... the WaldmannSnider equation: generalization to gas mixtures Lucio Demeio, Louis Monchick MSE ... more ... the WaldmannSnider equation: generalization to gas mixtures Lucio Demeio, Louis Monchick MSE Research Center, The Applied Physics Laboratory, The Johns Hopkins University, Laurel, MD 207236099 ... 1 ) (2q + 1 ) ]1 2 ZZZZ (1)Ji+Jf+mi+m; (q Iv s Mj J ) M; v,v',s,s' mim mfn,'l ...
... function / ^ f(x,v,t) and the electric field E = E{x, t) obey the Vlasov-Poisson system with ... more ... function / ^ f(x,v,t) and the electric field E = E{x, t) obey the Vlasov-Poisson system with collisions ^.^.E^-Cf f2n 9t+VQx J9^,-C' (2) 9E_ 9x ffdv, (2.2) 1 ... frequency, respectively) and C is the BGK collision operator [2,4] (Cf)(x, v, t) = -v(v) [f - c(x, t)f^(v)}, (2.3) with and T] '= fr(v)feq(v)dv. ...
In this paper, we introduce a transport model for the migration of contaminant through mineral ba... more In this paper, we introduce a transport model for the migration of contaminant through mineral barriers in the presence of chemical-and water gradients. Fluid and chemical flows are * included, and coupling flows and nonlinear diffusion are taken into account. The resulting transport equations are solved by an asymptotic expansion based on the multiple time scale technique. The steady state profile is calculated analytically.
Solutions of the Vlasov-Poisson system which correspond to undamped travelling waves near a maxwe... more Solutions of the Vlasov-Poisson system which correspond to undamped travelling waves near a maxwellian equilibrium are analysed numerically. The results are strongly in favour of a recently developed theory which predicts the existence of BGK modes arbitrarily close to any spatially homogeneous equilibrium.
Abstract An algorithm is given for the numerical solution of the Boltzmann equation for a one-dim... more Abstract An algorithm is given for the numerical solution of the Boltzmann equation for a one-dimensional unmagnetized plasma with immobile ions, in which collisional effects are described by the Bhatnagar-Gross-Krook (BGK) model. The algorithm is a straightforward generalization of the splitting scheme, which solves the one-dimensional Vlasov-Poisson system. The accuracy of the splitting scheme to second order in Δt is preserved.
Quarterly Journal of Mechanics and Applied Mathematics, May 11, 2006
The chattering oscillations for an inverted pendulum impacting between lateral walls, a prototype... more The chattering oscillations for an inverted pendulum impacting between lateral walls, a prototype of a class of impact dampers, are analysed. Attention is focused on the periodic chattering appearing when the rest positions cease to be attracting, and the aim is that of computing the time τ required by the micro-oscillations to come to rest. An algorithm is proposed to compute τ , and it is shown how this time depends on the excitation amplitude. When τ becomes equal to the excitation period, the considered chattering is observed to lose attractivity. This occurs for a certain excitation amplitude threshold, which is computed and whose (very weak) dependence on the excitation frequency is illustrated. An asymptotic estimate of the chattering time with respect to a small parameter proportional to the excitation amplitude is given. This is obtained by an appropriate expansion in Taylor series of the relevant quantities involved in the analysis. It is shown that τ is asymptotically proportional to the square root of the excitation amplitude.
The generalized Hess method (GHM) gives a line shape expression which is formally equivalent to t... more The generalized Hess method (GHM) gives a line shape expression which is formally equivalent to the Rautian–Sobel’man hard collision model of Dicke narrowing, but differs radically in the definition of one of the relaxation terms. The relaxation term leading to pressure broadening is the same, but the term leading to Dicke narrowing and ultimately to Doppler line shapes at zero density differs in certain important respects: (1) in GHM it is a weighted sum of the pressure broadening coefficient and an optical diffusion coefficient and (2) there is no sharp distinction between ‘‘velocity changing’’ and ‘‘phase changing’’ collisions. The Dicke narrowing term should thus be understood as including both collision types irretrievably intermixed, with GHM providing a prescription for both relaxation terms. Applied to HF v=0→1, j→j±1 absorption spectra in a bath of Ar and using an accurate interaction potential obtained from spectra of the van der Waals complex and essentially exact close coupling scattering S matrices, GHM provides a rather good description of recently measured line shapes.
