Critical Mass Ratio Research Articles

Stability of equilibrium points in a CR3BP with oblate bodies enclosed by a circular cluster of material points

We have investigated an improved version of the classic restricted three-body problem where both primaries are considered oblate and are enclosed by a homogeneous circular planar cluster of material points centered at the mass center of the system. In this dynamical model we have examined the effect on the number and on the linear stability of the equilibrium locations of the small particle due to both, the primaries’ oblateness and the potential created by the circular cluster. We have drawn the zero-velocity surfaces and we have found that in addition to the usual five Lagrangian equilibrium points of the classic restricted three-body problem, there exist two new collinear points L n1,L n2 due to the potential from the circular cluster of material points. Numerical investigations reveal that with the increase in the mass of the circular cluster of material points, L n2 comes nearer to the more massive primary, while L n1 moves away from it. Owing to oblateness of the bodies, L n1 comes nearer to the more massive primary, while L n2 moves towards the less massive primary. The collinear equilibrium points remain unstable, while the triangular points are stable for 0<μ<μ c and unstable for $\mu_{c} \le \mu \le \frac{1}{2}$ , where μ c is the critical mass ratio influenced by oblateness of the primaries and the potential from the circular cluster of material points. The oblateness and the circular cluster of material points have destabilizing tendency.

FIRST PHOTOMETRIC INVESTIGATION OF THE NEWLY DISCOVERED W UMa-TYPE BINARY STAR MR Com

By analyzing multi-color light curves of the newly discovered W UMa-type binary, MR Com, we discovered that it is a shallow-contact binary with a degree of contact factor of f = 10.0% +/- 2.1%. Photometric solutions reveal that MR Com is a W-type system with a mass ratio of q = 3.9 where the less massive component is about 90 K hotter than the more massive one. By investigating all of the available times of minimum light, we found that the general trend of the Observed-Calculated (O - C) curve shows a downward parabolic variation while it undergoes a cyclic variation with a small amplitude of 0.0031 days and a period of 10.1 yr. The downward parabolic change corresponds to a long-term decrease in the orbital period at a rate of (P) over dot = -5.3 x 10(-7) days yr(-1) that may be caused by a combination of a mass transfer and an angular momentum loss (AML) via magnetic braking. Among the 16 shallow-contact systems with a decreasing orbital period, MR Com has the lowest mass ratio (e.g., 1/q = 0.26). The shallow-contact configuration, the low-mass ratio, and the long-term period decrease all suggest that systems similar to MR Com are on the AML-controlled stage of the evolutionary scheme proposed by Qian. They will oscillate around a critical mass ratio and evolve into a deep contact with a higher mass ratio. The small-amplitude cyclic change in the O - C curve was analyzed for the light-travel time effect via the presence of an extremely cool stellar companion.

MASSIVE QUIESCENT CORES IN ORION: DYNAMICAL STATE REVEALED BY HIGH-RESOLUTION AMMONIA MAPS

We present combined VLA and Green Bank Telescope images of \ammonia\ inversion transitions (1,1) and (2,2) toward OMC2 and OMC3. We focus on the relatively quiescent Orion cores, which are away from the Trapezium cluster and have no sign of massive protostars nor evolved star formation, such as IRAS source, water maser, and methanol maser. The 5\arcsec\ angular resolution and $0.6 \rm{}km\,s^{-1}$ velocity resolution of these data enable us to study the thermal and dynamic state of these cores at $\sim{}0.02 \rm{}pc$ scales, comparable to or smaller than those of the current dust continuum surveys. We measure temperatures for a total of 30 cores, with average masses of $11\,\Ms$, radii of $0.039 \rm{}pc$, virial mass ratio $\bar{R_{vir}}$ = 3.9, and critical mass ratio $\bar{R_{C}}$ = 1.5. Twelve sources contain \textit{Spitzer} protostars. The thus defined starless and protostellar subsamples have similar temperature, line width, but different masses, with an average of $7.3\,\Ms$ for the former and $16\,\Ms$ for the latter. Compared to others Gould Belt dense cores, mores Orion cores have a high gravitational-to kinetic energy ratio and more cores have a larger thant unity critical mass ratio. Orion dense cores have velocity dispersion similar to those of cores in low-mass star-forming regions but larger masses for fiven size. Some cores appear to have truly supercritical gravitational-to-kinetic energy ratios, even when considering significant observational uncertainties: thermal and non-thermal gas mothins alone cannot prevent collapse.

