scholarly journals Linear analysis of the non-axisymmetric secular gravitational instability

2019 ◽  
Vol 487 (4) ◽  
pp. 5405-5415
Author(s):  
Mohsen Shadmehri ◽  
Razieh Oudi ◽  
Gohar Rastegarzadeh
Keyword(s):  
Amplification Factor ◽  
Gravitational Instability ◽  
Radial Distance ◽  
Dust Particles ◽  
Linear Perturbation ◽  
Model Parameters ◽  
Time Interval ◽  
Continuous Growth ◽  
Two Fluid ◽  
Axisymmetric Perturbations

Abstract In protoplanetary discs (PPDs) consisting of gas and dust particles, fluid instabilities induced by the drag force, including secular gravitational instability (SGI), can facilitate planet formation. Although SGI subject to the axisymmetric perturbations was originally studied in the absence of gas feedback and it then generalized using a two-fluid approach, the fate of the non-axisymmetric SGI, in either case, is an unexplored problem. We present a linear perturbation analysis of the non-axisymmetric SGI in a PPD by implementing a two-fluid model. We explore the growth of the local, non-axisymmetric perturbations using a set of linearized perturbation equations in a sheared frame. The non-axisymmetric perturbations display a significant growth during a finite time interval even when the system is stable against the axisymmetric perturbations. Furthermore, the surface density perturbations do not show the continuous growth but are temporally amplified. We also study cases where the dust component undergoes amplification whereas the gas component remains stable. The amplitude amplification, however, strongly depends on the model parameters. In the minimum mass solar nebula (MMSN), for instance, the dust fluid amplification at the radial distance 100 au occurs when the Stokes number is about unity. But the amplification factor reduces as the dust and gas coupling becomes weaker. Furthermore, perturbations with a larger azimuthal wavelength exhibit a larger amplification factor.

Saturation mechanism and generated viscosity in gravito-turbulent accretion disks

2020 ◽  
Vol 640 ◽  
pp. A53
Author(s):  
L. Löhnert ◽  
S. Krätschmer ◽  
A. G. Peeters
Keyword(s):  
Growth Rate ◽  
Numerical Simulations ◽  
Accretion Disks ◽  
Gravitational Instability ◽  
Turbulent Viscosity ◽  
Radial Distance ◽  
Maximum Growth ◽  
Wave Number ◽  
Radiative Cooling ◽  
Mixing Length

Here, we address the turbulent dynamics of the gravitational instability in accretion disks, retaining both radiative cooling and irradiation. Due to radiative cooling, the disk is unstable for all values of the Toomre parameter, and an accurate estimate of the maximum growth rate is derived analytically. A detailed study of the turbulent spectra shows a rapid decay with an azimuthal wave number stronger than ky−3, whereas the spectrum is more broad in the radial direction and shows a scaling in the range kx−3 to kx−2. The radial component of the radial velocity profile consists of a superposition of shocks of different heights, and is similar to that found in Burgers’ turbulence. Assuming saturation occurs through nonlinear wave steepening leading to shock formation, we developed a mixing-length model in which the typical length scale is related to the average radial distance between shocks. Furthermore, since the numerical simulations show that linear drive is necessary in order to sustain turbulence, we used the growth rate of the most unstable mode to estimate the typical timescale. The mixing-length model that was obtained agrees well with numerical simulations. The model gives an analytic expression for the turbulent viscosity as a function of the Toomre parameter and cooling time. It predicts that relevant values of α = 10−3 can be obtained in disks that have a Toomre parameter as high as Q ≈ 10.

A PARAMETRIZED VARIABLE DARK ENERGY MODEL: STRUCTURE FORMATION AND OBSERVATIONAL CONSTRAINTS

2006 ◽  
Vol 15 (09) ◽  
pp. 1455-1472 ◽  
Author(s):  
S. ARBABI BIDGOLI ◽  
M. SADEGH MOVAHED ◽  
S. RAHVAR
Keyword(s):  
Dark Energy ◽  
Dark Energy Model ◽  
Large Scale ◽  
High Redshift ◽  
Growth Index ◽  
Energy Model ◽  
Linear Perturbation ◽  
Model Parameters ◽  
Type Ia ◽  
Parametrization Scheme

