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Showing papers on "Hydrostatic equilibrium published in 2020"


Journal ArticleDOI
TL;DR: In this article, two different filtering techniques were used to disentangle bulk from turbulent motions in non-radiative high-resolution cosmological simulations of galaxy clusters using the cosmology hydro code ENZO, and the radial behavior of the ratio of non-thermal pressure to total gas pressure as a function of cluster-centric distance was described by a simple polynomial function.
Abstract: The degree of turbulent pressure support by residual gas motions in galaxy clusters is not well known. Mass modelling of combined X-ray and Sunyaev Zel'dovich observations provides an estimate of turbulent pressure support in the outer regions of several galaxy clusters. Here, we test two different filtering techniques to disentangle bulk from turbulent motions in non-radiative high-resolution cosmological simulations of galaxy clusters using the cosmological hydro code ENZO. We find that the radial behavior of the ratio of non-thermal pressure to total gas pressure as a function of cluster-centric distance can be described by a simple polynomial function. The typical non-thermal pressure support in the centre of clusters is $\sim$5%, increasing to $\sim$15% in the outskirts, in line with the pressure excess found in recent X-ray observations. While the complex dynamics of the ICM makes it impossible to reconstruct a simple correlation between turbulent motions and hydrostatic bias, we find that a relation between them can be established using the median properties of a sample of objects. Moreover, we estimate the contribution of radial accelerations to the non-thermal pressure support and conclude that it decreases moving outwards from 40% (in the core) to 15% (in the cluster's outskirts). Adding this contribution to one provided by turbulence, we show that it might account for the entire observed hydrostatic bias in the innermost regions of the clusters, and for less than 80% of it at $r > 0.8 r_{200, m}$.

51 citations


Journal ArticleDOI
TL;DR: In this paper, the authors analyzed more than 300 simulated massive clusters from the Three Hundred Project, and investigated the connection between mass bias and several diagnostics extracted from synthetic X-ray images of these simulated clusters.
Abstract: Accurate and precise measurement of the masses of galaxy clusters is key to deriving robust constraints on cosmological parameters. However, increasing evidence from observations confirms that X-ray masses obtained under the assumption of hydrostatic equilibrium might be underestimated, as previously predicted by cosmological simulations. We analyze more than 300 simulated massive clusters from the Three Hundred Project, and investigate the connection between mass bias and several diagnostics extracted from synthetic X-ray images of these simulated clusters. We find that the azimuthal scatter measured in 12 sectors of the X-ray flux maps is a statistically significant indication of the presence of an intrinsic (i.e., 3D) clumpy gas distribution. We verify that a robust correction to the hydrostatic mass bias can be inferred when estimates of the gas inhomogeneity from X-ray maps (such as the azimuthal scatter or the gas ellipticity) are combined with the asymptotic external slope of the gas density or pressure profiles, which can be respectively derived from X-ray and millimeter (Sunyaev-Zeldovich effect) observations. We also obtain that mass measurements based on either gas density and temperature or gas density and pressure result in similar distributions of the mass bias. In both cases, we provide corrections that help reduce both the dispersion and skewness of the mass bias distribution. These are effective even when irregular clusters are included leading to interesting implications for the modeling and correction of hydrostatic mass bias in cosmological analyses of current and future X-ray and SZ cluster surveys.

40 citations


Journal ArticleDOI
15 Jul 2020-Icarus
TL;DR: In this article, the authors used radio tracking data collected during the closest approach of Dione to estimate the full degree-2 gravity field by precise spacecraft orbit determination, which is dominated by J2 and C22.

31 citations


Journal ArticleDOI
TL;DR: In this article, the authors prove the global well-posedness of a scaled anisotropic Navier-Stokes system and a scaled HNS in a 2D striped domain with small analytic data in the tangential variable.

