TY - GEN A1 - Sposini, Vittoria A1 - Grebenkov, Denis S. A1 - Metzler, Ralf A1 - Oshanin, Gleb A1 - Seno, Flavio T1 - Universal spectral features of different classes of random-diffusivity processes T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments and the displacement probability density function. Here we develop the complementary power spectral description for a broad class of random-diffusivity processes. In our approach we cater for typical single particle tracking data in which a small number of trajectories with finite duration are garnered. Apart from the diffusing-diffusivity model we study a range of previously unconsidered random-diffusivity processes, for which we obtain exact forms of the probability density function. These new processes are different versions of jump processes as well as functionals of Brownian motion. The resulting behaviour subtly depends on the specific model details. Thus, the central part of the probability density function may be Gaussian or non-Gaussian, and the tails may assume Gaussian, exponential, log-normal, or even power-law forms. For all these models we derive analytically the moment-generating function for the single-trajectory power spectral density. We establish the generic 1/f²-scaling of the power spectral density as function of frequency in all cases. Moreover, we establish the probability density for the amplitudes of the random power spectral density of individual trajectories. The latter functions reflect the very specific properties of the different random-diffusivity models considered here. Our exact results are in excellent agreement with extensive numerical simulations. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 999 KW - diffusion KW - power spectrum KW - random diffusivity KW - single trajectories Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-476960 SN - 1866-8372 IS - 999 ER - TY - JOUR A1 - Grebenkov, Denis S. A1 - Metzler, Ralf A1 - Oshanin, Gleb T1 - From single-particle stochastic kinetics to macroscopic reaction rates BT - fastest first-passage time of N random walkers JF - New Journal of Physics N2 - We consider the first-passage problem for N identical independent particles that are initially released uniformly in a finite domain Ω and then diffuse toward a reactive area Γ, which can be part of the outer boundary of Ω or a reaction centre in the interior of Ω. For both cases of perfect and partial reactions, we obtain the explicit formulas for the first two moments of the fastest first-passage time (fFPT), i.e., the time when the first out of the N particles reacts with Γ. Moreover, we investigate the full probability density of the fFPT. We discuss a significant role of the initial condition in the scaling of the average fFPT with the particle number N, namely, a much stronger dependence (1/N and 1/N² for partially and perfectly reactive targets, respectively), in contrast to the well known inverse-logarithmic behaviour found when all particles are released from the same fixed point. We combine analytic solutions with scaling arguments and stochastic simulations to rationalise our results, which open new perspectives for studying the relevance of multiple searchers in various situations of molecular reactions, in particular, in living cells. KW - diffusion KW - first-passage KW - fastest first-passage time of N walkers Y1 - 2020 U6 - https://doi.org/10.1088/1367-2630/abb1de SN - 1367-2630 VL - 22 PB - Dt. Physikalische Ges. CY - Bad Honnef ER - TY - JOUR A1 - Grebenkov, Denis S. A1 - Sposini, Vittoria A1 - Metzler, Ralf A1 - Oshanin, Gleb A1 - Seno, Flavio T1 - Exact distributions of the maximum and range of random diffusivity processes JF - New Journal of Physics N2 - We study the extremal properties of a stochastic process xt defined by the Langevin equation ẋₜ =√2Dₜ ξₜ, in which ξt is a Gaussian white noise with zero mean and Dₜ is a stochastic‘diffusivity’, defined as a functional of independent Brownian motion Bₜ.We focus on threechoices for the random diffusivity Dₜ: cut-off Brownian motion, Dₜt ∼ Θ(Bₜ), where Θ(x) is the Heaviside step function; geometric Brownian motion, Dₜ ∼ exp(−Bₜ); and a superdiffusive process based on squared Brownian motion, Dₜ ∼ B²ₜ. For these cases we derive exact expressions for the probability density functions of the maximal positive displacement and of the range of the process xₜ on the time interval ₜ ∈ (0, T).We discuss the asymptotic behaviours of the associated probability density functions, compare these against the behaviour of the corresponding properties of standard Brownian motion with constant diffusivity (Dₜ = D0) and also analyse the typical behaviour of the probability density functions which is observed for a majority of