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The temperature profiles of tokamak plasmas are obtained from a solution of the generalized Ohm's law, taking into account neoclassical resistivity, bootstrap currents, and nonstationary effects. These profiles have been coupled to a... more
The temperature profiles of tokamak plasmas are obtained from a solution of the generalized Ohm's law, taking into account neoclassical resistivity, bootstrap currents, and nonstationary effects. These profiles have been coupled to a MHD equilibrium code and to a zero-dimensional transport code to simulate time dependent tokamak discharges. In this report, some examples are given of the effect on plasma equilibrium, flux consumption, and fusion plasma performances of strong temperature peaking due to nonstationary conditions. The present approach allows estimates of the current diffusion times inside the plasma volume, when nonstationary effects are taken into account. These estimates have been shown to account both for the temperature profiles and for the stabilization times of monsters and giant sawteeth at JET and have been assumed in the time dependent simulations given in this report.
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Conventional waste heat recovery systems usually require water (e.g. to supply steam for a turbine) and imply the wearing of moving parts, to the detriment of usability in case of drought and/or in the long term. Unconventional approaches... more
Conventional waste heat recovery systems usually require water (e.g. to supply steam for a turbine) and imply the wearing of moving parts, to the detriment of usability in case of drought and/or in the long term. Unconventional approaches (thermoacoustic and thermoelectric conversion of heat into electricity) overcome these obstacles, but their utilization for multi Kilowatt (KW) electric power in an industrial environment is jeopardized either by large working pressure, excessive noise, the need for cooling systems or huge magnetic fields. Welander and Erhard et al. discuss the existence and the stability of steady-state convection driven by an applied temperature gradient of a fluid circulating in a tube that forms a vertical, closed loop. Convection ensures the spontaneous conversion of heat into mechanical energy through competing buoyancy, drag and heat conduction between the fluid and the walls of the tube. Crucially, their results do not depend on the nature of the drag. If t...
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Independent assessment of the feasibility of controlled nuclear fusion in the proposed SPARC tokamak (Creely et al., J. Plasma Phys., vol. 86, 2020, 865860502; Rodriguez-Fernandez et al., J. Plasma Phys., vol. 86, 2020, 865860503) is... more
Independent assessment of the feasibility of controlled nuclear fusion in the proposed SPARC tokamak (Creely et al., J. Plasma Phys., vol. 86, 2020, 865860502; Rodriguez-Fernandez et al., J. Plasma Phys., vol. 86, 2020, 865860503) is difficult because of the uncertainties concerning energy transport in the plasma. We discuss a SPARC scenario – where a burning plasma is obtained – with the help of a well-known general constraint on transport in weakly collisional, axisymmetric, toroidal, low- $\beta$ turbulent plasma (Rogister et al., Phys. Fluids B, vol. 4, 1992, p. 804). This constraint is useful in reducing uncertainties on auxiliary heating as the fusion gain begins to be large. No particular ad hoc model for transport coefficients is invoked. The crucial roles of both suitable tuning of ion cyclotron radiofrequency power and high-temperature pedestal are highlighted.
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A mapping of nonextensive statistical mechanics into Gibbs' statistical mechanics exists, which leads to a generalization of Einstein's formula for fluctuations. A unified treatment of stability of relaxed states in nonextensive... more
A mapping of nonextensive statistical mechanics into Gibbs' statistical mechanics exists, which leads to a generalization of Einstein's formula for fluctuations. A unified treatment of stability of relaxed states in nonextensive statistical mechanics and Gibbs' statistical mechanics follows. The former and the latter are endowed with probability distribution of microstates ruled by power laws and Boltzmann exponentials respectively. We apply our treatment to the relaxed states described by a 1D nonlinear FokkerPlanck equation. If the latter is associated to the stochastic differential equation obtained in the continuous limit from a 1D, autonomous, discrete map affected by noise, then we may ascertain whether if a relaxed state follow a power law distribution (and with which exponent) by looking at both map dynamics and noise level, with no assumptions concerning the additive or multiplicative nature of the noise and with no numerical computation of the orbits. Results a...
