Chapter 4 Concluding Remarks
4.2 Recommendation for the future work
According to the study of this paper, several important future works were outlined as follows:
1. In order to study the helium droplets and xenon droplets pair collision in depth, we could improve the accuracy of simulation by changing the size of droplets and the relative velocity and distance between droplets and using the droplets rotated in the simulation.
2. In order to distinguish the behavior of collision under different molecular weights in detail, we could choose the other atoms of high or low molecular weight to simulate droplets pair collision.
3. In addition to vaccum circumstance, we could put the droplets in low or high pressure circumstances and consider the behaviour of multi-droplet collision.
4. Using droplets with different molecular weights, like Xe and He, to collide to each other to observe the phenomenon occurring after collision.
References
[1] Ashgriz, N. and Poo, J. Y., “Coalescence and separation in binary collisions of liquid drops”, Journal of Fluid Mechanics, 221, pp.183-204, 1990.
[2] Bertagnolli, M., Marchese, M., Jacuci, G. St., Doltsinis, I. and Noelting, S.,
“Thermo-mechanical simulation of the splashing of ceramic droplets on a rigid substract”, Journal of Computational Physics, 133, pp.205, 1997.
[3] Frenkel, D. and Smit, B., “Understanding Molecular Simulation, Academic”, Press, San Diego, 1996.
[4] Fox, G. C., Johnson, M. A., Lyzenga, G. A., Otto, S. W., Salmon, J. K. and Walker, D. W., “Solving Problems on Concurrent Processors: Volume 1”, Prentice Hall, Englewood Cliffs, NJ, 1988.
[5] Fukai, J., Shiiba, Y., Yamamoto, T., Miyatake, O., Poulikakos, D., Megaridis, C.
M. and Zhao, Z., “Wetting effects on the spreading of a liquid droplet colliding with a flat surface: experiment and modeling”, Physics Fluids, 7, pp.236-247, 1995.
[6] Greenspan, D. and Heath, L. F., “Supercomputer simulation of the modes of colliding microdrops of water”, Journal of Physics D, 24, pp.2121-2123, 1991.
[7] Harlow, F. H. and Shannon, J. P., “The splash of a liquid droplet, Journal of Applied Physics”, 38, pp.3855, 1967.
[8] Hsu, Y.-L., “Parallel MD Simulation of Droplet-Droplet Collision Dynamics”, Ph. D. Thesie, 2006.
[9] Hu, Z. L., Bruintjes, R. T. and Betterton, E.A., “Sensitivity of cloud droplet growth to collision and coalescence efficiencies in a parcel model”, Journal of Atmospheric Sciences, 15, pp.2502-2515, 1998.
[10] Inamuro, T., Ogatat, T., Tajimas, S., Konoshi, N., “A lattice Boltzmann method for incompressible two-phase flows with large density difference, Journal of Computational Physics”, 198, pp.628–644, 2004.
[11] Julius, J., Li, D. H., “Separation of the Energy of Overall Rotation in Any N-Body System”, Physical review letters, 62, pp.241-244, 1989
[12] Karypi, G. s, Schloegel, K. and Kumar, V., “ParMetis, University of Minnesota, Department of computer Science”, September, 1998.
[13] Lambrakos, S. G., Boris, J. P., Chandrasekhar, I., and Gaber, B., “A Vectorized Near-Neighbors Algorithm of Order N for Molecular Dynamics Simulations”
Ann. NY Acad. Sci., 482, pp.85, 1986.
[14] Lennard, J. E., “The determination of molecular fields. I. from the variation of
the viscosity of gas with temperature”, Proc. Roy. Soc. (Lond), 106A, pp.441, 1924.
[15] Liu, M., Nikola, M., Marcus, S., and Jan, B. C. P., “Collision dynamics of Large Argon Clusters” J. Phys. Chem. A, 101, pp.4011-4018, 1997.
[16] Mackay, G. D. M. and Mason, S. G., “The gravity approach and coalescence of fluid droplets and liquid interfaces”, Canadian Journal of Chemical Engineering, 41, pp.203, 1963.
