Chiral Anomaly and Dynamos from Inhomogeneous Chemical Potential Fluctuations.

In the standard model of particle physics, the chiral anomaly can occur in relativistic plasmas and plays a role in the early Universe, protoneutron stars, heavy-ion collisions, and quantum materials. It gives rise to a magnetic instability if the number densities of left- and right-handed electrically charged fermions are unequal. Using direct numerical simulations, we show this can result just from spatial fluctuations of the chemical potential, causing a chiral dynamo instability, magnetically driven turbulence, and ultimately a large-scale magnetic field through the magnetic α effect.

Electromagnetic Conversion into Kinetic and Thermal Energies.

The conversion of electromagnetic energy into magnetohydrodynamic energy occurs when the electric conductivity changes from negligible to finite values. This process is relevant during the epoch of reheating in the early universe at the end of inflation and before the emergence of the radiation-dominated era. We find that the conversion into kinetic and thermal energies is primarily the result of electric energy dissipation, while magnetic energy only plays a secondary role in this process. This means that since electric energy dominates over magnetic energy during inflation and reheating, significant amounts of electric energy can be converted into magnetohydrodynamic energy when conductivity emerges before the relevant length scales become stable.

Big Bang Nucleosynthesis Limits and Relic Gravitational-Wave Detection Prospects.

We revisit the big bang nucleosynthesis limits on primordial magnetic fields and/or turbulent motions accounting for the decaying nature of turbulent sources between the time of generation and big bang nucleosynthesis. This leads to larger estimates for the gravitational wave signal than previously expected. We address the detection prospects through space-based interferometers and pulsar timing arrays or astrometric missions for gravitational waves generated around the electroweak and quantum chromodynamics energy scale, respectively.

Production of a Chiral Magnetic Anomaly with Emerging Turbulence and Mean-Field Dynamo Action.

In relativistic magnetized plasmas, asymmetry in the number densities of left- and right-handed fermions, i.e., a nonzero chiral chemical potential µ_{5}, leads to an electric current along the magnetic field. This causes a chiral dynamo instability for a uniform µ_{5}, but our simulations reveal a dynamo even for fluctuating µ_{5} with zero mean. It produces magnetically dominated turbulence and generates mean magnetic fields via the magnetic α effect. Eventually, a universal scale-invariant k^{-1} spectrum of µ_{5} and a k^{-3} magnetic spectrum are formed independently of the initial condition.

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.

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.

The Limited Roles of Autocatalysis and Enantiomeric Cross-Inhibition in Achieving Homochirality in Dilute Systems.

To understand the effects of fluctuations on achieving homochirality, we employ a Monte-Carlo method where autocatalysis and enantiomeric cross-inhibition, as well as racemization and deracemization reactions are included. The results of earlier work either without autocatalysis or without cross-inhibition are reproduced. Bifurcation diagrams and the dependencies of the number of reaction steps on parameters are studied. In systems with 30,000 molecules, for example, up to a billion reaction steps may be needed to achieve homochirality without autocatalysis.

Classes of Hydrodynamic and Magnetohydrodynamic Turbulent Decay.

We perform numerical simulations of decaying hydrodynamic and magnetohydrodynamic turbulence. We classify our time-dependent solutions by their evolutionary tracks in parametric plots between instantaneous scaling exponents. We find distinct classes of solutions evolving along specific trajectories toward points on a line of self-similar solutions. These trajectories are determined by the underlying physics governing individual cases, while the infrared slope of the initial conditions plays only a limited role. In the helical case, even for a scale-invariant initial spectrum (inversely proportional to wave number k), the solution evolves along the same trajectory as for a Batchelor spectrum (proportional to k^{4}).

Nonhelical inverse transfer of a decaying turbulent magnetic field.

