TY - GEN A1 - Benini, Marco A1 - Schenkel, Alexander T1 - Quantum field theories on categories fibered in groupoids T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with extra geometric structures such as bundles, connections and spin structures. Using right Kan extensions, we can assign to any such theory an ordinary quantum field theory defined on the category of spacetimes and we shall clarify under which conditions it satisfies the axioms of locally covariant quantum field theory. The same constructions can be performed in a homotopy theoretic framework by using homotopy right Kan extensions, which allows us to obtain first toy-models of homotopical quantum field theories resembling some aspects of gauge theories. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 895 KW - C-asterisk-algebra KW - observables KW - covariance KW - locality Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-431541 SN - 1866-8372 IS - 895 ER - TY - GEN A1 - Clusella, Pau A1 - Politi, Antonio A1 - Rosenblum, Michael T1 - A minimal model of self-consistent partial synchrony T2 - Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe N2 - We show that self-consistent partial synchrony in globally coupled oscillatory ensembles is a general phenomenon. We analyze in detail appearance and stability properties of this state in possibly the simplest setup of a biharmonic Kuramoto-Daido phase model as well as demonstrate the effect in limit-cycle relaxational Rayleigh oscillators. Such a regime extends the notion of splay state from a uniform distribution of phases to an oscillating one. Suitable collective observables such as the Kuramoto order parameter allow detecting the presence of an inhomogeneous distribution. The characteristic and most peculiar property of self-consistent partial synchrony is the difference between the frequency of single units and that of the macroscopic field. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 890 KW - synchronization KW - collective dynamics KW - coupled oscillators Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-436266 SN - 1866-8372 IS - 890 ER - TY - GEN A1 - Gühr, Markus T1 - Ultrafast Soft X-ray Probing of Gas Phase Molecular Dynamics N2 - The molecular ability to selectively and efficiently convert sunlight into other forms of energy like heat, bond change, or charge separation is truly remarkable. The decisive steps in these transformations often happen on a femtosecond timescale and require transitions among different electronic states that violate the Born-Oppenheimer approximation (BOA). Non-BOA transitions pose challenges to both theory and experiment. From a theoretical point of view, excited state dynamics and nonadiabatic transitions both are difficult problems (see Figure 1(a)). However, the theory on non-BOA dynamics has advanced significantly over the last two decades. Full dynamical simulations for molecules of the size of nucleobases have been possible for a couple of years and allow predictions of experimental observables like photoelectron energy or ion yield. The availability of these calculations for isolated molecules has spurred new experimental efforts to develop methods that are sufficiently different from all optical techniques. For determination of transient molecular structure, femtosecond X-ray diffraction and electron diffraction have been implemented on optically excited molecules. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 268 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-97215 ER - TY - GEN A1 - Palyulin, Vladimir V. A1 - Ala-Nissila, Tapio A1 - Metzler, Ralf T1 - Polymer translocation: the first two decades and the recent diversification N2 - Probably no other field of statistical physics at the borderline of soft matter and biological physics has caused such a flurry of papers as polymer translocation since the 1994 landmark paper by Bezrukov, Vodyanoy, and Parsegian and the study of Kasianowicz in 1996. Experiments, simulations, and theoretical approaches are still contributing novel insights to date, while no universal consensus on the statistical understanding of polymer translocation has been reached. We here collect the published results, in particular, the famous–infamous debate on the scaling exponents governing the translocation process. We put these results into perspective and discuss where the field is going. In particular, we argue that the phenomenon of polymer translocation is non-universal and highly sensitive to the exact specifications of the models and experiments used towards its analysis. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 179 KW - solid-state nanopores KW - single-stranded-dna KW - posttranslational protein translocation KW - anomalous diffusion KW - monte-carlo KW - structured polynucleotides KW - dynamics simulation KW - equation approach KW - osmotic-pressure KW - membrane channel Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-76287 SP - 9016 EP - 9037 ER - TY - GEN A1 - Metzler, Ralf A1 - Bauer, Maximilian A1 - Rasmussen, Emil S. A1 - Lomholt, Michael A. T1 - Real sequence effects on the search dynamics of transcription factors on DNA N2 - Recent experiments show that transcription factors (TFs) indeed use the facilitated diffusion mechanism to locate their target sequences on DNA in living bacteria cells: TFs alternate between sliding motion along DNA and relocation events through the cytoplasm. From simulations and theoretical analysis we study the TF-sliding motion for a large section of the DNA-sequence of a common E. coli strain, based on the two-state TF-model with a fast-sliding search state and a recognition state enabling target detection. For the probability to detect the target before dissociating from DNA the TF-search times self-consistently depend heavily on whether or not an auxiliary operator (an accessible sequence similar to the main operator) is present in the genome section. Importantly, within our model the extent to which the interconversion rates between search and recognition states depend on the underlying nucleotide sequence is varied. A moderate dependence maximises the capability to distinguish between the main operator and similar sequences. Moreover, these auxiliary operators serve as starting points for DNA looping with the main operator, yielding a spectrum of target detection times spanning several orders of magnitude. Auxiliary operators are shown to act as funnels facilitating target detection by TFs. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 189 KW - gene regulatory networks KW - biological physics Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-79411 ER - TY - GEN A1 - Ghosh, Surya K. A1 - Cherstvy, Andrey G. A1 - Petrov, Eugene P. A1 - Metzler, Ralf T1 - Interactions of rod-like particles on responsive elastic sheets N2 - What are the physical laws of the mutual interactions of objects bound to cell membranes, such as various membrane proteins or elongated virus particles? To rationalise this, we here investigate by extensive computer simulations mutual interactions of rod-like particles adsorbed on the surface of responsive elastic two-dimensional sheets. Specifically, we quantify sheet deformations as a response to adhesion of such filamentous particles. We demonstrate that tip-to-tip contacts of rods are favoured for relatively soft sheets, while side-by-side contacts are preferred for stiffer elastic substrates. These attractive orientation-dependent substrate-mediated interactions between the rod-like particles on responsive sheets can drive their aggregation and self-assembly. The optimal orientation of the membrane-bound rods is established via responding to the elastic energy profiles created around the particles. We unveil the phase diagramme of attractive–repulsive rod–rod interactions in the plane of their separation and mutual orientation. Applications of our results to other systems featuring membrane-associated particles are also discussed. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 256 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-95882 ER - TY - GEN A1 - Goychuk, Igor T1 - Quantum ergodicity breaking in semi-classical electron transfer dynamics N2 - Can the statistical properties of single-electron transfer events be correctly predicted within a common equilibrium ensemble description? This fundamental in nanoworld question of ergodic behavior is scrutinized within a very basic semi-classical curve-crossing problem. It is shown that in the limit of non-adiabatic electron transfer (weak tunneling) well-described by the Marcus–Levich–Dogonadze(MLD) rate the answer is yes. However, in the limit of the so-called solvent-controlled adiabatic electron transfer, a profound breaking of ergodicity occurs. Namely, a common description based on the ensemble reduced density matrix with an initial equilibrium distribution of the reaction coordinate is not able to reproduce the statistics of single-trajectory events in this seemingly classical regime. For sufficiently large activation barriers, the ensemble survival probability in a state remains nearly exponential with the inverse rate given by the sum of the adiabatic curve crossing (Kramers) time and the inverse MLD rate. In contrast, near to the adiabatic regime, the single-electron survival probability is clearly non-exponential, even though it possesses an exponential tail which agrees well with the ensemble description. Initially, it is well described by a Mittag-Leffler distribution with a fractional rate. Paradoxically, the mean transfer time in this classical on the ensemble level regime is well described by the inverse of the nonadiabatic quantum tunneling rate on a single particle level. An analytical theory is developed which perfectly agrees with stochastic simulations and explains our findings. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 299 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-102264 ER - TY - GEN A1 - de Carvalho, Sidney J. A1 - Metzler, Ralf A1 - Cherstvy, Andrey G. T1 - Critical adsorption of polyelectrolytes onto planar and convex highly charged surfaces BT - the nonlinear Poisson–Boltzmann approach N2 - We study the adsorption–desorption transition of polyelectrolyte chains onto planar, cylindrical and spherical surfaces with arbitrarily high surface charge densities by massive Monte Carlo computer simulations. We examine in detail how the well known scaling relations for the threshold transition—demarcating the adsorbed and desorbed domains of a polyelectrolyte near weakly charged surfaces—are altered for highly charged interfaces. In virtue of high surface potentials and large surface charge densities, the Debye–Hückel approximation is often not feasible and the nonlinear Poisson–Boltzmann approach should be implemented. At low salt conditions, for instance, the electrostatic potential from the nonlinear Poisson–Boltzmann equation is smaller than the Debye–Hückel result, such that the required critical surface charge density for polyelectrolyte adsorption σc increases. The nonlinear relation between the surface charge density and electrostatic potential leads to a sharply increasing critical surface charge density with growing ionic strength, imposing an additional limit to the critical salt concentration above which no polyelectrolyte adsorption occurs at all. We contrast our simulations findings with the known scaling results for weak critical polyelectrolyte adsorption onto oppositely charged surfaces for the three standard geometries. Finally, we discuss some applications of our results for some physical–chemical and biophysical systems. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 292 KW - polyelectrolyte adsorption KW - electrostatic interactions KW - critical phenomena KW - Debye screening Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-100295 ER - TY - GEN A1 - Koseska, Aneta A1 - Zaikin, Alexey A1 - Kurths, Jürgen A1 - García-Ojalvo, Jordi T1 - Timing cellular decision making under noise via cell-cell communication N2 - Many cellular processes require decision making mechanisms, which must act reliably even in the unavoidable presence of substantial amounts of noise. However, the multistable genetic switches that underlie most decision-making processes are dominated by fluctuations that can induce random jumps between alternative cellular states. Here we show, via theoretical modeling of a population of noise-driven bistable genetic switches, that reliable timing of decision-making processes can be accomplished for large enough population sizes, as long as cells are globally coupled by chemical means. In the light of these results, we conjecture that cell proliferation, in the presence of cell-cell communication, could provide a mechanism for reliable decision making in the presence of noise, by triggering cellular transitions only when the whole cell population reaches a certain size. In other words , the summation performed by the cell population would average out the noise and reduce its detrimental impact. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 148 Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-45260 ER - TY - GEN A1 - Totz, Sonja Juliana A1 - Löber, Jakob A1 - Totz, Jan Frederik A1 - Engel, Harald T1 - Control of transversal instabilities in reaction-diffusion systems T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - In two-dimensional reaction-diffusion systems, local curvature perturbations on traveling waves are typically damped out and vanish. However, if the inhibitor diffuses much faster than the activator, transversal instabilities can arise, leading from flat to folded, spatio-temporally modulated waves and to spreading spiral turbulence. Here, we propose a scheme to induce or inhibit these instabilities via a spatio-temporal feedback loop. In a piecewise-linear version of the FitzHugh-Nagumo model, transversal instabilities and spiral turbulence in the uncontrolled system are shown to be suppressed in the presence of control, thereby stabilizing plane wave propagation. Conversely, in numerical simulations with the modified Oregonator model for the photosensitive Belousov-Zhabotinsky reaction, which does not exhibit transversal instabilities on its own, we demonstrate the feasibility of inducing transversal instabilities and study the emerging wave patterns in a well-controlled manner. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 962 KW - traveling waves KW - control KW - transversal instabilities Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-469762 SN - 1866-8372 IS - 962 ER - TY - GEN A1 - Mardoukhi, Yousof A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Spurious ergodicity breaking in normal and fractional Ornstein–Uhlenbeck process T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - The Ornstein–Uhlenbeck process is a stationary and ergodic Gaussian process, that is fully determined by its covariance function and mean. We show here that the generic definitions of the ensemble- and time-averaged mean squared displacements fail to capture these properties consistently, leading to a spurious ergodicity breaking. We propose to remedy this failure by redefining the mean squared displacements such that they reflect unambiguously the statistical properties of any stochastic process. In particular we study the effect of the initial condition in the Ornstein–Uhlenbeck process and its fractional extension. For the fractional Ornstein–Uhlenbeck process representing typical experimental situations in crowded environments such as living biological cells, we show that the stationarity of the process delicately depends on the initial condition. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 981 KW - Ornstein–Uhlenbeck process KW - stationary stochastic process KW - ensemble and time averaged mean squared displacement Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-474875 SN - 1866-8372 IS - 981 ER - TY - GEN A1 - Menzel, Ralf A1 - Heuer, Axel A1 - Milonni, Peter W. T1 - Entanglement, complementarity, and vacuum fields in spontaneous parametric down-conversion T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - Using two crystals for spontaneous parametric down-conversion in a parallel setup, we observe two-photon interference with high visibility. The high visibility is consistent with complementarity and the absence of which-path information. The observations are explained as the effects of entanglement or equivalently in terms of interfering probability amplitudes and also by the calculation of a second-order field correlation function in the Heisenberg picture. The latter approach brings out explicitly the role of the vacuum fields in the down-conversion at the crystals and in the photon coincidence counting. For comparison, we show that the Hong–Ou–Mandel dip can be explained by the same approach in which the role of the vacuum signal and idler fields, as opposed to entanglement involving vacuum states, is emphasized. We discuss the fundamental limitations of a theory in which these vacuum fields are treated as classical, stochastic fields. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1077 KW - complementarity KW - vacuum fields KW - entanglement KW - Hong-Ou-Mandel effect KW - spontaneous parametric down-conversion Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-473542 SN - 1866-8372 IS - 1077 ER - TY - GEN A1 - Schaal, Frederik A1 - Rutloh, Michael A1 - Weidenfeld, Susanne A1 - Stumpe, Joachim A1 - Michler, Peter A1 - Pruss, Christof A1 - Osten, Wolfgang T1 - Optically addressed modulator for tunable spatial polarization control T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - We present an optically addressed non-pixelated spatial light modulator. The system is based on reversible photoalignment of a LC cell using a red light sensitive novel azobenzene photoalignment layer. It is an electrode-free device that manipulates the liquid crystal orientation and consequently the polarization via light without artifacts caused by electrodes. The capability to miniaturize the spatial light modulator allows the integration into a microscope objective. This includes a miniaturized 200 channel optical addressing system based on a VCSEL array and hybrid refractive-diffractive beam shapers. As an application example, the utilization as a microscope objective integrated analog phase contrast modulator is shown. (C) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1001 KW - nematic liquid crystals KW - command surfaces KW - light modulator KW - alignment KW - films KW - polymer Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-446263 SN - 1866-8372 IS - 1001 SP - 28119 EP - 28130 ER - TY - GEN A1 - Granado, Felipe Le Vot A1 - Abad, Enrique A1 - Metzler, Ralf A1 - Yuste, Santos B. T1 - Continuous time random walk in a velocity field BT - role of domain growth, Galilei-invariant advection-diffusion, and kinetics of particle mixing T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - We consider the emerging dynamics of a separable continuous time random walk (CTRW) in the case when the random walker is biased by a velocity field in a uniformly growing domain. Concrete examples for such domains include growing biological cells or lipid vesicles, biofilms and tissues, but also macroscopic systems such as expanding aquifers during rainy periods, or the expanding Universe. The CTRW in this study can be subdiffusive, normal diffusive or superdiffusive, including the particular case of a Lévy flight. We first consider the case when the velocity field is absent. In the subdiffusive case, we reveal an interesting time dependence of the kurtosis of the particle probability density function. In particular, for a suitable parameter choice, we find that the propagator, which is fat tailed at short times, may cross over to a Gaussian-like propagator. We subsequently incorporate the effect of the velocity field and derive a bi-fractional diffusion-advection equation encoding the time evolution of the particle distribution. We apply this equation to study the mixing kinetics of two diffusing pulses, whose peaks move towards each other under the action of velocity fields acting in opposite directions. This deterministic motion of the peaks, together with the diffusive spreading of each pulse, tends to increase particle mixing, thereby counteracting the peak separation induced by the domain growth. As a result of this competition, different regimes of mixing arise. In the case of Lévy flights, apart from the non-mixing regime, one has two different mixing regimes in the long-time limit, depending on the exact parameter choice: in one of these regimes, mixing is mainly driven by diffusive spreading, while in the other mixing is controlled by the velocity fields acting on each pulse. Possible implications for encounter–controlled reactions in real systems are discussed. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1005 KW - diffusion KW - expanding medium KW - continuous time random walk Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-479997 SN - 1866-8372 IS - 1005 SP - 28 ER - TY - GEN A1 - Ślęzak, Jakub A1 - Metzler, Ralf A1 - Magdziarz, Marcin T1 - Codifference can detect ergodicity breaking and non-Gaussianity T2 - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe N2 - We show that the codifference is a useful tool in studying the ergodicity breaking and non-Gaussianity properties of stochastic time series. While the codifference is a measure of dependence that was previously studied mainly in the context of stable processes, we here extend its range of applicability to random-parameter and diffusing-diffusivity models which are important in contemporary physics, biology and financial engineering. We prove that the codifference detects forms of dependence and ergodicity breaking which are not visible from analysing the covariance and correlation functions. We also discuss a related measure of dispersion, which is a nonlinear analogue of the mean squared displacement. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 748 KW - diffusion KW - anomalous diffusion KW - stochastic time series Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-436178 IS - 748 ER - TY - GEN A1 - Sposini, Vittoria A1 - Metzler, Ralf A1 - Oshanin, Gleb T1 - Single-trajectory spectral analysis of scaled Brownian motion T2 - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe N2 - Astandard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the asymptotic limit of long observation times, T → ∞. In many experimental situations one is able to garner only relatively few stochastic time series of finite T, such that practically neither an ensemble average nor the asymptotic limit T → ∞ can be achieved. To accommodate for a meaningful analysis of such finite-length data we here develop the framework of single-trajectory spectral analysis for one of the standard models of anomalous diffusion, scaled Brownian motion.Wedemonstrate that the frequency dependence of the single-trajectory PSD is exactly the same as for standard Brownian motion, which may lead one to the erroneous conclusion that the observed motion is normal-diffusive. However, a distinctive feature is shown to be provided by the explicit dependence on the measurement time T, and this ageing phenomenon can be used to deduce the anomalous diffusion exponent.Wealso compare our results to the single-trajectory PSD behaviour of another standard anomalous diffusion process, fractional Brownian motion, and work out the commonalities and differences. Our results represent an important step in establishing singletrajectory PSDs as an alternative (or complement) to analyses based on the time-averaged mean squared displacement. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 753 KW - diffusion KW - anomalous diffusion KW - power spectral analysis KW - single trajectory analysis Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-436522 SN - 1866-8372 IS - 753 ER - TY - GEN A1 - Guggenberger, Tobias A1 - Pagnini, Gianni A1 - Vojta, Thomas A1 - Metzler, Ralf T1 - Fractional Brownian motion in a finite interval BT - correlations effect depletion or accretion zones of particles near boundaries T2 - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe N2 - Fractional Brownian motion (FBM) is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically FBM confined to a finite interval with reflecting boundary conditions. The probability density function of this reflected FBM at long times converges to a stationary distribution showing distinct deviations from the fully flat distribution of amplitude 1/L in an interval of length L found for reflected normal Brownian motion. While for superdiffusion, corresponding to a mean squared displacement (MSD) 〈X² (t)〉 ⋍ tᵅ with 1 < α < 2, the probability density function is lowered in the centre of the interval and rises towards the boundaries, for subdiffusion (0 < α < 1) this behaviour is reversed and the particle density is depleted close to the boundaries. The MSD in these cases at long times converges to a stationary value, which is, remarkably, monotonically increasing with the anomalous diffusion exponent α. Our a priori surprising results may have interesting consequences for the application of FBM for processes such as molecule or tracer diffusion in the confines of living biological cells or organelles, or other viscoelastic environments such as dense liquids in microfluidic chambers. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 755 KW - anomalous diffusion KW - fractional Brownian motion KW - reflecting boundary conditions Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-436665 SN - 1866-8372 IS - 755 ER - TY - GEN A1 - Ślęzak, Jakub A1 - Burnecki, Krzysztof A1 - Metzler, Ralf T1 - Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems T2 - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe N2 - Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is ascribed to the heterogeneity of the medium and is captured by random parameter models such as ‘superstatistics’ or ‘diffusing diffusivity’. Independently, scientists working in the area of time series analysis and statistics have studied a class of discrete-time processes with similar properties, namely, random coefficient autoregressive models. In this work we try to reconcile these two approaches and thus provide a bridge between physical stochastic processes and autoregressive models.Westart from the basic Langevin equation of motion with time-varying damping or diffusion coefficients and establish the link to random coefficient autoregressive processes. By exploring that link we gain access to efficient statistical methods which can help to identify data exhibiting Brownian yet non-Gaussian diffusion. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 765 KW - diffusion KW - Langevin equation KW - Brownian yet non-Gaussian diffusion KW - diffusing diffusivity KW - superstatistics KW - autoregressive models KW - time series analysis KW - codifference Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-437923 SN - 1866-8372 IS - 765 ER - TY - GEN A1 - Devchand, Chandrashekar A1 - Nuyts, Jean A1 - Weingart, Gregor T1 - Matryoshka of special democratic forms T2 - Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe N2 - Special p-forms are forms which have components fµ1…µp equal to +1, -1 or 0 in some orthonormal basis. A p-form ϕ ∈ � pRd is called democratic if the set of nonzero components {ϕμ1...μp} is symmetric under the transitive action of a subgroup of O(d,Z) on the indices {1, . . . , d}. Knowledge of these symmetry groups allows us to define mappings of special democratic p-forms in d dimensions to special democratic P-forms in D dimensions for successively higher P = p and D = d. In particular, we display a remarkable nested structure of special forms including a U(3)-invariant 2-form in six dimensions, a G2-invariant 3-form in seven dimensions, a Spin(7)-invariant 4-form in eight dimensions and a special democratic 6-form O in ten dimensions. The latter has the remarkable property that its contraction with one of five distinct bivectors, yields, in the orthogonal eight dimensions, the Spin(7)-invariant 4-form. We discuss various properties of this ten dimensional form. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 841 KW - commutator subgroup KW - transitive action KW - cycle decomposition KW - democratic form KW - special holonomy Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-429002 SN - 1866-8372 IS - 841 SP - 545 EP - 562 ER - TY - GEN A1 - Perovic, Milena A1 - Qin, Qing A1 - Oschatz, Martin T1 - From molecular precursors to nanoparticles BT - tailoring the adsorption properties of porous carbon materials by controlled chemical functionalization T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - Nanoporous carbon materials (NCMs) provide the "function" of high specific surface area and thus have large interface area for interactions with surrounding species, which is of particular importance in applications related to adsorption processes. The strength and mechanism of adsorption depend on the pore architecture of the NCMs. In addition, chemical functionalization can be used to induce changes of electron density and/or electron density distribution in the pore walls, thus further modifying the interactions between carbons and guest species. Typical approaches for functionalization of nanoporous materials with regular atomic construction like porous silica, metal-organic frameworks, or zeolites, cannot be applied to NCMs due to their less defined local atomic construction and abundant defects. Therefore, synthetic strategies that offer a higher degree of control over the process of functionalization are needed. Synthetic approaches for covalent functionalization of NCMs, that is, for the incorporation of heteroatoms into the carbon backbone, are critically reviewed with a special focus on strategies following the concept "from molecules to materials." Approaches for coordinative functionalization with metallic species, and the functionalization by nanocomposite formation between pristine carbon materials and heteroatom-containing carbons, are introduced as well. Particular focus is given to the influences of these functionalizations in adsorption-related applications. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1191 KW - composites KW - heteroatoms KW - metal species KW - porous carbon materials KW - surface functionalization Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-516140 SN - 1866-8372 ER - TY - GEN A1 - Thapa, Samudrajit A1 - Wyłomańska, Agnieszka A1 - Sikora, Grzegorz A1 - Wagner, Caroline E. A1 - Krapf, Diego A1 - Kantz, Holger A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectories T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - Extensive time-series encoding the position of particles such as viruses, vesicles, or individualproteins are routinely garnered insingle-particle tracking experiments or supercomputing studies.They contain vital clues on how viruses spread or drugs may be delivered in biological cells.Similar time-series are being recorded of stock values in financial markets and of climate data.Such time-series are most typically evaluated in terms of time-averaged mean-squareddisplacements (TAMSDs), which remain random variables for finite measurement times. Theirstatistical properties are different for differentphysical stochastic processes, thus allowing us toextract valuable information on the stochastic process itself. To exploit the full potential of thestatistical information encoded in measured time-series we here propose an easy-to-implementand computationally inexpensive new methodology, based on deviations of the TAMSD from itsensemble average counterpart. Specifically, we use the upper bound of these deviations forBrownian motion (BM) to check the applicability of this approach to simulated and real data sets.By comparing the probability of deviations fordifferent data sets, we demonstrate how thetheoretical bound for BM reveals additional information about observed stochastic processes. Weapply the large-deviation method to data sets of tracer beads tracked in aqueous solution, tracerbeads measured in mucin hydrogels, and of geographic surface temperature anomalies. Ouranalysis shows how the large-deviation properties can be efficiently used as a simple yet effectiveroutine test to reject the BM hypothesis and unveil relevant information on statistical propertiessuch as ergodicity breaking and short-time correlations. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1118 KW - diffusion KW - anomalous diffusion KW - large-deviation statistic KW - time-averaged mean squared displacement KW - Chebyshev inequality Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-493494 SN - 1866-8372 IS - 1118 ER - TY - GEN A1 - Cestnik, Rok A1 - Rosenblum, Michael T1 - Reconstructing networks of pulse-coupled oscillators from spike trains T2 - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe N2 - We present an approach for reconstructing networks of pulse-coupled neuronlike oscillators from passive observation of pulse trains of all nodes. It is assumed that units are described by their phase response curves and that their phases are instantaneously reset by incoming pulses. Using an iterative procedure, we recover the properties of all nodes, namely their phase response curves and natural frequencies, as well as strengths of all directed connections. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 760 KW - partial synchronization KW - neuronal connectivity Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-436285 SN - 1866-8372 IS - 760 ER - TY - GEN A1 - Böckmann, Christine A1 - Osterloh, Lukas T1 - Runge-Kutta type regularization method for inversion of spheroidal particle distribution from limited optical data T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - The Runge-Kutta type regularization method was recently proposed as a potent tool for the iterative solution of nonlinear ill-posed problems. In this paper we analyze the applicability of this regularization method for solving inverse problems arising in atmospheric remote sensing, particularly for the retrieval of spheroidal particle distribution. Our numerical simulations reveal that the Runge-Kutta type regularization method is able to retrieve two-dimensional particle distributions using optical backscatter and extinction coefficient profiles, as well as depolarization information. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 907 KW - inverse ill-posed problem KW - integral equation KW - laser remote sensing KW - inverse scattering KW - aerosol size distribution KW - 65R32 KW - 47A52 KW - 65R20 KW - 78A46 KW - iterative regularization Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-441200 SN - 1866-8372 IS - 907 SP - 150 EP - 165 ER - TY - GEN A1 - Xu, Pengbo A1 - Zhou, Tian A1 - Metzler, Ralf A1 - Deng, Weihua T1 - Stochastic harmonic trapping of a Lévy walk: transport and first-passage dynamics under soft resetting strategies T2 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - We introduce and study a Lévy walk (LW) model of particle spreading with a finite propagation speed combined with soft resets, stochastically occurring periods in which an harmonic external potential is switched on and forces the particle towards a specific position. Soft resets avoid instantaneous relocation of particles that in certain physical settings may be considered unphysical. Moreover, soft resets do not have a specific resetting point but lead the particle towards a resetting point by a restoring Hookean force. Depending on the exact choice for the LW waiting time density and the probability density of the periods when the harmonic potential is switched on, we demonstrate a rich emerging response behaviour including ballistic motion and superdiffusion. When the confinement periods of the soft-reset events are dominant, we observe a particle localisation with an associated non-equilibrium steady state. In this case the stationary particle probability density function turns out to acquire multimodal states. Our derivations are based on Markov chain ideas and LWs with multiple internal states, an approach that may be useful and flexible for the investigation of other generalised random walks with soft and hard resets. The spreading efficiency of soft-rest LWs is characterised by the first-passage time statistic. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1262 KW - diffusion KW - anomalous diffusion KW - stochastic resetting KW - Levy walks Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-560402 SN - 1866-8372 SP - 1 EP - 28 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - GEN A1 - Teichmann, Erik A1 - Lewandowski, Heather J. A1 - Alemani, Micol T1 - Investigating students’ views of experimental physics in German laboratory classes T2 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - There is a large variety of goals instructors have for laboratory courses, with different courses focusing on different subsets of goals. An often implicit, but crucial, goal is to develop students’ attitudes, views, and expectations about experimental physics to align with practicing experimental physicists. The assessment of laboratory courses upon this one dimension of learning has been intensively studied in U.S. institutions using the Colorado Learning Attitudes about Science Survey for Experimental Physics (E-CLASS). However, there is no such an instrument available to use in Germany, and the influence of laboratory courses on students views about the nature of experimental physics is still unexplored at German-speaking institutions. Motivated by the lack of an assessment tool to investigate this goal in laboratory courses at German-speaking institutions, we present a translated version of the E-CLASS adapted to the context at German-speaking institutions. We call the German version of the E-CLASS, the GE-CLASS. We describe the translation process and the creation of an automated web-based system for instructors to assess their laboratory courses. We also present first results using GE-CLASS obtained at the University of Potsdam. A first comparison between E-CLASS and GE-CLASS results shows clear differences between University of Potsdam and U.S. students’ views and beliefs about experimental physics. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1263 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-560429 SN - 1866-8372 SP - 010135-1 EP - 010135-17 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - GEN A1 - Sarabadani, Jalal A1 - Metzler, Ralf A1 - Ala-Nissila, Tapio T1 - Driven polymer translocation into a channel: Isoflux tension propagation theory and Langevin dynamics simulations T2 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - Isoflux tension propagation (IFTP) theory and Langevin dynamics (LD) simulations are employed to study the dynamics of channel-driven polymer translocation in which a polymer translocates into a narrow channel and the monomers in the channel experience a driving force fc. In the high driving force limit, regardless of the channel width, IFTP theory predicts τ ∝ f βc for the translocation time, where β = −1 is the force scaling exponent. Moreover, LD data show that for a very narrow channel fitting only a single file of monomers, the entropic force due to the subchain inside the channel does not play a significant role in the translocation dynamics and the force exponent β = −1 regardless of the force magnitude. As the channel width increases the number of possible spatial configurations of the subchain inside the channel becomes significant and the resulting entropic force causes the force exponent to drop below unity. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1292 Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-574387 SN - 1866-8372 IS - 1292 SP - 033003-1 EP - 033003-14 ER - TY - GEN A1 - Smirnov, Lev A. A1 - Bolotov, Maxim A1 - Bolotov, Dmitri A1 - Osipov, Grigory V. A1 - Pikovsky, Arkady T1 - Finite-density-induced motility and turbulence of chimera solitons T2 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - 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. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1291 KW - chimera KW - soliton KW - finite-size effects Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-574281 SN - 1866-8372 IS - 1291 ER - TY - GEN A1 - Vilk, Ohad A1 - Aghion, Erez A1 - Avgar, Tal A1 - Beta, Carsten A1 - Nagel, Oliver A1 - Sabri, Adal A1 - Sarfati, Raphael A1 - Schwartz, Daniel K. A1 - Weiß, Matthias A1 - Krapf, Diego A1 - Nathan, Ran A1 - Metzler, Ralf A1 - Assaf, Michael T1 - Unravelling the origins of anomalous diffusion BT - from molecules to migrating storks T2 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - Anomalous diffusion or, more generally, anomalous transport, with nonlinear dependence of the mean-squared displacement on the measurement time, is ubiquitous in nature. It has been observed in processes ranging from microscopic movement of molecules to macroscopic, large-scale paths of migrating birds. Using data from multiple empirical systems, spanning 12 orders of magnitude in length and 8 orders of magnitude in time, we employ a method to detect the individual underlying origins of anomalous diffusion and transport in the data. This method decomposes anomalous transport into three primary effects: long-range correlations (“Joseph effect”), fat-tailed probability density of increments (“Noah effect”), and nonstationarity (“Moses effect”). We show that such a decomposition of real-life data allows us to infer nontrivial behavioral predictions and to resolve open questions in the fields of single-particle tracking in living cells and movement ecology. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1303 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-577643 SN - 1866-8372 IS - 1303 ER - TY - GEN A1 - Abdalla, Hassan E. A1 - Adam, Remi A1 - Aharonian, Felix A. A1 - Benkhali, Faical Ait A1 - Angüner, Ekrem Oǧuzhan A1 - Arakawa, Masanori A1 - Arcaro, C A1 - Armand, Catherine A1 - Armstrong, T. A1 - Egberts, Kathrin T1 - Very high energy γ-ray emission from two blazars of unknown redshift and upper limits on their distance T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - We report on the detection of very high energy (VHE; E > 100 GeV) gamma-ray emission from the BL Lac objects KUV 00311-1938 and PKS 1440-389 with the High Energy Stereoscopic System (H.E.S.S.). H.E.S.S. observations were accompanied or preceded by multiwavelength observations with Fermi/LAT, XRT and UVOT onboard the Swift satellite, and ATOM. Based on an extrapolation of the Fermi/LAT spectrum towards the VHE gamma-ray regime, we deduce a 95 per cent confidence level upper limit on the unknown redshift of KUV 00311-1938 of z < 0.98 and of PKS 1440-389 of z < 0.53. When combined with previous spectroscopy results, the redshift of KUV 00311-1938 is constrained to 0.51 <= z < 0.98 and of PKS 1440-389 to 0.14 (sic) z < 0.53. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1202 KW - BL Lacertae objects: individual KW - galaxies: high-redshift KW - gamma-rays: general KW - Resolved and unresolved sources as a function of wavelength Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-526000 SN - 1866-8372 IS - 4 ER - TY - GEN A1 - Tröndle, Tim A1 - Lilliestam, Johan A1 - Marelli, Stefano A1 - Pfenninger, Stefan T1 - Trade-offs between geographic scale, cost, and infrastructure requirements for fully renewable electricity in Europe T2 - Postprints der Universität Potsdam Wirtschafts- und Sozialwissenschaftliche Reihe N2 - The European potential for renewable electricity is sufficient to enable fully renewable supply on different scales, from self-sufficient, subnational regions to an interconnected continent. We not only show that a continental-scale system is the cheapest, but also that systems on the national scale and below are possible at cost penalties of 20% or less. Transmission is key to low cost, but it is not necessary to vastly expand the transmission system. When electricity is transmitted only to balance fluctuations, the transmission grid size is comparable to today's, albeit with expanded cross-border capacities. The largest differences across scales concern land use and thus social acceptance: in the continental system, generation capacity is concentrated on the European periphery, where the best resources are. Regional systems, in contrast, have more dispersed generation. The key trade-off is therefore not between geographic scale and cost, but between scale and the spatial distribution of required generation and transmission infrastructure. T3 - Zweitveröffentlichungen der Universität Potsdam : Wirtschafts- und Sozialwissenschaftliche Reihe - 146 KW - levelized cost KW - energy-system KW - power-system KW - storage KW - wind KW - reanalysis KW - decarbonization KW - transmission KW - integration KW - deployment Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-539611 IS - 9 SP - 1929 EP - 1948 ER - TY - GEN A1 - Nöchel, Ulrich A1 - Reddy, Chaganti Srinivasa A1 - Wang, Ke A1 - Cui, Jing A1 - Zizak, Ivo A1 - Behl, Marc A1 - Kratz, Karl A1 - Lendlein, Andreas T1 - Nanostructural changes in crystallizable controlling units determine the temperature-memory of polymers N2 - Temperature-memory polymers remember the temperature, where they were deformed recently, enabled by broad thermal transitions. In this study, we explored a series of crosslinked poly[ethylene-co-(vinyl acetate)] networks (cPEVAs) comprising crystallizable polyethylene (PE) controlling units exhibiting a pronounced temperature-memory effect (TME) between 16 and 99 °C related to a broad melting transition (∼100 °C). The nanostructural changes in such cPEVAs during programming and activation of the TME were analyzed via in situ X-ray scattering and specific annealing experiments. Different contributions to the mechanism of memorizing high or low deformation temperatures (Tdeform) were observed in cPEVA, which can be associated to the average PE crystal sizes. At high deformation temperatures (>50 °C), newly formed PE crystals, which are established during cooling when fixing the temporary shape, dominated the TME mechanism. In contrast, at low Tdeform (<50 °C), corresponding to a cold drawing scenario, the deformation led preferably to a disruption of existing large crystals into smaller ones, which then fix the temporary shape upon cooling. The observed mechanism of memorizing a deformation temperature might enable the prediction of the TME behavior and the knowledge based design of other TMPs with crystallizable controlling units. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 194 Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-81124 SP - 8284 EP - 8293 ER - TY - GEN A1 - Yang, Jie A1 - Guehr, Markus A1 - Vecchione, Theodore A1 - Robinson, Matthew Scott A1 - Li, Renkai A1 - Hartmann, Nick A1 - Shen, Xiaozhe A1 - Coffee, Ryan A1 - Corbett, Jeff A1 - Fry, Alan A1 - Gaffney, Kelly A1 - Gorkhover, Tais A1 - Hast, Carsten A1 - Jobe, Keith A1 - Makasyuk, Igor A1 - Reid, Alexander A1 - Robinson, Joseph A1 - Vetter, Sharon A1 - Wang, Fenglin A1 - Weathersby, Stephen A1 - Yoneda, Charles A1 - Wang, Xijie A1 - Centurion, Martin T1 - Femtosecond gas phase electron diffraction with MeV electrons N2 - We present results on ultrafast gas electron diffraction (UGED) experiments with femtosecond resolution using the MeV electron gun at SLAC National Accelerator Laboratory. UGED is a promising method to investigate molecular dynamics in the gas phase because electron pulses can probe the structure with a high spatial resolution. Until recently, however, it was not possible for UGED to reach the relevant timescale for the motion of the nuclei during a molecular reaction. Using MeV electron pulses has allowed us to overcome the main challenges in reaching femtosecond resolution, namely delivering short electron pulses on a gas target, overcoming the effect of velocity mismatch between pump laser pulses and the probe electron pulses, and maintaining a low timing jitter. At electron kinetic energies above 3 MeV, the velocity mismatch between laser and electron pulses becomes negligible. The relativistic electrons are also less susceptible to temporal broadening due to the Coulomb force. One of the challenges of diffraction with relativistic electrons is that the small de Broglie wavelength results in very small diffraction angles. In this paper we describe the new setup and its characterization, including capturing static diffraction patterns of molecules in the gas phase, finding time-zero with sub-picosecond accuracy and first time-resolved diffraction experiments. The new device can achieve a temporal resolution of 100 fs root-mean-square, and sub-angstrom spatial resolution. The collimation of the beam is sufficient to measure the diffraction pattern, and the transverse coherence is on the order of 2 nm. Currently, the temporal resolution is limited both by the pulse duration of the electron pulse on target and by the timing jitter, while the spatial resolution is limited by the average electron beam current and the signal-to-noise ratio of the detection system. We also discuss plans for improving both the temporal resolution and the spatial resolution. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 326 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-394989 ER - TY - GEN A1 - Makwana, Kirit D. A1 - Yan, Huirong T1 - Properties of magnetohydrodynamic modes in compressively driven plasma turbulence T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - We study properties of magnetohydrodynamic (MHD) eigenmodes by decomposing the data of MHD simulations into linear MHD modes-namely, the Alfven, slow magnetosonic, and fast magnetosonic modes. We drive turbulence with a mixture of solenoidal and compressive driving while varying the Alfven Mach number (M-A), plasma beta, and the sonic Mach number from subsonic to transsonic. We find that the proportion of fast and slow modes in the mode mixture increases with increasing compressive forcing. This proportion of the magnetosonic modes can also become the dominant fraction in the mode mixture. The anisotropy of the modes is analyzed by means of their structure functions. The Alfven-mode anisotropy is consistent with the Goldreich-Sridhar theory. We find a transition from weak to strong Alfvenic turbulence as we go from low to high M-A. The slow-mode properties are similar to the Alfven mode. On the other hand, the isotropic nature of fast modes is verified in the cases where the fast mode is a significant fraction of the mode mixture. The fast-mode behavior does not show any transition in going from low to high M-A. We find indications that there is some interaction between the different modes, and the properties of the dominant mode can affect the properties of the weaker modes. This work identifies the conditions under which magnetosonic modes can be a major fraction of turbulent astrophysical plasmas, including the regime of weak turbulence. Important astrophysical implications for cosmic-ray transport and magnetic reconnection are discussed. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1225 KW - mhd turbulence KW - star formation KW - simulations KW - Anisotropy KW - diffusion Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-531607 SN - 1866-8372 VL - 10 IS - 3 PB - American Physical Society (APS) CY - College Park ER - TY - GEN A1 - Niebuhr, Mario A1 - Heuer, Axel T1 - Phase measurement and far-field reconstruction on externally coupled laser diode arrays N2 - Passive coherent combination of several discrete low power laser diodes is a promising way to overcome the issue of degrading beam quality when scaling single emitters to > 10W output power. Such systems would be an efficient alternative to current high power sources, yet they suffer from fatal coherence loss when operated well above threshold. We present a new way to obtain detailed coherence information for laser diode arrays using a spatial light modulator to help identify the underlying decoherence processes. Reconstruction tests of the emitted far-field distribution are conducted to evaluate the performance of our setup. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 383 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-402140 ER - TY - GEN A1 - Rätzel, Dennis A1 - Wilkens, Martin A1 - Menzel, Ralf T1 - Gravitational properties of light BT - the gravitational field of a laser pulse N2 - The gravitational field of a laser pulse of finite lifetime, is investigated in the framework of linearized gravity. Although the effects are very small, they may be of fundamental physical interest. It is shown that the gravitational field of a linearly polarized light pulse is modulated as the norm of the corresponding electric field strength, while no modulations arise for circular polarization. In general, the gravitational field is independent of the polarization direction. It is shown that all physical effects are confined to spherical shells expanding with the speed of light, and that these shells are imprints of the spacetime events representing emission and absorption of the pulse. Nearby test particles at rest are attracted towards the pulse trajectory by the gravitational field due to the emission of the pulse, and they are repelled from the pulse trajectory by the gravitational field due to its absorption. Examples are given for the size of the attractive effect. It is recovered that massless test particles do not experience any physical effect if they are co-propagating with the pulse, and that the acceleration of massless test particles counter-propagating with respect to the pulse is four times stronger than for massive particles at rest. The similarities between the gravitational effect of a laser pulse and Newtonian gravity in two dimensions are pointed out. The spacetime curvature close to the pulse is compared to that induced by gravitational waves from astronomical sources. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 222 KW - electromagnetic radiation KW - general relativity KW - gravity KW - laser pulses KW - linearized gravity KW - pp-wave solutions Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-90553 ER - TY - GEN A1 - Li, Yongge A1 - Mei, Ruoxing A1 - Xu, Yong A1 - Kurths, Jürgen A1 - Duan, Jinqiao A1 - Metzler, Ralf T1 - Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - This work focuses on the dynamics of particles in a confined geometry with position-dependent diffusivity, where the confinement is modelled by a periodic channel consisting of unit cells connected by narrow passage ways. We consider three functional forms for the diffusivity, corresponding to the scenarios of a constant (D ₀), as well as a low (D ₘ) and a high (D d) mobility diffusion in cell centre of the longitudinally symmetric cells. Due to the interaction among the diffusivity, channel shape and external force, the system exhibits complex and interesting phenomena. By calculating the probability density function, mean velocity and mean first exit time with the Itô calculus form, we find that in the absence of external forces the diffusivity D d will redistribute particles near the channel wall, while the diffusivity D ₘ will trap them near the cell centre. The superposition of external forces will break their static distributions. Besides, our results demonstrate that for the diffusivity D d, a high dependence on the x coordinate (parallel with the central channel line) will improve the mean velocity of the particles. In contrast, for the diffusivity D ₘ, a weak dependence on the x coordinate will dramatically accelerate the moving speed. In addition, it shows that a large external force can weaken the influences of different diffusivities; inversely, for a small external force, the types of diffusivity affect significantly the particle dynamics. In practice, one can apply these results to achieve a prominent enhancement of the particle transport in two- or three-dimensional channels by modulating the local tracer diffusivity via an engineered gel of varying porosity or by adding a cold tube to cool down the diffusivity along the central line, which may be a relevant effect in engineering applications. Effects of different stochastic calculi in the evaluation of the underlying multiplicative stochastic equation for different physical scenarios are discussed. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 974 KW - diffusion KW - channel KW - space-dependent diffusivity Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-474542 SN - 1866-8372 IS - 974 ER - TY - GEN A1 - Bouchoule, Isabelle A1 - Schemmer, Max A1 - Henkel, Carsten T1 - Cooling phonon modes of a Bose condensate with uniform few body losses T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - We present a general analysis of the cooling produced by losses on condensates or quasi-condensates. We study how the occupations of the collective phonon modes evolve in time, assuming that the loss process is slow enough so that each mode adiabatically follows the decrease of the mean density. The theory is valid for any loss process whose rate is proportional to the jth power of the density, but otherwise spatially uniform. We cover both homogeneous gases and systems confined in a smooth potential. For a low-dimensional gas, we can take into account the modified equation of state due to the broadening of the cloud width along the tightly confined directions, which occurs for large interactions. We find that at large times, the temperature decreases proportionally to the energy scale mc2, where m is the mass of the particles and c the sound velocity. We compute the asymptotic ratio of these two quantities for different limiting cases: a homogeneous gas in any dimension and a one-dimensional gas in a harmonic trap. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1029 KW - 3 body recombination KW - gas KW - scattering KW - Bose-Einstein condensates (BECs) KW - harmonic traps KW - one-dimensional Bose gas KW - phonon modes Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-468811 SN - 1866-8372 IS - 1029 ER - TY - GEN A1 - Lever, Fabiano A1 - Mayer, Dennis A1 - Metje, Jan A1 - Alisauskas, Skirmantas A1 - Calegari, Francesca A1 - Düsterer, Stefan A1 - Feifel, Raimund A1 - Niebuhr, Mario A1 - Manschwetus, Bastian A1 - Kuhlmann, Marion A1 - Mazza, Tommaso A1 - Robinson, Matthew Scott A1 - Squibb, Richard J. A1 - Trabattoni, Andrea A1 - Wallner, Måns A1 - Wolf, Thomas J. A. A1 - Gühr, Markus T1 - Core-level spectroscopy of 2-thiouracil at the sulfur L1 and L2,3 edges utilizing a SASE free-electron-laser T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - In this paper, we report X-ray absorption and core-level electron spectra of the nucleobase derivative 2-thiouracil at the sulfur L1- and L2,3-edges. We used soft X-rays from the free-electron laser FLASH2 for the excitation of isolated molecules and dispersed the outgoing electrons with a magnetic bottle spectrometer. We identified photoelectrons from the 2p core orbital, accompanied by an electron correlation satellite, as well as resonant and non-resonant Coster–Kronig and Auger–Meitner emission at the L1- and L2,3-edges, respectively. We used the electron yield to construct X-ray absorption spectra at the two edges. The experimental data obtained are put in the context of the literature currently available on sulfur core-level and 2-thiouracil spectroscopy. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1180 KW - X-ray KW - photoelectron KW - sulfur KW - thiouracil KW - nucleobases KW - Coster–Kronig KW - Auger–Meitner KW - NEXAFS KW - FLASH Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-524091 SN - 1866-8372 IS - 21 ER - TY - GEN A1 - Wiljes, Jana de A1 - Tong, Xin T. T1 - Analysis of a localised nonlinear ensemble Kalman Bucy filter with complete and accurate observations T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For spatial-temporal models, the ensemble Kalman filter with proper localisation techniques is considered to be a state-of-the-art DA methodology. This article proposes and investigates a localised ensemble Kalman Bucy filter for nonlinear models with short-range interactions. We derive dimension-independent and component-wise error bounds and show the long time path-wise error only has logarithmic dependence on the time range. The theoretical results are verified through some simple numerical tests. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1221 KW - data assimilation KW - stability and accuracy KW - dimension independent bound KW - localisation KW - high dimensional KW - filter KW - nonlinear Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-540417 SN - 1866-8372 VL - 33 IS - 9 SP - 4752 EP - 4782 PB - IOP Publ. CY - Bristol ER - TY - GEN A1 - Sposini, Vittoria A1 - Chechkin, Aleksei V. A1 - Flavio, Seno A1 - Pagnini, Gianni A1 - Metzler, Ralf T1 - Random diffusivity from stochastic equations BT - comparison of two models for Brownian yet non-Gaussian diffusion T2 - New Journal of Physics N2 - Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly non-Gaussian, and often of exponential(Laplace) shape. This apparently ubiquitous behaviour observed in very different physical systems has been interpreted as resulting from diffusion in inhomogeneous environments and mathematically represented through a variable, stochastic diffusion coefficient. Indeed different models describing a fluctuating diffusivity have been studied. Here we present a new view of the stochastic basis describing time dependent random diffusivities within a broad spectrum of distributions. Concretely, our study is based on the very generic class of the generalised Gamma distribution. Two models for the particle spreading in such random diffusivity settings are studied. The first belongs to the class of generalised grey Brownian motion while the second follows from the idea of diffusing diffusivities. The two processes exhibit significant characteristics which reproduce experimental results from different biological and physical systems. We promote these two physical models for the description of stochastic particle motion in complex environments. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 416 Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-409743 ER - TY - GEN A1 - Ślęzak, Jakub A1 - Metzler, Ralf A1 - Magdziarz, Marcin T1 - Superstatistical generalised Langevin equation BT - non-Gaussian viscoelastic anomalous diffusion N2 - Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 413 KW - anomalous diffusion KW - generalised langevin equation KW - superstatistics KW - non-Gaussian diffusion Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-409315 ER - TY - GEN A1 - Young, Linda A1 - Ueda, Kiyoshi A1 - Gühr, Markus A1 - Bucksbaum, Philip H. A1 - Simon, Marc A1 - Mukamel, Shaul A1 - Rohringer, Nina A1 - Prince, Kevin C. A1 - Masciovecchio, Claudio A1 - Meyer, Michael A1 - Rudenko, Artem A1 - Rolles, Daniel A1 - Bostedt, Christoph A1 - Fuchs, Matthias A1 - Reis, David A. A1 - Santra, Robin A1 - Kapteyn, Henry A1 - Murnane, Margaret A1 - Ibrahim, Heide A1 - Légaré, François A1 - Vrakking, Marc A1 - Isinger, Marcus A1 - Kroon, David A1 - Gisselbrecht, Mathieu A1 - L'Huillier, Anne A1 - Wörner, Hans Jakob A1 - Leone, Stephen R. T1 - Roadmap of ultrafast x-ray atomic and molecular physics T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - X-ray free-electron lasers (XFELs) and table-top sources of x-rays based upon high harmonic generation (HHG) have revolutionized the field of ultrafast x-ray atomic and molecular physics, largely due to an explosive growth in capabilities in the past decade. XFELs now provide unprecedented intensity (1020 W cm−2) of x-rays at wavelengths down to ~1 Ångstrom, and HHG provides unprecedented time resolution (~50 attoseconds) and a correspondingly large coherent bandwidth at longer wavelengths. For context, timescales can be referenced to the Bohr orbital period in hydrogen atom of 150 attoseconds and the hydrogen-molecule vibrational period of 8 femtoseconds; wavelength scales can be referenced to the chemically significant carbon K-edge at a photon energy of ~280 eV (44 Ångstroms) and the bond length in methane of ~1 Ångstrom. With these modern x-ray sources one now has the ability to focus on individual atoms, even when embedded in a complex molecule, and view electronic and nuclear motion on their intrinsic scales (attoseconds and Ångstroms). These sources have enabled coherent diffractive imaging, where one can image non-crystalline objects in three dimensions on ultrafast timescales, potentially with atomic resolution. The unprecedented intensity available with XFELs has opened new fields of multiphoton and nonlinear x-ray physics where behavior of matter under extreme conditions can be explored. The unprecedented time resolution and pulse synchronization provided by HHG sources has kindled fundamental investigations of time delays in photoionization, charge migration in molecules, and dynamics near conical intersections that are foundational to AMO physics and chemistry. This roadmap coincides with the year when three new XFEL facilities, operating at Ångstrom wavelengths, opened for users (European XFEL, Swiss-FEL and PAL-FEL in Korea) almost doubling the present worldwide number of XFELs, and documents the remarkable progress in HHG capabilities since its discovery roughly 30 years ago, showcasing experiments in AMO physics and other applications. Here we capture the perspectives of 17 leading groups and organize the contributions into four categories: ultrafast molecular dynamics, multidimensional x-ray spectroscopies; high-intensity x-ray phenomena; attosecond x-ray science. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 668 KW - ultrafast molecular dynamics KW - x-ray spectroscopies and phenomena KW - table-top sources KW - x-ray free-electron lasers KW - attosecond phenomena Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-424238 SN - 1866-8372 IS - 668 ER - TY - GEN A1 - Krapf, Diego A1 - Marinari, Enzo A1 - Metzler, Ralf A1 - Oshanin, Gleb A1 - Xu, Xinran A1 - Squarcini, Alessio T1 - Power spectral density of a single Brownian trajectory BT - what one can and cannot learn from it T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - The power spectral density (PSD) of any time-dependent stochastic processX (t) is ameaningful feature of its spectral content. In its text-book definition, the PSD is the Fourier transform of the covariance function of X-t over an infinitely large observation timeT, that is, it is defined as an ensemble-averaged property taken in the limitT -> infinity. Alegitimate question is what information on the PSD can be reliably obtained from single-trajectory experiments, if one goes beyond the standard definition and analyzes the PSD of a single trajectory recorded for a finite observation timeT. In quest for this answer, for a d-dimensional Brownian motion (BM) we calculate the probability density function of a single-trajectory PSD for arbitrary frequency f, finite observation time T and arbitrary number k of projections of the trajectory on different axes. We show analytically that the scaling exponent for the frequency-dependence of the PSD specific to an ensemble of BM trajectories can be already obtained from a single trajectory, while the numerical amplitude in the relation between the ensemble-averaged and single-trajectory PSDs is afluctuating property which varies from realization to realization. The distribution of this amplitude is calculated exactly and is discussed in detail. Our results are confirmed by numerical simulations and single-particle tracking experiments, with remarkably good agreement. In addition we consider a truncated Wiener representation of BM, and the case of a discrete-time lattice random walk. We highlight some differences in the behavior of a single-trajectory PSD for BM and for the two latter situations. The framework developed herein will allow for meaningful physical analysis of experimental stochastic trajectories. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 655 KW - power spectral density KW - single-trajectory analysis KW - probability density function KW - exact results Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-424296 SN - 1866-8372 IS - 655 ER - TY - GEN A1 - Jeon, Jae-Hyung A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion N2 - 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. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 180 KW - single-particle tracking KW - living cells KW - random-walks KW - subdiffusion KW - dynamics KW - nonergodicity KW - coefficients KW - transport KW - membrane KW - behavior Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-76302 SP - 15811 EP - 15817 ER - TY - GEN A1 - Goychuk, Igor A. A1 - Kharchenko, Vasyl O. A1 - Metzler, Ralf T1 - Molecular motors pulling cargos in the viscoelastic cytosol: how power strokes beat subdiffusion T2 - Physical Chemistry Chemical Physics N2 - The discovery of anomalous diffusion of larger biopolymers and submicron tracers such as endogenous granules, organelles, or virus capsids in living cells, attributed to the viscoelastic nature of the cytoplasm, provokes the question whether this complex environment equally impacts the active intracellular transport of submicron cargos by molecular motors such as kinesins: does the passive anomalous diffusion of free cargo always imply its anomalously slow active transport by motors, the mean transport distance along microtubule growing sublinearly rather than linearly in time? Here we analyze this question within the widely used two-state Brownian ratchet model of kinesin motors based on the continuous-state diffusion along microtubules driven by a flashing binding potential, where the cargo particle is elastically attached to the motor. Depending on the cargo size, the loading force, the amplitude of the binding potential, the turnover frequency of the molecular motor enzyme, and the linker stiffness we demonstrate that the motor transport may turn out either normal or anomalous, as indeed measured experimentally. We show how a highly efficient normal active transport mediated by motors may emerge despite the passive anomalous diffusion of the cargo, and study the intricate effects of the elastic linker. Under different, well specified conditions the microtubule-based motor transport becomes anomalously slow and thus significantly less efficient. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 181 KW - royal soc chemistry KW - thomas graham house KW - science park KW - milton rd KW - cambridge cb4 0wf KW - cambs KW - england Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-76478 SP - 16524 EP - 16535 PB - The Royal Society of Chemistry CY - Cambridge ER - TY - GEN A1 - Metzler, Ralf A1 - Cherstvy, Andrey G. A1 - Chechkin, Aleksei V. A1 - Bodrova, Anna S. T1 - Ultraslow scaled Brownian motion T2 - New journal of physics : the open-access journal for physics N2 - We define and study in detail utraslow scaled Brownian motion (USBM) characterized by a time dependent diffusion coefficient of the form . For unconfined motion the mean squared displacement (MSD) of USBM exhibits an ultraslow, logarithmic growth as function of time, in contrast to the conventional scaled Brownian motion. In a harmonic potential the MSD of USBM does not saturate but asymptotically decays inverse-proportionally to time, reflecting the highly non-stationary character of the process. We show that the process is weakly non-ergodic in the sense that the time averaged MSD does not converge to the regular MSD even at long times, and for unconfined motion combines a linear lag time dependence with a logarithmic term. The weakly non-ergodic behaviour is quantified in terms of the ergodicity breaking parameter. The USBM process is also shown to be ageing: observables of the system depend on the time gap between initiation of the test particle and start of the measurement of its motion. Our analytical results are shown to agree excellently with extensive computer simulations. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 188 KW - anomalous diffusion KW - stochastic processes KW - ageing Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-78618 ER - TY - GEN A1 - Herrmann, Carl J. J. A1 - Metzler, Ralf T1 - A self-avoiding walk with neural delays as a model of fixational eye movements N2 - Fixational eye movements show scaling behaviour of the positional mean-squared displacement with a characteristic transition from persistence to antipersistence for increasing time-lag. These statistical patterns were found to be mainly shaped by microsaccades (fast, small-amplitude movements). However, our re-analysis of fixational eye-movement data provides evidence that the slow component (physiological drift) of the eyes exhibits scaling behaviour of the mean-squared displacement that varies across human participants. These results suggest that drift is a correlated movement that interacts with microsaccades. Moreover, on the long time scale, the mean-squared displacement of the drift shows oscillations, which is also present in the displacement auto-correlation function. This finding lends support to the presence of time-delayed feedback in the control of drift movements. Based on an earlier non-linear delayed feedback model of fixational eye movements, we propose and discuss different versions of a new model that combines a self-avoiding walk with time delay. As a result, we identify a model that reproduces oscillatory correlation functions, the transition from persistence to antipersistence, and microsaccades. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 392 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-403742 ER - TY - GEN A1 - Menzel, Ralf A1 - Puhlmann, Dirk A1 - Heuer, Axel T1 - Complementarity in single photon interference – the role of the mode function and vacuum fields N2 - Background In earlier experiments the role of the vacuum fields could be demonstrated as the source of complementarity with respect to the temporal properties (Heuer et al., Phys. Rev. Lett. 114:053601, 2015). Methods Single photon first order interferences of spatially separated regions from the cone structure of spontaneous parametric down conversion allow for analyzing the role of the mode function in quantum optics regarding the complementarity principle. Results Here the spatial coherence properties of these vacuum fields are demonstrated as the physical reason for complementarity in these single photon quantum optical experiments. These results are directly connected to the mode picture in classical optics. Conclusion The properties of the involved vacuum fields selected via the measurement process are the physical background of the complementarity principle in quantum optics. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 333 KW - Complementarity KW - Mode function KW - Quantum optics KW - Vacuum fields Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-395210 ER - TY - GEN A1 - Cherstvy, Andrey G. A1 - Vinod, Deepak A1 - Aghion, Erez A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Time averaging, ageing and delay analysis of financial time series N2 - We introduce three strategies for the analysis of financial time series based on time averaged observables. These comprise the time averaged mean squared displacement (MSD) as well as the ageing and delay time methods for varying fractions of the financial time series. We explore these concepts via statistical analysis of historic time series for several Dow Jones Industrial indices for the period from the 1960s to 2015. Remarkably, we discover a simple universal law for the delay time averaged MSD. The observed features of the financial time series dynamics agree well with our analytical results for the time averaged measurables for geometric Brownian motion, underlying the famed Black–Scholes–Merton model. The concepts we promote here are shown to be useful for financial data analysis and enable one to unveil new universal features of stock market dynamics. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 347 KW - diffusion KW - financial time series KW - geometric Brownian motion KW - time averaging Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-400541 ER - TY - GEN A1 - Wolf, Thomas J. A. A1 - Holzmeier, Fabian A1 - Wagner, Isabella A1 - Berrah, Nora A1 - Bostedt, Christoph A1 - Bozek, John A1 - Bucksbaum, Philip H. A1 - Coffee, Ryan A1 - Cryan, James A1 - Farrell, Joe A1 - Feifel, Raimund A1 - Martinez, Todd J. A1 - McFarland, Brian A1 - Mucke, Melanie A1 - Nandi, Saikat A1 - Tarantelli, Francesco A1 - Fischer, Ingo A1 - Gühr, Markus T1 - Observing Femtosecond Fragmentation Using Ultrafast X-ray-Induced Auger Spectra N2 - Molecules often fragment after photoionization in the gas phase. Usually, this process can only be investigated spectroscopically as long as there exists electron correlation between the photofragments. Important parameters, like their kinetic energy after separation, cannot be investigated. We are reporting on a femtosecond time-resolved Auger electron spectroscopy study concerning the photofragmentation dynamics of thymine. We observe the appearance of clearly distinguishable signatures from thymine′s neutral photofragment isocyanic acid. Furthermore, we observe a time-dependent shift of its spectrum, which we can attribute to the influence of the charged fragment on the Auger electron. This allows us to map our time-dependent dataset onto the fragmentation coordinate. The time dependence of the shift supports efficient transformation of the excess energy gained from photoionization into kinetic energy of the fragments. Our method is broadly applicable to the investigation of photofragmentation processes. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 386 KW - Auger electron spectroscopy KW - photochemistry KW - photofragmentation KW - ultrafast dynamics Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-402692 ER -