Research Interests: Physics and Proceedings
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... 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.
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The analogy between self-similar time series with given Hurst exponent H and Markovian, Gaussian stochastic processes with multiplicative noise and entropic index q (Borland, PRE 57, 6, 6634-6642, 1998) allow us to explain the empirical... more
The analogy between self-similar time series with given Hurst exponent H and Markovian, Gaussian stochastic processes with multiplicative noise and entropic index q (Borland, PRE 57, 6, 6634-6642, 1998) allow us to explain the empirical results reported in (Pavithran et al., EPL, 129 2020 24004) and (Pavithran et al. Sci. Reports 10.1 (2020) 1-8) with the help of the properties of the nonextensive entropy Sq of index q: a dominant oscillating mode arises as H goes to zero in many different systems and its amplitude is proportional to 1/ H^2 . Thus, a decrease of H acts as precursor of large oscillations of the state variable, which corresponds to catastrophic events in many problems of practical interest. In contrast, if H goes to 1 then the time series is strongly intermittent, fluctuations of the state variable follow a power law whose exponent depends on H, and exceedingly large event are basically unpredictable. These predictions agree with observations in problems of aeroacoust...
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Abstract The objective of this study was to design and test a prototype fertigation controller for the management of container ornamental nursery stocks irrigated with different water sources, including saline water or reclaimed... more
Abstract The objective of this study was to design and test a prototype fertigation controller for the management of container ornamental nursery stocks irrigated with different water sources, including saline water or reclaimed municipal/industrial wastewater. The prototype could schedule irrigation in various ways, i.e. as a time clock, or by means of a soil moisture dielectric sensor, or using a crop evapotranspiration (ET) model. The prototype also monitored the salinity in the root zone using a dielectric sensor that measured both substrate moisture and electrical conductivity (EC), or a probe measuring the EC of the water draining out of the containers. Excessive substrate salinization of the containers irrigated with saline water (containing 10 mM of sodium chloride) was prevented by the automated adoption of a series of measures: irrigation with fresh water or a mixture of fresh water and saline water; progressive increase of irrigation dose for each event, and progressive reduction of fertilizer concentration in the nutrient solution delivered to the crop. The system was tested in three experiments conducted in Pistoia (Italy) between 2008 and 2010 with two ornamental species: Photinia × fraseri Dress (a salt-medium tolerant species) and Prunus laurocerasus L. (a salt-sensitive species). When irrigation with fresh water was controlled with a dielectric sensor or an ET model, total irrigation water use and the loss of both N and P were reduced by 17% to 84% compared with the time-controlled irrigation. The sensor-based control of saline water irrigation reduced the salinity effects on dry matter accumulation in both species; however, it did not prevent the occurrence of leaf damages (leaf scorch) on Prunus plants, which were unmarketable by the end of growing season. On the contrary, no leaf damages were visible on Photinia plants irrigated with saline and/or fresh water, such that all were classified in the top quality market category. The controller developed in this work could be used in commercial nurseries to improve profitability and sustainability of container hardy ornamental nursery stock production.
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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... 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, the interaction of the H+ ions with collective modes makes a tiny suprathermal fraction of the H+ population appear. Our results hold for similar transitions in metal deuterides, too. A vio...
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Recently, a unique collision between two large-scale magnetized plasmoids produced by coronal mass ejections in the heliosphere has been observed (C. Shen et al. Nature 8, 2012). Results suggest that the collision is super-elastic, i.e.... more
Recently, a unique collision between two large-scale magnetized plasmoids produced by coronal mass ejections in the heliosphere has been observed (C. Shen et al. Nature 8, 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 et al., Mon. Not. R. Astron. Soc. 406 1140-1145 (2010) and S. Ohsaki et al., Ap. J. Lett. 559 L61 (2001) and show that the anti-correlation is just a consequence of Hall magnetohydrodynamics.
