Equilibrium Radius Research Articles

On the neutronization radius of magnetic neutron stars: The field and temperature dependences of the chemical potential and minimum number density of a degenerate magnetized electron gas

The temperature and field dependences of the chemical potential and the field dependence of the Fermi energy for a degenerate relativistic electron gas in a magnetic field have been analyzed by numerical and analytical methods. An analytical expression has been derived for the dependence of the minimum electron number density and the corresponding neutronization radius on the magnetic field strength in a collapsing star upon its subsequent transformation into a neutron one. We believe that a similar relation also holds for the equilibrium neutron star radius. Our results refine the conclusions reached previously [1] in the case of a nonzero temperature and the influence of the star’s proton component on the neutronization process as well as confirm and generalize them in terms of a significant (by an order of magnitude or severalfold) decrease in the equilibrium radius of a neutron star in a superstrong (1014–1017 G) magnetic field compared to the case where there is no such field. We point out that there may exist a separate class of stellar objects—very small magnetar neutron stars that we propose to name “minimagnetars”. We hypothesize that they can be the final evolutionary stage of stars before their collapse into a black hole.

A possible decrease in the equilibrium radius of a neutron star due to the effect of a superstrong magnetic field

A possible decrease in the equilibrium radius of a neutron star due to the effect of a superstrong magnetic field

Electron shielding of vortons in high-density quark matter

We consider the effect of the electron cloud about a vorton in the CFL-${K}^{0}$ high-density phase by numerically solving the ultrarelativistic Thomas-Fermi equation about a toroidal charge. Including electrons removes the electric monopole contribution to the energy, and noticeably decreases the equilibrium radius of these stable vortex loops.

Modeling of dendritic growth and bubble formation

A two-dimensional (2D) lattice Boltzmann method (LBM)-cellular automaton (CA) coupled model is developed for the simulation of dendritic growth and bubble formation during solidification. In the model, the dendritic growth is simulated by a CA approach. The driving force of dendritic growth is determined by a local solute equilibrium approach. The LBM based on the Shan-Chen multiphase flow scheme is adopted to simulate the growth and the motion of bubbles in liquid. The interaction mechanism between dendrites and bubbles is embedded in the model. Model validation is carried out by comparing the simulations with the Laplace law, and by simulating the wettability of a bubble on a smooth solid surface. The proposed model is used to study the effect of gas-liquid interaction coefficient on single bubble growth. It is found that the growth velocity and the equilibrium radius of bubble increase with the gas-liquid interaction coefficient. The simulations of the dendritic growth and bubble formation during directional solidification reproduce the physical phenomena, including dendritic competitive growth, the preferential nucleation locations of bubbles, and bubble growth, coalescence, deformation due to the squeeze of neighboring dendrites, as well as bubble motion in the liquid channels. The simulation results are compared reasonably well with the experimental results. In addition, gas pore volume fraction increases with the initial gas content. The simulations of the present LBM-CA model provide an insight into the physical mechanism of bubble nucleation, growth, and motion, as well as the interaction between the dendritic growth and bubble formation during solidification.

On Possible Reduction of Equilibrium Radius of a Neutron Star Influenced by Superstrong Magnetic Field

Necessary condition forβ-decay suppression of a neutron in degenerate magnetized electron gas is formulated. Based on this, it is shown that, in superstrong magnetic field, equilibrium radius of a neutron star is approximately several times smaller than without the field influence. Therefore, we can make a prediction that in short-period pulsars, such fields can be observed. In fact, possible existence of new class of stellar objects is noted, the objects with superstrong magnetic field and supersmall radius about 1 km which we namedminimagnetars. They can be detected by gravitational red shift of their radiation.

