Institut für Physik und Astronomie
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Finite-size-induced transitions to synchrony in oscillator ensembles with nonlinear global coupling
(2015)
We report on finite-sized-induced transitions to synchrony in a population of phase oscillators coupled via a nonlinear mean field, which microscopically is equivalent to a hypernetwork organization of interactions. Using a self-consistent approach and direct numerical simulations, we argue that a transition to synchrony occurs only for finite-size ensembles and disappears in the thermodynamic limit. For all considered setups, which include purely deterministic oscillators with or without heterogeneity in natural oscillatory frequencies, and an ensemble of noise-driven identical oscillators, we establish scaling relations describing the order parameter as a function of the coupling constant and the system size.
We investigate the ultrafast magnetization dynamics of FePt in the L1(0) phase after an optical heating pulse, as used in heat-assisted magnetic recording. We compare continuous and nano-granular thin films and emphasize the impact of the finite size on the remagnetization dynamics. The remagnetization speeds up significantly with increasing external magnetic field only for the continuous film, where domain-wall motion governs the dynamics. The ultrafast remagnetization dynamics in the continuous film are only dominated by heat transport in the regime of high magnetic fields, whereas the timescale required for cooling is prevalent in the granular film for all magnetic field strengths. These findings highlight the necessary conditions for studying the intrinsic heat transport properties in magnetic materials.
We consider a large population of globally coupled noisy phase oscillators. In the thermodynamic limit N this system exhibits a nonequilibrium phase transition, at which amacroscopic mean field appears. It is shown that for large but finite system size N the system can be described by the noisy Stuart-Landau equation, yielding scaling behavior of statistical characteristics of the macroscopic mean field with N. The predictions of the theory are checked numerically.
Complex systems are known to display anomalous diffusion, whose signature is a space/time scaling x similar to t(delta) with delta not equal 1/2 in the probability density function (PDF). Anomalous diffusion can emerge jointly with both Gaussian, e.g. fractional Brownian motion, and power-law decaying distributions, e.g. Levy Flights or Levy Walks (LWs). Levy flights get anomalous scaling, but, being jumps of any size allowed even at short times, have infinite position variance, infinite energy and discontinuous paths. LWs, which are based on random trapping events, overcome these limitations: they resemble a Levy-type power-law distribution that is truncated in the large displacement range and have finite moments, finite energy and, even with discontinuous velocity, they are continuous. However, LWs do not take into account the role of strong heterogeneity in many complex systems, such as biological transport in the crowded cell environment. In this work we propose and discuss a model describing a heterogeneous ensemble of Brownian particles (HEBP). Velocity of each single particle obeys a standard underdamped Langevin equation for the velocity, with linear friction term and additive Gaussian noise. Each particle is characterized by its own relaxation time and velocity diffusivity. We show that, for proper distributions of relaxation time and velocity diffusivity, the HEBP resembles some LW statistical features, in particular power-law decaying PDF, long-range correlations and anomalous diffusion, at the same time keeping finite position moments and finite energy. The main differences between the HEBP model and two different LWs are investigated, finding that, even when both velocity and position PDFs are similar, they differ in four main aspects: (i) LWs are biscaling, while HEBP is monoscaling; (ii) a transition from anomalous (delta = 1/2) to normal (delta = 1/2) diffusion in the long-time regime is seen in the HEBP and not in LWs; (iii) the power-law index of the position PDF and the space/time diffusion scaling are independent in the HEBP, while they both depend on the scaling of the interevent time PDF in LWs; (iv) at variance with LWs, our HEBP model obeys a fluctuation-dissipation theorem.
We consider a one-dimensional oscillatory medium with a coupling through a diffusive linear field. In the limit of fast diffusion this setup reduces to the classical Kuramoto–Battogtokh model. We demonstrate that for a finite diffusion stable chimera solitons, namely localized synchronous domain in an infinite asynchronous environment, are possible. The solitons are stable also for finite density of oscillators, but in this case they sway with a nearly constant speed. This finite-density-induced motility disappears in the continuum limit, as the velocity of the solitons is inverse proportional to the density. A long-wave instability of the homogeneous asynchronous state causes soliton turbulence, which appears as a sequence of soliton mergings and creations. As the instability of the asynchronous state becomes stronger, this turbulence develops into a spatio-temporal intermittency.
