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Umbrella Sampling
Umbrella sampling is a technique in computational physics and chemistry, used to improve sampling of a system (or different systems) where ergodicity is hindered by the form of the system's energy landscape. It was first suggested by Torrie and Valleau in 1977. It is a particular physical application of the more general importance sampling in statistics. Systems in which an energy barrier separates two regions of configuration space may suffer from poor sampling. In Metropolis Monte Carlo runs, the low probability of overcoming the potential barrier can leave inaccessible configurations poorly sampled—or even entirely unsampled—by the simulation. An easily visualised example occurs with a solid at its melting point: considering the state of the system with an order parameter ''Q'', both liquid (low ''Q'') and solid (high ''Q'') phases are low in energy, but are separated by a free energy barrier at intermediate values of ''Q''. This prevents the simulation from adequately sa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ergodicity
In mathematics, ergodicity expresses the idea that a point of a moving system, either a dynamical system or a stochastic process, will eventually visit all parts of the space that the system moves in, in a uniform and random sense. This implies that the average behavior of the system can be deduced from the trajectory of a "typical" point. Equivalently, a sufficiently large collection of random samples from a process can represent the average statistical properties of the entire process. Ergodicity is a property of the system; it is a statement that the system cannot be reduced or factored into smaller components. Ergodic theory is the study of systems possessing ergodicity. Ergodic systems occur in a broad range of systems in physics and in geometry. This can be roughly understood to be due to a common phenomenon: the motion of particles, that is, geodesics on a hyperbolic manifold are divergent; when that manifold is compact, that is, of finite size, those orbits return to the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Potential Of Mean Force
When examining a system computationally one may be interested in knowing how the free energy changes as a function of some inter- or intramolecular coordinate (such as the distance between two atoms or a torsional angle). The free energy surface along the chosen coordinate is referred to as the potential of mean force (PMF). If the system of interest is in a solvent, then the PMF also incorporates the solvent effects. General description The PMF can be obtained in Monte Carlo or molecular dynamics simulations to examine how a system's energy changes as a function of some specific reaction coordinate parameter. For example, it may examine how the system's energy changes as a function of the distance between two residues, or as a protein is pulled through a lipid bilayer. It can be a geometrical coordinate or a more general energetic (solvent) coordinate. Often PMF simulations are used in conjunction with umbrella sampling, because typically the PMF simulation will fail to adequately s ... [...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] |
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 errors in ... [...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] |
Academic Press
Academic Press (AP) is an academic book publisher founded in 1941. It was acquired by Harcourt, Brace & World in 1969. Reed Elsevier bought Harcourt in 2000, and Academic Press is now an imprint of Elsevier. Academic Press publishes reference books, serials and online products in the subject areas of: * Communications engineering * Economics * Environmental science * Finance * Food science and nutrition * Geophysics * Life sciences * Mathematics and statistics * Neuroscience * Physical sciences * Psychology Well-known products include the ''Methods in Enzymology'' series and encyclopedias such as ''The International Encyclopedia of Public Health'' and the ''Encyclopedia of Neuroscience''. See also * Akademische Verlagsgesellschaft (AVG) — the German predecessor, founded in 1906 by Leo Jolowicz (1868–1940), the father of Walter Jolowicz Walter may refer to: People * Walter (name), both a surname and a given name * Little Walter, American blues harmonica player Marion Wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daan Frenkel
Daan Frenkel One or more of the preceding sentences incorporates text from the royalsociety.org website where: (born 1948, Amsterdam) is a Dutch computational physicist in the Department of Chemistry at the University of Cambridge. Education Frenkel completed his PhD at the University of Amsterdam in 1977 in experimental physical chemistry. Career and research Frenkel worked as postdoctoral research fellow in the Chemistry and Biochemistry Department at the University of California, Los Angeles (UCLA), subsequently at Shell and at the University of Utrecht. Between 1987 and 2007, Frenkel carried out his research at the FOM Institute for Atomic and Molecular Physics (AMOLF) in Amsterdam where he has been employed since 1987. In the same period, he was appointed (part-time) professor at the Universities of Utrecht and Amsterdam. From 2011 to 2015 he was Head of the Department of Chemistry at the University of Cambridge. Since 2007 he is a Professor of Chemistry at the Univers ... [...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] |
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] |
Free Energy Perturbation
Free energy perturbation (FEP) is a method based on statistical mechanics that is used in computational chemistry for computing free energy differences from molecular dynamics or Metropolis Monte Carlo simulations. The FEP method was introduced by Robert W. Zwanzig in 1954. According to the free-energy perturbation method, the free energy difference for going from state A to state B is obtained from the following equation, known as the ''Zwanzig equation'': :\Delta F(\mathbf \rightarrow \mathbf) = F_\mathbf - F_\mathbf = -k_\mathrm T \ln \left \langle \exp \left ( - \frac \right ) \right \rangle _\mathbf where ''T'' is the temperature, ''k''B is Boltzmann's constant, and the angular brackets denote an average over a simulation run for state A. In practice, one runs a normal simulation for state A, but each time a new configuration is accepted, the energy for state B is also computed. The difference between states A and B may be in the atom types involved, in which case the Δ''F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reaction Rate
The reaction rate or rate of reaction is the speed at which a chemical reaction takes place, defined as proportional to the increase in the concentration of a product per unit time and to the decrease in the concentration of a reactant per unit time. Reaction rates can vary dramatically. For example, the oxidative rusting of iron under Earth's atmosphere is a slow reaction that can take many years, but the combustion of cellulose in a fire is a reaction that takes place in fractions of a second. For most reactions, the rate decreases as the reaction proceeds. A reaction's rate can be determined by measuring the changes in concentration over time. Chemical kinetics is the part of physical chemistry that concerns how rates of chemical reactions are measured and predicted, and how reaction-rate data can be used to deduce probable reaction mechanisms. The concepts of chemical kinetics are applied in many disciplines, such as chemical engineering, enzymology and environmental engin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Likelihood
In statistics, maximum likelihood estimation (MLE) is a method of estimation theory, estimating the Statistical parameter, parameters of an assumed probability distribution, given some observed data. This is achieved by Mathematical optimization, maximizing a likelihood function so that, under the assumed statistical model, the Realization (probability), observed data is most probable. The point estimate, point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference. If the likelihood function is Differentiable function, differentiable, the derivative test for finding maxima can be applied. In some cases, the first-order conditions of the likelihood function can be solved analytically; for instance, the ordinary least squares estimator for a linear regression model maximizes the likelihood when ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
