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A rapidly increasing number of systems is identified in which the stochastic motion of tracer particles follows the Brownian law < r(2)(t)> similar or equal to Dt yet the distribution of particle displacements is strongly non-Gaussian. A central approach to describe this effect is the diffusing diffusivity (DD) model in which the diffusion coefficient itself is a stochastic quantity, mimicking heterogeneities of the environment encountered by the tracer particle on its path. We here quantify in terms of analytical and numerical approaches the first passage behaviour of the DD model. We observe significant modifications compared to Brownian-Gaussian diffusion, in particular that the DD model may have a faster first passage dynamics. Moreover we find a universal crossover point of the survival probability independent of the initial condition.
The two hallmark features of Brownian motion are the linear growth < x2(t)> = 2Ddt of the mean squared displacement (MSD) with diffusion coefficient D in d spatial dimensions, and the Gaussian distribution of displacements. With the increasing complexity of the studied systems deviations from these two central properties have been unveiled over the years. Recently, a large variety of systems have been reported in which the MSD exhibits the linear growth in time of Brownian (Fickian) transport, however, the distribution of displacements is pronouncedly non-Gaussian (Brownian yet non-Gaussian, BNG). A similar behaviour is also observed for viscoelastic-type motion where an anomalous trend of the MSD, i.e., <x2(t)> ~ ta, is combined with a priori unexpected non-Gaussian distributions (anomalous yet non-Gaussian, ANG). This kind of behaviour observed in BNG and ANG diffusions has been related to the presence of heterogeneities in the systems and a common approach has been established to address it, that is, the random diffusivity approach.
This dissertation explores extensively the field of random diffusivity models. Starting from a chronological description of all the main approaches used as an attempt of describing BNG and ANG diffusion, different mathematical methodologies are defined for the resolution and study of these models. The processes that are reported in this work can be classified in three subcategories, i) randomly-scaled Gaussian processes, ii) superstatistical models and iii) diffusing diffusivity models, all belonging to the more general class of random diffusivity models. Eventually, the study focuses more on BNG diffusion, which is by now well-established and relatively well-understood. Nevertheless, many examples are discussed for the description of ANG diffusion, in order to highlight the possible scenarios which are known so far for the study of this class of processes.
The second part of the dissertation deals with the statistical analysis of random diffusivity processes. A general description based on the concept of moment-generating function is initially provided to obtain standard statistical properties of the models. Then, the discussion moves to the study of the power spectral analysis and the first passage statistics for some particular random diffusivity models. A comparison between the results coming from the random diffusivity approach and the ones for standard Brownian motion is discussed. In this way, a deeper physical understanding of the systems described by random diffusivity models is also outlined.
To conclude, a discussion based on the possible origins of the heterogeneity is sketched, with the main goal of inferring which kind of systems can actually be described by the random diffusivity approach.
Lithium and boron are trace components of magmas, released during exsolution of a gas phase during volcanic activity.
In this study, we determine the diffusivity and isotopic fractionation of Li and B in hydrous silicate melts.
Two glasses were synthesized with the same rhyolitic composition (4.2 wt% water), having different Li and B contents; these were studied in diffusion-couple experiments that were performed using an internally heated pressure vessel, operated at 300 MPa in the temperature range 700-1250 degrees C for durations from 0 s to 24 h. From this we determined activation energies for Li and B diffusion of 57 +/- 4 kJ/mol and 152 +/- 15 kJ/mol with pre-exponential factors of 1.53 x 10(-7) m(2)/s and 3.80 x 10(-8) m(2)/s, respectively.
Lithium isotopic fractionation during diffusion gave beta values between 0.15 and 0.20, whereas B showed no clear isotopic fractionation.
Our Li diffusivities and isotopic fractionation results differ somewhat from earlier published values, but overall confirm that Li diffusivity increases with water content. Our results on B diffusion show that similarly to Li, B mobility increases in the presence of water.
By applying the Eyring relation, we confirm that B diffusivity is limited by viscous flow in silicate melts.
Our results on Li and B diffusion present a new tool for understanding degassing-related processes, offering a potential geospeedometer to measure volcanic ascent rates.
Li and B in ascending magmas: an experimental study on their mobility and isotopic fractionation
(2022)
This research study focuses on the behaviour of Li and B during magmatic ascent, and decompression-driven degassing related to volcanic systems. The main objective of this dissertation is to determine whether it is possible to use the diffusion properties of the two trace elements as a tool to trace magmatic ascent rate. With this objective, diffusion-couple and decompression experiments have been performed in order to study Li and B mobility in intra-melt conditions first, and then in an evolving system during decompression-driven degassing.
