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Transition Path Sampling
Transition path sampling (TPS) is a Rare Event Sampling method used in computer simulations of rare events: physical or chemical transitions of a system from one stable state to another that occur too rarely to be observed on a computer timescale. Examples include protein folding, chemical reactions and nucleation. Standard simulation tools such as molecular dynamics can generate the dynamical trajectories of all the atoms in the system. However, because of the gap in accessible time-scales between simulation and reality, even present supercomputers might require years of simulations to show an event that occurs once per microsecond without some kind of acceleration. Transition path ensemble TPS focuses on the most interesting part of the simulation, ''the transition''. For example, an initially unfolded protein will vibrate for a long time in an open-string configuration before undergoing a transition and fold on itself. The aim of the method is to reproduce precisely those fol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rare Event Sampling
Rare event sampling is an umbrella term for a group of computer simulation methods intended to selectively sample 'special' regions of the dynamic space of systems which are unlikely to visit those special regions through brute-force simulation. A familiar example of a rare event in this context would be nucleation of a raindrop from over-saturated water vapour: although raindrops form every day, relative to the length and time scales defined by the motion of water molecules in the vapour phase, the formation of a liquid droplet is extremely rare. Due to the wide use of computer simulation across very different domains, articles on the topic arise from quite disparate sources and it is difficult to make a coherent survey of rare event sampling techniques. Contemporary methods include Transition Path Sampling (TPS), Replica Exchange Transition Interface Sampling (RETIS), Repetitive Simulation Trials After Reaching Thresholds (RESTART), Forward Flux Sampling (FFS), Generalized ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-equilibrium
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with physical systems that are not in thermodynamic equilibrium but can be described in terms of macroscopic quantities (non-equilibrium state variables) that represent an extrapolation of the variables used to specify the system in thermodynamic equilibrium. Non-equilibrium thermodynamics is concerned with transport processes and with the rates of chemical reactions. Almost all systems found in nature are not in thermodynamic equilibrium, for they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems and to chemical reactions. Some systems and processes are, however, in a useful sense, near enough to thermodynamic equilibrium to allow description with useful accuracy by currently known non-equilibrium thermodynamics. Nevertheless, many natural systems and processes will always remain far beyond the scope o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monte Carlo Methods
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution. In physics-related problems, Monte Carlo methods are useful for simulating systems with many coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model, interacting particle systems, McKean–Vlasov processes, kinetic models of gases). Other examples include modeling phenomena with significant uncertainty in inputs such as the calculation of risk in b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Chemistry
Computational chemistry is a branch of chemistry that uses computer simulation to assist in solving chemical problems. It uses methods of theoretical chemistry, incorporated into computer programs, to calculate the structures and properties of molecules, groups of molecules, and solids. It is essential because, apart from relatively recent results concerning the hydrogen molecular ion (dihydrogen cation, see references therein for more details), the quantum many-body problem cannot be solved analytically, much less in closed form. While computational results normally complement the information obtained by chemical experiments, it can in some cases predict hitherto unobserved chemical phenomena. It is widely used in the design of new drugs and materials. Examples of such properties are structure (i.e., the expected positions of the constituent atoms), absolute and relative (interaction) energies, electronic charge density distributions, dipoles and higher multipole moments, vi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CP2K
CP2K is a freely available (GPL) quantum chemistry and solid state physics program package, written in Fortran 2008, to perform atomistic simulations of solid state, liquid, molecular, periodic, material, crystal, and biological systems. It provides a general framework for different methods: density functional theory (DFT) using a mixed Gaussian and plane waves approach (GPW) via LDA, GGA, MP2, or RPA levels of theory, classical pair and many-body potentials, semi-empirical ( AM1, PM3, MNDO, MNDOd, PM6) and tight-binding Hamiltonians, as well as Quantum Mechanics/Molecular Mechanics (QM/MM) hybrid schemes relying on the Gaussian Expansion of the Electrostatic Potential (GEEP). The Gaussian and Augmented Plane Waves method (GAPW) as an extension of the GPW method allows for all-electron calculations. CP2K can do simulations of molecular dynamics, metadynamics, Monte Carlo, Ehrenfest dynamics, vibrational analysis, core level spectroscopy, energy minimization, and transition sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LAMMPS
Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) is a molecular dynamics program from Sandia National Laboratories. LAMMPS makes use of Message Passing Interface (MPI) for parallel communication and is free and open-source software, distributed under the terms of the GNU General Public License. LAMMPS was originally developed under a Cooperative Research and Development Agreement (CRADA) between two laboratories from United States Department of Energy and three other laboratories from private sector firms. , it is maintained and distributed by researchers at the Sandia National Laboratories and Temple University. Features For computing efficiency, LAMMPS uses neighbor lists (Verlet lists) to keep track of nearby particles. The lists are optimized for systems with particles that repel at short distances, so that the local density of particles never grows too large. On parallel computers, LAMMPS uses spatial-decomposition techniques to partition the simulatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
OpenMP
OpenMP (Open Multi-Processing) is an application programming interface (API) that supports multi-platform shared-memory multiprocessing programming in C, C++, and Fortran, on many platforms, instruction-set architectures and operating systems, including Solaris, AIX, FreeBSD, HP-UX, Linux, macOS, and Windows. It consists of a set of compiler directives, library routines, and environment variables that influence run-time behavior. OpenMP is managed by the nonprofit technology consortium ''OpenMP Architecture Review Board'' (or ''OpenMP ARB''), jointly defined by a broad swath of leading computer hardware and software vendors, including Arm, AMD, IBM, Intel, Cray, HP, Fujitsu, Nvidia, NEC, Red Hat, Texas Instruments, and Oracle Corporation. OpenMP uses a portable, scalable model that gives programmers a simple and flexible interface for developing parallel applications for platforms ranging from the standard desktop computer to the supercomputer. An application built wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Process Rare Event Sampling
Stochastic-process rare event sampling (SPRES) is a rare-event sampling method in computer simulation, designed specifically for non-equilibrium calculations, including those for which the rare-event rates are time-dependent (non-stationary process). To treat systems in which there is time dependence in the dynamics, due either to variation of an external parameter or to evolution of the system itself, the scheme for branching paths must be devised so as to achieve sampling which is distributed evenly in time and which takes account of changing fluxes through different regions of the phase space. Algorithm summary The SPRES algorithm branches simulation paths at fixed time intervals. The process of branching requires that identical paths can be made to diverge from each other, such as by changing the seed in the computer's random number generator. For systems which would be naturally considered as deterministic, it may be possible to inject an element of randomness, for instance ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stationary Process
In mathematics and statistics, a stationary process (or a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose unconditional joint probability distribution does not change when shifted in time. Consequently, parameters such as mean and variance also do not change over time. If you draw a line through the middle of a stationary process then it should be flat; it may have 'seasonal' cycles, but overall it does not trend up nor down. Since stationarity is an assumption underlying many statistical procedures used in time series analysis, non-stationary data are often transformed to become stationary. The most common cause of violation of stationarity is a trend in the mean, which can be due either to the presence of a unit root or of a deterministic trend. In the former case of a unit root, stochastic shocks have permanent effects, and the process is not mean-reverting. In the latter case of a deterministic trend, the process is called ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Space
In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables. It is the outer product of direct space and reciprocal space. The concept of phase space was developed in the late 19th century by Ludwig Boltzmann, Henri Poincaré, and Josiah Willard Gibbs. Introduction In a phase space, every degree of freedom or parameter of the system is represented as an axis of a multidimensional space; a one-dimensional system is called a phase line, while a two-dimensional system is called a phase plane. For every possible state of the system or allowed combination of values of the system's parameters, a point is included in the multidimensional space. The system's evolving state over time traces a path (a phase-space trajectory for the system) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Simulation
Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict. Computer simulations have become a useful tool for the mathematical modeling of many natural systems in physics (computational physics), astrophysics, climatology, chemistry, biology and manufacturing, as well as human systems in economics, psychology, social science, health care and engineering. Simulation of a system is represented as the running of the system's model. It can be used to explore and gain new insights into new technology and to estimate the performance of systems too complex for analytical solutions. Computer simulations are realized by running computer programs that can be either small, running almost instantly on small devices, or large ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