20 citations


Journal ArticleDOI
TL;DR: In this paper, the authors proposed a new compact stellar object model existing in a space filled with a distribution of anisotropic fluid matter for stellar configuration exposed to the hydrostatic equilibrium.
Abstract: We propose a new compact stellar object model existing in a space filled with a distribution of anisotropic fluid matter for stellar configuration exposed to the hydrostatic equilibrium. An analytical solution was obtained using dark-energy (DE), which is characterized by a equation of state (EoS) of the type $$p=\gamma \rho - \rho $$ corresponding to the external Schwarzschild vacuum solution through a thin envelope. We have imposed a collective function based on an adjustable coefficient to solve the Einstein field equations (EFEs). We investigate the general physical characteristics of high-density astrophysical objects based on the required solutions, with the inside structure of the stellar objects, such as the energy conditions, stability analysis, mass function, surface redshift function, velocity of sound and compactness of stellar objects through theoretical expression as well as graphic plots. In terms of our results, the physical behavior of this model can be used to model ultra-compact objects.

20 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigate the relationship between the mass loss and the energy injection at the bottom of the envelope supplied by nuclear burning taking place inside the core of a massive star.
Abstract: Context. Observations suggest that some massive stars experience violent and eruptive mass loss associated with significant brightening that cannot be explained by hydrostatic stellar models. This event seemingly forms dense circumstellar matter (CSM). The mechanism of eruptive mass loss has not been fully explained. We focus on the fact that the timescale of nuclear burning gets shorter than the dynamical timescale of the envelope a few years before core collapse for some massive stars.Aims. To reveal the properties of the eruptive mass loss, we investigate its relation to the energy injection at the bottom of the envelope supplied by nuclear burning taking place inside the core. In this study, we do not specify the actual mechanism for transporting energy from the site of nuclear burning to the bottom of the envelope. Instead, we parameterize the amount of injected energy and the injection time and try to extract information on these parameters from comparisons with observations.Methods. We carried out 1D radiation hydrodynamical simulations for progenitors of red, yellow, and blue supergiants, and Wolf–Rayet stars. We calculated the evolution of the progenitors with a public stellar evolution code.Results. We obtain the light curve associated with the eruption, the amount of ejected mass, and the CSM distribution at the time of core-collapse.Conclusions. The energy injection at the bottom of the envelope of a massive star within a period shorter than the dynamical timescale of the envelope could reproduce some observed optical outbursts prior to the core-collapse and form the CSM, which can power an interaction supernova classified as Type IIn.

20 citations


Journal ArticleDOI
Tim Stauch1
TL;DR: The results of the X-HCFF for pressure-dependent intramolecular structural changes in the investigated molecules and molecular crystals as well as a simple pressure-induced dimerization reaction are chemically intuitive and fall within the range of other established computational methods.
Abstract: A novel mechanochemical method for the simulation of molecules and molecular crystals under hydrostatic pressure, the eXtended Hydrostatic Compression Force Field (X-HCFF) approach, is introduced. In contrast to comparable methods, the desired pressure can be adjusted non-iteratively and molecules of general shape retain chemically reasonable geometries even at high pressure. The implementation of the X-HCFF approach is straightforward, and the computational cost is practically the same as for regular geometry optimization. Pressure can be applied by using any desired electronic structure method for which a nuclear gradient is available. The results of the X-HCFF for pressure-dependent intramolecular structural changes in the investigated molecules and molecular crystals as well as a simple pressure-induced dimerization reaction are chemically intuitive and fall within the range of other established computational methods. Experimental spectroscopic data of a molecular crystal under pressure are reproduced accurately.

