@article{JeonChechkinMetzler2014,
  author    = {Jeon, Jae-Hyung and Chechkin, Aleksei V. and Metzler, Ralf},
  title     = {Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion},
  series = {Physical chemistry, chemical physics : PCCP},
  volume    = {30},
  journal   = {Physical chemistry, chemical physics : PCCP},
  number    = {16},
  publisher = {The Royal Society of Chemistry},
  address   = {Cambridge},
  doi       = {10.1039/C4CP02019G},
  pages     = {15811 -- 15817},
  year      = {2014},
  abstract  = {Anomalous diffusion is frequently described by scaled Brownian motion (SBM){,} a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is ?x2(t)? [similar{,} equals] 2K(t)t with K(t) [similar{,} equals] t[small alpha]-1 for 0 < [small alpha] < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion{,} for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely{,} we demonstrate that under confinement{,} the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments{,} in particular{,} under confinement inside cellular compartments or when optical tweezers tracking methods are used.},
  language  = {en}
}
@phdthesis{Schneider2004,
  author    = {Schneider, Judith},
  title     = {Dynamical structures and manifold detection in 2D and 3D chaotic flows},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-0001696},
  school      = {Universit{\"a}t Potsdam},
  year      = {2004},
  abstract  = {In dieser Arbeit werden die dynamischen Strukturen und Mannigfaltigkeiten in geschlossenen chaotischen Systemen untersucht. Das Wissen um diese dynamischen Strukturen (und Mannigfaltigkeiten) ist von Bedeutung, da sie uns einen ersten {\"U}berblick {\"u}ber die Dynamik des Systems geben, dass heisst, mit ihrer Hilfe sind wir in der Lage, das System zu charakterisieren und eventuell sogar seine Dynamik vorherzusagen. Die Visualisierung der dynamischen Strukturen, speziell in geschlossenen chaotischen Systemen, ist ein schwieriger und oft langer Prozess. Hier werden wir die sogenannte 'Leaking-Methode' (an Beispielen einfacher mathematischer Modelle wie der B{\"a}cker- oder der Sinus Abbildung) vorstellen, mit deren Hilfe wir die M{\"o}glichkeit haben, Teile der Mannigfaltigkeiten des chaotischen Sattels des Systems zu visualisieren. Vergleiche zwischen den gewonnenen Strukturen und Strukturen die durch chemische oder biologische Reaktionen hervorgerufen werden, werden anhand eines kinematischen Modells des Golfstroms durchgef{\"u}hrt. Es wird gezeigt, dass mittels der Leaking-Methode dynamische Strukturen auch in Umweltsystemen sichtbar gemacht werden k{\"o}nnen. Am Beispiel eines realistischen Modells des Mittelmeeres erweitern wir die Leaking-Methode zur sogenannten 'Exchange-Methode'. Diese erlaubt es den Transport zwischen zwei Regionen zu charakterisieren, die Transport-Routen und Austausch-Bassins sichtbar zu machen und die Austausch-Zeiten zu berechnen. Austausch-Bassins und Zeiten werden f{\"u}r die n{\"o}rdliche und s{\"u}dliche Region des westlichen Mittelmeeres pr{\"a}sentiert. Weiterhin werden Mischungseigenschaften im Erdmantel charakterisiert und die geometrischen Eigenschaften von Mannigfaltigkeiten in einem 3dimensionalen mathematischen Modell (ABC-Abbildung) untersucht.},
  language  = {en}
}
@misc{JeonChechkinMetzler2014,
  author    = {Jeon, Jae-Hyung and Chechkin, Aleksei V. and Metzler, Ralf},
  title     = {Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-76302},
  pages     = {15811 -- 15817},
  year      = {2014},
  abstract  = {Anomalous diffusion is frequently described by scaled Brownian motion (SBM){,} a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is ?x2(t)? [similar{,} equals] 2K(t)t with K(t) [similar{,} equals] t[small alpha]-1 for 0 < [small alpha] < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion{,} for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely{,} we demonstrate that under confinement{,} the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments{,} in particular{,} under confinement inside cellular compartments or when optical tweezers tracking methods are used.},
  language  = {en}
}
@article{BauerGodecMetzler2014,
  author    = {Bauer, Maximilian and Godec, Aljaž and Metzler, Ralf},
  title     = {Diffusion of finite-size particles in two-dimensional channels with random wall configurations},
  series = {Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies},
  volume    = {16},
  journal   = {Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies},
  number    = {13},
  publisher = {RSC Publications},
  address   = {Cambridge},
  issn      = {1463-9084},
  doi       = {10.1039/C3CP55160A},
  pages     = {6118 -- 6128},
  year      = {2014},
  abstract  = {Diffusion of chemicals or tracer molecules through complex systems containing irregularly shaped channels is important in many applications. Most theoretical studies based on the famed Fick-Jacobs equation focus on the idealised case of infinitely small particles and reflecting boundaries. In this study we use numerical simulations to consider the transport of finite-size particles through asymmetrical two-dimensional channels. Additionally, we examine transient binding of the molecules to the channel walls by applying sticky boundary conditions. We consider an ensemble of particles diffusing in independent channels, which are characterised by common structural parameters. We compare our results for the long-time effective diffusion coefficient with a recent theoretical formula obtained by Dagdug and Pineda [J. Chem. Phys., 2012, 137, 024107].},
