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where is a diffusion matrix specifying hydrodynamic interactions, Oseen tensor [4] for example, in non-diagonal entries interacting between the target particle and the surrounding particle , is the force exerted on the particle , and () is a Gaussian noise vector with zero mean and a standard deviation of in each vector entry.
In an ab initio MD simulation, the total energy of the system is calculated at each time step using density functional theory (DFT) or another method of quantum chemistry. The forces acting on each atom are then determined from the gradient of the energy with respect to the atomic coordinates, and the equations of motion are solved to predict ...
Brownian motion is the random motion of particles suspended in a medium (a liquid or a gas). [2] This motion pattern typically consists of random fluctuations in a particle's position inside a fluid sub-domain, followed by a relocation to another sub-domain. Each relocation is followed by more fluctuations within the new closed volume.
A molecular dynamics simulation requires the definition of a potential function, or a description of the terms by which the particles in the simulation will interact. In chemistry and biology this is usually referred to as a force field and in materials physics as an interatomic potential .
TCAM (Transport Chemical Aerosol Model; TCAM): a mathematical modelling method (computer simulation) designed to model certain aspects of the Earth's atmosphere. TCAM is one of several chemical transport models, all of which are concerned with the movement of chemicals in the atmosphere, and are thus used in the study of air pollution.
In computational chemistry, a constraint algorithm is a method for satisfying the Newtonian motion of a rigid body which consists of mass points. A restraint algorithm is used to ensure that the distance between mass points is maintained.
In a simulation this may be implemented by using small time steps for the simulation, using a fixed number of constraint-solving steps per time step, or solving constraints until they are met by a specific deviation. When approximating the constraints locally to first order, this is the same as the Gauss–Seidel method.
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 ...