This paper focuses on the calculation of the electrical conductivity of a methane–air flame in th... more This paper focuses on the calculation of the electrical conductivity of a methane–air flame in the presence of weak electric fields, solving the Boltzmann equation for free electrons self-consistently coupled with chemical kinetics. The chemical model GRI-Mech 3.0 has been completed with chemi-ionization reactions to model ionization in the absence of fields, and a database of cross sections for electron-impact-induced processes to account for reactions and transitions activated in the flame during discharge. The dependence of plasma properties on the frequency of an oscillating field has been studied under different pressure and gas temperature conditions. Fitting expressions of the electrical conductivity as a function of gas temperature and methane consumption are provided for different operational conditions in the Ansaldo Energia burner.
It is shown that a toroidal, axisymmeuic, Axed-boundary plasma relaxes to a steady state where th... more It is shown that a toroidal, axisymmeuic, Axed-boundary plasma relaxes to a steady state where the rate of entropy production through ohmic dissipation is a minimum, the value of which depends on the boundary conditions. The plasma is assumed to evolve on a time Scale slow enough for MHD equilibrium to hold at all times. Additional heating and non-inductive current drive (lower hybrid current drive, bootstrap effects) are explicitly taken into account.
Lazzaro and Minardi have claimed that a mathematical error in an equation invalidates the main re... more Lazzaro and Minardi have claimed that a mathematical error in an equation invalidates the main result of an earlier paper. It is now shown that the equation is physically justified and mathematically correct.
A maximum entropy production principle (MEPP) has been postulated to be a criterion of stability ... more A maximum entropy production principle (MEPP) has been postulated to be a criterion of stability for steady states of open systems [Martyushev et al., Phys. Rep. 426, 1 (2006)]. We find a necessary condition for stability of steady solutions of the complex Ginzburg-Landau equation. This condition violates MEPP.
Recently, a unique collision between two large-scale magnetized plasmoids produced by coronal mas... more Recently, a unique collision between two large-scale magnetized plasmoids produced by coronal mass ejections in the heliosphere has been observed [C. Shen, Y. Wang, S Wang, Y. Liu, R. Liu, A. Vourildas, B. Miao, P. Ye, J Liu, Zh. Zhou, Nature 8, 923–928 (2012)]. Results suggest that the collision is super-elastic, i.e. the total linear kinetic energy of the two plasmoids after the collision is larger than before the collision, and that an anti-correlation exists, i.e. the lower the initial relative velocity of the plasmoids, the larger the relative increase in total kinetic energy. Following an old suggestion of [W. H. Bostick, IEEE Trans. Plasma Science PS-14 703-717 (1986)], here we start from first principles, retrieve some results of [D. Kagan, S. M. Mahajan, Mon. Not. R. Astron. Soc. 406 1140-1145 (2010)] and [S. Ohsaki, N. L. Shatashvili, Z. Yoshida, Ap. J. Lett. 559 L61 (2001)] and show that the anti-correlation is just a consequence of Hall magnetohydrodynamics.
We show that a Faddeev-Niemi non-linear sigma model describes in the long wavelength limit a wide... more We show that a Faddeev-Niemi non-linear sigma model describes in the long wavelength limit a wide class of steady-state, knotted physical systems far from thermodynamic equilibrium which are stable against perturbations of temperature and interact weakly with the external world. In these systems temperature gradients are negligible, inertial effects are negligible in comparison with diffusion effects, entropy is mainly produced through Joule and/or viscous heating, the macroscopic state is described by specifying a unit vector n(x) at each point, and the Gauss linking number of n(x) is lower than a threshold. In fluids and plasmas, the model describes filamentary structures which adjust themselves in order to offer minimum resistance to the medium embedding them and to the electric currents (if any) flowing across them; in the latter case, Gauss linking number is related to magnetic helicity. Both n(x) and the relative velocity of the filament with respect to the medium are approximately Double Beltrami vector fields. We derive a stability criterion for a double helix. Moreover, a similar discussion describes the recently discovered ‘writing’ process of skyrmions in a magnetic film with the help of a beam of polarised electrons. We derive a lower bound on the value of beam current required to ‘write’ a skyrmion.
A LIMIT CYCLE FOR PRESSURE OSCILLATIONS IN A GAS TURBINE BURNER, Jul 13, 2014
Humming is a dangerous, combustion-driven acoustic oscillation phenomenon which can take
place i... more Humming is a dangerous, combustion-driven acoustic oscillation phenomenon which can take
place in gas-turbine burners. Any satisfactory description of humming should include both
acoustic- and convective-related events. In fact, the distance crossed by a fluid ”particle”
during one humming period is typically of the same order of the distance between the flame
and the inlet of the air-fuel mixture. Available models often postulate the Mach number to
vanish, which is a scarcely justifiable hypothesis. Furthermore, the combined effect of non-normality
and non-linearity might invalidate the familiar correspondence between humming
onset and the growth rate of the humming mode predicted by linear stability theory. The
prediction of humming amplitude, not available from linear theory, is required in order to
assess the impact of the phenomenon. Thus, a non-linear – albeit simplified – description is
required. We make use of a proprietary Ansaldo Energia model implemented in COMSOL
Multiphysics, a finite element commercial software. Nonlinear terms are introduced into the
heat release model and simulations are performed in the time domain. The initial condition in
the simulations is composed by a set of random frequencies. The employed model filters both
the fundamental frequency, the harmonics and the convective frequency from the initial signal;
the variables in the model, such as pressure, velocity and temperature perturbations, oscillate
in time without further application of external forces. The evolution scenarios of the pressure
perturbation depend on the flame position and the mean velocity distribution. Three possible
occurrences are observed: amplitude growth, decay and saturation.
In depth discussion of thermodynamics of a familiar system made of a room, a heater and
a window... more In depth discussion of thermodynamics of a familiar system made of a room, a heater and
a window reveals the rich complexity underlying the deceptively simple assumption of
local thermodynamic equilibrium. It displays also the failure of available approaches to
non-equilibrium thermodynamics.