  language  = {en}
}
@misc{BauerGodecMetzler2014,
  author    = {Bauer, Maximilian and Godec, Aljaž and Metzler, Ralf},
  title     = {Diffusion of finite-size particles in two-dimensional channels with random wall configurations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-76199},
  year      = {2014},
  abstract  = {Diffusion of chemicals or tracer molecules through complex systems containing irregularly shaped channels is important in many applications. Most theoretical studies based on the famed Fick-Jacobs equation focus on the idealised case of infinitely small particles and reflecting boundaries. In this study we use numerical simulations to consider the transport of finite-size particles through asymmetrical two-dimensional channels. Additionally, we examine transient binding of the molecules to the channel walls by applying sticky boundary conditions. We consider an ensemble of particles diffusing in independent channels, which are characterised by common structural parameters. We compare our results for the long-time effective diffusion coefficient with a recent theoretical formula obtained by Dagdug and Pineda [J. Chem. Phys., 2012, 137, 024107].},
  language  = {en}
}
@article{FeldmannMaduarSanteretal.2016,
  author    = {Feldmann, David and Maduar, Salim R. and Santer, Mark and Lomadze, Nino and Vinogradova, Olga I. and Santer, Svetlana},
  title     = {Manipulation of small particles at solid liquid interface},
  series = {Scientific reports},
  volume    = {6},
  journal   = {Scientific reports},
  publisher = {Nature Publishing Group},
  address   = {London},
  issn      = {2045-2322},
  doi       = {10.1038/srep36443},
  pages     = {10},
  year      = {2016},
  abstract  = {The strong adhesion of sub-micron sized particles to surfaces is a nuisance, both for removing contaminating colloids from surfaces and for conscious manipulation of particles to create and test novel micro/nano-scale assemblies. The obvious idea of using detergents to ease these processes suffers from a lack of control: the action of any conventional surface-modifying agent is immediate and global. With photosensitive azobenzene containing surfactants we overcome these limitations. Such photo-soaps contain optical switches (azobenzene molecules), which upon illumination with light of appropriate wavelength undergo reversible trans-cis photo-isomerization resulting in a subsequent change of the physico-chemical molecular properties. In this work we show that when a spatial gradient in the composition of trans- and cis- isomers is created near a solid-liquid interface, a substantial hydrodynamic flow can be initiated, the spatial extent of which can be set, e.g., by the shape of a laser spot. We propose the concept of light induced diffusioosmosis driving the flow, which can remove, gather or pattern a particle assembly at a solid-liquid interface. In other words, in addition to providing a soap we implement selectivity: particles are mobilized and moved at the time of illumination, and only across the illuminated area.},
  language  = {en}
}
@misc{FeldmannMaduarSanteretal.2016,
  author    = {Feldmann, David and Maduar, Salim R. and Santer, Mark and Lomadze, Nino and Vinogradova, Olga I. and Santer, Svetlana},
  title     = {Manipulation of small particles at solid liquid interface},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-100338},
  pages     = {10},
  year      = {2016},
  abstract  = {The strong adhesion of sub-micron sized particles to surfaces is a nuisance, both for removing contaminating colloids from surfaces and for conscious manipulation of particles to create and test novel micro/nano-scale assemblies. The obvious idea of using detergents to ease these processes suffers from a lack of control: the action of any conventional surface-modifying agent is immediate and global. With photosensitive azobenzene containing surfactants we overcome these limitations. Such photo-soaps contain optical switches (azobenzene molecules), which upon illumination with light of appropriate wavelength undergo reversible trans-cis photo-isomerization resulting in a subsequent change of the physico-chemical molecular properties. In this work we show that when a spatial gradient in the composition of trans- and cis- isomers is created near a solid-liquid interface, a substantial hydrodynamic flow can be initiated, the spatial extent of which can be set, e.g., by the shape of a laser spot. We propose the concept of light induced diffusioosmosis driving the flow, which can remove, gather or pattern a particle assembly at a solid-liquid interface. In other words, in addition to providing a soap we implement selectivity: particles are mobilized and moved at the time of illumination, and only across the illuminated area.},
  language  = {en}
}