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1. Magnetic reconnection on a Klein bottle

   https://doi.org/10.1063/5.0222454  

   Xia, Luke; Swisdak, M. (August 2024, Physics of Plasmas)

   We present a new boundary condition for simulations of magnetic reconnection based on the topology of a Klein bottle. When applicable, the new condition is computationally cheaper than fully periodic boundary conditions, reconnects more flux than systems with conducting boundaries, and does not require assumptions about regions external to the simulation as is necessary for open boundaries. The new condition reproduces the expected features of reconnection but cannot be straightforwardly applied in systems with asymmetric upstream plasmas. 

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2. A stochastic model of grain boundary dynamics: A Fokker–Planck perspective

   https://doi.org/10.1142/S021820252250052X  

   Epshteyn, Yekaterina; Liu, Chun; Mizuno, Masashi (October 2022, Mathematical Models and Methods in Applied Sciences)

   Many technologically useful materials are polycrystals composed of small monocrystalline grains that are separated by grain boundaries of crystallites with different lattice orientations. The energetics and connectivities of the grain boundaries play an essential role in defining the effective properties of materials across multiple scales. In this paper we derive a Fokker–Planck model for the evolution of the planar grain boundary network. The proposed model considers anisotropic grain boundary energy which depends on lattice misorientation and takes into account mobility of the triple junctions, as well as independent dynamics of the misorientations. We establish long time asymptotics of the Fokker–Planck solution, namely the joint probability density function of misorientations and triple junctions, and closely related the marginal probability density of misorientations. Moreover, for an equilibrium configuration of a boundary network, we derive explicit local algebraic relations, a generalized Herring Condition formula, as well as formula that connects grain boundary energy density with the geometry of the grain boundaries that share a triple junction. Although the stochastic model neglects the explicit interactions and correlations among triple junctions, the considered specific form of the noise, under the fluctuation–dissipation assumption, provides partial information about evolution of a grain boundary network, and is consistent with presented results of extensive grain growth simulations. 

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3. Theoretical investigations of asymmetric simple exclusion processes for interacting oligomers

   https://doi.org/https://doi.org/10.1088/1742-5468/aac139  

   Tripti Midha, Luiza V (May 2018, Journal of statistical mechanics)

   Motivated by biological transport phenomena that involve the motion of interacting molecular motors along linear filaments, we developed a theoretical framework to analyze the dynamics of interacting oligomers (extended size particles) on one-dimensional lattices. Our method extends the asymmetric simple exclusion processes for interacting monomers to particles of arbitrary size, and it utilizes cluster mean-field calculations supplemented by extensive Monte Carlo computer simulations. Interactions between particles are accounted for by a thermodynamically consistent method that views the formation and breaking bonds between particles as a chemical process. The dynamics of the system are analyzed for both periodic and open boundary conditions. It is found that the nature of the current-density relation depends on the strength of interactions, on the size of oligomers and on the way interactions influence particles transition rates. Stationary phase diagram is also fully evaluated, and it is shown how the dynamic properties depend on the interactions and on the sizes of the particles. To explain the dynamic behavior of the system particles density correlations are explicitly analyzed for different ranges of parameters. Theoretical calculations generally agree well with the results from the computer simulations, suggesting that our method correctly describes the main features of the molecular mechanisms of the transport of interacting oligomers. 

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4. Machine Learning for Molecular Simulation

   https://doi.org/10.1146/annurev-physchem-042018-052331  

   Noé, Frank; Tkatchenko, Alexandre; Müller, Klaus-Robert; Clementi, Cecilia (April 2020, Annual Review of Physical Chemistry)

   null (Ed.)

   Machine learning (ML) is transforming all areas of science. The complex and time-consuming calculations in molecular simulations are particularly suitable for an ML revolution and have already been profoundly affected by the application of existing ML methods. Here we review recent ML methods for molecular simulation, with particular focus on (deep) neural networks for the prediction of quantum-mechanical energies and forces, on coarse-grained molecular dynamics, on the extraction of free energy surfaces and kinetics, and on generative network approaches to sample molecular equilibrium structures and compute thermodynamics. To explain these methods and illustrate open methodological problems, we review some important principles of molecular physics and describe how they can be incorporated into ML structures. Finally, we identify and describe a list of open challenges for the interface between ML and molecular simulation. 

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5. Machine Learning for Molecular Simulation

   https://doi.org/10.1146/annurev-physchem-042018- 052331  

   Frank Noé, Alexandre Tkatchenko (February 2020, Annual review of physical chemistry)

   Machine learning (ML) is transforming all areas of science.The complex and time-consuming calculations in molecular simulations are particularly suitable for an ML revolution and have already been profoundly affected by the application of existing ML methods. Here we review recent ML methods for molecular simulation, with particular focus on (deep) neural networks for the prediction of quantum-mechanical energies and forces, on coarse-grained molecular dynamics, on the extraction of free energy surfaces and kinetics, and on generative network approaches to sample molecular equilibrium structures and compute thermodynamics. To explain these methods and illustrate open methodological problems,we review some important principles of molecular physics and describe how they can be incorporated into ML structures. Finally,we identify and describe a list of open challenges for the interface between ML and molecular simulation. 

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