Recently, it has been predicted that hydrogen-boron (p-11B) nuclear fusion may attain ignition
i... more Recently, it has been predicted that hydrogen-boron (p-11B) nuclear fusion may attain ignition
in the hot spots observed in a plasma focus (PF) pinch, due to their huge values of particle density,
magnetic field and (reportedly) ion temperature. Accordingly, large magnetic fields should raise electronic
Landau levels, thus reducing collisional exchange of energy from ion to electrons and Bremsstrahlung losses.
Moreover, large particle densities, together with ion viscous heating, should allow fulfilment of Lawson
criterion and provide effective screening of cyclotron radiation. We invoke both well-known, empirical
scaling laws of PF physics, Connor-Taylor scaling laws, Poynting balance of electromagnetic energy and the
balance of generalised helicity. We show that the evolution of PF hot spots is a succession of relaxed states,
described by the double Beltrami solutions of Hall-MHD equations of motion. We obtain some necessary
conditions for ignition, which are violated in most realistic conditions. Large electromagnetic fields in the
hot spot accelerate electrons at supersonic velocities and trigger turbulence, which raises electric resistivity
and Joule heating, thus spoiling further compression. Ignition is only possible if a significant fraction of the
Bremsstrahlung-radiated power is reflected back into the plasma. Injection of angular momentum decreases
the required reflection coefficient.
Recently, it has been predicted that hydrogen-boron (p-11B) nuclear fusion may attain ignition
i... more Recently, it has been predicted that hydrogen-boron (p-11B) nuclear fusion may attain ignition
in the hot spots observed in a plasma focus (PF) pinch, due to their huge values of particle density,
magnetic field and (reportedly) ion temperature. Accordingly, large magnetic fields should raise electronic
Landau levels, thus reducing collisional exchange of energy from ion to electrons and Bremsstrahlung losses.
Moreover, large particle densities, together with ion viscous heating, should allow fulfilment of Lawson
criterion and provide effective screening of cyclotron radiation. We invoke both well-known, empirical
scaling laws of PF physics, Connor-Taylor scaling laws, Poynting balance of electromagnetic energy and the
balance of generalised helicity. We show that the evolution of PF hot spots is a succession of relaxed states,
described by the double Beltrami solutions of Hall-MHD equations of motion. We obtain some necessary
conditions for ignition, which are violated in most realistic conditions. Large electromagnetic fields in the
hot spot accelerate electrons at supersonic velocities and trigger turbulence, which raises electric resistivity
and Joule heating, thus spoiling further compression. Ignition is only possible if a significant fraction of the
Bremsstrahlung-radiated power is reflected back into the plasma. Injection of angular momentum decreases
the required reflection coefficient.
Any satisfactorily description of humming (= dangerous, combustion-driven acoustic oscillation in... more Any satisfactorily description of humming (= dangerous, combustion-driven acoustic oscillation in gas-turbine burners [1]) should include both acoustic and convective phenomena. In fact, the distance v 0 crossed by an element of fluid (with speed v 0 10 m/s) during one humming period ( 10 ms) is typically the distance L between the flame and the inlet of the air-fuel mixture (L 10 cm). Accordingly, no fully linear approach seems to be successful.
Reply to 'Comment on ‘Maximum or minimum entropy production - How to select a necessary criterion of stability for a dissipative fluid or plasma’ ', 2012
In their Comment on Phys. Rev E 81, 041137 (2010), a paper that focused on the necessary conditio... more In their Comment on Phys. Rev E 81, 041137 (2010), a paper that focused on the necessary conditions for
the stability of dissipative fluids and plasmas, the authors claim that the basic equations of the paper are in
contradiction with the laws of thermodynamics of irreversible processes [Sonnino, Tlidi, and Evslin, preceding
paper, Phys. Rev. E 86, 043101 (2012)]. Here, we show that one of the basic equations of the Comment is just a
particular case of the results of the criticized paper. As for two further tenets of the Comment, counterexamples
are found in the literature and are discussed here.
We invoke the arguments of Qian JJ (1996) Phys A: Math Gen 29: 1305-1309 and show that the applic... more We invoke the arguments of Qian JJ (1996) Phys A: Math Gen 29: 1305-1309 and show that the application of Maximum Entropy (MaxEnt) approach to a 2D incompressible flow behind a circular cylinder with Reynolds number = 100 is not invariant with respect to scaling transformations, like those involved when changing the system of units from SI to CGS.
Metal hydrides are solutions of hydrogen in a metal, where phase transitions may occur
depending ... more Metal hydrides are solutions of hydrogen in a metal, where phase transitions may occur depending on temperature, pressure etc. We apply Le Chatelier’s principle of thermodynamics to a particular phase transition in TiHx, which can approximately be described as a second-order phase transition. We show that the fluctuations of the order parameter correspond to fluctuations both of the density of H+ ions and of the distance between adjacent H+ ions. Moreover, as the system approaches the transition and the correlation radius increases we show –with the help of statistical mechanics– that the statistical weight of modes involving a large number of H+ ions (‘collective modes’) increases sharply, in spite of the fact that the Boltzmann factor of each collective mode is exponentially small. As a result, it turns out that the interaction of the H+ ions with collective modes makes a tiny suprathermal fraction of the H+ population to appear. Our results hold for similar transitions in metal deuterides too. A violation of a – insofar undisputed– upper bound on hydrogen loading follows.
The usual assumption of axisymmetric current density distribution in MPD plasmas is questionable ... more The usual assumption of axisymmetric current density distribution in MPD plasmas is questionable at high plasma currents. In fact, collisions with neutrals induces instability in the axisymmetric plasma sheath whenever the velocity of the plasma center of mass exceeds the Alfven MHD speed, or, equivalently, when the electron Hall parameter exceeds a critical value slightly larger than unity. The non-linear phase of the instability leads to self-focussing of the current density into thin filaments with vanishing Lorentz force ( j // B ). The properties of the filaments are in agreement with the results of theoretical analysis available in literature. The geometry of filamentary current distribution is much more complex than the axisymmetric configuration: consequently, the instability induces significant increase of the inductance. Experiments at Centrospazio confirm this prediction, showing that L may attain much larger values than the nominal value computed with axisymmetric geometry. When force-free filamentation occurs, the external world feeds force-free magnetic fields which are useless for propulsion, thus lowering the overall MPD efficiency. This effect (already observed in Plasma Focus) suggests that filamentation plays a role in MPD onset.
