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In the first part of my work I have investigated the ageing properties of the first passage time distributions in a one-dimensional subdiffusive continuous time random walk with power law distributed waiting times of the form $\psi(\tau) \sim \tau^{-1-\alpha}$ with $0<\alpha<1$ and $1<\alpha<2$. The age or ageing time $t_a$ is the time span from the start of the stochastic process to the start of the observation of this process (at $t=0$). I have calculated the results for a single target and two targets, also including the biased case, where the walker is driven towards the boundary by a constant force. I have furthermore refined the previously derived results for the non-ageing case and investigated the changes that occur when the walk is performed in a discrete quenched energy landscape, where the waiting times are fixed for every site. The results include the exact Laplace space densities and infinite (converging) series as exact results in the time space. The main results are the dominating long time power law behavior regimes, which depend on the ageing time. For the case of unbiased subdiffusion ($\alpha < 1$) in the presence of one target, I find three different dominant terms for ranges of $t$ separated by $t_a$ and another crossover time $t^{\star}$, which depends on $t_a$ as well as on the anomalous exponent $\alpha$ and the anomalous diffusion coefficient $K_{\alpha}$. In all three regimes ($t \ll t_a$, $t_a \ll t \ll t^{\star}$, $t \gg t^{\star}$) one finds power law decay with exponents depending on $\alpha$. The middle regime only exists for $t_a \ll t^{\star}$. The dominant terms in the first two regimes (ageing regimes) come from the probability distribution of the forward waiting time, the time one has to wait for the stochastic process to make the first step during the observation. When the observation time is larger than the second crossover time $t^{\star}$, the first passage time density does not show ageing and the non-ageing first passage time dominates. The power law exponents in the respective regimes are $-\alpha$ for strong ageing, $-1-\alpha$ in the intermediate regime, and $-1-\alpha/2$ in the final non-ageing regime. A similar split into three regimes can be found for $1<\alpha<2$, only with a different second crossover time $t^*$. In this regime the diffusion is normal but also age-dependent. For the diffusion in quenched energy landscapes one cannot detect ageing. The first passage time density shows a quenched power law $^\sim t^{-(1+2\alpha)/(1+\alpha)}$. For diffusion between two target sites and the biased diffusion towards a target only two scaling regimes emerge, separated by the ageing time. In the ageing case $t \ll t_a$ the forward waiting time is again dominant with power law exponent $-\alpha$, while the non-ageing power law $-1-\alpha$ is found for all times $t \gg t_a$. An intermediate regime does not exist. The bias and the confinement have similar effects on the first passage time density. For quenched diffusion, the biased case is interesting, as the bias reduces correlations due to revisiting of the same waiting time. As a result, CTRW like behavior is observed, including ageing. Extensive computer simulations support my findings.
The second part of my research was done on the subject of ageing Scher-Montroll transport, which is in parts closely related to the first passage densities. It explains the electrical current in an amorphous material. I have investigated the effect of the width of a given initial distribution of charge carriers on the transport coefficients as well as the ageing effect on the emerging power law regimes and a constant initial regime. While a spread out initial distribution has only little impact on the Scher-Montroll current, ageing alters the behavior drastically. Instead of the two classical power laws one finds four current regimes, up to three of which can appear in a single experiment. The dominant power laws differ for $t \ll t_a, t_c$, $t_a \ll t \ll t_c$, $t_c \ll t \ll t_a$, and $t \gg t_a,t_c$. Here, $t_c$ is the crossover time of the non-aged Scher-Montroll current. For strongly aged systems one can observe a constant current in the first regime while the others are dominated by decaying power laws with exponents $\alpha -1$, $-\alpha$, and $-1-\alpha$. The ageing regimes are the 1st and 3rd one, while the classical regimes are the 2nd and the 4th. I have verified the theory using numerical integration of the exact integrals and applied the new results to experimental data.
In the third part I considered a single file of subdiffusing particles in an energy landscape. Every occupied site of the landscape acts as a boundary, from which a particle is immediately reflected to its previous site, if it tries to jump there. I have analysed the effects single-file diffusion a quenched landscape compared to an annealed landscape and I have related these results to the number of steps and related quantities. The diffusion changes from ultraslow logarithmic diffusion in the annealed or CTRW case to subdiffusion with an anomalous exponent $\alpha/(1+\alpha)$ in the quenched landscape. The behavior is caused by the forward waiting time, which changes drastically from the quenched to the annealed case. Single-file effects in the quenched landscape are even more complicated to consider in the ensemble average, since the diffusion in individual landscapes shows extremely diverse behavior. Extensive simulations support my theoretical arguments, which consider mainly the long time evolution of the mean square displacement of a bulk particle.
