Spherical Gas Research Articles

Aerothermodynamics of a sphere in a monatomic gas based on ab initio interatomic potentials over a wide range of gas rarefaction: subsonic flows

Aerothermodynamic characteristics of a sphere in a subsonic flow are calculated over a broad range of gas rarefaction by the direct simulation Monte Carlo method based on ab initio interatomic potentials and Cercignani–Lampis surface scattering kernel. Calculations of the drag and average energy transfer coefficients are performed for various noble gases in the range of Mach number from 0.1 to 1. The obtained results point out that the influence of the interatomic potential is weak in subsonic flows. A comparison of the present results with a linear theory shows that the numerical solutions at Mach number equal to 0.1 are close to those obtained from the linearized kinetic equation in the transitional and free-molecular regimes. In the near-continuum flow regime, the difference between the present solution and the linear theory is significant. To reveal the effects of the gas–surface accommodation, a few sets of the tangential momentum and normal energy accommodation coefficients are considered in simulations. It is shown that the effect of the accommodation coefficients on the sphere drag is not trivial, and, for non-diffuse scattering, the drag coefficient can be either larger or smaller than that for diffuse scattering. The effect of the sphere temperature is also investigated and the calculated values of the average energy transfer coefficient are used to find the Stanton number, recovery factor and adiabatic surface temperature. The numerical results for the sphere drag and energy transfer are compared with the semi-empirical fitting equations known from the literature.

A new fourth-order compact finite difference method for solving Lane-Emden-Fowler type singular boundary value problems

We develop a novel fourth-order compact finite difference scheme to solve nonlinear singular ordinary differential equations. Such problems occur in many fields of science and engineering, such as studying the equilibrium of an isothermal gas sphere, reaction–diffusion in a spherical permeable catalyst, etc. These problems are challenging to solve because of their singularity or nonlinearity. By our proposed method, we can easily solve these complex problems without removing or modifying the singularity. To construct the new fourth-order compact difference method, Initially, we created a uniform mesh within the solution domain and developed a compact finite difference scheme. This scheme approximates the derivatives at the boundary nodal points to handle the problem’s singularity effectively. Employing a matrix analysis approach, we discussed the convergence analysis of the methods. To demonstrate its efficacy, we apply our approach to solve various real-life problems from the literature. The new method offers high-order accuracy with minimal grid points and provides better numerical results than the nonstandard finite difference method and exponential compact finite difference method.

Linear pressure waves in mono- and poly-disperse bubbly liquids: Attenuation and propagation speed in slow and fast and evanescent modes

Using volumetric averaged equations from a two-fluid model, this study theoretically investigates linear pressure wave propagation in a quiescent liquid with many spherical gas bubbles. The speed and attenuation of sound are evaluated using the derived linear dispersion. Mono- and poly-disperse bubbly liquids are treated. To precisely describe the attenuation effect, some forms of bubble dynamics equations and temperature gradient models are employed. Focusing on the dissipative effect, we analyze the stop band that occurs in the linear dispersion relation. In the two-fluid model, even if the dissipation effect is considered, the inconvenience that the wavenumber diverges to infinity in the resonance frequency cannot be resolved. Additionally, the validity of terminating that wavenumber value in the middle of the frequency is demonstrated. To determine a linear dispersion relation that can exactly predict thermal conduction and acoustic radiation, wave propagation velocities and attenuation coefficients are compared with some experimental data and existing models. The results show that thermal conduction and acoustic radiation should be set appropriately to accurately predict the propagation velocity and attenuation except in the high frequency range, the phase velocity in the resonance frequency range, or the attenuation in the high frequency range.

Stability and cavitation of nanobubble: Insights from large-scale atomistic molecular dynamics simulations.

We perform large-scale atomistic simulations of a system containing 12 × 106 atoms, comprising an oxygen gas-filled bubble immersed in water, to understand the stability and cavitation induced by ultrasound. First, we propose a method to construct a bubble/water system. For a given bubble radius, the pressure inside the bubble is estimated using the Young-Laplace equation. Then, this pressure is used as a reference for a constant temperature, constant pressure simulation of an oxygen system, enabling us to extract a sphere of oxygen gas and place it into a cavity within an equilibrated water box. This ensures that the Young-Laplace equation is satisfied and the bubble is stable in water. Second, this stable bubble is used for ultrasound-induced cavitation simulations. We demonstrate that under weak ultrasound excitation, the bubble undergoes stable cavitation, revealing various fluid velocity patterns, including the first-order velocity field and microstreaming. These fluid patterns emerge around the bubble on a nanometer scale within a few nanoseconds, a phenomenon challenging to observe experimentally. With stronger ultrasound intensities, the bubble expands significantly and then collapses violently. The gas core of the collapsed bubble, measuring 3-4nm, exhibits starfish shapes with temperatures around 1500K and pressures around 6000bar. The simulation results are compared with those from Rayleigh-Plesset equation modeling, showing good agreement. Our simulations provide insights into the stability and cavitation of nanosized bubbles.