Lazzaro and Minardi have claimed that a mathematical error in an equation invalidates the main re... more Lazzaro and Minardi have claimed that a mathematical error in an equation invalidates the main result of an earlier paper. It is now shown that the equation is physically justified and mathematically correct.
To date, no MHD-based complete description of the tiny, relatively stable, well-ordered structure... more To date, no MHD-based complete description of the tiny, relatively stable, well-ordered structures (hot spots, filaments) observed in the pinch of a plasma focus seems to be feasible. Indeed, the large value of electron density suggests that a classification of such structures which is based on the approximation of local thermodynamical equilibrium (LTE) is possible. Starting from an often overlooked, far-reaching result of LTE, we derive a purely analytical description of both hot spots and filaments. In spite of their quite different topology, both configurations are extremals of the same variational principle. Well-known results of conventional MHD are retrieved as benchmark cases. It turns out that hot spots satisfy Taylor’s principle of constrained minimum of magnetic energy, the constraint being given by fixed magnetic helicity. Filaments are similar to the filaments of a superconductor and form a plasma with β = 0.11 and energy diffusion coefficient = 0.88DBohm. Any process – like e.g. radiative collapse – which raises particle density while reducing radial size may transform filaments into hot spots. A well-known scaling law is retrieved – the collisional Vlasov high beta scaling. A link between dissipation and topology is highlighted. Accordingly, a large-current pinch may give birth to tiny hot spots with large electron density and magnetic field.
Ten necessary criteria for stability of various dissipative fluids and plasmas are derived from t... more Ten necessary criteria for stability of various dissipative fluids and plasmas are derived from the first and the second principle of thermodynamics applied to a generic small mass element of the system, under the assumption that local thermodynamic equilibrium holds everywhere at all times. We investigate the stability of steady states of a mixture of different chemical species at the same temperature against volume-preserving perturbations. We neglect both electric and magnetic polarization, and assume negligible net mass sources and particle diffusion. We assume that both conduction- and radiation-induced heat losses increase with increasing temperature. We invoke no Onsager symmetry, no detailed model of heat transport and production, no “Extended Thermodynamics,” no “Maxent” method, and no “new” universal criterion of stability for steady states of systems with dissipation. Each criterion takes the form of—or is a consequence of—a variational principle. We retrieve maximization of entropy for isolated systems at thermodynamic equilibrium, as expected. If the boundary conditions keep the relaxed state far from thermodynamic equilibrium, the stability criterion we retrieve depends also on the detailed balance of momentum of a small mass element. This balance may include the grad-p-related force, the Lorenz force of electromagnetism and the forces which are gradients of potentials. In order to be stable, the solution of the steady-state equations of motion for a given problem should satisfy the relevant stability criterion. Retrieved criteria include among others Taylor’s minimization of magnetic energy with the constraint of given magnetic helicity in relaxed, turbulent plasmas, Rayleigh’s criterion of stability in thermoacoustics, Paltridge et al.’s maximum entropy production principle for Earth’s atmosphere, Chandrasekhar’ minimization of the adverse temperature gradient in Bénard’s convective cells, and Malkus’ maximization of viscous power with the constraint of given mean velocity for turbulent shear flow in channels. It turns out that characterization of systems far from equilibrium, e.g., by maximum entropy production is not a general property but—just like minimum entropy production—is reserved to special systems. A taxonomy of stability criteria is derived, which clarifies what is to be minimized, what is to be maximized and with which constraint for each problem.
This paper focuses on the calculation of the electrical conductivity of a methane–air flame in th... more This paper focuses on the calculation of the electrical conductivity of a methane–air flame in the presence of weak electric fields, solving the Boltzmann equation for free electrons self-consistently coupled with chemical kinetics. The chemical model GRI-Mech 3.0 has been completed with chemi-ionization reactions to model ionization in the absence of fields, and a database of cross sections for electron-impact-induced processes to account for reactions and transitions activated in the flame during discharge. The dependence of plasma properties on the frequency of an oscillating field has been studied under different pressure and gas temperature conditions. Fitting expressions of the electrical conductivity as a function of gas temperature and methane consumption are provided for different operational conditions in the Ansaldo Energia burner.
It is shown that a toroidal, axisymmeuic, Axed-boundary plasma relaxes to a steady state where th... more It is shown that a toroidal, axisymmeuic, Axed-boundary plasma relaxes to a steady state where the rate of entropy production through ohmic dissipation is a minimum, the value of which depends on the boundary conditions. The plasma is assumed to evolve on a time Scale slow enough for MHD equilibrium to hold at all times. Additional heating and non-inductive current drive (lower hybrid current drive, bootstrap effects) are explicitly taken into account.
Lazzaro and Minardi have claimed that a mathematical error in an equation invalidates the main re... more Lazzaro and Minardi have claimed that a mathematical error in an equation invalidates the main result of an earlier paper. It is now shown that the equation is physically justified and mathematically correct.
A maximum entropy production principle (MEPP) has been postulated to be a criterion of stability ... more A maximum entropy production principle (MEPP) has been postulated to be a criterion of stability for steady states of open systems [Martyushev et al., Phys. Rep. 426, 1 (2006)]. We find a necessary condition for stability of steady solutions of the complex Ginzburg-Landau equation. This condition violates MEPP.
Recently, a unique collision between two large-scale magnetized plasmoids produced by coronal mas... more Recently, a unique collision between two large-scale magnetized plasmoids produced by coronal mass ejections in the heliosphere has been observed [C. Shen, Y. Wang, S Wang, Y. Liu, R. Liu, A. Vourildas, B. Miao, P. Ye, J Liu, Zh. Zhou, Nature 8, 923–928 (2012)]. Results suggest that the collision is super-elastic, i.e. the total linear kinetic energy of the two plasmoids after the collision is larger than before the collision, and that an anti-correlation exists, i.e. the lower the initial relative velocity of the plasmoids, the larger the relative increase in total kinetic energy. Following an old suggestion of [W. H. Bostick, IEEE Trans. Plasma Science PS-14 703-717 (1986)], here we start from first principles, retrieve some results of [D. Kagan, S. M. Mahajan, Mon. Not. R. Astron. Soc. 406 1140-1145 (2010)] and [S. Ohsaki, N. L. Shatashvili, Z. Yoshida, Ap. J. Lett. 559 L61 (2001)] and show that the anti-correlation is just a consequence of Hall magnetohydrodynamics.
