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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 2561-2562 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A spin glass on a one-dimensional Ising lattice is considered. The entropy at fixed nonuniform bond and field energies is written down as a functional of singlet and pair spin expectations, in terms of which bond and field energies are then expressed. The solution is reformulated in terms of effective fields which, in a spin-glass ensemble, are distributed as in a Markov chain. This result, and the corresponding free energy, shows that the effective field approximation previously used is exact for such systems, an assertion which extends to Cayley trees.
    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 101 (1994), S. 4995-5012 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: As molecular dynamics simulations continue to provide important insights into biomolecular structure and function, a growing demand for increasing the time span of the simulations is emerging. Our focus here is developing a new algorithm, LIN (Langevin/implicit-Euler/normal mode), that combines normal-mode and implicit-integration techniques, for large time step biomolecular applications. In the normal-mode phase of LIN, we solve an approximate linearized Langevin formulation to resolve the rapidly varying components of the motion. In the implicit phase, we resolve the remaining components of the motion by numerical integration with the implicit-Euler scheme. Developments of the normal-mode phase of LIN are discussed in this paper. Specifically, we solve two crucial issues of the method. The first involves how to choose and how often to update the Hessian approximation for the linearized Langevin equation. This approximation must be computationally feasible and physically reasonable to capture the motion in the higher end of the vibrational spectrum. Three such general Hessian approximations are discussed. The related issue—the frequency of the Hessian update—is analyzed by projecting the motion onto the different vibrational modes. This analysis demonstrates that a one-picosecond interval is reasonable for updating the Hessian in the model system examined here.In this connection, we illustrate that the high-frequency motions are highly localized while the low-frequency motions are delocalized. We also show rigorously that the mode amplitudes are inversely proportional to the frequency (consistent with the equipartition theorem), with 90% of the displacement fluctuations coming from a very small group of low-frequency modes. Anharmonic effects essentially influence the low-frequency modes. The second issue involves how to solve the linearized Langevin equation at large timesteps correctly, where the usual discretized formulation of the random force is invalid. This is accomplished by using analytic expressions for the distributions associated with positions and velocities of the individual oscillators as a function of frequency, obtained as the solution of the corresponding Fokker–Planck equation. We apply LIN with these developments to the nucleic acid component deoxycytidine with timesteps ranging from 100 to 1000 fs. We demonstrate that LIN is stable in these simulations, with energies fluctuating about the same values—and possessing overall similar dynamical features—in comparison to 1 fs explicit simulations, though the fluctuations are significantly larger at larger timesteps. Moreover, continuous dynamics is maintained, and pathway information can be obtained. Computational performance is competitive only at very large time steps: a gain factor of 3–4 is obtained for runs with 1000 fs time steps. Larger gains may be achieved for biomolecules, where sparsity and parallelization can be exploited significantly.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 75 (1994), S. 6685-6687 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The temperature dependence of the magnetic properties of magnetic superlattices by using the Bethe approximation to the inhomogeneous Ising model is studied. A self-consistent equation which determines the variation of the magnetic moment for any layer thicknesses is derived. In particular, the crossover from bulk-dominated behavior for large thicknesses of layers to interface-dominated behavior for small thicknesses is discussed. The results both qualitatively and quantitatively differ from mean-field theory; the experimental observation for FeF2/CoF2 and CoO/NiO superlattices is explained.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 14 (1993), S. 1212-1233 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A central goal in molecular dynamics simulations is increasing the integration time-step to allow the capturing of biomolecular motion on biochemically interesting time frames. We previously made a step in that direction by developing the Langevin/implicit-Euler scheme. Here, we present a modified Langevin/implicit-Euler formulation for molecular dynamics. The new method still maintains the major advantage of the original scheme, namely, stability over a wide range of time-steps. However, it substantially reduces the damping effect of the high-frequency modes inherent in the original implicit scheme. The new formulation involves separation of the solution into two components, one of which is solved exactly using normal-mode techniques, the other of which is solved by implicit numerical integration. In this way, the high-frequency and fast-varying components are well resolved in the analytic solution component, while the remaining components of the motion are obtained by a large time-step integration phase. Full details of the new scheme are presented, accompanied by illustrative examples for a simple pendulum system. An application to liquid butane demonstrates stability of the simulations at time-steps up to 50 fs, still with activation of the high-frequency modes. © John Wiley & Sons, Inc.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 15 (1994), S. 532-552 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: We report the adaptation of the truncated Newton minimization package TNPACK for CHARMM and biomolecular energy minimization. TNPACK is based on the preconditioned linear conjugate-gradient technique for solving the Newton equations. The structure of the problem - sparsity of the Hessian - is exploited for preconditioning. Experience with the new version of TNPACK is presented on a series of molecular systems of biological and numerical interest: alanine dipeptide (N-methyl-alanyl-acetamide), a dimer of N-methyl-acetamide, deca-alanine, mellitin (26 residues), avian pancreatic polypeptide (36 residues), rubredoxin (52 residues), bovine pancreatic trypsin inhibitor (58 residues), a dimer of insulin (99 residues), and lysozyme (130 residues). Detailed comparisons among the minimization algorithms available in CHARMM, particularly those used for large-scale problems, are presented along with new mathematical developments in TNPACK. The new TNPACK version performs significantly better than ABNR, the most competitive minimizer in CHARMM, for all systems tested in terms of CPU time when curvature information (Hessian/vector product) is calculated by a finite-difference of gradients (the numeric option of TNPACK). The remaining derivative quantities are, however, evaluated analytically in TNPACK. The CPU gain is 50% or more (speedup factors of 1.5 to 2.5) for the largest molecular systems tested and even greater for smaller systems (CPU factors of 1 to 4 for small systems and 1 to 5 for medium systems). TNPACK uses curvature information to escape from undesired configurational regions and to ensure the identification of true local minima. It converges rapidly once a convex region is reached and achieves very low final gradient norms, such as of order 10-8, with little additional work. Even greater overall CPU gains are expected for large-scale minimization problems by making the architectures of CHARMM and TNPACK more compatible with respect to the second-derivative calculations. © 1994 by John Wiley & Sons, Inc.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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