arXiv subjects

Axel Brandenburg

Publications and source records attributed to Axel Brandenburg.

At least 91 records · Page 5Linked to original sources

arXiv2021

On the existence of shear-current effects in magnetized burgulence

The possibility of explaining shear flow dynamos by a magnetic shear-current (MSC) effect is examined via numerical simulations. Our primary diagnostics is the determination of the turbulent magnetic diffusivity tensor $\boldsymbolη$. In our setup, a negative sign of its component $η_{yx}$ is necessary for coherent dynamo action by the SC effect. To be able to measure turbulent transport coefficients from systems with magnetic background turbulence, we present an extension of the test-field method (TFM), applicable to our setup where the pressure gradient is dropped from the momentum equation: the nonlinear TFM (NLTFM). Our momentum equation is related to Burgers' equation and the resulting flows are referred to as magnetized burgulence. We use both stochastic kinetic and magnetic forcings to mimic cases without and with simultaneous small-scale dynamo action (SSD). When we force only kinetically, negative $η_{yx}$ are obtained with exponential growth in both the radial and azimuthal mean magnetic field components. Using isotropic magnetic forcing, the field growth is no longer exponential, while NLTFM yields positive $η_{yx}$. By employing an alternative forcing from which wavevectors having small components are removed, the exponential growth is recovered, but the NLTFM results do not change significantly. Analyzing the dynamo excitation conditions for the coherent SC and incoherent $α$ and SC effects shows that the incoherent effects are the main drivers of the dynamo in the majority of cases. We find no evidence for MSC-effect-driven dynamos in our simulations.

physics.flu-dyn↗

arXiv2020

Homochirality: a prerequisite or consequence of life?

Many of the building blocks of life such as amino acids and nucleotides are chiral, i.e., different from their mirror image. Contemporary life selects and synthesizes only one of two possible handednesses. In an abiotic environment, however, there are usually equally many left- and right-handed molecules. If homochirality was a prerequisite of life, there must have been physical or chemical circumstances that led to the selection of a certain preference. Conversely, if it was a consequence of life, we must identify possible pathways for accomplishing a transition from a racemic to a homochiral chemistry. After a discussion of the observational evidence, I will review ideas where homochirality of any handedness could emerge as a consequence of the first polymerization events of nucleotides in an emerging RNA world. These mechanisms are not limited to nucleotides, but can also occur for peptides, as a precursor to the RNA world. The question of homochirality is, in this sense, intimately tied to the origin of life. Future Mars missions may be able to detect biomolecules of extant or extinct life. We will therefore also discuss possible experimental setups for determining the chirality of primitive life forms in situ on Mars.

q-bio.BM↗

arXiv2020

Piecewise quadratic growth during the 2019 novel coronavirus epidemic

The temporal growth in the number of deaths in the COVID-19 epidemic is subexponential. Here we show that a piecewise quadratic law provides an excellent fit during the thirty days after the first three fatalities on January 20 and later since the end of March 2020. There is also a brief intermediate period of exponential growth. During the second quadratic growth phase, the characteristic time of the growth is about eight times shorter than in the beginning, which can be understood as the occurrence of separate hotspots. Quadratic behavior can be motivated by peripheral growth when further spreading occurs only on the outskirts of an infected region. We also study numerical solutions of a simple epidemic model, where the spatial extend of the system is taken into account. To model the delayed onset outside China together with the early one in China within a single model with minimal assumptions, we adopt an initial condition of several hotspots, of which one reaches saturation much earlier than the others. At each site, quadratic growth commences when the local number of infections has reached a certain saturation level. The total number of deaths does then indeed follow a piecewise quadratic behavior.