[17] Marcus, S., Liu, M., Nikola, M., and Jan, B. C. P., “Collision dynamics of large water clusters”, journal of chemical physics, 108, pp.5888-5897, 1998.
[18] Nicol, D. M. and J, Saltz. H., “Dynamic Remapping of Parallel Computations with Varying Resource Demands”, IEEE Transactions on Computer, 37, pp.1073-1087, 1988.
[19] Plimpton, S., “Fast Parallel Algorithms for Short-Range Molecular Dynamics”, J. of Computational Physics, 117, pp.1-19, 1995.
[20] Succi, S., “The lattice Boltzmann equation for fluid dynamics and beyond”, Oxford University Press, 2001.
[21] Svanberg, M., and Pettersson, J.B.C. and, “Collision dynamic of large argon clusters”, Journal of Physics and Chemistry, 101, pp.4011-4018, 1997.
[22] Trapaga, G. and Szekely, J., “Mathematical modeling of the isothermal impingment of liquid droplets in spraying processes”, Metall. Trans. B, 22, pp.901, 1991.
[23] Tsurutani. K. , Yao. M., Senda. J. and Fujimoto. H., Numerical analysis of the deformation process of a droplet impinging upon a wall., , JSME Int. Ser., pp.555, 1990.
[24] Verlet L., “Computer ‘Experiments’ on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules,” Phys. Rev., Vol.159, 98-103, 1967.
Tables
Table 1.1 System of units used in soft-sphere molecular dynamics programs
Figures
Fig. 1. 1 Terminology of possible droplet-droplet collision outcome.
(a)coalescence, (b) disruption and (c) fragmentation.
Fig. 1. 2 Impact parameter (b).
Fig. 2. 1 Cartesian frame
Fig. 2. 2 Lennard-Jones (LJ) pair wise intermolecular potential
Fig. 2. 3 Xenon and Helium Lennard-Jones (LJ) pair wise intermolecular potential
(a)
(b)
(c)
Fig. 2. 4 All pairs, (b) Cell-link, and (c) Neighbor Lists methods
Fig. 2. 5 Neighbor Lists method
Fig. 2. 6 Cell-link + Neighbor Lists
Fig. 2. 7 Periodic boundary conditions
Fig. 2. 8 Proposed flow chart for parallel molecular dynamics simulation using dynamic domain decomposition.
Fig. 3. 1 Head-on (b= 0) droplets pair collision initial setup on y-z plane.
Fig. 3. 2 Non-head-on (ex: b= 5nm) droplets pair collision initial setup on x-y plane.
Fig. 3. 3 Distribution map of various regimes of Xenon droplet-collision.
Fig. 3. 4 Distribution map of various regimes of Helium droplet-collision.
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Fig. 3. 5 Snapshot of Xenon droplet pair collision under vacuum, at (a) b=0, V=250m/s, (b) b=0,V=500m/s.
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Fig. 3. 6 Snapshot of Xenon droplet pair collision under vacuum, at (a) b=0, V=750m/s, (b) b=0, V=1250m/s.
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Fig. 3. 7 Snapshot of Xenon droplet pair collision under vacuum, at (a) b=0, V=1500m/s, (b) b=0, V=1750m/s.
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Fig. 3. 8 Snapshot of Xenon droplet pair collision under vacuum, at (a) b=0, V=2000m/s, (b) b=0, V=2250m/s.
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Fig. 3. 9 Snapshot of xenon droplet pair collision under vacuum, at (a) b=1.25nm, V=750m/s, (b) b=1.25nm, V=1000m/s.
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Fig. 3. 10 Snapshot of xenon droplet pair collision under vacuum, at (a) b=1.25nm, V=1250m/s, (b) b=1.25nm, V=1500m/s.
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Fig. 3. 11 Snapshot of xenon droplet pair collision under vacuum, at (a) b=1.25nm, V=1750m/s, (b) b=1.25nm, V=2000m/s.
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Fig. 3. 12 Snapshot of xenon droplet pair collision under vacuum, at (a) b=1.25nm, V=2250m/s, (b) b=2.5nm, V=750m/s.
