Polymer Dynamics in External Fields

The dynamics of single semiflexible polymers in solution under the influence of an external field are investigated with Brownian Dynamics simulations. Hydrodynamic interactions are included on the Rotne-Prager level and proof to be essential. Model equations are used to derive scaling laws. The work consists of five projects that are distinct but closely related to each other: In the first project, a neutral semiflexible particle is moved by centrifugal or gravitational forces relative to quiescent fluid. A coupling between hydrodynamic interactions and flexibility leads - depending on the elastic parameters - to a rod orientation perpendicular to the external field. This coupling is also investigated for a filament that is rotated at one end by some external torque (second project). Above a critical torque the filament folds itself around the rotational axis, with important consequences for the propulsion with a nano-machine. The third project deals with flexible polymers in an ultracentrifuge where a novel compactification and unfolding scenario is predicted: The established theories on sedimentation use the preaveraging approximation of the hydrodynamic interactions and cannot explain the polymer configurations at high fields consisting of a dense head and a long tail, which make a new efficient separation technique possible. In the forth project, the diffusion of charged semiflexible polymers under different salt conditions is treated. Ions are included explicitly and not on a mean-field level. The theory of electrolyte friction for spherical objects is qualitatively extended to semiflexible polymers. A heuristic formula for the diffusion constant over the whole range of persistence lengths is proposed. In the final project, the hydrodynamic orientation mechanism found in the first project is suggested as a possible source of anomalous electric birefringence which is observed for rod-like polymers. It is compared with the competing parallel induced dipole orientation. The dependence of the polarizability on rod length, salt and polymer concentration is clarified

Gossip vs. Markov Chains, and Randomness-Efficient Rumor Spreading

We study gossip algorithms for the rumor spreading problem which asks one node to deliver a rumor to all nodes in an unknown network. We present the first protocol for any expander graph $G$ with $n$ nodes such that, the protocol informs every node in $O(\log n)$ rounds with high probability, and uses $\tilde{O}(\log n)$ random bits in total. The runtime of our protocol is tight, and the randomness requirement of $\tilde{O}(\log n)$ random bits almost matches the lower bound of $\Omega(\log n)$ random bits for dense graphs. We further show that, for many graph families, polylogarithmic number of random bits in total suffice to spread the rumor in $O(\mathrm{poly}\log n)$ rounds. These results together give us an almost complete understanding of the randomness requirement of this fundamental gossip process. Our analysis relies on unexpectedly tight connections among gossip processes, Markov chains, and branching programs. First, we establish a connection between rumor spreading processes and Markov chains, which is used to approximate the rumor spreading time by the mixing time of Markov chains. Second, we show a reduction from rumor spreading processes to branching programs, and this reduction provides a general framework to derandomize gossip processes. In addition to designing rumor spreading protocols, these novel techniques may have applications in studying parallel and multiple random walks, and randomness complexity of distributed algorithms.Comment: 41 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1304.135

A numerical comparison of solvers for large-scale, continuous-time algebraic Riccati equations and LQR problems

In this paper, we discuss numerical methods for solving large-scale continuous-time algebraic Riccati equations. These methods have been the focus of intensive research in recent years, and significant progress has been made in both the theoretical understanding and efficient implementation of various competing algorithms. There are several goals of this manuscript: first, to gather in one place an overview of different approaches for solving large-scale Riccati equations, and to point to the recent advances in each of them. Second, to analyze and compare the main computational ingredients of these algorithms, to detect their strong points and their potential bottlenecks. And finally, to compare the effective implementations of all methods on a set of relevant benchmark examples, giving an indication of their relative performance

