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  • 1
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We consider a Markov chain modeling competition between two alleles in a haploid population of constant size and undergoing mutation, selection and Fisher-Wright mating. The Markov chain is rescaled to a diffusion process. We study the interaction of external noise (due to a random selection coefficient) and internal fluctuations (due to mating); the interaction is found to be additive. The stationary probability density displays a critical point. We draw an analogy between the behavior of the probability density at the critical point and the theory of phase transitions; critical exponents are introduced and calculated. We also analyze the effect of external noise on the genetic diversity of the population and on mean first passage times of the gene frequency.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 117 (2002), S. 2469-2473 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: This article constructs trajectories associated with various boundary conditions for the Smoluchowski equation on an interval. Single-particle diffusion processes are first constructed by taking the diffusion limits of random walks. The diffusion limit gives both boundary conditions which enforce the single-particle constraint and properties of underlying trajectories at those boundaries. Mean-field diffusions are then obtained as limits of sums of single-particle processes. The results help to interpret the application of diffusion models to both ion channels and wider pores that facilitate molecular transport across membranes. Potential applications to Brownian dynamics simulations are discussed. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 114 (2001), S. 76-83 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The lumped state approximation (LSA) is a method for handling boundary conditions for diffusion on an interval which simplifies the description of transitions into and out of the interval. It was originally motivated by the problem of proton conduction through the ion channel gramicidin. This paper discusses the mean first passage time of a diffuser crossing a potential barrier in the lumped state approximation. The LSA mean first passage time is shown to be identical to a different quantity, the interior mean first passage time, clarifying the nature of the approximation. We also discuss a variant of the LSA in which dependence on an applied electrical potential is made explicit; an optimal value for an effective electrical distance is found. A detailed comparison is made of the LSA mean first passage time with several other formulations of the mean time to cross a barrier. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 54 (1989), S. 1175-1188 
    ISSN: 1572-9613
    Keywords: Normal form ; noise ; thermal counterflow ; TI–TII transition ; noise-induced transition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Noise may be used as a probe of the dynamics of a nonlinear system. Weak noise provides information on the local dynamics near a transition. This information can be helpful for identifying the underlying bifurcation. The normal form of the bifurcation can then be used as a starting point for a phenomenological model of the system. Such an approach furnishes a unified explanation of the experimental data near the transition between superfluid turbulent states TI and TII in liquid helium counterflow. Strong external noise probes global features of the nonlinearities of a system. It may also dramatically affect the dynamical behavior of the system and give rise to noise-induced transitions. The problems of modeling this phenomenon in the liquid helium counterflow system are discussed and a first model, providing a unified description of the experimental observations for weak and strong noise, is developed.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 29 (1990), S. 1331-1349 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We obtain an analytical solution for the binding of 2-site ligands to a heterogeneous lattice. The model also describes the kinetics of chemical reactions between adjacent pendant groups of a copolymer. Our analysis is based on the principle of independence, as formulated by Gonzalez and Hemmer. Several special cases are solved in closed form; a power series solution is developed for the general problem. The results may be modified to take into account fixed total ligand. We also analyze competition between 1-site and 2-site ligands. As an illustration of the results, we examine in detail the kinetics and final extent of binding for two special cases.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Publication Date: 1978-12-01
    Print ISSN: 0003-2697
    Electronic ISSN: 1096-0309
    Topics: Biology , Chemistry and Pharmacology
    Published by Elsevier
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