We show that a Faddeev-Niemi non-linear sigma model describes in the long wavelength limit a wide... more We show that a Faddeev-Niemi non-linear sigma model describes in the long wavelength limit a wide class of steady-state, knotted physical systems far from thermodynamic equilibrium which are stable against perturbations of temperature and interact weakly with the external world. In these systems temperature gradients are negligible, inertial effects are negligible in comparison with diffusion effects, entropy is mainly produced through Joule and/or viscous heating, the macroscopic state is described by specifying a unit vector n(x) at each point, and the Gauss linking number of n(x) is lower than a threshold. In fluids and plasmas, the model describes filamentary structures which adjust themselves in order to offer minimum resistance to the medium embedding them and to the electric currents (if any) flowing across them; in the latter case, Gauss linking number is related to magnetic helicity. Both n(x) and the relative velocity of the filament with respect to the medium are approximately Double Beltrami vector fields. We derive a stability criterion for a double helix. Moreover, a similar discussion describes the recently discovered ‘writing’ process of skyrmions in a magnetic film with the help of a beam of polarised electrons. We derive a lower bound on the value of beam current required to ‘write’ a skyrmion.
A LIMIT CYCLE FOR PRESSURE OSCILLATIONS IN A GAS TURBINE BURNER, Jul 13, 2014
Humming is a dangerous, combustion-driven acoustic oscillation phenomenon which can take
place i... more Humming is a dangerous, combustion-driven acoustic oscillation phenomenon which can take
place in gas-turbine burners. Any satisfactory description of humming should include both
acoustic- and convective-related events. In fact, the distance crossed by a fluid ”particle”
during one humming period is typically of the same order of the distance between the flame
and the inlet of the air-fuel mixture. Available models often postulate the Mach number to
vanish, which is a scarcely justifiable hypothesis. Furthermore, the combined effect of non-normality
and non-linearity might invalidate the familiar correspondence between humming
onset and the growth rate of the humming mode predicted by linear stability theory. The
prediction of humming amplitude, not available from linear theory, is required in order to
assess the impact of the phenomenon. Thus, a non-linear – albeit simplified – description is
required. We make use of a proprietary Ansaldo Energia model implemented in COMSOL
Multiphysics, a finite element commercial software. Nonlinear terms are introduced into the
heat release model and simulations are performed in the time domain. The initial condition in
the simulations is composed by a set of random frequencies. The employed model filters both
the fundamental frequency, the harmonics and the convective frequency from the initial signal;
the variables in the model, such as pressure, velocity and temperature perturbations, oscillate
in time without further application of external forces. The evolution scenarios of the pressure
perturbation depend on the flame position and the mean velocity distribution. Three possible
occurrences are observed: amplitude growth, decay and saturation.
In depth discussion of thermodynamics of a familiar system made of a room, a heater and
a window... more In depth discussion of thermodynamics of a familiar system made of a room, a heater and
a window reveals the rich complexity underlying the deceptively simple assumption of
local thermodynamic equilibrium. It displays also the failure of available approaches to
non-equilibrium thermodynamics.
Recently, it has been predicted that hydrogen-boron (p-11B) nuclear fusion may attain ignition
i... more Recently, it has been predicted that hydrogen-boron (p-11B) nuclear fusion may attain ignition
in the hot spots observed in a plasma focus (PF) pinch, due to their huge values of particle density,
magnetic field and (reportedly) ion temperature. Accordingly, large magnetic fields should raise electronic
Landau levels, thus reducing collisional exchange of energy from ion to electrons and Bremsstrahlung losses.
Moreover, large particle densities, together with ion viscous heating, should allow fulfilment of Lawson
criterion and provide effective screening of cyclotron radiation. We invoke both well-known, empirical
scaling laws of PF physics, Connor-Taylor scaling laws, Poynting balance of electromagnetic energy and the
balance of generalised helicity. We show that the evolution of PF hot spots is a succession of relaxed states,
described by the double Beltrami solutions of Hall-MHD equations of motion. We obtain some necessary
conditions for ignition, which are violated in most realistic conditions. Large electromagnetic fields in the
hot spot accelerate electrons at supersonic velocities and trigger turbulence, which raises electric resistivity
and Joule heating, thus spoiling further compression. Ignition is only possible if a significant fraction of the
Bremsstrahlung-radiated power is reflected back into the plasma. Injection of angular momentum decreases
the required reflection coefficient.
Recently, it has been predicted that hydrogen-boron (p-11B) nuclear fusion may attain ignition
i... more Recently, it has been predicted that hydrogen-boron (p-11B) nuclear fusion may attain ignition
in the hot spots observed in a plasma focus (PF) pinch, due to their huge values of particle density,
magnetic field and (reportedly) ion temperature. Accordingly, large magnetic fields should raise electronic
Landau levels, thus reducing collisional exchange of energy from ion to electrons and Bremsstrahlung losses.
Moreover, large particle densities, together with ion viscous heating, should allow fulfilment of Lawson
criterion and provide effective screening of cyclotron radiation. We invoke both well-known, empirical
scaling laws of PF physics, Connor-Taylor scaling laws, Poynting balance of electromagnetic energy and the
balance of generalised helicity. We show that the evolution of PF hot spots is a succession of relaxed states,
described by the double Beltrami solutions of Hall-MHD equations of motion. We obtain some necessary
conditions for ignition, which are violated in most realistic conditions. Large electromagnetic fields in the
hot spot accelerate electrons at supersonic velocities and trigger turbulence, which raises electric resistivity
and Joule heating, thus spoiling further compression. Ignition is only possible if a significant fraction of the
Bremsstrahlung-radiated power is reflected back into the plasma. Injection of angular momentum decreases
the required reflection coefficient.