Effect of static pressure on acoustic energy radiated by cavitation bubbles in viscous liquids under ultrasound

The effect of static pressure on acoustic emissions including shock-wave emissions from cavitation bubbles in viscous liquids under ultrasound has been studied by numerical simulations in order to investigate the effect of static pressure on dispersion of nano-particles in liquids by ultrasound. The results of the numerical simulations for bubbles of 5 μm in equilibrium radius at 20 kHz have indicated that the optimal static pressure which maximizes the energy of acoustic waves radiated by a bubble per acoustic cycle increases as the acoustic pressure amplitude increases or the viscosity of the solution decreases. It qualitatively agrees with the experimental results by Sauter et al. [Ultrason. Sonochem. 15, 517 (2008)]. In liquids with relatively high viscosity (∼200 mPa s), a bubble collapses more violently than in pure water when the acoustic pressure amplitude is relatively large (∼20 bar). In a mixture of bubbles of different equilibrium radius (3 and 5 μm), the acoustic energy radiated by a 5 μm bubble is much larger than that by a 3 μm bubble due to the interaction with bubbles of different equilibrium radius. The acoustic energy radiated by a 5 μm bubble is substantially increased by the interaction with 3 μm bubbles.

Thermodynamic functions of degenerate magnetized electron gas

The Fermi energy, pressure, internal energy, entropy, and heat capacity of completely degenerate relativistic electron gas are calculated by numerical methods. It is shown that the maximum admissible magnetic field on the order of 109 G in white dwarfs increases the pressure by a factor of 1.06 in the central region, where the electron concentration is ∼1033 cm−3, while the equilibrium radius increases by approximately a factor of 1.03, which obviously cannot be observed experimentally. A magnetic field of ∼108 G or lower has no effect on the pressure and other thermodynamic functions. It is also shown that the contribution of degenerate electron gas to the total pressure in neutron stars is negligible compared to that of neutron gas even in magnetic fields with a maximum induction ∼1017 G possible in neutron stars. The neutron beta-decay forbiddeness conditions in a superstrong magnetic field are formulated. It is assumed that small neutron stars have such magnetic fields and that pulsars with small periods are the most probable objects that can have super-strong magnetic fields.

Effect of Ultrasonic Cavitation Acting on Solidified Structures of 7050 Aluminum Alloy

Imposing ultrasound on D.C.casting of the 7050 aluminum alloy could refine grains significantly. Among the physical effects accompanying the propagation of high power ultrasonic oscillations in melt, cavitation, or the formation of cavities filled mainly with gases dissolved in the molten melt. In this research, we have analyzed solidified structures which influenced by different power of ultrasound via using cavitation theory and experiment. The results indicated that after treating by ultrasound, the solidified structures of the aluminum alloy could be refined considerably and the degree of the structure refining rose along with the increase of the ultrasound power. Software MATLAB was chosen to simulate the relationship between acoustic pressure and relative radii of cavitation bubbles, ultrasonic frequency and relative radii and initial equilibrium radii and relative radii respectively. After that, the mechanism of grain refining have been discussed under the condition of stable cavitation and transient cavitation, providing some related references for ultrasound applying in the field of foundry industry.

Particle motion and separation in a laminar tube flow with downstream enlargement

Particle classification becomes difficult when the difference in density between particle and fluid is low or negligible and the fluid is viscous. For such applications, a process capable of separating the particles according to their size is needed. Such applications are, e.g. found in biological systems for cell separation or in the removal of gel particles from polymer melts. Particle transport in laminar tube flows at low but non zero Reynolds numbers leads to accumulation of large particles near the tube center and forms a particle free zone near the wall. Small particles find their position on their equilibrium radius. Downstream widening of the flow enhances segregation between large and small particles. Large particles can be collected in a centered collector tube downstream, whereas small particles follow their streamlines around the collector tube and can be removed with the remaining flow. The said particle migration is observed when the ratio of particle to tube diameter is 0.2< d/ D<0.51 and the tube Reynolds number is in between 0.2< Re<40. CFD simulations reveal the shape of the streamlines in the downstream enlargement with different tube Reynolds number. The efficiency of the classification process is characterized. Particles need a sufficient transportation length in the tube for proper demixing. This effect is analyzed by a laser sheet illuminated system within an acrylic glass tube.

Ostwald ripening of three-dimensional clusters on a surface studied with an ultrafast kinetic Monte Carlo algorithm

We have studied the Ostwald ripening of three-dimensional islands on a homogeneous surface with an original off-lattice kinetic Monte Carlo algorithm. In this algorithm, adatom trajectories are highly simplified, while still ensuring that the adatom fluxes between islands are exactly described. From the simulations, we obtained the evolution of the island size distribution over a large time range. The simulations obtained are compared with the results of numerical integration of rate equations derived from a mean-field approximation. Both results indicate that the equilibrium radius of the islands follows a power-law behavior in the limit of a very dilute phase, with an exponent close to 1/4. A general, excellent agreement is obtained, showing the validity of our approach, whereas the validity of the mean-field approximation is discussed for a very small mean island size, or for a large fraction of the surface covered by the islands.

