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Louis de Broglie's early results on the pilot wave theory were presented in his thesis (1924) in the context of atomic orbitals where the waves are stationary.Early attempts to develop a general formulation for the dynamics of these guiding waves in terms of a relativistic wave equation were unsuccessful until in 1926 Schrödinger developed his non-relativistic wave equation.
The term file dynamics is the motion of many particles in a narrow channel.. In science: in chemistry, physics, mathematics and related fields, file dynamics (sometimes called, single file dynamics) is the diffusion of N (N → ∞) identical Brownian hard spheres in a quasi-one-dimensional channel of length L (L → ∞), such that the spheres do not jump one on top of the other, and the ...
For a system of particles with masses , with coordinates = that constitute a time-dependent random variable, the resulting Langevin equation is [2] [3] ¨ = ˙ + (), where () is the particle interaction potential; is the gradient operator such that () is the force calculated from the particle interaction potentials; the dot is a time derivative ...
A Treatise on the Analytical Dynamics of Particles and Rigid Bodies is a treatise and textbook on analytical dynamics by British mathematician Sir Edmund Taylor Whittaker. Initially published in 1904 by the Cambridge University Press, the book focuses heavily on the three-body problem and has since gone through four editions and has been ...
One of the earliest particle methods is smoothed particle hydrodynamics, presented in 1977. [1] Libersky et al. [2] were the first to apply SPH in solid mechanics. The main drawbacks of SPH are inaccurate results near boundaries and tension instability that was first investigated by Swegle. [3] In the 1990s a new class of particle methods emerged.
Dissipative particle dynamics (DPD) is an off-lattice mesoscopic simulation technique [1] which involves a set of particles moving in continuous space and discrete time. Particles represent whole molecules or fluid regions, rather than single atoms, and atomistic details are not considered relevant to the processes addressed.
A collection of such particle trajectories can be used for analyzing the Lagrangian dynamics of the fluid motion, for performing Lagrangian statistics of various flow quantities etc. [1] [2] In computational fluid dynamics , the Lagrangian particle tracking (or in short LPT method) is a numerical technique for simulated tracking of particle ...