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  • 151. Käpylä, P. J.
    et al.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). University of Colorado, USA; Laboratory for Atmospheric and Space Physics, USA.
    Kleeorin, N.
    Käpylä, M. J.
    Rogachevskii, I.
    Magnetic flux concentrations from turbulent stratified convection2016Ingår i: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 588, artikel-id A150Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Context. The formation of magnetic flux concentrations within the solar convection zone leading to sunspot formation is unexplained. Aims. We study the self-organization of initially uniform sub-equipartition magnetic fields by highly stratified turbulent convection. Methods. We perform simulations of magnetoconvection in Cartesian domains representing the uppermost 8 : 5 24 Mm of the solar convection zone with the horizontal size of the domain varying between 34 and 96 Mm. The density contrast in the 24 Mm deep models is more than 3 x 10(3) or eight density scale heights, corresponding to a little over 12 pressure scale heights. We impose either a vertical or a horizontal uniform magnetic field in a convection-driven turbulent flow in set-ups where no small-scale dynamos are present. In the most highly stratified cases we employ the reduced sound speed method to relax the time step constraint arising from the high sound speed in the deep layers. We model radiation via the diffusion approximation and neglect detailed radiative transfer in order to concentrate on purely magnetohydrodynamic effects. Results. We find that super-equipartition magnetic flux concentrations are formed near the surface in cases with moderate and high density stratification, corresponding to domain depths of 12 : 5 and 24 Mm. The size of the concentrations increases as the box size increases and the largest structures (20 Mm horizontally near the surface) are obtained in the models that are 24 Mm deep. The field strength in the concentrations is in the range of 3-5 kG, almost independent of the magnitude of the imposed field. The amplitude of the concentrations grows approximately linearly in time. The effective magnetic pressure measured in the simulations is positive near the surface and negative in the bulk of the convection zone. Its derivative with respect to the mean magnetic field, however, is positive in most of the domain, which is unfavourable for the operation of the negative effective magnetic pressure instability (NEMPI). Simulations in which a passive vector field is evolved do not show a noticeable difference from magnetohydrodynamic runs in terms of the growth of the structures. Furthermore, we find that magnetic flux is concentrated in regions of converging flow corresponding to large-scale supergranulation convection pattern. Conclusions. The linear growth of large-scale flux concentrations implies that their dominant formation process is a tangling of the large-scale field rather than an instability. One plausible mechanism that can explain both the linear growth and the concentration of the flux in the regions of converging flow pattern is flux expulsion. A possible reason for the absence of NEMPI is that the derivative of the effective magnetic pressure with respect to the mean magnetic field has an unfavourable sign. Furthermore, there may not be sufficient scale separation, which is required for NEMPI to work.

  • 152. Käpylä, P. J.
    et al.
    Korpi, M. J.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Open and closed boundaries in large-scale convective dynamos2010Ingår i: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 518, artikel-id A22Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Context. Earlier work has suggested that large-scale dynamos can reach and maintain equipartition field strengths on a dynamical time scale only if magnetic helicity of the fluctuating field can be shed from the domain through open boundaries. Aims: Our aim is to test this scenario in convection-driven dynamos by comparing results for open and closed boundary conditions. Methods: Three-dimensional numerical simulations of turbulent compressible convection with shear and rotation are used to study the effects of boundary conditions on the excitation and saturation of large-scale dynamos. Open (vertical-field) and closed (perfect- conductor) boundary conditions are used for the magnetic field. The shear flow is such that the contours of shear are vertical, crossing the outer surface, and are thus ideally suited for driving a shear-induced magnetic helicity flux. Results: We find that for given shear and rotation rate, the growth rate of the magnetic field is larger if open boundary conditions are used. The growth rate first increases for small magnetic Reynolds number, Rm, but then levels off at an approximately constant value for intermediate values of Rm. For large enough Rm, a small-scale dynamo is excited and the growth rate of the field in this regime increases as Rm1/2. Regarding the nonlinear regime, the saturation level of the energy of the total magnetic field is independent of Rm when open boundaries are used. In the case of perfect-conductor boundaries, the saturation level first increases as a function of Rm, but then decreases proportional to Rm-1 for Rm ⪆ 30, indicative of catastrophic quenching. These results suggest that the shear-induced magnetic helicity flux is efficient in alleviating catastrophic quenching when open boundaries are used. The horizontally averaged mean field is still weakly decreasing as a function of Rm even for open boundaries.

  • 153. Käpylä, P. J.
    et al.
    Korpi, M. J.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    The alpha effect in rotating convection with sinusoidal shear2010Ingår i: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 402, nr 3, s. 1458-1466Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Using three-dimensional convection simulations, it is shown that a sinusoidal variation of horizontal shear leads to a kinematic alpha effect with a similar sinusoidal variation. The effect exists even for weak stratification and arises owing to the inhomogeneity of turbulence and the presence of impenetrable vertical boundaries. This system produces large-scale magnetic fields that also show a sinusoidal variation in the cross-stream direction. It is argued that earlier investigations overlooked these phenomena partly because of the use of horizontal averaging and also because measurements of alpha using an imposed field combined with long time averages give erroneous results. It is demonstrated that in such cases the actual horizontally averaged mean field becomes non-uniform. The turbulent magnetic diffusion term resulting from such non-uniform fields can then no longer be neglected and begins to balance the alpha effect.

  • 154. Käpylä, P. J.
    et al.
    Korpi, M. J.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    The α effect in rotating convection with sinusoidal shear2010Ingår i: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 402, nr 3, s. 1458-1466Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Using three-dimensional convection simulations, it is shown that a sinusoidal variation of horizontal shear leads to a kinematic α effect with a similar sinusoidal variation. The effect exists even for weak stratification and arises owing to the inhomogeneity of turbulence and the presence of impenetrable vertical boundaries. This system produces large-scale magnetic fields that also show a sinusoidal variation in the cross-stream direction. It is argued that earlier investigations overlooked these phenomena partly because of the use of horizontal averaging and also because measurements of α using an imposed field combined with long time averages give erroneous results. It is demonstrated that in such cases the actual horizontally averaged mean field becomes non-uniform. The turbulent magnetic diffusion term resulting from such non-uniform fields can then no longer be neglected and begins to balance the α effect.

  • 155. Käpylä, P. J.
    et al.
    Korpi, M. J.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Mitra, D.
    Tavakol, R.
    Convective dynamos in spherical wedge geometry2010Ingår i: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 331, nr 1, s. 73-81Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Self-consistent convective dynamo simulations in wedge-shaped spherical shells are presented. Differential rotation is generated by the interaction of convection with rotation. Equatorward acceleration and dynamo action are obtained only for sufficiently rapid rotation. The angular velocity tends to be constant along cylinders. Oscillatory large-scale fields are found to migrate in the poleward direction. Comparison with earlier simulations in full spherical shells and Cartesian domains is made.