Massive star cluster formation

The mode of star formation that results in the formation of globular clusters and young massive clusters is difficult to constrain through observations. We present models of massive star cluster formation using the TORCH framework, which uses the Astrophysical MUltipurpose Software Environment (AMUSE) to couple distinct multi-physics codes that handle star formation, stellar evolution and dynamics, radiative transfer, and magnetohydrodynamics. We upgraded TORCH by implementing the N-body code PETAR, thereby enabling TORCH to handle massive clusters forming from 106 M⊙ clouds with ≥105 individual stars. We present results from TORCH simulations of star clusters forming from 104, 105, and 106 M⊙ turbulent spherical gas clouds (named M4, M5, M6) of radius R = 11.7 pc. We find that star formation is highly efficient and becomes more so at a higher cloud mass and surface density. For M4, M5, and M6 with initial surface densities 2.325 × 101,2,3 M⊙ pc−2, after a free-fall time of tff = 6.7,2.1,0.67 Myr, we find that ∼30%, 40%, and 60% of the cloud mass has formed into stars, respectively. The end of simulation-integrated star formation efficiencies for M4, M5, and M6 are ϵ⋆ = M⋆/Mcloud = 36%, 65%, and 85%. Observations of nearby clusters similar in mass and size to M4 have instantaneous star formation efficiencies of ϵinst ≤ 30%, which is slightly lower than the integrated star formation efficiency of M4. The M5 and M6 models represent a different regime of cluster formation that is more appropriate for the conditions in starburst galaxies and gas-rich galaxies at high redshift, and that leads to a significantly higher efficiency of star formation. We argue that young massive clusters build up through short efficient bursts of star formation in regions that are sufficiently dense (Σ ≥ 102 M⊙ pc−2) and massive (Mcloud ≥ 105 M⊙). In such environments, stellar feedback from winds and radiation is not strong enough to counteract the gravity from gas and stars until a majority of the gas has formed into stars.

Disc novae: thermodynamics of gas-assisted binary black hole formation in AGN discs

ABSTRACT We investigate the thermodynamics of close encounters between stellar mass black holes (BHs) in the gaseous discs of active galactic nuclei (AGNs), during which binary black holes (BBHs) may form. We consider a suite of 2D viscous hydrodynamical simulations within a shearing box prescription using the Eulerian grid code athena++. We study formation scenarios where the fluid is either an isothermal gas or an adiabatic mixture of gas and radiation in local thermal equilibrium. We include the effects of viscous and shock heating, as well as optically thick cooling. We co-evolve the embedded BHs with the gas, keeping track of the energetic dissipation and torquing of the BBH by gas and inertial forces. We find that compared to the isothermal case, the minidiscs formed around each BH are significantly hotter and more diffuse, though BBH formation is still efficient. We observe massive blast waves arising from collisions between the radiative minidiscs during both the initial close encounter and subsequent periapsis periods for successfully bound BBHs. These ‘disc novae’ have a profound effect, depleting the BBH Hill sphere of gas and injecting energy into the surrounding medium. In analysing the thermal emission from these events, we observe periodic peaks in local luminosity associated with close encounters/periapses, with emission peaking in the optical/near-infrared (IR). In the AGN outskirts, these outbursts can reach 4 per cent of the AGN luminosity in the IR band, with flares rising over 0.5–1 yr. Collisions in different disc regions, or when treated in 3D with magnetism, may produce more prominent flares.

Investigating neutron scattering in a Spherical Proportional Counter: A tabletop experiment

In this paper, we report on a tabletop experiment studying neutron scattering in a Spherical Proportional Counter using an Am-Be source. Systematic studies were carried out to investigate the effect of gas mixture, pressure, operating voltage, and sphere size on the drift time-rise time relationship of the signal in a spherical proportional counter. Our experimental results showed good agreement with MagBoltz-based simulations. These findings are a crucial step towards measuring the quenching factor in gases using a neutron beam for the New Experiments With Spheres-Gas (NEWS-G) experiment and has important implications for the development of neutron detection techniques and their potential applications in nuclear and particle physics.

