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At least 829 records · Page 46

Weakly nonlinear dynamics in noncanonical Hamiltonian systems with applications to fluids and plasmas

A method, called beatification, is presented for rapidly extracting weakly nonlinear Hamiltonian systems that describe the dynamics near equilibria of systems possessing Hamiltonian form in terms of noncanonical Poisson brackets. The procedure applies to systems like fluids and plasmas in terms of Eulerian variables that have such noncanonical Poisson brackets, i.e., brackets with nonstandard and possibly degenerate form. A collection of examples of both finite and infinite dimensions is presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Molecular dynamics simulation of sodium aluminosilicate glass structures and glass surface-water reactions using the reactive force field (ReaxFF)

Reactive potentials are increasingly used to study the properties of glasses and glass water reactions in a reactive molecular dynamics (MD) framework. In this study, we have simulated a ternary sodium aluminosilicate glass and investigated the initial stages of the glass surface-water reactions at 300 K using reactive force field (ReaxFF). On comparison of the simulated glass structures generated using ReaxFF and classical Buckingham potentials, our results show that the atomic density profiles calculated for the surface glass structures indicate a bond-angle distribution dependency. The atomic density profiles also show higher concentrations of non-bridging oxygens (NBOs) and sodium ions at the glass surface. Additionally, we present our results of formation of silanol species and the diffusion of water molecules at the glass surface using ReaxFF.

Chemistry↗

Ab initio molecular dynamics simulation of Nd3+ incorporation in calcite

Trivalent rare-earth elements (REEs) readily incorporate in Ca-bearing minerals such as calcite (CaCO3), a phenomenon with important implications for the use of REEs as biogeochemical tracers as well as for environmental remediation. Despite substantial efforts, determining the incorporation modes of trivalent REEs in calcite has remained challenging due to their presence in multiple coordination environments. This is particularly problematic for the interpretation of extended X-ray absorption fine structure (EXAFS) spectroscopy. In this work, ab initio molecular dynamics (AIMD) simulations of Nd3+ incorporated in calcite were performed to resolve its incorporation modes. Nd3+ and Ca2+ have very similar ionic radii but the additional positive charge requires a charge compensation scheme (CCS). Five CCSs were considered in AIMD simulations, and the resulting atomic trajectories were then used to compute EXAFS spectra for direct fitting to a published experimental spectrum. The results of the fits indicated that Nd3+ incorporates at the Ca2+ site in calcite in a mixture of six- and seven-fold coordination environments and through three main incorporation modes: associated with a protonated nearest-neighbor Ca2+ vacancy, incorporated as NdOH2+, and charge compensated by a remote species (on the spatial scale probed by EXAFS). The incorporation of Nd3+ in calcite via multiple modes was consistent with previous work, but the AIMD-EXAFS approach allowed for resolving the nature, proportion, and structure of the different coordination environments.

Kerisit, Sebastien N.↗

GPU-accelerated Tersoff potentials for massively parallel Molecular Dynamics simulations

The Tersoff potential is one of the empirical many-body potentials that has been widely used in simulation studies at atomic scales. Unlike pair-wise potentials, the Tersoff potential involves three-body terms, which require much more arithmetic operations and data dependency. In this contribution, we have implemented the GPU-accelerated version of several variants of the Tersoff potential for LAMMPS, an open-source massively parallel Molecular Dynamics code. Compared to the existing MPI implementation in LAMMPS, the GPU implementation exhibits a better scalability and offers a speedup of 2.2X when run on 1000 compute nodes on the Titan supercomputer. On a single node, the speedup ranges from 2.0 to 8.0 times, depending on the number of atoms per GPU and hardware configurations. The most notable features of our GPU-accelerated version include its design for MPI/accelerator heterogeneous parallelism, its compatibility with other functionalities in LAMMPS, its ability to give deterministic results and to support both NVIDIA CUDA- and OpenCL-enabled accelerators. Our implementation is now part of the GPU package in LAMMPS and accessible for public use.