  • 156. Käpylä, P. J.
    et al.
    Käpylä, M. J.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Confirmation of bistable stellar differential rotation profiles2014Ingår i: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 570, artikel-id A43Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Context. Solar-like differential rotation is characterized by a rapidly rotating equator and slower poles. However, theoretical models and numerical simulations can also result in a slower equator and faster poles when the overall rotation is slow. Aims. We study the critical rotational influence under which differential rotation flips from solar-like (fast equator, slow poles) to an anti-solar one (slow equator, fast poles). We also estimate the non-diffusive (A effect) and diffusive (turbulent viscosity) contributions to the Reynolds stress. Methods. We present the results of three-dimensional numerical simulations of mildly turbulent convection in spherical wedge geometry. Here we apply a fully compressible setup which would suffer from a prohibitive time step constraint if the real solar luminosity was used. To avoid this problem while still representing the same rotational influence on the flow as in the Sun, we increase the luminosity by a factor of roughly 106 and the rotation rate by a factor of 10(2). We regulate the convective velocities by varying the amount of heat transported by thermal conduction, turbulent diffusion, and resolved convection. Results. Increasing the efficiency of resolved convection leads to a reduction of the rotational influence on the flow and a sharp transition from solar-like to anti-solar differential rotation for Coriolis numbers around 1.3. We confirm the recent finding of a large-scale flow bistability: contrasted with running the models from an initial condition with unprescribed differential rotation, the initialization of the model with certain kind of rotation profile sustains the solution over a wider parameter range. The anti-solar profiles are found to be more stable against perturbations in the level of convective turbulent velocity than the solar-type solutions. Conclusions. Our results may have implications for real stars that start their lives as rapid rotators implying solar-like rotation in the early main-sequence evolution. As they slow down, they might be able to retain solar-like rotation for lower Coriolis numbers, and thus longer in time, before switching to anti-solar rotation. This could partially explain the puzzling findings of anti-solar rotation profiles for models in the solar parameter regime.

  • 157. Käpylä, P. J.
    et al.
    Käpylä, M. J.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). University of Colorado, Colorado; Laboratory for Atmospheric and Space Physics, Colorado.
    Small-scale dynamos in simulations of stratified turbulent convection2018Ingår i: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 339, nr 2-3, s. 127-133Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Small-scale dynamo action is often held responsible for the generation of quiet Sun magnetic fields. We aim to determine the excitation conditions and saturation level of small-scale dynamos in nonrotating turbulent convection at low magnetic Prandtl numbers. We use high-resolution direct numerical simulations of weakly stratified turbulent convection. We find that the critical magnetic Reynolds number for dynamo excitation increases as the magnetic Prandtl number is decreased, which might suggest that small-scale dynamo action is not automatically evident in bodies with small magnetic Prandtl numbers, such as the Sun. As a function of the magnetic Reynolds number (Rm), the growth rate of the dynamo is consistent with an Rm(1/2) scaling. No evidence for a logarithmic increase of the growth rate with Rm is found.

  • 158. Käpylä, P. J.
    et al.
    Käpylä, M. J.
    Olspert, N.
    Warnecke, J.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). University of Colorado, USA; Laboratory for Atmospheric and Space Physics, USA.
    Convection-driven spherical shell dynamos at varying Prandtl numbers2017Ingår i: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 599, artikel-id A4Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Context. Stellar convection zones are characterized by vigorous high-Reynolds number turbulence at low Prandtl numbers. Aims. We study the dynamo and differential rotation regimes at varying levels of viscous, thermal, and magnetic diffusion. Methods. We perform three-dimensional simulations of stratified fully compressible magnetohydrodynamic convection in rotating spherical wedges at various thermal and magnetic Prandtl numbers (from 0.25 to 2 and from 0.25 to 5, respectively). Differential rotation and large-scale magnetic fields are produced self-consistently. Results. We find that for high thermal diffusivity, the rotation profiles show a monotonically increasing angular velocity from the bottom of the convection zone to the top and from the poles toward the equator. For sufficiently rapid rotation, a region of negative radial shear develops at mid-latitudes as the thermal diffusivity is decreased, corresponding to an increase of the Prandtl number. This coincides with and results in a change of the dynamo mode from poleward propagating activity belts to equatorward propagating ones. Furthermore, the clearly cyclic solutions disappear at the highest magnetic Reynolds numbers and give way to irregular sign changes or quasi-stationary states. The total (mean and fluctuating) magnetic energy increases as a function of the magnetic Reynolds number in the range studied here (5-151), but the energies of the mean magnetic fields level off at high magnetic Reynolds numbers. The differential rotation is strongly affected by the magnetic fields and almost vanishes at the highest magnetic Reynolds numbers. In some of our most turbulent cases, however, we find that two regimes are possible, where either differential rotation is strong and mean magnetic fields are relatively weak, or vice versa. Conclusions. Our simulations indicate a strong nonlinear feedback of magnetic fields on differential rotation, leading to qualitative changes in the behaviors of large-scale dynamos at high magnetic Reynolds numbers. Furthermore, we do not find indications of the simulations approaching an asymptotic regime where the results would be independent of diffusion coefficients in the parameter range studied here.

  • 159. Käpylä, P. J.
    et al.
    Mantere, M. J.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Effects of stratification in spherical shell convection2011Ingår i: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 332, artikel-id 883Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We report on simulations of mildly turbulent convection in spherical wedge geometry with varying density stratification. We vary the density contrast within the convection zone by a factor of 20 and study the influence of rotation on the solutions. We demonstrate that the size of convective cells decreases and the anisotropy of turbulence increases as the stratification is increased. Differential rotation is found to change from anti-solar (slow equator) to solar-like (fast equator) at roughly the same Coriolis number for all stratifications. The largest stratification runs, however, are sensitive to changes of the Reynolds number. Evidence for a near-surface shear layer is found in runs with strong stratification and large Reynolds numbers.

  • 160. Käpylä, P. J.
    et al.
    Mantere, M. J.
    Guerrero, G.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Chatterjee, P.
    Reynolds stress and heat flux in spherical shell convection2011Ingår i: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 531, artikel-id A162Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Context. Turbulent fluxes of angular momentum and enthalpy or heat due to rotationally affected convection play a key role in determining differential rotation of stars. Their dependence on latitude and depth has been determined in the past from convection simulations in Cartesian or spherical simulations. Here we perform a systematic comparison between the two geometries as a function of the rotation rate. Aims. Here we want to extend the earlier studies by using spherical wedges to obtain turbulent angular momentum and heat transport as functions of the rotation rate from stratified convection. We compare results from spherical and Cartesian models in the same parameter regime in order to study whether restricted geometry introduces artefacts into the results. In particular, we want to clarify whether the sharp equatorial profile of the horizontal Reynolds stress found in earlier Cartesian models is also reproduced in spherical geometry. Methods. We employ direct numerical simulations of turbulent convection in spherical and Cartesian geometries. In order to alleviate the computational cost in the spherical runs, and to reach as high spatial resolution as possible, we model only parts of the latitude and longitude. The rotational influence, measured by the Coriolis number or inverse Rossby number, is varied from zero to roughly seven, which is the regime that is likely to be realised in the solar convection zone. Cartesian simulations are performed in overlapping parameter regimes. Results. For slow rotation we find that the radial and latitudinal turbulent angular momentum fluxes are directed inward and equatorward, respectively. In the rapid rotation regime the radial flux changes sign in accordance with earlier numerical results, but in contradiction with theory. The latitudinal flux remains mostly equatorward and develops a maximum close to the equator. In Cartesian simulations this peak can be explained by the strong banana cells. Their effect in the spherical case does not appear to be as large. The latitudinal heat flux is mostly equatorward for slow rotation but changes sign for rapid rotation. Longitudinal heat flux is always in the retrograde direction. The rotation profiles vary from anti-solar (slow equator) for slow and intermediate rotation to solar-like (fast equator) for rapid rotation. The solar-like profiles are dominated by the Taylor-Proudman balance.

