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  • 1
    Electronic Resource
    Electronic Resource
    Consistently averaged hydrodynamic interaction for dumbbell models in elongational flow (1986)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 85 (1986), S. 1672-1675 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We apply the recently proposed consistent averaging approximation for the hydrodynamic interaction to elongational flow. This flow situation can be treated to a great extent analytically for Rouse and FENE-P dumbbells. In both cases expansions for the elongational viscosity are presented for low and high elongational rates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.451208
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  • 2
    Electronic Resource
    Electronic Resource
    A new model for polymer melts and concentrated solutions (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 1592-1602 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A new mesoscopic model is presented for polymer melts and concentrated solutions. It is a single Kramers chain model in which elementary motions of the Orwoll–Stockmayer type are allowed. However, for this model, the bead jumps are no longer given by a Markovian probability, but rather are described by "a waiting time distribution function.'' Such a distribution is supposed to occur when the chain is "frozen'' in space until a "gap'' in the solution or melt meets with the bead or chain segment. The time a bead must wait to jump is given by a distribution function with a single adjustable parameter β, which describes the long-time behavior of the distribution: ∼1/t1+β . We find that the model predicts non-Fickian diffusion in agreement with experimental data and Fickian diffusion for longer times which scales with chain length as 1/N2/α−1, where α is a function of β. For β=1.3, D∼1/N2.28. The autocorrelation of the end-to-end vector of the chain is a stretched-exponential form with a time constant which scales as the length of the chain to the 3.3 power for β=1.3.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.460714
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Continuous time simulation of the Doi–Edwards model (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 6327-6331 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A continuous time simulation algorithm for polymer melts is applied to the Doi–Edwards model. In this model a certain tube segment disappears when it is reached by either end of the primitive chain. The probability that this segment remains at a certain time is well-known analytically. In the underlying stochastic process a unit vector is chosen with new random orientation every time the diffusion process reaches one of its boundaries. To simulate this stochastic process an algorithm is used which is very similar to one introduced for transient network polymer models. In the special case of the Doi–Edwards model one can draw random birth times for the unit vectors from the appropriate probability distribution. The deterministic equations of motion are integrated analytically. This leads to a very efficient method for the simulation of the stochastic process.We compare the simulation results with results which were already obtained by other methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.458310
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  • 4
    Electronic Resource
    Electronic Resource
    Continuous time simulation of transient polymer network models (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 6322-6326 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A continuous time simulation algorithm for polymer melts is presented. The method is introduced via an explicit application to transient polymer network models, but it may be applied to a much larger class of models. The central quantity of the simulation is the lifetime of a strand. This can be calculated according to a proper distribution, which may depend on the orientation and length of the generated new strand. As the equation of motion of the strand can be integrated analytically during the lifetime of the strand, the procedure works much more efficiently than a previous simulation algorithm for transient network models. The material functions can be calculated as ensemble averages. The new method is shown to work for time-dependent flows. A simplified algorithm for steady flows is also given. Some predictions are made for a specific configuration-dependent transient network model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.458309
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  • 5
    Electronic Resource
    Electronic Resource
    How to build master equations for complex systems (1995)
    Springer
    Continuum mechanics and thermodynamics 7 (1995), S. 439-473 
    Details
    ISSN: 1432-0959
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Typical complex systems, e. g., complex chemical reactions, reaction-diffusion systems, and turbulent fluids are described on a macroscopic level, that is, neglecting fluctuations, with the help of deterministic equations for corresponding variables. In this article it is shown on a phenomenological level, that these systems can be described in terms of integer- or real-valued Markov processes as well, which are governed by master equations. The latter are constructed such that the macroscopic law and the fluctuations around it are reproduced correctly. Stochastic processes defined through master equations can easily be simulated. The efficiency, the stability and the parallelization of the algorithms for stochastic simulations are discussed for some examples. In the last part of the paper it is shown that the same phenomenological approach can be successfully applied to open quantum systems. The wave function is assumed to be a complex valued stochastic process in Hilbert space and the quantum master equation for the statistical operator is regarded as the equation of motion for the two-point correlation function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01175667
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  • 6
    Electronic Resource
    Electronic Resource
    Preface (1999)
    Springer
    Journal of superconductivity 12 (1999), S. 681-681 
    Details
    ISSN: 1572-9605
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007760321024
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  • 7
    Electronic Resource
    Electronic Resource
    Stochastic Wave Function Approach to Generalized Master Equations (1999)
    Springer
    Journal of superconductivity 12 (1999), S. 695-702 
    Details
    ISSN: 1572-9605
    Keywords: stochastic wave function ; generalized master equations ; time-convolutionless projection operator technique ; open quantum systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract A generalization of the stochastic wave function method is presented that allows the unraveling of arbitrary linear quantum master equations that are not necessarily in Lindblad form and, moreover, the explicit treatment of memory effects by employing the time-convolutionless projection operator technique. The crucial point of this construction is the description of the open system in a doubled Hilbert space, which has already been successfully used for the computation of multitime correlation functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007716506003
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  • 8
    Electronic Resource
    Electronic Resource
    On a Liouville-master equation formulation of open quantum systems (1995)
    Springer
    The European physical journal 98 (1995), S. 139-145 
    Details
    ISSN: 1434-6036
    Keywords: 42.50.Lc ; 02.50.Ga ; 02.70.Lq
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The dynamics of open quantum systems is formulated in terms of a probability distribution on the underlying Hilbert space. Defining the time-evolution of this probability distribution by means of a Liouvillemaster equation the time-dependent wave function of the system becomes a stochastic Markov process in the sense of classical probability theory. It is shown that the equation of motion for the two-point correlation function of the random wave function yields the quantum master equation for the statistical operator. Stochastic simulations of the Liouville-master equation are performed for a simple example from quantum optics and are shown to be in perfect agreement with the analytical solution of the corresponding equation for the statistical operator.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01318288
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    Paper (German National Licenses)
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  • 9
    Electronic Resource
    Electronic Resource
    A master equation investigation of coagulation reactions: Sol-gel transition (1994)
    Weinheim : Wiley-Blackwell
    Macromolecular Theory and Simulations 3 (1994), S. 585-599 
    Details
    ISSN: 1022-1344
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The kinetics of irreversible coagulation phenomena in spatially homogeneous systems is formulated in terms of a multivariate stochastic process. The latter is governed by a master equation for the joint probability distribution of the numbers of reacting species. An efficient numerical algorithm is used to simulate the complete time evolution of the stochastic process. The method is illustrated by simulating the coagulation reaction with configuration-dependent reaction kernels, Kij = (ij)ω, for clusters of mass i and j with 1/2 〈 ω ≤ 1, which are designed to model gelation phenomena. It is demonstrated that the stochastic simulation allows the determination of critical exponents and the gel point directly from the master equation. The results are compared to predictions of the rate equation approach to the sol-gel transition.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mats.1994.040030306
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