18 citations


Journal ArticleDOI
TL;DR: A new EOS is constructed respecting the condition μ_{n}^{∞}=const, required for hydrostatic (and diffusion) equilibrium of unbound neutrons, and it is demonstrated that it is close to the catalyzed EOS in most of the inner crust, being very different from EOSs of accreted crust discussed in the literature.
Abstract: We study the equation of state (EOS) of an accreting neutron star crust. Usually, such an EOS is obtained by assuming (implicitly) that the free (unbound) neutrons and nuclei in the inner crust move together. We argue that this assumption violates the condition μ_{n}^{∞}=const, required for hydrostatic (and diffusion) equilibrium of unbound neutrons (μ_{n}^{∞} is the redshifted neutron chemical potential). We construct a new EOS respecting this condition, working in the compressible liquid-drop approximation. We demonstrate that it is close to the catalyzed EOS in most of the inner crust, being very different from EOSs of accreted crust discussed in the literature. In particular, the pressure at the outer-inner crust interface does not coincide with the neutron drip pressure, usually calculated in the literature, and is determined by hydrostatic (and diffusion) equilibrium conditions within the star. We also find an instability at the bottom of the fully accreted crust that transforms nuclei into homogeneous nuclear matter. It guarantees that the structure of the fully accreted crust remains self-similar during accretion.

17 citations


Journal ArticleDOI
TL;DR: In this article, the existence of high dense compact objects in the light of Rastall gravity theory was investigated and the validity of the obtained model was checked by studying the main salient features such as energy density, radial and tangential pressures and anisotropy factor.
Abstract: We investigate the existence of high dense compact objects in the light of Rastall gravity theory. The material content is driven by an imperfect fluid distribution and the inner geometry is described by the Tolman–Kuchowicz space–time. The validity of the obtained model is checked by studying the main salient features such as energy–density, radial and tangential pressures and anisotropy factor. Since Einstein gravity theory shares the same vacuum solution with Rastall gravity theory, the interior geometry is joining in a smoothly way with the exterior Schwarzschild’s solution. The equilibrium of the model under different gradients is analyzed by using the modified hydrostatic equilibrium equation, containing the so–called Rastall gradient. The compact structure has a positive anisotropy factor which enhances the balance and stability mechanisms. To check the potentially stable behavior, we employ Abreu’s and adiabatic index criterion. It was found that the model is completely stable. The incidence of the Rastall’s parameter $\gamma $ on all the physical quantities that characterize the model is described by the help of graphical analysis. Concerning the $\gamma $ spectrum we have considered $0.3142\leq \gamma \leq 0.3157$ . All the results are compared with the general relativity case.

16 citations


Posted Content
TL;DR: In this paper, the stability of a two-dimensional Boussinesq system with only vertical dissipation and horizontal thermal diffusion was studied and it was shown that the temperature actually smooths and stabilizes the fluids.
Abstract: The Boussinesq system for buoyancy driven fluids couples the momentum equation forced by the buoyancy with the convection-diffusion equation for the temperature. One fundamental issue on the Boussinesq system is the stability problem on perturbations near the hydrostatic balance. This problem can be extremely difficult when the system lacks full dissipation. This paper solves the stability problem for a two-dimensional Boussinesq system with only vertical dissipation and horizontal thermal diffusion. We establish the stability for the nonlinear system and derive precise large-time behavior for the linearized system. The results presented in this paper reveal a remarkable phenomenon for buoyancy driven fluids. That is, the temperature actually smooths and stabilizes the fluids. If the temperature were not present, the fluid is governed by the 2D Navier-Stokes with only vertical dissipation and its stability remains open. It is the coupling and interaction between the temperature and the velocity in the Boussinesq system that makes the stability problem studied here possible. Mathematically the system can be reduced to degenerate and damped wave equations that fuel the stabilization.