  • 161. Käpylä, Petri J.
    et al.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    Turbulent Dynamos with Shear and Fractional Helicity2009Ingår i: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 699, s. 1059-1066Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Dynamo action owing to helically forced turbulence and large-scale shear is studied using direct numerical simulations. The resulting magnetic field displays propagating wave-like behavior. This behavior can be modeled in terms of an αΩ dynamo. In most cases super-equipartition fields are generated. By varying the fraction of helicity of the turbulence the regeneration of poloidal fields via the helicity effect (corresponding to the α-effect) is regulated. The saturation level of the magnetic field in the numerical models is consistent with a linear dependence on the ratio of the fractional helicities of the small and large-scale fields, as predicted by a simple nonlinear mean-field model. As the magnetic Reynolds number (Re M ) based on the wavenumber of the energy-carrying eddies is increased from 1 to 180, the cycle frequency of the large-scale field is found to decrease by a factor of about 6 in cases where the turbulence is fully helical. This is interpreted in terms of the turbulent magnetic diffusivity, which is found to be only weakly dependent on the Re M .

  • 162. Käpylä, Petri J.
    et al.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Korpi, Maarit J.
    Snellman, Jan E.
    Narayan, Ramesh
    Angular Momentum Transport in Convectively Unstable Shear Flows2010Ingår i: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 719, s. 67-76Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Angular momentum transport due to hydrodynamic turbulent convection is studied using local three-dimensional numerical simulations employing the shearing box approximation. We determine the turbulent viscosity from non-rotating runs over a range of values of the shear parameter and use a simple analytical model in order to extract the non-diffusive contribution (Λ-effect) to the stress in runs where rotation is included. Our results suggest that the turbulent viscosity is on the order of the mixing length estimate and weakly affected by rotation. The Λ-effect is non-zero and a factor of 2-4 smaller than the turbulent viscosity in the slow rotation regime. We demonstrate that for Keplerian shear, the angular momentum transport can change sign and be outward when the rotation period is greater than the turnover time, i.e., when the Coriolis number is below unity. This result seems to be relatively independent of the value of the Rayleigh number.

  • 163.
    Käpylä, Petri J.
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Georg-August-Universität Göttingen, Germany; Leibniz-Institut für Astrophysik, Germany; ReSoLVE Centre of Excellence, Finland; Max-Planck-Institut für Sonnensystemforschung, Germany.
    Gent, F. A.
    Olspert, N.
    Käpylä, M. J.
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. University of Colorado, USA; Laboratory for Atmospheric and Space Physics, Boulder, USA.
    Sensitivity to luminosity, centrifugal force, and boundary conditions in spherical shell convection2020Ingår i: Geophysical and Astrophysical Fluid Dynamics, ISSN 0309-1929, E-ISSN 1029-0419, Vol. 114, nr 1-2, s. 8-34Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We test the sensitivity of hydrodynamic and magnetohydrodynamic turbulent convection simulations with respect to Mach number, thermal and magnetic boundary conditions, and the centrifugal force. We find that varying the luminosity, which also controls the Mach number, has only a minor effect on the large-scale dynamics. A similar conclusion can also be drawn from the comparison of two formulations of the lower magnetic boundary condition with either vanishing electric field or current density. The centrifugal force has an effect on the solutions, but only if its magnitude with respect to acceleration due to gravity is by two orders of magnitude greater than in the Sun. Finally, we find that the parameterisation of the photospheric physics, either by an explicit cooling term or enhanced radiative diffusion, is more important than the thermal boundary condition. In particular, runs with cooling tend to lead to more anisotropic convection and stronger deviations from the Taylor-Proudman state. In summary, the fully compressible approach taken here with the Pencil Code is found to be valid, while still allowing the disparate timescales to be taken into account.

  • 164.
    Käpylä, Petri J.
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). University of Helsinki, Finland.
    Mantere, M. J.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Oscillatory large-scale dynamos from Cartesian convection simulations2013Ingår i: Geophysical and Astrophysical Fluid Dynamics, ISSN 0309-1929, E-ISSN 1029-0419, Vol. 107, nr 1-2, s. 244-257Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We present results from compressible Cartesian convection simulations with and without imposed shear. In the former case the dynamo is expected to be of 2 type, which is generally expected to be relevant for the Sun, whereas the latter case refers to 2 dynamos that are more likely to occur in more rapidly rotating stars whose differential rotation is small. We perform a parameter study where the shear flow and the rotational influence are varied to probe the relative importance of both types of dynamos. Oscillatory solutions are preferred both in the kinematic and saturated regimes when the negative ratio of shear to rotation rates, qS/, is between 1.5 and 2, i.e. when shear and rotation are of comparable strengths. Other regions of oscillatory solutions are found with small values of q, i.e. when shear is weak in comparison to rotation, and in the regime of large negative qs, when shear is very strong in comparison to rotation. However, exceptions to these rules also appear so that for a given ratio of shear to rotation, solutions are non-oscillatory for small and large shear, but oscillatory in the intermediate range. Changing the boundary conditions from vertical field to perfect conductor ones changes the dynamo mode from oscillatory to quasi-steady. Furthermore, in many cases an oscillatory solution exists only in the kinematic regime whereas in the nonlinear stage the mean fields are stationary. However, the cases with rotation and no shear are always oscillatory in the parameter range studied here and the dynamo mode does not depend on the magnetic boundary conditions. The strengths of total and large-scale components of the magnetic field in the saturated state, however, are sensitive to the chosen boundary conditions.

  • 165. Käpylä, Petri J.
    et al.
    Mantere, Maarit J.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    CYCLIC MAGNETIC ACTIVITY DUE TO TURBULENT CONVECTION IN SPHERICAL WEDGE GEOMETRY2012Ingår i: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 755, nr 1, artikel-id L22Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We report on simulations of turbulent, rotating, stratified, magnetohydrodynamic convection in spherical wedge geometry. An initially small-scale, random, weak-amplitude magnetic field is amplified by several orders of magnitude in the course of the simulation to form oscillatory large-scale fields in the saturated state of the dynamo. The differential rotation is solar-like (fast equator), but neither coherent meridional poleward circulation nor near-surface shear layer develop in these runs. In addition to a poleward branch of magnetic activity beyond 50 degrees latitude, we find for the first time a pronounced equatorward branch at around 20 degrees latitude, reminiscent of the solar cycle.

  • 166. Käpylä, Petri J.
    et al.
    Mantere, Maarit J.
    Cole, Elisabeth
    Warnecke, Jörn
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    Effects of strong stratification on equatorward dynamo wave propagationManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    We present results from simulations of rotating magnetized  turbulent convection in spherical wedge geometry representing parts  of the latitudinal and longitudinal extents of a star.  Here we consider a set of runs for which the density stratification is  varied, keeping the  Reynolds and Coriolis numbers at similar values. In the case of weak  stratification we find quasi-steady solutions for moderate rotation and oscillatory dynamos with poleward migration of activity belts  for more rapid rotation. For stronger stratification a similar transition as a function of the Coriolis number is found, but with an equatorward migrating branch near the equator. We test the domain size dependence of our results for a rapidly rotating run with equatorward migration by varying the longitudinal  extent of our wedge. The energy of the axisymmetric mean magnetic field decreases as the domain size increases and we find that an  m=1 mode is excited for a full 2π φ-extent, reminiscent of the  field configurations deduced from observations of rapidly rotating late-type stars.