realisations of the stochastic diffusivity process. KW - random diffusivity KW - extremal values KW - maximum and range KW - diffusion KW - Brownian motion Y1 - 2021 U6 - https://doi.org/10.1088/1367-2630/abd313 SN - 1367-2630 VL - 23 PB - Dt. Physikalische Ges. CY - Bad Honnef ER - TY - GEN A1 - Grebenkov, Denis S. A1 - Sposini, Vittoria A1 - Metzler, Ralf A1 - Oshanin, Gleb A1 - Seno, Flavio T1 - Exact distributions of the maximum and range of random diffusivity processes T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - We study the extremal properties of a stochastic process xt defined by the Langevin equation ẋₜ =√2Dₜ ξₜ, in which ξt is a Gaussian white noise with zero mean and Dₜ is a stochastic‘diffusivity’, defined as a functional of independent Brownian motion Bₜ.We focus on threechoices for the random diffusivity Dₜ: cut-off Brownian motion, Dₜt ∼ Θ(Bₜ), where Θ(x) is the Heaviside step function; geometric Brownian motion, Dₜ ∼ exp(−Bₜ); and a superdiffusive process based on squared Brownian motion, Dₜ ∼ B²ₜ. For these cases we derive exact expressions for the probability density functions of the maximal positive displacement and of the range of the process xₜ on the time interval ₜ ∈ (0, T).We discuss the asymptotic behaviours of the associated probability density functions, compare these against the behaviour of the corresponding properties of standard Brownian motion with constant diffusivity (Dₜ = D0) and also analyse the typical behaviour of the probability density functions which is observed for a majority of realisations of the stochastic diffusivity process. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1142 KW - random diffusivity KW - extremal values KW - maximum and range KW - diffusion KW - Brownian motion Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-503976 SN - 1866-8372 IS - 1142 ER - TY - JOUR A1 - Hajduk, Marcin A1 - Todt, Helge Tobias A1 - Hamann, Wolf-Rainer A1 - Borek, Karolina A1 - van Hoof, Peter A. M. A1 - Zijlstra, Albert A. T1 - The cooling-down central star of the planetary nebula SwSt 1 BT - a late thermal pulse in a massive post-AGB star? JF - Monthly notices of the Royal Astronomical Society N2 - SwSt 1 (PN G001.5-06.7) is a bright and compact planetary nebula containing a late [WC]-type central star. Previous studies suggested that the nebular and stellar lines are slowly changing with time. We studied new and archival optical and ultraviolet spectra of the object. The [O III] 4959 and 5007 angstrom to H beta line flux ratios decreased between about 1976 and 1997/2015. The stellar spectrum also shows changes between these epochs. We modelled the stellar and nebular spectra observed at different epochs. The analyses indicate a drop of the stellar temperature from about 42 kK to 40.5 kK between 1976 and 1993. We do not detect significant changes between 1993 and 2015. The observations show that the star performed a loop in the H-R diagram. This is possible when a shell source is activated during its post-AGB evolution. We infer that a late thermal pulse (LTP) experienced by a massive post-AGB star can explain the evolution of the central star. Such a star does not expand significantly as the result of the LTP and does not became a born-again red giant. However, the released energy can remove the tiny H envelope of the star. KW - stars: AGB and post-AGB KW - stars: atmospheres KW - stars: evolution KW - planetary KW - nebulae: general KW - planetary nebulae: individual: SwSt1 Y1 - 2020 U6 - https://doi.org/10.1093/mnras/staa2274 SN - 0035-8711 SN - 1365-2966 VL - 498 IS - 1 SP - 1205 EP - 1220 PB - Oxford Univ. Press CY - Oxford ER - TY - JOUR A1 - Gruner, David A1 - Barnes, Sydney A. T1 - Rotation periods for cool stars in the open cluster Ruprecht 147 (NGC 6774) Implications for gyrochronology JF - Astronomy and astrophysics : an international weekly journal N2 - Context: Gyrochronology allows the derivation of ages for cool main sequence stars based on their observed rotation periods and masses, or a suitable proxy thereof. It is increasingly well-explored for FGK stars, but requires further measurements for older ages and K - M-type stars. Aims: We study the 2.7 Gyr-old open cluster Ruprecht 147 to compare it with the previously-studied, but far more distant, NGC 6819 cluster, and especially to measure cooler stars than was previously possible there. Methods: We constructed an inclusive list of 102 cluster members from prior work, including Gaia DR2, and for which light curves were also obtained during Campaign 7 of the Kepler/K2 space mission. We placed them in the cluster color-magnitude diagram and checked the related information against appropriate isochrones. The light curves were then corrected for data