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Any satisfactorily description of humming (= dangerous, combustion-driven acoustic oscillation in gas-turbine burners) should include both acoustic and convective phenomena. In fact, the distance crossed by an element of fluid (with... more
Any satisfactorily description of humming (= dangerous, combustion-driven acoustic oscillation in gas-turbine burners) should include both acoustic and convective phenomena. In fact, the distance crossed by an element of fluid (with typical speed ca m/s) during one humming period (about 10 ms) is typically the distance L between the flame and the inlet of the air-fuel mixture (say 10 cm). Accordingly, no fully linear approach seems to be successful. Admittedly, humming-related pressure-perturbation amplitude (say, 10 mbar) is << the unperturbed working pressure (e.g. 10 bar), and the speed of a small fluid element in an acoustic wave (about 1 m/s) is << the unperturbed sound speed (about 500 m/s). Locally, however, the two velocities may be comparable, e.g. near the vortices' axis inside the burner, where the mean flow velocity vanishes. Moreover, available models often postulate the Mach number to vanish, a scarcely justifiable tenet]. Furthermore, the combined effe...
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Research Interests: Physics, Fluid Mechanics, Turbulence, Medicine, Physical sciences, and 11 moreShear Flow, Nonequilibrium thermodynamics, Nonequilbrium and irreversible thermodynamics, Symmetry Breaking, Boundary Layer, Couette Flow, Irreversible Thermodynamics, Initial Condition, Nonlinear Optimization, Optimal Path, and entropy production
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... 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 &quot;Extended Thermodynamics,&quot; no &quot;Maxent&quot; method, and no &quot;new&quot; 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 nablap-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&#39;s minimization of magnetic energy with the constraint of given magnetic helicity in relaxed, turbulent plasmas, Rayleigh&#39;s criterion of stability in thermoacoustics, Paltridge &#39;s maximum entropy production principle for Earth&#39;s atmosphere, Chandrasekhar&#39; minimization of the adverse temperature gradient in Bénard&#39;s convective cells, and Malkus&#39; 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.
Research Interests: Engineering, Thermodynamics, Medicine, Mathematical Sciences, Nonequilibrium and irreversible thermodynamics, and 11 morePhysical sciences, Shear Flow, Steady state, Nonequilbrium and irreversible thermodynamics, Temperature Gradient, Detailed Balance, Equation of Motion, Boolean Satisfiability, Boundary Condition, Heat Loss, and entropy production
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Some properties of the frequency spectrum of magnetic fluctuations in a tokamak two-species plasma are investigated. We start from the nonlinear resistive ballooning kinetic equation. A method based on the fluctuation-dissipation theorem... more
Some properties of the frequency spectrum of magnetic fluctuations in a tokamak two-species plasma are investigated. We start from the nonlinear resistive ballooning kinetic equation. A method based on the fluctuation-dissipation theorem of thermodynamics is employed. The frequency range |ωDe|/ω>|ω*e| is considered. The dependence of magnetic fluctuations on frequency and various macroscopic parameters is discussed. The influence of magnetic fluctuations on plasma thermodynamics is investigated.
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The role of filamentary current distributions in the evolution of plasma-focus discharges is discussed. The force-free structures affect the energy balance during the acceleration of the plasma sheath. As a consequence, saturation of the... more
The role of filamentary current distributions in the evolution of plasma-focus discharges is discussed. The force-free structures affect the energy balance during the acceleration of the plasma sheath. As a consequence, saturation of the neutron yield for high values of the energy stored in the capacitor bank occurs.
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A thermodynamic analysis of tokamak plasmas is developed, starting from a single-fluid model. Some general propertiesof entropy production in the plasma are discussed. An approach is employed that is more general than the one based on... more
A thermodynamic analysis of tokamak plasmas is developed, starting from a single-fluid model. Some general propertiesof entropy production in the plasma are discussed. An approach is employed that is more general than the one based on Onsager symmetry relationships. This choice appears to be justified by experiments. The concept of ‘thermodynamic stability’ is introduced, and a general criterion for the stability of stationary states far from thermodynamic equilibrium is assessed. An upper limit on the particle density is found to exist as a necessary condition in order to prevent disruptions. Analysis of the entropy balance shows that this limit is modified when neutral-beam heating is applied. Radial temperature profiles are shown to be stable against external heating under specific experimental conditions, inparticular when ion and electron temperatures are comparable. An offset scaling law for the energy confinement time TE = TE(Pinp) (with Pinp total input power) is obtained fo...