Visual outcome in Keratoconus with spherical rigid gas permeable contact lens

Introduction: Keratoconus is a bileteral asymetric progressive ecteria of cornea commonly associated with vernal keratoconjunctivitis and Atopic dermatitis. Rigid gas permeable (RGP) contact lens is the first choice for refractive correction in keratoconic eyes. The visual outcome in Keratoconus with spherical RGP contact lens along with the mean age of presentation, gender predominance, ethnicity, associated conditions, refractive error and corneal astigmatism was evaluated. Methods: The records of the Keratoconus patients attending cornea and contact lens clinic for last 6 years were reviewed and analyzed using SPSS-14 software. Data on laterality, race, age, gender, refractive error, visual acuity (VA), associated conditions and contact lens parameters were obtained. A total of 22 patients with 38 keratoconic eyes were included in the study. Results: The mean age of Keratoconus presentation was 18.11 ± 4.45 years. Sixteen cases (72.73 %) were bilateral; 6 (27.27 %) were unilateral. Mean uncorrected visual acuity (UCVA) was 0.86 ± 0.40 Log MAR. Mean spectacle visual acuity was 0.54 ± 0.38 Log MAR. Mean visual acuity with spherical RGP contact lenses was 0.08 ± 0.14 Log MAR. The difference between mean spectacle visual acuity and mean VA with spherical RGP contact lens was statistically significant (p < 0.001). Conclusion: In all stages of Keratoconus, improvement in visual acuity with spherical RGP contact lens was highly significant.

Analytical method for systems of nonlinear singular boundary value problems

The standard Lane–Emden equations model several physical phenomena such as isotropic continuous media, thermal behaviour of a spherical cloud of gas, and isothermal gas spheres. Systems of Lane–Emden-type equations appear in the modelling of the concentration of carbon substrate and oxygen, catalytic diffusion reactions, the steady state concentration of carbon dioxide, dusty fluid models, and pattern formation. In solving singular boundary value problems, one faces challenges resulting from the divergence of the associated variable coefficients at the singular points. This research article explores the power series approach to analytically approximate solutions to a class of systems of strongly nonlinear singular boundary value problems of Lane–Emden-type. The nonlinear terms in the proposed problems are transformed into power series using the generalised Cauchy product before establishing explicit recursion formulae for the expansion coefficients of the system of series solutions. The initial conditions required in the proposed boundary value problems are assumed and determined from a set of nonlinear algebraic equations resulting from the given right boundary conditions. Three special systems of nonlinear singular boundary value problems of Lane–Emden type are presented to demonstrate the proposed method’s reliability, effectiveness, and accuracy. The obtained approximate solutions are compared with the exact solutions (where they are available), or with other existing results (where the exact solution is not readily available). The series solution of the first example has a slow convergent rate, while the results of the other two examples are in excellent agreement with the exact solutions and other published results.

One-Step Preparation of Magnetic Lipid Bubbles: Magnetothermal Effect Induces the Simultaneous Formation of Gas Nuclei and Self-Assembly of Phospholipids.

In recent years, enveloped micro-nanobubbles have garnered significant attention in research due to their commendable stability, biocompatibility, and other notable properties. Currently, the preparation methods of enveloped micro-nanobubbles have limitations such as complicated preparation process, large bubble size, wide distribution range, low yield, etc. There exists an urgent demand to devise a simple and efficient method for the preparation of enveloped micro-nanobubbles, ensuring both high concentration and a uniform particle size distribution. Magnetic lipid bubbles (MLBs) are a multifunctional type of enveloped micro-nanobubble combining magnetic nanoparticles with lipid-coated bubbles. In this study, MLBs are prepared simply and efficiently by a magneto internal heat bubble generation process based on the interfacial self-assembly of iron oxide nanoparticles induced by the thermogenic effect in an alternating magnetic field. The mean hydrodynamic diameter of the MLBs obtained was 384.9 ± 8.5 nm, with a polydispersity index (PDI) of 0.248 ± 0.021, a zeta potential of -30.5 ± 1.0 mV, and a concentration of (7.92 ± 0.46) × 109 bubbles/mL. Electron microscopy results show that the MLBs have a regular spherical stable core-shell structure. The superparamagnetic iron oxide nanoparticles (SPIONs) and phospholipid layers adsorbed around the spherical gas nuclei of the MLBs, leading the particles to demonstrate commendable superparamagnetic and magnetic properties. In addition, the effects of process parameters on the morphology of MLBs, including phospholipid concentration, phospholipid proportiona, current intensity, magnetothermal time, and SPION concentration, were investigated and discussed to achieve controlled preparation of MLBs. In vitro imaging results reveal that the higher the concentration of MLBs loaded with iron oxide nanoparticles, the better the in vitro ultrasound (US) imaging and magnetic resonance imaging (MRI) results. This study proves that the magneto internal heat bubble generation process is a simple and efficient technique for preparing MLBs with high concentration, regular structure, and commendable properties. These findings lay a robust foundation for the mass production and application of enveloped micro-nanobubbles, particularly in biomedical fields and other related domains.

