<i>Stochastic Processes in Physics and Chemistry</i>

Kampen, N.G. Van; Reinhardt, William P.

doi:10.1063/1.2915501

Cited by 1,273 publications

(397 citation statements)

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“…In particular, it is assumed that during a metadynamics simulation all the microscopic variables different from the macroscopic reaction coordinate z are always in the equilibrium state corresponding to the value of z. This property is known with the name of Markov property, 32 and it summarizes the main assumption of the algorithm: all the slow modes of the system coupled to the reaction under study have to be known a priori and they have to be included in the number of the reaction coordinates. Therefore, metadynamics should be considered a quasi-equilibrium method, in which the knowledge about the variables that capture the mechanism of a reaction is exploited to gain insight on the transition states and more generally to compute the free energy landscape along the relevant reaction coordinates.…”

Section: Metadynamics Simulation: History-dependent Algorithms In Nonmentioning

confidence: 99%

“…45 The JE [eq. (32)] is seemingly a simpler route than the WFT [eq. (31)] to evaluate the full free energy profile along a given reaction coordinate.…”

Section: Steered Molecular Dynamicsmentioning

confidence: 99%

“…However, when the change is performed in a finite time, generally the final distribution is not an equilibrium, canonical distribution, and relations similar to eqs. (31) and (32) are needed to extract equilibrium informations from nonequilibrium experiments. Even if the idea of extending the WFT and the JE to thermal changes dates back to the end of the 1990s, 55,56 their application to Nosé-Hoover thermostatted dynamics recent.…”

Section: Implementation In Oracmentioning

confidence: 99%

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ORAC: A molecular dynamics simulation program to explore free energy surfaces in biomolecular systems at the atomistic level

et al. 2009

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Abstract:We present the new release of the ORAC engine (Procacci et al., Comput Chem 1997, 18, 1834, a FORTRAN suite to simulate complex biosystems at the atomistic level. The previous release of the ORAC code included multiple time steps integration, smooth particle mesh Ewald method, constant pressure and constant temperature simulations. The present release has been supplemented with the most advanced techniques for enhanced sampling in atomistic systems including replica exchange with solute tempering, metadynamics and steered molecular dynamics. All these computational technologies have been implemented for parallel architectures using the standard MPI communication protocol. ORAC is an open-source program distributed free of charge under the GNU general public license (GPL) at

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Section: Metadynamics Simulation: History-dependent Algorithms In Nonmentioning

confidence: 99%

“…45 The JE [eq. (32)] is seemingly a simpler route than the WFT [eq. (31)] to evaluate the full free energy profile along a given reaction coordinate.…”

Section: Steered Molecular Dynamicsmentioning

confidence: 99%

Section: Implementation In Oracmentioning

confidence: 99%

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ORAC: A molecular dynamics simulation program to explore free energy surfaces in biomolecular systems at the atomistic level

et al. 2009

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“…61 Many good books explain the methodology thoroughly. 54,59,62,64 Rather than repeating this classical derivation, we present a derivation for the Lie group case. In fact, this result is also known as shown in refs.…”

Section: Fokker-planck Equationsmentioning

confidence: 99%

Kinematic state estimation and motion planning for stochastic nonholonomic systems using the exponential map

Park¹,

Liu²,

et al. 2008

Robotica

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SUMMARYA nonholonomic system subjected to external noise from the environment, or internal noise in its own actuators, will evolve in a stochastic manner described by an ensemble of trajectories. This ensemble of trajectories is equivalent to the solution of a Fokker-Planck equation that typically evolves on a Lie group. If the most likely state of such a system is to be estimated, and plans for subsequent motions from the current state are to be made so as to move the system to a desired state with high probability, then modeling how the probability density of the system evolves is critical. Methods for solving Fokker-Planck equations that evolve on Lie groups then become important. Such equations can be solved using the operational properties of group Fourier transforms in which irreducible unitary representation (IUR) matrices play a critical role. Therefore, we develop a simple approach for the numerical approximation of all the IUR matrices for two of the groups of most interest in robotics: the rotation group in three-dimensional space, SO(3), and the Euclidean motion group of the plane, SE(2). This approach uses the exponential mapping from the Lie algebras of these groups, and takes advantage of the sparse nature of the Lie algebra representation matrices. Other techniques for density estimation on groups are also explored. The computed densities are applied in the context of probabilistic path planning for kinematic cart in the plane and flexible needle steering in three-dimensional space. In these examples the injection of artificial noise into the computational models (rather than noise in the actual physical systems) serves as a tool to search the configuration spaces and plan paths. Finally, we illustrate how density estimation problems arise in the characterization of physical noise in orientational sensors such as gyroscopes.

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“…We specify individual rates of movement, birth, and mortality in an individual-based stochastic framework, using a birthdeath master equation (van Kampen 2007;Gardiner 2009). The numbers of predators and prey that inhabit a patch at any given time is governed by stochastic processes and will therefore be represented by random variables.…”

Section: Stochastic Processesmentioning

confidence: 99%

Population-level consequences of heterospecific density-dependent movements in predator–prey systems

Sjödin

Brännström

Söderquist

et al. 2014

Journal of Theoretical Biology

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In this paper we elucidate how small-scale movements, such as those associated with searching for food and avoiding predators, affect the stability of predator-prey dynamics. We investigate an individual-based Lotka-Volterra model with density dependent movement, in which the predator and prey populations live in a very large number of coupled patches. The rates at which individuals leave patches depend on the local densities of heterospecifics, giving rise to one reaction norm for each of the two species. Movement rates are assumed to be much faster than demographics rates. A spatial structure of predators and prey emerges which affects the global population dynamics. We derive a criterion which reveals how demographic stability depends on the relationships between the per capita covariance and densities of predators and prey. Specifically, we establish that a positive relationship with prey density and a negative relationship with predator density tend to be stabilizing. On a more mechanistic level we show how these relationships are linked to the movement reaction norms of predators and prey. Numerical results show that these findings hold both for local and global movements, i.e., both when migration is biased towards neighboring patches and when all patches are reached with equal probability.

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Stochastic Processes in Physics and Chemistry

Cited by 1,273 publications

References 0 publications

ORAC: A molecular dynamics simulation program to explore free energy surfaces in biomolecular systems at the atomistic level

ORAC: A molecular dynamics simulation program to explore free energy surfaces in biomolecular systems at the atomistic level

Kinematic state estimation and motion planning for stochastic nonholonomic systems using the exponential map

Population-level consequences of heterospecific density-dependent movements in predator–prey systems

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