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  • 167. Käpylä, Petri J.
    et al.
    Mantere, Maarit J.
    Cole, Elizabeth
    Warnecke, Jörn
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    EFFECTS OF ENHANCED STRATIFICATION ON EQUATORWARD DYNAMO WAVE PROPAGATION2013Ingår i: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 778, nr 1, artikel-id 41Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We present results from simulations of rotating magnetized turbulent convection in spherical wedge geometry representing parts of the latitudinal and longitudinal extents of a star. Here we consider a set of runs for which the density stratification is varied, keeping the Reynolds and Coriolis numbers at similar values. In the case of weak stratification, we find quasi-steady dynamo solutions for moderate rotation and oscillatory ones with poleward migration of activity belts for more rapid rotation. For stronger stratification, the growth rate tends to become smaller. Furthermore, a transition from quasi-steady to oscillatory dynamos is found as the Coriolis number is increased, but now there is an equatorward migrating branch near the equator. The breakpoint where this happens corresponds to a rotation rate that is about three to seven times the solar value. The phase relation of the magnetic field is such that the toroidal field lags behind the radial field by about pi/2, which can be explained by an oscillatory alpha(2) dynamo caused by the sign change of the alpha-effect about the equator. We test the domain size dependence of our results for a rapidly rotating run with equatorward migration by varying the longitudinal extent of our wedge. The energy of the axisymmetric mean magnetic field decreases as the domain size increases and we find that an m = 1 mode is excited for a full 2 pi azimuthal extent, reminiscent of the field configurations deduced from observations of rapidly rotating late-type stars.

  • 168. Käpylä, Petri J.
    et al.
    Rheinhardt, Matthias
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). University of Colorado, USA; Laboratory for Atmospheric and Space Physics, USA.
    Arlt, Rainer
    Käpylä, Maarit J.
    Lagg, Andreas
    Olspert, Nigul
    Warnecke, Joern
    Extended Subadiabatic Layer in Simulations of Overshooting Convection2017Ingår i: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 845, nr 2, artikel-id L23Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We present numerical simulations of hydrodynamic overshooting convection in local Cartesian domains. We find that a substantial fraction of the lower part of the convection zone (CZ) is stably stratified according to the Schwarzschild criterion while the enthalpy flux is outward directed. This occurs when the heat conduction profile at the bottom of the CZ is smoothly varying, based either on a Kramers-like opacity prescription as a function of temperature and density or a static profile of a similar shape. We show that the subadiabatic layer arises due to nonlocal energy transport by buoyantly driven downflows in the upper parts of the CZ. Analysis of the force balance of the upflows and downflows confirms that convection is driven by cooling at the surface. We find that the commonly used prescription for the convective enthalpy flux being proportional to the negative entropy gradient does not hold in the stably stratified layers where the flux is positive. We demonstrate the existence of a non-gradient contribution to the enthalpy flux, which is estimated to be important throughout the convective layer. A quantitative analysis of downflows indicates a transition from a tree-like structure where smaller downdrafts merge into larger ones in the upper parts to a structure in the deeper parts where a height-independent number of strong downdrafts persist. This change of flow topology occurs when a substantial subadiabatic layer is present in the lower part of the CZ.

  • 169.
    Käpylä, Petri J.
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Georg-August-Universität Göttingen, Germany; Leibniz-Institut für Astrophysik, Germany; ReSoLVE Centre of Excellence, Finland, Max-Planck-Institut für Sonnensystemforschung, Germany.
    Viviani, M.
    Käpylä, M. J.
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. University of Colorado, USA; Laboratory for Atmospheric and Space Physics, USA.
    Spada, F.
    Effects of a subadiabatic layer on convection and dynamos in spherical wedge simulations2019Ingår i: Geophysical and Astrophysical Fluid Dynamics, ISSN 0309-1929, E-ISSN 1029-0419, Vol. 113, nr 1-2, s. 149-183Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider the effect of a subadiabatic layer at the base of the convection zone on convection itself and the associated large-scale dynamos in spherical wedge geometry. We use a heat conduction prescription based on the Kramers opacity law which allows the depth of the convection zone to dynamically adapt to changes in the physical characteristics such as rotation rate and magnetic fields. We find that the convective heat transport is strongly concentrated towards the equatorial and polar regions in the cases without a substantial radiative layer below the convection zone. The presence of a stable layer below the convection zone significantly reduces the anisotropy of radial enthalpy transport. Furthermore, the dynamo solutions are sensitive to subtle changes in the convection zone structure. We find that the kinetic helicity changes sign in the deeper parts of the convection zone at high latitudes in all runs. This region expands progressively towards the equator in runs with a thicker stably stratified layer.

  • 170.
    Li, Xiang-Yu
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Meteorologiska institutionen (MISU). Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Swedish e-Science Research Centre, Sweden; University of Colorado, USA.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). University of Colorado, USA.
    Haugen, N. E. L.
    Svensson, Gunilla
    Stockholms universitet, Naturvetenskapliga fakulteten, Meteorologiska institutionen (MISU). Swedish e-Science Research Centre, Sweden; National Center for Atmospheric Research, USA.
    Eulerian and Lagrangian approaches to multidimensional condensation and collection2017Ingår i: Journal of Advances in Modeling Earth Systems, ISSN 1942-2466, Vol. 9, nr 2, s. 1116-1137Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Turbulence is argued to play a crucial role in cloud droplet growth. The combined problem of turbulence and cloud droplet growth is numerically challenging. Here an Eulerian scheme based on the Smoluchowski equation is compared with two Lagrangian superparticle (or superdroplet) schemes in the presence of condensation and collection. The growth processes are studied either separately or in combination using either two-dimensional turbulence, a steady flow or just gravitational acceleration without gas flow. Good agreement between the different schemes for the time evolution of the size spectra is observed in the presence of gravity or turbulence. The Lagrangian superparticle schemes are found to be superior over the Eulerian one in terms of computational performance. However, it is shown that the use of interpolation schemes such as the cloud-in-cell algorithm is detrimental in connection with superparticle or superdroplet approaches. Furthermore, the use of symmetric over asymmetric collection schemes is shown to reduce the amount of scatter in the results. For the Eulerian scheme, gravitational collection is rather sensitive to the mass bin resolution, but not so in the case with turbulence. Plain Language Summary The bottleneck problem of cloud droplet growth is one of the most challenging problems in cloud physics. Cloud droplet growth is neither dominated by condensation nor gravitational collision in the size range of 15 mu m similar to 40 mu m [1]. Turbulence-generated collection has been thought to be the mechanism to bridge the size gap, i.e., the bottleneck problem. This study compares the Lagrangian and Eulerian schemes in detail to tackle with the turbulence-generated collection.

  • 171.
    Li, Xiang-Yu
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Meteorologiska institutionen (MISU). Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Swedish e-Science Research Centre, Sweden; University of Colorado Boulder, USA.
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. University of Colorado Boulder, USA.
    Svensson, Gunilla
    Stockholms universitet, Naturvetenskapliga fakulteten, Meteorologiska institutionen (MISU). Swedish e-Science Research Centre, Sweden.
    Haugen, Nils E. L.
    Mehlig, Bernhard
    Rogachevskii, Igor
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel.
    Condensational and Collisional Growth of Cloud Droplets in a Turbulent Environment2020Ingår i: Journal of the Atmospheric Sciences, ISSN 0022-4928, E-ISSN 1520-0469, Vol. 77, nr 1, s. 337-353Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We investigate the effect of turbulence on the combined condensational and collisional growth of cloud droplets by means of high-resolution direct numerical simulations of turbulence and a superparticle approximation for droplet dynamics and collisions. The droplets are subject to turbulence as well as gravity, and their collision and coalescence efficiencies are taken to be unity. We solve the thermodynamic equations governing temperature, water vapor mixing ratio, and the resulting supersaturation fields together with the Navier-Stokes equation. We find that the droplet size distribution broadens with increasing Reynolds number and/or mean energy dissipation rate. Turbulence affects the condensational growth directly through supersaturation fluctuations, and it influences collisional growth indirectly through condensation. Our simulations show for the first time that, in the absence of the mean updraft cooling, supersaturation-fluctuation-induced broadening of droplet size distributions enhances the collisional growth. This is contrary to classical (nonturbulent) condensational growth, which leads to a growing mean droplet size, but a narrower droplet size distribution. Our findings, instead, show that condensational growth facilitates collisional growth by broadening the size distribution in the tails at an early stage of rain formation. With increasing Reynolds numbers, evaporation becomes stronger. This counteracts the broadening effect due to condensation at late stages of rain formation. Our conclusions are consistent with results of laboratory experiments and field observations, and show that supersaturation fluctuations are important for precipitation.