The relaxation of a nonequilibrium distribution of electrons in molecular gases, and the transien... more The relaxation of a nonequilibrium distribution of electrons in molecular gases, and the transient and steady electron transport properties are studied with the Boltzmann equation, which accurately accounts for elastic and inelastic electron–moderator collisions. The elastic collision operator is a self-adjoint Fokker–Planck operator, whereas the inelastic collision term is a difference operator. We consider a discretization of the inelastic collision operator which is motivated by the discrete energy losses that occur. For small energy losses, a continuous approximation is introduced such that the inelastic collision term is approximated by a Fokker–Planck operator similar to the elastic collision operator. The transient electron transport properties are studied for an initial electron distribution function in terms of the eigenvalue spectrum of both the elastic and inelastic collision operators. The Fokker–Planck eigenvalue problem is transformed into a Schrödinger equation and the nature of the spectrum is studied in terms of the Wentzel–Kramers–Brillouin and supersymmetric Wentzel–Kramers–Brillouin approximations. The methodology is applied to model systems and the transport of electrons in methane.
We present an asymptotic solution of a moving-boundary problem which describes the nonlinear osci... more We present an asymptotic solution of a moving-boundary problem which describes the nonlinear oscillations of semiinfinite cables resting on an elastic substrate reacting in compression only, and subjected to a constant distributed load and to a small harmonic displacement applied to the finite boundary. Our solution is correct through the second-order terms in a smallness parameter, which we identify with the amplitude of the harmonic oscillation at the boundary, and it complements the first-order solution presented in an earlier work. The second-order analysis confirms the existence of two different regimes in the behaviour of the system, one below (called subcritical) and one above (called supercritical) a certain critical (cutoff) excitation frequency. In the latter, energy is lost by radiation at infinity, while in the former this phenomenon does not occur and various resonances are observed instead. We show that these two regimes exist at all orders in the expansion parameter, and that the cutoff frequency decreases at each order. We also perform a limited comparison of our asymptotic results with a numerical solution. The two approaches show very good agreement.
In this work we investigate a model for the description of the impact of a ball with a flexible b... more In this work we investigate a model for the description of the impact of a ball with a flexible beam. The coupling of the kinematic parameters of the ball (the velocity components) with the vibration modes of the beam are taken into account by using the Hertz theory of impact. We solve the model equations numerically in a few physically relevant cases and illustrate the variation of the modal coefficients of the beam and of the velocity components of the ball during the impact. The restitution coefficient, the size of the deformation region and the impact duration are also reported as functions of the impact velocity and of the impact location.
The transport properties of an ensemble of charged test particles diffusing from infinity through... more The transport properties of an ensemble of charged test particles diffusing from infinity through a second charged species that fills the positive half-space are studied. It is assumed that there are no in- coming particles at the boundary between the medium in the positive half-space and the vacuum that fills the negative half-space. This problem has been referred to as the Milne problem and has previously been considered for neutral species [M. J. Lindenfold and B. Shizgal, Phys. Rev. A 27, 1657 (1983)]. The present paper examines the rarefied-gas dynamical effects for the Coulomb interaction between the two species. The distribution function of the background gas is taken to be a Maxwellian and the test- particle distribution is determined from a solution of the Boltzmann equation with its expansion in Bur- nett functions, products of Laguerre polynomials, and spherical harmonics. The extrapolation length is calculated together with the density and temperature profiles and compared with the Chapman-Enskog results valid far from the boundary. A comparison with the previous results for the hard-sphere cross section describing collisions between two neutral species is also presented.
In this seminar, we illustrate the use of the Splitting-Scheme algorithm in the numerical solutio... more In this seminar, we illustrate the use of the Splitting-Scheme algorithm in the numerical solution of the quantum transport equations for the Wigner function. This algorithm was originally developed for the integration along the characteristics of some classical kinetic equations of the hyperbolic type, such as the Vlasov equation of plasma physics. Here, we briefly outline how the methodology can be transferred to the quantum case, we illustrate some results and discuss some open problems
Journal of Computational Electronics, Jan 18, 2007
The aim of this work is to present an extension of the "kp" multiband model derived in , to inclu... more The aim of this work is to present an extension of the "kp" multiband model derived in , to include the description of the degenerate bands and the spin-orbit coupling, and its application to some spin-sensitive devices. The model is derived within the usual Bloch-Wannier formalism by a k-expansion, and it is applied to calculate the spin dependent transmission coefficients for an asymmetric resonant interband diode.