The effect of photogravitational force and oblateness in the perturbed restricted three-body problem

The model of restricted three-body is generalized to include the effects of the oblateness, the radiation pressure and fictitious forces. The positions of libration points, their stability, the critical mass ratio and periodic orbits emanating from these points are analyzed under the influence of these effects. The results obtained are more generalized. In addition the locations of the out of plane equilibrium points are studied. We also observe that there is no explicit effect for the perturbation of Coriolis force on the positions of the out of plane equilibrium points. It is worth mentioning that this model can be degraded into 128 special cases.

The equilibrium points in the perturbed R3BP with triaxial and luminous primaries

This study explores the effects of small perturbations in the Coriolis and centrifugal forces, radiation pressures and triaxiality of the two stars (primaries) on the position and stability of an infinitesimal mass (third body) in the framework of the planar circular restricted three-body problem (R3BP). it is observed that the positions of the usual five (three collinear and two triangular) equilibrium points are affected by the radiation, triaxiality and a small perturbation in the centrifugal force, but are unaffected by that of the Coriolis force. The collinear points are found to remain unstable, while the triangular points are seen to be stable for 0<μ<μ c and unstable for \(\mu_{c} \le\mu\le\frac{1}{2}\), where μ c is the critical mass ratio influenced by the small perturbations in the Coriolis and centrifugal forces, radiation and triaxiality. It is also noticed that the former one and all the latter three posses stabilizing and destabilizing behavior respectively. Therefore, the overall effect is that the size of the region of stability decreases with increase in the values of the parameters involved.

Highly polarized Fermi gases in two dimensions

We investigate the highly polarized limit of a two-dimensional (2D) Fermi gas, where we effectively have a single spin-down impurity atom immersed in a spin-up Fermi sea. By constructing variational wave functions for the impurity, we map out the ground state phase diagram as a function of mass ratio M/m and interaction strength. In particular, we determine when it is favorable for the dressed impurity (polaron) to bind particles from the Fermi sea to form a dimer, trimer or even larger clusters. Similarly to 3D, we find that the Fermi sea favors the trimer state so that it exists for M/m less than the critical mass ratio for trimer formation in the vacuum. We also find a region where dimers have finite momentum in the ground state, a scenario which corresponds to the Fulde-Ferrell-Larkin-Ovchinnikov superfluid state in the limit of large spin imbalance. For equal masses (M=m), we compute rigorous bounds on the polaron-dimer transition, and we show that the polaron energy and residue is well captured by the variational approach, with the former quantity being in good agreement with experiment. When there is a finite density of impurities, we find that this polaron-dimer transition is preempted by a first-order superfluid-normal transition at zero temperature, but it remains an open question what happens at finite temperature.

