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  • 1
    Unknown
    Boston : Academic Press
    Call number: B086:85
    Keywords: Markov processes
    Pages: xxi, 565 p. : ill.
    Edition: Transferred to digital printing 2008
    ISBN: 9780122839559
    Signatur Availability
    B086:85 departmental collection or stack – please contact the library
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  • 2
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1572-9613
    Keywords: Chemical kinetics ; master equations ; collision probabilities ; one-dimensional gas ; stochastic processes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A simple argument advanced recently in support of the legitimacy of the stochastic formulation of chemical kinetics has been criticized because it seems to require the imminent collision of widely separated molecules. It is argued here that this criticism is unwarranted because it is based on an incorrect use of probabilities. To illustrate the various probabilistic considerations involved, a detailed analysis is presented of a closely related but mathematically simpler problem: the calculation of the collision probability per unit time for a thermally equilibrized one-dimensional gas of point particles.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1572-9516
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Quantum mechanics posits that the wave function of a one-particle system evolves with time according to the Schrödinger equation, and furthermore has a square modulus that serves as a probability density function for the position of the particle. It is natural to wonder if this stochastic characterization of the particle's position can be framed as a univariate continuous Markov process, sometimes also called a classical diffusion process, whose temporal evolution is governed by the classically transparent equations of Langevin and Fokker-Planck. It is shown here that this cannot generally be done in a consistent way, despite recent suggestions to the contrary.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 83 (1998), S. 3118-3128 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Continuous Markov process theory is used to model the electrical noise induced in a passive wire loop by the thermal motions of ions in a nearby solution. The ions, being charged particles in Brownian motion, generate a fluctuating magnetic field, and that in turn induces a fluctuating electromotive force (emf) that augments the loop's Johnson emf. It is shown that the spectral density function of the equilibrium current in the wire loop is thereby increased, for moderate cycle frequencies ν, by approximately a factor (1+αν2), where α is determined by the geometry of the system, the resistance of the loop, and the charges, diffusion coefficients, and concentrations of the solution ions. It is also shown that the temporal trajectory of the loop current becomes "thickened," in a randomly fuzzy way, by an approximate factor of the form (1+β)1/2, where β depends not only on the aforementioned parameters that determine α, but also on the hydrated masses of the ions. These findings may be useful for estimating the intrinsic background noise in the detector coil of a medical magnetic resonance imaging machine, or any other sensitive electronic circuit that is required to operate in an immediate "salt water" environment.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 11 (2001), S. 548-562 
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The time-dependent measurement probabilities for the simple two-state quantum oscillator seem to invite description as a classical two-state stochastic process. It has been shown that such a description cannot be achieved using a Markov process. Constructing a more general non-Markov process is a challenging task, requiring as it does the proper generalizations of the Markovian Chapman–Kolmogorov and master equations. Here we describe those non-Markovian generalizations in some detail, and we then apply them to the two-state quantum oscillator. We devise two non-Markovian processes that correctly model the measurement statistics of the oscillator, we clarify a third modeling process that was proposed earlier by others, and we exhibit numerical simulations of all three processes. Our results illuminate some interesting though widely unappreciated points in the theory of non-Markovian stochastic processes. But since quantum theory does not tell us which one of these quite different modeling processes "really" describes the behavior of the oscillator, and also since none of these processes says anything about the dynamics of other (noncommuting) oscillator observables, we can see no justification for regarding any of these processes as being fundamentally descriptive of quantum dynamics. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 115 (2001), S. 1716-1733 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The stochastic simulation algorithm (SSA) is an essentially exact procedure for numerically simulating the time evolution of a well-stirred chemically reacting system. Despite recent major improvements in the efficiency of the SSA, its drawback remains the great amount of computer time that is often required to simulate a desired amount of system time. Presented here is the "τ-leap" method, an approximate procedure that in some circumstances can produce significant gains in simulation speed with acceptable losses in accuracy. Some primitive strategies for control parameter selection and error mitigation for the τ-leap method are described, and simulation results for two simple model systems are exhibited. With further refinement, the τ-leap method should provide a viable way of segueing from the exact SSA to the approximate chemical Langevin equation, and thence to the conventional deterministic reaction rate equation, as the system size becomes larger.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 297-306 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The stochastic dynamical behavior of a well-stirred mixture of N molecular species that chemically interact through M reaction channels is accurately described by the chemical master equation. It is shown here that, whenever two explicit dynamical conditions are satisfied, the microphysical premise from which the chemical master equation is derived leads directly to an approximate time-evolution equation of the Langevin type. This chemical Langevin equation is the same as one studied earlier by Kurtz, in contradistinction to some other earlier proposed forms that assume a deterministic macroscopic evolution law. The novel aspect of the present analysis is that it shows that the accuracy of the equation depends on the satisfaction of certain specific conditions that can change from moment to moment, rather than on a static system size parameter. The derivation affords a new perspective on the origin and magnitude of noise in a chemically reacting system. It also clarifies the connection between the stochastically correct chemical master equation, and the deterministic but often satisfactory reaction rate equation.
    Type of Medium: Electronic Resource
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