Any satisfactorily description of humming (= dangerous, combustion-driven acoustic oscillation in... more Any satisfactorily description of humming (= dangerous, combustion-driven acoustic oscillation in gas-turbine burners [1]) should include both acoustic and convective phenomena. In fact, the distance v 0 crossed by an element of fluid (with speed v 0 10 m/s) during one humming period ( 10 ms) is typically the distance L between the flame and the inlet of the air-fuel mixture (L 10 cm). Accordingly, no fully linear approach seems to be successful.
Reply to 'Comment on ‘Maximum or minimum entropy production - How to select a necessary criterion of stability for a dissipative fluid or plasma’ ', 2012
In their Comment on Phys. Rev E 81, 041137 (2010), a paper that focused on the necessary conditio... more In their Comment on Phys. Rev E 81, 041137 (2010), a paper that focused on the necessary conditions for
the stability of dissipative fluids and plasmas, the authors claim that the basic equations of the paper are in
contradiction with the laws of thermodynamics of irreversible processes [Sonnino, Tlidi, and Evslin, preceding
paper, Phys. Rev. E 86, 043101 (2012)]. Here, we show that one of the basic equations of the Comment is just a
particular case of the results of the criticized paper. As for two further tenets of the Comment, counterexamples
are found in the literature and are discussed here.
We invoke the arguments of Qian JJ (1996) Phys A: Math Gen 29: 1305-1309 and show that the applic... more We invoke the arguments of Qian JJ (1996) Phys A: Math Gen 29: 1305-1309 and show that the application of Maximum Entropy (MaxEnt) approach to a 2D incompressible flow behind a circular cylinder with Reynolds number = 100 is not invariant with respect to scaling transformations, like those involved when changing the system of units from SI to CGS.
Metal hydrides are solutions of hydrogen in a metal, where phase transitions may occur
depending ... more Metal hydrides are solutions of hydrogen in a metal, where phase transitions may occur depending on temperature, pressure etc. We apply Le Chatelier’s principle of thermodynamics to a particular phase transition in TiHx, which can approximately be described as a second-order phase transition. We show that the fluctuations of the order parameter correspond to fluctuations both of the density of H+ ions and of the distance between adjacent H+ ions. Moreover, as the system approaches the transition and the correlation radius increases we show –with the help of statistical mechanics– that the statistical weight of modes involving a large number of H+ ions (‘collective modes’) increases sharply, in spite of the fact that the Boltzmann factor of each collective mode is exponentially small. As a result, it turns out that the interaction of the H+ ions with collective modes makes a tiny suprathermal fraction of the H+ population to appear. Our results hold for similar transitions in metal deuterides too. A violation of a – insofar undisputed– upper bound on hydrogen loading follows.
The usual assumption of axisymmetric current density distribution in MPD plasmas is questionable ... more The usual assumption of axisymmetric current density distribution in MPD plasmas is questionable at high plasma currents. In fact, collisions with neutrals induces instability in the axisymmetric plasma sheath whenever the velocity of the plasma center of mass exceeds the Alfven MHD speed, or, equivalently, when the electron Hall parameter exceeds a critical value slightly larger than unity. The non-linear phase of the instability leads to self-focussing of the current density into thin filaments with vanishing Lorentz force ( j // B ). The properties of the filaments are in agreement with the results of theoretical analysis available in literature. The geometry of filamentary current distribution is much more complex than the axisymmetric configuration: consequently, the instability induces significant increase of the inductance. Experiments at Centrospazio confirm this prediction, showing that L may attain much larger values than the nominal value computed with axisymmetric geometry. When force-free filamentation occurs, the external world feeds force-free magnetic fields which are useless for propulsion, thus lowering the overall MPD efficiency. This effect (already observed in Plasma Focus) suggests that filamentation plays a role in MPD onset.
Lazzaro and Minardi have claimed that a mathematical error in an equation invalidates the main re... more Lazzaro and Minardi have claimed that a mathematical error in an equation invalidates the main result of an earlier paper. It is now shown that the equation is physically justified and mathematically correct.
To date, no MHD-based complete description of the tiny, relatively stable, well-ordered structure... more To date, no MHD-based complete description of the tiny, relatively stable, well-ordered structures (hot spots, filaments) observed in the pinch of a plasma focus seems to be feasible. Indeed, the large value of electron density suggests that a classification of such structures which is based on the approximation of local thermodynamical equilibrium (LTE) is possible. Starting from an often overlooked, far-reaching result of LTE, we derive a purely analytical description of both hot spots and filaments. In spite of their quite different topology, both configurations are extremals of the same variational principle. Well-known results of conventional MHD are retrieved as benchmark cases. It turns out that hot spots satisfy Taylor’s principle of constrained minimum of magnetic energy, the constraint being given by fixed magnetic helicity. Filaments are similar to the filaments of a superconductor and form a plasma with β = 0.11 and energy diffusion coefficient = 0.88DBohm. Any process – like e.g. radiative collapse – which raises particle density while reducing radial size may transform filaments into hot spots. A well-known scaling law is retrieved – the collisional Vlasov high beta scaling. A link between dissipation and topology is highlighted. Accordingly, a large-current pinch may give birth to tiny hot spots with large electron density and magnetic field.