In the presence of magnetic helicity, inverse transfer from small to large scales is well known in magnetohydrodynamic (MHD) turbulence and has applications in astrophysics, cosmology, and fusion plasmas. Using high resolution direct numerical simulations of magnetically dominated self-similarly decaying MHD turbulence, we report a similar inverse transfer even in the absence of magnetic helicity. We compute for the first time spectral energy transfer rates to show that this inverse transfer is about half as strong as with helicity, but in both cases the magnetic gain at large scales results from velocity at similar scales interacting with smaller-scale magnetic fields. This suggests that both inverse transfers are a consequence of universal mechanisms for magnetically dominated turbulence. Possible explanations include inverse cascading of the mean squared vector potential associated with local near two dimensionality and the shallower k^{2} subinertial range spectrum of kinetic energy forcing the magnetic field with a k^{4} subinertial range to attain larger-scale coherence. The inertial range shows a clear k^{-2} spectrum and is the first example of fully isotropic magnetically dominated MHD turbulence exhibiting weak turbulence scaling.

Particle energization through time-periodic helical magnetic fields.

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.

Kinetic helicity needed to drive large-scale dynamos.

Magnetic field generation on scales that are large compared with the scale of the turbulent eddies is known to be possible via the so-called α effect when the turbulence is helical and if the domain is large enough for the α effect to dominate over turbulent diffusion. Using three-dimensional turbulence simulations, we show that the energy of the resulting mean magnetic field of the saturated state increases linearly with the product of normalized helicity and the ratio of domain scale to eddy scale, provided this product exceeds a critical value of around unity. This implies that large-scale dynamo action commences when the normalized helicity is larger than the inverse scale ratio. Our results show that the emergence of small-scale dynamo action does not have any noticeable effect on the large-scale dynamo. Recent findings by Pietarila Graham et al. [Phys. Rev. E 85, 066406 (2012)] of a smaller minimal helicity may be an artifact due to the onset of small-scale dynamo action at large magnetic Reynolds numbers. However, the onset of large-scale dynamo action is difficult to establish when the kinetic helicity is small. Instead of random forcing, they used an ABC flow with time-dependent phases. We show that such dynamos saturate prematurely in a way that is reminiscent of inhomogeneous dynamos with internal magnetic helicity fluxes. Furthermore, even for very low fractional helicities, such dynamos display large-scale fields that change direction, which is uncharacteristic of turbulent dynamos.

Breakdown of chiral symmetry during saturation of the Tayler instability.

We study spontaneous breakdown of chiral symmetry during the nonlinear evolution of the Tayler instability. We start with an initial steady state of zero helicity. Within linearized perturbation calculations, helical perturbations of this initial state have the same growth rate for either sign of helicity. Direct numerical simulations (DNS) of the fully nonlinear equations, however, show that an infinitesimal excess of one sign of helicity in the initial perturbation gives rise to a saturated helical state. We further show that this symmetry breaking can be described by weakly nonlinear finite-amplitude equations with undetermined coefficients which can be deduced solely from symmetry consideration. By fitting solutions of the amplitude equations to data from DNS, we further determine the coefficients of the amplitude equations.

Dynamics of saturated energy condensation in two-dimensional turbulence.

In two-dimensional forced Navier-Stokes turbulence, energy cascades to the largest scales in the system to form a pair of coherent vortices known as the Bose condensate. We show, both numerically and analytically, that the energy condensation saturates and the system reaches a statistically stationary state. The time scale of saturation is inversely proportional to the viscosity and the saturation energy level is determined by both the viscosity and the force. We further show that, without sufficient resolution to resolve the small-scale enstrophy spectrum, numerical simulations can give a spurious result for the saturation energy level. We also find that the movement of the condensate is similar to the motion of an inertial particle with an effective drag force. Furthermore, we show that the profile of the saturated coherent vortices can be described by a Gaussian core with exponential wings.

Mean-field diffusivities in passive scalar and magnetic transport in irrotational flows.

