Function Of Mass Ratio Research Articles

A stable second-order scheme for fluid–structure interaction with strong added-mass effects

In this paper, we present a stable second-order time accurate scheme for solving fluid–structure interaction problems. The scheme uses so-called Combined Field with Explicit Interface (CFEI) advancing formulation based on the Arbitrary Lagrangian–Eulerian approach with finite element procedure. Although loosely-coupled partitioned schemes are often popular choices for simulating FSI problems, these schemes may suffer from inherent instability at low structure to fluid density ratios. We show that our second-order scheme is stable for any mass density ratio and hence is able to handle strong added-mass effects. Energy-based stability proof relies heavily on the connections among extrapolation formula, trapezoidal scheme for second-order equation, and backward difference method for first-order equation.Numerical accuracy and stability of the scheme is assessed with the aid of two-dimensional fluid–structure interaction problems of increasing complexity. We confirm second-order temporal accuracy by numerical experiments on an elastic semi-circular cylinder problem. We verify the accuracy of coupled solutions with respect to the benchmark solutions of a cylinder-elastic bar and the Navier–Stokes flow system. To study the stability of the proposed scheme for strong added-mass effects, we present new results using the combined field formulation for flexible flapping motion of a thin-membrane structure with low mass ratio and strong added-mass effects in a uniform axial flow. Using a systematic series of fluid–structure simulations, a detailed analysis of the coupled response as a function of mass ratio for the case of very low bending rigidity has been presented.

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.

Role of Alkaline Activator in Development of Eco-friendly Fly Ash Based Geo Polymer Concrete

Ordinary portland cement (OPC) is conventionally used as primary binder to produce concrete. The amount of carbon dioxide released during the manufacture of OPC and the extent of energy required to produce OPC are the matters of environmental concern in view of global warming and the poor availability of power. Fly-ash, abundantly available byproduct of coal fired thermal power stations is posing great environmental problems through its disposal. Fly ash with combination of alkalis like sodium hydroxide and sodium silicate can produce binding material depending upon the characteristics of these ingredients. The possibility of eco-friendly use of locally available fly-ash with commercially available alkalis in the development of effective binder; and the effect of various parameters on the compressive strength of geo-polymer concrete is explored in the present paper. The laboratory investigations under ambient and oven dry curing conditions suggested that locally available low calcium fly-ash is suitable for development of geo-polymer concrete; and the compressive strength of geo-polymer concrete is a function of mass ratio of alkaline liquid to fly-ash, mass ratio of sodium silicate to sodium hydroxide and molar concentration of sodium hydroxide.

COLLISIONS BETWEEN GRAVITY-DOMINATED BODIES. I. OUTCOME REGIMES AND SCALING LAWS

Numerical simulations of the stochastic end stage of planet formation typically begin with a population of embryos and planetesimals that grow into planets by merging. We analyzed the impact parameters of collisions leading to the growth of terrestrial planets from recent $N$-body simulations that assumed perfect merging and calculated more realistic outcomes using a new analytic collision physics model. We find that collision outcomes are diverse and span all possible regimes: hit-and-run, merging, partial accretion, partial erosion, and catastrophic disruption. The primary outcomes of giant impacts between planetary embryos are approximately evenly split between partial accretion, graze-and-merge, and hit-and-run events. To explore the cumulative effects of more realistic collision outcomes, we modeled the growth of individual planets with a Monte Carlo technique using the distribution of impact parameters from $N$-body simulations. We find that fewer planets reached masses $>0.7 M_{\rm Earth}$ using the collision physics model compared to simulations that assumed every collision results in perfect merging. For final planets with masses $>0.7 M_{\rm Earth}$, 60% are enriched in their core-to-mantle mass fraction by >10% compared to the initial embryo composition. Fragmentation during planet formation produces significant debris ($\sim15$% of the final mass) and occurs primarily by erosion of the smaller body in partial accretion and hit-and-run events. In partial accretion events, the target body grows by preferentially accreting the iron core of the projectile and the escaping fragments are derived primarily from the silicate mantles of both bodies. Thus, the bulk composition of a planet can evolve via stochastic giant impacts.