Computer Science↗

Anisotropic single-particle dissipative particle dynamics model

We have developed a new single-particle dissipative particle dynamics (DPD) model for anisotropic particles with different shapes, e.g., prolate or oblate spheroids. In particular, the conservative and dissipative interactions between anisotropic single DPD particles are formulated using a linear mapping from the isotropic model of spherical particles. The proper mapping operator is constructed between each interacting pair of particles at every time step. Correspondingly, the random forces are properly formulated to satisfy the fluctuation-dissipation theorem (FDT). Notably, the model exactly conserves both linear and angular momentum. We demonstrate the proposed model's accuracy and efficiency by applying it for modeling colloidal ellipsoids. Specifically, we show it efficiently captures the static properties of suspensions of colloidal ellipsoids. The isotropic-nematic transition in an ellipsoidal suspension is reproduced by increasing its volume fraction or the aspect ratio of ellipsoid particles. Moreover, the hydrodynamics and diffusion of a single colloidal ellipsoid (prolate or oblate with moderate aspect ratios) are accurately captured. The calculated drag force on the ellipsoid and its diffusion coefficients (both translational and rotational) agree quantitatively with the theoretical predictions in the Stokes limit.

Computer Science↗

Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders

Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such as balanced truncation, rational interpolation, the reduced-basis method, and (balanced) proper orthogonal decomposition (POD). Unfortunately, restricting the state to evolve in a linear subspace imposes a fundamental limitation to the accuracy of the resulting reduced-order model (ROM). In particular, linear-subspace ROMs can be expected to produce low-dimensional models with high accuracy only if the problem admits a fast decaying Kolmogorov n -width (e.g., diffusion-dominated problems). Unfortunately, many problems of interest exhibit a slowly decaying Kolmogorov n-width (e.g., advection-dominated problems). To address this, we propose a novel framework for projecting dynamical systems onto nonlinear manifolds using minimum-residual formulations at the time-continuous and time-discrete levels; the former leads to manifold Galerkin projection, while the latter leads to manifold least-squares Petrov–Galerkin (LSPG) projection. We perform analyses that provide insight into the relationship between these proposed approaches and classical linear-subspace reduced-order models; we also derive a posteriori discrete-time error bounds for the proposed approaches. In addition, we propose a computationally practical approach for computing the nonlinear manifold, which is based on convolutional autoencoders from deep learning. Lastly, we demonstrate the ability of the method to significantly outperform even the optimal linear-subspace ROM on benchmark advection-dominated problems, thereby demonstrating the method's ability to overcome the intrinsic n -width limitations of linear subspaces.

97 MATHEMATICS AND COMPUTING↗

Impact of Cr and Co on 99Tc retention in magnetite: A combined study of ab initio molecular dynamics and experiments

This work explores the effect of co-mingled dopants, Co(II) and Cr(III), on Tc(IV) incorporation and retention in magnetite when heat treated to 625 or 700 °C. Key trends in Tc retention in the high temperature regime were identified using a combination of density-functional-theory based ab initio molecular dynamics (AIMD) simulations, and batch experiments including solid phase characterization techniques, e.g. X-ray absorption spectroscopy. A stabilizing effect on Tc(IV) was observed when the number of Tc and Cr atoms are equal or when the magnetite surface is oversaturated with Tc and Cr inclusions. Here, oversaturation is hypothesized to force Cr from the magnetite surface to form a Cr2O3 phase, which may act as a protective layer that prevents Tc release. With the addition of Co, Tc(IV) is stabilized via redox processes. The presence of Cr in low concentrations interferes with this redox stabilization and Cr is preferentially stabilized as opposed to Tc. As a result, using Co as a stabilizing dopant for Tc may be compromised in the presence of Cr. When the relative concentration of Tc, Cr and Co is the same, or more Co atoms are added to high Cr incorporated systems, the formation of the Cr2O3 phase may be suppressed. Although waste streams with co-mingled Tc and Cr potentially may benefit from a Co dopant, since the formation of a Cr2O3 passivation layer may protect incorporated Tc from being released, the relative concentration of the three elements will be a critical parameter for maximizing effectiveness of this strategy.

Lee, Mal Soon↗