@article{BodrovaSchmidtSpahnetal.2012, author = {Bodrova, Anna and Schmidt, J{\"u}rgen and Spahn, Frank and Brilliantov, Nikolai V.}, title = {Adhesion and collisional release of particles in dense planetary rings}, series = {Icarus : international journal of solar system studies}, volume = {218}, journal = {Icarus : international journal of solar system studies}, number = {1}, publisher = {Elsevier}, address = {San Diego}, issn = {0019-1035}, doi = {10.1016/j.icarus.2011.11.011}, pages = {60 -- 68}, year = {2012}, abstract = {We propose a simple theoretical model for aggregative and fragmentative collisions in Saturn's dense rings. In this model the ring matter consists of a bimodal size distribution: large (meter sized) boulders and a population of smaller particles (tens of centimeters down to dust). The small particles can adhesively stick to the boulders and can be released as debris in binary collisions of their carriers. To quantify the adhesion force we use the JKR theory (Johnson, K., Kendall, K., Roberts, A. [1971]. Proc. R. Soc. Lond. A 324, 301-313). The rates of release and adsorption of particles are calculated, depending on material parameters, sizes, and plausible velocity dispersions of carriers and debris particles. In steady state we obtain an expression for the amount of free debris relative to the fraction still attached to the carriers. In terms of this conceptually simple model a paucity of subcentimeter particles in Saturn's rings (French, R.G., Nicholson, P.D. [2000]. Icarus 145, 502-523; Marouf, E. et al. [2008]. Abstracts for "Saturn after Cassini-Huygens" Symposium, Imperial College London, UK, July 28 to August 1, p. 113) can be understood as a consequence of the increasing strength of adhesion (relative to inertial forces) for decreasing particle size. In this case particles smaller than a certain critical radius remain tightly attached to the surfaces of larger boulders, even when the boulders collide at their typical speed. Furthermore, we find that already a mildly increased velocity dispersion of the carrier-particles may significantly enhance the fraction of free debris particles, in this way increasing the optical depth of the system.}, language = {en} } @article{SafdariCherstvyChechkinetal.2017, author = {Safdari, Hadiseh and Cherstvy, Andrey G. and Chechkin, Aleksei V. and Bodrova, Anna and Metzler, Ralf}, title = {Aging underdamped scaled Brownian motion}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {95}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, publisher = {American Physical Society}, address = {College Park}, issn = {2470-0045}, doi = {10.1103/PhysRevE.95.012120}, pages = {15}, year = {2017}, abstract = {We investigate both analytically and by computer simulations the ensemble- and time-averaged, nonergodic, and aging properties of massive particles diffusing in a medium with a time dependent diffusivity. We call this stochastic diffusion process the (aging) underdamped scaled Brownian motion (UDSBM). We demonstrate how the mean squared displacement (MSD) and the time-averaged MSD of UDSBM are affected by the inertial term in the Langevin equation, both at short, intermediate, and even long diffusion times. In particular, we quantify the ballistic regime for the MSD and the time-averaged MSD as well as the spread of individual time-averaged MSD trajectories. One of the main effects we observe is that, both for the MSD and the time-averaged MSD, for superdiffusive UDSBM the ballistic regime is much shorter than for ordinary Brownian motion. In contrast, for subdiffusive UDSBM, the ballistic region extends to much longer diffusion times. Therefore, particular care needs to be taken under what conditions the overdamped limit indeed provides a correct description, even in the long time limit. We also analyze to what extent ergodicity in the Boltzmann-Khinchin sense in this nonstationary system is broken, both for subdiffusive and superdiffusive UDSBM. Finally, the limiting case of ultraslow UDSBM is considered, with a mixed logarithmic and power-law dependence of the ensemble-and time-averaged MSDs of the particles. In the limit of strong aging, remarkably, the ordinary UDSBM and the ultraslow UDSBM behave similarly in the short time ballistic limit. The approaches developed here open ways for considering other stochastic processes under physically important conditions when a finite particle mass and aging in the system cannot be neglected.