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Fig. 3. 13 Snapshot of xenon droplet pair collision under vacuum, at (a) b=2.5nm, V=1000m/s, (b) b=2.5nm, V=1250m/s.
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Fig. 3. 14 Snapshot of xenon droplet pair collision under vacuum, at (a) b=2.5nm, V=1500m/s, (b) b=2.5nm, V=1750m/s.
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Fig. 3. 15 Snapshot of xenon droplet pair collision under vacuum, at (a) b=2.5nm, V=2000m/s, (b) b=2.5nm, V=2250m/s.
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Fig. 3. 16 Snapshot of xenon droplet pair collision under vacuum, at (a) b=3.75nm, V=250m/s, (b) b=3.75nm, V=500m/s.
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Fig. 3. 17 Snapshot of xenon droplet pair collision under vacuum, at (a) b=3.75nm, V=750m/s, (b) b=3.75nm, V=1000m/s.
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Fig. 3. 18 Snapshot of xenon droplet pair collision under vacuum, at (a) b=3.75nm, V=1250m/s, (b) b=3.75nm, V=1500m/s.
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Fig. 3. 19 Snapshot of xenon droplet pair collision under vacuum, at (a) b=3.75nm, V=1750m/s, (b) b=3.75nm, V=2000m/s.
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Fig. 3. 20 Snapshot of xenon droplet pair collision under vacuum, at (a) b=3.75nm, V=2250m/s, (b) b=5nm, V=250m/s.
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Fig. 3. 21 Snapshot of xenon droplet pair collision under vacuum, at (a) b=5nm, V=500m/s, (b) b=5nm, V=750m/s.
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Fig. 3. 22 Snapshot of xenon droplet pair collision under vacuum, at (a) b=5nm, V=1000m/s, (b) b=5nm, V=1250m/s..
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Fig. 3. 23 Snapshot of xenon droplet pair collision under vacuum, at (a) b=5nm, V=1500m/s, (b) b=5nm, V=1750m/s.
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Fig. 3. 24 Snapshot of xenon droplet pair collision under vacuum, at (a) b=5nm, V=2000m/s, (b) b=5nm, V=2250m/s.
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Fig. 3. 25 Snapshot of xenon droplet pair collision under vacuum, at (a) b=6.25nm, V=250m/s, (b) b=6.25nm, V=500m/s.
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Fig. 3. 26 Snapshot of xenon droplet pair collision under vacuum, at (a) b=6.25nm, V=750m/s, (b) b=6.25nm, V=1000m/s.
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Fig. 3. 27 Snapshot of xenon droplet pair collision under vacuum, at (a) b=6.25nm, V=1250m/s, (b) b=6.25nm, V=1500m/s..
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Fig. 3. 28 Snapshot of xenon droplet pair collision under vacuum, at (a) b=6.25nm, V=1750m/s, (b) b=6.25nm, V=2000m/s.
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Fig. 3. 29 Snapshot of xenon droplet pair collision under vacuum, at (a) b=6.25nm, V=2250m/s, (b) b=7.5nm, V=250m/s.
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Fig. 3. 30 Snapshot of xenon droplet pair collision under vacuum, at (a) b=7.5nm, V=500m/s, (b) b=7.5nm, V=750m/s.
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Fig. 3. 31 Snapshot of xenon droplet pair collision under vacuum, at (a) b=7.5nm, V=1000m/s, (b) b=7.5nm, V=1250m/s..
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Fig. 3. 32 Snapshot of xenon droplet pair collision under vacuum, at (a) b=7.5nm, V=1500m/s, (b) b=7.5nm, V=1750m/s.
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Fig. 3. 33 Snapshot of xenon droplet pair collision under vacuum, at (a) b=7.5nm, V=2000m/s, (b) b=7.5nm, V=2250m/s.
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Fig. 3. 34 Snapshot of xenon droplet pair collision under vacuum, at (a) b=8.75nm, V=250m/s, (b) b=8.75, V=500m/s.