THE FIRST PHOTOMETRIC INVESTIGATION OF THE NEGLECTED W-UMa-TYPE BINARY STAR UZ CMi

UZ CMi was a W-UMa-type binary star found more than 80 years ago. However, it has been neglected in photometric investigations. Here, the first complete light curves in the B, V, R, and I bands are presented and analyzed using the Wilson and Devinney method. It is discovered that UZ CMi is a contact binary (f = 38.4(+/- 2.3)%) with amass ratio of 0.45. The derived orbital inclination (i = 87 degrees) indicates that it is a total eclipsing binary, which suggests that the determined parameters are reliable. By using 17 new eclipse times together with those collected from the literature, we found that the general trend of the observed-calculated (O - C) curve shows an upward parabolic variation that corresponds to a long-term increase in the orbital period at a rate of (P) over dot = +4.1 x 10(-8) days yr(-1). The continuous increase may be caused by a mass transfer from the less massive component to the more massive one. This suggests that UZ CMi is in the thermal relaxation oscillation controlled stage of the evolutionary scheme proposed by Qian. UZ CMi will oscillate around a critical mass ratio and the contact configuration cannot be broken. After the upward parabolic change was removed, the (O - C)(2) curve of the photoelectric and charge-coupled device data revealed a cyclic variation with a small amplitude of 0.0026 days and a period of 21.1 yr. The cyclic change was analyzed for the light-travel time effect via the presence of an extremely cool stellar companion.

Mathematical modeling of stability in rough elliptic bore misaligned journal bearing considering thermal and non-Newtonian effects

The paper briefly introduces a finite difference method based mathematical model to predict the stability of a finite journal bearing. The proposed method is used to integrate the geometrical irregularities of bearing such as non-circularity and surface roughness with the operational error like misalignment to represent more accurate film thickness. The bearing bore is assumed elliptic with longitudinal or transverse type wave pattern of roughness. A combined solution of Reynolds equation and Energy equation is made using effective influence Newton–Raphson method of error convergence. The non-Newtonian behavior of lubricant is addressed based on Power Law model. Thermal effect is considered adiabatic. Further to this analysis, the steady state and related perturbed pressures are estimated using linearization of bearing reaction. The dimensionless spring and damping coefficients are evaluated to find the critical mass and whirl ratio. Finally, the effect of misalignment bore ellipticity and roughness pattern on stability of such journal bearing is discussed in detail.

Motion in the generalized restricted three-body problem

This paper investigates the motion of an infinitesimal body in the generalized restricted three-body problem. It is generalized in the sense that both primaries are radiating, oblate bodies, together with the effect of gravitational potential from a belt. It derives equations of the motion, locates positions of the equilibrium points and examines their linear stability. It has been found that, in addition to the usual five equilibrium points, there appear two new collinear points L n1, L n2 due to the potential from the belt, and in the presence of all these perturbations, the equilibrium points L 1, L 3 come nearer to the primaries; while L 2, L 4, L 5, L n1 move towards the less massive primary and L n2 moves away from it. The collinear equilibrium points remain unstable, while the triangular points are stable for 0<μ<μ c and unstable for \(\mu_{c} \le\mu\le\frac{1}{2}\), where μ c is the critical mass ratio influenced by the oblateness and radiation of the primaries and potential from the belt, all of which have destabilizing tendency. A practical application of this model could be the study of the motion of a dust particle near the oblate, radiating binary stars systems surrounded by a belt.

The criteria for dynamical mass transfer of the main-sequence donor stars

AbstractMass transfer is very common in binary evolution and it dominates the evolutionary fate of binaries. Two crucial problems i.e. dynamical mass transfer and common envelope evolution, are not well understood yet. Here we focus on the first problem, and systematically show the critical mass ratio for dynamical mass transfer when the donor stars are still on the main sequence (MS).

