arXiv subjects

G. R. Sarson

Publications and source records attributed to G. R. Sarson.

10 recordsLinked to original sources

arXiv2021

Mean fields and fluctuations in compressible magnetohydrodynamic flows

We apply Gaussian smoothing to obtain mean magnetic field, density, velocity, and magnetic and kinetic energy densities from our numerical model of the interstellar medium, based on three-dimensional magnetohydrodynamic equations in a shearing box $1 \times 1 \times 2 \, {\rm kpc}$ in size. The interstellar medium is highly compressible, as the turbulence is transonic or supersonic; it is thus an excellent context in which to explore the use of smoothing to represent physical variables in a compressible medium in terms of their mean and fluctuating parts. Unlike alternative averaging procedures, such as horizontal averaging, Gaussian smoothing retains the three-dimensional structure of the mean fields. Although Gaussian smoothing does not obey the Reynolds rules of averaging, physically meaningful and mathematically sound central statistical moments are defined as suggested by Germano (1992). We discuss methods to identify an optimal smoothing scale $\ell$ and the effects of this choice on the results. From spectral analysis of the magnetic, density and velocity fields, we find a suitable smoothing length for all three fields, of $\ell \approx 75 \, {\rm pc}$. Such a smoothing scale is likely to be sensitive to the choice of simulation parameters; this may be considered in future work, but here we just explore the methodology. We discuss the properties of third-order statistical moments in fluctuations of kinetic energy density in compressible flows, and suggest their physical interpretation. The mean magnetic field, amplified by a mean-field dynamo, significantly alters the distribution of kinetic energy in space and between scales, reducing the magnitude of kinetic energy at intermediate scales. This intermediate-scale kinetic energy is a useful diagnostic of the importance of SN-driven outflows.

astro-ph.GA↗

arXiv2020

The Pencil Code, a modular MPI code for partial differential equations and particles: multipurpose and multiuser-maintained

The Pencil Code is a highly modular physics-oriented simulation code that can be adapted to a wide range of applications. It is primarily designed to solve partial differential equations (PDEs) of compressible hydrodynamics and has lots of add-ons ranging from astrophysical magnetohydrodynamics (MHD) to meteorological cloud microphysics and engineering applications in combustion. Nevertheless, the framework is general and can also be applied to situations not related to hydrodynamics or even PDEs, for example when just the message passing interface or input/output strategies of the code are to be used. The code can also evolve Lagrangian (inertial and noninertial) particles, their coagulation and condensation, as well as their interaction with the fluid.

astro-ph.IM↗

arXiv2019

Fickian and non-Fickian diffusion of cosmic rays

Fluid approximations to cosmic ray (CR) transport are often preferred to kinetic descriptions in studies of the dynamics of the interstellar medium (ISM) of galaxies, because they allow simpler analytical and numerical treatments. Magnetohydrodynamic (MHD) simulations of the ISM usually incorporate CR dynamics as an advection-diffusion equation for CR energy density, with anisotropic, magnetic field-aligned diffusion with the diffusive flux assumed to obey Fick's law. We compare test-particle and fluid simulations of CRs in a random magnetic field. We demonstrate that a non-Fickian prescription of CR diffusion, which corresponds to the telegraph equation for the CR energy density, can be easily calibrated to match the test particle simulations with great accuracy. In particular, we consider a random magnetic field in the fluid simulation that has a lower spatial resolution than that used in the particle simulation to demonstrate that an appropriate choice of the diffusion tensor can account effectively for the unresolved (subgrid) scales of the magnetic field. We show that the characteristic time which appears in the telegraph equation can be physically interpreted as the time required for the particles to reach a diffusive regime and we stress that the Fickian description of the CR fluid is unable to describe complex boundary or initial conditions for the CR energy flux.

