Alkis Grecos - Academia.edu (original) (raw)
Papers by Alkis Grecos
International Journal for Numerical Methods in Fluids, 2009
A numerical study of tangential layers in steady-state magnetohydrodynamic rotating flows is pres... more A numerical study of tangential layers in steady-state magnetohydrodynamic rotating flows is presented using CFD to solve the inductionless governing equations. The analysis considers two basic flow configurations. In the first, a fluid is enclosed in a cylinder with electrically perfect conducting walls and the flow is driven by a small rotating, conducting disk. In the second, a flow is considered in a spherical shell with an inner rotating sphere. The fluid in both cases is subjected to an external axial uniform magnetic field. The results show that these flows exhibit two different types of flow cores separated from each other by a tangential layer parallel to the axis of rotation. The inner core follows a solid-body rotation while the outer is quasistagnant. A counter-rotating jet is developed in the tangential layer between the cores. The characteristics of the tangential layer and the properties of the meridional motion are determined for a wide range of Hartmann numbers. Distributions of angular velocity of circumferential flow and electric potential are obtained and the results are compared with those of analytic methods.
Advances in Chemical Physics, 2000
Physica, 1971
ABSTRACT Les méthodes de la mécanique statistique de non équilibre développées par l'écol... more ABSTRACT Les méthodes de la mécanique statistique de non équilibre développées par l'école de Bruxelles (et spécialement l'introduction de l'opérateur de collision Ψ(z)) permettant d'étendre la théorie des systèmes dynamiques intégrables tant en mécanique classique que quantique. En particulier une formulation nouvelle du théorème fondamental de Poincaré sur la non existence d'invariants est présentée qui ne fait pas appel à des développements en série en la constante de couplage mais est basée directement sur les propriétés spectrales de la résolvante. La distinction entre systèmes “dissipatifs” et non-dissipatifs” introduite par Prigogine et al. est confirmée et précisée.
Physics Letters A
The behaviour of the constants of motion with respect to the collision operator is discussed in t... more The behaviour of the constants of motion with respect to the collision operator is discussed in the ease of a finite quantum system.
Physica, 1972
ABSTRACT Les phénomènes irréversibles au sein d'un système simple caractérisé par un hami... more ABSTRACT Les phénomènes irréversibles au sein d'un système simple caractérisé par un hamiltonien ayant un spectre continu sont étudiés à l'aide des méthodes de la mécanique statistique de non-équilibre. En particulier, nous montrons le lien entre la possibilité d'une description cinétique et la nature des invariants du système. Cette reformulation du problème ergodique permet d'aborder cette question des systèmes à nombre infini de degrés liberté que nous allons étudier dans une publication ultérieure.
Lecture Notes in Physics, 2000
Without Abstract
A multivariate Fokker-Planck-type ki netic equ ation modeling a test -panicle weakly interacting ... more A multivariate Fokker-Planck-type ki netic equ ation modeling a test -panicle weakly interacting with an electrostatic plasma. in the presence of a magnetic field B . is analytically solved in an Ornstein -Uhlenbeck -type approximation. A new set of analytic expressions are obtained for variable moments and panicle density as a function of time. The process is diffusive.
Physica A: Statistical Mechanics and its Applications, 1998
Generalised Wigner and Weyl transformations of quantum operators are defined and their properties... more Generalised Wigner and Weyl transformations of quantum operators are defined and their properties, as well as those of the algebraic structure induced on the phase-space are studied. Using such transformations, quantum linear evolution equations are given a phase-space representation. In particular this is done for the general kinetic equation of the Lindblad type. The resulting expressions are better suited for the passage to the classical limit and for a general comparison of classical and quantum systems. In this context a preliminary discussion of a number of problems of kinetic theory of open systems is given, whereas explicit applications are made in the next paper of the series. * Association Euratom, Etat Belge.