16 citations


Posted Content
TL;DR: The Mock-X analysis framework as mentioned in this paper generates synthetic images from cosmological simulations and derives halo properties via observational methods using a single temperature fit to a spectrum produced by gas with a wide temperature distribution in quasi pressure equilibrium.
Abstract: Surveys in the next decade will deliver large samples of galaxy clusters that transform our understanding of their formation. Cluster astrophysics and cosmology studies will become systematics limited with samples of this magnitude. With known properties, hydrodynamical simulations of clusters provide a vital resource for investigating potential systematics. However, this is only realized if we compare simulations to observations in the correct way. Here we introduce the \textsc{Mock-X} analysis framework, a multiwavelength tool that generates synthetic images from cosmological simulations and derives halo properties via observational methods. We detail our methods for generating optical, Compton-$y$ and X-ray images. Outlining our synthetic X-ray image analysis method, we demonstrate the capabilities of the framework by exploring hydrostatic mass bias for the IllustrisTNG, BAHAMAS and MACSIS simulations. Using simulation derived profiles we find an approximately constant bias $b\approx0.13$ with cluster mass, independent of hydrodynamical method or subgrid physics. However, the hydrostatic bias derived from synthetic observations is mass-dependent, increasing to $b=0.3$ for the most massive clusters. This result is driven by a single temperature fit to a spectrum produced by gas with a wide temperature distribution in quasi-pressure equilibrium. The spectroscopic temperature and mass estimate are biased low by cooler gas dominating the emission, due to its quadratic density dependence. The bias and the scatter in estimated mass remain independent of the numerical method and subgrid physics. Our results are consistent with current observations and future surveys will contain sufficient samples of massive clusters to confirm the mass dependence of the hydrostatic bias.

Journal ArticleDOI
TL;DR: In this article, a non-minimal geometry-matter coupling (GMC) theory of gravity is proposed to describe the mass of massive pulsars, such as PSR J2215 + 5135.
Abstract: In this work we analyze hydrostatic equilibrium configurations of neutron stars in a non-minimal geometry-matter coupling (GMC) theory of gravity. We begin with the derivation of the hydrostatic equilibrium equations for the f(R, L) gravity theory, where R and L are the Ricci scalar and Lagrangian of matter, respectively. We assume $$f(R,L)=R/2+[1+\sigma R]L$$ , with $$\sigma $$ constant. To describe matter inside neutron stars we assume a relativistic polytropic equation of state $$p=K \rho ^{\gamma }$$ , with $$\rho $$ being the energy density, K and $$\gamma = 5/3 $$ being constants. We also consider the more realistic equation of state (EoS) known as SLy4, which is a Skyrme type one based on effective nuclear interaction. We show that in this theory it is possible to reach the mass of massive pulsars, such as PSR J2215 + 5135, for both equations of state. Also, results for mass-radius relation in GMC gravity are strongly dependent on the stiffness of the EoS.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the impact of a tsunami bore traveling at high speed on a sloping beach on a simplified coastal building and found that the profile of peak impact pressures is similar to a hydrostatic distribution for each heading, but one order of magnitude greater than the hydrostatic pressure.
Abstract: The present study experimentally investigated the flow kinematics and hydrodynamic pressures and forces on a simplified coastal building under tsunami bore impact. A rectangular structure sitting on a 1/10 sloping beach at four different headings, at 0°, 15°, 30° and 45°, was considered under bore impacts. The input wave condition was designed to generate a tsunami bore traveling at high speed on a sloping beach. The interaction between bore and structure (oriented at four different headings) was investigated using the nonintrusive bubble image velocimetry technique that enables the quantitative visualization of the full-field flow behavior. Simultaneous measurements of forces and pressures during the impacts were correlated with the measured flow velocities. As the tsunami bore is highly turbulent, ensemble averages from repeated tests were obtained for the investigation. To model the interaction, the validity of a dam break solution for a sloping bed as a suitable representation was examined, while the initial water depth was approximated using wave properties and calibrated with measured bore celerity. The study found that the profile of peak impact pressures is similar to a hydrostatic distribution for each heading, but one order of magnitude greater than the hydrostatic pressure. Similar linear distribution is also found in the correlation between peak impact pressure and angle of heading. By correlating the peak impact pressures with the impact velocity, the impact coefficient was estimated as 0.55. The measured pressures were further applied to model the surge force. By examining the peak surge forces against the heading angle, the lowest magnitude occurred when the structure was orientated at 30°.