Ten necessary criteria for stability of various dissipative fluids and plasmas are derived from t... more Ten necessary criteria for stability of various dissipative fluids and plasmas are derived from the first and the second principle of thermodynamics applied to a generic small mass element of the system, under the assumption that local thermodynamic equilibrium holds everywhere at all times. We investigate the stability of steady states of a mixture of different chemical species at the same temperature against volume-preserving perturbations. We neglect both electric and magnetic polarization, and assume negligible net mass sources and particle diffusion. We assume that both conduction- and radiation-induced heat losses increase with increasing temperature. We invoke no Onsager symmetry, no detailed model of heat transport and production, no “Extended Thermodynamics,” no “Maxent” method, and no “new” universal criterion of stability for steady states of systems with dissipation. Each criterion takes the form of—or is a consequence of—a variational principle. We retrieve maximization of entropy for isolated systems at thermodynamic equilibrium, as expected. If the boundary conditions keep the relaxed state far from thermodynamic equilibrium, the stability criterion we retrieve depends also on the detailed balance of momentum of a small mass element. This balance may include the grad-p-related force, the Lorenz force of electromagnetism and the forces which are gradients of potentials. In order to be stable, the solution of the steady-state equations of motion for a given problem should satisfy the relevant stability criterion. Retrieved criteria include among others Taylor’s minimization of magnetic energy with the constraint of given magnetic helicity in relaxed, turbulent plasmas, Rayleigh’s criterion of stability in thermoacoustics, Paltridge et al.’s maximum entropy production principle for Earth’s atmosphere, Chandrasekhar’ minimization of the adverse temperature gradient in Bénard’s convective cells, and Malkus’ maximization of viscous power with the constraint of given mean velocity for turbulent shear flow in channels. It turns out that characterization of systems far from equilibrium, e.g., by maximum entropy production is not a general property but—just like minimum entropy production—is reserved to special systems. A taxonomy of stability criteria is derived, which clarifies what is to be minimized, what is to be maximized and with which constraint for each problem.
Rayleigh's criterion is a necessary condition of stability in thermo-acoustics. It plays a fundam... more Rayleigh's criterion is a necessary condition of stability in thermo-acoustics. It plays a fundamental role in the discussion of 'humming', i.e. of dangerous combustion instabilities affecting lean, premix gas turbine combustors. The present work includes a comparison between different forms of Rayleigh's criterion which are available in the literature. It deals also with the connections of Rayleigh's criterion with 1) experimental results incl. Sondhass and Rijke's observations in XIX century, Rauschenbach's hypothesis and Biwa et al.'s experiments in XX century; 2) Myers' energy corollary of thermo-acoustics; 3) other branches of physics, notably astrophysics (Eddington's model of Cepheid oscillating stars) and thermodynamics (Le Chatelier's principle and its corollary in systems far from thermodynamic equilibrium, namely Glansdorff and Prigogine's general evolution criterion). With the help of the results obtained above, we are able to provide information on the shape of thin, premix, far-from-flat flames which satisfy Rayleigh's criterion in the form of a variational principle involving both the flame velocity, the velocity of the unburnt flow, and the unit vector normal to the flame surface. We apply this result to flames in a real burner and obtain both commutation between open and closed flame configurations at given swirl number, as well as hysteresis - in agreement with previous results. Moreover, we write down a quality factor (in the form of a Strouhal number, where the total curvature plays the role of typical length) for the assessment of flame robustness against the occurrence of humming. Finally, we discuss both the impact of applied electromagnetic fields on humming suppression and the feasibility of such approach to humming suppression in commercial gas turbine combustors.
Recently, it has been shown [M. Polettini et al., 12th Joint European Thermodynamics Conference, ... more Recently, it has been shown [M. Polettini et al., 12th Joint European Thermodynamics Conference, Brescia, Italy, July 1-5, 2013] that dieomorphisms in the state space of a wide class of physical systems leave the amount Π of entropy produced per unit time inside the bulk of the system unaected. Starting from this invariance, we show that if the boundary conditions allow the system to relax towards some nal ('relaxed') state, then the necessary condition for the stability of the relaxed state against slowly evolving perturbations is the same for all the systems of this class, regardless of the detailed dynamics of the system, the amplitude of uctuations around mean values, and the possible occurrence of periodic oscillations in the relaxed state. We invoke also no Onsager symmetry, no detailed model of heat transport and production, and no approximation of local thermodynamic equilibrium. This necessary condition is the constrained minimization of suitably time-and path-ensemble-averaged Π [G. E. Crooks, Phys. Rev. E 61, 3, 2361 (2000)], the constraints being provided by the equations of motion. Even if the latter may dier, the minimum property of stable relaxed states remains the same in dierent systems. Relaxed states satisfy the equations of motion; stable relaxed states satises also the minimum condition. (Thermodynamic equilibrium corresponds to Π ≡ 0 and satises trivially this condition). Our class of physical systems includes both some mesoscopic systems described by a probability distribution function which obeys a simple Fokker-Planck equation and some macroscopic, classical uids with no net mass source and no mass ow across the boundaries; the problems of stability of these systems are dual to each other. As particular cases, we retrieve some necessary criteria for stability of relaxed states in both macroscopic and mesoscopic systems. Retrieved criteria include (among others) constrained minimization of dissipated power for plasma laments in a Dense Plasma Focus [A.
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Papers by Andrea Di Vita
place in gas-turbine burners. Any satisfactory description of humming should include both
acoustic- and convective-related events. In fact, the distance crossed by a fluid ”particle”
during one humming period is typically of the same order of the distance between the flame
and the inlet of the air-fuel mixture. Available models often postulate the Mach number to
vanish, which is a scarcely justifiable hypothesis. Furthermore, the combined effect of non-normality
and non-linearity might invalidate the familiar correspondence between humming
onset and the growth rate of the humming mode predicted by linear stability theory. The
prediction of humming amplitude, not available from linear theory, is required in order to
assess the impact of the phenomenon. Thus, a non-linear – albeit simplified – description is
required. We make use of a proprietary Ansaldo Energia model implemented in COMSOL
Multiphysics, a finite element commercial software. Nonlinear terms are introduced into the
heat release model and simulations are performed in the time domain. The initial condition in
the simulations is composed by a set of random frequencies. The employed model filters both
the fundamental frequency, the harmonics and the convective frequency from the initial signal;
the variables in the model, such as pressure, velocity and temperature perturbations, oscillate
in time without further application of external forces. The evolution scenarios of the pressure
perturbation depend on the flame position and the mean velocity distribution. Three possible
occurrences are observed: amplitude growth, decay and saturation.
a window reveals the rich complexity underlying the deceptively simple assumption of
local thermodynamic equilibrium. It displays also the failure of available approaches to
non-equilibrium thermodynamics.
in the hot spots observed in a plasma focus (PF) pinch, due to their huge values of particle density,
magnetic field and (reportedly) ion temperature. Accordingly, large magnetic fields should raise electronic
Landau levels, thus reducing collisional exchange of energy from ion to electrons and Bremsstrahlung losses.
