poisson equationの例文

• Note that, with the opposite sign convention ( used in Physics ), this is the potential generated by a point particle, for an inverse-square law force, arising in the solution of Poisson equation.
• This introduces an additional factor of 8? into Newton's law of universal gravitation but simplifies Einstein's equations, the Einstein Hilbert action, the Friedmann equations and the Newtonian Poisson equation by removing the corresponding factor.
• Therefore, when " ? " is very small, the solution approaches that of the unscreened Poisson equation, which, in dimension n = 3, is a superposition of 1 / " r " functions weighted by the source function " f ":
• Where " G " is Newton's constant and { \ rho } is the density ( number of particles at the mesh points ), is trivial to solve by using the fast Fourier transform to go to the frequency domain where the Poisson equation has the simple form
• The Lagrangian may be constructed so that "'a N "'satisfies the usual Newton-Poisson equation, and is then used to find "'a "'via an additional algebraic but non-linear step, which is chosen to satisfy Milgrom's law.
• ;SCHRED : calculates envelope wavefunctions and the corresponding bound-state energies in a typical Metal-Oxide-Semiconductor ( MOS ) or Semiconductor-Oxide-Semiconductor ( SOS ) structure and a typical SOI structure by solving self-consistently the one-dimensional ( 1D ) Poisson equation and the 1D Schr鰀inger equation.
• This fact can be used to prove existence and uniqueness of solutions to the Dirichlet problem for the Poisson equation in suitably regular domains, and for suitably well-behaved functions ? : one first applies a Newtonian potential to obtain a solution, and then adjusts by adding a harmonic function to get the correct boundary data.
• The equation for local ion density can be substituted into the Poisson equation under the assumptions that the work being done is only electric work, that our solution is composed of a 1 : 1 salt ( i . e . NaCl ), and that the concentration of salt is much higher than the concentration of ions.
• Knowing the potential, " ? ( r ) ", the charge density can then be recovered from the Poisson equation, whose solution may be expressed as a modified Bessel function of the first kind, " I 0 ", and scaled to the capillary radius, " a ".
• The general theoretical description of a Langmuir probe measurement requires the simultaneous solution of the Poisson equation, the collision-free Boltzmann equation or Vlasov equation, and the continuity equation with regard to the boundary condition at the probe surface and requiring that, at large distances from the probe, the solution approaches that expected in an undisturbed plasma.