Kinetics of Brownian Transport

The rate of progress of Brownian processes is not easily quantifiable. An importantmeasure of the ”speed” of Brownian motion is themean first-passage time (FPT) to a given distance. FPTs exist in various flavours including exit- and transition-path times, which, for instance, can be used to quantify the length of reaction paths in folding transitions inmolecules such as DNA. Due to their inherently stochastic nature, measurements of any FPTs require repeated experiments under controlled conditions. In my thesis, I systematically explore FPTs in various contexts using a custom-built automated holographic optical tweezers (HOT) setup. More precisely, I investigate transition- and exit-path-time symmetries in equilibrium systems and demonstrate the breakdown of the symmetry in out-of-equilibriumsystems. Experimental data from folding DNA-hairpins show that the principles established on the mesoscale extend well into the molecular regime. In Kramers escape problem, the reciprocal of the escape rate corresponds to the time of first-passage to leave the initial state. A lower bound for the achievable FPT, e.g. of the reaction coordinate of a folding molecule, therefore corresponds to a speed-limit of the ensemble reaction rate. Using my setup, I show that certain barrier shapes can substantially lower the escape time across the barrier without changing the overall energy balance. This result has deep implications for reaction kinetics, e.g. in protein folding. Furthermore, I investigate the role of entropic forces in Brownian transport, show that hydrodynamic drag plays a crucial role in Brownian motion in confined systems, and give an experimental realisation of Fick-Jacobs theory. The thermodynamic applications of HOTs considered here necessitate the creation of fine-tuned optical landscapes, which requires precise phase-retrieval to compute the necessary holograms. In order to address this problem, I explore novel algorithms based on deep conditional generative models and test whether such models can assist in finding holograms for a given desired light distribution. I compare several differentmodels, including conditional generative-adversarial networks and conditional variational autoencoders, which are trained on data sets sampled on the HOT setup. Furthermore, I propose a novel forward-loss-minimising architecture and demonstrate its excellent performance on both validation and artificially-created test data sets.European Training Network (ETN) Grant No. 674979-NANOTRANS Winton Programme for the Physics of Sustainabilit

Particle transport across a channel via an oscillating potential

Membrane protein transporters alternate their substrate-binding sites between the extracellular and cytosolic side of the membrane according to the alternating access mechanism. Inspired by this intriguing mechanism devised by nature, we study particle transport through a channel coupled with an energy well that oscillates its position between the two entrances of the channel. We optimize particle transport across the channel by adjusting the oscillation frequency. At the optimal oscillation frequency, the translocation rate through the channel is a hundred times higher with respect to free diffusion across the channel. Our findings reveal the effect of time dependent potentials on particle transport across a channel and will be relevant for membrane transport and microfluidics application

Duality in matrix lattice Boltzmann models

The notion of duality between the hydrodynamic and kinetic (ghost) variables of lattice kinetic formulations of the Boltzmann equation is introduced. It is suggested that this notion can serve as a guideline in the design of matrix versions of the lattice Boltzmann equation in a physically transparent and computationally efficient way.Comment: 12 pages, 3 figure

Exploring performance and power properties of modern multicore chips via simple machine models

Modern multicore chips show complex behavior with respect to performance and power. Starting with the Intel Sandy Bridge processor, it has become possible to directly measure the power dissipation of a CPU chip and correlate this data with the performance properties of the running code. Going beyond a simple bottleneck analysis, we employ the recently published Execution-Cache-Memory (ECM) model to describe the single- and multi-core performance of streaming kernels. The model refines the well-known roofline model, since it can predict the scaling and the saturation behavior of bandwidth-limited loop kernels on a multicore chip. The saturation point is especially relevant for considerations of energy consumption. From power dissipation measurements of benchmark programs with vastly different requirements to the hardware, we derive a simple, phenomenological power model for the Sandy Bridge processor. Together with the ECM model, we are able to explain many peculiarities in the performance and power behavior of multicore processors, and derive guidelines for energy-efficient execution of parallel programs. Finally, we show that the ECM and power models can be successfully used to describe the scaling and power behavior of a lattice-Boltzmann flow solver code.Comment: 23 pages, 10 figures. Typos corrected, DOI adde

Lattice Boltzmann model with hierarchical interactions

We present a numerical study of the dynamics of a non-ideal fluid subject to a density-dependent pseudo-potential characterized by a hierarchy of nested attractive and repulsive interactions. It is shown that above a critical threshold of the interaction strength, the competition between stable and unstable regions results in a short-ranged disordered fluid pattern with sharp density contrasts. These disordered configurations contrast with phase-separation scenarios typically observed in binary fluids. The present results indicate that frustration can be modelled within the framework of a suitable one-body effective Boltzmann equation. The lattice implementation of such an effective Boltzmann equation may be seen as a preliminary step towards the development of complementary/alternative approaches to truly atomistic methods for the computational study of glassy dynamics.Comment: 14 pages, 5 figure