Moreover, large particle densities, together with ion viscous heating, should allow fulfilment of Lawson
criterion and provide effective screening of cyclotron radiation. We invoke both well-known, empirical
scaling laws of PF physics, Connor-Taylor scaling laws, Poynting balance of electromagnetic energy and the
balance of generalised helicity. We show that the evolution of PF hot spots is a succession of relaxed states,
described by the double Beltrami solutions of Hall-MHD equations of motion. We obtain some necessary
conditions for ignition, which are violated in most realistic conditions. Large electromagnetic fields in the
hot spot accelerate electrons at supersonic velocities and trigger turbulence, which raises electric resistivity
and Joule heating, thus spoiling further compression. Ignition is only possible if a significant fraction of the
Bremsstrahlung-radiated power is reflected back into the plasma. Injection of angular momentum decreases
the required reflection coefficient.
in the hot spots observed in a plasma focus (PF) pinch, due to their huge values of particle density,
magnetic field and (reportedly) ion temperature. Accordingly, large magnetic fields should raise electronic
Landau levels, thus reducing collisional exchange of energy from ion to electrons and Bremsstrahlung losses.
Moreover, large particle densities, together with ion viscous heating, should allow fulfilment of Lawson
criterion and provide effective screening of cyclotron radiation. We invoke both well-known, empirical
scaling laws of PF physics, Connor-Taylor scaling laws, Poynting balance of electromagnetic energy and the
balance of generalised helicity. We show that the evolution of PF hot spots is a succession of relaxed states,
described by the double Beltrami solutions of Hall-MHD equations of motion. We obtain some necessary
conditions for ignition, which are violated in most realistic conditions. Large electromagnetic fields in the
hot spot accelerate electrons at supersonic velocities and trigger turbulence, which raises electric resistivity
and Joule heating, thus spoiling further compression. Ignition is only possible if a significant fraction of the
Bremsstrahlung-radiated power is reflected back into the plasma. Injection of angular momentum decreases
the required reflection coefficient.
the stability of dissipative fluids and plasmas, the authors claim that the basic equations of the paper are in
contradiction with the laws of thermodynamics of irreversible processes [Sonnino, Tlidi, and Evslin, preceding
paper, Phys. Rev. E 86, 043101 (2012)]. Here, we show that one of the basic equations of the Comment is just a
particular case of the results of the criticized paper. As for two further tenets of the Comment, counterexamples
are found in the literature and are discussed here.
depending on temperature, pressure etc. We apply Le Chatelier’s principle of thermodynamics to a
particular phase transition in TiHx, which can approximately be described as a second-order phase
transition. We show that the fluctuations of the order parameter correspond to fluctuations both of the
density of H+ ions and of the distance between adjacent H+ ions. Moreover, as the system approaches the
transition and the correlation radius increases we show –with the help of statistical mechanics– that the
statistical weight of modes involving a large number of H+ ions (‘collective modes’) increases sharply, in
spite of the fact that the Boltzmann factor of each collective mode is exponentially small. As a result, it
turns out that the interaction of the H+ ions with collective modes makes a tiny suprathermal fraction of the
H+ population to appear. Our results hold for similar transitions in metal deuterides too. A violation of a –
insofar undisputed– upper bound on hydrogen loading follows.
Well-known results of conventional MHD are retrieved as benchmark cases. It turns out that hot spots satisfy Taylor’s principle of constrained minimum of magnetic energy, the constraint being given by fixed magnetic helicity. Filaments are similar to the filaments of a superconductor and form a plasma with β = 0.11 and energy diffusion coefficient = 0.88DBohm. Any process – like e.g. radiative collapse – which raises particle density while reducing radial size may transform filaments into hot spots. A well-known scaling law is retrieved – the collisional Vlasov high beta scaling. A link between dissipation and topology is highlighted. Accordingly, a large-current pinch may give birth to tiny hot spots with large electron density and magnetic field.
Thermodynamics,” no “Maxent” method, and no “new” universal criterion of stability for steady states of systems with dissipation. Each criterion takes the form of—or is a consequence of—a variational principle. We
retrieve maximization of entropy for isolated systems at thermodynamic equilibrium, as expected. If the
boundary conditions keep the relaxed state far from thermodynamic equilibrium, the stability criterion we
retrieve depends also on the detailed balance of momentum of a small mass element. This balance may include
the grad-p-related force, the Lorenz force of electromagnetism and the forces which are gradients of potentials. In
order to be stable, the solution of the steady-state equations of motion for a given problem should satisfy the
relevant stability criterion. Retrieved criteria include among others Taylor’s minimization of magnetic energy
with the constraint of given magnetic helicity in relaxed, turbulent plasmas, Rayleigh’s criterion of stability in
thermoacoustics, Paltridge et al.’s maximum entropy production principle for Earth’s atmosphere, Chandrasekhar’
minimization of the adverse temperature gradient in Bénard’s convective cells, and Malkus’ maximization of viscous power with the constraint of given mean velocity for turbulent shear flow in channels. It turns out that characterization of systems far from equilibrium, e.g., by maximum entropy production is not a
general property but—just like minimum entropy production—is reserved to special systems. A taxonomy of stability criteria is derived, which clarifies what is to be minimized, what is to be maximized and with which constraint for each problem.
place in gas-turbine burners. Any satisfactory description of humming should include both
acoustic- and convective-related events. In fact, the distance crossed by a fluid ”particle”
during one humming period is typically of the same order of the distance between the flame
and the inlet of the air-fuel mixture. Available models often postulate the Mach number to
vanish, which is a scarcely justifiable hypothesis. Furthermore, the combined effect of non-normality
and non-linearity might invalidate the familiar correspondence between humming
onset and the growth rate of the humming mode predicted by linear stability theory. The
prediction of humming amplitude, not available from linear theory, is required in order to
assess the impact of the phenomenon. Thus, a non-linear – albeit simplified – description is
required. We make use of a proprietary Ansaldo Energia model implemented in COMSOL
Multiphysics, a finite element commercial software. Nonlinear terms are introduced into the
heat release model and simulations are performed in the time domain. The initial condition in
the simulations is composed by a set of random frequencies. The employed model filters both
the fundamental frequency, the harmonics and the convective frequency from the initial signal;
the variables in the model, such as pressure, velocity and temperature perturbations, oscillate
in time without further application of external forces. The evolution scenarios of the pressure
perturbation depend on the flame position and the mean velocity distribution. Three possible
occurrences are observed: amplitude growth, decay and saturation.
a window reveals the rich complexity underlying the deceptively simple assumption of
local thermodynamic equilibrium. It displays also the failure of available approaches to
non-equilibrium thermodynamics.
in the hot spots observed in a plasma focus (PF) pinch, due to their huge values of particle density,
magnetic field and (reportedly) ion temperature. Accordingly, large magnetic fields should raise electronic
Landau levels, thus reducing collisional exchange of energy from ion to electrons and Bremsstrahlung losses.