astro-ph.HE↗

arXiv2016

Global diffusion of cosmic rays

The propagation of charged particles, including cosmic rays, in a partially ordered magnetic field is characterized by a diffusion tensor whose components depend on the particle's Larmor radius $R_L$ and the degree of order in the magnetic field. Most studies of the particle diffusion presuppose a scale separation between the mean and random magnetic fields (e.g., there being a pronounced minimum in the magnetic power spectrum at intermediate scales). Scale separation is often a good approximation in laboratory plasmas, but not in most astrophysical environments such as the interstellar medium (ISM). Modern simulations of the ISM have numerical resolution of order 1 pc, so the Larmor radius of the cosmic rays that dominate in energy density is at least $10^{6}$ times smaller than the resolved scales. Large-scale simulations of cosmic ray propagation in the ISM thus rely on oversimplified forms of the diffusion tensor. We take the first steps towards a more realistic description of cosmic ray diffusion for such simulations, obtaining direct estimates of the diffusion tensor from test particle simulations in random magnetic fields (with the Larmor radius scale being fully resolved), for a range of particle energies corresponding to $10^{-2}\lesssim R_L/l_c \lesssim 10^{3}$, where $l_c$ is the magnetic correlation length. We obtain explicit expressions for the cosmic ray diffusion tensor for $R_L/l_c \ll 1$, that might be used in a sub-grid model of cosmic ray diffusion. The diffusion coefficients obtained are closely connected with existing transport theories that include the random walk of magnetic lines.

astro-ph.HE↗

arXiv2015

Productivity of pre-modern agriculture in the Cucuteni-Trypillia area

(Abridged) We present palaeoeconomy reconstructions for pre-modern agriculture, with the Cucuteni-Trypillia Cultural unity (5,400-2,700 BC, modern Ukraine, Moldova and Romania) as example. The starting point of our analysis is the palaeodiet structure suggested by archaeological data, stable isotope analyses of human remains, and palynology. We allow for the archeologically attested contributions of domesticated and wild animal products to the diet, develop plausible estimates of the yield of ancient cereal varieties cultivated with ancient techniques, and quantify the yield dependence on the time after initial planting and on rainfall (as a climate proxy). Our conclusions involve analysis of the labour costs of the agricultural cycle of both an individual and a farmer's family. Finally, we put our results into the context of the exploitation territory and catchment analysis. The simplest economic complex based on cereals, domestic and wild animal products, with fallow cropping, appears to be capable of supporting an isolated, relatively small farming community of 50-300 people (2-10 ha). Our results strongly suggest that dairy products played a significant role in the dietary and labour balance. The smaller settlements are typical of the earliest Trypillia A but remain predominant at the later stages. A larger settlement of several hundred people could function in isolation only with technological innovations, such as manure fertiliser and ard tillage. Very large settlements of a few hundred hectares could function only if supported by satellite farming villages and stable exchange networks. We also discuss, quantify and assess some strategies to mitigate the risks of arable agriculture associated with strong temporal fluctuations in the cereal yield, such as manure fertilisation, increased fraction of cereals in the diet combined with producing grain surplus for emergency storage.

q-bio.PE↗

arXiv2013

The supernova-regulated ISM. I. The multi-phase structure

We simulate the multi-phase interstellar medium randomly heated and stirred by supernovae, with gravity, differential rotation and other parameters of the solar neighbourhood. Here we describe in detail both numerical and physical aspects of the model, including injection of thermal and kinetic energy by SN explosions, radiative cooling, photoelectric heating and various transport processes. With 3D domain extending 1 kpc^2 horizontally and 2 kpc vertically, the model routinely spans gas number densities 10^-5 - 10^2 cm^-3, temperatures 10-10^8 K, local velocities up to 10^3 km s^-1 (with Mach number up to 25). The thermal structure of the modelled ISM is classified by inspection of the joint probability density of the gas number density and temperature. We confirm that most of the complexity can be captured in terms of just three phases, separated by temperature borderlines at about 10^3 K and 5x10^5 K. The probability distribution of gas density within each phase is approximately lognormal. We clarify the connection between the fractional volume of a phase and its various proxies, and derive an exact relation between the fractional volume and the filling factors defined in terms of the volume and probabilistic averages. These results are discussed in both observational and computational contexts. The correlation scale of the random flows is calculated from the velocity autocorrelation function; it is of order 100 pc and tends to grow with distance from the mid-plane. We use two distinct parameterizations of radiative cooling to show that the multi-phase structure of the gas is robust, as it does not depend significantly on this choice.

