Variation of the gas and radiation content in the sub-Keplerian accretion disk around black holes and its impact to the solutions

We investigate the variation of the gas and the radiation pressure in accretion disks during the infall of matter to the black hole and its effect to the flow. While the flow far away from the black hole might be non-relativistic, in the vicinity of the black hole it is expected to be relativistic behaving more like radiation. Therefore, the ratio of gas pressure to total pressure (β) and the underlying polytropic index (γ) should not be constant throughout the flow. We obtain that accretion flows exhibit significant variation of β and then γ, which affects solutions described in the standard literature based on constant β. Certain solutions for a particular set of initial parameters with a constant β do not exist when the variation of β is incorporated appropriately. We model the viscous sub-Keplerian accretion disk with a nonzero component of advection and pressure gradient around black holes by preserving the conservations of mass, momentum, energy, supplemented by the evolution of β. By solving the set of five coupled differential equations, we obtain the thermo-hydrodynamical properties of the flow. We show that during infall, β of the flow could vary up to ∼300%, while γ up to ∼20%. This might have a significant impact to the disk solutions in explaining observed data, e.g. super-luminal jets from disks, luminosity, and then extracting fundamental properties from them. Hence any conclusion based on constant γ and β should be taken with caution and corrected.     

Thermal expansion of Mg(OH)<Subscript>2</Subscript> brucite under high pressure and pressure dependence of entropy

An equation of state for Mg(OH)₂ brucite under high-pressure and high-temperature conditions has been obtained by measuring temperature dependence of volume up to 600 K at ambient pressure and pressure dependence of volume up to 16 GPa at 300, 473, 673, and 873 K with in situ X-ray diffraction. Pressure dependence of entropy of brucite has been calculated with thermal expansion coefficient and volume which are derived from the present EoS. This dependence indicates that generation of secondary OH dipoles affects entropy. The OH dipoles probably appear around 2 GPa and the number seems not to change over 8 GPa at 300 K.     

Computational validation of the Generalized Sutherland Equation for bubble–particle encounter efficiency in flotation

Bubble–particle encounter during flotation is governed by liquid flow relative to the rising bubble, which is a function of the adsorbed frothers, collectors, and other surfactants and surface contaminants. Due to surface contamination, the bubble surface in flotation has been considered as immobile (rigid). However, surface contamination can be swept to the backside of the rising bubble due to the relative liquid flow, leaving the front surface of the rising bubble mobile with a non-zero tangential component of the liquid velocity. The bubble with a mobile surface was considered by Sutherland who applied the potential flow condition and analyzed the bubble–particle encounter using a simplified particle motion equation without inertia. The Sutherland model was found to over-predict the encounter efficiency and has been improved by incorporating inertial forces which are amplified at the mobile surface with a non-zero tangential velocity component of the liquid phase. An analytical solution was obtained for the encounter efficiency using approximate equations and is called the Generalized Sutherland Equation (GSE). In this paper, the bubble–particle encounter interaction with the potential flow condition has been analyzed by solving the full motion equation for the particle employing a numerical computational approach. The GSE model was compared with the exact numerical results for the encounter efficiency. The comparison only shows good agreement between the GSE prediction and the numerical data for ultrafine particles (< 10 μm in diameter), the inertial forces of which are vanishingly small. For non-ultrafine particles, a significant deviation of the GSE model from the numerical data has been observed. Details of the numerical methodology and solutions for the (collision) angle of tangency and encounter efficiency are described.     

Crystal structure and cation lone electron pair activity of Bi2S3 between 0 and 10 GPa

Crystal structure of Bi₂S₃ was refined at eight distinct hydrostatic pressures in the range 0–10 GPa using a CCD equipped 4-circle diffractometer and a diamond-anvil cell. Coefficients of the BM3 equation of state are as follows: zero-pressure volume 498.4(7) Å³, bulk modulus K ₀ 36.6(15) GPa and its pressure derivative 6.4(5). The bulk of compression takes place in the structural space between Bi₄S₆ ribbons, where lone-electron pairs are accommodated. Eccentricity of Bi in its coordination polyhedra decreases in the process, with long Bi–S distances decreasing, whereas the opposing short Bi–S distances stay constant or even increase in length. All these phenomena are compatible with the movement of lone-electron pairs of Bi closer to the parent atom at increasing pressure.     

Effect of incorporation of iron and aluminum on the thermoelastic properties of magnesium silicate perovskite

In situ X-ray diffraction measurements of Fe- and Al-bearing MgSiO₃-rich perovskite (FeAl-Pv), which was synthesized from a natural orthopyroxene, were performed at pressures of 19–32 GPa and temperatures of 300–1,500 K using a combination of a Kawai-type apparatus with eight sintered-diamond anvils and synchrotron radiation. Two runs were performed using a high-pressure cell with two sample chambers, and both MgSiO₃ perovskite (Mg-Pv) and FeAl-Pv were synthesized simultaneously in the same cell. Thus we were able to measure specific volumes (V/V ₀) of Mg-Pv and FeAl-Pv at the same P−T conditions. At all the measurement conditions, values of the specific volume of FeAl-Pv are consistent with those of Mg-Pv within 2 Standard Deviation, strongly suggesting that effect of incorporation of iron and aluminum on the thermoelastic properties of magnesium silicate perovskite is undetectable in this composition, pressure, and temperature range. Two additional runs were performed using a high-pressure cell that has one sample chamber and unit-cell volumes of FeAl-Pv were measured at pressures and temperatures up to 32 GPa and 1,500 K, respectively. All the unit-cell volume data of FeAl-Pv perovskite were fitted to the high temperature Birch–Murnaghan equation of state and a complete set of thermoelastic parameters of this perovskite was determined with an assumption of K′ _300,0 = 4. The determined parameters are K _300,0 = 243(3) GPa, (∂K _T,0/∂T) _P = −0.030(8) GPa/K, a ₀ = 2.78(18) × 10⁻⁵ K⁻¹, and b ₀ = 0.88(28) × 10⁻⁸ K⁻², where a ₀ and b ₀ are the coefficients of the following expression describing the zero-pressure thermal expansion: α _T,0 = a ₀ + b ₀ T. The equation-of-state parameters of FeAl-Pv are in good agreement with those of MgSiO₃ perovskite at the conditions corresponding to the uppermost part of the lower mantle.     

