Thermally damped linear compressional waves in a 2D solar coronal model

The high resolution observations (TRACE and SOHO) of waves in coronal structures have revealed a rapid damping of modes, sometimes their damping length being of the same order as their wavelength. The rapid damping of modes in coronal loops permits us to derive values for magnetic field and transport coefficients. In this contribution we study the damping of linear compressional waves considering a two-dimensional propagation in gravitationally stratified plasma in the presence of thermal conduction. By considering this 2D model, we show that the presence of an additional transversal motion has an important effect on the damping of the waves. This theoretical model allows as to conclude that the main effects influencing the damping of the waves are the degree of the transversal structuring and temperature

Dynamical phenomena in stratified solar coronal plasma

Different dynamical phenomena in the solar corona are investigated in the present Thesis. We aim to investigate using a semi-analytical approach of the effect of the surrounding environment on the period ratio of the fundamental to first harmonic of a thin coronal loop. Investigation of geometrical effects are taken into account, namely asymmetry of the coronal loop, i.e. its deviation from a semi-circular shape. It is found that if we are to obtain more accurate estimates on the effect of the environment on the transversal oscillations of a coronal loop, we have to take into account that in reality a coronal loop depends on more than one coordinate, secondly, isothermal supposition of the loop and its environment also need refinement, as observations show that the loops are not always in hydrostatic equilibrium. The study on the expansion of a coronal loop indicates that in order to have more realistic results one would need to include damping processes, resonant absorption and cooling processes. Further in an expanding loop, the growth of the amplitude due to emergence and decay of amplitude due to resonant damping or cooling will be competing processes. When it expands, a loop can also have accelerated motion upwards in the corona with cross section modification of the ux tube. The final piece of work in this thesis is a numerical investigation into a 2D magnetic reconnection process, where we study reconnection rates and how different parameters such as resistivity and Hall term affect the process of field line reconnection. The Hall effect does speed up the reconnection process, but it depends significantly on the initial conditions of the problem. These initial conditions, i.e. different magnetic field configuration, density stratification, gravity play an important role in the reconnection process

Sausage mode propagation in a thick magnetic flux tube

The aim of this paper is to model the propagation of slow magnetohydrodynamic (MHD) sausage waves in a thick expanding magnetic flux tube in the context of the quiescent (VAL-C) solar atmosphere. The propagation of these waves is found to be described by the Klein–Gordon equation. Using the governing MHD equations and the VAL-C atmosphere model we study the variation of the cut-off frequency along and across the magnetic tube guiding the waves. Due to the radial variation of the cut-off frequency the flux tubes act as low frequency filters for the waves

Transverse kink oscillations of expanding coronal loops

We investigate the nature of transverse kink oscillations of loops expanding through the solar corona and how can oscillations be used to diagnose the plasma parameters and the magnetic field. In particular, we aim to analyse how the temporal dependence of the loop length (here modelling the expansion) will affect the P1 /P2 period ratio of transverse loop oscillations. Due to the uncertainty of the loop's shape through its expansion, we discuss separately the case of the loop that maintains its initial semi-circular shape and the case of the loop that from a semi-circular shape evolve into an elliptical shape loop. The equations that describe the oscillations in expanding flux tube are complicated due to the spatial and temporal dependence of coefficients. Using the WKB approximation we find approximative values for periods and their evolution, as well as the period ratio. For small values of time (near the start of the expansion) we can employ a regular perturbation method to find approximative relations for eigenfunctions and eigenfrequencies. Using simple analytical and numerical methods we show that the period of oscillations are affected by the rising of the coronal loop. The change in the period due to the increase in the loop's length is more pronounced for those loops that expand into a more structured (or cooler corona). The deviation of periods will have significant implications in determining the degree of stratification in the solar corona. The effect of expansion on the periods of oscillations is considerable only in the process of expansion of the loop but not when it reached its final stage

