@article{CvetkovićConradLie2021,
  author    = {Cvetković, Nada and Conrad, Tim and Lie, Han Cheng},
  title     = {A convergent discretization method for transition path theory for diffusion processes},
  series = {Multiscale modeling \& simulation : a SIAM interdisciplinary journal},
  volume    = {19},
  journal   = {Multiscale modeling \& simulation : a SIAM interdisciplinary journal},
  number    = {1},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  issn      = {1540-3459},
  doi       = {10.1137/20M1329354},
  pages     = {242 -- 266},
  year      = {2021},
  abstract  = {Transition path theory (TPT) for diffusion processes is a framework for analyzing the transitions of multiscale ergodic diffusion processes between disjoint metastable subsets of state space. Most methods for applying TPT involve the construction of a Markov state model on a discretization of state space that approximates the underlying diffusion process. However, the assumption of Markovianity is difficult to verify in practice, and there are to date no known error bounds or convergence results for these methods. We propose a Monte Carlo method for approximating the forward committor, probability current, and streamlines from TPT for diffusion processes. Our method uses only sample trajectory data and partitions of state space based on Voronoi tessellations. It does not require the construction of a Markovian approximating process. We rigorously prove error bounds for the approximate TPT objects and use these bounds to show convergence to their exact counterparts in the limit of arbitrarily fine discretization. We illustrate some features of our method by application to a process that solves the Smoluchowski equation on a triple-well potential.},
  language  = {en}
}
@article{HollandMoritzGraupnerMoelleretal.2018,
  author    = {Holland-Moritz, Henry and Graupner, Julia and M{\"o}ller, Wolfhard and Pacholski, Claudia and Ronning, Carsten},
  title     = {Dynamics of nanoparticle morphology under low energy ion irradiation},
  series = {Nanotechnology},
  volume    = {29},
  journal   = {Nanotechnology},
  number    = {31},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {0957-4484},
  doi       = {10.1088/1361-6528/aac36c},
  pages     = {7},
  year      = {2018},
  abstract  = {If nanostructures are irradiated with energetic ions, the mechanism of sputtering becomes important when the ion range matches about the size of the nanoparticle. Gold nanoparticles with diameters of similar to 50 nm on top of silicon substrates with a native oxide layer were irradiated by gallium ions with energies ranging from 1 to 30 keV in a focused ion beam system. High resolution in situ scanning electron microscopy imaging permits detailed insights in the dynamics of the morphology change and sputter yield. Compared to bulk-like structures or thin films, a pronounced shaping and enhanced sputtering in the nanostructures occurs, which enables a specific shaping of these structures using ion beams. This effect depends on the ratio of nanoparticle size and ion energy. In the investigated energy regime, the sputter yield increases at increasing ion energy and shows a distinct dependence on the nanoparticle size. The experimental findings are directly compared to Monte Carlo simulations obtained from iradina and TRI3DYN, where the latter takes into account dynamic morphological and compositional changes of the target.},
  language  = {en}
}
@phdthesis{Richter2007,
  author    = {Richter, Andreas},
  title     = {Structure formation and fractionation in systems of colloidal rods},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13090},
  school      = {Universit{\"a}t Potsdam},
  year      = {2007},
  abstract  = {Nowadays, colloidal rods can be synthesized in large amounts. The rods are typically cylindrically and their length ranges from several nanometers to a few micrometers. In solution, systems of colloidal rodlike molecules or aggregates can form liquid-crystalline phases with long-range orientational and spatial order. In the present work, we investigate structure formation and fractionation in systems of rodlike colloids with the help of Monte Carlo simulations in the NPT ensemble. Repulsive interactions can successfully be mimicked by the hard rod model, which has been studied extensively in the past. In many cases, attractive interactions like van der Waals or depletion forces cannot be neglected, however. In the first part of this work, the phase behavior of monodisperse attractive rods is characterized for different interaction strengths. Phase diagrams as a function of rod length and pressure are presented. Most systems of synthesized mesoscopic rods have a polydisperse length distribution as a consequence of the longitudinal growth process of the rods. For many technical and research applications, a rather small polydispersity is desired in order to have well defined material properties. The polydispersity can be reduced by a spatial demixing (fractionation) of long and short rods. Fractionation and structure formation is studied in a tridisperse and a polydisperse bulk suspension of rods. We observe that the resulting structures depend distinctly on the interaction strength. The fractionation in the system is strongly enhanced with increasing interaction strength. Suspensions are typically confined in a container. We also examine the influence of adjacent substrates in systems of tridisperse and polydisperse rod suspensions. Three different substrate types are studied in detail: a planar wall, a corrugated substrate, and a substrate with rectangular cavities. We analyze the fluid structure close to the substrate and substrate controlled fractionation. The spatial arrangement of long and short rods in front of the substrate depends sensitively on the substrate structure and the pressure. Rods with a predefined length are segregated at substrates with rectangular cavities.},
  language  = {en}
}