We consider a one-dimensional oscillatory medium with a coupling through a diffusive linear field. In the limit of fast diffusion this setup reduces to the classical Kuramoto–Battogtokh model. We demonstrate that for a finite diffusion stable chimera solitons, namely localized synchronous domain in an infinite asynchronous environment, are possible. The solitons are stable also for finite density of oscillators, but in this case they sway with a nearly constant speed. This finite-density-induced motility disappears in the continuum limit, as the velocity of the solitons is inverse proportional to the density. A long-wave instability of the homogeneous asynchronous state causes soliton turbulence, which appears as a sequence of soliton mergings and creations. As the instability of the asynchronous state becomes stronger, this turbulence develops into a spatio-temporal intermittency.
This thesis is concerned with the development of numerical methods using finite difference techniques for the discretization of initial value problems (IVPs) and initial boundary value problems (IBVPs) of certain hyperbolic systems which are first order in time and second order in space. This type of system appears in some formulations of Einstein equations, such as ADM, BSSN, NOR, and the generalized harmonic formulation. For IVP, the stability method proposed in [14] is extended from second and fourth order centered schemes, to 2n-order accuracy, including also the case when some first order derivatives are approximated with off-centered finite difference operators (FDO) and dissipation is added to the right-hand sides of the equations. For the model problem of the wave equation, special attention is paid to the analysis of Courant limits and numerical speeds. Although off-centered FDOs have larger truncation errors than centered FDOs, it is shown that in certain situations, off-centering by just one point can be beneficial for the overall accuracy of the numerical scheme. The wave equation is also analyzed in respect to its initial boundary value problem. All three types of boundaries - outflow, inflow and completely inflow that can appear in this case, are investigated. Using the ghost-point method, 2n-accurate (n = 1, 4) numerical prescriptions are prescribed for each type of boundary. The inflow boundary is also approached using the SAT-SBP method. In the end of the thesis, a 1-D variant of BSSN formulation is derived and some of its IBVPs are considered. The boundary procedures, based on the ghost-point method, are intended to preserve the interior 2n-accuracy. Numerical tests show that this is the case if sufficient dissipation is added to the rhs of the equations.
We describe how inversion symmetry separation of electronic state manifolds in resonant inelastic soft X-ray scattering (RIXS) can be applied to probe excited-state dynamics with compelling selectivity. In a case study of Fe L3-edge RIXS in the ferricyanide complex Fe(CN)63−, we demonstrate with multi-configurational restricted active space spectrum simulations how the information content of RIXS spectral fingerprints can be used to unambiguously separate species of different electronic configurations, spin multiplicities, and structures, with possible involvement in the decay dynamics of photo-excited ligand-to-metal charge-transfer. Specifically, we propose that this could be applied to confirm or reject the presence of a hitherto elusive transient Quartet species. Thus, RIXS offers a particular possibility to settle a recent controversy regarding the decay pathway, and we expect the technique to be similarly applicable in other model systems of photo-induced dynamics.
The total population of Wolf-Rayet (WR) stars in the Galaxy is predicted by models to be as many as ~6000 stars, and yet the number of catalogued WR stars as a result of optical surveys was far lower than this (~200) at the turn of this century. When beginning our WR searches using infrared techniques it was not clear whether WR number predictions were too optimistic or whether there was more hidden behind interstellar and circumstellar extinction. During the last decade we pioneered a technique of exploiting the near- and mid-infrared continuum colours for individual point sources provided by large-format surveys of the Galaxy, including 2MASS and Spitzer/GLIMPSE, to pierce through the dust and reveal newly discovered WR stars throughout the Galactic Plane. The key item to the colour discrimination is via the characteristic infrared spectral index produced by the strong winds of the WR stars, combined with dust extinction, which place WR stars in a relatively depopulated area of infrared colour-colour diagrams. The use of the Spitzer/GLIMPSE 8µm and, more recently, WISE 22µm fluxes together with cross-referencing with X-ray measurements in selected Galactic regions have enabled improved candidate lists that increased our confirmation success rate, achieved via follow-up infrared and optical spectroscopy. To date a total of 102 new WR stars have been found with many more
candidates still available for follow-up. This constitutes an addition of ~16% to the current
inventory of 642 Galactic WR stars. In this talk we review our methods and provide some
new results and a preliminary review of their stellar and interstellar medium environments. We provide a roadmap for the future of this search, including statistical modeling, and what we can add to star formation and high mass star evolution studies.
We summarize past and current surveys for WRs among the Local Group galaxies, empha- sizing both the why and how. Such studies are invaluable for helping us learn about massive star evolution, and for providing sensitive tests of the stellar evolution models. But for such surveys to be useful, the completeness limits must be well understood. We illustrate that point by following the “evolution” of the observed WC/WN ratio in nearby galaxies. We end by examining our new survey for WR stars in the Magellanic Clouds, which has revealed a new type of WN star, never before seen.