Moreover, large particle densities, together with ion viscous heating, should allow fulfilment of Lawson
criterion and provide effective screening of cyclotron radiation. We invoke both well-known, empirical
scaling laws of PF physics, Connor-Taylor scaling laws, Poynting balance of electromagnetic energy and the
balance of generalised helicity. We show that the evolution of PF hot spots is a succession of relaxed states,
described by the double Beltrami solutions of Hall-MHD equations of motion. We obtain some necessary
conditions for ignition, which are violated in most realistic conditions. Large electromagnetic fields in the
hot spot accelerate electrons at supersonic velocities and trigger turbulence, which raises electric resistivity
and Joule heating, thus spoiling further compression. Ignition is only possible if a significant fraction of the
Bremsstrahlung-radiated power is reflected back into the plasma. Injection of angular momentum decreases
the required reflection coefficient.
in the hot spots observed in a plasma focus (PF) pinch, due to their huge values of particle density,
magnetic field and (reportedly) ion temperature. Accordingly, large magnetic fields should raise electronic
Landau levels, thus reducing collisional exchange of energy from ion to electrons and Bremsstrahlung losses.
Moreover, large particle densities, together with ion viscous heating, should allow fulfilment of Lawson
criterion and provide effective screening of cyclotron radiation. We invoke both well-known, empirical
scaling laws of PF physics, Connor-Taylor scaling laws, Poynting balance of electromagnetic energy and the
balance of generalised helicity. We show that the evolution of PF hot spots is a succession of relaxed states,
described by the double Beltrami solutions of Hall-MHD equations of motion. We obtain some necessary
conditions for ignition, which are violated in most realistic conditions. Large electromagnetic fields in the
hot spot accelerate electrons at supersonic velocities and trigger turbulence, which raises electric resistivity
and Joule heating, thus spoiling further compression. Ignition is only possible if a significant fraction of the
Bremsstrahlung-radiated power is reflected back into the plasma. Injection of angular momentum decreases
the required reflection coefficient.
the stability of dissipative fluids and plasmas, the authors claim that the basic equations of the paper are in
contradiction with the laws of thermodynamics of irreversible processes [Sonnino, Tlidi, and Evslin, preceding
paper, Phys. Rev. E 86, 043101 (2012)]. Here, we show that one of the basic equations of the Comment is just a
particular case of the results of the criticized paper. As for two further tenets of the Comment, counterexamples
are found in the literature and are discussed here.
depending on temperature, pressure etc. We apply Le Chatelier’s principle of thermodynamics to a
particular phase transition in TiHx, which can approximately be described as a second-order phase
transition. We show that the fluctuations of the order parameter correspond to fluctuations both of the
density of H+ ions and of the distance between adjacent H+ ions. Moreover, as the system approaches the
transition and the correlation radius increases we show –with the help of statistical mechanics– that the
statistical weight of modes involving a large number of H+ ions (‘collective modes’) increases sharply, in
spite of the fact that the Boltzmann factor of each collective mode is exponentially small. As a result, it
turns out that the interaction of the H+ ions with collective modes makes a tiny suprathermal fraction of the
H+ population to appear. Our results hold for similar transitions in metal deuterides too. A violation of a –
insofar undisputed– upper bound on hydrogen loading follows.
Well-known results of conventional MHD are retrieved as benchmark cases. It turns out that hot spots satisfy Taylor’s principle of constrained minimum of magnetic energy, the constraint being given by fixed magnetic helicity. Filaments are similar to the filaments of a superconductor and form a plasma with β = 0.11 and energy diffusion coefficient = 0.88DBohm. Any process – like e.g. radiative collapse – which raises particle density while reducing radial size may transform filaments into hot spots. A well-known scaling law is retrieved – the collisional Vlasov high beta scaling. A link between dissipation and topology is highlighted. Accordingly, a large-current pinch may give birth to tiny hot spots with large electron density and magnetic field.
Thermodynamics,” no “Maxent” method, and no “new” universal criterion of stability for steady states of systems with dissipation. Each criterion takes the form of—or is a consequence of—a variational principle. We
retrieve maximization of entropy for isolated systems at thermodynamic equilibrium, as expected. If the
boundary conditions keep the relaxed state far from thermodynamic equilibrium, the stability criterion we
retrieve depends also on the detailed balance of momentum of a small mass element. This balance may include
the grad-p-related force, the Lorenz force of electromagnetism and the forces which are gradients of potentials. In
order to be stable, the solution of the steady-state equations of motion for a given problem should satisfy the
relevant stability criterion. Retrieved criteria include among others Taylor’s minimization of magnetic energy
with the constraint of given magnetic helicity in relaxed, turbulent plasmas, Rayleigh’s criterion of stability in
thermoacoustics, Paltridge et al.’s maximum entropy production principle for Earth’s atmosphere, Chandrasekhar’
minimization of the adverse temperature gradient in Bénard’s convective cells, and Malkus’ maximization of viscous power with the constraint of given mean velocity for turbulent shear flow in channels. It turns out that characterization of systems far from equilibrium, e.g., by maximum entropy production is not a
general property but—just like minimum entropy production—is reserved to special systems. A taxonomy of stability criteria is derived, which clarifies what is to be minimized, what is to be maximized and with which constraint for each problem.