Experimental study of vortex-induced vibrations of a tethered cylinder

This paper presents an experimental study of the motions, forces and flow patterns of a positively buoyant tethered cylinder (m⁎<1) in uniform flow undergoing vortex-induced vibration (VIV). The flow fields have been measured using digital Particle Image Velocimetry (PIV) technique, in conjunction with a piezoelectric load cell for direct measurement of drag and lift forces acting on the tethered cylinder. The effects of varying mass ratio and Reynolds number over the range 0.61≤m⁎≤0.92 and 4000≤Re≤12 000 are examined. Results of a fixed (or stationary) cylinder at the same Reynolds numbers are provided to serve as the benchmark reference. The peak amplitude of oscillation, θmax/θD, generally increases with Re and deceases with m⁎. Similar to previous studies, the results reveal the existence of a critical mass ratio mcrit⁎≈0.7, below which large-amplitude oscillations would take place when Re is high enough, with the largest peak amplitude of θmax/θD=0.9 observed for the case of m⁎=0.61 and Re=12 000. Thus two distinct states of oscillation are categorized, namely, the small- and large-amplitude oscillation states. The distinction between the two states is also vivid in the mean and root-mean-square (r.m.s.) force coefficients (including C¯D, CD′ and CL′). The frequency of vortex shedding (fV) from the tethered cylinder is always synchronized with the cylinder's oscillation frequency (fosc), regardless of the oscillation state. A time series of instantaneous vorticity fields illustrate that vortex shedding from the tethered cylinder undergoing VIV maintains the 2S mode, but at an inclined angle to the free stream, which is most obvious in the large-amplitude oscillation state. This leads to an asymmetry in the shear layers separated from opposite sides of the cylinder, as shown by the distribution of ensemble-averaged Reynolds stress.

MOTION IN THE PHOTOGRAVITATIONAL ELLIPTIC RESTRICTED THREE-BODY PROBLEM UNDER AN OBLATE PRIMARY

This paper studies the motion of an infinitesimal mass around seven equilibrium points in the framework of the elliptic restricted three-body problem under the assumption that the primary of the system is a non-luminous, oblate spheroid and the secondary is luminous. A practical application of this case could be the study of the dynamical evolution of dust particles in orbits around a binary system with a dark degenerate primary and a secondary stellar companion. Conditional stability of the motion around the triangular points exists for 0 < μ < μc , where μ is the mass ratio. The critical mass ratio value μc depends on the combined effect of radiation pressure, oblateness, eccentricity, and the semimajor axis of the elliptic orbits; an increase in any of these parameters has destabilizing results on the orbits of the test particles. The overall effect is therefore that the size of the region of stability decreases when the value of these parameters increases. The collinear points and the out-of-plane equilibrium points are found to be unstable for any combination of the parameters considered here. Further, a numerical exploration computing the positions of the triangular points and the critical mass ratio of two binaries RX J0450.1-5856 and Nova Cen 1969 (Cen X-4) is given.

Crystallization behavior and melting characteristics of wollastonite filled β-isotactic polypropylene composites

In order to obtain wollastonite filled β-iPP composites, wollastonite treated with pimelic acid (W*) were prepared with various mass ratios of wollastonite/pimelic acid (W/PA). The crystallization behavior, melting characteristics and β-nucleating ability of iPP composites filled with wollastonite (W) and W* were investigated by DSC and XRD. The results indicated that addition of wollastonite increased the crystallization temperatures of iPP, but the crystallization temperatures of iPP in iPP/W* composites were higher than those of iPP/W composites, which proved that the β-nucleation of W* is stronger than untreated wollastonite. Although iPP/wollastonite composites mainly form α-phase iPP, modification of wollastonite by PA significantly enhanced nucleation of β-phase iPP. The β-nucleating ability of W* depend on the amount of formed calcium pimelate, therefore the β-phase contents of β-iPP/W* composites increased with increasing W* content and decreasing mass ratio of W/PA. Moreover, there exist different critical mass ratios of W/PA for preparation of β-iPP composites filled with different W* contents with highest β-phase content and low cost.