In this work, we introduce a multiband transport model for quantum electron transport in semicond... more In this work, we introduce a multiband transport model for quantum electron transport in semiconductors following the Wigner-function approach. By using the Bloch-Floquet decomposition of the density matrix, we obtain the Bloch-Floquet projections of the Wigner function and derive their evolution equations for energy bands of arbitrary shape. The equations of the model are very general and allow (in principle)
... the WaldmannSnider equation: generalization to gas mixtures Lucio Demeio, Louis Monchick MSE ... more ... the WaldmannSnider equation: generalization to gas mixtures Lucio Demeio, Louis Monchick MSE Research Center, The Applied Physics Laboratory, The Johns Hopkins University, Laurel, MD 207236099 ... 1 ) (2q + 1 ) ]1 2 ZZZZ (1)Ji+Jf+mi+m; (q Iv s Mj J ) M; v,v',s,s' mim mfn,'l ...
... function / ^ f(x,v,t) and the electric field E = E{x, t) obey the Vlasov-Poisson system with ... more ... function / ^ f(x,v,t) and the electric field E = E{x, t) obey the Vlasov-Poisson system with collisions ^.^.E^-Cf f2n 9t+VQx J9^,-C' (2) 9E_ 9x ffdv, (2.2) 1 ... frequency, respectively) and C is the BGK collision operator [2,4] (Cf)(x, v, t) = -v(v) [f - c(x, t)f^(v)}, (2.3) with and T] '= fr(v)feq(v)dv. ...
In this paper, we introduce a transport model for the migration of contaminant through mineral ba... more In this paper, we introduce a transport model for the migration of contaminant through mineral barriers in the presence of chemical-and water gradients. Fluid and chemical flows are * included, and coupling flows and nonlinear diffusion are taken into account. The resulting transport equations are solved by an asymptotic expansion based on the multiple time scale technique. The steady state profile is calculated analytically.
Solutions of the Vlasov-Poisson system which correspond to undamped travelling waves near a maxwe... more Solutions of the Vlasov-Poisson system which correspond to undamped travelling waves near a maxwellian equilibrium are analysed numerically. The results are strongly in favour of a recently developed theory which predicts the existence of BGK modes arbitrarily close to any spatially homogeneous equilibrium.
Abstract An algorithm is given for the numerical solution of the Boltzmann equation for a one-dim... more Abstract An algorithm is given for the numerical solution of the Boltzmann equation for a one-dimensional unmagnetized plasma with immobile ions, in which collisional effects are described by the Bhatnagar-Gross-Krook (BGK) model. The algorithm is a straightforward generalization of the splitting scheme, which solves the one-dimensional Vlasov-Poisson system. The accuracy of the splitting scheme to second order in Δt is preserved.
Quarterly Journal of Mechanics and Applied Mathematics, May 11, 2006
The chattering oscillations for an inverted pendulum impacting between lateral walls, a prototype... more The chattering oscillations for an inverted pendulum impacting between lateral walls, a prototype of a class of impact dampers, are analysed. Attention is focused on the periodic chattering appearing when the rest positions cease to be attracting, and the aim is that of computing the time τ required by the micro-oscillations to come to rest. An algorithm is proposed to compute τ , and it is shown how this time depends on the excitation amplitude. When τ becomes equal to the excitation period, the considered chattering is observed to lose attractivity. This occurs for a certain excitation amplitude threshold, which is computed and whose (very weak) dependence on the excitation frequency is illustrated. An asymptotic estimate of the chattering time with respect to a small parameter proportional to the excitation amplitude is given. This is obtained by an appropriate expansion in Taylor series of the relevant quantities involved in the analysis. It is shown that τ is asymptotically proportional to the square root of the excitation amplitude.
The generalized Hess method (GHM) gives a line shape expression which is formally equivalent to t... more The generalized Hess method (GHM) gives a line shape expression which is formally equivalent to the Rautian–Sobel’man hard collision model of Dicke narrowing, but differs radically in the definition of one of the relaxation terms. The relaxation term leading to pressure broadening is the same, but the term leading to Dicke narrowing and ultimately to Doppler line shapes at zero density differs in certain important respects: (1) in GHM it is a weighted sum of the pressure broadening coefficient and an optical diffusion coefficient and (2) there is no sharp distinction between ‘‘velocity changing’’ and ‘‘phase changing’’ collisions. The Dicke narrowing term should thus be understood as including both collision types irretrievably intermixed, with GHM providing a prescription for both relaxation terms. Applied to HF v=0→1, j→j±1 absorption spectra in a bath of Ar and using an accurate interaction potential obtained from spectra of the van der Waals complex and essentially exact close coupling scattering S matrices, GHM provides a rather good description of recently measured line shapes.
