Both first-principles-based and data-driven methods provide powerful tools for modeling physical systems. As such, there is a strong push for harnessing both approaches by combining them in the form of gray-box models. Automatic differentiation of ordinary differential equation (ODE) models and physical model parts enables flexible gray-box modeling in system identification tasks. Local model networks (LMNs) with their excellent interpretability and sparing use of model parameters are an ideal model class to provide data-driven elements in a gray-box model. Unfortunately, LMNs’ intricate training procedures currently do not allow for end-to-end training within larger model architectures. To remedy this, we propose a new LMN training algorithm and corresponding model called rectified linear unit model tree (ReLUMoT). ReLUMoT provides fully gradient-based training of LMNs, which permits us to train within gray-box ODE models. In essence, ReLUMoT pioneers the use of piecewise linear neural networks (PLNNs) as a training engine for LMNs. This is accomplished by distilling the locally linear structure of a PLNN into an LMN. We thoroughly review all theoretical concepts needed to train gray-box ODE models, ranging from state space modeling to initializing latent states during the training procedure. In particular, we give a critical review of sensitivity analysis methods, discussing their suitability for system identification tasks. We provide extensive experimental validation of ReLUMoT’s usefulness in practical modeling tasks. ReLUMoT is benchmarked against a variety of state-of-the-art modeling algorithms in learning both static and dynamic processes. In black-box settings, ReLUMoT matches or exceeds the performance of existing LMNs. Properly incorporating prior knowledge is shown to lead to vast improvements in model performance and size.

The discovery of the Higgs boson in 2012 marked a milestone in confirming the Standard Model (SM) of particle physics, yet the SM remains incomplete, failing to account for phenomena such as gravity, dark matter, and the matter–antimatter asymmetry in the universe. This motivates precision studies of collider processes, where more accurate theoretical predictions are needed to match the increasing experimental precision. Key challenges arise from Quantum Chromodynamics (QCD), which demands both calculations to high loop-orders in the perturbative regime and a careful separation of perturbative and non-perturbative dynamics. This thesis is split into two parts, each addressing issues in one of these categories. In the first part of this thesis, we present an all-order analysis of double-logarithmic corrections to the soft-overlap contribution in heavy-to-light transition form factors at large hadronic recoil. We focus on $B_c \to \eta_c$ transitions in a perturbative non-relativistic setup, treating both the bottom and charm quarks as heavy, with the hierarchy $m_b \gg m_c \gg \Lambda_{\rm QCD}$. Our diagrammatic analysis identifies two independent sources of double logarithms: soft-gluon effects, described by standard exponential Sudakov factors, and rapidity-ordered soft-quark configurations, which generate a novel set of coupled integral equations. These equations capture the intricate interplay between soft-quark and soft-gluon dynamics at the double-logarithmic level. As an independent consistency check, we employ a bare factorization formula within Soft-Collinear Effective Theory. Although endpoint-divergent convolution integrals prevent its use for resumming logarithmic corrections with renormalization group methods, its structure enables us to derive logarithmic corrections up to the two-loop level. By computing the only unknown contribution, we confirm the correctness of the integral equations to this order. While a closed-form solution of the integral equations remains currently elusive, we provide iterative expressions for the double-logarithmic series and derive the asymptotic behavior of the soft-overlap form factor at infinite recoil, showing that the Sudakov suppression is slightly weakened by the combined effects of soft quarks and soft gluons. In the second part of this thesis, we study the phase-space integral of the double-emission soft limit of generic QCD amplitudes with massless and massive emitters at an arbitrary angle to each other. This is a necessary ingredient to extend the nested soft-collinear subtraction scheme to cases with massive final states at hadron colliders. We employ integration-by-parts identities and the differential equations method to obtain an analytic expression for the expansion around the small-velocity limit of the massive emitter, which is an important cross-check for the exact calculation with full dependence on the velocity.

