This study is based on the hypothesis that the bubbles-induced vortex flows could enhance the release of carbon dioxide (CO2) from a glass of effervescent wine. To provide tangible evidence, we conducted a series of experiments, the first of which aimed to correlate the filling height and the bubble-induced flow dynamics with the CO2 volume flux released from the vessel during a tasting. The results obtained through micro-weighing and PIV experiments showed a correlation between the filling height, the mixing flow dynamics, and the amount of CO2 released at the air/wine interface by several mechanisms (bubble burst, diffusion). In order to hide the role of bubbles, we proposed a simple experimental device that consisted in stirring the wine (supersaturated in dissolved gas) mechanically, while avoiding the phenomenon of nucleation. This mechanical stirring system allowed for controlling the intensity of convective movements of the liquid phase by varying the rotation frequency of a glass rod. The results of this experiment have provided irrefutable evidence of a close link between the stirring dynamics of a wine supersaturated in dissolved gases and the release of CO2 by a mass convection-diffusion phenomenon.
{"title":"Role of Mixing Dynamics on Mass Convection-Diffusion in Sparkling Wines: A Laboratory Study","authors":"F. Beaumont, F. Bogard, S. Murer, G. Polidori","doi":"10.3390/dynamics2040018","DOIUrl":"https://doi.org/10.3390/dynamics2040018","url":null,"abstract":"This study is based on the hypothesis that the bubbles-induced vortex flows could enhance the release of carbon dioxide (CO2) from a glass of effervescent wine. To provide tangible evidence, we conducted a series of experiments, the first of which aimed to correlate the filling height and the bubble-induced flow dynamics with the CO2 volume flux released from the vessel during a tasting. The results obtained through micro-weighing and PIV experiments showed a correlation between the filling height, the mixing flow dynamics, and the amount of CO2 released at the air/wine interface by several mechanisms (bubble burst, diffusion). In order to hide the role of bubbles, we proposed a simple experimental device that consisted in stirring the wine (supersaturated in dissolved gas) mechanically, while avoiding the phenomenon of nucleation. This mechanical stirring system allowed for controlling the intensity of convective movements of the liquid phase by varying the rotation frequency of a glass rod. The results of this experiment have provided irrefutable evidence of a close link between the stirring dynamics of a wine supersaturated in dissolved gases and the release of CO2 by a mass convection-diffusion phenomenon.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79302358","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}
We investigate in detail an apparently unnoticed consequence of special relativity. It consists in time dilation/contraction and frequency shift for emitted light affecting accelerated reference frames at astronomical distances from an inertial observer. The frequency shift is non-cosmological and non-Doppler in nature. We derive the main formulae and compare their predictions with the astronomical data available for Proxima Centauri. We found no correspondence with observations. Since the implications of the new time dilation/contraction and frequency shift are blatantly paradoxical, we do not expect to find one. By all indications, we are dealing with a genuine, and not a merely apparent, relativity paradox.
{"title":"Non-Cosmological, Non-Doppler Relativistic Frequency Shift over Astronomical Distances","authors":"G. D’Abramo","doi":"10.3390/dynamics2030017","DOIUrl":"https://doi.org/10.3390/dynamics2030017","url":null,"abstract":"We investigate in detail an apparently unnoticed consequence of special relativity. It consists in time dilation/contraction and frequency shift for emitted light affecting accelerated reference frames at astronomical distances from an inertial observer. The frequency shift is non-cosmological and non-Doppler in nature. We derive the main formulae and compare their predictions with the astronomical data available for Proxima Centauri. We found no correspondence with observations. Since the implications of the new time dilation/contraction and frequency shift are blatantly paradoxical, we do not expect to find one. By all indications, we are dealing with a genuine, and not a merely apparent, relativity paradox.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":"95 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89100171","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}
The setting is a system containing achiral reactants which form a chiral compound. In 1983, Kondepudi and Nelson proposed a model for the breaking of chiral symmetry. The present article reduces the conditions for bifurcation to a single condition which is shown to be both necessary and sufficient. A number of other papers on this topic also propose models for the breaking of chiral symmetry. These are shown to be essentially special cases of the model of Kondepudi and Nelson, with the same necessary and sufficient condition. The central question of this line of research is: in a racemic mixture of a chiral compound, could an excess of one enantiomer over the other develop on its own? Our answer is yes, if and only if a certain simple condition is satisfied. This answer should prove useful in further research, both theoretical and experimental, into the origin of life.