Locally cold flows from large-scale structure

Abstract We show that the ‘cold’ Hubble flow observed for galaxies around the Milky Way does not represent a problem in cosmology but is due to the particular geometry and dynamics of our local wall. The behaviour of the perturbed Hubble flow around the Milky Way is the result of two main factors: at small scales (R &amp;lt; 1 Mpc) the inflow is dominated by the gravitational influence of the Milky Way and at large scales (R &amp;gt; 1 Mpc) the outflow reflects the expansion of our local wall which ‘cools down’ the peculiar velocities. This is an intrinsic property of walls and is independent of cosmology. We find the dispersion of the local Hubble flow (1 &amp;lt; R &amp;lt; 3 Mpc) around simulated ‘Milky Way’ haloes located at the centre of low-density cosmological walls to be σH∼ 30 km s-1, in excellent agreement with observations. The expansion of our local wall is also reflected in the value of the measured local Hubble constant. For ‘Milky Way’ haloes inside walls, we find super-Hubble flows with hlocal≃ 0.77–1.13 over a range of increasingly ‘clean’ environments. The radius of equilibrium (R0) depends not only on the mass of the central halo and the Hubble expansion, but also on the dynamics given by the local LSS geometry. The super-Hubble flow inside our local wall has the effect of reducing the radius at which the local expansion balances the gravitational influence of the Milky Way. By ignoring the dynamical effect of the local wall, the mass of the Milky Way estimated from R0 can be underestimated by as much as ∼30 per cent.

Production flux of sea spray aerosol

Knowledge of the size‐ and composition‐dependent production flux of primary sea spray aerosol (SSA) particles and its dependence on environmental variables is required for modeling cloud microphysical properties and aerosol radiative influences, interpreting measurements of particulate matter in coastal areas and its relation to air quality, and evaluating rates of uptake and reactions of gases in sea spray drops. This review examines recent research pertinent to SSA production flux, which deals mainly with production of particles with r80 (equilibrium radius at 80% relative humidity) less than 1 μm and as small as 0.01 μm. Production of sea spray particles and its dependence on controlling factors has been investigated in laboratory studies that have examined the dependences on water temperature, salinity, and the presence of organics and in field measurements with micrometeorological techniques that use newly developed fast optical particle sizers. Extensive measurements show that water‐insoluble organic matter contributes substantially to the composition of SSA particles with r80 &lt; 0.25 μm and, in locations with high biological activity, can be the dominant constituent. Order‐of‐magnitude variation remains in estimates of the size‐dependent production flux per white area, the quantity central to formulations of the production flux based on the whitecap method. This variation indicates that the production flux may depend on quantities such as the volume flux of air bubbles to the surface that are not accounted for in current models. Variation in estimates of the whitecap fraction as a function of wind speed contributes additional, comparable uncertainty to production flux estimates.

Dynamic analysis on temperature evolution inside a single bubble due to hydrodynamic cavitation under turbulence

Considering such factors as liquid compressibility, surface tension, liquid viscosity, heat transfer through bubble wall and water vapor inside bubble, the temperature evolution and its influence factors inside a single cavitation bubble driven by turbulent pressure field are investigated by adopting dynamics method and regarding water as work medium. Detailed analysis is conducted to understand the effects of cavitation bubble equilibrium radius, operating and structural parameters of the orifice hydrodynamic cavitation reaction on the bubble collapse temperature. A comprehensive significant fitting equation is obtained to quickly forecast the bubble collapse temperature under various conditions. The achievements obtained may provide theoretical guidance and technical support for optimization design of hydrodynamic cavitation reactor and practical application of hydrodynamic cavitation technology.