  • 172.
    Li, Xiang-Yu
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Meteorologiska institutionen (MISU). Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Swedish e-Science Research Centre, Sweden; University of Colorado, USA.
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. University of Colorado, USA.
    Svensson, Gunilla
    Stockholms universitet, Naturvetenskapliga fakulteten, Meteorologiska institutionen (MISU). Swedish e-Science Research Centre, Sweden; Global & Climate Dynamics, National Center for Atmospheric Research, USA.
    Haugen, Nils E. L.
    Mehlig, Bernhard
    Rogachevskii, Igor
    Effect of turbulence on collisional growth of cloud droplets2018Ingår i: Journal of the Atmospheric Sciences, ISSN 0022-4928, E-ISSN 1520-0469, Vol. 75, s. 3469-3487Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We investigate the effect of turbulence on the collisional growth of um-sized droplets through high- resolution numerical simulations with well resolved Kolmogorov scales, assuming a collision and coalescence efficiency of unity. The droplet dynamics and collisions are approximated using a superparticle approach. In the absence of gravity, we show that the time evolution of the shape of the droplet-size distribution due to turbulence-induced collisions depends strongly on the turbulent energy-dissipation rate, but only weakly on the Reynolds number. This can be explained through the energy dissipation rate dependence of the mean collision rate described by the Saffman-Turner collision model. Consistent with the Saffman-Turner collision model and its extensions, the collision rate increases as the square root of the energy dissipation rate even when coalescence is invoked. The size distribution exhibits power law behavior with a slope of -3.7 between a maximum at approximately 10 um up to about 40 um. When gravity is invoked, turbulence is found to dominate the time evolution of an initially monodisperse droplet distribution at early times. At later times, however, gravity takes over and dominates the collisional growth. We find that the formation of large droplets is very sensitive to the turbulent energy dissipation rate. This is due to the fact that turbulence enhances the collisional growth between similar sized droplets at the early stage of raindrop formation. The mean collision rate grows exponentially, which is consistent with the theoretical prediction of the continuous collisional growth even when turbulence-generated collisions are invoked. This consistency only reflects the mean effect of turbulence on collisional growth.

  • 173.
    Li, Xiang-Yu
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Meteorologiska institutionen (MISU). Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Mehlig, Bernhard
    Svensson, Gunilla
    Stockholms universitet, Naturvetenskapliga fakulteten, Meteorologiska institutionen (MISU).
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Haugen, Nils
    Fluctuations and growth histories of cloud droplets: super-particle simulations of the collision-coalescence processManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    Direct numerical simulations of collisional aggregation in turbulent aerosols are computationally demanding. Many authors therefore use an approximate model of the collision-coalescence process that is computationally more efficient: it relies on representing physical particles in terms of ‘superparticles’. One monitors collisions between superparticles and accounts for collisions between physical particles using a Monte-Carlo algorithm. It has been shown that this algorithm can faithfully represent mean particle growth in turbulent aerosols. Here we investigate how fluctuations are represented in this algorithm. We study particles of different sizes settling under gravity, assuming that the effect of turbulence is simply to mix the particles horizontally. We compute the statistics of growth histories and analyze their fluctuations in terms of the ‘lucky-droplet’ model. We discuss under which circumstances artefacts change the fluctuations of the growth histories, how these can be avoided, and which questions remain to be answered when turbulent fluctuations are explicitly incorporated.

  • 174.
    Li, Xiang-Yu
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Meteorologiska institutionen (MISU). Stockholms universitet, Naturvetenskapliga fakulteten, Bolincentret för klimatforskning (tills m KTH & SMHI). Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Swedish e-Science Research Centre, Sweden; University of Colorado Boulder, USA.
    Mehlig, Bernhard
    Svensson, Gunilla
    Stockholms universitet, Naturvetenskapliga fakulteten, Meteorologiska institutionen (MISU). Stockholms universitet, Naturvetenskapliga fakulteten, Bolincentret för klimatforskning (tills m KTH & SMHI). Swedish e-Science Research Centre, Sweden.
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC). University of Colorado Boulder, USA.
    Haugen, Nils E. L.
    Collision Fluctuations of Lucky Droplets with Superdroplets2022Ingår i: Journal of the Atmospheric Sciences, ISSN 0022-4928, E-ISSN 1520-0469, Vol. 79, nr 7, s. 1821-1835Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    It was previously shown that the superdroplet algorithm for modeling the collision-coalescence process can faithfully represent mean droplet growth in turbulent clouds. An open question is how accurately the superdroplet algorithm accounts for fluctuations in the collisional aggregation process. Such fluctuations are particularly important in dilute suspensions. Even in the absence of turbulence, Poisson fluctuations of collision times in dilute suspensions may result in substantial variations in the growth process, resulting in a broad distribution of growth times to reach a certain droplet size. We quantify the accuracy of the superdroplet algorithm in describing the fluctuating growth history of a larger droplet that settles under the effect of gravity in a quiescent fluid and collides with a dilute suspension of smaller droplets that were initially randomly distributed in space (lucky droplet model). We assess the effect of fluctuations upon the growth history of the lucky droplet and compute the distribution of cumulative collision times. The latter is shown to be sensitive enough to detect the subtle increase of fluctuations associated with collisions between multiple lucky droplets. The superdroplet algorithm incorporates fluctuations in two distinct ways: through the random spatial distribution of superdroplets and through the Monte Carlo collision algorithm involved. Using specifically designed numerical experiments, we show that both on their own give an accurate representation of fluctuations. We conclude that the superdroplet algorithm can faithfully represent fluctuations in the coagulation of droplets driven by gravity.

  • 175.
    Li, Xiang-Yu
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Meteorologiska institutionen (MISU). Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Swedish e-Science Research Centre, Sweden; University of Colorado, USA.
    Svensson, Gunilla
    Stockholms universitet, Naturvetenskapliga fakulteten, Meteorologiska institutionen (MISU). Swedish e-Science Research Centre, Sweden; National Center for Atmospheric Research, USA.
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. University of Colorado, USA.
    Haugen, Nils E. L.
    Cloud-droplet growth due to supersaturation fluctuations in stratiform clouds2019Ingår i: Atmospheric Chemistry And Physics, ISSN 1680-7316, E-ISSN 1680-7324, Vol. 19, nr 1, s. 639-648Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Condensational growth of cloud droplets due to supersaturation fluctuations is investigated by solving the hydrodynamic and thermodynamic equations using direct numerical simulations (DNS) with droplets being modeled as Lagrangian particles. The supersaturation field is calculated directly by simulating the temperature and water vapor fields instead of being treated as a passive scalar. Thermodynamic feedbacks to the fields due to condensation are also included for completeness. We find that the width of droplet size distributions increases with time, which is contrary to the classical theory without supersaturation fluctuations, where condensational growth leads to progressively narrower size distributions. Nevertheless, in agreement with earlier Lagrangian stochastic models of the condensational growth, the standard deviation of the surface area of droplets increases as t(1/2). Also, for the first time, we explicitly demonstrate that the time evolution of the size distribution is sensitive to the Reynolds number, but insensitive to the mean energy dissipation rate. This is shown to be due to the fact that temperature fluctuations and water vapor mixing ratio fluctuations increase with increasing Reynolds number; therefore the resulting supersaturation fluctuations are enhanced with increasing Reynolds number. Our simulations may explain the broadening of the size distribution in stratiform clouds qualitatively, where the mean updraft velocity is almost zero.

