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P3M
Particle–Particle–Particle–Mesh (P3M) is a Fourier-based Ewald summation method to calculate potentials in N-body simulations. The potential could be the electrostatic potential among N point charges i.e. molecular dynamics, the gravitational potential among N gas particles in e.g. smoothed particle hydrodynamics, or any other useful function. It is based on the particle mesh method, where particles are interpolated onto a grid, and the potential is solved for this grid (e.g. by solving the discrete Poisson equation Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with t ...). This interpolation introduces errors in the force calculation, particularly for particles that are close together. Essentially, the particles are forced to have a lower spatial resolution during the force calcul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molecular Dynamics
Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of the system. In the most common version, the trajectories of atoms and molecules are determined by numerically solving Newton's equations of motion for a system of interacting particles, where forces between the particles and their potential energies are often calculated using interatomic potentials or molecular mechanical force fields. The method is applied mostly in chemical physics, materials science, and biophysics. Because molecular systems typically consist of a vast number of particles, it is impossible to determine the properties of such complex systems analytically; MD simulation circumvents this problem by using numerical methods. However, long MD simulations are mathematically ill-conditioned, generating cumulative erro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Particle Mesh
Particle Mesh (PM) is a computational method for determining the forces in a system of particles. These particles could be atoms, stars, or fluid components and so the method is applicable to many fields, including molecular dynamics and astrophysics. The basic principle is that a system of particles is converted into a grid (or "mesh") of density values. The potential is then solved for this density grid, and forces are applied to each particle based on what cell it is in, and where in the cell it lies. Various methods for converting a system of particles into a grid of densities exist. One method is that each particle simply gives its mass to the closest point in the mesh. Another method is the Cloud-in-Cell (CIC) method, where the particles are modelled as constant density cubes, and one particle can contribute mass to several cells. Once the density distribution is found, the potential energy of each point in the mesh can be determined from the differential form of Gauss's law, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smoothed Particle Hydrodynamics
Smoothed-particle hydrodynamics (SPH) is a computational method used for simulating the mechanics of continuum media, such as solid mechanics and fluid flows. It was developed by Gingold and Monaghan and Lucy in 1977, initially for astrophysical problems. It has been used in many fields of research, including astrophysics, ballistics, volcanology, and oceanography. It is a meshfree Lagrangian method (where the co-ordinates move with the fluid), and the resolution of the method can easily be adjusted with respect to variables such as density. Method Advantages * By construction, SPH is a meshfree method, which makes it ideally suited to simulate problems dominated by complex boundary dynamics, like free surface flows, or large boundary displacement. * The lack of a mesh significantly simplifies the model implementation and its parallelization, even for many-core architectures. * SPH can be easily extended to a wide variety of fields, and hybridized with some other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ewald Summation
Ewald summation, named after Paul Peter Ewald, is a method for computing long-range interactions (e.g. electrostatic interactions) in periodic systems. It was first developed as the method for calculating electrostatic energies of ionic crystals, and is now commonly used for calculating long-range interactions in computational chemistry. Ewald summation is a special case of the Poisson summation formula, replacing the summation of interaction energies in real space with an equivalent summation in Fourier space. In this method, the long-range interaction is divided into two parts: a short-range contribution, and a long-range contribution which does not have a singularity. The short-range contribution is calculated in real space, whereas the long-range contribution is calculated using a Fourier transform. The advantage of this method is the rapid convergence of the energy compared with that of a direct summation. This means that the method has high accuracy and reasonable speed when ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N-body Simulation
In physics and astronomy, an ''N''-body simulation is a simulation of a dynamical system of particles, usually under the influence of physical forces, such as gravity (see n-body problem, ''n''-body problem for other applications). ''N''-body simulations are widely used tools in astrophysics, from investigating the dynamics of few-body systems like the Earth-Moon-Sun system to understanding the evolution of the large-scale structure of the universe. In physical cosmology, ''N''-body simulations are used to study processes of non-linear structure formation such as galaxy filaments and galaxy halos from the influence of dark matter. Direct ''N''-body simulations are used to study the dynamical evolution of star clusters. Nature of the particles The 'particles' treated by the simulation may or may not correspond to physical objects which are particulate in nature. For example, an N-body simulation of a star cluster might have a particle per star, so each particle has some physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poisson Equation
Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with the potential field known, one can then calculate electrostatic or gravitational (force) field. It is a generalization of Laplace's equation, which is also frequently seen in physics. The equation is named after French mathematician and physicist Siméon Denis Poisson. Statement of the equation Poisson's equation is \Delta\varphi = f where \Delta is the Laplace operator, and f and \varphi are real or complex-valued functions on a manifold. Usually, f is given and \varphi is sought. When the manifold is Euclidean space, the Laplace operator is often denoted as and so Poisson's equation is frequently written as \nabla^2 \varphi = f. In three-dimensional Cartesian coordinates, it takes the form \left( \frac + \frac + \frac \right)\varp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
