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For a fully quantitative comparison between MCT and simulation, the required static input has to be obtained with sufficiently high precision. Because of this restrictive condition, there have been only a limited number of such comparative studies. At present, they include a model for amorphous SiO2 melts [PRLTAO 0031-9007 10.1103/PhysRevLett.86.648
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We have explicitly compared the dynamics resulting with and without the use of the equivalent-site approximation 15 for short Gaussian chains where chain-end effects are more prominent. No substantial differences have been found.
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We have explicitly compared the dynamics resulting with and without the use of the equivalent-site approximation 15 for short Gaussian chains where chain-end effects are more prominent. No substantial differences have been found.
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Without any further approximation introduced in the main text, a typical CPU time requested to solve the full matrix MCT equations 22 26 for the present model (N=10) at a temperature near the MCT critical point Tc is estimated to be of the order of one month on a Pentium IV processor with 2.80 GHz clock speed.
-
Without any further approximation introduced in the main text, a typical CPU time requested to solve the full matrix MCT equations 22 26 for the present model (N=10) at a temperature near the MCT critical point Tc is estimated to be of the order of one month on a Pentium IV processor with 2.80 GHz clock speed.
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The regular contribution, which is not taken into account in our theory, might contain some polymer-specific (e.g., chain-length-dependent) features.
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The regular contribution, which is not taken into account in our theory, might contain some polymer-specific (e.g., chain-length-dependent) features.
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For example, the long-time limit of the coherent density correlator f (q) (q,t→) can be determined by solving Eq. 55, and one has to solve analogous matrix equations for obtaining that of the single-chain density correlators F ab s (q,t→). The solution of Eq. 55 can be found numerically by an iterative procedure f (j+1) (q) / [1- f (j+1) (q)] = Fq [f (j)] starting with f (0) (q) =1, and is obtained as f (q) = limj→ f (j) (q). The convergence of this iterative procedure is ruled by the spectral radius of a so-called stability matrix which can be defined in terms of the mode-coupling functional Fq. The stability matrix attains the maximum eigenvalue unity at the MCT critical point Tc, and more iterations are necessary to solve Eq. 55 closer to Tc. However, this does not apply to the corresponding iterative procedure for solving the equations for the single-chain density correlators, and a much smaller number of iterations is sufficient for obtaining F ab s (q,t→).
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We confirmed from our independent computer simulations performed for a bead-spring model similar to the one studied here that the wave vector at which the high-temperature collective dynamics is slowest does not shift with N.
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We confirmed from our independent computer simulations performed for a bead-spring model similar to the one studied here that the wave vector at which the high-temperature collective dynamics is slowest does not shift with N.
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