellingShingle | Federica Di Michele Bruno Rubino Rosella Sampalmieri Kateryna Stiepanova Stationary solutions to a hybrid viscous hydrodynamic model with classical boundaries Mathematics in Engineering hybrid model quantum models hydrodynamic viscous terms quantum devices |
| title | Stationary solutions to a hybrid viscous hydrodynamic model with classical boundaries |
| title_full | Stationary solutions to a hybrid viscous hydrodynamic model with classical boundaries |
| title_fullStr | Stationary solutions to a hybrid viscous hydrodynamic model with classical boundaries |
| title_full_unstemmed | Stationary solutions to a hybrid viscous hydrodynamic model with classical boundaries |
| title_short | Stationary solutions to a hybrid viscous hydrodynamic model with classical boundaries |
| title_sort | stationary solutions to a hybrid viscous hydrodynamic model with classical boundaries |
| topic | hybrid model quantum models hydrodynamic viscous terms quantum devices |
| url | https://www.aimspress.com/article/doi/10.3934/mine.2024027 |
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