Small-N collisional dynamics – V. From N ≲ 10 to N ≳ 103

2021 ◽  
Vol 502 (3) ◽  
pp. 3374-3384
Author(s):  
Carlos Barrera ◽  
Nathan W C Leigh ◽  
Bastián Reinoso ◽  
Amelia M Stutz ◽  
Dominik Schleicher
Keyword(s):  
Star Clusters ◽  
Mean Free Path ◽  
Point Particle ◽  
Important Application ◽  
Interacting Particles ◽  
Particle Properties ◽  
Stellar Collisions ◽  
Collisional Dynamics ◽  
Path Approximation ◽  
The Mean

ABSTRACT Direct collisions between finite-sized particles occur commonly in many areas of astrophysics. Such collisions are typically mediated by chaotic, bound gravitational interactions involving small numbers of particles. An important application is stellar collisions, which occur commonly in dense star clusters, and their relevance for the formation of various types of stellar exotica. In this paper, we return to our study of the collision rates and probabilities during small-number chaotic gravitational interactions ($N\, \lesssim$ 10), moving beyond the small-number particle limit and into the realm of larger particle numbers ($N\, \gtrsim$ 103) to test the extent of validity of our analytic model as a function of the particle properties and the number of interacting particles. This is done using direct N-body simulations of stellar collisions in dense star clusters, by varying the relative numbers of particles with different particle masses and radii. We compute the predicted rate of collisions using the mean free path approximation, adopting the point-particle limit and using the sticky-star approximation as our collision criterion. We evaluate its efficacy in the regime where gravitational focusing is important by comparing the theoretical rates to numerical simulations. Using the tools developed in previous papers in this series, in particular Collision Rate Diagrams, we illustrate that our predicted and simulated rates are in excellent agreement, typically consistent with each other to within 1 standard deviation.

scholarly journals Formation of supermassive black hole seeds in nuclear star clusters via gas accretion and runaway collisions

2021 ◽  
Author(s):  
Arpan Das ◽  
Dominik R G Schleicher ◽  
Nathan W C Leigh ◽  
Tjarda C N Boekholt
Keyword(s):  
Black Holes ◽  
Initial Conditions ◽  
High Redshift ◽  
Star Clusters ◽  
Gas Reservoir ◽  
Highly Sensitive ◽  
Stellar Collisions ◽  
Key Variables ◽  
Chaotic Nature ◽  
Gas Accretion

Abstract More than two hundred supermassive black holes (SMBHs) of masses ≳ 109 M⊙ have been discovered at z ≳ 6. One promising pathway for the formation of SMBHs is through the collapse of supermassive stars (SMSs) with masses ∼103 − 5 M⊙ into seed black holes which could grow upto few times 109 M⊙ SMBHs observed at z ∼ 7. In this paper, we explore how SMSs with masses ∼103 − 5 M⊙ could be formed via gas accretion and runaway stellar collisions in high-redshift, metal-poor nuclear star clusters (NSCs) using idealised N-body simulations. We explore physically motivated accretion scenarios, e.g. Bondi-Hoyle-Lyttleton accretion and Eddington accretion, as well as simplified scenarios such as constant accretions. While gas is present, the accretion timescale remains considerably shorter than the timescale for collisions with the most massive object (MMO). However, overall the timescale for collisions between any two stars in the cluster can become comparable or shorter than the accretion timescale, hence collisions still play a crucial role in determining the final mass of the SMSs. We find that the problem is highly sensitive to the initial conditions and our assumed recipe for the accretion, due to the highly chaotic nature of the problem. The key variables that determine the mass growth mechanism are the mass of the MMO and the gas reservoir that is available for the accretion. Depending on different conditions, SMSs of masses ∼103 − 5 M⊙ can form for all three accretion scenarios considered in this work.

scholarly journals Ballistic Heat Transport in Nanocomposite: The Role of the Shape and Interconnection of Nanoinclusions

Nanomaterials ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 1982
Author(s):  
Paul Desmarchelier ◽  
Alice Carré ◽  
Konstantinos Termentzidis ◽  
Anne Tanguy
Keyword(s):  
Thermal Conductivity ◽  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Free Path ◽  
Mean Free Path ◽  
Strong Increase ◽  
Moderate Increase ◽  
Energy Propagation ◽  
The Mean ◽  
Dynamics Simulations

In this article, the effect on the vibrational and thermal properties of gradually interconnected nanoinclusions embedded in an amorphous silicon matrix is studied using molecular dynamics simulations. The nanoinclusion arrangement ranges from an aligned sphere array to an interconnected mesh of nanowires. Wave-packet simulations scanning different polarizations and frequencies reveal that the interconnection of the nanoinclusions at constant volume fraction induces a strong increase of the mean free path of high frequency phonons, but does not affect the energy diffusivity. The mean free path and energy diffusivity are then used to estimate the thermal conductivity, showing an enhancement of the effective thermal conductivity due to the existence of crystalline structural interconnections. This enhancement is dominated by the ballistic transport of phonons. Equilibrium molecular dynamics simulations confirm the tendency, although less markedly. This leads to the observation that coherent energy propagation with a moderate increase of the thermal conductivity is possible. These findings could be useful for energy harvesting applications, thermal management or for mechanical information processing.