Calculation of chloride concentration at color change boundary of AgNO 3 colorimetric measurement

AgNO 3 colorimetric measurement of chloride in cement-based materials can be implemented owing to chemical reactions between Ag + and Cl − or OH − ions, which result in the precipitation of AgCl and Ag 2O. When the mass ratio of AgCl to precipitated AgCl + Ag 2O reaches a critical value (P crit-AgCl), a color change boundary appears. In this paper, chloride concentrations required for the formation of the critical mass ratio of AgCl to precipitated AgCl + Ag 2O derived from the AgNO 3–NaCl–NaOH system were calculated based on the solubility products of silver hydroxide and silver chloride, and mass conservation of the chemical reactions. P crit-AgCl was determined as 0.65 through a series of AgNO 3 colorimetric measurements on cement-based materials. Calculated results indicated that if Ag + could react with all OH − and Cl −, there existed a linear relationship between the critical chloride concentration for color change (C crit-Cl – ) and OH − concentration (C OH – ), namely C crit-Cl – = 1.6C OH – . If Ag + could react with only partial OH − and Cl −, there existed an exponential relationship among C crit-Cl – and C OH – , Ag + concentration (C Ag + ), volume of AgNO 3 solution (V Ag + ) as well as the volume of NaCl + NaOH solution (V OH – + Cl – ), namely C crit-Cl – = 0.00695C OH – + 0.608C Ag + V Ag + /V OH – + Cl – . It can be concluded that the alkalinity of cement-based materials, concentration and volume of sprayed AgNO 3 solution and volume of pore solution have effects on chloride concentration at the color change boundary (C d). Calculated C d values ranged between 0.03 and 0.96 mol/L (in pore solution) or 0.011% to 2.27% (by the mass of binder), respectively. This explains why reported range of chloride concentration at the color change boundary in publications varied in a broad range.

Hysteresis in vortex-induced vibrations: critical blockage and effect ofm*

The hysteretic behaviour of a freely vibrating cylinder, near the low-Reynolds-number end of synchronization/lock-in, in the laminar regime is investigated. Computations are carried out using a stabilized finite-element method. The flow remains two-dimensional in this Reynolds number regime. This is verified via comparison of two- and three-dimensional computations. The cylinder is free to undergo crossflow as well as in-line vibrations. The combined effect of mass ratio (1 ≤m* ≤ 100) and blockage (0.25% ≤B≤ 12.5%) is studied in detail. The existence of a critical mass ratio (m*cr= 10.11), below which hysteresis disappears for an unbounded flow situation, is identified. For higher mass ratio the hysteretic behaviour is observed for all blockage. However, the hysteresis loop width is found to vary withB; its variation withm* andBis studied. The concept of critical blockageBcris introduced. ForB≤Bcrthe response of the cylinder is virtually the same as that in an unbounded flow domain. The variation ofBcrwithm* is investigated. Furthermore,Bcris found to vary non-monotonically withm* form* ≤m*crand is almost constant form* ≥ 20. The effect of damping, as well as restricting the cylinder to undergo transverse vibrations only, on the hysteresis behaviour is studied. The transverse-only motion leads to a larger hysteresis loop width compared with the transverse and the in-line motion of the cylinder. An attempt is made to explain this by comparing the results from forced vibrations.

Tuning correlations in multi-component plasmas

Spontaneous, correlation-driven structure formation is one of the most fundamental collective processes in nature. In particular, particle ensembles in externally controlled confinement geometries allow for a systematic investigation of strong correlation and quantum effects over broad ranges of the relevant trap and plasma parameters. An exceptional feature inherent to finite systems is the governing role of symmetry and surface effects leading to similar collective behaviour in physical systems on vastly different length and energy scales. Considering (i) confined complex (dusty) plasmas and (ii) charge asymmetric bilayers, the effective range of the pair interaction emerges as a key quantity taking effect on the self-organized structure formation. Additional interest arises from the possible mass asymmetry of the plasma constituents in bilayers. Translating the results from (unconfined) 3D plasmas to bilayer systems, it is shown that the critical mass ratio required for crystallization of the heavy plasma component can be drastically reduced such that this effect becomes experimentally accessible.

The outcome of protoplanetary dust growth: pebbles, boulders, or planetesimals?