Trimers, Molecules, and Polarons in Mass-Imbalanced Atomic Fermi Gases

We consider the ground state of a single "spin-down" impurity atom interacting attractively with a "spin-up" atomic Fermi gas. By constructing variational wave functions for polarons, molecules, and trimers, we perform a detailed study of the transitions between these dressed bound states as a function of mass ratio r=m↑/m↓ and interaction strength. Crucially, we find that the presence of a Fermi sea enhances the stability of the p-wave trimer, which can be viewed as a Fulde-Ferrell-Larkin-Ovchinnikov molecule that has bound an additional majority atom. For sufficiently large r, we find that the transitions lie outside the region of phase separation of the imbalanced Fermi gas and should thus be observable in experiment, unlike the well-studied equal-mass case.

A COLD NEPTUNE-MASS PLANET OGLE-2007-BLG-368Lb: Cold neptunes are common

We present the discovery of a Neptune-mass planet OGLE-2007-BLG-368Lb with a planet-star mass ratio of q=[9.5 +/- 2.1] x 10^{-5} via gravitational microlensing. The planetary deviation was detected in real-time thanks to the high cadence of the MOA survey, real-time light curve monitoring and intensive follow-up observations. A Bayesian analysis returns the stellar mass and distance at M_l = 0.64_{-0.26}^{+0.21} M_\sun and D_l = 5.9_{-1.4}^{+0.9} kpc, respectively, so the mass and separation of the planet are M_p = 20_{-8}^{+7} M_\oplus and a = 3.3_{-0.8}^{+1.4} AU, respectively. This discovery adds another cold Neptune-mass planet to the planetary sample discovered by microlensing, which now comprise four cold Neptune/Super-Earths, five gas giant planets, and another sub-Saturn mass planet whose nature is unclear. The discovery of these ten cold exoplanets by the microlensing method implies that the mass ratio function of cold exoplanets scales as dN_{\rm pl}/d\log q \propto q^{-0.7 +/- 0.2} with a 95% confidence level upper limit of n < -0.35 (where dN_{\rm pl}/d\log q \propto q^n). As microlensing is most sensitive to planets beyond the snow-line, this implies that Neptune-mass planets are at least three times more common than Jupiters in this region at the 95% confidence level.

THE IMPORTANCE OF BINARY GRAVITATIONAL MICROLENSING EVENTS THROUGH HIGH-MAGNIFICATION CHANNEL

We estimate the detection efficiency of binary gravitational lensing events through the channel of high-magnification events. From this estimation, we find that binaries in the separations ranges of 0.1 < s < 10, 0.2 < s < 5, and 0.3 < s < 3 can be detected with ~ 100% efficiency for events with magnifications higher than A=100, 50, and 10, respectively, where s represents the projected separation between the lens components normalized by the Einstein radius. We also find that the range of high efficiency covers nearly the whole mass-ratio range of stellar companions. Due to the high efficiency in wide ranges of parameter space, we point out that majority of binary-lens events will be detected through the high-magnification channel in lensing surveys that focus on high-magnification events for efficient detections of microlensing planets. In addition to the high efficiency, the simplicity of the efficiency estimation makes the sample of these binaries useful in the statistical studies of the distributions of binary companions as functions of mass ratio and separation. We also discuss other importance of these events.

HOW DO DISKS SURVIVE MERGERS?