Steady state properties of a driven granular medium

We study a two-dimensional granular system where external driving force is applied to each particle in the system in such a way that the system is driven into a steady state by balancing the energy input and the dissipation due to inelastic collision between particles. The velocities of the particles in the steady state satisfy the Maxwellian distribution. We measure the density-density correlation and the velocity-velocity correlation functions in the steady state and find that they are of power-law scaling forms. The locations of collision events are observed to be time-correlated and such a correlation is described by another power-law form. We also find that the dissipated energy obeys a power-law distribution. These results indicate that the system evolves into a critical state where there are neither characteristic spatial nor temporal scales in the correlation functions. A test particle exhibits an anomalous diffusion which is apparently similar to the Richardson law in a three-dimensional turbulent flow.Comment: REVTEX, submitted to Phys. Rev.

The effect of the environment on the P1/P2 period ratio for kink oscillations of coronal loops

The P1/P2 period ratio of transversal loop oscillations is currently used for the diagnostics of longitudinal structuring of coronal loops as its deviation from 2 is intrinsically connected to the density scale-height along coronal loops and/or the sub-resolution structure of the magnetic field. The same technique can be applied not only to coronal structures, but also to other oscillating magnetic structures. The oscillations in magnetic structures are described by differential equations whose coefficients depend on the longitudinal structure of the plasma. Using a variational principle written for the transversal component of the velocity vector, developed earlier by McEwan et al. (2008), we investigate how the different temperature of the environment compared to the temperature of the magnetic structure will influence the P1/P2 ratio for typical coronal and prominence conditions. The possible changes are translated into quantities that are used in the process of remote plasma diagnostics in the solar atmosphere

Transport Coefficients for Granular Media from Molecular Dynamics Simulations

Under many conditions, macroscopic grains flow like a fluid; kinetic theory pred icts continuum equations of motion for this granular fluid. In order to test the theory, we perform event driven molecular simulations of a two-dimensional gas of inelastic hard disks, driven by contact with a heat bath. Even for strong dissipation, high densities, and small numbers of particles, we find that continuum theory describes the system well. With a bath that heats the gas homogeneously, strong velocity correlations produce a slightly smaller energy loss due to inelastic collisions than that predicted by kinetic theory. With an inhomogeneous heat bath, thermal or velocity gradients are induced. Determination of the resulting fluxes allows calculation of the thermal conductivity and shear viscosity, which are compared to the predictions of granular kinetic theory, and which can be used in continuum modeling of granular flows. The shear viscosity is close to the prediction of kinetic theory, while the thermal conductivity can be overestimated by a factor of 2; in each case, transport is lowered with increasing inelasticity.Comment: 14 pages, 17 figures, 39 references, submitted to PRE feb 199

Further insights into the operation of the Chinese number system: Competing effects of Arabic and Mandarin number formats

Here we report the results of a speeded relative quantity task with Chinese participants. On each trial a single numeral (the probe) was presented and the instructions were to respond as to whether it signified a quantity less than or greater than five (the standard). In separate blocks of trials, the numerals were either presented in Mandarin or in Arabic number formats. In addition to the standard influence of numerical distance, a significant predictor of performance was the degree of physical similarity between the probe and the standard as depicted in Mandarin. Additionally, competing effects of physical similarity, defined in terms of the Arabic number format, were also found. Critically the size of these different effects of physical similarity varied systematically across individuals such that larger effects of one compensated for smaller effects of the other. It is argued that the data favor accounts of processing that assume that different number formats access different format-specific representations of quantities. Moreover, for Chinese participants the default is to translate numerals into a Mandarin format prior to accessing quantity information. The efficacy of this translation process is itself influenced by a competing tendency to carry out a translation into Arabic format

Sausage Mode Propagation in a Thick Magnetic Flux Tube

The aim of this paper is to model the propagation of slow magnetohydrodynamic (MHD) sausage waves in a thick expanding magnetic flux tube in the context of the quiescent (VAL C) solar atmosphere. The propagation of these waves is found to be described by the Klein-Gordon equation. Using the governing MHD equations and the VAL C atmosphere model we study the variation of the cut-off frequency along and across the magnetic tube guiding the waves. Due to the radial variation of the cut-off frequency the flux tubes act as low frequency filters for waves