q-bio.PE↗

arXiv2020

Hall cascade with fractional magnetic helicity in neutron star crusts

The ohmic decay of magnetic fields in the crusts of neutron stars is generally believed to be governed by Hall drift which leads to what is known as a Hall cascade. Here we show that helical and fractionally helical magnetic fields undergo strong inverse cascading like in magnetohydrodynamics (MHD), but the magnetic energy decays more slowly with time $t$: $\propto t^{-2/5}$ instead of $\propto t^{-2/3}$ in MHD. Even for a nonhelical magnetic field there is a certain degree of inverse cascading for sufficiently strong magnetic fields. The inertial range scaling with wavenumber $k$ is compatible with earlier findings for the forced Hall cascade, i.e., proportional to $k^{-7/3}$, but in the decaying cases, the subinertial range spectrum steepens to a novel $k^5$ slope instead of the $k^4$ slope in MHD. The energy of the large-scale magnetic field can increase quadratically in time through inverse cascading. For helical fields, the energy dissipation is found to be inversely proportional to the large-scale magnetic field and proportional to the fifth power of the root-mean square (rms) magnetic field. For neutron star conditions with an rms magnetic field of a few times $10^{14}\,$G, the large-scale magnetic field might only be $10^{11}\,$G, while still producing magnetic dissipation of $10^{33}\,$erg$\,$s$^{-1}$ for thousands of years, which could manifest itself through X-ray emission. Finally, it is shown that the conclusions from local unstratified models agree rather well with those from stratified models with boundaries.

astro-ph.HE↗

arXiv2020

Primordial magnetic helicity evolution with a homogeneous magnetic field from inflation

Motivated by a scenario of magnetogenesis in which a homogeneous magnetic field is generated during inflation, we study the magnetohydrodynamic evolution of the primordial plasma motions for two kinds of initial conditions -- (i) a spatially homogeneous field with an unlimited correlation length, and (ii) a zero flux scale-invariant statistically homogeneous magnetic field. In both cases, we apply, for a short initial time interval, monochromatic forcing at a certain wave number so that the correlation length is finite, but much smaller than the typical length scale of turbulence. In particular, we investigate the decay of nonhelical and helical hydromagnetic turbulence. We show that, in the presence of a homogeneous magnetic field, the decay of helical and nonhelical small-scale fields can occur rapidly. This is a special property of a system with a perfectly homogeneous magnetic field, which is sometimes considered as a local approximation to a slowly varying background field. It can never change and acts as an imposed magnetic field. This is in a sharp contrast to the case of a statistically homogeneous magnetic field, where we recover familiar decay properties: a much slower decay of magnetic energy and a faster growth of the correlation length, especially in the case with magnetic felicity. The result suggests that a homogeneous magnetic field, if generated during inflation, should persist under the influence of small-scale fields and could be the origin of the large-scale magnetic field in the Universe.

astro-ph.CO↗

arXiv2020

Prospective Prediction of Future SARS-CoV-2 Infections Using Empirical Data on a National Level to Gauge Response Effectiveness

Predicting an accurate expected number of future COVID-19 cases is essential to properly evaluate the effectiveness of any treatment or preventive measure. This study aimed to identify the most appropriate mathematical model to prospectively predict the expected number of cases without any intervention. The total number of cases for the COVID-19 epidemic in 28 countries was analyzed and fitted to several simple rate models including the logistic, Gompertz, quadratic, simple square, and simple exponential growth models. The resulting model parameters were used to extrapolate predictions for more recent data. While the Gompertz growth models (mean R2 = 0.998) best fitted the current data, uncertainties in the eventual case limit made future predictions with logistic models prone to errors. Of the other models, the quadratic rate model (mean R2 = 0.992) fitted the current data best for 25 (89 %) countries as determined by R2 values. The simple square and quadratic models accurately predicted the number of future total cases 37 and 36 days in advance respectively, compared to only 15 days for the simple exponential model. The simple exponential model significantly overpredicted the total number of future cases while the quadratic and simple square models did not. These results demonstrated that accurate future predictions of the case load in a given country can be made significantly in advance without the need for complicated models of population behavior and generate a reliable assessment of the efficacy of current prescriptive measures against disease spread.

