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We study the probability density function (PDF) of the first-reaction times between a diffusive ligand and a membrane-bound, immobile imperfect target region in a restricted 'onion-shell' geometry bounded by two nested membranes of arbitrary shapes. For such a setting, encountered in diverse molecular signal transduction pathways or in the narrow escape problem with additional steric constraints, we derive an exact spectral form of the PDF, as well as present its approximate form calculated by help of the so-called self-consistent approximation. For a particular case when the nested domains are concentric spheres, we get a fully explicit form of the approximated PDF, assess the accuracy of this approximation, and discuss various facets of the obtained distributions. Our results can be straightforwardly applied to describe the PDF of the terminal reaction event in multi-stage signal transduction processes.
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.
Reflexion – unhinterfragt eines der wichtigsten Worte im Kontext der Lehrkräftebildung. Fest verankert in den bundesdeutschen Bildungsstandards sind in Forschung und Lehre die Suche nach Evidenz und die Unterstützung (angehender) Lehrkräfte ständiger Antrieb unzähliger Akteur:innen aller Phasen der Lehrkräftebildung. Wenngleich begriff liche Unklarheiten die Kommunikation von Forschungsergebnissen nicht immer intuitiv und die Unterstützung in der Lehre nicht immer praktikabel werden lassen, besteht Einigkeit darüber, dass ein Diskurs zur reflexiven Professionalisierung von Lehrkräften geführt werden muss. Aus diesem Grund veranstalteten die beiden QLB-Projekte PSI-Potsdam der Universität Potsdam und K2teach der Freien Universität Berlin vom 5. bis 7. Oktober 2022 die Onlinetagung „Reflexion in der Lehrkräftebildung. Empirisch – Phasenübergreifend – Interdisziplinär“. Ausgehend von den verschiedensten Fachdisziplinen diskutierten Akteur:innen aller Phasen der Lehrkräftebildung unterschiedlicher Standorte Ergebnisse empirischer Studien und Erfahrungen aus der Arbeit mit (angehenden) Lehrkräften. Beiträge der Tagung sind in diesem Buch festgehalten und sind als Momentaufnahme eines sich ständig entwickelnden Themenfelds zu verstehen. Forschende und Lehrende haben mit dieser Momentaufnahme die Möglichkeit, Eindrücke für die eigene Arbeit aufzunehmen und weiterzuentwickeln.
Schulpraktische Phasen stellen eine bedeutende praxisnahe Lerngelegenheit im Lehramtsstudium dar, da sie Raum für umfangreiche Reflexionen der eigenen Lernerfahrung bieten. Das im Studium erworbene theoretisch-formale Wissen steht hierbei dem praktischen Wissen und Können gegenüber. Mit der professionellen Entwicklung im Referendariat, besonders im Kompetenzbereich des Unterrichtens, kann geschlussfolgert werden, dass sich eine Reflexion über eher fachliche Aspekte unter den Studierenden im Referendariat auf eine Reflexion über eher überfachliche und pädagogische Aspekte weitet. Infolge der Analyse von N = 55 schriftlichen Fremdreflexionen von angehenden Physiklehrkräften aus Studium und Referendariat konnte diese Hypothese für den Bereich der Unterrichtsanalyse und -reflexion unterstützt werden. Weiter wurde aus der Videovignette ein Workshopangebot für Lehrkräfte der zweiten und dritten Phase der Lehrkräftebildung entwickelt, erprobt und evaluiert.
Computation of the instantaneous phase and amplitude via the Hilbert Transform is a powerful tool of data analysis. This approach finds many applications in various science and engineering branches but is not proper for causal estimation because it requires knowledge of the signal’s past and future. However, several problems require real-time estimation of phase and amplitude; an illustrative example is phase-locked or amplitude-dependent stimulation in neuroscience. In this paper, we discuss and compare three causal algorithms that do not rely on the Hilbert Transform but exploit well-known physical phenomena, the synchronization and the resonance. After testing the algorithms on a synthetic data set, we illustrate their performance computing phase and amplitude for the accelerometer tremor measurements and a Parkinsonian patient’s beta-band brain activity.
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.
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.
Anomalous-diffusion, the departure of the spreading dynamics of diffusing particles from the traditional law of Brownian-motion, is a signature feature of a large number of complex soft-matter and biological systems. Anomalous-diffusion emerges due to a variety of physical mechanisms, e.g., trapping interactions or the viscoelasticity of the environment. However, sometimes systems dynamics are erroneously claimed to be anomalous, despite the fact that the true motion is Brownian—or vice versa. This ambiguity in establishing whether the dynamics as normal or anomalous can have far-reaching consequences, e.g., in predictions for reaction- or relaxation-laws. Demonstrating that a system exhibits normal- or anomalous-diffusion is highly desirable for a vast host of applications. Here, we present a criterion for anomalous-diffusion based on the method of power-spectral analysis of single trajectories. The robustness of this criterion is studied for trajectories of fractional-Brownian-motion, a ubiquitous stochastic process for the description of anomalous-diffusion, in the presence of two types of measurement errors. In particular, we find that our criterion is very robust for subdiffusion. Various tests on surrogate data in absence or presence of additional positional noise demonstrate the efficacy of this method in practical contexts. Finally, we provide a proof-of-concept based on diverse experiments exhibiting both normal and anomalous-diffusion.
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.
How do different reset protocols affect ergodicity of a diffusion process in single-particle-tracking experiments? We here address the problem of resetting of an arbitrary stochastic anomalous-diffusion process (ADP) from the general mathematical points of view and assess ergodicity of such reset ADPs for an arbitrary resetting protocol. The process of stochastic resetting describes the events of the instantaneous restart of a particle’s motion via randomly distributed returns to a preset initial position (or a set of those). The waiting times of such resetting events obey the Poissonian, Gamma, or more generic distributions with specified conditions regarding the existence of moments. Within these general approaches, we derive general analytical results and support them by computer simulations for the behavior of the reset mean-squared displacement (MSD), the new reset increment-MSD (iMSD), and the mean reset time-averaged MSD (TAMSD). For parental nonreset ADPs with the MSD(t)∝ tμ we find a generic behavior and a switch of the short-time growth of the reset iMSD and mean reset TAMSDs from ∝ _μ for subdiffusive to ∝ _1 for superdiffusive reset ADPs. The critical condition for a reset ADP that recovers its ergodicity is found to be more general than that for the nonequilibrium stationary state, where obviously the iMSD and the mean TAMSD are equal. The consideration of the new statistical quantifier, the iMSD—as compared to the standard MSD—restores the ergodicity of an arbitrary reset ADP in all situations when the μth moment of the waiting-time distribution of resetting events is finite. Potential applications of these new resetting results are, inter alia, in the area of biophysical and soft-matter systems.