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Research Interests: Physics, Plasma Physics, Plasma based particle acceleration, Nuclear Fusion, Fusion research, and 9 moreExperimental Plasma Physics, Plasma, Physical sciences, Thermo Nuclear fusion, Control of Nuclear Fusion Devices, Theoretical plasma physics, Plasma Physics and Controlled Fusion, Basic Plasma Physics, and Fusion Science
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... 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 at each point, and the Gauss linking number of this unit vector 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 and the relative velocity of the filament with respect to the medium are appr...
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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... 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 nonnormality 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 Multiphy...
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The analogy between self-similar time series with given Hurst exponent H and Markovian, Gaussian stochastic processes with moltiplicative noise and entropic index q (Borland, PRE 57, 6, 6634-6642, 1998) allow us to explain the empirical... more
The analogy between self-similar time series with given Hurst exponent H and Markovian, Gaussian stochastic processes with moltiplicative noise and entropic index q (Borland, PRE 57, 6, 6634-6642, 1998) allow us to explain the empirical results reported in (Pavithran et al., EPL, 129 202
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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... 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.
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In a wide class of physical systems, diffeomorphisms in the state space leave the amount of entropy produced per unit time inside the bulk of the system unaffected [M. Polettini et al., 12th Joint European Thermodynamics Conference,... more
In a wide class of physical systems, diffeomorphisms in the state space leave the amount of entropy produced per unit time inside the bulk of the system unaffected [M. Polettini et al., 12th Joint European Thermodynamics Conference, Brescia, Italy, July 1-5, 2013]. This invariance implies that if relaxation towards some final ('relaxed') state occurs, 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 both detailed dynamics of the system, amplitude of fluctuations around mean values and possible occurrence of periodic oscillations in the relaxed state. Our discussion invokes no Onsager symmetry, no detailed model of heat transport and production, and no approximation of local thermodynamic equilibrium. This necessary condition of stability is the constrained minimization of time- and path-ensemble-averaged amount of entropy produced per unit time inside the bul...
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Abstract In monodimensional systems where a nonlinear Fokker-Planck equation [G.A. Casas et al., Phys. Rev. E 86 , 061136 (2012)] describes relaxation to a distribution function which behaves like a power law in the tail, we show that... more
Abstract In monodimensional systems where a nonlinear Fokker-Planck equation [G.A. Casas et al., Phys. Rev. E 86 , 061136 (2012)] describes relaxation to a distribution function which behaves like a power law in the tail, we show that perturbations of the relaxed distribution behave as avalanches in the sense of Self Organized Criticality [J. Nagler et al., Phys. Rev. E 60 , 2706 (1999)]. We determine the power laws followed by both size and return time of these avalanches whenever the relaxed distribution is resilient against perturbation of arbitrary amplitude in the tail. We apply our results to a class of problems in econophysics [J.R. Sanchez et al., Europhys. J. 143 , 241 (2007)] where the relaxed distribution of wealth is approximately described by Pareto’s principle [A. Di Vita, Europhys. J. 92 , 255 (2019)]. If the destruction of wealth associated with an avalanche is identified with a war, then we retrieve Richardson’s model of arms race [L.F. Richardson, Nature 136 , 1025 (1935)], prove that the largest avalanches follow Richardson’s scaling law of warfare [L.F. Richardson, J. Am. Stat. Assoc. 43 , 244 (1948)] and show that the probability of war outbreak per unit time follows a Poisson law [L.F. Richardson, Nature 155 , 610 (1945)], in agreement with the findings of [L. Cederman, Am. Polit. Sci. Rev. 97 , 135 (2003), A. Clauset, Sci. Adv. 4 (2018), G. Martelloni et al. arXiv:1812.08071 (2018)]. Graphical abstract
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Both in physical and in non-physical systems, the probability of extreme events depends on the slope of the tail of a distribution function. Prediction of this slope is often jeopardized by either poor knowledge of dynamics or statistical... more
