Hydrostatic equilibrium

About: Hydrostatic equilibrium is a research topic. Over the lifetime, 2451 publications have been published within this topic receiving 62172 citations.

Stability near hydrostatic equilibrium to the three-dimensional Boussinesq equations with partial dissipation

Abstract: This paper focuses on the stability problem for perturbations near a hydrostatic equilibrium associated with the three-dimensional Boussinesq equations with partial dissipation. We mainly study the global stability and large-time behavior of solutions to this system with only horizontal dissipation and obtain three results. The first establishes the global $$H^2$$ -stability, the second obtains the large-time asymptotic of the solutions, and the last assesses the asymptotic linear stability with explicit decay rates. Finally, we remark that these results can also be extended to the system with mixed partial dissipation.

One-dimensional prominence threads. I. Equilibrium models

Abstract: Context. Threads are the building blocks of solar prominences and very often show longitudinal oscillatory motions that are strongly attenuated with time. The damping mechanism responsible for the reported oscillations is not fully understood yet.Aims. To understand the oscillations and damping of prominence threads we must first investigate the nature of the equilibrium solutions that arise under static conditions and under the presence of radiative losses, thermal conduction, and background heating. This provides the basis to calculate the eigenmodes of the thread models.Methods. The non-linear ordinary differential equations for hydrostatic and thermal equilibrium under the presence of gravity are solved using standard numerical techniques and simple analytical expressions are derived under certain approximations. The solutions to the equations represent a prominence thread, a dense and cold plasma region of a certain length that connects with the corona through a prominence corona transition region (PCTR). The solutions can also match with a chromospheric-like layer if a spatially dependent heating function localised around the footpoints is considered.Results. We have obtained static solutions representing prominence threads and have investigated in detail the dependence of these solutions on the different parameters of the model. Among other results, we show that multiple condensations along a magnetic field line are possible, and that the effect of partial ionisation in the model can significantly modify the thermal balance in the thread, and therefore their length. This last parameter is also shown to be comparable to that reported in the observations when the radiative losses are reduced for typical thread temperatures.

MAGRATHEA: an open-source spherical symmetric planet interior structure code

Abstract: MAGRATHEA is an open-source planet structure code that considers the case of fully differentiated spherically symmetric interiors. Given the mass of each layer and the surface temperature, the code iterates the boundary conditions of the hydrostatic equations using the method of shooting to a fitting point in order to find the planet radius. The first version of MAGRATHEA supports a maximum of four layers of iron, silicates, water, and ideal gas. With a few exceptions, the temperature profile can be chosen between isothermal, isentropic, and user-defined functions. The user has many options for the phase diagram and equation of state in each layer and we document how to add additional equations of state. We present MAGRATHEA’s capabilities and discuss its applications. We encourage the community to participate in the development of MAGRATHEA at https://github.com/Huang-CL/Magrathea .

Slow magnetoacoustic gravity waves in an equilibrium stratified solar atmosphere: cut-off periods through the transition region

Abstract: Assuming the thin flux tube approximation, we introduce an analytical model that contemplates the presence of: a non-isothermal temperature; a varying magnetic field and a non-uniform stratified medium in hydrostatic equilibrium due to a constant gravity acceleration. This allows the study of slow magnetoacoustic cut-off periods across the solar transition region, from the base of the solar chromosphere to the lower corona. The used temperature profile approaches the VAC solar atmospheric model. The periods obtained are consistent with observations. Similar to the acoustic cut-off periods, the resulting magnetoacoustic gravity ones follow the sharp temperature profile, but shifted towards larger heights; in other words, at a given height the magnetoacoustic cut-off period is significantly lower than the corresponding acoustic one. Along a given longitude of an inclined thin magnetic tube, the greater its inclination the softener the temperature gradient it crosses. Changes in the magnetic field intensity do not significantly modify the periods at the coronal level but modulate the values below the transition region within periods between $\sim [2\,- 6]\,$min. Within the limitations of our model, we show that monochromatic oscillations of the solar atmosphere are the atmospheric response at its natural frequency to random or impulsive perturbations, and not a consequence of the forcing from the photosphere.

The effects of hydrostatic pressure on the compressive mechanical behavior of L1 2 Al 3 Ti-based intermetallic

Abstract: A Mn-modified Ll2 Al3Ti-base intermetallic was subjected to compressive deformation at room temperature under superimposed hydrostatic pressures up to 1000 MPa. It is found that its yield strength is essentially unaffected by hydrostatic pressure. The apparent work-hardening rate of true stress-strain curves increases substantially with increasing hydrostatic pressure. Vickers microhardness of pressurized samples always increases with increasing compressive strain, indicating the work-hardening behavior, but it is independent of the superimposed hydrostatic pressure up to 1000 MPa. The density of microcracks (cm/cm2) observed in specimens compressed under hydrostatic pressure increases with increasing compressive strain for each level of pressure. At each constant compressive strain, the corresponding density of microcracks is higher for specimens tested under 170 MPa hydrostatic pressure than that for specimens tested in the 400 to 1000 MPa hydrostatic pressure range. This may imply that besides propagation, the nucleation stage may also be suppressed by a superimposed hydrostatic pressure. It is proposed that both the cataclastic (characteristic for deformation of some rocks) and plastic deformation occur simultaneously during compressive deformation of Ti trialuminides under hydrostatic pressure.