In this paper we investigate a simple parametrization scheme of the quintessence model given by Wetterich [Phys. Lett. B594, 17 (2004)]. The crucial parameter of this model is the bending parameter b, which is related to the amount of dark energy in the early universe. Using the linear perturbation and the spherical infall approximations, we investigate the evolution of matter density perturbations in the variable dark energy model, and obtain an analytical expression for the growth index f. We show that increasing b leads to less growth of the density contrast δ, and also decreases the growth index. Giving a fitting formula for the growth index at the present time, we verify that the approximation relation [Formula: see text] also holds in this model. To compare predictions of the model with observations, we use the Supernovae type Ia (SNIa) Gold Sample and the parameters of the large scale structure determined by the 2-degree Field Galaxy Redshift Survey (2dFGRS). The best fit values for the model parameters by marginalizing on the remained ones, are [Formula: see text], [Formula: see text] and [Formula: see text] at 1σ confidence level. As a final test we calculate the age of universe for different choices of the free parameters in this model and compare it with the age of old stars and some high redshift objects. Then we show that the predictions of this variable dark energy model are consistent with the age observation of old star and can solve the "age crisis" problem.

scholarly journals Spiral-arm instability – III. Fragmentation of primordial protostellar discs

2019 ◽  
Vol 491 (1) ◽  
pp. L24-L28 ◽  
Author(s):  
Shigeki Inoue ◽  
Naoki Yoshida
Keyword(s):  
Gravitational Instability ◽  
Finite Thickness ◽  
Linear Perturbation ◽  
Gas Cooling ◽  
Formation And Evolution ◽  
Linear Perturbation Theory ◽  
The Stability ◽  
Protostellar Discs ◽  
Self Gravity ◽  
Spiral Arm

ABSTRACT We study the gravitational instability and fragmentation of primordial protostellar discs by using high-resolution cosmological hydrodynamics simulations. We follow the formation and evolution of spiral arms in protostellar discs, examine the dynamical stability, and identify a physical mechanism of secondary protostar formation. We use linear perturbation theory based on the spiral-arm instability (SAI) analysis in our previous studies. We improve the analysis by incorporating the effects of finite thickness and shearing motion of arms, and derive the physical conditions for SAI in protostellar discs. Our analysis predicts accurately the stability and the onset of arm fragmentation that is determined by the balance between self-gravity and gas pressure plus the Coriolis force. Formation of secondary and multiple protostars in the discs is explained by the SAI, which is driven by self-gravity and thus can operate without rapid gas cooling. We can also predict the typical mass of the fragments, which is found to be in good agreement with the actual masses of secondary protostars formed in the simulation.

scholarly journals Astronomical bounds on the modified Chaplygin gas as a unified dark fluid model

2019 ◽  
Vol 623 ◽  
pp. A28
Author(s):  
Hang Li ◽  
Weiqiang Yang ◽  
Liping Gai
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Fluid Model ◽  
Chaplygin Gas ◽  
Linear Perturbation ◽  
Model Parameters ◽  
Modified Chaplygin Gas ◽  
Dark Fluid ◽  
Type Ia ◽  
Linear Perturbation Theory

The modified Chaplygin gas could be considered to abide by the unified dark fluid model because the model might describe the past decelerating matter dominated era and at present time it provides an accelerating expansion of the Universe. In this paper, we have employed the Planck 2015 cosmic microwave background anisotropy, type-Ia supernovae, observed Hubble parameter data sets to measure the full parameter space of the modified Chaplygin gas as a unified dark matter and dark energy model. The model parameters Bs, α, and B determine the evolutional history of this unified dark fluid model by influencing the energy density ρMCG = ρMCG0[Bs + (1 − Bs)a−3(1 + B)(1 + α)]1/(1 + α). We assumed the pure adiabatic perturbation of unified modified Chaplygin gas in the linear perturbation theory. In the light of Markov chain Monte Carlo method, we find that Bs = 0.727+0.040+0.075−0.039−0.079, α = −0.0156+0.0982+0.2346−0.1380−0.2180, B = 0.0009+0.0018+0.0030−0.0017−0.0030 at 2σ level. The model parameters α and B are very close to zero and the nature of unified dark energy and dark matter model is very similar to cosmological standard model ΛCDM.