systematics using Principal Component Analysis on all observed K2 C07 stars and subsequently subjected to periodicity analysis. Results: Periodic signals are found for 32 stars, 21 of which are considered to be both highly reliable and to represent single, or effectively single, Ru 147 stars. These stars cover the spectral types from late-F to mid-M stars, and they have periods ranging from 6 d - 33 d, allowing for a comparison of Ruprecht 147 to both other open clusters and to models of rotational spindown. The derived rotation periods connect reasonably to, overlap with, and extend to lower masses the known rotation period distribution of the 2.5 Gyr-old cluster NGC 6819. Conclusions: The data confirm that cool stars lie on a single surface in rotation period-mass-age space, and they simultaneously challenge its commonly assumed shape. The shape at the low mass region of the color-period diagram at the age of Ru 147 favors a recently-proposed model which requires a third mass-dependent timescale in addition to the two timescales required by a former model, suggesting that a third physical process is required to model rotating stars effectively. KW - stars: late-type KW - stars: low-mass KW - stars: rotation KW - stars: solar-type Y1 - 2020 U6 - https://doi.org/10.1051/0004-6361/202038984 SN - 0004-6361 SN - 1432-0746 VL - 644 PB - EDP Sciences CY - Les Ulis ER - TY - JOUR A1 - Wang, Wei A1 - Seno, Flavio A1 - Sokolov, Igor M. A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Unexpected crossovers in correlated random-diffusivity processes JF - New Journal of Physics N2 - The passive and active motion of micron-sized tracer particles in crowded liquids and inside living biological cells is ubiquitously characterised by 'viscoelastic' anomalous diffusion, in which the increments of the motion feature long-ranged negative and positive correlations. While viscoelastic anomalous diffusion is typically modelled by a Gaussian process with correlated increments, so-called fractional Gaussian noise, an increasing number of systems are reported, in which viscoelastic anomalous diffusion is paired with non-Gaussian displacement distributions. Following recent advances in Brownian yet non-Gaussian diffusion we here introduce and discuss several possible versions of random-diffusivity models with long-ranged correlations. While all these models show a crossover from non-Gaussian to Gaussian distributions beyond some correlation time, their mean squared displacements exhibit strikingly different behaviours: depending on the model crossovers from anomalous to normal diffusion are observed, as well as a priori unexpected dependencies of the effective diffusion coefficient on the correlation exponent. Our observations of the non-universality of random-diffusivity viscoelastic anomalous diffusion are important for the analysis of experiments and a better understanding of the physical origins of 'viscoelastic yet non-Gaussian' diffusion. KW - diffusion KW - anomalous diffusion KW - non-Gaussianity KW - fractional Brownian motion Y1 - 2020 U6 - https://doi.org/10.1088/1367-2630/aba390 SN - 1367-2630 VL - 22 PB - Dt. Physikalische Ges. CY - Bad Honnef ER - TY - GEN A1 - Wang, Wei A1 - Seno, Flavio A1 - Sokolov, Igor M. A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Unexpected crossovers in correlated random-diffusivity processes N2 - The passive and active motion of micron-sized tracer particles in crowded liquids and inside living biological cells is ubiquitously characterised by 'viscoelastic' anomalous diffusion, in which the increments of the motion feature long-ranged negative and positive correlations. While viscoelastic anomalous diffusion is typically modelled by a Gaussian process with correlated increments, so-called fractional Gaussian noise, an increasing number of systems are reported, in which viscoelastic anomalous diffusion is paired with non-Gaussian displacement distributions. Following recent advances in Brownian yet non-Gaussian diffusion we here introduce and discuss several possible versions of random-diffusivity models with long-ranged correlations. While all these models show a crossover from non-Gaussian to Gaussian distributions beyond some correlation time, their mean squared displacements exhibit strikingly different behaviours: depending on the model crossovers from anomalous to normal diffusion are observed, as well as a priori unexpected dependencies of the effective diffusion coefficient on the correlation exponent. Our observations of the non-universality of random-diffusivity viscoelastic anomalous diffusion are important for the analysis of experiments and a better understanding of the physical origins of 'viscoelastic yet non-Gaussian' diffusion. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1006 KW - diffusion KW - anomalous diffusion KW - non-Gaussianity KW - fractional Brownian motion Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-480049 SN - 1866-8372 IS - 1006 ER - TY - JOUR A1 - Kulgemeyer, Christoph A1 - Borowski, Andreas A1 - Buschhüter, David A1 - Enkrott, Patrick A1 - Kempin, Maren A1 - Reinhold, Peter A1 - Riese, Josef A1 - Schecker, Horst A1 - Schröder, Jan A1 - Vogelsang, Christoph T1 - Professional knowledge affects action-related skills BT - the development of preservice physics teachers' explaining skills during a field experience JF - Journal of research in science teaching : the official journal of the National Association for Research in Science Teaching N2 - Professional knowledge is an important source of science teachers' actions in the classroom (e.g., personal professional content knowledge [pedagogical content knowledge, PCK] is the source of enacted PCK in the refined consensus model [RCM] for PCK). However, the evidence for this claim is ambiguous at best. This study applied a cross-lagged panel design to examine the relationship between professional knowledge and actions in one particular instructional situation: explaining physics. Pre- and post a field experience (one semester), 47 preservice physics teachers from four different universities were tested for their content knowledge (CK), PCK, pedagogical knowledge (PK), and action-related skills in explaining physics. The study showed that joint professional knowledge (the weighted sum of CK, PCK, and PK scores) at the beginning of the field experience impacted the development of explaining skills during the field experience (beta = .38**). We interpret this as a particular relationship between professional knowledge and science teachers' action-related skills (enacted PCK): professional knowledge is necessary for the development of explaining skills. That is evidence that personal PCK affects enacted PCK. In addition, field experiences are often supposed to bridge the theory-practice gap by transforming professional knowledge into instructional practice. Our results suggest that for field experiences to be effective, preservice teachers should start with profound professional knowledge. KW - enacted PCK KW - field experience KW - instructional explanation KW - instructional KW - quality KW - practicum KW - professional knowledge KW - school internship Y1 - 2020 U6 - https://doi.org/10.1002/tea.21632 SN - 0022-4308 SN - 1098-2736 VL - 57 IS - 10 SP - 1554 EP - 1582 PB - Wiley CY - Hoboken ER - TY - JOUR A1 - Emanuel, Marc D. A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf A1 - Gompper, Gerhard T1 - Buckling transitions and soft-phase invasion of two-component icosahedral shells JF - Physical review / publ. by The American Physical Society. E, Statistical, nonlinear, and soft matter physics N2 - What is the optimal distribution of two types of crystalline phases on the surface of icosahedral shells, such as of many viral capsids? We here investigate the distribution of a thin layer of soft material on a crystalline convex icosahedral shell. We demonstrate how the shapes of spherical viruses can be understood from the perspective of elasticity theory of thin two-component shells. We develop a theory of shape transformations of an icosahedral shell upon addition of a softer, but still crystalline, material onto its surface. We show how the soft component "invades" the regions with the highest elastic energy and stress imposed by the 12 topological defects on the surface. We explore the phase diagram as a function of the surface fraction of the soft material, the shell size, and the incommensurability of the elastic moduli of the rigid and soft phases. We find that, as expected, progressive filling of the rigid shell by the soft phase starts from the most deformed regions of the icosahedron. With a progressively increasing soft-phase coverage, the spherical segments of domes are filled first (12 vertices of the shell), then the cylindrical segments connecting the domes (30 edges) are invaded, and, ultimately, the 20 flat faces of the icosahedral shell tend to be occupied by the soft material. We present a detailed theoretical investigation of the first two stages of this invasion process and develop a model of morphological changes of the cone structure that permits noncircular cross sections. In conclusion, we discuss the biological relevance of some structures predicted from our calculations, in particular for the shape of viral capsids. Y1 - 2020 U6 - https://doi.org/10.1103/PhysRevE.102.062104 SN - 2470-0045 SN - 2470-0053 SN - 2470-0061 SN - 1538-4519 VL - 102 IS - 6 PB - Woodbury CY - New York ER -