Synthetic glasses were prepared with rhyolitic composition and an initial water content of 4.2 wt%, and all the experiments were performed using an internally heated pressure vessel, in order to ensure a precise control on the experimental parameters such as temperature and pressure.
Diffusion-couple experiments were performed with a fix pressure 300 MPa. The temperature was varied in the range of 700-1250 °C with durations between 0 seconds and 24 hours. The diffusion-couple results show that Li diffusivity is very fast and starts already at very low temperature. Significant isotopic fractionation occurs due to the faster mobility of 6Li compared to 7Li. Boron diffusion is also accelerated by the presence of water, but the results of the isotopic ratios are unclear, and further investigation would be necessary to well constrain the isotopic fractionation process of boron in hydrous silicate melts. The isotopic ratios results show that boron isotopic fractionation might be affected by the speciation of boron in the silicate melt structure, as 10B and 11B tend to have tetrahedral and trigonal coordination, respectively.
Several decompression experiments were performed at 900 °C and 1000 °C, with pressures going from 300 MPa to 71-77 MPa and durations of 30 minutes, two, five and ten hours, in order to trigger water exsolution and the formation of vesicles in the sample. Textural observations and the calculation of the bubble number density confirmed that the bubble size and distribution after decompression is directly proportional to the decompression rate.
The overall SIMS results of Li and B show that the two trace elements tend to progressively decrease their concentration with decreasing decompression rates. This is explained because for longer decompression times, the diffusion of Li and B into the bubbles has more time to progress and the melt continuously loses volatiles as the bubbles expand their volumes.
For fast decompression, Li and B results show a concentration increase with a δ7Li and δ11B decrease close to the bubble interface, related to the sudden formation of the gas bubble, and the occurrence of a diffusion process in the opposite direction, from the bubble meniscus to the unaltered melt. When the bubble growth becomes dominant and Li and B start to exsolve into the gas phase, the silicate melt close to the bubble gets depleted in Li and B, because of a stronger diffusion of the trace elements into the bubble.
Our data are being applied to different models, aiming to combine the dynamics of bubble nucleation and growth with the evolution of trace elements concentration and isotopic ratios. Here, first considerations on these models will be presented, giving concluding remarks on this research study. All in all, the final remarks constitute a good starting point for further investigations. These results are a promising base to continue to study this process, and Li and B can indeed show clear dependences on decompression-related magma ascent rates in volcanic systems.
We study Brownian motion in a confining potential under a constant-rate resetting to a reset position x(0). The relaxation of this system to the steady-state exhibits a dynamic phase transition, and is achieved in a light cone region which grows linearly with time. When an absorbing boundary is introduced, effecting a symmetry breaking of the system, we find that resetting aids the barrier escape only when the particle starts on the same side as the barrier with respect to the origin. We find that the optimal resetting rate exhibits a continuous phase transition with critical exponent of unity. Exact expressions are derived for the mean escape time, the second moment, and the coefficient of variation (CV).
Understanding of wave environments is critical for the understanding of how particles are accelerated and lost in space. This study shows that in the vicinity of Europa and Ganymede, that respectively have induced and internal magnetic fields, chorus wave power is significantly increased. The observed enhancements are persistent and exceed median values of wave activity by up to 6 orders of magnitude for Ganymede. Produced waves may have a pronounced effect on the acceleration and loss of particles in the Jovian magnetosphere and other astrophysical objects. The generated waves are capable of significantly modifying the energetic particle environment, accelerating particles to very high energies, or producing depletions in phase space density. Observations of Jupiter's magnetosphere provide a unique opportunity to observe how objects with an internal magnetic field can interact with particles trapped in magnetic fields of larger scale objects.
Organic solar cells have the potential to become the cheapest form of electricity. Rapid increase in the power conversion efficiency of organic solar cells (OSCs) has been achieved with the development of non-fullerene small-molecule acceptors. Next generation photovoltaics based upon environmentally benign "green solvent" processing of organic semiconductors promise a step-change in the adaptability and versatility of solar technologies and promote sustainable development. However, high-performing OSCs are still processed by halogenated (non-environmentally friendly) solvents, so hindering their large-scale manufacture. In this perspective, we discuss the recent progress in developing highly efficient OSCs processed from eco-compatible solvents, and highlight research challenges that should be addressed for the future development of high power conversion efficiencies devices.