NUMERICAL PROCEDURE: The governing equations together with the corresponding boundary conditions ... more NUMERICAL PROCEDURE: The governing equations together with the corresponding boundary conditions are solved numerically, employing a finite-volume method. The Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) of Patankar (3) is used to couple the momentum and continuity equations in a uniform staggered grid in the horizontal and vertical directions. The momentum equations for U and V, the energy equation and the magnetic induction equations (for all cases studied, except the Low-Rm) are solved using the QUICK scheme of Leonard (4) in the modified form of Hayase et al. (5) in order to minimize numerical diffusion. In all calculations presented here, under-relaxation factors with values of 0.5, 0.5, 0.6, 0.6, 0.6 and 0.3 were applied to U, V, Θ, Bx, By and P, respectively. The iterative procedure is initiated with an arbitrary velocity field followed by the solution of the energy and magnetic induction equations and is continued until convergence is achieved. Before the fina...
Following Langevin, the system of equations describing the motion of a charged particle in a unif... more Following Langevin, the system of equations describing the motion of a charged particle in a uniform, homogeneous, stationary magnetic field B, subject to additive random forces modelling the interaction with the plasma, is dt t dt r u and dt tt dt x u ue u c t . Here, is the position and t r t u the velocity of the particle, while is the unit vector in the x-direction. The parameters , x e [| | / ] qm B and c represent the cyclotron frequency, the friction coefficient, and the strength of the random component of the force, respectively. It is assumed that this force consists of a deterministic component proportional to the velocity, and a fluctuating component t , usually referred to as "noise". In this work the stochastic term is assumed to be a Gaussian stationary process with vanishing mean and (diagonal) covariance matrix ii i j tt . Simulations have been performed with the following four correlation functions : i) White noise: ii) Gaussian noise: 1 22 exp / iii) Colo...
Physica A: Statistical Mechanics and its Applications
The formalism of generalized Wigner transformations developped in a previous paper, is applied to... more The formalism of generalized Wigner transformations developped in a previous paper, is applied to kinetic equations of the Lindblad type for quantum harmonic oscillator models. It is first applied to an oscillator coupled to an equilibrium chain of other oscillators having nearest-neighbour interactions. The kinetic equation is derived without using the so called rotating-wave approximation. Then it is shown that the classical limit of the corresponding phase-space equation is independent of the ordering of operators corresponding to the inverse of the generalized Wigner transformation, provided the latter is involutive. Moreover, this limit equation, which conserves the probabilistic nature of the distribution function and obeys an H-theorem, coincides with the kinetic equation for the corresponding classical system, which is derived independently and is distinct from that usually obtained in the litterature and not sharing the above properties. Finally the same formalism is applie...
Cooperative Phenomena, 1973
The main purpose of this work is to test and validate a new numerical tool for comparative studie... more The main purpose of this work is to test and validate a new numerical tool for comparative studies of the 3D MHD features in natural convection flows with or without internal heat sources with 2D cases and to validate the Low-Rm model with the full induction problem of the magnetic flux. In this application we study the flow dumping in natural convection flows caused by the imposed magnetic field in cubic and rectangular cavities filled by liquid metal (1-3). The combined action of the electrical boundary conditions and of the different orientation of the external magnetic field is observed in flows driven by buoyancy. The validation of the numerical model is performed using experimental and numerical results and analytic solutions. Initially, indicative results of velocity and temperature distributions are presented, showing significant reduction of the convection as the Ha increases. This trend is more intensive when Ra exceeds 10 4 . The electrically conducting walls affect the i...
