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  • 1
    Electronic Resource
    Electronic Resource
    Faber and Newton polynomial integrators for open-system density matrix propagation (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 5538-5547 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Two polynomial expansions of the time-evolution superoperator to directly integrate Markovian Liouville–von Neumann (LvN) equations for quantum open systems, namely the Newton interpolation and the Faber approximation, are presented and critically compared. Details on the numerical implementation including error control, and on the performance of either method are given. In a first physical application, a damped harmonic oscillator is considered. Then, the Faber approximation is applied to compute a condensed phase absorption spectrum, for which a semianalytical expression is derived. Finally, even more general applications are discussed. In all applications considered here it is found that both the Newton and Faber integrators are fast, general, stable, and accurate. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.478451
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    Paper (German National Licenses)
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  • 2
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    Chebyshev-Approximation for Wavepacket-Dynamics: better than expected (1996)
    Details
    Publication Date: 2014-02-26
    Description: The aim of this work is to study the accuracy and stability of the Chebyshev--approximation method as a time--discretization for wavepacket dynamics. For this frequently used discretization we introduce estimates of the approximation and round--off error. These estimates mathematically confirm the stability of the Chebyshev--approximation with respect to round--off errors, especially for very large stepsizes. But the results also disclose threads to the stability due to large spatial dimensions. All theoretical statements are illustrated by numerical simulations of an analytically solvable example, the harmonic quantum oszillator.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 3
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    From Simulation Data to Conformational Ensembles: Structure and Dynamics based Methods (1998)
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    Publication Date: 2014-02-26
    Description: Statistical methods for analyzing large data sets of molecular configurations within the chemical concept of molecular conformations are described. The strategies are based on dependencies between configurations of a molecular ensemble; the article concentrates on dependencies induces by a) correlations between the molecular degrees of freedom, b) geometrical similarities of configurations, and c) dynamical relations between subsets of configurations. The statistical technique realizing aspect a) is based on an approach suggested by {\sc Amadei et al.} (Proteins, 17 (1993)). It allows to identify essential degrees of freedom of a molecular system and is extended in order to determine single configurations as representatives for the crucial features related to these essential degrees of freedom. Aspects b) and c) are based on statistical cluster methods. They lead to a decomposition of the available simulation data into {\em conformational ensembles} or {\em subsets} with the property that all configurations in one of these subsets share a common chemical property. In contrast to the restriction to single representative conformations, conformational ensembles include information about, e.g., structural flexibility or dynamical connectivity. The conceptual similarities and differences of the three approaches are discussed in detail and are illustrated by application to simulation data originating from a hybrid Monte Carlo sampling of a triribonucleotide.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 4
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    A Direct Approach to Conformational Dynamics based on Hybrid Monte Carlo (1999)
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    Publication Date: 2014-02-26
    Description: Recently, a novel concept for the computation of essential features of the dynamics of Hamiltonian systems (such as molecular dynamics) has been proposed. The realization of this concept had been based on subdivision techniques applied to the Frobenius--Perron operator for the dynamical system. The present paper suggests an alternative but related concept that merges the conceptual advantages of the dynamical systems approach with the appropriate statistical physics framework. This approach allows to define the phrase ``conformation'' in terms of the dynamical behavior of the molecular system and to characterize the dynamical stability of conformations. In a first step, the frequency of conformational changes is characterized in statistical terms leading to the definition of some Markov operator $T$ that describes the corresponding transition probabilities within the canonical ensemble. In a second step, a discretization of $T$ via specific hybrid Monte Carlo techniques is shown to lead to a stochastic matrix $P$. With these theoretical preparations, an identification algorithm for conformations is applicable. It is demonstrated that the discretization of $T$ can be restricted to few essential degrees of freedom so that the combinatorial explosion of discretization boxes is prevented and biomolecular systems can be attacked. Numerical results for the n-pentane molecule and the triribonucleotide adenylyl\emph{(3'-5')}cytidylyl\emph{(3'-5')}cytidin are given and interpreted.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 5
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    On Conformational Dynamics induced by Langevin Processes (1999)
    Details
    Publication Date: 2014-02-26
    Description: The function of many important biomolecules is related to their dynamic properties and their ability to switch between different {\em conformations}, which are understood as {\em almost invariant} or {\em metastable} subsets of the positional state space of the system. Recently, the present authors and their coworkers presented a novel algorithmic scheme for the direct numerical determination of such metastable subsets and the transition probability between them. Although being different in most aspects, this method exploits the same basic idea as {\sc Dellnitz} and {\sc Junge} in their approach to almost invariance in discrete dynamical systems: the almost invariant sets are computed via certain eigenvectors of the Markov operators associated with the dynamical behavior. In the present article we analyze the application of this approach to (high--friction) Langevin models describing the dynamical behavior of molecular systems coupled to a heat bath. We will see that this can be related to theoretical results for (symmetric) semigroups of Markov operators going back to {\sc Davies}. We concentrate on a comparison of our approach in respect to random perturbations of dynamical systems.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 6
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    Identification of Almost Invariant Aggregates in Reversible Nearly Uncoupled Markov Chains (2000)
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    Publication Date: 2020-10-02
    Language: English
    Type: article , doc-type:article
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  • 7
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    Self-Organizing Maps Combined with Eigenmode Analysis for Automated Cluster Identification (2000)
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    Publication Date: 2020-10-02
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
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  • 8
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    From Simulation Data to Conformational Ensembles (1999)
    Details
    Publication Date: 2021-01-21
    Language: English
    Type: article , doc-type:article
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    OPUS
  • 9
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    A Direct Approach to Conformational Dynamics Based on Hybrid Monte Carlo (1999)
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    Publication Date: 2020-10-02
    Language: English
    Type: article , doc-type:article
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  • 10
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    Transfer operator approach to conformational dynamics in biomolecular systems (2001)
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    Publication Date: 2020-10-02
    Language: English
    Type: bookpart , doc-type:bookPart
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