Posted ContentDOI
TL;DR: In this paper, high order well-balanced finite volume methods for the full compressible Euler system with gravity source term were proposed, which require no a priori knowledge of the hydrostatic solution.
Abstract: We introduce novel high order well-balanced finite volume methods for the full compressible Euler system with gravity source term. They require no a priori knowledge of the hydrostatic solution which is to be well-balanced and are not restricted to certain classes of hydrostatic solutions. In one spatial dimension we construct a method that exactly balances a high order discretization of any hydrostatic state. The method is extended to two spatial dimensions using a local high order approximation of a hydrostatic state in each cell. The proposed simple, flexible, and robust methods are not restricted to a specific equation of state. Numerical tests verify that the proposed method improves the capability to accurately resolve small perturbations on hydrostatic states.

Journal ArticleDOI
TL;DR: The same model can be applied to study metre-scale waves, even beyond breaking, with results closely matching those obtained using small-scale Euler/Navier-Stokes models, and coastal or global scale dispersive waves, with an accuracy and efficiency comparable to extended Boussinesq wave models.


Journal ArticleDOI
TL;DR: A two-layer model with two different axes of integration and a well-balanced finite volume method to study submarine avalanches and generated tsunamis by a depth-averaged model with different averaged directions for the fluid and the granular layers is proposed.

Journal ArticleDOI
TL;DR: In this article, the authors investigated the observational signatures of a two-component molecular disc by theoretically modeling two components in a sample of eight nearby spiral galaxies and solved the joint Poisson's-Boltzmann equation to estimate the three-dimensional distribution of the molecular gas and the molecular scale height in the sample galaxies.
Abstract: As recent observations of the molecular discs in spiral galaxies point to the existence of a diffuse, low-density thick molecular disc along with the prominent thin one, we investigate the observational signatures of this thick disc by theoretically modelling two-component molecular discs in a sample of eight nearby spiral galaxies. Assuming a prevailing hydrostatic equilibrium, we set up and solved the joint Poisson's-Boltzmann equation to estimate the three-dimensional distribution of the molecular gas and the molecular scale height in our sample galaxies. The molecular scale height in a two-component molecular disc is found to vary between $50-300$ pc, which is higher than what is found in a single-component disc. We find that this scale height can vary significantly depending on the assumed thick disc molecular gas fraction. We also find that the molecular gas flares as a function of the radius and follows a tight exponential law with a scale length of $\left(0.48 \pm 0.01 \right) r_{25}$. We used the density solutions to produce the column density maps and spectral cubes to examine the ideal observing conditions to identify a thick molecular disc in galaxies. We find that unless the molecular disc is an edge-on system and imaged with a high spatial resolution ($\lesssim 100$ pc), it is extremely hard to identify a thick molecular disc in a column density map. The spectral analysis further reveals that at moderate to high inclination ($i \gtrsim 40^o$), spectral broadening can fictitiously introduce the signatures of a two-component disc into the spectral cube of a single-component disc. Hence, we conclude that a low inclination molecular disc imaged with high spatial resolution would serve as the ideal site for identifying the thick molecular disc in galaxies.

Journal ArticleDOI
TL;DR: In this article, a finite element model of a static seal assembled in its housing has been built and is utilized to study how the seal deforms under varying loading conditions, and the simulation showed that the surface profile is distorted due to the hydrostatic pressure.
Abstract: A finite element model of a static seal assembled in its housing has been built and is utilized to study how the seal deforms under varying loading conditions. The total contact load on the sealing surface is balanced by the sealed fluid pressure and the friction between the seal and the housing sidewall perpendicular to the sealing surface. The effect of the sealed fluid pressure between the sealing surfaces was investigated and the simulation showed that the surface profile is distorted due to the hydrostatic pressure. We study the distorted contact profile with varying sealed fluid pressure and propose five parameters to describe the corresponding contact pressure profile. One of these parameters, overshoot pressure, a measure of the difference between maximum contact pressure and the sealed fluid pressure, is an indicator of sealing performance. The simulations performed show different behaviors of the overshoot pressure with sealed fluid pressure for cosinusoidal and parabolic surfaces with the same peak to valley (PV) value.

