## Proposed PhD thesis topics at DP DOCC

- Biomolecular chemistry
- Environmental engineering
- Engineering
- Mathematics
- Nano- and biophysics
- Material sciences
- Structural engineering

### Biomolecular chemistry

*Admission requirement: Master's degree in chemistry, biophysics, mathematics or informatics (or equivalent).*

#### Machine Learning in Analysis of Molecular Dynamics Simulations (CMD-1)

Molecular dynamics simulations result in large amounts of data. Thus, state of the art methods relying on information theory and stochastics need to be developed and optimized to describe properties like hydration and aggregation. Pattern recognition of electrostatic and hydrophobic properties on complex surfaces will be applied using cutting-edge machine learning techniques. The aim of the project is to develop artificial intelligence-driven solutions for the development of therapeutic antibodies and related biologics.

*Supervisor: Liedl; Co-supervisor: Haltmeier*.

#### Reweighting and regularisation for accelerated biomolecular dynamics simulations (CMD-2)

Biomolecular processes occur on time scales not yet accessible by conventional molecular dynamics simulations. Different algorithms have been developed that modify the energy landscape to access longer time scales. However, after modification of the energy landscape, probabilities of the conformations have to be reweighted to regain a realistic ensemble. Most existing algorithms for reweighting suffer from large errors resulting in distorted probability distributions. In this project we will develop an alternative and more reliable solution to this problem based on Tikhonov type functionals.

*Supervisor: Liedl; Co-supervisor: Haltmeier/Probst*.

### Environmental engineering

*Admission requirement: Master's degree in civil or environmental engineering science (or equivalent).*

#### Lagrangian microscopic biokinetic model (CFD-1)

Application of Lagrangian based CFD methods in urban water management (such as smoothed particle hydrodynamics) is a relatively recent method which allows for a novel treatment of biochemical processes in the water phase. The thesis aims to couple the flow simulation with a microscopic description of biokinetic conversion, based on a stochastic distribution of particles representing microbial flocs. This will allow to decouple fluid and particle phase in the numerical description of biokinetic processes in urban water systems.

High-resolution simulation of fluids (denoted as Computational Fluid Dynamics CFD) is a challenging and computationally expensive task, that occurs in a broad range of research and engineering disciplines. In Environmental Engineering these methods are used to investigate flow dynamics in reactors and natural water bodies alike, typical examples being mechanical mixing in anaerobic digestion processes and free surface flow behavior in urban water infrastructure.

In this project we aim to apply Smoothed Particle Hydrodynamics - a fully Lagrangian meshless CFD method, which was introduced app. 40 years ago for astrophysical simulations. Since then SPH has been successfully applied to fluid mechanics to simulate e.g. free surface flows, multiphase problems, transport phenomena but also biochemical reactions. Due to its Lagrangian nature SPH has various advantages: E.g. advection is accounted for exactly and mass, momentum and energy are conserved; free surfaces are implicitly supported; multiphase flow simulations with density ratios between the phases - as required for two-phase water-particle flow - are realisable and (larger) particles can be described as rigid bodies.

The key idea of SPH is to divide the fluid into a large number of particles (interpolation points), each of those is associated with physical parameters like mass m, volume V, velocity v, density ρ, pressure p and (e.g. oxygen) concentration C. Time evolution of a particle follows a kernel-smoothed influence of its neighbourhood.

In the project "Lagrangian microscopic biokinetic model" we use the particle approach of the SPH method. Each SPH particle can mimic either a soluble, an inert or any non-degradable material (e.g. metal, glass, etc.). This is an advantageous feature of SPH in computational studies of e.g. anaerobic digesters, which makes it better suited to include the effects of sedimentation, non-degradable materials, etc.

The standard approach is that each SPH particle describing the biomass flow, carries also the information regarding the biological concentrations of substances in the water (denoted as Ci,bio in the figure above). The biochemical equations are then solved for each particle and the spatial mass transfer interactions are taken into account by solving the diffusion equation over the neighbouring particles.

In this project we will take a microscopic view on biokinetics. The bacteria biomass will be represented by means of a stochastic distribution as (a second set of) microbial particles. These microbial particles are linked to the fluid particles of the SPH method. Thus, flow dynamics are computed for fluid particles and biokinetics for microbial ones. This will allow to decouple fluid and particle phase in the kinetic description of biokinetic processes and thus allow for a novel and more detailed calculation scheme as e.g. the inclusion of population balance models.

*Supervisor: Rauch; Co-supervisor: Franosch/Rotach*.

#### Lagrangian sewer solids transport model (CFD-2)

The transport of solids in sewers is usually simulated by one-dimensional Navier-Stokes equations coupled with simplified transport models. Despite significant research efforts these models show limited predictive capabilities for special problems like clogging by textile materials or FOG (fat, oil and grease). Contrarily, this thesis should apply a Lagrangian computational fluid dynamics method, i.e. smoothed particle hydrodynamics (SPH), for establishing a multiphase (water, gas and particles) model of the sewer. The multiphase SPH model will be coupled with transport models for special objects like textiles and buildup / erosion of FOG deposits.