КОМП'ЮТЕРНЕ МОДЕЛЮВАННЯ ЕЛЕКТРИЧНИХ ПРОЦЕСІВ ПІД ЧАС ВИНИКНЕННЯ ЧАСТКОВИХ РОЗРЯДІВ У СУЧАСНІЙ ПОЛІМЕРНІЙ ІЗОЛЯЦІЇ СИЛОВИХ КАБЕЛІВ

A Simulink model of modern polymer insulation of power cables with a spherical gas micro-inclusion, in which high-frequency partial discharges (PDs) occur, has been developed. The magnitude of the voltage both at the beginning of the PD appearance and during its decay was taken into account during numerical calculations and research of such threshold electro-physical processes as PD in solid polymer insulation. The dependence of the voltage drop on the gas micro-inclusion on its size, as well as the time interval between discharges, which is necessary for the formation of free electrons in this gas micro-inclusion, as a necessary condition for the appearance of the next PD, was also taken into account. Based on the results of the calculations, the electro-physical dependences that occur during the PD, such as the influence of the size of the inclusion, the amplitude and frequency of the applied sinusoidal voltage on the above-mentioned characteristics were investigated. It has been revealed that with an increase in the diameter d of a gas mi-croinclusion, such characteristics as the number of discharges per period and the charge of one PD also increase, and this charge increases in proportion to a power function . When the voltage on the cable insulation increases, the number of PDs per period increases, which causes an increase in other characteristics, and when the frequency of the applied voltage increases, the average value of the PDs current increases almost proportionally to the increase in this frequency. Having obtained the results of the calculation of the level of PDs that occur when high-frequency voltage is applied, it is possible to obtain results for the main characteristics of PDs that occur at other frequencies, in particular at the industrial frequency of 50 Hz, which will make it possible to predict the technical condition of the insulation in terms of the residual resource of its trouble-free operation. References 18, figures 6, table 1.

Polytropic Dynamical Systems with Time Singularity

In this paper we consider a class of second order singular homogeneous differential equations called the Lane-Emden-type with time singularity in the drift coefficient. Lane-Emden equations are singular initial value problems that model phenomena in astrophysics such as stellar structure and are governed by polytropics with applications in isothermal gas spheres. A hybrid method that combines two simple methods; Euler's method and shooting method, is proposed to approximate the solution of this type of dynamic equations. We adopt the shooting method to reduce the boundary value problem, then we apply Euler's algorithm to the resulted initial value problem to get approximations for the solution of the Lane-Emden equation. Finally, numerical examples and simulation are provided to show the validity and efficiency of the proposed technique, as well as the convergence and error estimation are analyzed.

Fluid statics of a self-gravitating isothermal sphere of van der Waals' gas

We subject to scrutiny the physical consistency of adopting the perfect-gas thermodynamic model within self-gravitation circumstances by studying the fluid statics of a self-gravitating isothermal sphere with the van der Waals' thermodynamic model, whose equation of state features well-known terms that account for molecular attraction and size. The governing equations are formulated for any thermodynamic model with two intensive degrees of freedom, applied with the van der Waals' model and solved numerically in nondimensional form by finite-difference algorithms. After a brief summary of thermodynamic characteristics possessed by the van der Waals' model, and relevant to the present study, we proceed to the description of the results in terms of comparative graphs illustrating radial profiles of density, pressure, and gravitational field. We complement them with graphs that compare the dependence of central and wall densities on gravitational number for both perfect-gas and van der Waals' models and that attest dramatically and unequivocally how the presence of molecular-attraction and -size terms removes questionable fluid-statics results systematically found accompanying the perfect-gas model in standard treatments. We also describe, within a very brief and preliminary digression, how the sanitizing action of the mentioned terms affects the thermodynamics of the isothermal sphere by providing evidence of how the gravitational correction to entropy corresponding to the van der Waals' model makes sure that there is no risk of gravothermal catastrophes, negative specific heats, and thermal instabilities. Furthermore, we investigate the phenomenology related to self-gravitationally induced both liquid-gas phase equilibria and metastable-gas states and we describe how they arise naturally and self-consistently from the governing equations. We conclude with a summary of the main results and with a challenging proposal of future work meant to attempt a revalorization the perfect-gas model.