Journal ArticleDOI
TL;DR: In this paper, the authors developed spherically symmetric time-dependent and steady-state hydrodynamical models of the radiation-driven wind outflows and associated mass loss from classical Wolf-Rayet stars.
Abstract: Vigorous mass loss in the classical Wolf-Rayet (WR) phase is important for the late evolution and final fate of massive stars. We develop spherically symmetric time-dependent and steady-state hydrodynamical models of the radiation-driven wind outflows and associated mass loss from classical WR stars. The simulations are based on combining the opacities typically used in static stellar structure and evolution models with a simple parametrised form for the enhanced line-opacity expected within a supersonic outflow. Our simulations reveal high mass-loss rates initiated in deep and hot optically thick layers around T\approx 200kK. The resulting velocity structure is non-monotonic and can be separated into three phases: i) an initial acceleration to supersonic speeds ii) stagnation and even deceleration, and iii) an outer region of rapid re-acceleration. The characteristic structures seen in converged steady-state simulations agree well with the outflow properties of our time-dependent models. By directly comparing our dynamic simulations to corresponding hydrostatic models, we demonstrate explicitly that the need to invoke extra energy transport in convectively inefficient regions of stellar structure and evolution models is merely an artefact of enforcing a hydrostatic outer boundary. Moreover, the "dynamically inflated" inner regions of our simulations provide a natural explanation for the often-found mismatch between predicted hydrostatic WR radii and those inferred from spectroscopy. Finally, we contrast our simulations with alternative recent WR wind models based on co-moving frame radiative transfer for computing the radiation force. Since CMF transfer currently cannot handle non-monotonic velocity fields, the characteristic deceleration regions found here are avoided in such simulations by invoking an ad-hoc very high degree of clumping.

Journal ArticleDOI
TL;DR: A novel apparatus for acoustic wave transmission measurements at low static confinement pressure is presented, using a voice-coil-driven wall, with a large variety of signal shapes, frequencies, and amplitudes, which enables experiments in both the linear and strongly nonlinear regimes.
Abstract: Elastic properties of a granular packing show nonlinear behavior determined by its discrete structure and nonlinear inter-grain force laws. Acoustic waves show a transition from constant, pressure-dependent sound speed to a shock-wave like behavior with amplitude-determined propagation speed. This becomes increasingly visible at low static confinement pressure as the transient regime shifts to lower wave amplitudes for lower static pressure. In microgravity, confinement pressure can be orders of magnitude lower than in a ground based experiment. Also, the absence of hydrostatic gradients allows for much more homogeneous and isotropic pressure distribution. We present a novel apparatus for acoustic wave transmission measurements at such low packing pressures. A pressure control loop is implemented by a microcontroller that monitors static force sensor readings and adjusts the position of a movable wall with a linear motor until the desired pressure is reached. Measurements of acoustic waves are possible using accelerometers embedded in the granular packing as well as piezos. For excitation we use a voice coil-driven wall, with a large variety of signal shapes, frequencies and amplitudes. This enables experiments both in the linear and strongly nonlinear regime.

Journal ArticleDOI
TL;DR: In this paper, the authors study non-rotating and isotropic strange quark stars in Lorentz-violating theories of gravity, and in particular in Hořava gravity and Einstein-aether theory.
Abstract: We study non-rotating and isotropic strange quark stars in Lorentz-violating theories of gravity, and in particular in Hořava gravity and Einstein-aether theory. For quark matter we adopt both linear and non-linear equations of state, corresponding to the MIT bag model and color flavor locked state, respectively. The new structure equations describing hydrostatic equilibrium generalize the usual Tolman–Oppenheimer–Volkoff (TOV) equations of Einstein’s general relativity. A dimensionless parameter $$ u $$ measures the deviation from the standard TOV equations, which are recovered in the limit $$ u \rightarrow 0$$. We compute the mass, the radius as well as the compactness of the stars, and we show graphically the impact of the parameter $$ u $$ on the mass-to-radius profiles for different equations of state describing quark matter. The energy conditions and stability criteria are also considered, and they are all found to be fulfilled.