The relaxation of a nonequilibrium distribution of electrons in molecular gases, and the transien... more The relaxation of a nonequilibrium distribution of electrons in molecular gases, and the transient and steady electron transport properties are studied with the Boltzmann equation, which accurately accounts for elastic and inelastic electron–moderator collisions. The elastic collision operator is a self-adjoint Fokker–Planck operator, whereas the inelastic collision term is a difference operator. We consider a discretization of the inelastic collision operator which is motivated by the discrete energy losses that occur. For small energy losses, a continuous approximation is introduced such that the inelastic collision term is approximated by a Fokker–Planck operator similar to the elastic collision operator. The transient electron transport properties are studied for an initial electron distribution function in terms of the eigenvalue spectrum of both the elastic and inelastic collision operators. The Fokker–Planck eigenvalue problem is transformed into a Schrödinger equation and the nature of the spectrum is studied in terms of the Wentzel–Kramers–Brillouin and supersymmetric Wentzel–Kramers–Brillouin approximations. The methodology is applied to model systems and the transport of electrons in methane.
We present an asymptotic solution of a moving-boundary problem which describes the nonlinear osci... more We present an asymptotic solution of a moving-boundary problem which describes the nonlinear oscillations of semiinfinite cables resting on an elastic substrate reacting in compression only, and subjected to a constant distributed load and to a small harmonic displacement applied to the finite boundary. Our solution is correct through the second-order terms in a smallness parameter, which we identify with the amplitude of the harmonic oscillation at the boundary, and it complements the first-order solution presented in an earlier work. The second-order analysis confirms the existence of two different regimes in the behaviour of the system, one below (called subcritical) and one above (called supercritical) a certain critical (cutoff) excitation frequency. In the latter, energy is lost by radiation at infinity, while in the former this phenomenon does not occur and various resonances are observed instead. We show that these two regimes exist at all orders in the expansion parameter, and that the cutoff frequency decreases at each order. We also perform a limited comparison of our asymptotic results with a numerical solution. The two approaches show very good agreement.
In this work we investigate a model for the description of the impact of a ball with a flexible b... more In this work we investigate a model for the description of the impact of a ball with a flexible beam. The coupling of the kinematic parameters of the ball (the velocity components) with the vibration modes of the beam are taken into account by using the Hertz theory of impact. We solve the model equations numerically in a few physically relevant cases and illustrate the variation of the modal coefficients of the beam and of the velocity components of the ball during the impact. The restitution coefficient, the size of the deformation region and the impact duration are also reported as functions of the impact velocity and of the impact location.
The transport properties of an ensemble of charged test particles diffusing from infinity through... more The transport properties of an ensemble of charged test particles diffusing from infinity through a second charged species that fills the positive half-space are studied. It is assumed that there are no in- coming particles at the boundary between the medium in the positive half-space and the vacuum that fills the negative half-space. This problem has been referred to as the Milne problem and has previously been considered for neutral species [M. J. Lindenfold and B. Shizgal, Phys. Rev. A 27, 1657 (1983)]. The present paper examines the rarefied-gas dynamical effects for the Coulomb interaction between the two species. The distribution function of the background gas is taken to be a Maxwellian and the test- particle distribution is determined from a solution of the Boltzmann equation with its expansion in Bur- nett functions, products of Laguerre polynomials, and spherical harmonics. The extrapolation length is calculated together with the density and temperature profiles and compared with the Chapman-Enskog results valid far from the boundary. A comparison with the previous results for the hard-sphere cross section describing collisions between two neutral species is also presented.
In this seminar, we illustrate the use of the Splitting-Scheme algorithm in the numerical solutio... more In this seminar, we illustrate the use of the Splitting-Scheme algorithm in the numerical solution of the quantum transport equations for the Wigner function. This algorithm was originally developed for the integration along the characteristics of some classical kinetic equations of the hyperbolic type, such as the Vlasov equation of plasma physics. Here, we briefly outline how the methodology can be transferred to the quantum case, we illustrate some results and discuss some open problems
Journal of Computational Electronics, Jan 18, 2007
The aim of this work is to present an extension of the "kp" multiband model derived in , to inclu... more The aim of this work is to present an extension of the "kp" multiband model derived in , to include the description of the degenerate bands and the spin-orbit coupling, and its application to some spin-sensitive devices. The model is derived within the usual Bloch-Wannier formalism by a k-expansion, and it is applied to calculate the spin dependent transmission coefficients for an asymmetric resonant interband diode.
In this work, we introduce a multiband transport model for quantum electron transport in semicond... more In this work, we introduce a multiband transport model for quantum electron transport in semiconductors following the Wigner-function approach. By using the Bloch-Floquet decomposition of the density matrix, we obtain the Bloch-Floquet projections of the Wigner function and derive their evolution equations for energy bands of arbitrary shape. The equations of the model are very general and allow (in principle)
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