TY - GEN A1 - Grebenkov, Denis S. A1 - Metzler, Ralf A1 - Oshanin, Gleb T1 - Effects of the target aspect ratio and intrinsic reactivity onto diffusive search in bounded domains N2 - We study the mean first passage time (MFPT) to a reaction event on a specific site in a cylindrical geometry—characteristic, for instance, for bacterial cells, with a concentric inner cylinder representing the nuclear region of the bacterial cell. Asimilar problem emerges in the description of a diffusive search by a transcription factor protein for a specific binding region on a single strand of DNA.We develop a unified theoretical approach to study the underlying boundary value problem which is based on a self-consistent approximation of the mixed boundary condition. Our approach permits us to derive explicit, novel, closed-form expressions for the MFPT valid for a generic setting with an arbitrary relation between the system parameters.Weanalyse this general result in the asymptotic limits appropriate for the above-mentioned biophysical problems. Our investigation reveals the crucial role of the target aspect ratio and of the intrinsic reactivity of the binding region, which were disregarded in previous studies. Theoretical predictions are confirmed by numerical simulations. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 391 KW - aspect ratio KW - cylindrical geometry KW - first passage time KW - protein search Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-403726 ER - TY - GEN A1 - Grebenkov, Denis S. A1 - Sposini, Vittoria A1 - Metzler, Ralf A1 - Oshanin, Gleb A1 - Seno, Flavio T1 - Exact distributions of the maximum and range of random diffusivity processes T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - We study the extremal properties of a stochastic process xt defined by the Langevin equation ẋₜ =√2Dₜ ξₜ, in which ξt is a Gaussian white noise with zero mean and Dₜ is a stochastic‘diffusivity’, defined as a functional of independent Brownian motion Bₜ.We focus on threechoices for the random diffusivity Dₜ: cut-off Brownian motion, Dₜt ∼ Θ(Bₜ), where Θ(x) is the Heaviside step function; geometric Brownian motion, Dₜ ∼ exp(−Bₜ); and a superdiffusive process based on squared Brownian motion, Dₜ ∼ B²ₜ. For these cases we derive exact expressions for the probability density functions of the maximal positive displacement and of the range of the process xₜ on the time interval ₜ ∈ (0, T).We discuss the asymptotic behaviours of the associated probability density functions, compare these against the behaviour of the corresponding properties of standard Brownian motion with constant diffusivity (Dₜ = D0) and also analyse the typical behaviour of the probability density functions which is observed for a majority of realisations of the stochastic diffusivity process. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1142 KW - random diffusivity KW - extremal values KW - maximum and range KW - diffusion KW - Brownian motion Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-503976 SN - 1866-8372 IS - 1142 ER - TY - GEN A1 - Grebenkov, Denis S. A1 - Metzler, Ralf A1 - Oshanin, Gleb T1 - A molecular relay race: sequential first-passage events to the terminal reaction centre in a cascade of diffusion controlled processes T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - We consider a sequential cascade of molecular first-reaction events towards a terminal reaction centre in which each reaction step is controlled by diffusive motion of the particles. The model studied here represents a typical reaction setting encountered in diverse molecular biology systems, in which, e.g. a signal transduction proceeds via a series of consecutive 'messengers': the first messenger has to find its respective immobile target site triggering a launch of the second messenger, the second messenger seeks its own target site and provokes a launch of the third messenger and so on, resembling a relay race in human competitions. For such a molecular relay race taking place in infinite one-, two- and three-dimensional systems, we find exact expressions for the probability density function of the time instant of the terminal reaction event, conditioned on preceding successful reaction events on an ordered array of target sites. The obtained expressions pertain to the most general conditions: number of intermediate stages and the corresponding diffusion coefficients, the sizes of the target sites, the distances between them, as well as their reactivities are arbitrary. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1159 KW - diffusion KW - reaction cascade KW - first passage time Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-521942 SN - 1866-8372 ER - TY - GEN A1 - Omel'chenko, Oleh T1 - Travelling chimera states in systems of phase oscillators with asymmetric nonlocal coupling T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - We study travelling chimera states in a ring of nonlocally coupled heterogeneous (with Lorentzian distribution of natural frequencies) phase oscillators. These states are coherence-incoherence patterns moving in the lateral direction because of the broken reflection symmetry of the coupling topology. To explain the results of direct numerical simulations we consider the continuum limit of the system. In this case travelling chimera states correspond to smooth travelling wave solutions of some integro-differential equation, called the Ott–Antonsen equation, which describes the long time coarse-grained dynamics of the oscillators. Using the Lyapunov–Schmidt reduction technique we suggest a numerical approach for the continuation of these travelling waves. Moreover, we perform their linear stability analysis and show that travelling chimera states can lose their stability via fold and Hopf bifurcations. Some of the Hopf bifurcations turn out to be supercritical resulting in the observation of modulated travelling chimera states. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1169 KW - chimera states KW - nonlocally coupled phase oscillators KW - Ott–Antonsen equation KW - forced symmetry breaking KW - travelling waves KW - continuation KW - stability Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-518141 SN - 1866-8372 IS - 2 SP - 611 EP - 642 ER - TY - GEN A1 - Mientus, Lukas A1 - Hume, Anne Christine A1 - Wulff, Peter A1 - Meiners, Antoinette A1 - Borowski, Andreas T1 - Modelling STEM Teachers’ Pedagogical Content Knowledge in the Framework of the Refined Consensus Model: A Systematic Literature Review T2 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - Science education researchers have developed a refined understanding of the structure of science teachers’ pedagogical content knowledge (PCK), but how to develop applicable and situation-adequate PCK remains largely unclear. A potential problem lies in the diverse conceptualisations of the PCK used in PCK research. This study sought to systematize existing science education research on PCK through the lens of the recently proposed refined consensus model (RCM) of PCK. In this review, the studies’ approaches to investigating PCK and selected findings were characterised and synthesised as an overview comparing research before and after the publication of the RCM. We found that the studies largely employed a qualitative case-study methodology that included specific PCK models and tools. However, in recent years, the studies focused increasingly on quantitative aspects. Furthermore, results of the reviewed studies can mostly be integrated into the RCM. We argue that the RCM can function as a meaningful theoretical lens for conceptualizing links between teaching practice and PCK development by proposing pedagogical reasoning as a mechanism and/or explanation for PCK development in the context of teaching practice. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1273 KW - pedagogical content knowledge (PCK) KW - refined consensus model (RCM) KW - pedagogical reasoning KW - teaching practice KW - science teaching KW - literature review Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-569127 SN - 1866-8372 SP - 1 EP - 25 ER - TY - GEN A1 - Loebner, Sarah A1 - Jelken, Joachim A1 - Yadavalli, Nataraja Sekhar A1 - Sava, Elena A1 - Hurduc, Nicolae A1 - Santer, Svetlana T1 - Motion of adsorbed nano-particles on azobenzene containing polymer films N2 - We demonstrate in situ recorded motion of nano-objects adsorbed on a photosensitive polymer film. The motion is induced by a mass transport of the underlying photoresponsive polymer material occurring during irradiation with interference pattern. The polymer film contains azobenzene molecules that undergo reversible photoisomerization reaction from trans- to cis-conformation. Through a multi-scale chain of physico-chemical processes, this finally results in the macro-deformations of the film due to the changing elastic properties of polymer. The topographical deformation of the polymer surface is sensitive to a local distribution of the electrical field vector that allows for the generation of dynamic changes in the surface topography during irradiation with different light interference patterns. Polymer film deformation together with the motion of the adsorbed nano-particles are recorded using a homemade set-up combining an optical part for the generation of interference patterns and an atomic force microscope for acquiring the surface deformation. The particles undergo either translational or rotational motion. The direction of particle motion is towards the topography minima and opposite to the mass transport within the polymer film. The ability to relocate particles by photo-induced dynamic topography fluctuation offers a way for a non-contact simultaneous manipulation of a large number of adsorbed particles just in air at ambient conditions. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 352 KW - motion of adsorbed nano-particles KW - azobenzene containing polymer films KW - fluctuating surfaces Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-400423 ER - TY - GEN A1 - Yadavalli, Nataraja Sekhar A1 - Loebner, Sarah A1 - Papke, Thomas A1 - Sava, Elena A1 - Hurduc, Nicolae A1 - Santer, Svetlana T1 - A comparative study of photoinduced deformation in azobenzene containing polymer films T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - In this paper two groups supporting different views on the mechanism of light induced polymer deformation argue about the respective underlying theoretical conceptions, in order to bring this interesting debate to the attention of the scientific community. The group of Prof. Nicolae Hurduc supports the model claiming that the cyclic isomerization of azobenzenes may cause an athermal transition of the glassy azobenzene containing polymer into a fluid state, the so-called photo-fluidization concept. This concept is quite convenient for an intuitive understanding of the deformation process as an anisotropic flow of the polymer material. The group of Prof. Svetlana Santer supports the re-orientational model where the mass-transport of the polymer material accomplished during polymer deformation is stated to be generated by the light-induced re-orientation of the azobenzene side chains and as a consequence of the polymer backbone that in turn results in local mechanical stress, which is enough to irreversibly deform an azobenzene containing material even in the glassy state. For the debate we chose three polymers differing in the glass transition temperature, 32 °C, 87 °C and 95 °C, representing extreme cases of flexible and rigid materials. Polymer film deformation occurring during irradiation with different interference patterns is recorded using a homemade set-up combining an optical part for the generation of interference patterns and an atomic force microscope for acquiring the kinetics of film deformation. We also demonstrated the unique behaviour of azobenzene containing polymeric films to switch the topography in situ and reversibly by changing the irradiation conditions. We discuss the results of reversible deformation of three polymers induced by irradiation with intensity (IIP) and polarization (PIP) interference patterns, and the light of homogeneous intensity in terms of two approaches: the re-orientational and the photo-fluidization concepts. Both agree in that the formation of opto-mechanically induced stresses is a necessary prerequisite for the process of deformation. Using this argument, the deformation process can be characterized either as a flow or mass transport. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 458 KW - light-induced deformation KW - surface-relief gratings KW - optical near-field KW - chromophore orientations KW - atomic-force; nano-objects KW - brushes KW - raman KW - elastomers KW - microscopy Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-413510 SN - 1866-8372 IS - 458 ER - TY - GEN A1 - Raman Venkatesan, Thulasinath A1 - Gerhard, Reimund T1 - Origin of the mid-temperature transition in vinylidenefluoride-based ferro-, pyro- and piezoelectric homo-, co- and ter-polymers T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - The existence of an intermediate transition between the glass and the Curie/melting temperatures in Poly(vinylidene fluoride) (PVDF) and some of its co- and ter-polymers has been reported by several authors. In spite (or because?) of various different explanations in the literature, the origins of the transition are still not clear. Here, we try to understand the extra transition in more detail and study it with thermal and dielectric methods on PVDF, on its co-polymers with trifluoroethylene (P(VDF-TrFE)) and tetrafluoroethylene (P(VDF-TFE)), and on its ter-polymer with trifluoroethylene and chlorofluoroethylene (P(VDF-TrFE-CFE). Based on interpretations from the literature and our experimental studies, we propose the new hypothesis that the intermediate transition should have several interrelated origins. Especially since the relevant range is not far above room temperature, better understanding and control of their properties may also have practical implications for the use of the respective polymer materials in devices. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 977 KW - mid-temperature transition KW - vinylidenefluoride (VDF)-based polymers KW - Differential Scanning Calorimetry (DSC) KW - Dielectric Relaxation Spectroscopy (DRS) KW - ferroelectric polymers KW - pyroelectric polymers KW - piezoelectric polymers Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-474672 SN - 1866-8372 IS - 977 ER - TY - GEN A1 - Jelken, Joachim A1 - Santer, Svetlana T1 - Light induced reversible structuring of photosensitive polymer films T2 - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe N2 - In this paper we report on photoswitchable polymer surfaces with dynamically and reversibly fluctuating topographies. It is well known that when azobenzene containing polymer films are irradiated with optical interference patterns the film topography changes to form a surface relief grating. In the simplest case, the film shape mimics the intensity distribution and deforms into a wave like, sinusoidal manner with amplitude that may be as large as the film thickness. This process takes place in the glassy state without photo-induced softening. Here we report on an intriguing discovery regarding the formation of reliefs under special illumination conditions. We have developed a novel setup combining the optical part for creating interference patterns, an AFM for in situ acquisition of topography changes and diffraction efficiency signal measurements. In this way we demonstrate that these gratings can be “set in motion” like water waves or dunes in the desert. We achieve this by applying repetitive polarization changes to the incoming interference pattern. Such light responsive surfaces represent the prerequisite for providing practical applications ranging from conveyer or transport systems for adsorbed liquid objects and colloidal particles to generation of adaptive and dynamic optical devices. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 750 KW - surface-relief gratings KW - induced deformation KW - mass-transport KW - azobenzene elastomers KW - thin-films KW - birefringence KW - roughness KW - network KW - erasure Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-436432 SN - 1866-8372 IS - 750 SP - 20295 EP - 20305 ER - TY - GEN A1 - Sharma, Anjali A1 - Bekir, Marek A1 - Lomadze, Nino A1 - Santer, Svetlana T1 - Photo-Isomerization Kinetics of Azobenzene Containing Surfactant Conjugated with Polyelectrolyte T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - Ionic complexation of azobenzene-containing surfactants with any type of oppositely charged soft objects allows for making them photo-responsive in terms of their size, shape and surface energy. Investigation of the photo-isomerization kinetic and isomer composition at a photo-stationary state of the photo-sensitive surfactant conjugated with charged objects is a necessary prerequisite for understanding the structural response of photo-sensitive complexes. Here, we report on photo-isomerization kinetics of a photo-sensitive surfactant in the presence of poly(acrylic acid, sodium salt). We show that the photo-isomerization of the azobenzene-containing cationic surfactant is slower in a polymer complex compared to being purely dissolved in aqueous solution. In a photo-stationary state, the ratio between the trans and cis isomers is shifted to a higher trans-isomer concentration for all irradiation wavelengths. This is explained by the formation of surfactant aggregates near the polyelectrolyte chains at concentrations much lower than the bulk critical micelle concentration and inhibition of the photo-isomerization kinetics due to steric hindrance within the densely packed aggregates. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1101 KW - azobenzene KW - photo-sensitive surfactant KW - photo-isomerization kinetics KW - poly (acrylic acid, sodium salt) Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-489427 SN - 1866-8372 IS - 1101 ER -