Distorted, nonspherical transiting planets: impact on the transit depth and on the radius determination

We quantify the systematic impact of the non-spherical shape of transiting planets and brown dwarfs, due to tidal forces and rotation, on the observed transit depth. Such a departure from sphericity leads to a bias in the derivation of the transit radius from the light curve and affects the comparison with planet structure and evolution models which assume spherical symmetry. As the tidally deformed planet projects its smallest cross section area during the transit, the measured effective radius is smaller than the one of the unperturbed spherical planet. This effect can be corrected by calculating the theoretical shape of the observed planet. We derive simple analytical expressions for the ellipsoidal shape of a fluid object (star or planet) accounting for both tidal and rotational deformations and calibratre it with fully numerical evolution models in the 0.3Mjup-75Mjup mass range. Our calculations yield a 20% effect on the transit depth, i.e. a 10% decrease of the measured radius, for the extreme case of a 1Mjup planet orbiting a Sun-like star at 0.01AU. For the closest planets detected so far (< 0.05 AU), the effect on the radius is of the order of 1 to 10%, by no means a negligible effect, enhancing the puzzling problem of the anomalously large bloated planets. These corrections must thus be taken into account for a correct determination of the radius from the transit light curve. Our analytical expressions can be easily used to calculate these corrections, due to the non-spherical shape of the planet, on the observed transit depth and thus to derive the planet's real equilibrium radius. They can also be used to model ellipsoidal variations of the stellar flux now detected in the CoRoT and Kepler light curves. We also derive directly usable analytical expressions for the moment of inertia, oblateness and Love number (k_2) of a fluid planet as a function of its mass.

Application of the Englert–Schwinger model to the equation of state and the fullerene molecule

The Englert–Schwinger model (ESM) is applied to two problems. One is the calculation of zero-temperature equation of state (EOS) of elements within the spherically symmetric Wigner–Sietz cell approximation. The other is to obtain the equilibrium radius of fullerene molecule using March’s approach [N. H. March, Proc. Camb. Philos. Soc. 48, 665 (1952)]. In each case, the results of the ESM are compared with those of Thomas–Fermi–Dirac (TFD) and Thomas–Fermi–Dirac–Weizsacker (TFDW) models. Zero-temperature equation of state calculations are done for Al and Cu. The results of the ESM show an enormous improvement over those of the TFD model. Also, the ESM is in good agreement with the TFDW model for compressions greater than 2. In the regime of validity of TFDW theory, i.e., compressions greater than 20 and 10 for Al and Cu, respectively, the deviations between the results of the two models are negligible. Hence, the ESM may be used in lieu of the TFDW model for EOS calculations. In the fullerene case, we have obtained the cohesive energy using the models assuming the radius obtained from accurate calculations of the fullerene molecule. We have also obtained the equilibrium radius predicted by each model. The results obtained show that the ESM results are not much of an improvement over the TFD results. This shows that the ESM cannot always improve the results of the TFD model and be a replacement for the TFDW model. However, as in the EOS case, it would give results in good agreement with TFDW results for properties that are dependent on the electron density at the outer reaches of the atom.

The determination of planetary structure in tidally relaxed inclined systems

[Abridged] The recent discovery of a transiting planet on a non-circular orbit with a massive highly eccentric companion orbiting HAT-P-13 offers the possibility of probing the structure of the short-period planet. The ability to do this relies on the system being in a quasi-equilibrium state in the sense that the eccentricities are constant on the usual secular timescale, and decay on a timescale which is much longer than the age of the system. Since the equilibrium eccentricity is effectively a function only of observable system parameters and the unknown Love number of the short-period planet, the latter can be determined with accurate measurements of the planet's eccentricity and radius. However, this analysis relies on the unlikely assumption that the system is coplanar. Here we generalize our recent analysis of this fixed-point phenomenon to mutually inclined systems and show that the fixed point of coplanar systems is replaced by a limit cycle, with the average value of the eccentricity decreasing and its amplitude of variation increasing with increasing mutual inclination. This behaviour significantly reduces the ability to unambiguously determine the Love number of the short-period planet if the mutual inclination is higher than around 10^o. We show that for Q-values less than 10^6, the HAT-P-13 system cannot have a mutual inclination between 54 and 126^o because Kozai oscillations coupled with tidal dissipation would act to quickly move the inclination outside this range, and that the behaviour of retrograde systems is the mirror image of that for prograde systems. We derive a relationship between the equilibrium radius of the short-period planet, its Q-value and its core mass, and show that given current estimates of e_b and the planet radius, the HAT-P-13 system is likely to be close to coplanar [...]