<i>Context. <i/>The sticking of micron-sized dust particles caused by surface forces within circumstellar disks is the first stage in the production of asteroids and planets. The key components describing this process are the relative velocity between the dust particles in this environment and the complex physics of dust aggregate collisions.<i>Aims. <i/>We present the results of a collision model based on laboratory experiments of these aggregates. We investigate the maximum aggregate size and mass that can be reached by coagulation in protoplanetary disks.<i>Methods. <i/>We use the results of laboratory experiments to establish the collision model previously published by Güttler et al. The collision model is based on the assumptions that we model the aggregates as spheres with compact and porous “phases” and that there is a continuous transition between these two. We apply this collision model to the Monte Carlo method developed previously by Zsom & Dullemond and include Brownian motion, radial drift, and turbulence as contributors of relative velocity between dust particles.<i>Results. <i/>We model the growth of dust aggregates at 1 AU in the midplane for three different gas densities. We find that the evolution of the dust does not follow the previously assumed growth-fragmentation cycles. Catastrophic fragmentation hardly occurs in the three disk models. Furthermore, we see long-lived, quasi-steady states in the distribution function of the aggregates caused by bouncing. We explore how the mass and the porosity depend on both the turbulence parameter and the critical mass ratio of dust particles. Upon varying the turbulence parameter, the system behaves in a non-linear way, and we find that the critical mass ratio has a strong effect on the particle sizes and masses. Particles reach Stokes numbers of roughly 10<sup>-4<sup/> during the simulations.<i>Conclusions. <i/>The particle growth is stopped by bouncing rather than fragmentation in these models. The final Stokes number of the aggregates is rather insensitive to the variations in the gas density and the strength of turbulence. The maximum mass of the particles is limited to <i>≈<i/>1 g (chondrule-sized particles). Planetesimal formation can proceed by the means of the turbulent concentration of these aerodynamically size-sorted, chondrule-sized particles.

Static and dynamic characteristics of short wavy journal bearings

AbstractA general analysis has been done to investigate the static and dynamic performance of short wavy journal bearing. Reynolds equation is solved for both steady‐ and unsteady‐state operations. The steady‐state analysis has been done and compared with circular bearing with respect to their load capacity, flow rate, pressure distribution and friction factor. The unsteady‐state analysis has been used to determine the rotor dynamic coefficients for various eccentricity ratios. These coefficients are used to determine the stability parameters, such as critical mass and whirl ratio, and prove that wave bearing has not only better load carrying capacity but also provides better stability at high speed than circular bearing. Copyright © 2010 John Wiley &amp; Sons, Ltd.

Dynamic Characteristics and Stability of Short Wave Journal Bearings

A general analysis has been done to investigate the dynamic performance and stability of short wave journal bearing. Reynolds equation is solved for unsteady-state operations. The unsteady analysis has been used to determine the rotor dynamic coefficients for various eccentricity ratios and wave eccentricity ratios. These coefficients has been used to determine the stability parameters such as critical mass and whirl ratio to show that wave bearing provides better stability at higher speed than circular bearing.

Vortex-induced vibration of a prism in internal flow

In this article, we study the influence of solid-to-fluid density ratio m on the type of vortex-induced oscillation of a square section prism placed inside a two-dimensional channel. We assume that the solid body has neither structural damping nor spring restoring force. Accordingly, the prism equation of motion contains only inertia and aerodynamics forces. The problem is considered in the range of Reynolds numbers Re ∈ [50 200] (based on the prism cross-section height h) and channel widths H = H′/h ∈ [2.5 10]. We found that, for each Re and H, there is a critical mass ratio mc that separates two different oscillation regimes. For m &gt; mc, the prism oscillation is periodical and contains a single harmonic. For m &lt; mc, the prism oscillation changes completely and assumes an irregular pattern that is characterized by multiple harmonics that appear to belong to a uniform spectrum. The change from one regime to the other is abrupt and we were not able to observe a transitional regime in which the number of response harmonics grew by finite steps. The value of the critical mass ratio grows along with the Reynolds number and the channel width.