We study the dynamics of polymer chains in a bath of self-propelled particles (SPP) by extensive Langevin dynamics simulations in a two-dimensional model system. Specifically, we analyse the polymer looping properties versus the SPP activity and investigate how the presence of the active particles alters the chain conformational statistics. We find that SPPs tend to extend flexible polymer chains, while they rather compactify stiffer semiflexible polymers, in agreement with previous results. Here we show that higher activities of SPPs yield a higher effective temperature of the bath and thus facilitate the looping kinetics of a passive polymer chain. We explicitly compute the looping probability and looping time in a wide range of the model parameters. We also analyse the motion of a monomeric tracer particle and the polymer's centre of mass in the presence of the active particles in terms of the time averaged mean squared displacement, revealing a giant diffusivity enhancement for the polymer chain via SPP pooling. Our results are applicable to rationalising the dimensions and looping kinetics of biopolymers at constantly fluctuating and often actively driven conditions inside biological cells or in suspensions of active colloidal particles or bacteria cells.
One of the biggest successes of the Cassini mission is the detection of small moons (moonlets) embedded in Saturns rings that cause S-shaped density structures in their close vicinity, called propellers. Here, we present isothermal hydrodynamic simulations of moonlet-induced propellers in Saturn's A ring that denote a further development of the original model. We find excellent agreement between these new hydrodynamic and corresponding N-body simulations. Furthermore, the hydrodynamic simulations confirm the predicted scaling laws and the analytical solution for the density in the propeller gaps. Finally, this mean field approach allows us to simulate the pattern of the giant propeller Blériot, which is too large to be modeled by direct N-body simulations. Our results are compared to two stellar occultation observations by the Cassini Ultraviolet Imaging Spectrometer (UVIS), which intersect the propeller Blériot. Best fits to the UVIS optical depth profiles are achieved for a Hill radius of 590 m, which implies a moonlet diameter of about 860 m. Furthermore, the model favors a kinematic shear viscosity of the surrounding ring material of ν0 = 340 cm2 s−1, a dispersion velocity in the range of 0.3 cm s−1 < c0 < 1.5 cm s−1, and a fairly high bulk viscosity 7 < ξ0/ν0 < 17. These large transport values might be overestimated by our isothermal ring model and should be reviewed by an extended model including thermal fluctuations.
A single predator charging a herd of prey: effects of self volume and predator-prey decision-making
(2016)
We study the degree of success of a single predator hunting a herd of prey on a two-dimensional square lattice landscape. We explicitly consider the self volume of the prey restraining their dynamics on the lattice. The movement of both predator and prey is chosen to include an intelligent, decision making step based on their respective sighting ranges, the radius in which they can detect the other species (prey cannot recognise each other besides the self volume interaction): after spotting each other the motion of prey and predator turns from a nearest neighbour random walk into directed escape or chase, respectively. We consider a large range of prey densities and sighting ranges and compute the mean first passage time for a predator to catch a prey as well as characterise the effective dynamics of the hunted prey. We find that the prey's sighting range dominates their life expectancy and the predator profits more from a bad eyesight of the prey than from his own good eye sight. We characterise the dynamics in terms of the mean distance between the predator and the nearest prey. It turns out that effectively the dynamics of this distance coordinate can be captured in terms of a simple Ornstein–Uhlenbeck picture. Reducing the many-body problem to a simple two-body problem by imagining predator and nearest prey to be connected by an effective Hookean bond, all features of the model such as prey density and sighting ranges merge into the effective binding constant.
Parts without a whole?
(2015)
This explorative study gives a descriptive overview of what organizations do and experience when they say they practice design thinking. It looks at how the concept has been appropriated in organizations and also describes patterns of design thinking adoption. The authors use a mixed-method research design fed by two sources: questionnaire data and semi-structured personal expert interviews. The study proceeds in six parts: (1) design thinking¹s entry points into organizations; (2) understandings of the descriptor; (3) its fields of application and organizational localization; (4) its perceived impact; (5) reasons for its discontinuation or failure; and (6) attempts to measure its success. In conclusion the report challenges managers to be more conscious of their current design thinking practice. The authors suggest a co-evolution of the concept¹s introduction with innovation capability building and the respective changes in leadership approaches. It is argued that this might help in unfolding design thinking¹s hidden potentials as well as preventing unintended side-effects such as discontented teams or the dwindling authority of managers.