Interplay of coupling and common noise at the transition to synchrony in oscillator populations
(2016)
There are two ways to synchronize oscillators: by coupling and by common forcing, which can be pure noise. By virtue of the Ott-Antonsen ansatz for sine-coupled phase oscillators, we obtain analytically tractable equations for the case where both coupling and common noise are present. While noise always tends to synchronize the phase oscillators, the repulsive coupling can act against synchrony, and we focus on this nontrivial situation. For identical oscillators, the fully synchronous state remains stable for small repulsive coupling; moreover it is an absorbing state which always wins over the asynchronous regime. For oscillators with a distribution of natural frequencies, we report on a counter-intuitive effect of dispersion (instead of usual convergence) of the oscillators frequencies at synchrony; the latter effect disappears if noise vanishes.
The plasmon resonance of metal nanoparticles determines their optical response in the visible spectral range. Many details such as the electronic properties of gold near the particle surface and the local environment of the particles influence the spectra. We show how the cheap but highly precise fabrication of composite nanolayers by spin-assisted layer-by-layer deposition of polyelectrolytes can be used to investigate the spectral response of gold nanospheres (GNS) and gold nanorods (GNR) in a self-consistent way, using the established Maxwell–Garnett effective medium (MGEM) theory beyond the limit of homogeneous media. We show that the dielectric function of gold nanoparticles differs from the bulk value and experimentally characterize the shape and the surrounding of the particles thoroughly by SEM, AFM and ellipsometry. Averaging the dielectric functions of the layered surrounding by an appropriate weighting with the electric field intensity yields excellent agreement for the spectra of several nanoparticles and nanorods with various cover-layer thicknesses.
In this Thesis, the properties of aqueous hemicellulose polysaccharides are investigated using computer simulations. The high swelling capacity of materials composed of these molecules allows the generation of directed motion in plant materials entirely controlled by water uptake.
To explore the molecular origin of this swelling capacity, a computational model with atomistic resolution for hemicellulose polysaccharides is build and validated in comparison with experiments. Using this model, simulations of small polysaccharides are employed to gain an understanding of the interactions of these molecules with water, the influence of water on their conformational freedom, and the swelling capacity quantified in terms of osmotic pressure. It is revealed that the branched hemicellulose polysaccharides show different hydration characteristics compared to linear polysaccharides.
To study swelling properties on length and time scales that exceed the limitations imposed by atomistic simulations, a procedure to obtain transferable coarse-grain models is developed. The transferability of the coarse-grain models over both different degrees of polymerization as well as different solute concentrations is demonstrated. Therefore, the procedure allows the construction of large coarse-grained systems based on small atomistic reference systems. Finally, the coarse-grain model is applied to demonstrate that linear and branched polysaccharides show a different swelling behavior when coupled to a water bath.
We have investigated the electrochemical, spectroscopic and electroluminescent properties of a family of aza-aromatic complexes of ruthenium of type [RuII(bpy/phen)2(L)]2+ (4d6) with three isomeric L ligands, where, bpy = 2,2′-bipyridine, phen = 1,10-phenanthroline and the L ligands are 3-(2-pyridyl)[1,2,4]triazolo[1,5-a]pyridine (L1), 3-(2-pyridyl[1,2,3])triazolo[1,5-a]pyridine (L2) and 2-(2-pyridyl)[1,2,4]triazolo[1,5-a]pyridine (L3). The complexes display two bands in the visible region near 410–420 and 440–450 nm. The complexes are diamagnetic and show well defined 1H NMR lines. They are electroactive in acetonitrile solution and exhibit a well defined RuII/RuIII couple near 1.20 to 1.30 V and −1.40 to −1.50 V due to ligand reduction versus Saturated Calomel Electrode (SCE). The solutions are also luminescent, with peaks are near 600 nm. All the complexes are electroluminescent in nature with peaks lying near 580 nm. L1 and L3 ligated complexes with two bpy co-ligands show weak photoluminescence (PL) but stronger electroluminescence (EL) compared to corresponding L2 ligated analogues.
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.
We introduce azobenzene-functionalized polyelectrolyte multilayers as efficient, inexpensive optoacoustic transducers for hyper-sound strain waves in the GHz range. By picosecond transient reflectivity measurements we study the creation of nanoscale strain waves, their reflection from interfaces, damping by scattering from nanoparticles and propagation in soft and hard adjacent materials like polymer layers, quartz and mica. The amplitude of the generated strain ε ∼ 5 × 10−4 is calibrated by ultrafast X-ray diffraction.