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Fig. 3. 35 Snapshot of xenon droplet pair collision under vacuum, at (a) b=8.75nm, V=750m/s, (b) b=8.75, V=1000m/s.
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Fig. 3. 36 Snapshot of xenon droplet pair collision under vacuum, at (a) b=8.75nm, V=1250m/s, (b) b=8.75, V=1500m/s.
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Fig. 3. 37 Snapshot of xenon droplet pair collision under vacuum, at (a) b=8.75nm, V=1750m/s, (b) b=8.75nm, V=2000m/s.
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Fig. 3. 38 Snapshot of xenon droplet pair collision under vacuum, at (a) b=8.75nm, V=2550m/s.
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Fig. 3. 39 Snapshot of helium droplet pair collision under vacuum, at (a) b=0, V=250m/s, (b) b=0, V=500m/s.
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Fig. 3. 40 Snapshot of helium droplet pair collision under vacuum, at (a) b=0, V=750m/s.
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Fig. 3. 41 Snapshot of helium droplet pair collision under vacuum, at (a) b=1.25nm, V=250m/s, (b) b=1.25nm, V=500m/s.
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Fig. 3. 42 Snapshot of helium droplet pair collision under vacuum, at (a) b=1.25nm, V=750m/s, (b) b=2.5nm, V=250m/s.
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Fig. 3. 43 Snapshot of helium droplet pair collision under vacuum, at (a) b=1.25nm, V=500m/s, (b) b=1.25nm, V=750m/s.
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Fig. 3. 44 Snapshot of helium droplet pair collision under vacuum, at (a) b=2.5nm, V=250m/s, (b) b=2.5nm, V=500m/s.
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Fig. 3. 45 Snapshot of helium droplet pair collision under vacuum, at (a) b=2.5nm, V=750m/s, (b) b=3.75nm, V=250m/s.
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Fig. 3. 46 Snapshot of helium droplet pair collision under vacuum, at (a) b=3.75nm, V=500m/s, (b) b=3.75nm, V=750m/s.
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Fig. 3. 47 Snapshot of helium droplet pair collision under vacuum, at (a) b=5nm, V=250m/s, (b) b=5nm, V=500m/s.
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Fig. 3. 48 Snapshot of helium droplet pair collision under vacuum, at (a) b=5nm, V=750m/s, (b) b=6.25nm, V=250m/s.
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Fig. 3. 49 Snapshot of helium droplet pair collision under vacuum, at (a) b=6.25nm, V=500m/s, (b) b=6.25nm, V=750m/s.
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Fig. 3. 50 Snapshot of helium droplet pair collision under vacuum, at (a) b=7.5nm, V=250m/s, (b) b=7.5nm, V=500m/s.
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Fig. 3. 51 Snapshot of helium droplet pair collision under vacuum, at (a) b=7.5nm, V=750m/s, (b) b=8.75nm, V=250m/s.
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Fig. 3. 52 Snapshot of helium droplet pair collision under vacuum, at (a) b=8.75nm, V=500m/s, (b) b=8.75nm, V=750m/s.
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Fig. 3. 53 Snapshot of density contour and clusters size distribution of Xenon droplets collision, b=0, V=250m/s, at (a) 25ps, (b) 75ps, (c) 150ps.
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Fig. 3. 54 Snapshot of density contour and clusters size distribution of Xenon droplets collision, b=0, V=500m/s, at (a) 25ps, (b) 75ps, (c) 150ps.
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Fig. 3. 55 Snapshot of density contour and clusters size distribution of Xenon droplets collision, b=0, V=750m/s, at (a) 25ps, (b) 75ps, (c) 150ps.
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Fig. 3. 56 Snapshot of density contour and clusters size distribution of Xenon droplets collision, b=0, V=1250m/s, at (a) 25ps, (b) 75ps, (c) 150ps.
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Fig. 3. 57 Snapshot of density contour and clusters size distribution of Xenon droplets collision, b=0, V=1500m/s, at (a) 25ps, (b) 75ps, (c) 150ps.