{"title":"A Necessary and Sufficient Condition in the Model of Kondepudi and Nelson for the Breaking of Chiral Symmetry","authors":"Jason Andrew Colwell","doi":"10.3390/dynamics2030016","DOIUrl":"https://doi.org/10.3390/dynamics2030016","url":null,"abstract":"The setting is a system containing achiral reactants which form a chiral compound. In 1983, Kondepudi and Nelson proposed a model for the breaking of chiral symmetry. The present article reduces the conditions for bifurcation to a single condition which is shown to be both necessary and sufficient. A number of other papers on this topic also propose models for the breaking of chiral symmetry. These are shown to be essentially special cases of the model of Kondepudi and Nelson, with the same necessary and sufficient condition. The central question of this line of research is: in a racemic mixture of a chiral compound, could an excess of one enantiomer over the other develop on its own? Our answer is yes, if and only if a certain simple condition is satisfied. This answer should prove useful in further research, both theoretical and experimental, into the origin of life.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":"84 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75906893","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}
We perform non-hydrodynamical 2.5D simulations to study the dynamics of material above accretion disk based on the disk radiation pressure acting on dust. We assume a super-accreting underlying disk with the accretion rate of 10 times the Eddington rate with central black hole mass ranging from 107 up to 109M⊙. Such high accretion rates are characteristic for extreme sources. We show that for high accretors the radiatively dust-driving mechanism based on the FRADO model always leads to a massive outflow from the disk surface, and the failed wind develops only at larger radii. The outflow rate strongly depends on the black hole mass, and an optically thick energy-driven solution can exceed the accretion rate for masses larger than 108M⊙ but momentum-driven outflow does not exceed the accretion rate even for super-Eddington accretion, therefore not violating the adopted stationarity of the disk. However, even in this case the outflow from the disk implies a strong mechanical feedback.
{"title":"The Wind Dynamics of Super-Eddington Sources in FRADO","authors":"M. Naddaf, B. Czerny, M. Zajaček","doi":"10.3390/dynamics2030015","DOIUrl":"https://doi.org/10.3390/dynamics2030015","url":null,"abstract":"We perform non-hydrodynamical 2.5D simulations to study the dynamics of material above accretion disk based on the disk radiation pressure acting on dust. We assume a super-accreting underlying disk with the accretion rate of 10 times the Eddington rate with central black hole mass ranging from 107 up to 109M⊙. Such high accretion rates are characteristic for extreme sources. We show that for high accretors the radiatively dust-driving mechanism based on the FRADO model always leads to a massive outflow from the disk surface, and the failed wind develops only at larger radii. The outflow rate strongly depends on the black hole mass, and an optically thick energy-driven solution can exceed the accretion rate for masses larger than 108M⊙ but momentum-driven outflow does not exceed the accretion rate even for super-Eddington accretion, therefore not violating the adopted stationarity of the disk. However, even in this case the outflow from the disk implies a strong mechanical feedback.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":"55 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90451560","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}
Enzymatic reactions can successfully replace complex chemical syntheses using milder reaction conditions and generating less waste. The developed model-based numerical analysis turned out to be a beneficial tool to determine the optimal operating policies of complex multienzymatic reactors. As proved, for such cases, the determination of a Fed-Batch Reactor (FBR) optimal operating policy results in a difficult multiobjective optimization problem. Exemplification is made for the bienzymatic reduction of D-fructose to mannitol by using MDH (mannitol dehydrogenase) and nicotinamide adenine dinucleotide (NADH) cofactor with the in situ continuous regeneration of NADH at the expense of formate degradation in the presence of FDH (formate dehydrogenase). For such a coupled system, the model-based engineering evaluations must account for multiple competing (opposable) optimization objectives. Among the multiple novelty elements: i) an optimally operated FBR with a tightly controlled variable feeding (of the time stepwise type) during the batch can lead to higher performance; ii) the optimally operated FBR reported better performance compared to an optimally single or cyclic BR, or to optimally serial batch-to-batch reactors (SeqBR), when considering a multiobjective optimization; iii) the concomitant variable feeding with substrate, enzymes, and cofactor during the FBR “time-arcs” is an option seldom approached in the literature but which is proved here, leading to consistent economic benefits.
