Computational physics Computational physics The Arbitrary-Lagrangian-Eulerian General Research Applications (ALEGRA) code is a next-generation large-deformation shock physics code created by researchers at Sandia National Laboratory. This code uses an "Arbitrary Lagrangian-Eulerian" (ALE) formulation on an unstructured mesh, allowing one to designate whether material should flow through a stationary mesh (pure Eulerian), whether the mesh should move with the material (pure Lagrangian), or whether the mesh should be allowed to move independently of the material motion (arbitrary). The arbitrary formulation permits a simulation to proceed in Lagrangian fashion until the mesh becomes too highly distorted. Points in the most deformed regions of the mesh are then repositioned to reduce the distortion to acceptable levels. This reduces the overall computational expense of a purely Lagrangian approach while being more accurate than the traditional Eulerian method. ...more on Wikipedia about "ALEGRA"
In physical simulations, video games and computational geometry, collision detection includes algorithms from checking for collision, i.e. intersection, of two given solids, to calculating trajectories, impact times and impact points in a physical simulation. ...more on Wikipedia about "Collision detection"
Computational physics is the study and implementation of numerical algorithms in order to solve problems in physics for which a quantitative theory already exists. It is often regarded as a subdiscipline of theoretical physics. ...more on Wikipedia about "Computational physics"
Dynamical simulation, in computational physics, is the simulation of systems of objects that are free to move, usually in three dimensions according to Newton's laws of dynamics, or approximations thereto. Dynamical simulation is used in computer animation to assist animators to produce realistic motion, in industrial design (for example to simulate crashes as an early step in crash testing), and in video games. Body movement is calculated using time integration methods. ...more on Wikipedia about "Dynamical simulation"
In computational physics and computational chemistry, the Hartree-Fock (HF) or self-consistent field (SCF) calculation scheme is a self-consistent iterative variational procedure to calculate the Slater determinant (or the molecular orbitals which it is made of) for which the expectation value of the electronic molecular Hamiltonian is minimum. Whilst it calculates the exchange energy exactly, it does not include the effect of electron correlation. The procedure is named after Douglas Hartree, who devised the self-consistent field method, and V. A. Fock, who improved the rigour of Hartree's method to make it consistent with the Pauli principle and reformulated it into the matrix form used today. Expressed in a Slater-type or Gaussian-type basis set, the Hartree-Fock equation can be transformed into matrix form called Roothaan equations. ...more on Wikipedia about "Hartree-Fock"
Inverse kinematics is the process of determining the parameters of a jointed flexible object in order to achieve a desired pose. For example, with a 3D model of a human body, what are the required wrist and elbow angles to move the hand from a resting position to a waving position? This question is vital in robotics, where manipulator arms are commanded in terms of joint angles. Inverse kinematics are also relevant to game programming and 3D modeling, though its importance there has decreased with the rise of use of large libraries of motion capture data. ...more on Wikipedia about "Inverse kinematics"
Description: The Philosophiae Naturalis Principia Mathematica ( Latin: "mathematical principles of natural philosophy", often Principia or Principia Mathematica for short) is a three-volume work by Isaac Newton published on July 5, 1687. Probably the most influential scientific book ever published, it contains the statement of Newton's laws of motion forming the foundation of classical mechanics as well as his law of universal gravitation. He derives Kepler's laws for the motion of the planets (which were first obtained empirically). ...more on Wikipedia about "List of publications in physics"
Monte Carlo methods are a class of computational algorithms for simulating the behavior of various physical and mathematical systems. They are distinguished from other simulation methods (such as molecular dynamics) by being stochastic, that is nondeterministic in some manner - usually by using random numbers (or more often pseudo-random numbers) - as opposed to deterministic algorithms. A classic use is for the evaluation of definite integrals, particularly multidimensional integrals with complicated boundary conditions. ...more on Wikipedia about "Monte Carlo method"
In quantum chemistry, the Multi-configurational self-consistent field or MCSCF method is a post-Hartree-Fock method that uses a linear combination of CSFs to approximate the true electronic wavefunction of an atom or molecule. In an MCSCF calculation, the set of CSF coefficients is varied along with the sets of basis function coefficients associated with each CSF in order to obtain the total electronic wavefunction with the lowest possible energy. ...more on Wikipedia about "Multi-configurational self-consistent field"
A navigation mesh is an abstract data structure used in artificial intelligence applications to aid agents in path-finding through large spaces. Meshes that do not map to static obstacles in the environment they model offer the additional advantage that agents with access to the mesh will not consider these obstacles in path-finding, reducing computational effort and making collision detection between agents and static obstacles moot. Meshes are typically implemented as graphs, opening their use to a large number of algorithms defined on these structures. ...more on Wikipedia about "Navigation mesh"
Numerical relativity is a subfield of computational physics that aims to establish numerical solutions to Einstein's field equations in general relativity. Numerical relativists use supercomputers to study black holes, gravitational waves, and other phenomena predicted by Einstein's Theory of General Relativity. The goal of numerical relativity is to study spacetimes that cannot be studied by analytic means. The focus is therefore primarily on dynamical systems. Numerical relativity has been applied in many areas: cosmological models, critical phenomena, perturbed black holes and neutron stars, and the coalescence of black holes and neutron stars, for example. In any of these cases, Einstein's equations can be formulated in several ways that allow us to evolve the dynamics. While Cauchy methods have received a majority of the attention, characteristic and Regge calculus based methods have also been used. All of these methods begin with a snapshot of the gravitational fields on some hypersurface, the initial data, and evolve these data to neighboring hypersurfaces. ** ...more on Wikipedia about "Numerical relativity"
The study of the physics of computation relates to understanding the fundamental physical limits of computers. This field has led to the investigation of how thermodynamics limits information processing, the understanding of chaos and dynamical systems, and a rapidly growing effort to invent new quantum computers. ...more on Wikipedia about "Physics of computation"
In Quantum Mechanics, the pseudopotential formalism is an attempt to replace the complicated effects of the motion of the core (i.e. non- valence) electrons of an atom or ion and its nucleus with an effective potential, or pseudopotential, so that the Schrodinger equation contains a modified potential term instead of e.g. the Coulombic potential term normally found in the Schrodinger equation. By construction of this pseudopotential, the valence wavefunction generated is also guaranteed to be orthogonal to all the core states. ...more on Wikipedia about "Pseudopotential"
Softening is a numerical trick used in N-body tecniques to prevent numerical divergences when a particle comes too close to another (and the force goes to infinity). This is obtained by modifying the gravitational potential of each particle as ...more on Wikipedia about "Softening"
The VEGAS algorithm, due to G. P. Lepage, is a method for reducing error in the Monte Carlo simulation by using a known or approximate probability distribution function to concentrate the search in those areas of the graph that make the greatest contribution to the final integral. ...more on Wikipedia about "VEGAS algorithm"
The Vienna Ab-initio Simulation Package, better known as VASP (or alternatively VAMP), is a package for performing ab-initio quantum mechanical molecular dynamics (MD) using pseudopotentials and a plane wave basis set. VASP is based on CASTEP initially written by Mike Payne at MIT, which was brought to the University of Vienna in Vienna, Austria in July 1989 by Jürgen Hafner. The main program was written by himself, Jürgen Furthmüller, who joined the group at the Institut für Materialphysik in January 1993, and Georg Kresse. ...more on Wikipedia about "Vienna Ab-initio Simulation Package"
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