Critical Mass Parameter Research Articles

Stability of equilibrium points in the generalized perturbed restricted three-body problem

This paper studies the existence and stability of equilibrium points under the influence of small perturbations in the Coriolis and the centrifugal forces, together with the non-sphericity of the primaries. The problem is generalized in the sense that the bigger and smaller primaries are respectively triaxial and oblate spheroidal bodies. It is found that the locations of equilibrium points are affected by the non-sphericity of the bodies and the change in the centrifugal force. It is also seen that the triangular points are stable for 0<μ<μ c and unstable for \(\mu_{c}\le\mu <\frac{1}{2}\), where μ c is the critical mass parameter depending on the above perturbations, triaxiality and oblateness. It is further observed that collinear points remain unstable.

Possibility of catastrophic black hole growth in the warped brane-world scenario at the LHC

In this paper, we present the results of our analysis of the growth and decay of black holes possibly produced at the Large Hadron Collider, based on our previous study of black holes in the context of the warped brane-world scenario. The black hole mass accretion and decay is obtained as a function of time, and the maximum black hole mass are obtained as a function of a critical mass parameter. The latter occurs in our expression for the luminosity and is related to the size of extra-dimensional corrections to Newton's law. Based on this analysis, we argue against the possibility of catastrophic black hole growth at the LHC.

Linear Stability Analysis of the Herringbone Groove Journal Bearings in Microsystems: Consideration of Gas Rarefaction Effects

The dynamic performance of the herringbone groove journal bearings (HGJBs) with the effects of gas rarefaction taken into account is considered for applications in microsystems. Two important parameters (the Knudsen number Kn and the tangential momentum accommodation coefficients, TMACs or the accommodation coefficients, ACs) that affect gas rarefaction significantly are considered. Small variations in film thickness and pressure from the equilibrium state are substituted into the transient modified molecular gas lubrication (MMGL) equation, which considers effects of gas rarefactions with the Poiseuille and Couette flow rate correctors. The gas film in the rotor-bearing system is modeled as stiffness and damping elements with coefficients dependent on the exciting frequency. The dynamic coefficients are then obtained by solving the linearized MMGL equations. The equations of motion of the rotor as well as the dynamic coefficients are performed for the present linear stability analysis. Due to the exciting frequency-dependent nature of the dynamic coefficients, an iterative method with the golden section technique is introduced in the linear stability analysis of rotor-bearing systems. The critical mass parameters and the related threshold speed are computed and discussed. The results of this study prove that HGJBs in microsystems can operate at concentric conditions at very high speeds.

Secular solutions at triangular equilibrium point in the generalized photogravitational restricted three body problem

In this paper we have found secular solutions at the triangular equilibrium point in the generalized photogravitational restricted three body problem. The problem is generalised in the sense that smaller primary is an oblate spheroid and more massive primary as source of radiation. The triangular point has long or short-period retrograde elliptical orbits. The critical mass parameter decreases with the increase in oblateness and radiation pressure.

Combined Effects of Perturbations, Radiation, and Oblateness on the Stability of Equilibrium Points in the Restricted Three-Body Problem

This paper investigates the stability of equilibrium points under the influence of small perturbations in the Coriolis and the centrifugal forces, together with the effects of oblateness and radiation pressures of the primaries. It is found that collinear points remain unstable. It is also seen that triangular points are stable for 0 ≤ μ < μc and unstable for μc ≤ μ ≤ , where μ is the critical mass parameter and depends on the above parameters. It is further observed that the Coriolis force has a stabilizing tendency, while the centrifugal force, radiation, and oblateness of the primaries have destabilizing effects; the presence of any one or more of the latter makes weak the stabilizing ability of the former. Therefore, the overall effect is that the range of stability of the triangular points decreases.

Linear stability analysis of hydrodynamic journal bearings under micropolar lubrication

The dynamic characteristics of hydrodynamic journal bearings lubricated with micropolar fluids are presented. The modified Reynolds equation is obtained using the micropolar lubrication theory. Applying the first order perturbation of the film thickness and steady state film pressure, the dynamic characteristics in terms of the components of stiffness and damping coefficients, critical mass parameter and whirl ratio are obtained with respect to the micropolar property for varying eccentricity ratios and slenderness ratios. The results show that micropolar fluid exhibits better stability in comparison with Newtonian fluid.

Existence and Stability of Libration Points in the Restricted Three-Body Problem When the Primaries are Triaxial Rigid Bodies

This paper deals with the stationary solutions of the planar restricted three-body problem when the primaries are triaxial rigid bodies with one of the axes as the axis of symmetry and its equatorial plane coinciding with the plane of motion. It is seen that there are five libration points, two triangular and three collinear. It is further observed that the collinear points are unstable, while the triangular points are stable for the mass parameter 0 ≤ μ < μcrit(the critical mass parameter). It is further seen that the triangular points have long or short periodic elliptical orbits in the same range of μ.

The linear stability of libration points of the photogravitational restricted three-body problem when the smaller primary is an oblate spheroid

This paper deals with the stationary solutions of the planar restricted three-body problem when the more massive primary is a source of radiation and the smaller primary is an oblate spheroid with its equatorial plane coincident with the plane of motion. The collinear equilibria have conditional retrograde elliptical periodic orbits around them in the linear sense, while the triangular points have long- or short-periodic retrograde elliptical orbits for the mass parameter 0 ≤ μ < μcrit, the critical mass parameter, which decreases with the increase in oblateness and radiation force. Through special choice of initial conditions, retrograde elliptical periodic orbits exist for the case μ = μcrit, whose eccentricity increases with oblateness and decreases with radiation force for non-zero oblateness.

Yeast Biotechnological Processes Monitored by Analysis of Segregated Data with Structured Models

Several biological parameters have been measured in populations of budding yeast growing in a glucose-limited chemostat, both in steady state and during perturbed growth conditions. The population structure has been determined with a segregated data analysis performed on protein distribution and on volume distributions. A new structured model for budding yeast population is presented, in which the entire system is described only in terms of critical cell mass parameters. This approach allows to integrate in a fairly simple way the population model with the bioreactor performance and to describe transient states of growth.

Minimum Critical Mass of Uranium-235 Reflected by Natural Uranium in Water

An analytical study has been completed to define minimum critical mass parameters for a spherical region containing a 235U-H2O mixture reflected by a natural uranium-water mixture. The study indica...