An active flow control method is used with the aim of friction drag reduction. The method utilizes streamwise oscillation of spanwise velocity at the wall. Owing to reduced turbulence intensity, less energy is required to drive the flow against viscous resistance. The key question is how compressibility affects the drag reduction results. A huge dataset of different flow cases with carefully selected parameter combinations has been created to reliably extract the influence of important flow parameters on the flow behavior. Direct numerical simulations and large eddy simulations of subsonic and supersonic channel flow were run with Mach numbers based on the mean velocity of Ma = 0.3, 1.5 and 3.0 and Reynolds numbers Re based on the friction velocity in the range of 190 up to 2540. Mean property effects are predominant in supersonic channel flow through large variations of the mean density and temperature and wall cooling. Consequences are a higher Reynolds stress anisotropy, increased length scales in the viscous sublayer flow and enhanced streak stability. The pressure-strain correlation and spanwise dissipation terms undergo a strong attenuation compared to the incompressible counterparts, especially in the controlled flows. Higher drag reduction and a larger optimum control wavelength are observed compared to the corresponding incompressible flows. Increasing the Mach number enhances these effects due to stronger mean property variations. A mitigation of near-wall compressibility effects occurs with an increase of the bulk Reynolds number, though, which attenuates the drag reduction benefits in the controlled flow as well. In the second part of this work, cooling terms were introduced in the Navier-Stokes equations to mimic the wall-normal temperature profile of an external boundary layer flow and to minimize variable property effects within the complete channel, respectively. This approach allows for a better isolation of intrinsic compressibility effects and wall cooling effects. The cooling strategies highlight the importance of intrinsic compressibility effects, which contribute to an increased control efficiency, too. As a potential case of application for the flow control method, a jet flow emanating from a round pipe is considered in the third part of this work. The turbulent subsonic pipe flow is manipulated by the transverse wall velocity and the focus is on the impact on the jet development. No direct interference of the streanwise oscillation pattern of transverse velocity within the pipe and the jet region is detected. However, the lowered turbulence intensity at the pipe exit noticeably affects the jet flow development, independent of how the reduction is achieved. The shear layer of the controlled jet flow develops with higher turbulence intensities associated with intensified Kelvin-Helmholtz instabilities. The effects can be relativized if the maximum transverse velocity is located directly at the pipe exit. Consequently, a jet with similar characteristics to the uncontrolled one can be generated with the advantage of a substantially lowered energy expenditure.

This thesis focuses on advancing the synthesis of polydivinylbenzene (PDVB) microparticles via precipitation polymerization and swelling techniques, aiming to tailor their morphological features for enhanced applications, particularly in size exclusion chromatography (SEC). The first part focuses on the synthesis of core-shell particles via precipitation polymerization, consisting of a non-porous core and a porous shell, intended as column material for SEC. Monodisperse, non-porous core particles were reliably produced using cost-efficient standard laboratory equipment in place of specialized devices. Next to shell growth, it could be shown that low-molecular-weight porogens common for suspension polymerization do not yield pores suitable for SEC in precipitation polymerization under the tested conditions. This could be explained by the lack of confined space during particle formation in precipitation polymerization. The synthesized particles proved effective for hydrodynamic chromatography (HDC) and can be used as size standards for analytical applications like particle size analyzers. The second part presents an approach to PDVB particle synthesis by combining precipitation polymerization with a template-swelling technique. Three distinct strategies involving different polystyrene templates were explored, resulting in particles with intricate morphologies, including surface grooves and hollow cores. SEM analysis revealed the impact of template architecture on the particle morphology. The resulting particles with adjustable void sizes hold promise for various applications, like catalysis and delivery systems. This work provides a proof of concept, and future research may further extend control over the nanoarchitecture and explore other templating methods. The third part explores an alternative route to create a porous shell on a highly crosslinked PDVB core particle, utilizing the template swelling method with macromolecular porogen aiming at pore sizes larger than 10 nm. The two-step swelling method sought to integrate the PS porogen into the precursor particle shells and subsequently remove it to leave behind the desired porous structure. However, despite successful incorporation of the PS template during the initial swelling stage, the subsequent removal of the porogen did not lead to the expected porous structure. Excessive, unintended crosslinking, possibly due to chain transfer reactions or residual double bonds in the PDVB system, appears to have hindered the removal of the PS template. While the procedure still seems promising, further research needs to be done to lower the crosslinking degree of the precursor particle shell. The findings contribute to the ongoing efforts to enhance the versatility of PDVB particles for diverse applications, like for example for HDC chromatography or in the biomedical field, emphasizing the importance of combining and tailoring synthesis methods to achieve specific morphological features. Parts of this thesis were performed in collaboration with PSS GmbH, Mainz and LiNaCon Dr. Ingo Lieberwirth, Mainz.