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Advanced Computer Simulation Approaches for Soft Matter by Marcus Müller, Friederike Schmid (auth.), Christian Holm, PDF

By Marcus Müller, Friederike Schmid (auth.), Christian Holm, Kurt Kremer (eds.)

ISBN-10: 3540260919

ISBN-13: 9783540260912

This sequence offers serious studies of the current and destiny developments in polymer and biopolymer technology together with chemistry, actual chemistry, physics and fabrics technology. it really is addressed to all scientists at universities and in who desire to maintain abreast of advances within the issues coated.

Impact issue rating: continuously #1 in Polymer technological know-how. additional info in addition to the digital model of the full content material on hand at: www.springerlink.com

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G(xn ) + (63) i,j In the original Anderson mixing scheme, the (n + 1)th guess xn+1 is given by xn+1 = g An . More generally, the method can be combined with simple mixing xn+1 = xAn + λ g An – xAn . (64) This summarizes some methods which can be used to solve the self-consistent equations. Regardless of the particular choice, the single most time-consuming part in every SCF or EP calculation is the repeated solution of the diffusion equation (Eqs. 19 and 20). Therefore, the next task is to find an efficient method to Fluctuations and Dynamics in Self-Consistent Field Theories 21 solve equations of the type ∂q(r, t) R2e = ∆q(r, t) – W(r)q(r, t) .

In the vicinity of a Lifshitz point self-consistent field theory pre√ dicts the interface stiffness to vanish like κ ∼ kB T N¯ t 5/4 which is compatible with the Ginzburg criterion (Eq. 73) [63]. Similar arguments hold for a tricritical Lifshitz point, where a Lifshitz point happens to merge with a regular tricritical point. Here, fluctuations are important if t≡ χN – χt N χt N N¯ –2/3 (74) Again this √ behavior is compatible with the behavior of the bending stiffness, κ ∼ kB T N¯ t 3/4 , as obtained from self-consistent field calculations [63].

Therefore, we can use the free energy functional H [W] from Eq. 42 and describe the dynamics of the field W through the relaxational dynamics of a model B system, referring to the classification introduced by Hohenberg and Halperin [94]. ∂W(r, t) = ∇r ∂t dd rΛEPD (r, r )∇r µW (r , t) + η(r, t) (121) Fluctuations and Dynamics in Self-Consistent Field Theories 41 with the chemical potential µW being the first derivative of the free energy H [W] with respect to the order parameter W, √ N¯ kB T W + χN φA∗ (r) – φB∗ (r) δH [W(r)] = , (122) µW (r) = δW(r) 2χN Rde ΛEPD is a kinetic Onsager coefficient, and η denotes noise that satisfies the fluctuation-dissipation theorem.

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Advanced Computer Simulation Approaches for Soft Matter Sciences II by Marcus Müller, Friederike Schmid (auth.), Christian Holm, Kurt Kremer (eds.)


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