Probing a black hole in Starobinsky-Bel-Robinson gravity with thermodynamical analysis, effective force and gravitational weak lensing

In this work, we investigate the effects of plasma and the coupling parameter β>0, on the thermodynamic properties and weak gravitational lensing by the Schwarzschild-like black hole in the Starobinsky-Bel-Robinson gravity (SBRG). We observe that the horizon radius and the corrected entropy of the Schwarzschild-like black hole in the SBRG are not much sensitive to the parameter β. In contrast the energy emission rate of the Schwarzschild-like black hole in the SBRG is sensitive to the parameter β and decreases with an increase in the values of the parameter β. We see that the Schwarzschild-like black hole in the SBRG is stable as the thermodynamical temperature is positive for different values of the parameter β. Moreover we observe that the deflection angle of a photon beam by the black hole in uniform plasma, nonuniform self-interacting scalar plasma and non-singular isothermal gas sphere reduces with the parameter β, against the impact parameter b. We see that the deflection angle enhances with an increase in the concentration of the plasma fields for all the three types of plasma media. Further we find that the magnification of the image due to lensing increases in a higher concentration of the plasma field. It is interesting to notice that the image magnification in a uniform plasma is much higher as compared to the one in a nonuniform plasma field. We compare our results with those for the Schwarzschild black hole of General Relativity. Further, the effective force is also calculated for the Schwarzschild-like black hole in the SBRG.

Influence of powder surface chemistry on the defect formation in AlSi10Mg alloy processed via laser powder bed fusion additive manufacturing

In laser powder bed fusion(LPBF) additive manufacturing(AM) of Al alloys, surface chemistry and dissolved gas composition(oxygen/oxides/hydroxides, hydrogen and moisture) of AM powders is a major influencing factor for porosity formation. Therefore, in the present investigation, this aspect is addressed using two sets of virgin AM AlSi10Mg powders, namely, Hi-Ox (2770 ppm oxygen) and Lo-Ox (660 ppm oxygen), to assess the printability under various processing parameters and defect formation in printed parts. Comprehensive and in-depth metallurgical analysis of both powders utilizing multiple characterisation techniques established the presence of various types of oxides/hydroxides with different complex chemistries on the powders’ surface. Enhanced spherical gas porosity and oxide inclusions were witnessed in Hi-Ox print coupons in contrast to the least defects in Lo-Ox coupons rationalized due to surface chemistry difference between the virgin powders. Consequently, the mechanical properties of the Hi-Ox print coupons, even with minimum defect density, are significantly inferior to Lo-Ox specimens. These observations suggest a competing influence of surface chemistry/dissolved gas composition and laser parameters for the processing of both powders. Overall, by correlating the microstructures with processing conditions and oxide concentration, defects morphology, the probable melt pool formation mechanism in LPBF of AlSi10Mg alloy (for high and low oxygen concentration) is elucidated.

A modified fixed point iterative scheme based on Green’s function with application to BVPs

This paper presents a new faster iteration approach that is based upon the well-known three-step fixed point iteration scheme called SP-iterative scheme for a broad and larger class of non-linear BVPs. The scheme is constructed using Green’s function based integral operator and the new modified scheme in the paper will be called SP–Green’s iterative scheme. We present a fixed point convergence theorem using some assumption on the sequences of scalars in our scheme. We also prove the weak [Formula: see text]-stability for our scheme and present a numerical example to support our scheme. We provide eventually applications of our scheme to a second-order BVP and a singular BVP of isothermal gas sphere.