Innerhalb dieser Doktorarbeit wurde eine neuartige Mikromanipulationstechnik für die lokale Flüssigkeitsabgabe am komplexen Drüsengewebe der Schabe P. americana charakterisiert und für die damit verbundene gezielte Manipulation von einzelnen Zellen in einem Zellkomplex (Gewebe) angewandt. Bei dieser Mikromanipulationstechnik handelt es sich um die seit 2009 bekannte nanofluidische Rasterkraftmikroskopie (FluidFM = fluidic force microscopy). Dabei werden sehr kleine mikrokanälige Rasterkraftspitzen bzw. Mikro-/Nanopipetten mit einer Öffnung zwischen 300 nm und 2 µm verwendet, mit denen es möglich ist, sehr kleine Volumina im Pikoliter- bis Femtoliter-Bereich (10-12 L – 10-15 L) gezielt und ortsgenau abzugeben. Das Ziel dieser Arbeit war die Analyse zellulärer Prozesse, wie z. B. Zell-Zell-Kommunikation oder Signalweiterleitung, zwischen benachbarten Zellen unter Zuhilfenahme der Fluoreszenzmikroskopie. Mit dieser Methode können die Zellen und ihre Bestandteile mittels vorheriger Farbstoffbeladung unter einem Mikroskop mit hohem Kontrast optisch dargestellt werden. Mit Hilfe der Fluoreszenzmikroskopie sollten schlussendlich die zellulären Reaktionen innerhalb des Gewebes nach der lokalen Manipulation visualisiert werden.
Zunächst wurde die Anwendung des Systems an Luft und wässriger Umgebung beschrieben. In diesem Zusammenhang wurde eine Reinigungs- und Beladungsmethode entwickelt, mit der es möglich war, die kostspieligen Mikro-/Nanopipetten zu reinigen und anschließend mehrmals wiederzuverwenden. Hierzu wurde eine alternative Methode getestet, mit der das Diffusionsverhalten von Farbstoffmolekülen in unterschiedlichen Medien untersucht werden kann. Des Weiteren wurden die Systemparameter optimiert, welche nötig sind, um zwischen der Probenoberfläche und der Pipette einen guten Pipettenöffnungs-abschluss zu erhalten. Dieser Abschluss ist essentiell, damit die abgegebene Flüssigkeit ausschließlich in der Abgaberegion mit der Probe wechselwirkt und die darauffolgenden Reaktionen nur innerhalb des Gewebes erfolgen, da ansonsten die Zell-Zell-Signalweiterleitung zwischen den Zellen nicht eindeutig nachvollzogen werden kann. Diese interzelluläre Kommunikation wurde anhand zweier sekundärer Botenstoffe (Ca2+ und NO) untersucht. Hierbei war es möglich einzelne lokale Reaktionen zu detektieren, welche sich über weitere Zellen ausbreiteten. Schlussendlich wurde die Fertigung einer speziellen Injektionspipette beschrieben, welche an zwei biologischen Systemen getestet wurde.
Polymer multicomponent coatings such as multilayers mimic an extracellular, matrix (ECM) that attracts significant attention for the use of the multilayers as functional supports for advanced cell culture and tissue engineering. Herein, biodegradation and molecular transport in hyaluronan/polylysine multilayers coated with gold nanoparticles were described. Nanoparticle coating acts as a semipermeable barrier that governs molecular transport into/from the multilayers, and makes them biodegradation-resistant. Model protein lysozyme (mimics of ECM-soluble signals) diffuses into the multilayers as fast- and, slow-diffusing populations existing in an equilibrium,. Such a. composite system may have high potential to be exploited as degradation-resistant drug-delivery platforms suitable for cell-based applications.
Polyelectrolyte multilayer films are nowadays very attractive for bioapplications due to their tunable properties and ability to control cellular response. Here we demonstrate that multilayers made of hyaluronic acid and poly-l-lysine act as high-capacity reservoirs for small charged molecules. Strong accumulation within the film is explained by electrostatically driven binding to free charges of polyelectrolytes. Binding and release mechanisms are discussed based on charge balance and polymer dynamics in the film. Our results show that transport of molecules through the film-solution interface limits the release rate. The multilayers might serve as an effective platform for drug delivery and tissue engineering due to high potential for drug loading and controlled release.
The Bologna Process has inspired harmonisation strategies for higher education systems in other parts of the world. However, developments in other contexts are not much under review in the European debate. The present article describes the case of Southeast Asia and the attempt to promote harmonisation of its higher education systems. It further compares the processes in ASEAN and the European Higher Education Area to then discuss open questions for future comparative research. To do so the authors re-contextualise data from a study in ASEAN against the background of future research needs in the field of higher education harmonisation.
