Высказывания ученых о механике дискретных сред

Материал из Department of Theoretical and Applied Mechanics
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Кафедра ТМ > Научный справочник > Механика > МДС > Высказывания ученых

"If in some cataclysm all scientic knowledge were to be destroyed and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis that all things are made of atoms-little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence, you will see there is an enormous amount of information about the world, if just a little imagination and thinking are applied."
“The particle method is not only an approximation of the continuum fluid equations, but also gives the rigorous equations for a particle system, which approximates the molecular system underlying, and more fundamental than the continuum equations.” (J. Von Neumann Proposal and analysis of a new numerical method for the treatment of hydrodynamical shock problems: in Von Neumann Collected Works, ed. A. Taub (Oxford: Pergamon))
"Macroscopic continuum simulations can be based on an unstructured moving spatial grid made up of “smooth particles”. The smooth particles’ equations of motion include interpolated values of the macroscopic stress gradient at each particle’s position. Microscopic solid-state simulations can be based on the motion of “embedded atoms”, with equations of motion based on a physical idea – embedding atoms in the local electronic density. The embedded atoms then move according to Newtonian equations of motion, based on electronic density gradients at each particle position. I show here that these two descriptions, macroscopic smooth particles and microscopic embedded atoms, can give identical particle trajectories. This demonstration facilitates the understanding of macroscopic models for surface tension and also suggests that certain macroscopic continuum approaches to smooth particle applied mechanics could have useful analogs in microscopic molecular dynamics." (W.G. Hoover, Isomorphism linking smooth particles and embedded atoms. Physica A, Vol. 260, Iss. 3–4, 1998, pp. 244–254.)
"Smoothed particle hydrodynamics (SPH) is a method for obtaining approximate numerical solutions of the equations of fluid dynamics by replacing the fluid with a set of particles. For the mathematician, the particles are just interpolation points from which properties of the fluid can be calculated. For the physicist, the SPH particles are material particles which can be treated like any other particle system." (J.J. Monaghan. Smoothed particle hydrodynamics. Rep. Prog. Phys. 68, 2005, pp. 1703–1759)