Stochastic theory of the classical molecular dynamics method
The work is devoted to fundamental aspects of the classical molecular dynamics method, which was developed half a century ago as a means of solving computational problems in statistical physics and has now become one of the most important numerical methods in the theory of condensed state. At the same time, the molecular dynamics method based on solving the equations of motion for a multiparticle system proved to be directly related to the basic concepts of classical statistical physics, in particular, to the problem of the occurrence of irreversibility. This paper analyzes the dynamic and stochastic properties of molecular dynamics systems connected with the local instability of trajectories and the errors of the numerical integration. The probabilistic nature of classical statistics is discussed. We propose a concept explaining the finite dynamic memory time and the emergence of irreversibility in real systems.
The method ofWave Packet Molecular Dynamics Method (WPMD) is a promising replacement of the classical molecular dynamics for the simulations of many-electron systems including nonideal plasmas. In this contribution we report on a packet splitting technique where an electron is represented by multiple Gaussians, with mixing coefficients playing the role of additional dynamic variables. It provides larger flexibility and better accuracy than the original WPMD with a single Gaussian per electron. As a test case we consider ionization of hydrogen atom in a short laser pulse, where the split packets provide a basis for quantum branching.
The wave packet molecular dynamics (WPMD) method provides a variational approximation to the solution of the time-dependent Schr¨odinger equation. Its application in the field of high-temperature dense plasmas has yielded diverging electron width (spreading), which results in diminishing electron-nuclear interactions. Electron spreading has previously been ascribed to a shortcoming of the WPMD method and has been counteracted by various heuristic additions to the models used. We employ more accurate methods to determine if spreading continues to be predicted by them and how WPMD can be improved. A scattering process involving a single dynamic electron interacting with a periodic array of statically screened protons is used as a model problem for comparison. We compare the numerically exact split operator Fourier transform method, the Wigner trajectory method, and the time-dependent variational principle (TDVP). Within the framework of the TDVP, we use the standard variational form of WPMD, the single Gaussian wave packet (WP), as well as a sum of Gaussian WPs, as in the split WP method. Wave packet spreading is predicted by all methods, so it is not the source of the unphysical diminishing of electron-nuclear interactions in WPMD at high temperatures. Instead, the Gaussian WP’s inability to correctly reproduce breakup of the electron’s probability density into localized density near the protons is responsible for the deviation from more accurate predictions. Extensions of WPMD must include a mechanism for breakup to occur in order to yield dynamics that lead to accurate electron densities.
This paper describes the surface environment of the dense plasma arcs that damage rf accelerators, tokamaks, and other high gradient structures. We simulate the dense, nonideal plasma sheath near a metallic surface using molecular dynamics (MD) to evaluate sheaths in the non-Debye region for high density, low temperature plasmas. We use direct two-component MD simulations where the interactions between all electrons and ions are computed explicitly. We find that the non-Debye sheath can be extrapolated from the Debye sheath parameters with small corrections. We find that these parameters are roughly consistent with previous particle-in-cell code estimates, pointing to densities in the range 10^24–10^25 m^3. The high surface fields implied by these results could produce field emission that would short the sheath and cause an instability in the time evolution of the arc, and this mechanism could limit the maximum density and surface field in the arc. These results also provide a way of understanding how the properties of the arc depend on the properties (sublimation energy, for example) of the metal. Using these results, and equating surface tension and plasma pressure, it is possible to infer a range of plasma densities and sheath potentials from scanning electron microscope images of arc damage. We find that the high density plasma these results imply and the level of plasma pressure they would produce is consistent with arc damage on a scale 100 nm or less, in examples where the liquid metal would cool before this structure would be lost. We find that the submicron component of arc damage, the burn voltage, and fluctuations in the visible light production of arcs may be the most direct indicators of the parameters of the dense plasma arc, and the most useful diagnostics of the mechanisms limiting gradients in accelerators.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.
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By using superconducting quantum interference device (SQUID) magnetometry, we investigated anisotropic high-field (H less than or similar to 7T) low-temperature (10 K) magnetization response of inhomogeneous nanoisland FeNi films grown by rf sputtering deposition on Sitall (TiO2) glass substrates. In the grown FeNi films, the FeNi layer nominal thickness varied from 0.6 to 2.5 nm, across the percolation transition at the d(c) similar or equal to 1.8 nm. We discovered that, beyond conventional spin-magnetism of Fe21Ni79 permalloy, the extracted out-of-plane magnetization response of the nanoisland FeNi films is not saturated in the range of investigated magnetic fields and exhibits paramagnetic-like behavior. We found that the anomalous out-of-plane magnetization response exhibits an escalating slope with increase in the nominal film thickness from 0.6 to 1.1 nm, however, it decreases with further increase in the film thickness, and then practically vanishes on approaching the FeNi film percolation threshold. At the same time, the in-plane response demonstrates saturation behavior above 1.5-2T, competing with anomalously large diamagnetic-like response, which becomes pronounced at high magnetic fields. It is possible that the supported-metal interaction leads to the creation of a thin charge-transfer (CT) layer and a Schottky barrier at the FeNi film/Sitall (TiO2) interface. Then, in the system with nanoscale circular domains, the observed anomalous paramagnetic-like magnetization response can be associated with a large orbital moment of the localized electrons. In addition, the inhomogeneous nanoisland FeNi films can possess spontaneous ordering of toroidal moments, which can be either of orbital or spin origin. The system with toroidal inhomogeneity can lead to anomalously strong diamagnetic-like response. The observed magnetization response is determined by the interplay between the paramagnetic-and diamagnetic-like contributions.
A form for an unbiased estimate of the coefficient of determination of a linear regression model is obtained. It is calculated by using a sample from a multivariate normal distribution. This estimate is proposed as an alternative criterion for a choice of regression factors.