We develop a physical model for how galactic disks survive and/or are destroyed in interactions. Based on dynamical arguments, we show gas primarily loses angular momentum to internal torques in a merger. Gas within some characteristic radius (a function of the orbital parameters, mass ratio, and gas fraction of the merging galaxies), will quickly lose angular momentum to the stars sharing the perturbed disk, fall to the center and be consumed in a starburst. A similar analysis predicts where violent relaxation of the stellar disks is efficient. Our model allows us to predict the stellar and gas content that will survive to re-form a disk in the remnant, versus being violently relaxed or contributing to a starburst. We test this in hydrodynamic simulations and find good agreement as a function of mass ratio, orbital parameters, and gas fraction, in simulations spanning a wide range in these properties and others, including different prescriptions for gas physics and feedback. In an immediate sense, the amount of disk that re-forms can be understood in terms of well-understood gravitational physics, independent of details of ISM gas physics or feedback. This allows us to explicitly quantify the requirements for such feedback to (indirectly) enable disk survival, by changing the pre-merger gas content and distribution. The efficiency of disk destruction is a strong function of gas content: we show how and why sufficiently gas-rich major mergers can, under general conditions, yield systems with small bulges (B/T<0.2). We provide prescriptions for inclusion of our results in semi-analytic models.

The Radical Consequences of Realistic Satellite Orbits for the Heating and Implied Merger Histories of Galactic Disks

Previous models of galactic disk heating in interactions invoke restrictive assumptions not necessarily valid in modern ΛCDM contexts: that satellites are rigid and orbits are circular, with slow decay over many orbital periods from dynamical friction. This leads to a linear scaling of disk heating with satellite mass: disk heights and velocity dispersions scale --> Msat/Mdisk. In turn, observed disk thicknesses present strong constraints on merger histories: the implication for the Milky Way is that z ~ 2, in conflict with cosmological predictions. More realistically, satellites merge on nearly radial orbits, and once near the disk, resonant interactions efficiently remove angular momentum while tidal stripping removes mass, leading to rapid merger/destruction in a couple of free-fall plunges. Under these conditions the proper heating efficiency is nonlinear in mass ratio, --> (Msat/Mdisk)2. We derive the scaling of disk scale heights and velocity dispersions as a function of mass ratio and disk gas content in this regime, and show that this accurately describes the results of simulations with appropriate live halos and disks. Under realistic circumstances, we show that disk heating in minor mergers is suppressed by an order of magnitude relative to the expectations of previous analyses. We show that the Milky Way disk could have experienced ~5-10 independent 1:10 mass ratio mergers since -->z ~ 2, in agreement with cosmological models. Because the realistic heating rates are nonlinear in mass, the predicted heating is dominated by the more stochastic, rare low mass ratio mergers, and the existence of populations with little or no thick disk does not require fundamental modifications to the cosmology. This also leads to important differences in the predicted isophotal shapes of bulge-disk systems along the Hubble sequence.

크랙을 가진 탄성지지된 유체유동 외팔파이프의 동적 안정성

The dynamic stability of elastically restrained cantilever pipe conveying fluid with crack is investigated in this paper. The pipe, which is fixed at one end, is assumed to rest on an intermediate spring support. Based on the Euler-Bernoulli beam theory, the equation of motion is derived by the energy expressions using extended Hamilton's Principle. The crack section is represented by a local flexibility matrix connecting two undamaged pipe segments. The influence of a crack severity and position, mass ratio and the velocity of fluid flow on the stability of a cantilever pipe by the numerical method are studied. Also, the critical flow velocity for the flutter and divergence due to variation in the support location and the stiffness of the spring support is presented. The stability maps of the pipe system are obtained as a function of mass ratios and effect of crack.

유체유동 외팔 파이프의 안정성에 미치는 크랙의 영향

In this paper, the dynamic stability of a cracked cantilever pipe conveying fluid with tip mass is investigated. The pipe is modelled by the Euler-Bernoulli beam theory in which rotatory inertia and shear deformation effects are ignored. The equation of motion is derived by the energy expressions using extended Hamilton's Principle. The crack section is represented by a local flexibility matrix connecting two undamaged pipe segments. The influence of the crack severity, the position of crack, the mass ratio, and a tip mass on the stability of a cantilever pipe conveying fluid are studied by the numerical method. Besides, the critical flow velocity and the stability maps of the pipe system as a function of mass ratios(<TEX>$\beta$</TEX>) for the changing each parameter are obtained.

