5,740 research outputs found
Impact of strong magnetic fields on collision mechanism for transport of charged particles
One of the main applications in plasma physics concerns the energy production
through thermo-nuclear fusion. The controlled fusion is achieved by magnetic
confinement i.e., the plasma is confined into a toroidal domain (tokamak) under
the action of huge magnetic fields. Several models exist for describing the
evolution of strongly magnetized plasmas, most of them by neglecting the
collisions between particles. The subject matter of this paper is to
investigate the effect of large magnetic fields with respect to a collision
mechanism. We consider here linear collision Boltzmann operators and derive, by
averaging with respect to the fast cyclotronic motion due to strong magnetic
forces, their effective collision kernels
Moduli Spaces of Curves with Homology Chains and c=1 Matrix Models
We show that introducing a periodic time coordinate in the models of
Penner-Kontsevich type generalizes the corresponding constructions to the case
of the moduli space of curves with homology chains
\gamma\in H_1(C,\zet_k). We make a minimal extension of the resulting models
by adding a kinetic term, and we get a new matrix model which realizes a simple
dynamics of \zet_k-chains on surfaces. This gives a representation of
matter coupled to two-dimensional quantum gravity with the target space being a
circle of finite radius, as studied by Gross and Klebanov.Comment: IFUM 459/FT (LaTeX, 9 pages; a few misprints have been corrected and
the introduction has been slightly modified
Propagation of and Maxwellian weighted bounds for derivatives of solutions to the homogeneous elastic Boltzmann Equation
We consider the -dimensional space homogeneous Boltzmann equation for
elastic collisions for variable hard potentials with Grad (angular) cutoff. We
prove sharp moment inequalities, the propagation of -Maxwellian weighted
estimates, and consequently, the propagation -Maxwellian weighted
estimates to all derivatives of the initial value problem associated to the
afore mentioned problem.
More specifically, we extend to all derivatives of the initial value problem
associated to this class of Boltzmann equations corresponding sharp moment
(Povzner) inequalities and time propagation of -Maxwellian weighted
estimates as originally developed A.V. Bobylev in the case of hard spheres in 3
dimensions; an improved sharp moments inequalities to a larger class of angular
cross sections and -exponential bounds in the case of stationary states to
Boltzmann equations for inelastic interaction problems with `heating' sources,
by A.V. Bobylev, I.M. Gamba and V.Panferov, where high energy tail decay rates
depend on the inelasticity coefficient and the the type of `heating' source;
and more recently, extended to variable hard potentials with angular cutoff by
I.M. Gamba, V. Panferov and C. Villani in the elastic case collision case and
so -Maxwellian weighted estimated were shown to propagate if initial
states have such property. In addition, we also extend to all derivatives the
propagation of -Maxwellian weighted estimates to solutions of the
initial value problem to the Boltzmann equations for elastic collisions for
variable hard potentials with Grad (angular) cutoff.Comment: 24 page
High Performance Computing With A Conservative Spectral Boltzmann Solver
We present new results building on the conservative deterministic spectral method for the space inhomogeneous Boltzmann equation developed by Gamba and Tharkabhushaman. This approach is a two-step process that acts on the weak form of the Boltzmann equation, and uses the machinery of the Fourier transform to reformulate the collisional integral into a weighted convolution in Fourier space. A constrained optimization problem is solved to preserve the mass, momentum, and energy of the resulting distribution. We extend this method to second order accuracy in space and time, and explore how to leverage the structure of the collisional formulation for high performance computing environments. The locality in space of the collisional term provides a straightforward memory decomposition, and we perform some initial scaling tests on high performance computing resources. We also use the improved computational power of this method to investigate a boundary-layer generated shock problem that cannot be described by classical hydrodynamics.Mathematic
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