Snapping Shrimp Sound Measured Under Laboratory Conditions

The typical temporal waveforms and spectra of the sounds produced by the three species of snapping shrimp with different claw shapes and almost the same claw lengths were investigated under laboratory conditions. The sound spectra generated by one species of snapping shrimp were also investigated for various claw lengths. For the three species of snapping shrimp, their typical temporal waveforms were similar, but their sound spectra and pulse durations differed. This difference was related to the size of the single cavitation bubble, which was generated by the high-speed water jet emitted from the snapping shrimp claw. The range of difference in the times between the snapping shrimp claw closure and the collapse of the single cavitation bubble for the three species of snapping shrimp seemed to be determined by the difference in the claw shape. The collapse time, the equilibrium radius, and the maximal radius of the cavitation bubble for each species were estimated from the first peak frequency component in the snapping shrimp sound spectrum. For one species of snapping shrimp, the peak frequency components in the sound spectra were observed for various claw lengths and their superposition could be considered as the cause that the broad peak frequency components were variously observed in the averaged snapping shrimp sound spectra, which were measured in many shallow water areas.

ORBITAL MIGRATION OF LOW-MASS PLANETS IN EVOLUTIONARY RADIATIVE MODELS: AVOIDING CATASTROPHIC INFALL

Outward migration of low-mass planets has recently been shown to be a possibility in non-barotropic disks. We examine the consequences of this result in evolutionary models of protoplanetary disks. Planet migration occurs towards equilibrium radii with zero torque. These radii themselves migrate inwards because of viscous accretion and photoevaporation. We show that as the surface density and temperature fall, the planet orbital migration and disk depletion timescales eventually become comparable, with the precise timing depending on the mass of the planet. When this occurs, the planet decouples from the equilibrium radius. At this time, however, the gas surface density is already too low to drive substantial further migration. A higher mass planet, of 10 Earth masses, can open a gap during the late evolution of the disk, and stops migrating. Low mass planets, with 1 or 0.1 Earth masses, released beyond 1 AU in our models, avoid migrating into the star. Our results provide support for the reduced migration rates adopted in recent planet population synthesis models.

Stability analysis of an encapsulated microbubble against gas diffusion

Linear stability analysis is performed for a mathematical model of diffusion of gases from an encapsulated microbubble. It is an Epstein–Plesset model modified to account for encapsulation elasticity and finite gas permeability. Although bubbles, containing gases other than air, are considered, the final stable bubble, if any, contains only air, and stability is achieved only when the surrounding medium is saturated or oversaturated with air. In absence of encapsulation elasticity, only a neutral stability is achieved for zero surface tension, the other solution being unstable. For an elastic encapsulation, different equilibrium solutions are obtained depending on the saturation level and whether the surface tension is smaller or higher than the elasticity. For an elastic encapsulation, elasticity can stabilize the bubble. However, imposing a non-negativity condition on the effective surface tension (consisting of reference surface tension and the elastic stress) leads to an equilibrium radius which is only neutrally stable. If the encapsulation can support a net compressive stress, it achieves actual stability. The linear stability results are consistent with our recent numerical findings. Physical mechanisms for the stability or instability of various equilibriums are provided.

Multibubble cavitation inception

The inception of cavitation in multibubble cases is studied numerically and theoretically to show that it is different from that in single-bubble cases in several aspects. Using a multibubble model based on the Rayleigh–Plesset equation with an acoustic interaction term, we confirmed that the recently reported suppression of cavitation inception due to the interaction of nonidentical bubbles can take place not only in liquid mercury but also in water, and we found that a relatively large bubble can significantly decrease the cavitation threshold pressure of a nearby small bubble. By examining in detail the transition region where the dynamics of the suppressed bubble changes drastically as the interbubble distance changes, we determined that the explosive expansion of a bubble under negative pressure can be interrupted and turn into collapse even though the far-field liquid pressure well exceeds the bubble’s threshold pressure. Numerical results suggest that the interruption of expansion occurs when the bubble radius is exceeded by the instantaneous unstable equilibrium radius of the bubble determined using the total pressure acting on the bubble. When we extended the discussion to systems of larger numbers of bubbles, we found that a larger number of bubbles have a stronger suppression effect. The present findings would be useful in understanding the complex behavior of cavitation bubbles in practical applications where, in general, many cavitation nuclei exist and may interact with each other.