Certain aspects of the mean-field theory of turbulent passive scalar transport and of mean-field electrodynamics are considered with particular emphasis on aspects of compressible fluids. It is demonstrated that the total mean-field diffusivity for passive scalar transport in a compressible flow may well be smaller than the molecular diffusivity. This is in full analogy to an old finding regarding the magnetic mean-field diffusivity in an electrically conducting turbulently moving compressible fluid. These phenomena occur if the irrotational part of the motion dominates the vortical part, the Péclet or magnetic Reynolds number is not too large, and, in addition, the variation of the flow pattern is slow. For both the passive scalar and the magnetic cases several further analytical results on mean-field diffusivities and related quantities found within the second-order correlation approximation are presented, as well as numerical results obtained by the test-field method, which applies independently of this approximation. Particular attention is paid to nonlocal and noninstantaneous connections between the turbulence-caused terms and the mean fields. Two examples of irrotational flows, in which interesting phenomena in the above sense occur, are investigated in detail. In particular, it is demonstrated that the decay of a mean scalar in a compressible fluid under the influence of these flows can be much slower than without any flow, and can be strongly influenced by the so-called memory effect, that is, the fact that the relevant mean-field coefficients depend on the decay rates themselves.

Pumping velocity in homogeneous helical turbulence with shear.

Using different analytical methods (the quasilinear approach, the path-integral technique, and the tau-relaxation approximation) we develop a comprehensive mean-field theory for a pumping effect of the mean magnetic field in homogeneous nonrotating helical turbulence with imposed large-scale shear. The effective pumping velocity is proportional to the product of α effect and large-scale vorticity associated with the shear, and causes a separation of the toroidal and poloidal components of the mean magnetic field along the direction of the mean vorticity. We also perform direct numerical simulations of sheared turbulence in different ranges of hydrodynamic and magnetic Reynolds numbers and use a kinematic test-field method to determine the effective pumping velocity. The results of the numerical simulations are in agreement with the theoretical predictions.

Model of driven and decaying magnetic turbulence in a cylinder.

Using mean-field theory, we compute the evolution of the magnetic field in a cylinder with outer perfectly conducting boundaries and imposed axial magnetic and electric fields. The thus injected magnetic helicity in the system can be redistributed by magnetic helicity fluxes down the gradient of the local current helicity of the small-scale magnetic field. A weak reversal of the axial magnetic field is found to be a consequence of the magnetic helicity flux in the system. Such fluxes are known to alleviate so-called catastrophic quenching of the α effect in astrophysical applications. A stronger field reversal can be obtained if there is also a significant kinetic α effect. Application to the reversed field pinch in plasma confinement devices is discussed.

Spontaneous chiral symmetry breaking by hydromagnetic buoyancy.

Evidence for the parity-breaking nature of the magnetic buoyancy instability in a stably stratified gas is reported. In the absence of rotation, no helicity is produced, but the nonhelical state is found to be unstable to small helical perturbations during the development of the instability. The parity-breaking nature of this magnetohydrodynamic instability appears to be the first of its kind and has properties similar to those in chiral symmetry breaking in biochemistry. Applications to the production of mean fields in galaxy clusters are discussed.

Decay of helical and nonhelical magnetic knots.

We present calculations of the relaxation of magnetic field structures that have the shape of particular knots and links. A set of helical magnetic flux configurations is considered, which we call n-foil knots of which the trefoil knot is the most primitive member. We also consider two nonhelical knots; namely, the Borromean rings as well as a single interlocked flux rope that also serves as the logo of the Inter-University Centre for Astronomy and Astrophysics in Pune, India. The field decay characteristics of both configurations is investigated and compared with previous calculations of helical and nonhelical triple-ring configurations. Unlike earlier nonhelical configurations, the present ones cannot trivially be reduced via flux annihilation to a single ring. For the n-foil knots the decay is described by power laws that range form t(-2/3) to t(-1/3), which can be as slow as the t(-1/3) behavior for helical triple-ring structures that were seen in earlier work. The two nonhelical configurations decay like t(-1), which is somewhat slower than the previously obtained t(-3/2) behavior in the decay of interlocked rings with zero magnetic helicity. We attribute the difference to the creation of local structures that contain magnetic helicity which inhibits the field decay due to the existence of a lower bound imposed by the realizability condition. We show that net magnetic helicity can be produced resistively as a result of a slight imbalance between mutually canceling helical pieces as they are being driven apart. We speculate that higher order topological invariants beyond magnetic helicity may also be responsible for slowing down the decay of the two more complicated nonhelical structures mentioned above.

Autocatalyses.

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.