{"title":"Multiobjective Optimization of a Fed-Batch Bienzymatic Reactor for Mannitol Production","authors":"G. Maria, Laura Renea, C. Maria","doi":"10.3390/dynamics2030014","DOIUrl":"https://doi.org/10.3390/dynamics2030014","url":null,"abstract":"Enzymatic reactions can successfully replace complex chemical syntheses using milder reaction conditions and generating less waste. The developed model-based numerical analysis turned out to be a beneficial tool to determine the optimal operating policies of complex multienzymatic reactors. As proved, for such cases, the determination of a Fed-Batch Reactor (FBR) optimal operating policy results in a difficult multiobjective optimization problem. Exemplification is made for the bienzymatic reduction of D-fructose to mannitol by using MDH (mannitol dehydrogenase) and nicotinamide adenine dinucleotide (NADH) cofactor with the in situ continuous regeneration of NADH at the expense of formate degradation in the presence of FDH (formate dehydrogenase). For such a coupled system, the model-based engineering evaluations must account for multiple competing (opposable) optimization objectives. Among the multiple novelty elements: i) an optimally operated FBR with a tightly controlled variable feeding (of the time stepwise type) during the batch can lead to higher performance; ii) the optimally operated FBR reported better performance compared to an optimally single or cyclic BR, or to optimally serial batch-to-batch reactors (SeqBR), when considering a multiobjective optimization; iii) the concomitant variable feeding with substrate, enzymes, and cofactor during the FBR “time-arcs” is an option seldom approached in the literature but which is proved here, leading to consistent economic benefits.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84096780","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}
We study the thermodynamic limit of very long walks on finite, connected, non-random graphs subject to possible random modifications and transportation capacity noise. As walks might represent the chains of interactions between system units, statistical mechanics of very long walks may be used to quantify the structural properties important for the dynamics of processes defined in networks. Networks open to random structural modifications are characterized by a Fermi–Dirac distribution of node’s fugacity in the framework of grand canonical ensemble of walks. The same distribution appears as the unique stationary solution of a discrete Fokker–Planck equation describing the time evolution of probability distribution of stochastic processes in networks. Nodes of inferior centrality are the most likely candidates for the future structural changes in the network.
{"title":"Statistical Mechanics of Long Walks in Dynamic Complex Networks: Statistical Arguments for Diversifying Selection","authors":"D. Volchenkov, C. Suh","doi":"10.3390/dynamics2030013","DOIUrl":"https://doi.org/10.3390/dynamics2030013","url":null,"abstract":"We study the thermodynamic limit of very long walks on finite, connected, non-random graphs subject to possible random modifications and transportation capacity noise. As walks might represent the chains of interactions between system units, statistical mechanics of very long walks may be used to quantify the structural properties important for the dynamics of processes defined in networks. Networks open to random structural modifications are characterized by a Fermi–Dirac distribution of node’s fugacity in the framework of grand canonical ensemble of walks. The same distribution appears as the unique stationary solution of a discrete Fokker–Planck equation describing the time evolution of probability distribution of stochastic processes in networks. Nodes of inferior centrality are the most likely candidates for the future structural changes in the network.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76164598","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}
S. Gebai, G. Cumunel, M. Hammoud, G. Foret, Emmanuel Roze, Elodie Hainque
The current work promotes the use of non-invasive devices for reducing involuntary tremor of human upper limb. It concentrates on building up an upper limb model used to reflect the measured tremor signal and is suitable for the design of a passive vibration controller. A dynamic model of the upper limb is excited by the measured electromyography signal scaled to reach the wrist joint angular displacement measured by an inertial measurement unit for a patient with postural tremor. A passive tuned-mass-damper (TMD) placed on the hand is designed as a stainless-steel beam with a length of 91 mm and a cross-sectional diameter of 0.79 mm, holding a mass of 14.13 g. The damping ratio and mass position of the TMD are optimized numerically. The fundamental frequency of the TMD is derived and validated experimentally through measurements for different mass positions, with a relative error of 0.65%. The modal damping ratio of the beam is identified experimentally as 0.14% and increases to 0.26–0.46% after adding the mass at different positions. The optimized three TMDs reduce 97.4% of the critical amplitude of the power spectral density at the wrist joint.