q-bio.PE↗

arXiv2020

Dynamo in weakly collisional nonmagnetized plasmas impeded by Landau damping of magnetic fields

We perform fully kinetic simulations of flows known to produce dynamo in magnetohydrodynamics (MHD), considering scenarios with low Reynolds number and high magnetic Prandtl number, relevant for galaxy cluster scale fluctuation dynamos. We find that Landau damping on the electrons leads to a rapid decay of magnetic perturbations, impeding the dynamo. This collisionless damping process operates on spatial scales where electrons are nonmagnetized, reducing the range of scales where the magnetic field grows in high magnetic Prandtl number fluctuation dynamos. When electrons are not magnetized down to the resistive scale, the magnetic energy spectrum is expected to be limited by the scale corresponding to magnetic Landau damping or, if smaller, the electron gyroradius scale, instead of the resistive scale. In simulations we thus observe decaying magnetic fields where resistive MHD would predict a dynamo.

physics.plasm-ph↗

arXiv2020

Application of a helicity proxy to edge-on galaxies

We study the prospects of detecting magnetic helicity in galaxies by observing the dust polarization of the edge-on galaxy NGC 891. Our numerical results of mean-field dynamo calculations show that there should be a large-scale component of the rotationally invariant parity-odd B polarization that we predict to be negative in the first and third quadrants, and positive in the second and fourth quadrants. The large-scale parity-even E polarization is predicted to be negative near the axis and positive further away in the outskirts. These properties are shown to be mostly a consequence of the magnetic field being azimuthal and the polarized intensity being maximum at the center of the galaxy and are not a signature of magnetic helicity.

astro-ph.GA↗

arXiv2020

On the measurement of handedness in Fermi Large Area Telescope data

A handedness in the arrival directions of high-energy photons from outside our Galaxy can be related to the helicity of an intergalactic magnetic field. Previous estimates by arXiv:1310.4826 and arXiv:1412.3171 showed a hint of a signal present in the photons observed by the Fermi Large Area Telescope (LAT). An update on the measurement of handedness in Fermi-LAT data is presented using more than 10 years of observations. Simulations are performed to study the uncertainty of the measurements, taking into account the structure of the exposure caused by the energy-dependent instrument response and its observing profile, as well as the background from the interstellar medium. The simulations are required to accurately estimate the uncertainty and to show that previously the uncertainty was significantly underestimated. The apparent signal in the earlier analysis of {\em Fermi}-LAT data is rendered non-significant.

astro-ph.HE↗

arXiv2020

Hemispheric handedness in the Galactic synchrotron polarization foreground

The large-scale magnetic field of the Milky Way is thought to be created by an alpha-Omega dynamo, which implies that it should have opposite handedness North and South of the Galactic midplane. Here we attempt to detect a variation in handedness using polarization data from the Wilkinson Microwave Anisotropy Probe. Previous analyzes of the parity-even and parity-odd parts of linear polarization of the global dust and synchrotron emission have focused on quadratic correlations in spectral space of, and between, these two components. Here, by contrast, we analyze the parity-odd polarization itself and show that it has, on average, opposite signs in Northern and Southern Galactic hemispheres. Comparison with a Galactic mean-field dynamo model shows broad qualitative agreement and reveals that the sign of the observed hemispheric dependence of the azimuthally averaged parity-odd polarization is not determined by the sign of alpha, but by the sense of differential rotation.

astro-ph.GA↗

arXiv2020

Magnetic field evolution in solar-type stars

We discuss selected aspects regarding the magnetic field evolution of solar-type stars. Most of the stars with activity cycles are in the range where the normalized chromospheric Calcium emission increases linearly with the inverse Rossby number. For Rossby numbers below about a quarter of the solar value, the activity saturates and no cycles have been found. For Rossby numbers above the solar value, again no activity cycles have been found, but now the activity goes up again for a major fraction of the stars. Rapidly rotating stars show nonaxisymmetric large-scale magnetic fields, but there is disagreement between models and observations regarding the actual value of the Rossby number where this happens. We also discuss the prospects of detecting the sign of magnetic helicity using various linear polarization techniques both at the stellar surface using the parity-odd contribution to linear polarization and above the surface using Faraday rotation.

