Sürüler Probleminin Topluluk Bağlamı Açısından Modellenmesi

Çağatay Kok; Seven Burçin Çellek; Çağlar Koşun; Serhan Özdemir

doi:10.21605/cukurovaummfd.316778

Araştırma Makalesi

Casting the Swarms Problem in the Ensembles Context

Yıl 2016, Cilt: 31 Sayı: ÖS2, 229 - 236, 15.10.2016

Çağatay Kok Seven Burçin Çellek Çağlar Koşun Serhan Özdemir

https://doi.org/10.21605/cukurovaummfd.316778

Öz

Robotic swarms have been modeled in a myriad of ways. One property of the swarms is their multitude. As their numbers increase to uncountable numbers, the thermostatistical mechanics may come into play. Authors took advantage of this fact so as to generate global statistics for the swarm. Three distinct ensembles are explained and formulated. When isolated, the swarms behave as if microcanonical ensemble reigns. But when a predator or a prey appears, transitions are observed depending on the conditions. Therefore, both the formulations and the transitions are all contingent. Finally, observed probabilities were discussed.

Anahtar Kelimeler

Swarm modeling, Statistical physics, Ensembles, Robotics

Kaynakça

1. Rauch, E.M., Millonas, M.M., Chialvo, D.R., 1995. Pattern Formation and Functionality in Swarm Models, Physics Letters A 207, no. 3-4: 185-93. doi:10.1016/0375-9601(95)00624-c.
2. Martinoli, A., Easton, K., Agassounon, W., 2004. Modeling Swarm Robotic Systems: A Case Study in Collaborative Distributed Manipulation, Int J Robot Res The International Journal of Robotics Research 23, no. 4: 415-36. doi:10.1177/0278364904042197.
3. Chen, S., Fang, H., 2006. Modeling and Stability Analysis of Social Foraging Swarms in Multi-obstacle Environment. J. Control Theory Appl, Journal of Control Theory and Applications 4, no. 4: 343-48. doi:10.1007/s11768-006-5170-8.
4. Arlotti, L., Deutsch, A., Lachowicz, M., 2005. A Discrete Boltzmann-type Model of Swarming, Mathematical and Computer Modelling 41, no. 10: 1193-201. doi: 10.1016/j.mcm.2005.05.011.
5. Zhao, Y., Zu, W., Zeng, H., 2009. A Modified Particle Swarm Optimization via Particle Visual Modeling Analysis, Computers & Mathematics with Applications 57, no. 11-12: 2022-029. doi: 10.1016/j.camwa.2008.10.007.
6. Lin, Y., Chang, W., Hsieh, J., 2008. A Particle Swarm Optimization Approach to Nonlinear Rational Filter Modeling, Expert Systems with Applications 34, no. 2: 1194-199. doi: 10.1016/j.eswa.2006.12.004.
7. Wu, Q., 2010. A Hybrid-forecasting Model Based on Gaussian Support Vector Machine and Chaotic Particle Swarm Optimization, Expert Systems with Applications 37, no. 3: 2388-394. doi: 10.1016/j.eswa.2009.07.057.
8. Chan, K.Y., Dillon, T.S., Kwong, C.K., 2011. Polynomial Modeling for Time-varying Systems Based on a Particle Swarm Optimization Algorithm, Information Sciences 181, no. 9: 1623-640. doi: 10.1016/j.ins.2011. 01.006.
9. Cleghorn, C.W., Engelbrecht, A.P., 2014. A Generalized Theoretical Deterministic Particle Swarm Model, Swarm Intell Swarm Intelligence 8, no. 1: 35-59. doi:10.1007/s11721-013-0090-y.
10. Zhang, J., 2013. Canonical Ensemble Model for the Black Hole Quantum Tunneling Radiation, Chinese Physics Letters Chinese Phys. Lett. 30, no. 7: 070401. doi:10.1088/0256-307x/30/7/070401.
11. Sierra, G., Román, J.M., Dukelsky, J., 2004. The Elementary Excitations of the Bcs Model in the Canonical Ensemble, International Journal of Modern Physics A Int. J. Mod. Phys. A 19, no. Supp02: 381-95. doi:10.1142/ s0217751x04020531.
12. Zhang, J., 2014. Canonical Ensemble Model for Black Hole Radiation, J. Astrophys Astron Journal of Astrophysics and Astronomy 35, no. 3: 573-75. doi:10.1007/s12036-014-9290-0.
13. Nogawa, T., Ito, N., Watanabe, H., 2011. Evaporation-condensation Transition of the Two-dimensional Potts Model in the Microcanonical Ensemble, Physical Review E Phys. Rev. E 84, no. 6. doi:10.1103/physreve.84.061107.
14. Wang, J., Yang, T., 1996. Numerical Microcanonical Ensemble Method for Calculation on Statistical Models with Large Lattice Sizes, Phys. Rev. B Physical Review B 54, no. 19: 13635-3642. doi:10.1103/physrevb. 54.13635.
15. Hilbert, S., Dunkel, J., 2006. Nonanalytic Microscopic Phase Transitions and Temperature Oscillations in the Microcanonical Ensemble: An Exactly Solvable One-dimensional Model for Evaporation, Physical Review E Phys. Rev. E 74, no. 1. doi:10.1103/physreve.74.011120.
16. Alkhimov, V.I., 2014. A D-dimensional Model of the Canonical Ensemble of Open Strings, Theoretical and Mathematical Physics Theor Math Phys 180, no. 1: 862-79. doi:10.1007/ s11232-014-0185-7.
17. Knani, S., Khalfaoui, M., Hachicha, M.A., Ben, Lamine, A., Mathlouthi, M., 2012. Modelling of Water Vapour Adsorption on Foods Products by a Statistical Physics Treatment Using the Grand Canonical Ensemble, Food Chemistry 132, no. 4: 1686-692. doi: 10.1016/j.foodchem.2011.11.065.
18. Knani, S., Mathlouthi, M., Ben Lamine, A., 2007. Modeling of the Psychophysical Response Curves Using the Grand Canonical Ensemble in Statistical Physics, Food Biophysics 2, no. 4: 183-92. doi:10.1007/ s11483-007-9042-7.
19. William C., Kalmykov, Yu.P., Waldron, J.T., 1996. The Langevin Equation: With Applications in Physics, Chemistry, and Electrical Engineering, Singapore: World Scientific.
20. Sethna, James, P., 2006. Statistical Mechanics: Entropy, Order Parameters, and Complexity, Oxford, UK: New York.
21. Tsallis, C., 2009. Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World, New York: Springer.
22. Bowley, R., Sánchez, M., 1996. Introductory Statistical Mechanics, Oxford: Clarendon Press.
23. Balian, R., 1991. From Microphysics to Macrophysics: Methods and Applications of Statistical Physics, Berlin: Springer-Verlag.