Sequential and Near-Simultaneous Multi-Body Collisions

2004 ◽  
Author(s):  
D. Dane Quinn ◽  
Kalyan Bairavarasu
Keyword(s):  
Initial Conditions ◽  
Coefficient Of Restitution ◽  
Initial Configuration ◽  
Collision Model ◽  
Sufficient Distance ◽  
Initial Spacing ◽  
Compliance Model ◽  
The Masses ◽  
Multi Body ◽  
Impact Duration

This work considers a three mass collision model with finite-time, compliant contacts. If the masses are initially separated by a sufficient distance, the collision sequence is sequential, that is, comprised of a sequence of pairwise impacts. The final velocities of each mass are then independent of the specific initial spacing. In contrast, if the initial spacing between the masses is sufficiently small there exists an interval during which the three masses interact simultaneously. In this instance the final velocity state also depends on the initial configuration of the system. Given an assumed impact duration and coefficient of restitution for a pairwise collision, a two-dimensional map is derived to describe those initial conditions that lead to pairwise sequences. Finally, for a specific nonlinear compliance model the variation in the final velocities is characterized in terms of the initial configuration and velocity state of the system.

OBSERVATION OF THE COLLINEAR MULTI-BODY DECAYS IN THE REACTION 238U+4He (40 MEV)

2008 ◽  
Vol 17 (10) ◽  
pp. 2226-2230 ◽  
Author(s):  
◽  
YU. PYATKOV
Keyword(s):  
Inelastic Scattering ◽  
Flight Path ◽  
Scission Point ◽  
Magic Clusters ◽  
A Chain ◽  
The Masses ◽  
Multi Body

Two different modes of the multibody collinear decay from the reaction 238 U +4 He (40 MeV ) are discussed. Basing on the masses of three detected fragments one can come to conclusion that the decaying system in each mode looks like a chain consisting of two or three magic clusters respectively. Some of the clusters involved undergo "second" clusterisation in the scission point leading to formation of dinuclear molecules. These latter can disintegrate via inelastic scattering on the materials on the flight path.

scholarly journals Mass determination of the 1:3:5 near-resonant planets transiting GJ 9827 (K2-135)

2018 ◽  
Vol 618 ◽  
pp. A116 ◽  
Author(s):  
J. Prieto-Arranz ◽  
E. Palle ◽  
D. Gandolfi ◽  
O. Barragán ◽  
E. W. Guenther ◽  
...  
Keyword(s):  
Planetary System ◽  
Initial Conditions ◽  
Dynamical Evolution ◽  
Space Mission ◽  
Mass Determination ◽  
Velocity Measurements ◽  
Orbital Periods ◽  
The Masses ◽  
Better Than

Context. Multiplanet systems are excellent laboratories to test planet formation models as all planets are formed under the same initial conditions. In this context, systems transiting bright stars can play a key role, since planetary masses, radii, and bulk densities can be measured. Aims. GJ 9827 (K2-135) has recently been found to host a tightly packed system consisting of three transiting small planets whose orbital periods of 1.2, 3.6, and 6.2 days are near the 1:3:5 ratio. GJ 9827 hosts the nearest planetary system (~30 pc) detected by NASA’s Kepler or K2 space mission. Its brightness (V = 10.35 mag) makes the star an ideal target for detailed studies of the properties of its planets. Methods. Combining the K2 photometry with high-precision radial-velocity measurements gathered with the FIES, HARPS, and HARPS-N spectrographs we revised the system parameters and derive the masses of the three planets. Results. We find that GJ 9827 b has a mass of Mb = 3.69−0.46+0.48 M⊕ and a radius of Rb = 1.58−0.13+0.14 R⊕, yielding a mean density of ρb = 5.11−1.27+1.74 g cm−3. GJ 9827 c has a mass of Mc = 1.45−0.57+0.58 M⊕, radius of Rc = 1.24−0.11+0.11 R⊕, and a mean density of ρc = 4.13−1.77+2.31 g cm−3. For GJ 9827 d, we derive Md = 1.45−0.57+0.58 M⊕, Rd = 1.24−0.11+0.11 R⊕, and ρd = 1.51−0.53+0.71 g cm−3. Conclusions. GJ 9827 is one of the few known transiting planetary systems for which the masses of all planets have been determined with a precision better than 30%. This system is particularly interesting because all three planets are close to the limit between super-Earths and sub-Neptunes. The planetary bulk compositions are compatible with a scenario where all three planets formed with similar core and atmosphere compositions, and we speculate that while GJ 9827 b and GJ 9827 c lost their atmospheric envelopes, GJ 9827 d maintained its primordial atmosphere, owing to the much lower stellarirradiation. This makes GJ 9827 one of the very few systems where the dynamical evolution and the atmosphericescape can be studied in detail for all planets, helping us to understand how compact systems form and evolve.