Transport Theory and Statistical Physics, 1999
The probabilistic description of finite classical systems often leads to linear kinetic equations... more The probabilistic description of finite classical systems often leads to linear kinetic equations. A set of physically motivated mathematical requirements is accordingly formulated. We show that it necessarily implies that solutions of such a kinetic equation in the Heisenberg representation, define Markov semigroups on the space of observables. Moreover, a general H-theorem for the adjoint of such semigroups is formulated and proved provided that at least locally, an invariant measure exists. Under a certain continuity assumption, the Markov semigroup property is sufficient for a linear kinetic equation to be a second order differential equation with nonegative-definite leading coefficient. Conversely it is shown that such equations define Markov semigroups satisfying an H-theorem, provided there exists a nonnegative equilibrium solution for their formal adjoint, vanishing at infinity. † Association Euratom-Etat Belge
International Journal for Numerical Methods in Fluids, 2009
A numerical study of tangential layers in steady-state magnetohydrodynamic rotating flows is pres... more A numerical study of tangential layers in steady-state magnetohydrodynamic rotating flows is presented using CFD to solve the inductionless governing equations. The analysis considers two basic flow configurations. In the first, a fluid is enclosed in a cylinder with electrically perfect conducting walls and the flow is driven by a small rotating, conducting disk. In the second, a flow is considered in a spherical shell with an inner rotating sphere. The fluid in both cases is subjected to an external axial uniform magnetic field. The results show that these flows exhibit two different types of flow cores separated from each other by a tangential layer parallel to the axis of rotation. The inner core follows a solid-body rotation while the outer is quasistagnant. A counter-rotating jet is developed in the tangential layer between the cores. The characteristics of the tangential layer and the properties of the meridional motion are determined for a wide range of Hartmann numbers. Distributions of angular velocity of circumferential flow and electric potential are obtained and the results are compared with those of analytic methods.
Advances in Chemical Physics, 2000
Physica, 1971
ABSTRACT Les méthodes de la mécanique statistique de non équilibre développées par l'écol... more ABSTRACT Les méthodes de la mécanique statistique de non équilibre développées par l'école de Bruxelles (et spécialement l'introduction de l'opérateur de collision Ψ(z)) permettant d'étendre la théorie des systèmes dynamiques intégrables tant en mécanique classique que quantique. En particulier une formulation nouvelle du théorème fondamental de Poincaré sur la non existence d'invariants est présentée qui ne fait pas appel à des développements en série en la constante de couplage mais est basée directement sur les propriétés spectrales de la résolvante. La distinction entre systèmes “dissipatifs” et non-dissipatifs” introduite par Prigogine et al. est confirmée et précisée.
Physics Letters A
The behaviour of the constants of motion with respect to the collision operator is discussed in t... more The behaviour of the constants of motion with respect to the collision operator is discussed in the ease of a finite quantum system.
Physica, 1972
ABSTRACT Les phénomènes irréversibles au sein d'un système simple caractérisé par un hami... more ABSTRACT Les phénomènes irréversibles au sein d'un système simple caractérisé par un hamiltonien ayant un spectre continu sont étudiés à l'aide des méthodes de la mécanique statistique de non-équilibre. En particulier, nous montrons le lien entre la possibilité d'une description cinétique et la nature des invariants du système. Cette reformulation du problème ergodique permet d'aborder cette question des systèmes à nombre infini de degrés liberté que nous allons étudier dans une publication ultérieure.
Lecture Notes in Physics, 2000
Without Abstract
A multivariate Fokker-Planck-type ki netic equ ation modeling a test -panicle weakly interacting ... more A multivariate Fokker-Planck-type ki netic equ ation modeling a test -panicle weakly interacting with an electrostatic plasma. in the presence of a magnetic field B . is analytically solved in an Ornstein -Uhlenbeck -type approximation. A new set of analytic expressions are obtained for variable moments and panicle density as a function of time. The process is diffusive.
Physica A: Statistical Mechanics and its Applications, 1998
Generalised Wigner and Weyl transformations of quantum operators are defined and their properties... more Generalised Wigner and Weyl transformations of quantum operators are defined and their properties, as well as those of the algebraic structure induced on the phase-space are studied. Using such transformations, quantum linear evolution equations are given a phase-space representation. In particular this is done for the general kinetic equation of the Lindblad type. The resulting expressions are better suited for the passage to the classical limit and for a general comparison of classical and quantum systems. In this context a preliminary discussion of a number of problems of kinetic theory of open systems is given, whereas explicit applications are made in the next paper of the series. * Association Euratom, Etat Belge.