{"title":"Biomechanical Upper Limb Model for Postural Tremor Absorber Design","authors":"S. Gebai, G. Cumunel, M. Hammoud, G. Foret, Emmanuel Roze, Elodie Hainque","doi":"10.3390/dynamics2030012","DOIUrl":"https://doi.org/10.3390/dynamics2030012","url":null,"abstract":"The current work promotes the use of non-invasive devices for reducing involuntary tremor of human upper limb. It concentrates on building up an upper limb model used to reflect the measured tremor signal and is suitable for the design of a passive vibration controller. A dynamic model of the upper limb is excited by the measured electromyography signal scaled to reach the wrist joint angular displacement measured by an inertial measurement unit for a patient with postural tremor. A passive tuned-mass-damper (TMD) placed on the hand is designed as a stainless-steel beam with a length of 91 mm and a cross-sectional diameter of 0.79 mm, holding a mass of 14.13 g. The damping ratio and mass position of the TMD are optimized numerically. The fundamental frequency of the TMD is derived and validated experimentally through measurements for different mass positions, with a relative error of 0.65%. The modal damping ratio of the beam is identified experimentally as 0.14% and increases to 0.26–0.46% after adding the mass at different positions. The optimized three TMDs reduce 97.4% of the critical amplitude of the power spectral density at the wrist joint.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77035652","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}
L. Morozyuk, B. Kosoy, Viktoriia Sokolovska-Yefymenko, V. Ierin
The present study is an analysis of the processes in the components of the LPG (propane/butane) reliquefaction plant under the conditions of co-mingling in tanks when transporting by sea. For the analysis, the monitoring data of an LPG cargo operation have been used. An energy analysis of the mixture-based reliquefaction plant has been performed. The characteristics of the mixture in the tanks, the operating conditions of the reliquefaction plant, and the performance of the system have been considered. The method of equivalence has been applied for thermodynamic analysis. The result of the substitution of actual processes with equivalent ones allows for the accomplishment of the parameters control of each working fluid within the mixture as a pure working fluid. It is shown that the low-boiling component determines the operating parameters of the entire reliquefaction plant. The method of equivalence and visualization of the processes within the LPG as a mixture using the thermodynamic diagrams of pure working fluids is recommended to shorten the path to set up the appropriate reliquefaction plant management strategy. The energy analysis performed using the method of equivalent cycles has been validated with the existing reliquefaction plant characteristics. The inaccuracies are in the limit of 4%.
{"title":"Analysis of Mixing Processes of LPG Gases in Tanks When Transporting by Sea","authors":"L. Morozyuk, B. Kosoy, Viktoriia Sokolovska-Yefymenko, V. Ierin","doi":"10.3390/dynamics2030011","DOIUrl":"https://doi.org/10.3390/dynamics2030011","url":null,"abstract":"The present study is an analysis of the processes in the components of the LPG (propane/butane) reliquefaction plant under the conditions of co-mingling in tanks when transporting by sea. For the analysis, the monitoring data of an LPG cargo operation have been used. An energy analysis of the mixture-based reliquefaction plant has been performed. The characteristics of the mixture in the tanks, the operating conditions of the reliquefaction plant, and the performance of the system have been considered. The method of equivalence has been applied for thermodynamic analysis. The result of the substitution of actual processes with equivalent ones allows for the accomplishment of the parameters control of each working fluid within the mixture as a pure working fluid. It is shown that the low-boiling component determines the operating parameters of the entire reliquefaction plant. The method of equivalence and visualization of the processes within the LPG as a mixture using the thermodynamic diagrams of pure working fluids is recommended to shorten the path to set up the appropriate reliquefaction plant management strategy. The energy analysis performed using the method of equivalent cycles has been validated with the existing reliquefaction plant characteristics. The inaccuracies are in the limit of 4%.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":"172 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72423235","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}
We describe non-equilibrium quantum brain dynamics (QBD) for the breakdown of symmetry and propose the possibility of hologram memory based on QBD. We begin with the Lagrangian density of QBD with water rotational dipole fields and photon fields in 3+1 dimensions, and derive time evolution equations of coherent fields. We show a solution for super-radiance derived from the Lagrangian of QBD and propose a scenario of holography by the interference of two incident super-radiant waves. We investigate the time evolution of coherent dipole fields and photon fields in the presence of quantum fluctuations in numerical simulations. We find that the breakdown of the rotational symmetry of dipoles occurs in inverted populations for incoherent dipoles. We show how the waveforms of holograms with interference patterns evolve over time in an inverted population for incoherent dipoles. The optical information of hologram memory can be transferred to the whole brain during information processing. The integration of holography and QBD will provide us with a prospective approach in memory formation.
