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Dynamics of gravitationally interacting systems

Dynamics of gravitationally interacting systems. Pasquale Londrillo INAF-Osservatorio Astronomico-Bologna (Italy) Email pasquale.londrillo@bo.astro.it. Trying to look at possible intersections with beam-dynamics ==  seemingly none. Fenomenology.

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Dynamics of gravitationally interacting systems

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  1. Dynamics of gravitationally interacting systems Pasquale Londrillo INAF-Osservatorio Astronomico-Bologna (Italy) Email pasquale.londrillo@bo.astro.it Trying to look at possible intersections with beam-dynamics == seemingly none

  2. Fenomenology • Dark-Matter dominated Large Scale structures => collisionless regime • The Galaxies => collisionless regime • The Globular Clusters => collisionality important

  3. Elliptical Galaxies

  4. Violent relaxation (Lynden-Bell (1967) Relaxation to dynamical large-scale equilibria and/or Relaxation to statistical mechanics equilibria The debate on fine-graining and coarse-graining

  5. The Numerical approach:The Particle method Well posed Mathematical set-up: 1) the Vlasov-Poisson equation for f(x,v,t) is replaced by a lagrangian fluid ot orbits [x(t),v(t)] preserving f f(x,v,t)=f(x(t),v(t)] and moving under the collective forces F(x,t)= 2) The infinite-dimensional set of characteristic orbits is sampled by a finite-N-set of particles moving under an Є(N)- softened gravitational force Є(N) →0 N→infinity 3)Theorems are available to assure convergence (in some norm) of N-body representation to the limit Vlasov-Poisson solution

  6. Numerical procedures for N- body codes 1- The set of N-representative particles aremoved in time using a simplectic integrator2- the gravitational forces and potential are computed:a)- either directely on particles, using thetwo-body softened Green-functionb)- or by solving the Poisson equation on agrid. Using a density distribution recoveredfrom particle positions by some interpolation (PIC) Methods a) have clear (mathematical) advantages Now even faster than b) => Multipole expansion techniques having O(N) computational complexity

  7. Other numerical methods to solve thecollisionless Vlasov-Poisson equation Methods to solve f(x,v,t) directely on a six-dimensional eulerian grid Proposed mainly for Plasma-Physics computations (where Electromagnetic fields can be represented on a grid in a natural way)

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