2,299 research outputs found
Coarse Molecular Dynamics of a Peptide Fragment: Free Energy, Kinetics, and Long-Time Dynamics Computations
We present a ``coarse molecular dynamics'' approach and apply it to studying
the kinetics and thermodynamics of a peptide fragment dissolved in water. Short
bursts of appropriately initialized simulations are used to infer the
deterministic and stochastic components of the peptide motion parametrized by
an appropriate set of coarse variables. Techniques from traditional numerical
analysis (Newton-Raphson, coarse projective integration) are thus enabled;
these techniques help analyze important features of the free-energy landscape
(coarse transition states, eigenvalues and eigenvectors, transition rates,
etc.). Reverse integration of (irreversible) expected coarse variables backward
in time can assist escape from free energy minima and trace low-dimensional
free energy surfaces. To illustrate the ``coarse molecular dynamics'' approach,
we combine multiple short (0.5-ps) replica simulations to map the free energy
surface of the ``alanine dipeptide'' in water, and to determine the ~ 1/(1000
ps) rate of interconversion between the two stable configurational basins
corresponding to the alpha-helical and extended minima.Comment: The article has been submitted to "The Journal of Chemical Physics.
The fully-implicit log-conformation formulation and its application to three-dimensional flows
The stable and efficient numerical simulation of viscoelastic flows has been
a constant struggle due to the High Weissenberg Number Problem. While the
stability for macroscopic descriptions could be greatly enhanced by the
log-conformation method as proposed by Fattal and Kupferman, the application of
the efficient Newton-Raphson algorithm to the full monolithic system of
governing equations, consisting of the log-conformation equations and the
Navier-Stokes equations, has always posed a problem. In particular, it is the
formulation of the constitutive equations by means of the spectral
decomposition that hinders the application of further analytical tools.
Therefore, up to now, a fully monolithic approach could only be achieved in two
dimensions, as, e.g., recently shown in [P. Knechtges, M. Behr, S. Elgeti,
Fully-implicit log-conformation formulation of constitutive laws, J.
Non-Newtonian Fluid Mech. 214 (2014) 78-87].
The aim of this paper is to find a generalization of the previously made
considerations to three dimensions, such that a monolithic Newton-Raphson
solver based on the log-conformation formulation can be implemented also in
this case. The underlying idea is analogous to the two-dimensional case, to
replace the eigenvalue decomposition in the constitutive equation by an
analytically more "well-behaved" term and to rely on the eigenvalue
decomposition only for the actual computation. Furthermore, in order to
demonstrate the practicality of the proposed method, numerical results of the
newly derived formulation are presented in the case of the sedimenting sphere
and ellipsoid benchmarks for the Oldroyd-B and Giesekus models. It is found
that the expected quadratic convergence of Newton's method can be achieved.Comment: 21 pages, 9 figure
Some Further Results for the Stationary Points and Dynamics of Supercooled Liquids
We present some new theoretical and computational results for the stationary
points of bulk systems. First we demonstrate how the potential energy surface
can be partitioned into catchment basins associated with every stationary point
using a combination of Newton-Raphson and eigenvector-following techniques.