Flapping dynamics of a flag in a uniform stream

We consider the flapping stability and response of a thin two-dimensional flag of high extensional rigidity and low bending rigidity. The three relevant non-dimensional parameters governing the problem are the structure-to-fluid mass ratio, μ = ρsh/(ρfL); the Reynolds number,Rey=VL/ν; and the non-dimensional bending rigidity,KB=EI/(ρfV2L3). The soft cloth of a flag is represented by very low bending rigidity and the subsequent dominance of flow-induced tension as the main structural restoring force. We first perform linear analysis to help understand the relevant mechanisms of the problem and guide the computational investigation. To study the nonlinear stability and response, we develop a fluid–structure direct simulation (FSDS) capability, coupling a direct numerical simulation of the Navier–Stokes equations to a solver for thin-membrane dynamics of arbitrarily large motion. With the flow grid fitted to the structural boundary, external forcing to the structure is calculated from the boundary fluid dynamics. Using a systematic series of FSDS runs, we pursue a detailed analysis of the response as a function of mass ratio for the case of very low bending rigidity (KB= 10−4) and relatively high Reynolds number (Rey= 103). We discover three distinct regimes of response as a function of mass ratio μ: (I) a small μ regime of fixed-point stability; (II) an intermediate μ regime of period-one limit-cycle flapping with amplitude increasing with increasing μ; and (III) a large μ regime of chaotic flapping. Parametric stability dependencies predicted by the linear analysis are confirmed by the nonlinear FSDS, and hysteresis in stability is explained with a nonlinear softening spring model. The chaotic flapping response shows up as a breaking of the limit cycle by inclusion of the 3/2 superharmonic. This occurs as the increased flapping amplitude yields a flapping Strouhal number (St= 2Af/V) in the neighbourhood of the natural vortex wake Strouhal number,St≃ 0.2. The limit-cycle von Kármán vortex wake transitions in chaos to a wake with clusters of higher intensity vortices. For the largest mass ratios, strong vortex pairs are distributed away from the wake centreline during intermittent violent snapping events, characterized by rapid changes in tension and dynamic buckling.

Polarized Fermi Condensates with Unequal Masses: Tuning the Tricritical Point

We consider a two-component atomic Fermi gas within a mean-field, single-channel model, where both the mass and population of each component are unequal. We show that the tricritical point at zero temperature evolves smoothly from the BEC to BCS side of the resonance as a function of mass ratio r. We find that the interior gap state proposed by Liu and Wilczek is always unstable to phase separation, while the breached pair state with one Fermi surface for the excess fermions exhibits differences in its density of states and pair correlation functions depending on which side of the resonance it lies. Finally, we show that, when r greater, similar 3.95, the finite-temperature phase diagram of trapped gases at unitarity becomes topologically distinct from the equal mass system.

A Search for Companions to L Dwarfs

We present the results of two imaging surveys for companions to low-luminosity dwarfs, one with Keck to a limiting magnitude of K = 20, and the other with HST to a limiting magnitude of I = 23. No companions were found at separations of 0″.5 to 20″.0, but seven companions were found within 0″.5. Based on sub-stellar evolutionary models, we estimate the companion detection efficiency as a function of mass ratio. This modeling, coupled with the data, place strong upper limits on the mass ratios of unobserved companions. We conclude that no companions exist in the optimal sensitivity regions of both surveys for q &gt; 0.85 (HST), and q &gt; 0.4 (Keck).

Kinetic temperatures for a granular mixture.

An isolated mixture of smooth, inelastic hard spheres supports a homogeneous cooling state with different kinetic temperatures for each species. This phenomenon is explored here by molecular dynamics simulation of a two component fluid, with comparison to predictions of the Enskog kinetic theory. The ratio of kinetic temperatures is studied for two values of the restitution coefficient alpha=0.95 and 0.80, as a function of mass ratio, size ratio, composition, and density. Good agreement between theory and simulation is found for the lower densities and higher restitution coefficient; significant disagreement is observed otherwise. The phenomenon of different temperatures is also discussed for driven systems, as occurs in recent experiments. Differences between the freely cooling state and driven steady states are illustrated.

