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Stochastic entropy production in the quite Sun magnetic fields
The second law of thermodynamics imposes an increase of macroscopic entropy with time in an isolated system. Microscopically, however, the entropy production can be negative for a single, microscopic realization of a thermodynamic process. The so-called fluctuation theorems provide exact relations between the stochastic entropy consumption and generation. Here, we analyse pixel-to-pixel fluctuations in time of small-scale magnetic fields (SSMF) in the quiet Sun observed with the SDO/HMI instrument. We demonstrate that entropy generated by SSMF obeys the fluctuation theorems. In particular, the SSMF entropy consumption probability is exactly exponentially smaller than the SSMF entropy generation probability. This may have fundamental implications for the magnetic energy budget of the Sun. © The Author(s) 2018. Published by Oxford University Press on behalf of The Royal Astronomical Society.
On the longtime behavior of a viscous Cahn-Hilliard system with convection and dynamic boundary conditions
In this paper, we study the longtime asymptotic behavior of a phase separation process occurring in a three-dimensional domain containing a fluid flow of given velocity. This process is modeled by a viscous convective CahnHilliard system, which consists of two nonlinearly coupled second-order partial differential equations for the unknown quantities, the chemical potential and an order parameter representing the scaled density of one of the phases. In contrast to other contributions, in which zero Neumann boundary conditions were are assumed for both the chemical potential and the order parameter, we consider the case of dynamic boundary conditions, which model the situation when another phase transition takes place on the boundary. The phase transition processes in the bulk and on the boundary are driven by free energies functionals that may be nondifferentiable and have derivatives only in the sense of (possibly set-valued) subdifferentials. For the resulting initial-boundary value system of CahnHilliard type, general well-posedness results have been established in a recent contribution by the same authors. In the present paper, we investigate the asymptotic behavior of the solutions as times approaches infinity. More precisely, we study the w-limit (in a suitable topology) of every solution trajectory. Under the assumptions that the viscosity coefficients are strictly positive and that at least one of the underlying free energies is differentiable, we prove that the w-limit is meaningful and that all of its elements are solutions to the corresponding stationary system, where the component representing the chemical potential is a constant.
The Propagation of Coherent Waves Across Multiple Solar Magnetic Pores
Solar pores are efficient magnetic conduits for propagating magnetohydrodynamic wave energy into the outer regions of the solar atmosphere. Pore observations often contain isolated and/or unconnected structures, preventing the statistical examination of wave activity as a function of the atmospheric height. Here, using high-resolution observations acquired by the Dunn Solar Telescope, we examine photospheric and chromospheric wave signatures from a unique collection of magnetic pores originating from the same decaying sunspot. Wavelet analysis of high-cadence photospheric imaging reveals the ubiquitous presence of slow sausage-mode oscillations, coherent across all photospheric pores through comparisons of intensity and area fluctuations, producing statistically significant in-phase relationships. The universal nature of these waves allowed an investigation of whether the wave activity remained coherent as they propagate. Utilizing bisector Doppler velocity analysis of the Ca ii 8542 Å line, alongside comparisons of the modeled spectral response function, we find fine-scale 5 mHz power amplification as the waves propagate into the chromosphere. Phase angles approaching zero degrees between co-spatial line depths spanning different line depths indicate standing sausage modes following reflection against the transition region boundary. Fourier analysis of chromospheric velocities between neighboring pores reveals the annihilation of the wave coherency observed in the photosphere, with examination of the intensity and velocity signals from individual pores indicating they behave as fractured waveguides, rather than monolithic structures. Importantly, this work highlights that wave morphology with atmospheric height is highly complex, with vast differences observed at chromospheric layers, despite equivalent wave modes being introduced into similar pores in the photosphere.