astro-ph.SR↗

arXiv2020

The turbulent stress spectrum in the inertial and subinertial ranges

For velocity and magnetic fields, the turbulent pressure and, more generally, the squared fields such as the components of the turbulent stress tensor, play important roles in astrophysics. For both one and three dimensions, we derive the equations relating the energy spectra of the fields to the spectra of their squares. We solve the resulting integrals numerically and show that for turbulent energy spectra of Kolmogorov type, the spectral slope of the stress spectrum is also of Kolmogorov type. For shallower turbulence spectra, the slope of the stress spectrum quickly approaches that of white noise, regardless of how blue the spectrum of the field is. For fully helical fields, the stress spectrum is elevated by about a factor of two in the subinertial range, while that in the inertial range remains unchanged. We discuss possible implications for understanding the spectrum of primordial gravitational waves from causally generated magnetic fields during cosmological phase transitions in the early universe. We also discuss potential diagnostic applications to the interstellar medium, where polarization and scintillation measurements characterize the square of the magnetic field.

astro-ph.CO↗

arXiv2020

Turbulent viscosity and effective magnetic Prandtl number from simulations of isotropically forced turbulence

(abridged) Context: Turbulent diffusion of large-scale flows and magnetic fields play major roles in many astrophysical systems. Aims: Our goal is to compute turbulent viscosity and magnetic diffusivity, relevant for diffusing large-scale flows and magnetic fields, respectively, and their ratio, the turbulent magnetic Prandtl number, ${\rm Pm}_{\rm t}$, for isotropically forced homogeneous turbulence. Methods: We use simulations of forced turbulence in fully periodic cubes composed of isothermal gas with an imposed large-scale sinusoidal shear flow. Turbulent viscosity is computed either from the resulting Reynolds stress or from the decay rate of the large-scale flow. Turbulent magnetic diffusivity is computed using the test-field method. The scale dependence of the coefficients is studied by varying the wavenumber of the imposed sinusoidal shear and test fields. Results: We find that turbulent viscosity and magnetic diffusivity are in general of the same order of magnitude. Furthermore, the turbulent viscosity depends on the fluid Reynolds number (${\rm Re}$) and scale separation ratio of turbulence. The scale dependence of the turbulent viscosity is found to be well approximated by a Lorentzian. The results for the turbulent transport coefficients appear to converge at sufficiently high values of ${\rm Re}$ and the scale separation ratio. However, a weak decreasing trend is found even at the largest values of ${\rm Re}$. The turbulent magnetic Prandtl number converges to a value that is slightly below unity for large ${\rm Re}$ whereas for small ${\rm Re}$, we find values between 0.5 and 0.6. Conclusions: The turbulent magnetic diffusivity is in general consistently higher than the turbulent viscosity. The actual value of ${\rm Pm}_{\rm t}$ found from the simulations ($\approx0.9\ldots0.95$) at large ${\rm Re}$ and scale separation ratio is higher than any of the analytic predictions.

astro-ph.SR↗

arXiv2020

Condensational and collisional growth of cloud droplets in a turbulent environment

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 (non-turbulent) 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.