Sputtering pressure dependence of hydrogen-sensing effect of palladium films

2009 ◽  
Vol 24 (6) ◽  
pp. 1919-1927 ◽  
Author(s):  
Chung Wo Ong ◽  
Yu Ming Tang
Keyword(s):  
Electrical Resistivity ◽  
Magnetron Sputtering ◽  
Mean Free Path ◽  
Induced Response ◽  
Resistivity Ratio ◽  
Hydrogen Sensing ◽  
The Mean ◽  
Sputtering Pressure ◽  
Specific Volumes ◽  
Hydride Phases

The electrical resistivity ρ of palladium (Pd) films prepared by using magnetron sputtering at different pressures φ ranging from 2 to 15 mTorr showed very different hydrogen (H)-induced response. This reaction is because the mean free path of the particles in vacuum changes substantially with φ, such that the structure of the deposits is altered accordingly. A film prepared at a moderate φ value of 6 mTorr has a moderate strength. After a few hydrogenation-dehydrogenation cycles, some cracks are generated because of the great difference in the specific volumes of the metal and hydride phases. Breathing of the cracks in subsequent switching cycles occurred, which led to the response gain of ρ, defined as the resistivity ratio of the dehydrogenated-to-hydrogenated states during a cycle, to increase to 17. This result demonstrates the attractiveness of using the Pd films in H2 detection application. The H-induced resistive response of the films prepared at other φ values was found to be much smaller.

Experiments on the flow of heat in liquid helium below 0.7 °K

1958 ◽  
Vol 246 (1246) ◽  
pp. 390-405 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Liquid Helium ◽  
Free Path ◽  
Empirical Relation ◽  
Mean Free Path ◽  
Series Of Experiments ◽  
The Mean ◽  
Set Up ◽  
Low Pressures ◽  
Measured Thermal Conductivity

A series of experiments has been performed to study the steady flow of heat in liquid helium in tubes of diameter 0.05 to 1.0 cm at temperatures between 0.25 and 0.7 °K. The results are interpreted in terms of the flow of a gas of phonons, in which the mean free path λ varies with temperature, and may be either greater or less than the diameter of the tube d . When λ ≫ d the flow is limited by the scattering of the phonons at the walls, and the effect of the surface has been studied, but when λ ≪ d viscous flow is set up in which the measured thermal conductivity is increased above that for wall scattering. This behaviour is very similar to that observed in the flow of gases at low pressures, and by applying kinetic theory to the problem it can be shown that the mean free path of the phonons characterizing viscosity can be expressed by the empirical relation λ = 3.8 x 10 -3 T -4.3 cm. This result is inconsistent with the temperature dependence of λ as T -9 predicted theoretically by Landau & Khalatnikov (1949).

Light scattering by phonons in the presence of a heat flow

1968 ◽  
Vol 46 (24) ◽  
pp. 2843-2845 ◽  
Author(s):  
Allan Griffin
Keyword(s):  
Light Scattering ◽  
Heat Flow ◽  
Temperature Gradient ◽  
Free Path ◽  
Mean Free Path ◽  
Photon Scattering ◽  
The Mean ◽  
Anti Stokes

If the temperature in an insulating crystal decreases in the z-direction, there are more phonons with momentum qz > 0 than with qz < 0. The resulting difference between the Stokes and anti-Stokes Brillouin intensities is proportional to the mean free path of the phonon involved and to the temperature gradient. The effect should be observable by either neutron or photon scattering.

A numerical study of the sedimentation of fibre suspensions

1998 ◽  
Vol 376 ◽  
pp. 149-182 ◽  
Author(s):  
MICHAEL B. MACKAPLOW ◽  
ERIC S. G. SHAQFEH
Keyword(s):  
Monte Carlo ◽  
Steady State ◽  
Monte Carlo Simulations ◽  
Numerical Study ◽  
Point Particle ◽  
Hydrodynamic Interactions ◽  
Dynamic Simulations ◽  
Slender Body Theory ◽  
Fibre Suspensions ◽  
The Mean

The sedimentation of fibre suspensions at low Reynolds number is studied using two different, but complementary, numerical simulation methods: (1) Monte Carlo simulations, which consider interparticle hydrodynamic interactions at all orders within the slender-body theory approximation (Mackaplow & Shaqfeh 1996), and (ii) dynamic simulations, which consider point–particle interactions and are accurate for suspension concentrations of nl3=1, where n and l are the number density and characteristic half-length of the fibres, respectively. For homogeneous, isotropic suspensions, the Monte Carlo simulations show that the hindrance of the mean sedimentation speed is linear in particle concentration up to at least nl3=7. The speed is well predicted by a new dilute theory that includes the effect of two-body interactions. Our dynamic simulations of dilute suspensions, however, show that interfibre hydrodynamic interactions cause the spatial and orientational distributions to become inhomogeneous and anisotropic. Most of the fibres migrate into narrow streamers aligned in the direction of gravity. This drives a downward convective flow within the streamers which serves to increase the mean fibre sedimentation speed. A steady-state orientation distribution develops which strongly favours fibre alignment with gravity. Although the distribution reaches a steady state, individual fibres continue to rotate in a manner that can be qualitatively described as a flipping between the two orientations aligned with gravity. The simulation results are in good agreement with published experimental data.

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