{"title":"Quantum Brain Dynamics and Holography","authors":"A. Nishiyama, S. Tanaka, J. Tuszynski","doi":"10.3390/dynamics2020010","DOIUrl":"https://doi.org/10.3390/dynamics2020010","url":null,"abstract":"We describe non-equilibrium quantum brain dynamics (QBD) for the breakdown of symmetry and propose the possibility of hologram memory based on QBD. We begin with the Lagrangian density of QBD with water rotational dipole fields and photon fields in 3+1 dimensions, and derive time evolution equations of coherent fields. We show a solution for super-radiance derived from the Lagrangian of QBD and propose a scenario of holography by the interference of two incident super-radiant waves. We investigate the time evolution of coherent dipole fields and photon fields in the presence of quantum fluctuations in numerical simulations. We find that the breakdown of the rotational symmetry of dipoles occurs in inverted populations for incoherent dipoles. We show how the waveforms of holograms with interference patterns evolve over time in an inverted population for incoherent dipoles. The optical information of hologram memory can be transferred to the whole brain during information processing. The integration of holography and QBD will provide us with a prospective approach in memory formation.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81603138","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}
The paper announces a family of exact solutions to Navier–Stokes equations describing gradient inhomogeneous unidirectional fluid motions (nonuniform Poiseuille flows). The structure of the fluid motion equations is such that the incompressibility equation enables us to establish the velocity defect law for nonuniform Poiseuille flow. In this case, the velocity field is dependent on two coordinates and time, and it is an arbitrary-degree polynomial relative to the horizontal (longitudinal) coordinate. The polynomial coefficients depend on the vertical (transverse) coordinate and time. The exact solution under consideration was built using the method of indefinite coefficients and the use of such algebraic operations was for addition and multiplication. As a result, to determine the polynomial coefficients, we derived a system of simplest homogeneous and inhomogeneous parabolic partial equations. The order of integration of the resulting system of equations was recurrent. For a special case of steady flows of a viscous fluid, these equations are ordinary differential equations. The article presents an algorithm for their integration. In this case, all components of the velocity field, vorticity vector, and shear stress field are polynomial functions. In addition, it has been noted that even without taking into account the thermohaline convection (creeping current) all these fields have a rather complex structure.
{"title":"Exact Solutions to Navier–Stokes Equations Describing a Gradient Nonuniform Unidirectional Vertical Vortex Fluid Flow","authors":"N. Burmasheva, E. Prosviryakov","doi":"10.3390/dynamics2020009","DOIUrl":"https://doi.org/10.3390/dynamics2020009","url":null,"abstract":"The paper announces a family of exact solutions to Navier–Stokes equations describing gradient inhomogeneous unidirectional fluid motions (nonuniform Poiseuille flows). The structure of the fluid motion equations is such that the incompressibility equation enables us to establish the velocity defect law for nonuniform Poiseuille flow. In this case, the velocity field is dependent on two coordinates and time, and it is an arbitrary-degree polynomial relative to the horizontal (longitudinal) coordinate. The polynomial coefficients depend on the vertical (transverse) coordinate and time. The exact solution under consideration was built using the method of indefinite coefficients and the use of such algebraic operations was for addition and multiplication. As a result, to determine the polynomial coefficients, we derived a system of simplest homogeneous and inhomogeneous parabolic partial equations. The order of integration of the resulting system of equations was recurrent. For a special case of steady flows of a viscous fluid, these equations are ordinary differential equations. The article presents an algorithm for their integration. In this case, all components of the velocity field, vorticity vector, and shear stress field are polynomial functions. In addition, it has been noted that even without taking into account the thermohaline convection (creeping current) all these fields have a rather complex structure.","PeriodicalId":80276,"journal":{"name":"Dynamics (Pembroke, Ont.)","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88770616","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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