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.
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The book describes the concepts of chaos and order in the "hard" and "soft" sciences.
The authors propose new approach to self-organization of complex distributed systems in logistics. That approach is based on combination of multi-agent paradigm with constraint satisfaction techniques. The proposed solution expresses major features of Swarm Intelligence approach and replaces traditional stochastic adaptation of the swarm of the autonomous agents by constraint-driven adaptation.
The monograph is devoted to the consideration of complex systems from the position of the end the 21st century. The considerable breakthrough in the understanding of complex systems is comprehensively analyzed. Such a breakthrough is connected with the use of the newest methods of nonlinear dynamics, of organization of the modern computational experiments. The book is meant for specialists in different fields of natural sciences and the humanities as well as for all readers who are interested in the recent advancements in science.
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.
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.