  • 176.
    Losada, Illa Rivero
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Warnecke, Jörn
    Max-Planck Insitute for Solar system Research.
    Glogowski, Kolja
    Kiepenheuer-Institu für Sonnenphysik.
    Roth, Markus
    Kiepenheuer-Institu für Sonnenphysik.
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Kleeorin, Nathan
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Department of Mechanical Engineering, Ben-Gurion University of the Negev.
    Rogachevskii, Igor
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Department of Mechanical Engineering, Ben-Gurion University of the Negev.
    A new look at sunspot formation using theory and observations2017Ingår i: Proceedings of the International Astronomical Union, 2017, Vol. 327, s. 46-59Konferensbidrag (Refereegranskat)
    Abstract [en]

    Sunspots are of basic interest in the study of the Sun. Their relevance ranges from them being an activity indicator of magnetic fields to being the place where coronal mass ejections and flares erupt. They are therefore also an important ingredient of space weather. Their formation, however, is still an unresolved problem in solar physics. Observations utilize just 2D surface information near the spot, but it is debatable how to infer deep structures and properties from local helioseismology. For a long time, it was believed that flux tubes rising from the bottom of the convection zone are the origin of the bipolar sunspot structure seen on the solar surface. However, this theory has been challenged, in particular recently by new surface observation, helioseismic inversions, and numerical models of convective dynamos. In this article we discuss another theoretical approach to the formation of sunspots: the negative effective magnetic pressure instability. This is a large-scale instability, in which the total (kinetic plus magnetic) turbulent pressure can be suppressed in the presence of a weak large-scale magnetic field, leading to a converging downflow, which eventually concentrates the magnetic field within it. Numerical simulations of forced stratified turbulence have been able to produce strong super-equipartition flux concentrations, similar to sunspots at the solar surface. In this framework, sunspots would only form close to the surface due to the instability constraints on stratification and rotation. Additionally, we present some ideas from local helioseismology, where we plan to use the Hankel analysis to study the pre-emergence phase of a sunspot and to constrain its deep structure and formation mechanism.

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  • 177.
    Madarassy, Eniko J. M.
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    Calibrating passive scalar transport in shear-flow turbulence2010Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 82, nr 1, artikel-id 16304Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The turbulent diffusivity tensor is determined for linear shear-flow turbulence using numerical simulations. For moderately strong shear, the diagonal components are found to increase quadratically with Peclet and Reynolds numbers below about 10 and then become constant. The diffusivity tensor is found to have components proportional to the symmetric and antisymmetric parts of the velocity gradient matrix, as well as products of these. All components decrease with the wave number of the mean field in a Lorentzian fashion. The components of the diffusivity tensor are found not to depend significantly on the presence of helicity in the turbulence. The signs of the leading terms in the expression for the diffusion tensor are found to be in good agreement with estimates based on a simple closure assumption.

  • 178. Miesch, Mark
    et al.
    Matthaeus, William
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Petrosyan, Arakel
    Pouquet, Annick
    Cambon, Claude
    Jenko, Frank
    Uzdensky, Dmitri
    Stone, James
    Tobias, Steve
    Toomre, Juri
    Velli, Marco
    Large-Eddy Simulations of Magnetohydrodynamic Turbulence in Heliophysics and Astrophysics2015Ingår i: Space Science Reviews, ISSN 0038-6308, E-ISSN 1572-9672, Vol. 194, nr 1-4, s. 97-137Artikel, forskningsöversikt (Refereegranskat)
    Abstract [en]

    We live in an age in which high-performance computing is transforming the way we do science. Previously intractable problems are now becoming accessible by means of increasingly realistic numerical simulations. One of the most enduring and most challenging of these problems is turbulence. Yet, despite these advances, the extreme parameter regimes encountered in space physics and astrophysics (as in atmospheric and oceanic physics) still preclude direct numerical simulation. Numerical models must take a Large Eddy Simulation (LES) approach, explicitly computing only a fraction of the active dynamical scales. The success of such an approach hinges on how well the model can represent the subgrid-scales (SGS) that are not explicitly resolved. In addition to the parameter regime, heliophysical and astrophysical applications must also face an equally daunting challenge: magnetism. The presence of magnetic fields in a turbulent, electrically conducting fluid flow can dramatically alter the coupling between large and small scales, with potentially profound implications for LES/SGS modeling. In this review article, we summarize the state of the art in LES modeling of turbulent magnetohydrodynamic (MHD) flows. After discussing the nature of MHD turbulence and the small-scale processes that give rise to energy dissipation, plasma heating, and magnetic reconnection, we consider how these processes may best be captured within an LES/SGS framework. We then consider several specific applications in heliophysics and astrophysics, assessing triumphs, challenges, and future directions.

  • 179. Mitra, D.
    et al.
    Candelaresi, S.
    Chatterjee, P.
    Tavakol, R.
    Brandenburg, A.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    Equatorial magnetic helicity flux in simulations with different gauges2010Ingår i: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 331, nr 1, s. 130-135Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    % We use direct numerical simulations of forced MHD turbulence with a forcing function that produces two different signs of kinetic helicity in the upper and lower parts of the domain. We show that the mean flux of magnetic helicity from the small-scale field between the two parts of the domain can be described by a Fickian diffusion law with a diffusion coefficient that is approximately independent of the magnetic Reynolds number and about one third of the estimated turbulent magnetic diffusivity. The data suggest that the turbulent diffusive magnetic helicity flux can only be expected to alleviate catastrophic quenching at Reynolds numbers of more than several thousands. We further calculate the magnetic helicity density and its flux in the domain for three different gauges. We consider the Weyl gauge, in which the electrostatic potential vanishes, the pseudo-Lorenz gauge, where the speed of light is replaced by the sound speed, and the `resistive gauge' in which the Laplacian of the magnetic vector potential acts as a resistive term. We find that, in the statistically steady state, the time-averaged magnetic helicity density and the magnetic helicity flux are the same in all three gauges.

  • 180. Mitra, D.
    et al.
    Moss, D.
    Tavakol, R.
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    Alleviating alpha quenching by solar wind and meridional flows2011Ingår i: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 526, s. A138-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Aims. We study the ability of magnetic helicity expulsion to alleviate catastrophic alpha-quenching in mean field dynamos in two-dimensional spherical wedge domains. Methods. Motivated by the physical state of the outer regions of the Sun, we consider alpha(2)Omega mean field models with a dynamical a quenching. We include two mechanisms which have the potential to facilitate helicity expulsion, namely advection by a mean flow (solar wind) and meridional circulation. Results. We find that a wind alone can prevent catastrophic quenching, with the field saturating at finite amplitude. In certain parameter ranges, the presence of a large-scale meridional circulation can reinforce this alleviation. However, the saturated field strengths are typically below the equipartition field strength. We discuss possible mechanisms that might increase the saturated field.

  • 181.
    Mitra, Dhrubaditya
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Scaling and intermittency in incoherent alpha-shear dynamo2012Ingår i: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 420, nr 3, s. 2170-2177Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider mean-field dynamo models with fluctuating a effect, both with and without large-scale shear. The a effect is chosen to be Gaussian white noise with zero mean and a given covariance. In the presence of shear, we show analytically that (in infinitely large domains) the mean-squared magnetic field shows exponential growth. The growth rate of the fastest growing mode is proportional to the shear rate. This result agrees with earlier numerical results of Yousef et al. and the recent analytical treatment by Heinemann, McWilliams & Schekochihin who use a method different from ours. In the absence of shear, an incoherent a2 dynamo may also be possible. We further show by explicit calculation of the growth rate of third- and fourth-order moments of the magnetic field that the probability density function of the mean magnetic field generated by this dynamo is non-Gaussian.