Journal ArticleDOI
TL;DR: In this paper, the authors studied the possibility of forming anisotropic compact stars in the framework of f(R)-modified gravity in a static spherically symmetric space-time.
Abstract: We study the possibility of forming anisotropic compact stars in the framework of f(R)-modified gravity in a static spherically symmetric space-time. We find the unknown coefficients involved in the metric using masses and radii of the compact stars 4U 1820-30, Cen X-3, EXO 1785-248, and LMC X-4. We obtain the hydrostatic equilibrium equation for different forces and use the generalized Tolman-Oppenheimer-Volkoff equation to analyze the behavior of stars. Moreover, we verify the regularity conditions, anisotropic behavior, energy conditions, and stability of the compact stars. We use the effective energy-momentum tensor in f(R) gravity for the analysis. We show that in the framework of f(R) gravity theory, these compact stars have physically acceptable patterns. Our results here also agree with those in general relativity, which is a special case of f(R) gravity.

Journal ArticleDOI
TL;DR: A non-hydrostatic depth-averaged model for dry granular flows is proposed, taking into account vertical acceleration, and it is shown that non-Hydrostatic models are less sensitive to the choice of the coordinate system.
Abstract: A non-hydrostatic depth-averaged model for dry granular flows is proposed, taking into account vertical acceleration. A variable friction coefficient based on the $\mu(I)$ rheology is considered. The model is obtained from an asymptotic analysis in a local reference system, where the non-hydrostatic contribution is supposed to be small compared to the hydrostatic one. The non-hydrostatic counterpart of the pressure may be written as the sum of two terms: one corresponding to the stress tensor and the other to the vertical acceleration. The model introduced here is weakly non-hydrostatic, in the sense that the non-hydrostatic contribution related to the stress tensor is not taken into account due to its complex implementation. A simple and efficient numerical scheme is proposed. It consists of a three-step splitting procedure, and it is based on a hydrostatic reconstruction. Two key points are: (i) the friction force has to be taken into account before solving the non-hydrostatic pressure. Otherwise, the incompressibility condition is not ensured; (ii) both the hydrostatic and the non-hydrostatic pressure are taken into account when dealing with the friction force. The model and numerical scheme are then validated based on several numerical tests, including laboratory experiments of granular collapse. The influence of non-hydrostatic terms and of the choice of the coordinate system (Cartesian or local) is analyzed. We show that non-hydrostatic models are less sensitive to the choice of the coordinate system. In general, the non-hydrostatic model introduced here much better reproduces granular collapse experiments compared to hydrostatic models. An important result is that the simulated mass profiles up to the deposit and the front velocity are greatly improved. As expected, the influence of the non-hydrostatic pressure is shown to be larger for small values of the slope.

Journal ArticleDOI
TL;DR: In this paper, the Tolman-Oppenheimer-Volkov (TOV) equation of hydrostatic equilibrium and the ideal gas equation of state were used to calculate the masses of 12 relaxed clusters with Chandra X-ray data.