NUMERICAL PROCEDURE: The governing equations together with the corresponding boundary conditions ... more NUMERICAL PROCEDURE: The governing equations together with the corresponding boundary conditions are solved numerically, employing a finite-volume method. The Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) of Patankar (3) is used to couple the momentum and continuity equations in a uniform staggered grid in the horizontal and vertical directions. The momentum equations for U and V, the energy equation and the magnetic induction equations (for all cases studied, except the Low-Rm) are solved using the QUICK scheme of Leonard (4) in the modified form of Hayase et al. (5) in order to minimize numerical diffusion. In all calculations presented here, under-relaxation factors with values of 0.5, 0.5, 0.6, 0.6, 0.6 and 0.3 were applied to U, V, Θ, Bx, By and P, respectively. The iterative procedure is initiated with an arbitrary velocity field followed by the solution of the energy and magnetic induction equations and is continued until convergence is achieved. Before the fina...
Following Langevin, the system of equations describing the motion of a charged particle in a unif... more Following Langevin, the system of equations describing the motion of a charged particle in a uniform, homogeneous, stationary magnetic field B, subject to additive random forces modelling the interaction with the plasma, is dt t dt r u and dt tt dt x u ue u c t . Here, is the position and t r t u the velocity of the particle, while is the unit vector in the x-direction. The parameters , x e [| | / ] qm B and c represent the cyclotron frequency, the friction coefficient, and the strength of the random component of the force, respectively. It is assumed that this force consists of a deterministic component proportional to the velocity, and a fluctuating component t , usually referred to as "noise". In this work the stochastic term is assumed to be a Gaussian stationary process with vanishing mean and (diagonal) covariance matrix ii i j tt . Simulations have been performed with the following four correlation functions : i) White noise: ii) Gaussian noise: 1 22 exp / iii) Colo...
Physica A: Statistical Mechanics and its Applications
The formalism of generalized Wigner transformations developped in a previous paper, is applied to... more The formalism of generalized Wigner transformations developped in a previous paper, is applied to kinetic equations of the Lindblad type for quantum harmonic oscillator models. It is first applied to an oscillator coupled to an equilibrium chain of other oscillators having nearest-neighbour interactions. The kinetic equation is derived without using the so called rotating-wave approximation. Then it is shown that the classical limit of the corresponding phase-space equation is independent of the ordering of operators corresponding to the inverse of the generalized Wigner transformation, provided the latter is involutive. Moreover, this limit equation, which conserves the probabilistic nature of the distribution function and obeys an H-theorem, coincides with the kinetic equation for the corresponding classical system, which is derived independently and is distinct from that usually obtained in the litterature and not sharing the above properties. Finally the same formalism is applie...
Cooperative Phenomena, 1973
The main purpose of this work is to test and validate a new numerical tool for comparative studie... more The main purpose of this work is to test and validate a new numerical tool for comparative studies of the 3D MHD features in natural convection flows with or without internal heat sources with 2D cases and to validate the Low-Rm model with the full induction problem of the magnetic flux. In this application we study the flow dumping in natural convection flows caused by the imposed magnetic field in cubic and rectangular cavities filled by liquid metal (1-3). The combined action of the electrical boundary conditions and of the different orientation of the external magnetic field is observed in flows driven by buoyancy. The validation of the numerical model is performed using experimental and numerical results and analytic solutions. Initially, indicative results of velocity and temperature distributions are presented, showing significant reduction of the convection as the Ha increases. This trend is more intensive when Ra exceeds 10 4 . The electrically conducting walls affect the i...
Transport Theory and Statistical Physics, 1999
The probabilistic description of finite classical systems often leads to linear kinetic equations... more The probabilistic description of finite classical systems often leads to linear kinetic equations. A set of physically motivated mathematical requirements is accordingly formulated. We show that it necessarily implies that solutions of such a kinetic equation in the Heisenberg representation, define Markov semigroups on the space of observables. Moreover, a general H-theorem for the adjoint of such semigroups is formulated and proved provided that at least locally, an invariant measure exists. Under a certain continuity assumption, the Markov semigroup property is sufficient for a linear kinetic equation to be a second order differential equation with nonegative-definite leading coefficient. Conversely it is shown that such equations define Markov semigroups satisfying an H-theorem, provided there exists a nonnegative equilibrium solution for their formal adjoint, vanishing at infinity. † Association Euratom-Etat Belge