N-Body Simulations of Planetesimal Evolution: Effect of Varying Impactor Mass Ratio

We present results from direct N-body simulations of collisions between gravitational aggregates of varying size as part of a study to parameterize planetesimal growth in the Solar System. We find that as the ratio of projectile to target mass departs from unity, the impact angle has less effect on the outcome. At the same time, the probability of planetesimal growth increases. Conversely, for a fixed impact energy, collisions between impactors with mass ratio near unity are more dispersive than those with impactor mass ratio far from unity. We derive an expression for the accretion probability as a function of mass ratio. For an average mass ratio of 1:5, we find an accretion probability of ∼60% over all impact parameters. We also compute the critical specific dispersal energy Q* D as a function of projectile size. Extrapolating to a projectile size of 1 m with a 1-km target, we find Q* D =10 3−10 4 J kg −1, in agreement with several other collision models that use fundamentally different techniques. Our model assumes that the components of each gravitational aggregate are identical and indestructible over the range of sampled impact speeds. In future work we hope to incorporate a simple fracture model to extend the range of applicable speeds and we plan to implement our results in a large-scale planetesimal evolution code.

Time Series Energy Production in Smoothed Particle Hydrodynamics Accretion Disks: Superhumps in the AM Canum Venaticorum Stars

The energy production time series of our purely hydrodynamic accretion disk simulations display remarkable similarities with the observed light curves of dwarf novae superhumps in general and the AM CVn stars in particular. The superhump period excess as a function of mass ratio agrees well with earlier theoretical and numerical results, and the amplitudes and relative phases of the harmonics in the power spectra agree well with the observations. The morphology of the mean pulse profile appears to be a useful predictor of system mass ratio. Our modified smoothed particle hydrodynamics code time symmetrizes the interparticle forces when individual time steps are used that differ from each other by a power of 2 and advances the internal energy using a very simple method based on fundamental principles that requires the calculation of only a single vector dot product per particle per time step instead of a separate pairwise internal energy equation. Both of these modifications act to increase the stability of the internal energy changes, resulting in a significant reduction in the noise in the energy production time series. The periodicities in our models are primarily the result of changes in the viscous energy production as the disks experience tidal stressing and oscillate between nearly circular and highly distorted shapes over a superhump period. We follow the system in an inertial frame of reference, and the symmetry axis of the disk during peak energy production is aligned roughly perpendicular to the line joining the center of the stars. This axis precesses slowly in the inertial frame on a timescale of ~35-75 orbital periods, where the precession period is a function of the system mass ratio. The disks are thickest in the quadrant undergoing the largest radial excursions. This feature is stationary in the slowly precessing frame. The particle trajectories also show quasi-periodic m ≈ 2 vertical oscillations that generally agree with published analytical predictions.

Accretion of a Satellite onto a Spherical Galaxy: Binary Evolution and Orbital Decay

We study the dynamical evolution of a satellite (of mass M) orbiting around a companion spherical galaxy. The satellite is subject to a back-reaction force FΔ resulting from the density fluctuations excited in the primary stellar system. We evaluate this force using the linear response theory developed by Colpi & Pallavicini in 1998. FΔ is computed in the reference frame comoving with the primary galaxy and is expanded in multipoles. To lowest order, the force depends on a time integral involving a dynamical four-point correlation function of the unperturbed background. The equilibrium stellar system (of mass Nm) is described in terms of a Gaussian one-particle distribution function. To capture the relevant features of the physical process determining the evolution of the detached binary, we introduce in the Hamiltonian the harmonic potential as interaction potential among stars. The evolution of the composite system is derived solving for a set of ordinary differential equations; the dynamics of the satellite and of the stars is computed self-consistently. We determine the conditions for tidal capture of a satellite from an asymptotic free state and give an estimate of the maximum kinetic energy above which encounters do not end in a merger as a function of the mass ratio M/Nm. We find that capture always leads to final coalescence. If the binary forms as a bound pair, stability against orbital decay is lost if the pericentric distance is smaller than a critical value. This instability is interpreted in terms of a near-resonance condition and establishes when the orbital Keplerian frequency becomes comparable to the internal frequency ω of the stellar system. We show that before coalescence, eccentric orbits become progressively less eccentric; the circularization is explored as a function of mass ratio. The timescale of binary coalescence τb is a sensitive function of the eccentricity e for a fixed semimajor axis a and M/Nm ratio: the mismatch between τb at e ~ 0 and τb at e ~ 1 can be very large, typically τb(e 1) ~ 6ω-1, and the time ratio τb(0)/τb(1) 5 (for M/Nm = 0.05). In addition, we find that τb obeys a scaling relation with M/Nm for circular orbits: τb ∝ (M/Nm)-α, with α ~ 0.4. In grazing encounters, τb is nearly independent of mass.