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Fig. 3. 58 Snapshot of density contour and clusters size distribution of Xenon droplets collision, b=0, V=1750m/s, at (a) 25ps, (b) 75ps, (c) 150ps.
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Fig. 3. 59 Snapshot of density contour and clusters size distribution of Xenon droplets collision, b=0, V=2000m/s, at (a) 25ps, (b) 75ps, (c) 150ps.
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Fig. 3. 60 Snapshot of density contour and clusters size distribution of Xenon droplets collision, b=0, V=2250m/s, at (a) 25ps, (b) 75ps, (c) 150ps.
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Fig. 3. 61 Snapshot of density contour and clusters size distribution of Helium droplets collision, b=0, V=250m/s, at (a) 25ps, (b) 75ps, (c) 150ps.
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Fig. 3. 62 Snapshot of density contour and clusters size distribution of Helium droplets collision, b=0, V=500m/s, at (a) 25ps, (b) 75ps, (c) 150ps.
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Fig. 3. 63 Snapshot of density contour and clusters size distribution of Helium droplets collision, b=0, V=750m/s, at (a) 25ps, (b) 75ps, (c) 150ps.
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Fig. 3. 64 Measurements of largest fragment of Xenon droplet pair collision, b=0, V=250m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 65 Measurements of largest fragment of Xenon droplet pair collision, b=0, V=500m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 66 Measurements of largest fragment of Xenon droplet pair collision, b=0, V=750m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 67 Measurements of largest fragment of Xenon droplet pair collision, b=2.5nm, V=250m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 68 Measurements of largest fragment of Xenon droplet pair collision, b=2.5nm, V=500m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 69 Measurements of largest fragment of Xenon droplet pair collision, b=2.5nm, V=750m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 70 Measurements of largest fragment of Xenon droplet pair collision, b=5nm, V=250 m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 71 Measurements of largest fragment of Xenon droplet pair collision, b=5nm, V=500m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 72 Measurements of largest fragment of Xenon droplet pair collision, b=5nm, V=750m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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(b)
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Fig. 3. 73 Measurements of largest fragment of Xenon droplet pair collision, b=7.5nm, V=250m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 74 Measurements of largest fragment of Xenon droplet pair collision, b=7.5nm, V=500m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 75 Measurements of largest fragment of Xenon droplet pair collision, b=7.5nm, V=750m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 76 Measurements of largest fragment of Helium droplet pair collision, b=0, V=250m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 77 Measurements of largest fragment of Helium droplet pair collision, b=0, V=500m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 78 Measurements of largest fragment of Helium droplet pair collision, b=0, V=750m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 79 Measurements of largest fragment of Helium droplet pair collision, b=2.5nm, V=250m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 80 Measurements of largest fragment of Helium droplet pair collision, b=2.5nm, V=500m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 81 Measurements of largest fragment of Helium droplet pair collision, b=2.5nm, V=750m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 82 Measurements of largest fragment of Helium droplet pair collision, b=5nm, V=250m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 83 Measurements of largest fragment of Helium droplet pair collision, b=5nm, V=500m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 84 Measurements of largest fragment of Helium droplet pair collision, b=5nm, V=750m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 85 Measurements of largest fragment of Helium droplet pair collision, b=7.5nm, V=250m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 86 Measurements of largest fragment of Helium droplet pair collision, b=7.5nm, V=500m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 87 Measurements of largest fragment of Helium droplet pair collision, b=7.5nm, V=750m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 88 Measurements of largest fragment of Helium droplet pair collision, b=2.5nm, V=250m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 89 Measurements of largest fragment of Helium droplet pair collision, b=5nm, V=250m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 90 Measurements of largest fragment of Helium droplet pair collision, b=5nm, V=500m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
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Fig. 3. 91 Measurements of largest fragment of Helium droplet pair collision, b=7.5nm, V=750m/s, (a) Number of atoms, (b) Vibration temperature (k), (c) Rotation energy, (d) Angular momentum, respectively.
Fig. 3. 92 Distribution map of various regimes of Xenon, Argon, and Helium droplet pair collision.