Posted Content
TL;DR: In this paper, the authors used the Poisson's-Boltzmann equation to estimate the vertical scale height (defined as the Half Width at Half Maxima (HWHM) of the density distribution) of atomic hydrogen (HI) as a function of radius.
Abstract: Assuming a vertical hydrostatic equilibrium in the baryonic discs, joint Poisson's-Boltzmann equation was set up and solved numerically in a sample of 23 nearby dwarf galaxies from the LITTLE-THINGS survey. This is the largest sample to date for which detailed hydrostatic modeling is performed. The solutions of the Poisson's-Boltzmann equation provide a complete three-dimensional distribution of the atomic hydrogen (HI) in these galaxies. Using these solutions, we estimate the vertical scale height (defined as the Half Width at Half Maxima (HWHM) of the density distribution) of the HI as a function of radius. We find that the scale height in our sample galaxies varies between a few hundred parsecs at the center to a few kiloparsecs at the edge. These values are significantly higher than what is observed in spiral galaxies. We further estimate the axial ratios to investigate the thickness of the HI discs in dwarf galaxies. For our sample galaxies, we find a median axial ratio to be 0.40, which is much higher than the same observed in the Milky Way. This indicates that the vertical hydrostatic equilibrium results in thicker HI discs in dwarf galaxies naturally.

Posted Content
TL;DR: In this article, the authors used the versatile relative entropy inequality to prove rigorously the limit from the compressible Navier-Stokes equations to compressible Primitive Equations.
Abstract: In this work, we obtain the hydrostatic approximation by taking the small aspect ratio limit to the Navier-Stokes equations. The aspect ratio (the ratio of the depth to horizontal width) is a geometrical constraint in general large scale geophysical motions that the vertical scale is significantly smaller than horizontal. We use the versatile relative entropy inequality to prove rigorously the limit from the compressible Navier-Stokes equations to the compressible Primitive Equations. This is the first work to use relative entropy inequality for proving hydrostatic approximation and derive the compressible Primitive Equations.

Journal ArticleDOI
TL;DR: In this article, a theoretical study of the nonlinear optical properties of shallow-donor impurities in semiconductors subjected to magnetic fields, hydrostatic pressures, and intense laser illumination within the Voigt configuration is presented.
Abstract: We present a theoretical study of the nonlinear optical properties of shallow-donor impurities in semiconductors subjected to magnetic fields, hydrostatic pressures, and intense laser illumination within the Voigt configuration. The donor energy levels and their wave functions are obtained using a combination of nonperturbative and variational methods where intense laser field effects are exactly taken into account through a laser-dressed Coulomb potential (LdCP). The combined effects of radiation and magnetic fields, hydrostatic pressures, and temperatures on the linear, third-order nonlinear, and total optical absorption coefficients (OACs) for the 1 s → 2 p ± and 2 p z transitions are investigated using a compact density-matrix approach. We find that the transition energies and geometric factors can be increased or decreased by changing external fields via the LdCP or by changing hydrostatic pressures and temperatures. In this way, saturable absorption depends not only on the incident optical intensity but also on the laser field, which is more easily realized in the z-polarization direction. The peak positions and magnitudes of the linear, third-order nonlinear, and total OACs can be effectively adjusted with an appropriate choice of these external perturbations. Moreover, hydrostatic pressures and temperatures affect these OACs in an opposite way. This opens a promising route to design new and efficient impurity-based devices manipulated by external perturbations.

Journal ArticleDOI
TL;DR: In this paper, a pressure control loop is implemented by using a microcontroller that monitors static force sensor readings and adjusts the position of a movable wall with a linear-motor until the desired pressure is reached.
Abstract: Elastic properties of a granular packing show a nonlinear behavior determined by its discrete structure and nonlinear inter-grain force laws. Acoustic waves show a transition from constant, pressure-dependent sound speed to a shock-wave-like behavior with an amplitude-determined propagation speed. This becomes increasingly visible at low static confinement pressure as the transient regime shifts to lower wave amplitudes for lower static pressure. In microgravity, confinement pressure can be orders of magnitude lower than in a ground-based experiment. In addition, the absence of hydrostatic gradients allows for much more homogeneous and isotropic pressure distribution. We present a novel apparatus for acoustic wave transmission measurements at such low packing pressures. A pressure control loop is implemented by using a microcontroller that monitors static force sensor readings and adjusts the position of a movable wall with a linear-motor until the desired pressure is reached. Measurements of acoustic wav...