Ion mass effects on shock-like structures in multi-species plasma

Ion acoustic type shock-like structures based on the extended steady-state theory in multi-species plasma with different ion masses are studied. Using theoretical treatments, three simple models using continuous electron distribution functions at the separatrix , have been considered. From numerical studies on the existence of shock-like structures, we find the lowest limits of propagation velocity and amplitude of shock-like structures as a function of mass ratio (or density). In particle simulations, it is established for the case of a current driven system. Simulations are performed with an axially bounded electrostatic particle-in-cell (PIC) code XPDP1, which is a workstation version of the one-dimensional electrostatic bounded plasma code PDW1 [35-37]. The effect of the massive ion is to decrease the propagating velocity of the shock-like structures and decrease its maximum (or net) amplitude. Also, by increasing the density of the massive ion component, both the velocity of propagation and the maximum (or net) amplitude of the shock-like structure decreases.

Comparison of chemical analysis of residual monomer in a chemical-cured dental acrylic material to an FTIR method

Objective The purpose of this work was to perform quantitative analysis of residual monomer in chemical-cured acrylic using an infrared spectroscopic method and to compare it to an accepted form of quantitative chemical analysis. Identical samples of acrylic were analyzed and compared using Fourier transform infrared (FTIR) spectroscopy with multiple standard additions vs. “wet” chemical analysis of bromination followed by titration. Methods Two 6 g disks from a single mix of cold-cured acrylic (Lang Dental Mfg. Co., Inc.) were prepared and cured in room air for 1 hr using a ratio of 12 g of powder to 8 mL of liquid. One of the cold-cured acrylic disks was dissolved in glacial acetic acid and analyzed according to the “wet” technique described by Smith and Bains (Smith and Bains,1956). The other disk was dissolved in methyl isobutyrate (MIBT). Five aliquots, zero plus four incremental additions of pure methyl methacrylate (MMA), were prepared from the MIBT solution. Absorption spectra were collected for all five aliquots. The data were plotted with the ratio of the mass of methyl methacrylate added to the mass of aliquot of MIBT solution as the independent variable, and the absorption, corrected for dilution, as the dependent variable. Least squares fit of the data yielded the slope and intercept. The ratio of intercept to slope divided by the weight fraction of the acrylic disk dissolved in MIBT yielded the concentration of methyl methacrylate in the disk. Results The plot of absorbance as a function of mass ratio of MMA added to MIBT solution was linear over the concentration range covered (r = 0.999). Analysis of the spectroscopic data revealed a concentration of residual C=C double bonds of 0.32 ± 0.01 mol/kg. “Wet” chemical analysis of the acrylic yielded a concentration of residual C=C double bonds of 0.288 ± 0.003 mol/kg. There was significant difference (students Mest, 99% confidence level) between the two techniques with respect to the amount of residual monomer calculated. Significance The multiple standard additions technique works well for the quantitative analysis of small amounts of residual double bonds in the poly(methyl methacrylate) chemical-cured acrylic polymer system, eliminating the need for an internal standard or external calibration.