scholarly journals Dusty clumps in circumbinary discs

2019 ◽  
Vol 489 (2) ◽  
pp. 2204-2215 ◽  
Author(s):  
Pedro P Poblete ◽  
Nicolás Cuello ◽  
Jorge Cuadra
Keyword(s):  
Binary System ◽  
Gas Dynamics ◽  
Dust Particles ◽  
Feature Location ◽  
Complex Interplay ◽  
Orbital Parameters ◽  
Orbital Periods ◽  
Azimuthal Asymmetries ◽  
Two Fluid ◽  
Protoplanetary Discs

ABSTRACT Recent observations have revealed that protoplanetary discs often exhibit cavities and azimuthal asymmetries such as dust traps and clumps. The presence of a stellar binary system in the inner disc regions has been proposed to explain the formation of these structures. Here, we study the dust and gas dynamics in circumbinary discs around eccentric and inclined binaries. This is done through two-fluid simulations of circumbinary discs, considering different values of the binary eccentricity and inclination. We find that two kinds of dust structures can form in the disc: a single horseshoe-shaped clump, on top of a similar gaseous over-density; or numerous clumps, distributed along the inner disc rim. The latter features form through the complex interplay between the dust particles and the gaseous spirals caused by the binary. All these clumps survive between one and several tens of orbital periods at the feature location. We show that their evolution strongly depends on the gas–dust coupling and the binary parameters. Interestingly, these asymmetric features could in principle be used to infer or constrain the orbital parameters of a stellar companion – potentially unseen – inside the inner disc cavity. Finally, we apply our findings to the disc around AB Aurigae.

Self-similar coalescence of clean foams

2013 ◽  
Vol 722 ◽  
pp. 645-664 ◽  
Author(s):  
Peter S. Stewart ◽  
Stephen H. Davis
Keyword(s):  
Large Scale ◽  
Liquid Fraction ◽  
Model Parameters ◽  
Time Interval ◽  
Quasi Equilibrium ◽  
Film Rupture ◽  
Network Modelling ◽  
Self Similar ◽  
The Stability ◽  
Free Films

AbstractWe consider the stability of a planar gas–liquid foam with low liquid fraction, in the absence of surfactants and stabilizing particles. We adopt a network modelling approach introduced by Stewart & Davis (J. Rheol., vol. 56, 2012, p. 543), treating the gas bubbles as polygons, the accumulation of liquid at the bubble vertices (Plateau borders) as dynamic nodes and the liquid bridges separating the bubbles as uniformly thinning free films; these films can rupture due to van der Waals intermolecular attractions. The system is initialized as a periodic array of equally pressurized bubbles, with the initial film thicknesses sampled from a normal distribution. After an initial transient, the first film rupture initiates a phase of dynamic rearrangement where the bubbles rapidly coalesce, evolving toward a new quasi-equilibrium. We present Monte Carlo simulations of this coalescence process, examining the time intervals over which large-scale rearrangement occurs as a function of the model parameters. In addition, we show that when this time interval is rescaled appropriately, the evolution of the normalized number of bubbles is approximately self-similar.

scholarly journals The influence of vertical density and velocity distributions on snow avalanche runout

2010 ◽  
Vol 51 (54) ◽  
pp. 200-206 ◽  
Author(s):  
Ashok K. Keshari ◽  
Deba P. Satapathy ◽  
Amod Kumar
Keyword(s):  
Flux Distribution ◽  
Numerical Solutions ◽  
Model Parameters ◽  
Dynamics Model ◽  
Turbulent Friction ◽  
One Dimensional ◽  
Variation Diminishing ◽  
Flow Features ◽  
Vertical Density ◽  
Two Fluid

AbstractA one-dimensional avalanche dynamics model accounting for vertical density and velocity distributions is presented. Mass and momentum flux distribution factors are derived to incorporate the effect of density and velocity variations within the framework of depth-integrated models. Using experiments of avalanche flows on an inclined snow chute at Dhundhi, Manali, India, we conceptualize snow flow rheology as a Voellmy fluid where the distribution of internal shearing is given by a Newtonian fluid (NF) or Criminale–Ericksen–Filbey fluid (CEFF). Then the generalized mass and momentum distribution factors are computed for these two fluid models for different density stratifications. Numerical solutions are obtained using a total variation diminishing Lax–Friedrichs (TVDLF) finite-difference method. The model is validated with the experimental results. We find that the flow features of the chute experiments are simulated well by the model. The velocities and runout distances are obtained for the Voellmy model with both NF and CEFF extensions for various input volumes, and the optimum values of the model parameters, namely, coefficients of dynamic and turbulent friction, are determined.