Analytical Study of the Oblique Impact of a Rod with a Flat Using an Elasto-Plastic Contact Model

2015 ◽  
Vol 801 ◽  
pp. 25-32
Author(s):  
Ozdes Cermik ◽  
Hamid Ghaednia ◽  
Dan B. Marghitu
Keyword(s):  
Impact Velocity ◽  
Contact Force ◽  
Analytical Study ◽  
Initial Conditions ◽  
Permanent Deformation ◽  
Oblique Impact ◽  
Coefficient Of Restitution ◽  
Contact Model ◽  
Impact Angles ◽  
The Impact

In the current study a flattening contact model, combined with a permanent deformation expression, has been analyzed for the oblique impact case. The model has been simulated for different initial conditions using MATLAB. The initial impact velocity used for the simulations ranges from 0.5 to 3 m/s. The results are compared theoretically for four different impact angles including 20, 45, 70, and 90 degrees. The contact force, the linear and the angular motion, the permanent deformation, and the coefficient of restitution have been analyzed. It is assumed that sliding occurs throughout the impact.

scholarly journals Formation sites of Population III star formation: The effects of different levels of rotation and turbulence on the fragmentation behaviour of primordial gas

2020 ◽  
Vol 494 (2) ◽  
pp. 1871-1893 ◽  
Author(s):  
Katharina M J Wollenberg ◽  
Simon C O Glover ◽  
Paul C Clark ◽  
Ralf S Klessen
Keyword(s):  
Star Formation ◽  
Initial Conditions ◽  
Turbulent Energy ◽  
Star Forming ◽  
Wide Range ◽  
Population Iii Stars ◽  
The Individual ◽  
The Masses ◽  
Different Levels ◽  
Population Iii

ABSTRACT We use the moving-mesh code arepo to investigate the effects of different levels of rotation and turbulence on the fragmentation of primordial gas and the formation of Population III stars. We consider nine different combinations of turbulence and rotation and carry out five different realizations of each setup, yielding one of the largest sets of simulations of Population III star formation ever performed. We find that fragmentation in Population III star-forming systems is a highly chaotic process and show that the outcomes of individual realizations of the same initial conditions often vary significantly. However, some general trends are apparent. Increasing the turbulent energy promotes fragmentation, while increasing the rotational energy inhibits fragmentation. Within the ∼1000 yr period that we simulate, runs including turbulence yield flat protostellar mass functions while purely rotational runs show a more top-heavy distribution. The masses of the individual protostars are distributed over a wide range from a few $10^{-3} \, {\rm M_{\odot }}$ to several tens of M⊙. The total mass growth rate of the stellar systems remains high throughout the simulations and depends only weakly on the degree of rotation and turbulence. Mergers between protostars are common, but predictions of the merger fraction are highly sensitive to the criterion used to decide whether two protostars should merge. Previous studies of Population III star formation have often considered only one realization per set of initial conditions. However, our results demonstrate that robust trends can only be reliably identified by considering averages over a larger sample of runs.

