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Simulation of Crystalline Nanoporous Materials and the Computation of Adsorption/Diffusion Properties
Published in T. Grant Glover, Bin Mu, Gas Adsorption in Metal-Organic Frameworks, 2018
The following sets of algorithms are commonly employed for local energy minimization [170]: methods which only use the energy (e.g., simplex method [171,172]), methods which use the energy and first derivatives (e.g., steepest descent, conjugate gradient, Snyman's method [173,174]), methods which use the energy, first derivatives, and approximate second derivatives (e.g., Quasi-Newton method), methods which use the energy, first derivatives, and exact second derivatives (e.g., Newton–Raphson), and methods which use the energy, first derivatives, second derivatives, and the eigenvalues/eigenvectors of the Hessian matrix (e.g., mode-following technique [175] also known as Baker's minimization [176]). The conjugate gradient minimization is the most commonly used technique. Whereas steepest descent takes a step always based on the gradient, the conjugate gradient method starts along the steepest descent direction, continues along this direction until a minimum is reached, but then proceeds along a perpendicular (or “conjugate”) direction.
Graph Cuts—Combinatorial Optimization in Vision
Published in Olivier Lézoray, Leo Grady, Image Processing and Analysis with Graphs, 2012
The image that satisfies the “less noise” condition (2) the most, which minimizes the quantity (2.6), is a constant image, either all black or all white. On the other hand, the condition (1) is perfectly satisfied if we set X = Y, as mentioned above. Thus, the two conditions conflict unless Y is a constant image, leading to a need of a tradeoff. The heart of the energy minimization methods is that we attempt to treat such a tradeoff in a principled way by defining it as minimization of an energy. That is, we translate various factors in the tradeoff as terms which are added up to form an energy. The relative importance of each factor can be controlled by multiplying it by a weight.
Active surfaces acceleration methods
Published in João Manuel, R. S. Tavares, R. M. Natal Jorge, Computational Modelling of Objects Represented in Images, 2018
Julien Olivier, Julien Mille, Romuald Boné, J.-Jacques Rousselle
Global energy minimization is performed via successive local optimizations: at each iteration, a cubic neighborhood of side length w around each vertex is considered. The energy is computed at each voxel belonging to the neighborhood and the vertex is moved to the location leading to the lowest energy.
NOVEL SARS-CoV-2 INHIBITORS FROM PHENETHYLTHIAZOLETHIOUREA DERIVATIVES USING HYBRID QSAR MODELS AND DOCKING SIMULATION
Published in Smart Science, 2021
Pham Van Tat, Tran Thai Hoa, Au Vo Ky, Pham Nu Ngoc Han
The molecular structures are built and optimized by a quick energy minimization algorithm (Dreiding). The force field used is Dreiding with the steepest descent minimizer to optimize all. Then small molecules (ligand) are built up in an sdf database. After building and optimizing small molecules, we prepared the parameters needed for the docking process. The second phase is to prepare the ligands for importing into other protocols, perform the tasks of removing duplicates, enumerating isomers and tautomers, and generating 3D conformations. The Specify Ligands parameter allows you to select a primary ligand source in the sdf data file. Database of selected ligands with change parameters of change Inonization method is at maximum and minimum pH 6.5; The Generate tautomers parameter is true and the maximum Tautomer number is 10; Amides Tautomerization is Tauomerize Only Diamides. Tao Isomers is true; Generate coordinates are 3D.
Ion effects on the extraction of cesium (I) by 1,3-Diisopropoxycalix [4] arenecrown-6(BPC6) and the highly efficient extraction under neutral conditions
Published in Solvent Extraction and Ion Exchange, 2022
Huifang Xing, Liangrong Yang, Lu Wang, Mengfang Li, Jiemiao Yu, Diannan Lu, Gang Ye, Huizhou Liu
In all simulations an energy minimization procedure was performed followed by a molecular dynamic simulation under NpT conditions for 10 ns. The Verlet algorithm[37] with a time step of 10 fs was employed. The cutoff radius for nonbonded van der Waals and short-range Coulomb interactions was 14 Å. Long-range Coulomb interactions were treated using the Ewald method as implemented in the PME (Particle Mesh Ewald) procedure.[38] Periodic boundary conditions were employed for all xyz directions. The simulation temperature was kept at 298 K with the v-rescale[39] algorithm using a time constant of 1 ps. The pressure was kept at 1 bar using the Parrinello – Rahman[40] algorithm and a time constant of 2 ps.
Machine learning and molecular dynamics based models to predict the temperature dependent elastic properties of silver nanowires
Published in International Journal for Computational Methods in Engineering Science and Mechanics, 2023
S. K. Joshi, Sanjeev K. Singh, Santosh Dubey
In present work, the Classical MD simulator, LAMMPS [44] used to simulate the stress-strain response of Silver nanowire with an aspect ratio of 12, at different temperatures. MD approach tracks the individual atomic trajectories, starting from a given reference point. Newton’s equations of motion are solved for the interacting particles to obtain their time evolution. The pair interactions of these particles modeled using Embedded Atom Method (EAM) potential function [45]. Periodic boundary conditions are applied along the length of the nanowire (y-axis) and fixed boundary conditions are applied along the other two directions. MD simulations have been performed at different temperatures (200–900 K), considering NVT ensemble. All these parameters can be implemented in a LAMMPS input script which primarily has following parts:Initialization – This part of input script sets the initial parameters, which are necessary before the creation of atoms. This part defines units, dimension, processors, boundary conditions and atom style of the virtual sample.Atom definition – This part of the input script sets the particle types in the LAMMPS simulation. This can be either be done reading the molecular topology details from a previously created data file or atoms can also be created over a lattice, using several LAMMPS commands within the input script, especially when a large periodic system to be simulated.Settings – After defining atoms and setting the molecular topology, one has to specify other simulation parameters like force field coefficients, output options, etc. Selection of appropriate Force fields is very important for the appropriate modeling and prediction of any system. It is possible to model a few hundreds to millions of particles in classical MD using phenomenological interatomic and intermolecular potentials. In general, the flexibility, accuracy, transferability, and computational efficiency of the interatomic potentials each have to be carefully considered.Running a simulation – Once the input script is completed, it should be run by LAMMPS simulator to perform the calculations under stated conditions. In LAMMPS, the system energy minimization is performed by iteratively adjusting atom coordinates. These iterations are stopped, when one of the stopping criteria is satisfied. At this point the system will be in local minimum potential energy. Table 1 lists the simulation parameters used in the present simulation.