physics.ao-ph↗

arXiv2020

Magnetic helicity dissipation and production in an ideal MHD code

We study a turbulent helical dynamo in a periodic domain by solving the ideal magnetohydrodynamic (MHD) equations with the FLASH code using the divergence-cleaning eight-wave method and compare our results with direct numerical simulations (DNS) using the Pencil Code. At low resolution, FLASH reproduces the DNS results qualitatively by developing the large-scale magnetic field expected from DNS, but at higher resolution, no large-scale magnetic field is obtained. In all those cases in which a large-scale magnetic field is generated, the ideal MHD results yield too little power at small scales. As a consequence, the small-scale current helicity is too small compared with that of the DNS. The resulting net current helicity has then always the wrong sign, and its statistical average also does not approach zero at late times, as expected from the DNS. Our results have implications for astrophysical dynamo simulations of stellar and galactic magnetism using ideal MHD codes.

astro-ph.SR↗

arXiv2019

The nature of mean-field generation in three classes of optimal dynamos

In recent years, several optimal dynamos have been discovered. They minimize the magnetic energy dissipation or, equivalently, maximize the growth rate at a fixed magnetic Reynolds number. In the optimal dynamo of Willis (2012, Phys. Rev. Lett. 109, 251101), we find mean-field dynamo action for planar averages. One component of the magnetic field grows exponentially while the other decays in an oscillatory fashion near onset. This behavior is different from that of an alpha^2 dynamo, where the two non-vanishing components of the planar averages are coupled and have the same growth rate. For the Willis dynamo, we find that the mean field is excited by a negative turbulent magnetic diffusivity, which has a non-uniform spatial profile near onset. The temporal oscillations in the decaying component are caused by the corresponding component of the diffusivity tensor being complex when the mean field is decaying and, in this way, time-dependent. The growing mean field can be modeled by a negative magnetic diffusivity combined with a positive magnetic hyperdiffusivity. In two other classes of optimal dynamos of Chen et al. (2015, J. Fluid Mech. 783, 23), we find, to some extent, similar mean-field dynamo actions. When the magnetic boundary conditions are mixed, the two components of the planar averaged field grow at different rates when the dynamo is 15% supercritical. When the mean magnetic field satisfies homogeneous boundary conditions (where the magnetic field is tangential to the boundary), mean-field dynamo action is found for one-dimensional averages, but not for planar averages. Despite having different spatial profiles, both dynamos show negative turbulent magnetic diffusivities. Our finding suggests negative turbulent magnetic diffusivities may support a broader class of dynamos than previously thought, including these three optimal dynamos.

physics.flu-dyn↗

arXiv2019

The time step constraint in radiation hydrodynamics

Explicit radiation hydrodynamic simulations of the atmospheres of massive stars and of convection in accretion discs around white dwarfs suffer from prohibitively short time steps due to radiation. This constraint is related to the cooling time rather than the radiative pressure, which also becomes important in hot stars and discs. We show that the radiative time step constraint is governed by the minimum of the sum of the optically thick and thin contributions rather than the smaller one of the two. In simulations with the Pencil Code, their weighting fractions are found empirically. In three-dimensional convective accretion disc simulations, the Deardorff term is found to be the main contributor to the enthalpy flux rather than the superadiabatic gradient. We conclude with a discussion of how the radiative time step problem could be mitigated in certain types of investigations.

astro-ph.SR↗

arXiv2019

Convergence properties of detonation simulations

We present a high-resolution convergence study of detonation initiated by a temperature gradient in a stoichiometric hydrogen-oxygen mixture using the Pencil Code and compare with a code that employs a fifth order weighted essentially non-oscillating (WENO) scheme. With Mach numbers reaching 10-30, a certain amount of shock viscosity is needed in the Pencil Code to remove or reduce numerical pressure oscillations on the grid scale at the position of the shock. Detonation is found to occur for intermediate values of the shock viscosity parameter. At fixed values of this parameter, the numerical error associated with those small wiggles in the pressure profile is found to decrease with decreasing mesh width $δx$ like $δx^{-1.4}$ down to $δx=0.2μ$m. With the WENO scheme, solutions are smooth at $δx=10μ$m, but no detonation is obtained for $δx=5μ$m. This is argued to be an artifact of a decoupling between pressure and reaction fronts.

physics.flu-dyn↗