Modeling and Simulation of Stochastic Lorenz Systems by Polynomial Chaos Approach

2007 ◽  
Author(s):  
Lin Li ◽  
Corina Sandu
Keyword(s):  
Polynomial Chaos ◽  
Initial Conditions ◽  
Nonlinear Problems ◽  
System Response ◽  
Structural Vibrations ◽  
System Parameters ◽  
Highly Nonlinear ◽  
Body Dynamics ◽  
The Lorenz System ◽  
Multi Body

The Lorenz problem is one of the paradigms of the chaotic systems, which are sensitive to initial conditions and for which the performance is hard to predict. However, in many cases and dynamic systems, the initial conditions of a dynamic system and the system parameters can’t be measured accurately, and the response of the system must indeed be explored in advance. In this study, the polynomial chaos approach is used to handle uncertain initial conditions and system parameters of the Lorenz system. The method has been successfully applied by the authors and co-workers in multi-body dynamics and terrain profile and soil modeling. Other published studies illustrate the benefits of using the polynomial chaos, especially for problems involving large uncertainties and highly nonlinear problems in fluid mechanics, structural vibrations, and air quality studies. This study is an attempt to use the polynomial chaos approach to treat the Lorenz problem, and the results are compared with a classical Monte Carlo approach. Error bars are used to illustrate the standard deviation of the system response. Different meshing schemes are simulated, and the convergence of the method is analyzed.

The Efficacy of Impact-Absorbing Materials during Collision with a Soccer Ball

2013 ◽  
Vol 440 ◽  
pp. 363-368
Author(s):  
Zahari Taha ◽  
Mohd Hasnun Arif Hassan ◽  
Mohd Azri Aris
Keyword(s):  
High Speed ◽  
Impact Force ◽  
Coefficient Of Restitution ◽  
Soccer Ball ◽  
Absorbing Materials ◽  
The Subject ◽  
The Impact ◽  
The Brain ◽  
Peak Impact Force ◽  
Impact Duration

The uniqueness of soccer is that the players are allowed to use their head to pass the ball to a teammate of even try to score goal. Studies have shown that heading in soccer might be dangerous to the brain and could lead to brain trauma. There are headgears available for soccer players to protect their head, but studies have proven that currently available headgears are ineffective in reducing the impact caused by a soccer ball. The objective of this study is to test the efficacy of six different types of impact-absorbing materials in reducing the linear impact force from a soccer ball. The soccer ball was dropped from the height of 2.3 m onto a force platform to measure the impact force. A high-speed camera is used to record the motion and the impact duration, and then the coefficient of restitution for each impact was determined. Polyurethane (PU) comb-gel was found to be the most effective material in reducing the peak impact force and impulse compared with other materials. The reduction in peak force was associated with longer impact duration between the soccer ball and the PU comb-gel. However, the coefficient of restitution was reduced by 21.7%, implying that using the gel alone will reduce the speed of the ball after heading, thus reducing the performance of a player wearing it. A combination of PU gel and another stiffer material is suggested and the effectiveness of the composite will be the subject of future investigation.

Modeling Impacts Between a Continuous System and a Rigid Obstacle Using Coefficient of Restitution

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
Chandrika P. Vyasarayani ◽  
John McPhee ◽  
Stephen Birkett
Keyword(s):  
Initial Conditions ◽  
Equations Of Motion ◽  
Continuous System ◽  
Coefficient Of Restitution ◽  
Continuous Systems ◽  
Rigid Obstacle ◽  
Unit Impulse ◽  
Before And After ◽  
System Equations ◽  
The Impact

In this work, we discuss the limitations of the existing collocation-based coefficient of restitution method for simulating impacts in continuous systems. We propose a new method for modeling the impact dynamics of continuous systems based on the unit impulse response. The developed method allows one to relate modal velocity initial conditions before and after impact without requiring the integration of the system equations of motion during impact. The proposed method has been used to model the impact of a pinned-pinned beam with a rigid obstacle. Numerical simulations are presented to illustrate the inability of the collocation-based coefficient of restitution method to predict an accurate and energy-consistent response. We also compare the results obtained by unit impulse-based coefficient of restitution method with a penalty approach.

scholarly journals Correlation of gas dynamics and dust in the evolved filament G82.65-02.00

2017 ◽  
Vol 608 ◽  
pp. A21 ◽  
Author(s):  
M. Saajasto ◽  
M. Juvela ◽  
K. Dobashi ◽  
T. Shimoikura ◽  
I. Ristorcelli ◽  
...  
Keyword(s):  
Column Density ◽  
Velocity Structure ◽  
Accretion Rate ◽  
Initial Conditions ◽  
Dust Emission ◽  
Line Emission ◽  
Star Forming ◽  
Virial Mass ◽  
The Masses ◽  
Main Filament

