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Gaussian Theory for Derivation of Continuum Equations of Self-propelled Particles

Allaei, Hamid | 2016

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 49158 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Ejtehadi, Mohammad Reza; Moghimi, Saman
  7. Abstract:
  8. The collective behavior of active matters, e.g. colony of micro swimmers and flocks of birds is modeled with self-propelled particles. It is evident that a continuum description of such systems is useful in determining the collective behavior in large scales. One can make continuum equations in active matter with the help of symmetry arguments. However, the equation is in a phenomenological level with undetermined transport coefficients. It is possible to construct the continuum equations from microscopic rules to find the transport coefficients in terms of microscopic parameters with approximations. One of the usual approximations called truncation method is to truncate the Fourier series of the orientation distribution of the particles. Although the truncation method gives a reasonable description of ordered to disordered transition, the resulting transport coefficients are not correct in low noise limit. In this thesis, we introduce a novel technique in obtaining transport coefficients from microscopic rules. In this technique the distribution of the particles orientations is approximated by a wrapped Gaussian distribution function. We show that the resulting continuum equations describe qualitatively all features of the system in all range of noise intensities. Therefore we can accurately describe the collective behavior of the system in low noise. To illustrate the effectiveness of the Gaussian approximation, we apply it to a simple model of self-propelled particles which like Quincke rotors produce a vortex with defect lines when the particles are confined in a squared box. Then, we numerically solved the continuum equations and obtained similar vortex pattern. In contrast, one can not find the vortex solution with truncation approximation at second order. Therefor we conclude that the Gaussian approximation is an applicable method which is easy to apply and gives astonishing accurate behavior of the system, specially in low noise intensities
  9. Keywords:
  10. Hydrodynamic Equations ; Self-Propelled Particles ; Active Matter ; Collective Behavior

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