Numerical results are presented for a 256-atom supercell representation of a
binary Lennard-Jones system. We then derive analytical formulae for the number
of stationary points as a function of both system size and the Hessian index,
using a framework based upon weakly interacting subsystems. This analysis
reveals a simple relation between the total number of stationary points, the
number of local minima, and the number of transition states connected on
average to each minimum. Finally we calculate two measures of localisation for
the displacements corresponding to Hessian eigenvectors in samples of
stationary points obtained from the Newton-Raphson-based geometry optimisation
scheme. Systematic differences are found between the properties of eigenvectors
corresponding to positive and negative Hessian eigenvalues, and localised
character is most pronounced for stationary points with low values of the
Hessian index.Comment: 16 pages, 2 figure
Coarse Stability and Bifurcation Analysis Using Stochastic Simulators: Kinetic Monte Carlo Examples
We implement a computer-assisted approach that, under appropriate conditions,
allows the bifurcation analysis of the coarse dynamic behavior of microscopic
simulators without requiring the explicit derivation of closed macroscopic
equations for this behavior. The approach is inspired by the so-called
time-step per based numerical bifurcation theory. We illustrate the approach
through the computation of both stable and unstable coarsely invariant states
for Kinetic Monte Carlo models of three simple surface reaction schemes. We
quantify the linearized stability of these coarsely invariant states, perform
pseudo-arclength continuation, detect coarse limit point and coarse Hopf
bifurcations and construct two-parameter bifurcation diagrams.Comment: 26 pages, 5 figure
Energy Minimization
The energetic state of a protein is one of the most important representative parameters of its stability. The energy of a protein can be defined as a function of its atomic coordinates. This energy function consists of several components: 1. Bond energy and angle energy, representative of the covalent bonds, bond angles. 2. Dihedral energy, due to the dihedral angles. 3. A van der Waals term (also called Leonard-Jones potential) to ensure that atoms do not have steric clashes. 4. Electrostatic energy accounting for the Coulomb’s Law m protein structure, i.e. the long-range forces between charged and partially charged atoms. All these quantitative terms have been parameterized and are collectively referred to as the ‘force-field’, for e.g. CHARMM, AMBER, AMBERJOPLS and GROMOS. The goal of energy Minimization is to find a set of coordinates representing the minimum energy conformation for the given structure. Various algorithms have been formulated by varying the use of derivatives. Three common algorithms used for this optimization are steepest descent, conjugate gradient and Newton–Raphson. Although energy Minimization is a tool to achieve the nearest local minima, it is also an indispensable tool in correcting structural anomalies, viz. bad stereo-chemistry and short contacts. An efficient optimization protocol could be devised from these methods in conjunction with a larger space exploration algorithm, e.g. molecular dynamics
Symmetry and equivalence restrictions in electronic structure calculations
A simple method for obtaining MCSCF orbitals and CI natural orbitals adapted to degenerate point groups, with full symmetry and equivalnece restrictions, is described. Among several advantages accruing from this method are the ability to perform atomic SCF calculations on states for which the SCF energy expression cannot be written in terms of Coulomb and exchange integrals over real orbitals, and the generation of symmetry-adapted atomic natural orbitals for use in a recently proposed method for basis set contraction
Accelerating crystal plasticity simulations using GPU multiprocessors
Crystal plasticity models are often used to model the deformation behavior of polycrystalline materials. One major drawback with such models is that they are computationally very demanding. Adopting the common Taylor assumption requires calculation of the response of several hundreds of individual grains to obtain the stress in a single integration point in the overlying FEM structure. However, a large part of the operations can be executed in parallel to reduce the computation time. One emerging technology for running massively parallel computations without having to rely on the availability of large computer clusters is to port the parallel parts of the calculations to a graphical processing unit (GPU). GPUs are designed to handle vast numbers of floating point operations in parallel. In the present work, different strategies for the numerical implementation of crystal plasticity are investigated as well as a number of approaches to parallelization of the program execution. It is identified that a major concern is the limited amount of memory available on the GPU. However, significant reductions in computational time – up to 100 times speedup – are achieved in the present study, and possible also on a standard desktop computer equipped with a GPU
Discontinuous Molecular Dynamics for Semi-Flexible and Rigid Bodies
A general framework for performing event-driven simulations of systems with
semi-flexible or rigid bodies interacting under impulsive torques and forces is
outlined. Two different approaches are presented. In the first, the dynamics
and interaction rules are derived from Lagrangian mechanics in the presence of
constraints. This approach is most suitable when the body is composed of
relatively few point masses or is semi-flexible. In the second method, the
equations of rigid bodies are used to derive explicit analytical expressions
for the free evolution of arbitrary rigid molecules and to construct a simple
scheme for computing interaction rules. Efficient algorithms for the search for
the times of interaction events are designed in this context, and the handling
of missed interaction events is discussed.Comment: 16 pages, double column revte
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