Modelling and experimental evidence of the cathode erosion in a plasma spray torch
The lifetime of tungsten cathodes used in plasma spray torches is limited by processes leading to a loss of cathode material. It was reported in the literature that the mechanism of their erosion is the evaporation. A model of the ionization layer of a cathode is developed to study the diffusive transport of evaporated tungsten atoms and tungsten ions produced due to ionization by electron impact in a background argon plasma. It is shown that the Stefan-Maxwell equations do not reduce to Fick law as one could expect for the transport of diluted species, which is due to significant diffusion velocities of argon ions. The ionization of tungsten atoms occurs in a distance of a few micrometers from the cathode surface and leads to a strong sink, which increases the net flux of tungsten atoms far beyond that obtained in absence of tungsten ions. This shows that the tungsten ions are driven by the electric field towards the cathode resulting in no net diffusive flux and no removal of tungsten species from the ionization layer even if convection is accounted for. A possible mechanism of removal is found by extending the model to comprise an anode. The extended model resolves the inter-electrode region and provides the plasma parameters for a current density corresponding to the value at the center of the cathode under typical arc currents of 600 A and 800 A. The presence of the anode causes a reversal of the electric field on the anode side, which pulls the ions away from the ionization layer of the cathode. The net flux of tungsten ions can be further fortified by convection. This model allows one to evaluate the loss of cathode material under realistic operating conditions in a quantitative agreement with measured values.
On a Cahn-Hilliard system with convection and dynamic boundary conditions
This paper deals with an initial and boundary value problem for a system coupling equation and boundary condition both of CahnHilliard type; an additional convective term with a forced velocity field, which could act as a control on the system, is also present in the equation. Either regular or singular potentials are admitted in the bulk and on the boundary. Both the viscous and pure CahnHilliard cases are investigated, and a number of results is proven about existence of solutions, uniqueness, regularity, continuous dependence, uniform boundedness of solutions, strict separation property. A complete approximation of the problem, based on the regularization of maximal monotone graphs and the use of a FaedoGalerkin scheme, is introduced and rigorously discussed.
Regional Saharan dust modelling during the SAMUM 2006 campaign
The regional dust model system LM-MUSCAT-DES was developed in the framework of the SAMUM project. Using the unique comprehensive data set of near-source dust properties during the 2006SAMUMfield campaign, the performance of the model system is evaluated for two time periods in May and June 2006. Dust optical thicknesses, number size distributions and the position of the maximum dust extinction in the vertical profiles agree well with the observations. However, the spatio-temporal evolution of the dust plumes is not always reproduced due to inaccuracies in the dust source placement by the model. While simulated winds and dust distributions are well matched for dust events caused by dry synoptic-scale dynamics, they are often misrepresented when dust emissions are caused by moist convection or influenced by small-scale topography that is not resolved by the model. In contrast to long-range dust transport, in the vicinity of source regions the model performance strongly depends on the correct prediction of the exact location of sources. Insufficiently resolved vertical grid spacing causes the absence of inversions in the model vertical profiles and likely explains the absence of the observed sharply defined dust layers.
Asymptotic limits and optimal control for the Cahn-Hilliard system with convection and dynamic boundary conditions
In this paper, we study initial-boundary value problems for the CahnHilliard system with convection and nonconvex potential, where dynamic boundary conditions are assumed for both the associated order parameter and the corresponding chemical potential. While recent works addressed the case of viscous CahnHilliard systems, the pure nonviscous case is investigated here. In its first part, the paper deals with the asymptotic behavior of the solutions as time approaches infinity. It is shown that the w-limit of any trajectory can be characterized in terms of stationary solutions, provided the initial data are sufficiently smooth. The second part of the paper deals with the optimal control of the system by the fluid velocity. Results concerning existence and first-order necessary optimality conditions are proved. Here, we have to restrict ourselves to the case of everywhere defined smooth potentials. In both parts of the paper, we start from corresponding known results for the viscous case, derive sufficiently strong estimates that are uniform with respect to the (positive) viscosity parameter, and then let the viscosity tend to zero to establish the sought results for the nonviscous case.
Nanometer-thick lateral polyelectrolyte micropatterns induce macrosopic electro-osmotic chaotic fluid instabilities
Electro-convective vortices in ion concentration polarization under shear flow have been of practical relevance for desalination processes using electrodialysis. The phenomenon has been scientifically disregarded for decades, but is recently embraced by a growing fluid dynamics community due its complex superposition of multi-scale gradients in electrochemical potential and space charge interacting with emerging complex fluid momentum gradients. While the visualization, quantification and fundamental understanding of the often-chaotic fluid dynamics is evolving rapidly due to sophisticated simulations and experimentation, little is known whether these instabilities can be induced and affected by chemical topological heterogeneity in surface properties. In this letter, we report that polyelectrolyte layers applied as micropatterns on ion exchange membranes induce and facilitate the electro-osmotic fluid instabilities. The findings stimulate a variety of fundamental questions comparable to the complexity of today's turbulence research.