We consider the mean first-passage time of a random walker moving in a potential landscape on a finite interval, the starting and end points being at different potentials. From analytical calculations and Monte Carlo simulations we demonstrate that the mean first-passage time for a piecewise linear curve between these two points is minimized by the introduction of a potential barrier. Due to thermal fluctuations, this barrier may be crossed. It turns out that the corresponding expense for this activation is less severe than the gain from an increased slope towards the end point. In particular, the resulting mean first-passage time is shorter than for a linear potential drop between the two points.
Based on the space-fractional Fokker-Planck equation with a delta-sink term, we study the efficiency of random search processes based on Levy flights with power-law distributed jump lengths in the presence of an external drift, for instance, an underwater current, an airflow, or simply the preference of the searcher based on prior experience. While Levy flights turn out to be efficient search processes when the target is upstream relative to the starting point, in the downstream scenario, regular Brownian motion turns out to be advantageous. This is caused by the occurrence of leapovers of Levy flights, due to which Levy flights typically overshoot a point or small interval. Studying the solution of the fractional Fokker-Planck equation, we establish criteria when the combination of the external stream and the initial distance between the starting point and the target favours Levy flights over the regular Brownian search. Contrary to the common belief that Levy flights with a Levy index alpha = 1 (i.e. Cauchy flights) are optimal for sparse targets, we find that the optimal value for alpha may range in the entire interval (1, 2) and explicitly include Brownian motion as the most efficient search strategy overall.
In low-accumulation regions, the reliability of delta O-18-derived temperature signals from ice cores within the Holocene is unclear, primarily due to the small climate changes relative to the intrinsic noise of the isotopic signal. In order to learn about the representativity of single ice cores and to optimise future ice-core-based climate reconstructions, we studied the stable-water isotope composition of firn at Kohnen Station, Dronning Maud Land, Antarctica. Analysing delta O-18 in two 50m long snow trenches allowed us to create an unprecedented, two-dimensional image characterising the isotopic variations from the centimetre to the 100-metre scale. Our results show seasonal layering of the isotopic composition but also high horizontal isotopic variability caused by local stratigraphic noise. Based on the horizontal and vertical structure of the isotopic variations, we derive a statistical noise model which successfully explains the trench data. The model further allows one to determine an upper bound for the reliability of climate reconstructions conducted in our study region at seasonal to annual resolution, depending on the number and the spacing of the cores taken.
The isotopic composition of water in ice sheets is extensively used to infer past climate changes. In low-accumulation regions their interpretation is, however, challenged by poorly constrained effects that may influence the initial isotope signal during and after deposition of the snow. This is reflected in snow-pit isotope data from Kohnen Station, Antarctica, which exhibit a seasonal cycle but also strong interannual variations that contradict local temperature observations. These inconsistencies persist even after averaging many profiles and are thus not explained by local stratigraphic noise. Previous studies have suggested that post-depositional processes may significantly influence the isotopic composition of East Antarctic firn. Here, we investigate the importance of post-depositional processes within the open-porous firn (greater than or similar to 10 cm depth) at Kohnen Station by separating spatial from temporal variability. To this end, we analyse 22 isotope profiles obtained from two snow trenches and examine the temporal isotope modifications by comparing the new data with published trench data extracted 2 years earlier. The initial isotope profiles undergo changes over time due to downward advection, firn diffusion and densification in magnitudes consistent with independent estimates. Beyond that, we find further modifications of the original isotope record to be unlikely or small in magnitude (<< 1 parts per thousand RMSD). These results show that the discrepancy between local temperatures and isotopes most likely originates from spatially coherent processes prior to or during deposition, such as precipitation intermittency or systematic isotope modifications acting on drifting or loose surface snow.
We study the first passage dynamics for a diffusing particle experiencing a spatially varying diffusion coefficient while driven by correlated additive Gaussian white noise and multiplicative coloured non-Gaussian noise. We consider three functional forms for position dependence of the diffusion coefficient: power-law, exponential, and logarithmic. The coloured non-Gaussian noise is distributed according to Tsallis' q-distribution. Tracks of the non-Markovian systems are numerically simulated by using the fourth-order Runge-Kutta algorithm and the first passage times (FPTs) are recorded. The FPT density is determined along with the mean FPT (MFPT). Effects of the noise intensity and self-correlation of the multiplicative noise, the intensity of the additive noise, the cross-correlation strength, and the non-extensivity parameter on the MFPT are discussed.