THE DENSITIES OF CHANGJIANG ESTUARINE WATERS

The International Eq一lation of State of Seawater,1980 and the PraeticalSalinity Scale,1978 have been adoPted by theUNESCO江CES沼COR八APSOJoint Panel ono‘eanogral,hie Tables and Standards(JPOTS),and endorsed bythese organizati6ns(Miller‘〕and Poisson,1981;Uneseo,1981).Th已new equa-tion and the Praetieal Salinity Seale are to be used for all values Published fromJan .1,1982 .The new equation 15 aeeurate for use in all oeeanie surfaee waters,but eannot be aeeurately aPPlied to…     

The Gibbs energy formulation of the α, β, and γ forms of Mg2SiO4 using Grover, Getting and Kennedy's empirical relation between volume and bulk modulus

 The empirical linear relation between volume and logarithm of bulk modulus of a material, discovered by Grover, Getting and Kennedy is taken as the basis for our equation of state. Using the latest experimental information on the adiabatic bulk modulus, the equation of state is applied to the three polymorphs of Mg₂SiO₄ to develop a consistent dataset of their thermodynamic properties in the temperature range of 200–2273 K and a pressure range of 0.1 MPa–30 GPa. The results imply that the bulk sound velocity contrast (v ^β−v ^α)/v ^α increases with temperature along the α–β phase boundary and reaches the value 8.9% at 13.5 GPa, a pressure equivalent to 410 km depth in the Earth. The bulk sound velocity contrast (v ^γ−v ^β)/v ^β decreases with temperature along the β–γ phase boundary and becomes less than 0.7% at temperatures and pressures equivalent to those associated with the 520-km seismic discontinuity in the Earth. Received: 1 August 2000 / Accepted: 1 March 2001     

A comparative method for various approaches to the isothermal equation of state

Various three-parameter approximations of the isothermal equation of state of matter can be systematized and, in consequence, mutually compared by using the uniquely associated relationships between first and second pressure derivatives of the bulk modulus of any substance at zero pressure. Thus quantitative or, at least qualitative information on the capability of such approximations for volumetric contractions down to about 0.5 can be obtained directly. This comparative method will be discussed with the aid of 19 approximations considered in high-pressure physics and geophysics. Its application to the Grüneisen parameter analysis yields a number of additional practical approximations.     

The equation of motion for a small aerosol in a continuum

Summary The motion of an aerosol can be described by a general force balance equation, independent of the detailed structure of the flow, provided that the interaction between the external flow field and the local flow induced by the aerosol is weak. A necessary and sufficient condition for the interaction to be weak is that the length scale of the aerosol is much less than that of the external flow. High and low Reynolds number regimes can be distinguished for the motion of an aerosol relative to the external flow. In some extreme conditions the equation of motion reduces to an algebraic equation for the aerosol velocity.After submission of this article the author was made aware of a similar treatment published inTopics of Appl. Phys., 12 (Turbulence, Chapter 7), Springer Verlag, Berlin, which at the time of the article's submission had not yet appeared in Australia. (Ed.)     

Urbanization on the Mongolian Plateau after economic reform: Changes and causes

In response to changes in human and natural environments over the past three decades, transitional countries have experienced dramatic urbanization. In the context of socioeconomic and biophysical changes, our knowledge on these urbanization processes remains limited. Here, we used the Mongolian Plateau (i.e., Inner Mongolia (IM) and Mongolia (MG)) as a testbed and applied the coupled natural and human (CNH) concept to understand the processes and causes of urbanization. We selected six cities on the Mongolian Plateau, classified their urban built-up areas using Geographic Object-Based Image Analysis (GEOBIA) from 1990 through 2015, and examined the driving forces of urbanization (i.e., economy, social goods, and environmental variables) through Partial Least Squares Structural Equation Modeling (PLS-SEM). We found that the spatial characteristics of urbanization in IM and MG have both similarities and differences. The cities in IM and MG have experienced rapid urban expansion, with urban areas increasing by 4.36 times and 3.12 times, respectively, since 1990. Cities in IM, however, were less dense and more sprawling whereas cities in MG were linearly aggregated. We also found through PLS-SEM that multiple driving forces affected urbanization in IM and MG during the transitional period. Results (path coef.) demonstrated that economic development (0.559) is a major driver for urbanization in IM, whereas social goods (0.646) and economic development (0.433) strongly influence urbanization in MG. These differences are likely due to the divergent governmental roles in urban development and in infrastructure/social support, as well as the differing economic structures in IM and MG.