Both in physical and in non-physical systems, the probability of extreme events depends on the slope of the tail of a distribution function. Prediction of this slope is often jeopardized by either poor knowledge of dynamics or statistical uncertainties. In many cases, however, the system attains a relaxed state, and extreme events correspond to large fluctuations near this state. Rather than starting from full (and often unavailable) knowledge of dynamics, we assume that a relaxed state exists and derive a necessary condition for its stability against fluctuations of arbitrary amplitude localized in the tail. In many problems, for suitably chosen variables this tail resembles either an exponential distribution or a power law. We take a q-exponential as a proxy of the tail; its slope depends on the dimensionless parameter q (q = 1 corresponds to an exponential). In turn, q-exponentials describe maxima of the non-extensive entropy Sq, and probabilities of fluctuations near a Sq = max state follow a generalized Einstein’s rule [E. Vives, A. Planes, Phys. Rev. Lett. 88, 020601 (2002)]. This rule provides the desired condition of stability, which allows us to write down a set of rules for semi-anaytical computation of the value qc of q in the relaxed state even with limited knowledge of dynamics. We apply these rules to a problem in econophysics [J.R. Sanchez, R. Lopez-Ruiz, Eur. Phys. J. Special Topics 143, 241 (2007)] and retrieve the main results of numerical solutions, namely the transition of a relaxed distribution of wealth from an exponential to a Pareto-like behaviour in the tail by suitable tuning of the relevant control parameters. A similar discussion holds for the scale parameter of lognormal distributions; we retrieve the results of [Z.N. Wu, J. Li, C.Y. Bai, Entropy 19, 56 (2017)].
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Recently, a unique collision between two large-scale magnetized plasmoids produced by coronal mass ejections in the heliosphere has been observed [C. Shen et al., Nat. Phys. 8, 923 (2012)]. Results suggest that the collision is... more
Recently, a unique collision between two large-scale magnetized plasmoids produced by coronal mass ejections in the heliosphere has been observed [C. Shen et al., Nat. Phys. 8, 923 (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 Bostick [IEEE Trans. Plasma Sci. PS-14, 703 (1986)], here we start from rst principles, retrieve some results of Ohsaki et al. [Astrophys. J. Lett. 559, L61 (2001)] and Kagan et al. [Mon. Not. R. Astron. Soc. 406, 1140 (2010)] and show that the anti-correlation is just a consequence of the properties of Joule and viscous dissipation inside the plasmoids. On the other end, if the initial relative velocity of the plasmoids is greater than the Alfve...
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A mapping of non-extensive statistical mechanics with non-additivity parameter q = 1 into Gibbs' statistical mechanics exists (E. Vives, A. Planes, PRL 88 2, 020601 (2002)) which allows generalization to q = 1 both of Einstein's... more
A mapping of non-extensive statistical mechanics with non-additivity parameter q = 1 into Gibbs' statistical mechanics exists (E. Vives, A. Planes, PRL 88 2, 020601 (2002)) which allows generalization to q = 1 both of Einstein's formula for fluctuations and of the 'general evolution criterion' (P. Glansdorff, I. Prigogine, Physica 30 351 (1964)), an inequality involving the time derivatives of thermodynamical quantities. Unified thermodynamic description of relaxation to stable states with either Boltzmann (q = 1) or power-law (q = 1) distribution of probabilities of microstates follows. If a 1D (possibly nonlinear) Fokker-Planck equation describes relaxation, then generalized Einstein's formula predicts whether the relaxed state exhibits a Boltzmann or a power law distribution function. If this Fokker-Planck equation is associated to the stochastic differential equation obtained in the continuous limit from a 1D, autonomous, discrete, noise-affected map, then we...
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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... 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 at each point, and the Gauss linking number of this unit vector 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 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.
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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,... 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.
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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... 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 approxim...