scholarly journals Nonhomogeneous Poisson Process and Compound Poisson Process in the Modelling of Random Processes Related to Road Accidents

2019 ◽  
Vol 26 (1) ◽  
pp. 39-46
Author(s):  
Franciszek Grabski
Keyword(s):  
Poisson Process ◽  
Compound Poisson Process ◽  
Statistical Distribution ◽  
Nonhomogeneous Poisson Process ◽  
Model Parameters ◽  
Time Interval ◽  
Road Accidents ◽  
Compound Poisson ◽  
The Road ◽  
The Given

Abstract The stochastic processes theory provides concepts and theorems that allow building probabilistic models concerning accidents. So called counting process can be applied for modelling the number of the road, sea and railway accidents in the given time intervals. A crucial role in construction of the models plays a Poisson process and its generalizations. The new theoretical results regarding compound Poisson process are presented in the paper. A nonhomogeneous Poisson process and the corresponding nonhomogeneous compound Poisson process are applied for modelling the road accidents number and number of injured and killed people in the Polish road. To estimate model parameters were used data coming from the annual reports of the Polish police [9, 10]. Constructed models allowed anticipating number of accidents at any time interval with a length of h and the accident consequences. We obtained the expected value of fatalities or injured and the corresponding standard deviation in the given time interval. The statistical distribution of fatalities number in a single accident and statistical distribution of injured people number and also probability distribution of fatalities or injured number in a single accident are computed. It seems that the presented examples explain basic concepts and results discussed in the paper.

scholarly journals Context Effects in Temporal Differentiation: Some Data and a Model

2015 ◽  
Vol 28 ◽  
Author(s):  
Marilia Pinheiro de Carvalho ◽  
Armando Machado ◽  
Marco Vasconcelos
Keyword(s):  
Context Effects ◽  
Phase 1 ◽  
Temporal Context ◽  
Model Parameters ◽  
Time Interval ◽  
Interval Duration ◽  
Phase 2 ◽  
Time Model ◽  
Temporal Differentiation ◽  
Range Of Values

We examined whether temporal context influences how animals produce a time interval. Six pigeons pecked one key to start an interval and then another key to end the interval. Reinforcement followed whenever the interval duration fell within a range of values signaled by the keylight colors. During Phase 1, keylight colors S1 and L1, intermixed across trials, signaled the ranges (0.5-1.5 s) and (1.5- 4.5 s), respectively. During Phase 2, colors S2 and L2 signaled the ranges (1.5-4.5 s) and (4.5-13.5 s), respectively. We asked whether the intervals produced in the presence of L1 and S2, stimuli signalling the same range, varied with their temporal context, short in Phase 1, long in Phase 2. The results showed that a) the intervals produced in the presence of the different keylight colors accorded with the main properties of temporal differentiation, including Weber’s law, b) the L1 intervals had slightly higher means than the S2 intervals, a weak contrast effect, c) the L1 intervals also had higher variability than the S2 intervals. An extension of the learning-to-time model to temporal differentiation tasks reproduced some of the major features of the data but left unanswered how context might change the model parameters.

scholarly journals Anomaly detection on in-home activities data based on time interval

2019 ◽  
Vol 15 (2) ◽  
pp. 778
Author(s):  
Soon-Chang Poh ◽  
Yi-Fei Tan ◽  
Soon-Nyean Cheong ◽  
Chee-Pun Ooi ◽  
Wooi-Haw Tan
Keyword(s):  
Anomaly Detection ◽  
Past Research ◽  
The Elderly ◽  
Behavioral Changes ◽  
Time Interval ◽  
World Population ◽  
Continuous Growth ◽  
Detection Model ◽  
Health Decline ◽  
Testing Data

<span>The world population of the elderly is expected to have a continuous growth and the number of elderly living in solitude is also expected to increase in the coming years. As our health decline with age, early detection of possible deterioration in health becomes important. Behavioral changes in in-home activities can be used as an indicator of health decline. For example, changes in routine of in-home activities. Past research mainly focused on detecting anomalies in routine of each type of in-home activities individually. In this paper, an anomaly detection model to detect changes in routine of in-home activities collectively for a day is proposed. The experiment was evaluated with an existing public dataset. The experimental results demonstrated that the anomaly detection model performed well on unseen testing data with an accuracy of 94.44%.</span>

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