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

Privacy and security in cyber-physical systems

Data privacy has attracted increasing attention in the past decade due to the emerging technologies that require our data to provide utility. Service providers (SPs) encourage users to share their personal data in return for a better user experience. However, users' raw data usually contains implicit sensitive information that can be inferred by a third party. This raises great concern about users' privacy. In this dissertation, we develop novel techniques to achieve a better privacy-utility trade-off (PUT) in various applications. We first consider smart meter (SM) privacy and employ physical resources to minimize the information leakage to the SP through SM readings. We measure privacy using information-theoretic metrics and find private data release policies (PDRPs) by formulating the problem as a Markov decision process (MDP). We also propose noise injection techniques for time-series data privacy. We characterize optimal PDRPs measuring privacy via mutual information (MI) and utility loss via added distortion. Reformulating the problem as an MDP, we solve it using deep reinforcement learning (DRL) for real location trace data. We also consider a scenario for hiding an underlying ``sensitive'' variable and revealing a ``useful'' variable for utility by periodically selecting from among sensors to share the measurements with an SP. We formulate this as an optimal stopping problem and solve using DRL. We then consider privacy-aware communication over a wiretap channel. We maximize the information delivered to the legitimate receiver, while minimizing the information leakage from the sensitive attribute to the eavesdropper. We propose using a variational-autoencoder (VAE) and validate our approach with colored and annotated MNIST dataset. Finally, we consider defenses against active adversaries in the context of security-critical applications. We propose an adversarial example (AE) generation method exploiting the data distribution. We perform adversarial training using the proposed AEs and evaluate the performance against real-world adversarial attacks.Open Acces

Quasi One-Dimensional Modelling of Turbulence and Interaction of Combustion Chambers in a Shockless Explosion Combustor

This thesis deals with the modelling of two-dimensional coupling of quasi one-dimensional domains and turbulence within a quasi one-dimensional combustion chamber. Also an interpolation-free finite volume moving mesh method is described. First, the basic framework of a gas turbine is introduced including an uncommon approach for constant volume combustion: the shockless explosion combustion (SEC). In a preceding work a simulation code for this combustion process solving quasi one-dimensional reactive Euler equations with a finite volume (FV) Riemann solver has been developed and was extended for the thesis at hand. A network model is presented, allowing for the investigation of interaction of multiple pulsating combustion chambers of an SEC gas turbine with the plenums and each other. It couples the quasi one-dimensional domains using boundary conditions and flux corrections such that interactions of slanted combustion chambers with the plenums are possible. A series of simulations utilising this model is carried out to show possible fields of research for this tool. As the simulation of combustion processes are especially sensitive to spacial resolution but complex chemistry also imposes restrictions on the number of grid cells a feature for adaptive remeshing is described. It uses the moving mesh idea within the FV solver. As interpolation introduces too much numerical diffusion a flux correction is given which evolves governing equations and mesh simultaneously without changing the Euler equations themselves. The performance of this feature is demonstrated with simulations of a detonation and a cyclic SEC. Finally, the prerequisites for the research of the starting process of an SEC gas turbine are created by including molecular transport and turbulence in the SEC-code. Towards this aim, the one-dimensional turbulence (ODT) model is adjusted for this application. The ODT-line on which the stochastic eddy events, representing the turbulence, occur is aligned with the streamwise direction of the long-stretched combustion chamber. Also ODT is used as a stand-alone and subgrid-scale model. The main features of turbulence and ODT are compared to the new variant ODT-FHD. This study reveals that the ODT-FHD is able to generally reproduce the correct dependency of turbulence on mean flow velocity along with a plausible distribution of eddy sizes and kinetic energies. While lacking the possibility to generate new extrema of flow properties along the ODT-line it incorporates turbulent diffusion very well. The influence of the three model parameter is shown in addition to the simulation of a turbulent flame and a turbulent single-tube SEC

Classical and quantum algorithms for scaling problems

This thesis is concerned with scaling problems, which have a plethora of connections to different areas of mathematics, physics and computer science. Although many structural aspects of these problems are understood by now, we only know how to solve them efficiently in special cases.We give new algorithms for non-commutative scaling problems with complexity guarantees that match the prior state of the art. To this end, we extend the well-known (self-concordance based) interior-point method (IPM) framework to Riemannian manifolds, motivated by its success in the commutative setting. Moreover, the IPM framework does not obviously suffer from the same obstructions to efficiency as previous methods. It also yields the first high-precision algorithms for other natural geometric problems in non-positive curvature.For the (commutative) problems of matrix scaling and balancing, we show that quantum algorithms can outperform the (already very efficient) state-of-the-art classical algorithms. Their time complexity can be sublinear in the input size; in certain parameter regimes they are also optimal, whereas in others we show no quantum speedup over the classical methods is possible. Along the way, we provide improvements over the long-standing state of the art for searching for all marked elements in a list, and computing the sum of a list of numbers.We identify a new application in the context of tensor networks for quantum many-body physics. We define a computable canonical form for uniform projected entangled pair states (as the solution to a scaling problem), circumventing previously known undecidability results. We also show, by characterizing the invariant polynomials, that the canonical form is determined by evaluating the tensor network contractions on networks of bounded size