  • 182.
    Mitra, Dhrubaditya
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Dasgupta, Brahmananda
    Niklasson, Eyvind
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Ram, Abhay
    Particle energization through time-periodic helical magnetic fields2014Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 89, nr 4, s. 042919-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We solve for the motion of charged particles in a helical time-periodic ABC (Arnold-Beltrami-Childress) magnetic field. The magnetic field lines of a stationary ABC field with coefficients A = B = C = 1 are chaotic, and we show that the motion of a charged particle in such a field is also chaotic at late times with positive Lyapunov exponent. We further show that in time-periodic ABC fields, the kinetic energy of a charged particle can increase indefinitely with time. At late times the mean kinetic energy grows as a power law in time with an exponent that approaches unity. For an initial distribution of particles, whose kinetic energy is uniformly distributed within some interval, the probability density function of kinetic energy is, at late times, close to a Gaussian but with steeper tails.

  • 183.
    Mitra, Dhrubaditya
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Kleeorin, N.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel; N. I. Lobachevsky State University of Nizhny Novgorod, Russia.
    Rogachevskii, Igor
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Ben-Gurion University of the Negev, Israel; N. I. Lobachevsky State University of Nizhny Novgorod, Russia.
    Intense bipolar structures from stratified helical dynamos2014Ingår i: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 445, nr 1, s. 761-769Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We perform direct numerical simulations of the equations of magnetohydrodynamics with external random forcing and in the presence of gravity. The domain is divided into two parts: a lower layer where the forcing is helical and an upper layer where the helicity of the forcing is zero with a smooth transition in between. At early times, a large-scale helical dynamo develops in the bottom layer. At later times the dynamo saturates, but the vertical magnetic field continues to develop and rises to form dynamic bipolar structures at the top, which later disappear and reappear. Some of the structures look similar to delta spots observed in the Sun. This is the first example of magnetic flux concentrations, owing to strong density stratification, from self-consistent dynamo simulations that generate bipolar, super-equipartition strength, magnetic structures whose energy density can exceeds the turbulent kinetic energy by even a factor of 10.

  • 184. Mitra, Dhrubaditya
    et al.
    Tavakol, Reza
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Käpylä, Petri J.
    Oscillatory migratory large-scale fields in mean-field and direct simulations2009Ingår i: Proceedings of the International Astronomical Union, ISSN 1743-9213, E-ISSN 1743-9221, Vol. 5, s. 197-201Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We summarise recent results form direct numerical simulations of both non-rotating helically forced and rotating convection driven MHD equations in spherical wedge-shape domains. In the former, using perfect-conductor boundary conditions along the latitudinal boundaries we observe oscillations, polarity reversals and equatorward migration of the large-scale magnetic fields. In the latter we obtain angular velocity with cylindrical contours and large-scale magnetic field which shows oscillations, polarity reversals but poleward migration. The occurrence of these behviours in direct numerical simulations is clearly of interest. However the present models as they stand are not directly applicable to the solar dynamo problem. Nevertheless, they provide general insights into the operation of turbulent dynamos.

  • 185. Mitra, Dhrubaditya
    et al.
    Tavakol, Reza
    Käpylä, Petri J.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    OSCILLATORY MIGRATING MAGNETIC FIELDS IN HELICAL TURBULENCE IN SPHERICAL DOMAINS2010Ingår i: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 719, nr 1, s. L1-L4Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We present direct numerical simulations of the equations of compressible magnetohydrodynamics in a wedge-shaped spherical shell, without shear, but with random helical forcing which has negative (positive) helicity in the northern (southern) hemisphere. We find a large-scalemagnetic field that is nearly uniform in the azimuthal direction and approximately antisymmetric about the equator. Furthermore, the large-scale field in each hemisphere oscillates on nearly dynamical timescales with reversals of polarity and equatorward migration. Corresponding mean-field models also show similar migratory oscillations with a frequency that is nearly independent of the magnetic Reynolds number. This mechanism may be relevant for understanding equatorward migration seen in the solar dynamo.

  • 186.
    Mitra, Dhrubaditya
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Wettlaufer, John S.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    CAN PLANETESIMALS FORM BY COLLISIONAL FUSION?2013Ingår i: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 773, nr 2, s. 120-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    As a test bed for the growth of protoplanetary bodies in a turbulent circumstellar disk, we examine the fate of a boulder using direct numerical simulations of particle seeded gas flowing around it. We provide an accurate description of the flow by imposing no-slip and non-penetrating boundary conditions on the boulder surface using the immersed boundary method pioneered by Peskin. Advected by the turbulent disk flow, the dust grains collide with the boulder and we compute the probability density function of the normal component of the collisional velocity. Through this examination of the statistics of collisional velocities, we test the recently developed concept of collisional fusion which provides a physical basis for a range of collisional velocities exhibiting perfect sticking. A boulder can then grow sufficiently rapidly to settle into a Keplerian orbit on disk evolution timescales.

  • 187. Mizerski, Krzysztof A.
    et al.
    Yokoi, Nobumitsu
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC). School of Natural Sciences and Medicine, Georgia; Carnegie Mellon University, USA.
    Cross-helicity effect on α-type dynamo in non-equilibrium turbulence2023Ingår i: Journal of Plasma Physics, ISSN 0022-3778, E-ISSN 1469-7807, Vol. 89, nr 4, artikel-id 905890412Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Turbulence is typically not in equilibrium, i.e. mean quantities such as the mean energy and helicity are typically time-dependent. The effect of non-stationarity on the turbulent hydromagnetic dynamo process is studied here with the use of the two-scale direct-interaction approximation, which allows one to explicitly relate the mean turbulent Reynolds and Maxwell stresses and the mean electromotive force to the spectral characteristics of turbulence, such as the mean energy, as well as kinetic and cross-helicity. It is demonstrated that the non-equilibrium effects can enhance the dynamo process when the magnetohydrodynamic turbulence is both helical and cross-helical. This effect is based on the turbulent infinitesimal-impulse cross-response functions, which do not affect turbulent flows in equilibrium. The evolution and sources of the cross-helicity in magnetohydrodynamic turbulence are also discussed.

  • 188.
    Modestov, Mikhail
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Bychkov, V.
    Brodin, G.
    Marklund, M.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Evolution of the magnetic field generated by the Kelvin-Helmholtz instability2014Ingår i: Physics of Plasmas, ISSN 1070-664X, E-ISSN 1089-7674, Vol. 21, nr 7, s. 072126-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The Kelvin-Helmholtz instability in an ionized plasma is studied with a focus on the magnetic field generation via the Biermann battery (baroclinic) mechanism. The problem is solved by using direct numerical simulations of two counter-directed flows in 2D geometry. The simulations demonstrate the formation of eddies and their further interaction and merging resulting in a large single vortex. In contrast to general belief, it is found that the instability generated magnetic field may exhibit significantly different structures from the vorticity field, despite the mathematically identical equations controlling the magnetic field and vorticity evolution. At later stages of the nonlinear instability development, the magnetic field may keep growing even after the hydrodynamic vortex strength has reached its maximum and started decaying due to dissipation.