}, language = {en} } @article{BodrovaChechkinCherstvyetal.2015, author = {Bodrova, Anna and Chechkin, Aleksei V. and Cherstvy, Andrey G. and Metzler, Ralf}, title = {Quantifying non-ergodic dynamics of force-free granular gases}, series = {Physical chemistry, chemical physics : PCCP ; a journal of European Chemical Societies}, journal = {Physical chemistry, chemical physics : PCCP ; a journal of European Chemical Societies}, number = {17}, issn = {1463-9084}, doi = {10.1039/C5CP02824H}, pages = {21791 -- 21798}, year = {2015}, abstract = {Brownianmotion is ergodic in the Boltzmann-Khinchin sense that long time averages of physical observables such as the mean squared displacement provide the same information as the corresponding ensemble average, even at out-of-equilibrium conditions. This property is the fundamental prerequisite for single particle tracking and its analysis in simple liquids. We study analytically and by event-driven molecular dynamics simulations the dynamics of force-free cooling granular gases and reveal a violation of ergodicity in this Boltzmann- Khinchin sense as well as distinct ageing of the system. Such granular gases comprise materials such as dilute gases of stones, sand, various types of powders, or large molecules, and their mixtures are ubiquitous in Nature and technology, in particular in Space. We treat—depending on the physical-chemical properties of the inter-particle interaction upon their pair collisions—both a constant and a velocity-dependent (viscoelastic) restitution coefficient e. Moreover we compare the granular gas dynamics with an effective single particle stochastic model based on an underdamped Langevin equation with time dependent diffusivity. We find that both models share the same behaviour of the ensemble mean squared displacement (MSD) and the velocity correlations in the limit of weak dissipation. Qualitatively, the reported non-ergodic behaviour is generic for granular gases with any realistic dependence of e on the impact velocity of particles.}, language = {en} } @article{BodrovaChechkinCherstvyetal.2015, author = {Bodrova, Anna and Chechkin, Aleksei V. and Cherstvy, Andrey G. and Metzler, Ralf}, title = {Quantifying non-ergodic dynamics of force-free granular gases}, series = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, volume = {17}, journal = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, number = {34}, publisher = {Royal Society of Chemistry}, address = {Cambridge}, issn = {1463-9076}, doi = {10.1039/c5cp02824h}, pages = {21791 -- 21798}, year = {2015}, abstract = {Brownian motion is ergodic in the Boltzmann-Khinchin sense that long time averages of physical observables such as the mean squared displacement provide the same information as the corresponding ensemble average, even at out-of-equilibrium conditions. This property is the fundamental prerequisite for single particle tracking and its analysis in simple liquids. We study analytically and by event-driven molecular dynamics simulations the dynamics of force-free cooling granular gases and reveal a violation of ergodicity in this Boltzmann-Khinchin sense as well as distinct ageing of the system. Such granular gases comprise materials such as dilute gases of stones, sand, various types of powders, or large molecules, and their mixtures are ubiquitous in Nature and technology, in particular in Space. We treat-depending on the physical-chemical properties of the inter-particle interaction upon their pair collisions-both a constant and a velocity-dependent (viscoelastic) restitution coefficient epsilon. Moreover we compare the granular gas dynamics with an effective single particle stochastic model based on an underdamped Langevin equation with time dependent diffusivity. We find that both models share the same behaviour of the ensemble mean squared displacement (MSD) and the velocity correlations in the limit of weak dissipation. Qualitatively, the reported non-ergodic behaviour is generic for granular gases with any realistic dependence of epsilon on the impact velocity of particles.}, language = {en} } @article{BrilliantovKrapivskyBodrovaetal.2015, author = {Brilliantov, Nikolai V. and Krapivsky, P. L. and Bodrova, Anna and Spahn, Frank and Hayakawa, Hisao and Stadnichuk, Vladimir and Schmidt, Jurgen}, title = {Size distribution of particles in Saturn's rings from aggregation and fragmentation}, series = {Proceedings of the National Academy of Sciences of the United States of America}, volume = {112}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, number = {31}, publisher = {National Acad. of Sciences}, address = {Washington}, issn = {0027-8424}, doi = {10.1073/pnas.1503957112}, pages = {9536 -- 9541}, year = {2015}, abstract = {Saturn's rings consist of a huge number of water ice particles, with a tiny addition of rocky material. They form a flat disk, as the result of an interplay of angular momentum conservation and the steady loss of energy in dissipative interparticle collisions. For particles in the size range from a few centimeters to a few meters, a power-law distribution of radii, similar to r(-q) with q approximate to 3, has been inferred; for larger sizes, the distribution has a steep cutoff. It has been suggested that this size distribution may arise from a balance between aggregation and fragmentation of ring particles, yet neither the power-law dependence nor the upper size cutoff have been established on theoretical grounds. Here we propose a model for the particle size distribution that quantitatively explains the observations. In accordance with data, our model predicts the exponent q to be constrained to the interval 2.75 <= q <= 3.5. Also an exponential cutoff for larger particle sizes establishes naturally with the cutoff radius being set by the relative frequency of aggregating and disruptive collisions. This cutoff is much smaller than the typical scale of microstructures seen in Saturn's rings.}, language = {en} }