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  • 21
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Macromolecules 26 (1993), S. 235-247 
    ISSN: 1520-5835
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 22
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Biochemistry 6 (1967), S. 3791-3800 
    ISSN: 1520-4995
    Source: ACS Legacy Archives
    Topics: Biology , Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 23
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 8214-8224 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We use the maximum-entropy method to calculate the chain-length distribution as a function of time for cooperative polymerization models involving nucleation and growth. At least the first two moments of the distribution are required for the maximum-entropy method. To obtain the moments we use a generating function to give the moment rate equations which in general involves an infinite set of coupled differential equations which can be truncated to give a finite set by using various closure approximations. In particular we use the maximum-entropy method to treat the reversible growth of chains from a fixed concentration of initiators in which case the initial distribution is a sharp Poisson-type one that then evolves slowly to the very broad equilibrium distribution. For this model we find that there is a scaled time that reduces the time dependence of the moments to a universal set of asymptotic curves. © 1999 American Institute of Physics.
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  • 24
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 106 (1997), S. 1628-1640 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We continue our investigation of a model lattice polymer where only local conformational changes (cooperative trans ↔ cis transitions) are allowed requiring the diffusion of randomness into the interior from the ends of the chain for the process of contraction of an initially extended (all-trans) chain. Simulations of the kinetics show that in the early stages of the dynamics there is a marked tendency for the cis states entering the chain to exist largely on either odd or even numbered sites in the chain thus generating a sublattice asymmetry or order in the molecule, a pattern that is largely lost at equilibrium. A similar soluble continuum model suggests that the net amount of cis in the chain should increase with time approximately as a simple exponential with the relaxation time proportional to the square of the chain length. This suggests that if a given dynamic function is plotted versus the scaled time (time divided by the chain length squared) one will obtain a general function independent of chain length. Simulations of the kinetics of the net amount of cis in the system support this scaling precisely. The difference in the number of cis states on the odd and even sublattices approaches a limiting scaled form, but develops a maximum as the chain length increases. The kinetics of the decrease in the end-to-end distance on contraction slowly approaches a limiting form in the scaled time, developing a t−1/2 tail as the chain length goes to infinity. This later behavior is similar to the critical slowing down in the mean-field approximation to relaxation in the three-dimensional Ising model near the critical point. © 1997 American Institute of Physics.
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  • 25
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Journal of the American Chemical Society 107 (1985), S. 4760-4767 
    ISSN: 1520-5126
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 26
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 112 (2000), S. 6554-6562 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We use the maximum-entropy method to calculate molecular energy distributions from the moments of the distribution which in turn can be obtained from the temperature dependence of the heat capacity. If one knows the temperature expansion of the heat capacity through the nth power of the temperature, this then gives the exact first (n+2) energy moments. We illustrate the method for the ideal gas (the Maxwell–Boltzmann distribution of kinetic energy) and then use a model function to show that if one knows four or more moments of the energy distribution this allows one to resolve two or more distinct peaks in this function. We examine argon above the critical pressure, a one-dimensional model, and the protein barnase, all of which exhibit bimodal energy distributions. © 2000 American Institute of Physics.
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  • 27
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 6530-6537 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We compare upper and lower bounds for the rate of the reversible, cooperative adsorption of hard particles from a reservoir at constant activity to a lattice surface where the only cooperative effect is excluded volume. The adsorption rate is proportional to the density of groups of unoccupied lattice sites: holes, large enough to accommodate a particle. The bounds on the rate of adsorption are then bounds on the density of holes. The upper bound for particles that are infinitely mobile on the surface is obtained from the equilibrium Mayer activity series for the pressure, while the lower bound is obtained from the extensive exact series calculated by Gan and Wang [J. Chem. Phys. 108, 3010 (1998)] for the case of irreversible random sequential adsorption where the particles are immobile once adsorbed. In all cases the bounds coincide at low densities. For the one-dimensional lattice with nearest-neighbor exclusion (where the bounds are known exactly) the upper and lower bounds are very close for all densities below the limit of random close packing as they are for the adsorption of hard dimers on two-dimensional lattices. Thus in these cases equilibrium statistical mechanics can give useful information about the kinetics of cooperative processes. © 1999 American Institute of Physics.
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  • 28
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 55 (1989), S. 389-415 
    ISSN: 1572-9613
    Keywords: Cooperative kinetics ; time power series ; radius of convergence ; singularities
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Exact 15-term series expansions are given for the cooperative kinetics of adsorption of particles to a one-dimensional lattice with nearest-neighbor exclusion. Padé approximants to various forms of the series accurately describe the relaxation process, which is found to be well-approximated by assuming instantaneous internal equilibrium on the lattice. The series do not describe the very last stages of decay to equilibrium well and it has not been possible to extract from them the limiting relaxation parameters. The series show that the rate of change of the particle density on the lattice is not analytic in the density when expanded about the equilibrium state.
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  • 29
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 61 (1990), S. 765-802 
    ISSN: 1572-9613
    Keywords: Cooperative relaxation ; time power series ; virial series ; kinetic Ising model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The coefficients in power series in the variable time that describe relaxation in a cooperative system can be calculated using a combinatorial approach where one considers how many ways one can introduce a given number of properly defined events in a system. The coefficients obtained in this manner can be related to the equilibrium virial coefficients for a mixture. If one assumes rapid internal equilibration, the relaxation process can be expressed completely in terms of the viral coefficients for a mixture with at most one solute particle, or, in some cases, just the virial coefficients for a single-component system. Thus, equilibrium virial coefficients can give useful information about the time evolution of processes in cooperative systems.
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  • 30
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 5 (1972), S. 159-171 
    ISSN: 1572-9613
    Keywords: Radial distribution function ; lattice solution ; one-dimensional ; matrix formulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract It is pointed out that the size of the matrix required to formulate the grand partition function for a one-dimensional lattice fluid for a fixed and finite range of the interatomic potential varies linearly with the density of lattice points used and hence is much smaller and more manageable than the expected size (which varies exponentially with the same quantity) and thus allows very fine grids to be examined. Using the matrix treatment of the grand partition function, it is shown that the radial distribution function for a one-dimensional fluid or solution can be formulated as an explicit matrix product which is simply performed by computer. The resulting distribution functions (which can be extrapolated to the continuum by varying the lattice spacing) are useful as starting solutions for the iterative solution of integral equations for three-dimensional fluids.
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