  • 189. Mtchedlidze, Salome
    et al.
    Domínguez-Fernández, Paola
    Du, Xiaolong
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC).
    Kahniashvili, Tina
    O'Sullivan, Shane
    Schmidt, Wolfram
    Brüggen, Marcus
    Evolution of Primordial Magnetic Fields during Large-scale Structure Formation2022Ingår i: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 929, nr 2, artikel-id 127Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Primordial magnetic fields (PMFs) could explain the large-scale magnetic fields present in the universe. Inflation and phase transitions in the early universe could give rise to such fields with unique characteristics. We investigate the magnetohydrodynamic evolution of these magnetogenesis scenarios with cosmological simulations. We evolve inflation-generated magnetic fields either as (i) uniform (homogeneous) or as (ii) scale-invariant stochastic fields, and phase-transition-generated ones either as (iii) helical or as (iv) nonhelical fields from the radiation-dominated epoch. We find that the final distribution of magnetic fields in the simulated cosmic web shows a dependence on the initial strength and the topology of the seed field. Thus, the observed field configuration retains information on the initial conditions at the moment of the field generation. If detected, PMF observations would open a new window for indirect probes of the early universe. The differences between the competing models are revealed on the scale of galaxy clusters, bridges, as well as filaments and voids. The distinctive spectral evolution of different seed fields produces imprints on the correlation length today. We discuss how the differences between rotation measures from highly ionized regions can potentially be probed with forthcoming surveys.

  • 190. Mtchedlidze, Salome
    et al.
    Domínguez-Fernández, Paola
    Du, Xiaolong
    Schmidt, Wolfram
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC). Ilia State University, Georgia; Carnegie Mellon University, USA.
    Niemeyer, Jens
    Kahniashvili, Tina
    Inflationary and Phase-transitional Primordial Magnetic Fields in Galaxy Clusters2023Ingår i: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 944, nr 1, artikel-id 100Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Primordial magnetic fields (PMFs) are possible candidates for explaining the observed magnetic fields in galaxy clusters. Two competing scenarios of primordial magnetogenesis have been discussed in the literature: inflationary and phase-transitional. We study the amplification of both large- and small-scale correlated magnetic fields, corresponding to inflation- and phase transition–generated PMFs, in a massive galaxy cluster. We employ high-resolution magnetohydrodynamic cosmological zoom-in simulations to resolve the turbulent motions in the intracluster medium. We find that the turbulent amplification is more efficient for the large-scale inflationary models, while the phase transition–generated seed fields show moderate growth. The differences between the models are imprinted on the spectral characteristics of the field (such as the amplitude and the shape of the magnetic power spectrum) and therefore also on the final correlation length. We find a one order of magnitude difference between the final strengths of the inflation- and phase transition–generated magnetic fields, and a factor of 1.5 difference between their final coherence scales. Thus, the final configuration of the magnetic field retains information about the PMF generation scenarios. Our findings have implications for future extragalactic Faraday rotation surveys with the possibility of distinguishing between different magnetogenesis scenarios.

  • 191. Perri, B.
    et al.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). University of Colorado, USA.
    Spontaneous flux concentrations from the negative effective magnetic pressure instability beneath a radiative stellar surface2018Ingår i: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 609, artikel-id A99Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Context. The formation of sunspots requires the concentration of magnetic flux near the surface. The negative effective magnetic pressure instability (NEMPI) might be a possible mechanism for accomplishing this, but it has mainly been studied in simple systems using an isothermal equation of state without a natural free surface. Aims. We study NEMPI in a stratified Cartesian mean-field model where turbulence effects are parameterized. We use an ideal equation of state and include radiation transport, which establishes selfconsistently a free surface. Methods. We use a Kramers-type opacity with adjustable exponents chosen such that the deeper layers are approximately isentropic. No convection is therefore possible in this model, allowing us to study NEMPI with radiation in isolation. We restrict ourselves to two-dimensional models. We use artificially enhanced mean-field coefficients to allow NEMPI to develop, thereby making it possible to study the reason why it is much harder to excite in the presence of radiation. Results. NEMPI yields moderately strong magnetic flux concentrations a certain distance beneath the surface where the optical depth is unity. The instability is oscillatory and in the form of upward traveling waves. This seems to be a new effect that has not been found in earlier models without radiative transport. The horizontal wavelength is about ten times smaller than what has previously been found in more idealized isothermal models. Conclusions. In our models, NEMPI saturates at field strengths too low to explain sunspots. Furthermore, the structures appear too narrow and too far beneath the surface to cause significant brightness variations at the radiative surface. We speculate that the failure to reproduce effects resembling sunspots may be related to the neglect of convection.

  • 192. Plasson, Raphael
    et al.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Jullien, Ludovic
    Bersini, Hugues
    Autocatalyses2011Ingår i: Journal of Physical Chemistry A, ISSN 1089-5639, E-ISSN 1520-5215, Vol. 115, nr 28, s. 8073-8085Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Autocatalysis is a fundamental concept, used in a wide range of domains. From the most general definition of autocatalysis, that is, a process in which a chemical compound is able to catalyze its own formation, several different systems can be described. We detail the different categories of autocatalyses and compare them on the basis of their mechanistic, kinetic, and dynamic properties. It is shown how autocatalytic patterns can be generated by different systems of chemical reactions. With the notion of autocatalysis covering a large variety of mechanistic realizations with very similar behaviors, it is proposed that the key signature of autocatalysis is its kinetic pattern expressed in a mathematical form.

  • 193. Plasson, Raphael
    et al.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Jullien, Ludovic
    Bersini, Hugues
    Autocatalysis: At the Root of Self-Replication2011Ingår i: Artificial Life, ISSN 1064-5462, E-ISSN 1530-9185, Vol. 17, nr 3, s. 219-236Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Autocatalysis is a fundamental concept, used in a wide range of domains. From its most general definition, that is, a process in which a chemical compound is able to catalyze its own formation, several different systems can be described. We detail the different categories of autocatalyses, and compare them on the basis of their mechanistic, kinetic, and dynamic properties. It is shown how autocatalytic patterns can be generated by different systems of chemical reactions. The notion of autocatalysis covers a large variety of mechanistic realizations with very similar behaviors; it is proposed that its key signature is its kinetic pattern expressed in a mathematical form. This notion, while describing dynamic behaviors at the most fundamental level, is at the basis for developing higher-level concepts towards life: autocatalytic sets and autopoietic systems.

  • 194. Plasson, Raphaël
    et al.
    Brandenburg, Axel
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi.
    Homochirality and the Need for Energy2010Ingår i: Origins of life and evolution of the biosphere, ISSN 0169-6149, E-ISSN 1573-0875, Vol. 40, s. 93-110Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The mechanisms for explaining how a stable asymmetric chemical system can be formed from a symmetric chemical system, in the absence of any asymmetric influence other than statistical fluctuations, have been developed during the last decades, focusing on the non-linear kinetic aspects. Besides the absolute necessity of self-amplification processes, the importance of energetic aspects is often underestimated. Going down to the most fundamental aspects, the distinction between a single object—that can be intrinsically asymmetric—and a collection of objects—whose racemic state is the more stable one—must be emphasized. A system of strongly interacting objects can be described as one single object retaining its individuality and a single asymmetry; weakly or non-interacting objects keep their own individuality, and are prone to racemize towards the equilibrium state. In the presence of energy fluxes, systems can be maintained in an asymmetric non-equilibrium steady-state. Such dynamical systems can retain their asymmetry for times longer than their racemization time.

  • 195. Pol, Alberto Roper
    et al.
    Mandal, Sayan
    Brandenburg, Axel
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för astronomi. Stockholms universitet, Naturvetenskapliga fakulteten, Oskar Klein-centrum för kosmopartikelfysik (OKC). Carnegie Mellon University, U.S.A.; Ilia State University, Georgia.
    Kahniashvili, Tina
    Polarization of gravitational waves from helical MHD turbulent sources2022Ingår i: Journal of Cosmology and Astroparticle Physics, E-ISSN 1475-7516, nr 4, artikel-id 019Artikel i tidskrift (Refereegranskat)
    Abstract [en]