astro-ph.GA↗

arXiv2012

The supernova-regulated ISM. II. The mean magnetic field

The origin and structure of the magnetic fields in the interstellar medium of spiral galaxies is investigated with 3D, non-ideal, compressible MHD simulations, including stratification in the galactic gravity field, differential rotation and radiative cooling. A rectangular domain, 1x1x2 kpc^{3} in size, spans both sides of the galactic mid-plane. Supernova explosions drive transonic turbulence. A seed magnetic field grows exponentially to reach a statistically steady state within 1.6 Gyr. Following Germano (1992) we use volume averaging with a Gaussian kernel to separate magnetic field into a mean field and fluctuations. Such averaging does not satisfy all Reynolds rules, yet allows a formulation of mean-field theory. The mean field thus obtained varies in both space and time. Growth rates differ for the mean-field and fluctuating field and there is clear scale separation between the two elements, whose integral scales are about 0.7 kpc and 0.3 kpc, respectively.

astro-ph.GA↗

arXiv2007

Multiple Sources of the European Neolithic: Mathematical Modelling Constrained by Radiocarbon Dates

We present a mathematical model, based on the compilation and statistical processing of radiocarbon dates, of the transition from the Mesolithic to the Neolithic, from about 7,000 to 4,000 BC in Europe. The arrival of the Neolithic is traditionally associated with the establishment of farming-based economies; yet in considerable areas of north-eastern Europe it is linked with the beginning of pottery-making in the context of foraging-type communities. Archaeological evidence, radiocarbon dates and genetic markers are consistent with the spread of farming from a source in the Near East. However, farming was less important in the East; the Eastern and Western Neolithic have distinct signatures. We use a population dynamics model to suggest that this distinction can be attributed to the presence of two waves of advance, one from the Near East, and another through Eastern Europe. Thus, we provide a quantitative framework in which a unified interpretation of the Western and Eastern Neolithic can be developed.

q-bio.PE↗

arXiv2005

Environmental effects on the spread of the Neolithic

The causes and implications of the regional variations in the spread of the incipient agriculture in Europe remain poorly understood. We apply population dynamics models to study the dispersal of the Neolithic in Europe from a localized area in the Near East, solving the two-dimensional reaction-diffusion equation on a spherical surface. We focus on the role of major river paths and coastlines in the advance of farming to model the rapid advances of the Linear Pottery (LBK) and the Impressed Ware traditions along the Danube-Rhine corridor and the Mediterranean coastline respectively. We argue that the random walk of individuals, which results in diffusion of the population, can be anisotropic in those areas. The standard reaction-diffusion equation is thus supplemented with advection-like terms confined to the proximity of major rivers and coastlines. The model allows for the spatial variation in both the human mobility (diffusivity) and the carrying capacity of landscapes, reflecting the local altitude and latitude. This approach can easily be generalised to include other environmental factors, such as the bioproductivity of landscapes. Our model successfully accounts for the regional variations in the spread of the Neolithic, consistent with the radiocarbon dated data, and reproduces a time delay in the spread of farming to the Eastern Europe and Scandinavia.

q-bio.PE↗

arXiv2003

How magnetic helicity ejection helps large scale dynamos

There is mounting evidence that the ejection of magnetic helicity from the solar surface is important for the solar dynamo. Observations suggest that in the northern hemisphere the magnetic helicity flux is negative. We propose that this magnetic helicity flux is mostly due to small scale magnetic fields; in contrast to the more systematic large scale field of the 11 year cycle, whose helicity flux may be of opposite sign, and may be excluded from the observational interpretation. Using idealized simulations of MHD turbulence as well as a simple two-scale model, we show that shedding small scale (helical) field has two important effects. (i) The strength of the large scale field reaches the observed levels. (ii) The evolution of the large scale field proceeds on time scales shorter than the resistive time scale, as would otherwise be enforced by magnetic helicity conservation. In other words, the losses ensure that the solar dynamo is always in the near-kinematic regime. This requires, however, that the ratio of small scale to large scale losses cannot be too small, for otherwise the large scale field in the near-kinematic regime will not reach the observed values.

astro-ph↗