COMPUTING POLYTROPIC AND ISOTHERMAL MODELS USING MONTE CARLO METHOD

Polytropic and isothermal gas spheres are crucial in the theory of stellar structure and evolution, galaxy cluster modeling, thermodynamics, and various other physics, chemistry, and engineering disciplines. Based on two Monte Carlo algorithms (MC1 and MC2), we introduce a numerical approach for solving Lane-Emden (LE) equations of the polytropic and isothermal gas spheres. We found that the MC1 and MC2 models agree with each other and also with numerical and analytical models. We tested the compatibility between the MC and the numerical polytropic models by calculating the mass-radius relation and the pressure profile for the polytrope with n=3.

Effect of Shrinkage Versus Hydrogen Pores on Fatigue Life of Cast AlSi11Mg Alloy

AbstractShrinkage pores in cast aluminum components are often the reason for premature failure during cyclic loading due to their large size and fissured morphology. Complete avoidance is technically not possible due to processing constraints, but shrinkage pores can be substituted by significantly smaller and spherical gas pores by means of controlled hydrogen upgassing. The newly developed and simulation-optimized casting system enables precise and reproducible casting of various pore distributions, which have been extensively characterized. Correlations between shrinkage vs. hydrogen pores and fatigue behavior were quantified concerning very high cycle fatigue and crack propagation behavior as well as analyzed by 3D µ-CT to identify the failure mechanisms. In the as-cast condition, fissured shrinkage pores, especially near the surface, lead to crack initiation and premature fatigue failure. The strong scattering of fatigue life can be significantly reduced by the controlled insertion of hydrogen pores. Furthermore, the experimental studies indicate that hydrogen pores increase the critical crack growth threshold and reduce the crack propagation rate by crack deflection, crack splitting and crack tip blunting.

Sensitivity analysis for acoustic-driven gas bubble dynamics in tangent hyperbolic fluid

Ultrasound imaging, or sonography, utilizes high-frequency sound waves to create images of the internal structures of the human body. It is widely applied in medical diagnostics due to its non-invasive nature and real-time capabilities. Ultrasound waves are emitted into the body, and their reflections are captured to generate detailed images of organs, tissues, fetuses during pregnancy, and more. The interaction between sound waves and biological tissues and issues related to propagation, reflection, and absorption of ultrasound are crucial considerations for improving image quality and safety. It is frequently used to keep an eye on the health and development of the fetus throughout pregnancy. The examination of several organs, including the heart, liver, kidneys, and blood arteries, is also done to look for anomalies, tumors, and other diseases. The dynamics of spherical gas bubbles within a non-Newtonian fluid exposed to an external sonic field are examined in this paper. The mathematical model offers a useful foundation for examining bubble behavior since it incorporates the additional stress tensor of a tangent hyperbolic fluid. The generalized RP problem may be transformed into an ordinary differential equation that can be solved using numerical methods, allowing a large range of parameter values to be investigated and resolving convergence difficulties. Particularly noteworthy are the numerical results for long acoustic cycles. The link between input and output variables is also investigated using an experimental methodology closely related to sensitivity analysis, which is important for possible device development. This innovative approach offers a fresh perspective on the subject.

Bridging Scales in Black Hole Accretion and Feedback: Magnetized Bondi Accretion in 3D GRMHD

Fueling and feedback couple supermassive black holes (SMBHs) to their host galaxies across many orders of magnitude in spatial and temporal scales, making this problem notoriously challenging to simulate. We use a multi-zone computational method based on the general relativistic magnetohydrodynamic (GRMHD) code KHARMA that allows us to span 7 orders of magnitude in spatial scale, to simulate accretion onto a non-spinning SMBH from an external medium with a Bondi radius of R B ≈ 2 × 105 GM •/c 2, where M • is the SMBH mass. For the classic idealized Bondi problem, spherical gas accretion without magnetic fields, our simulation results agree very well with the general relativistic analytic solution. Meanwhile, when the accreting gas is magnetized, the SMBH magnetosphere becomes saturated with a strong magnetic field. The density profile varies as ∼r −1 rather than r −3/2 and the accretion rate is consequently suppressed by over 2 orders of magnitude below the Bondi rate . We find continuous energy feedback from the accretion flow to the external medium at a level of . Energy transport across these widely disparate scales occurs via turbulent convection triggered by magnetic field reconnection near the SMBH. Thus, strong magnetic fields that accumulate on horizon scales transform the flow dynamics far from the SMBH and naturally explain observed extremely low accretion rates compared to the Bondi rate, as well as at least part of the energy feedback.