We analyse mobile-immobile transport of particles that switch between the mobile and immobile phases with finite rates. Despite this seemingly simple assumption of Poissonian switching, we unveil a rich transport dynamics including significant transient anomalous diffusion and non-Gaussian displacement distributions. Our discussion is based on experimental parameters for tau proteins in neuronal cells, but the results obtained here are expected to be of relevance for a broad class of processes in complex systems. Specifically, we obtain that, when the mean binding time is significantly longer than the mean mobile time, transient anomalous diffusion is observed at short and intermediate time scales, with a strong dependence on the fraction of initially mobile and immobile particles. We unveil a Laplace distribution of particle displacements at relevant intermediate time scales. For any initial fraction of mobile particles, the respective mean squared displacement (MSD) displays a plateau. Moreover, we demonstrate a short-time cubic time dependence of the MSD for immobile tracers when initially all particles are immobile.

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.

It has been experimentally demonstrated that reaction rates for molecules embedded in microfluidic optical cavities are altered when compared to rates observed under "ordinary" reaction conditions. However, precise mechanisms of how strong coupling of an optical cavity mode to molecular vibrations affects the reactivity and how resonance behavior emerges are still under dispute. In the present work, we approach these mechanistic issues from the perspective of a thermal model reaction, the inversion of ammonia along the umbrella mode, in the presence of a single-cavity mode of varying frequency and coupling strength. A topological analysis of the related cavity Born-Oppenheimer potential energy surface in combination with quantum mechanical and transition state theory rate calculations reveals two quantum effects, leading to decelerated reaction rates in qualitative agreement with experiments: the stiffening of quantized modes perpendicular to the reaction path at the transition state, which reduces the number of thermally accessible reaction channels, and the broadening of the barrier region, which attenuates tunneling. We find these two effects to be very robust in a fluctuating environment, causing statistical variations of potential parameters, such as the barrier height. Furthermore, by solving the time-dependent Schrodinger equation in the vibrational strong coupling regime, we identify a resonance behavior, in qualitative agreement with experimental and earlier theoretical work. The latter manifests as reduced reaction probability when the cavity frequency omega(c) is tuned resonant to a molecular reactant frequency. We find this effect to be based on the dynamical localization of the vibro-polaritonic wavepacket in the reactant well.

We formulate a linear phase and frequency response theory for hyperbolic flows, which generalizes phase response theory for autonomous limit cycle oscillators to hyperbolic chaotic dynamics. The theory is based on a shadowing conjecture, stating the existence of a perturbed trajectory shadowing every unperturbed trajectory on the system attractor for any small enough perturbation of arbitrary duration and a corresponding unique time isomorphism, which we identify as phase such that phase shifts between the unperturbed trajectory and its perturbed shadow are well defined. The phase sensitivity function is the solution of an adjoint linear equation and can be used to estimate the average change of phase velocity to small time dependent or independent perturbations. These changes in frequency are experimentally accessible, giving a convenient way to define and measure phase response curves for chaotic oscillators. The shadowing trajectory and the phase can be constructed explicitly in the tangent space of an unperturbed trajectory using co-variant Lyapunov vectors. It can also be used to identify the limits of the regime of linear response.

This dissertation focuses on the understanding of the optical manipulation of microgels dispersed in aqueous solution of azobenzene containing surfactant. The work consists of three parts where each part is a systematic investigation of the (1) photo-isomerization kinetics of the surfactant in complex with the microgel polymer matrix, (2) light driven diffusiosmosis (LDDO) in microgels and (3) photo-responsivity of microgel on complexation with spiropyran. The first part comprises three publications where the first one [P1] investigates the photo-isomerization kinetics and corresponding isomer composition at a photo-stationary state of the photo-sensitive surfactant conjugated with charged polymers or micro sized polymer networks to understand the structural response of such photo-sensitive complexes. We report that the photo-isomerization of the azobenzene-containing cationic surfactant is slower in a polymer complex compared to being purely dissolved in an aqueous solution. The surfactant aggregates near the polyelectrolyte chains at concentrations much lower than the bulk critical micelle concentration. This, along with the inhibition of the photo-isomerization kinetics due to steric hindrance within the densely packed aggregates, pushes the isomer-ratio to a higher trans-isomer concentration for all irradiation wavelengths. The second publication [P2] combines experimental results and non-adiabatic dynamic simulations for the same surfactant molecules embedded in the micelles with absorption spectroscopy measurements of micellar solutions to uncover the reasons responsible for the slowdown in photo induced trans → cis azobenzene isomerization at concentrations higher than the critical micelle concentration (CMC). The simulations reveal a decrease of isomerization quantum yields for molecules inside the micelles and observes a reduction of extinction coefficients upon micellization. These findings explain the deceleration of the trans → cis switching in micelles of the azobenzene-containing surfactants. Finally, the third publication [P3] focusses on the kinetics of adsorption and desorption of the same surfactant within anionic microgels in the dark and under continuous irradiation. Experimental data demonstrate, that microgels can serve as a selective absorber of the trans isomers. The interaction of the isomers with the gel matrix induces a remotely controllable collapse or swelling on appropriate irradiation wavelengths. Measuring the kinetics of the microgel size response and knowing the exact isomer composition under light exposure, we calculate the adsorption rate of the trans-isomers. The second part comprises two publications. The first publication [P4] reports on the phenomenon of light-driven diffusioosmotic (DO) long-range attractive and repulsive interactions between micro-sized objects, whose range extends several times the size of microparticles and can be adjusted to point towards or away from the particle by varying irradiation parameters such as intensity or wavelength of light. The phenomenon is fueled by the aforementioned photosensitive surfactant. The complex interaction of dynamic exchange of isomers and photo-isomerization rate yields to relative concentrations gradients of the isomers in the vicinity of micro-sized object inducing a local diffusioosmotic (DO) flow thereby making a surface act as a micropump. The second publication [P5] exclusively aims the visualization and investigation of the DO flows generated from microgels by using small tracer particles. Similar to micro sized objects, the flow is able to push adjacent tracers over distances several times larger than microgel size. Here we report that the direction and the strength of the l-LDDO depends on the intensity, irradiation wavelength and the amount of surfactant adsorbed by the microgel. For example, the flow pattern around a microgel is directed radially outward and can be maintained quasi-indefinitely under exposure at 455 nm when the trans:cis ratio is 2:1, whereas irradiation at 365 nm, generates a radially transient flow pattern, which inverts at lower intensities. Lastly, the third part consists of one publication [P6] which, unlike the previous works, reports on the study of the kinetics of photo- and thermo-switching of a new surfactant namely, spiropyran, upon exposure with light of different wavelengths and its interaction with p(NIPAM-AA) microgels. The surfactant being an amphiphile, switches between its ring closed spiropyran (SP) form and ring open merocyanine (MC) form which results in a change in the hydrophilic–hydrophobic balance of the surfactant as MC being a zwitterionic form along with the charged head group, generates three charges on the molecule. Therefore, the MC form of the surfactant is more hydrophilic than in the case of the neutral SP state. Here, we investigate the initial shrinkage of the gel particles via charge compensation on first exposure to SP molecules which results from the complex formation of the molecules with the gel matrix, triggering them to become photo responsive. The size and VPTT of the microgels during irradiation is shown to be a combination of heating up of the solution during light absorption by the surfactant (more pronounced in the case of UV irradiation) and the change in the hydrophobicity of the surfactant.