Context. The combination of line and continuum observations can provide vital insight into the formation and fragmentation of filaments and the initial conditions for star formation. We have carried out line observations to map the kinematics of an evolved, actively star forming filament G82.65-2.00. The filament was first identified from the Planck data as a region of particularly cold dust emission and was mapped at 100–500 μm as a part of the Herschel key program Galactic Cold Cores. The Herschel observations cover the central part of the filament, corresponding to a filament length of ~ 12 pc at the assumed distance of 620 pc. Aims. CO observations show that the filament has an intriguing velocity field with several velocity components around the filament. In this paper, we study the velocity structure in detail, to quantify possible mass accretion rate onto the filament, and study the masses of the cold cores located in the filament. Methods. We have carried out line observations of several molecules, including CO isotopologues, HCO+, HCN, and CS with the Osaka 1.85 m telescope and the Nobeyama 45 m telescope. The spectral line data are used to derive velocity and column density information. Results. The observations reveal several velocity components in the field, with strongest line emission concentrated to velocity range ~[3,5] km s-1. The column density of molecular hydrogen along the filament varies from 1.0 to 2.3 × 1022cm2. We have examined six cold clumps from the central part of the filament. The clumps have masses in the range 10−20M⊙ (~ 70 M⊙ in total) and are close to or above the virial mass. Furthermore, the main filament is heavily fragmented and most of the substructures have a mass lower than or close to the virial mass, suggesting that the filament is dispersing as a whole. Position-velocity maps of 12CO and 13CO lines indicate that at least one of the striations is kinematically connected to two of the clumps, potentially indicating mass accretion from the striation onto the main filament. We tentatively estimate the accretion rate to be Ṁ = 2.23 × 10-6M⊙/ yr. Conclusions. Our line observations have revealed two or possibly three velocity components connected to the filament G82.65-2.00 and putative signs of mass accretion onto the filament. The line observations combined with Herschel and WISE maps suggest a possible collision between two cloud components.

REGULAR AND CHAOTIC DYNAMICS IN BOUNCING BALL MODELS

2011 ◽  
Vol 21 (03) ◽  
pp. 869-884 ◽  
Author(s):  
SEBASTIAN VOGEL ◽  
STEFAN J. LINZ
Keyword(s):  
Chaotic Dynamics ◽  
Temporal Dynamics ◽  
Initial Conditions ◽  
Coefficient Of Restitution ◽  
Velocity Dependence ◽  
System Parameters ◽  
Bouncing Ball ◽  
Ball Bouncing ◽  
Long Time ◽  
Inelastic Ball

One of the prime paradigms for complex temporal dynamics, the motion of an inelastic ball bouncing on a sinusoidally oscillating table, is revisited. Using extensive numerical simulations, we address the not yet conclusively settled problem of the occurrence of chaos in the partially elastic case. We systematically investigate the spectrum of long-time solutions as function of the initial conditions and system parameters. Subsequently, we generalize the bouncing ball system by taking the velocity dependence of the coefficient of restitution into account and exemplarily demonstrate the drastic impact of such a generalization on the overall dynamics.

Analysis of Vehicle Tire Impact Force Based on Collision Model

2014 ◽  
Vol 945-949 ◽  
pp. 576-580
Author(s):  
Wen Jun Ma ◽  
Xin Guan ◽  
Ping Ping Lu
Keyword(s):  
Impact Force ◽  
Model Simulation ◽  
Coefficient Of Restitution ◽  
Collision Model ◽  
Impact Function ◽  
Complex Process ◽  
Language Analysis ◽  
Hysteretic Damping ◽  
Vertical Landing ◽  
Damping Model

The effect of impact force on vehicle tires is a complex process. Accurately chassis dynamics analysis need to consider the influence of impact force. This paper uses collision model to solve it and then successfully establish Impact function model Hysteretic damping model and Modified hysteretic damping model based on the C language. Analysis the result of impact contact force of tire vertical landing. In the coefficient of restitution close to 1, the simulation results of the three models have no greater difference. While the Hysteretic damping model simulation result is different from the other two models in the coefficient of restitution is relatively small.

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