High-resolution simulation of fluids (denoted as Computational Fluid Dynamics CFD) is a challenging and computationally expensive task, that occurs in a broad range of research and engineering disciplines. In Environmental Engineering these methods are used to investigate flow dynamics in reactors and natural water bodies alike, typical examples being mechanical mixing in anaerobic digestion processes and free surface flow behavior in urban water infrastructure.

In this project we aim to apply Smoothed Particle Hydrodynamics - a fully Lagrangian meshless CFD method, which was introduced app. 40 years ago for astrophysical simulations. Since then SPH has been successfully applied to fluid mechanics to simulate e.g. free surface flows, multiphase problems, transport phenomena but also biochemical reactions. Due to its Lagrangian nature SPH has various advantages: E.g. advection is accounted for exactly and mass, momentum and energy are conserved; free surfaces are implicitly supported; multiphase flow simulations with density ratios between the phases - as required for two-phase water-particle flow - are realisable and (larger) particles can be described as rigid bodies.

The key idea of SPH is to divide the fluid into a large number of particles (interpolation points), each of those is associated with physical parameters like mass m, volume V, velocity v, density ρ, pressure p and (e.g. oxygen) concentration C. Time evolution of a particle follows a kernel-smoothed influence of its neighbourhood.

In the project Lagrangian sewer solids transport model we aim to contribute to one of the great challenges in urban drainage modelling, that is the transport of solids in sewers. The accumulation of sediments in the sewer system reduces the hydraulic capacity of the sewer network and thus increases the risk of surface flooding as well as the amount of pollutants that is subsequently discharged into the receiving water.

The simulation of sediment transport in sewers is currently restricted to non-cohesive material (sand etc.) and is to be divided into morphological and mathematical models. Morphological (or detailed sediment transport) models, calculate shear stress as the main physical force reacting to the particles. Description of fluid flow is received by a hydrodynamic simulation - usually derived from one-dimensional Navier-Stokes equations. The sediment transport is then coupled to the hydraulic computation.

Mathematical models use the one-dimensional advection-dispersion equation (ADE) to compute mass conservation of substances transported with the fluid. ADE´s are widely applied for modelling the transport of dissolved substances in natural flow processes. For the transport of particles, the equation has to be adapted.

Despite significant research efforts these models show limited predictive capabilities for special problems like cohesive materials, clogging of sewers by textile materials or FOG (fat, oil and grease) accumulation. Contrarily, we will here apply a Lagrangian computational fluid dynamics method, i.e. smoothed particle hydrodynamics (SPH), for establishing a multiphase (water, gas and particles) model of the sewer. The multiphase SPH model will be coupled with transport models for special objects like textiles and buildup / erosion of FOG deposits.

*Supervisor: Rauch; Co-supervisor: Franosch/Harders*.

### Engineering

*Admission requirement: Topic specific, see below.*

#### 3D simulation of deep tunnel advance with interactions between multiple tubes (OTA-1)

*Admission requirement: Master's degree in civil or environmental engineering science, technical or numerical mathematics and computer sciences (or equivalent).*

Development of 3D time-dependent numerical models of deep tunnel advance with a focus on the challenging task of interactions between several tubes. For this purpose advanced constitutive models for rock mass and shotcrete are already available. In addition, powerful numerical solution methods, adapted for use with the advanced constitutive models, are needed to solve the large systems of equations inherent to a 3D modeling approach. The aim of the thesis is to develop a holistic computational approach, accounting for both constitutive modeling and mathematical solution aspects, for time-dependent 3D simulation of deep tunnel advance, and to use it for predictions in situations with interacting tunnel tubes.

Information on preliminary work on this topic can be found in the paper by

M. Neuner, M. Schreter, P. Gamnitzer, G. Hofstetter: *On Discrepancies between Time-Dependent Nonlinear 3D and 2D Finite Element Simulations of Deep Tunnel Advance: A Numerical Study on the Brenner Base Tunnel*, Computers and Geotechnics, 119(2020), 103355.

It can be requested by email from guenter.hofstetter@uibk.ac.at.

*Supervisor: Hofstetter; Co-supervisor: Lackner/Ostermann*.

#### Modeling of existing and emerging discontinuities in a rock mass with applications to numerical simulations of tunneling (OTA-2)

*Admission requirement: Master's degree in civil or environmental engineering science (or equivalent).*

Rock mass is composed of intact rock and discontinuities, e.g. bedding planes and joints. The latter are already present in the prevailing in-situ conditions. However, discontinuities may also emerge from the stress changes in the rock mass due to tunnel advance. The aim of the thesis is to evaluate different approaches of modeling existing and emerging discontinuities in rock mass with special emphasis on applications to numerical simulations of tunnel advance.

Information on preliminary work on this topic can be found in the paper by

M. Schreter, M. Neuner, D. Unteregger, G. Hofstetter: *On the Importance of Advanced Constitutive Models in Finite Element Simulations of Deep Tunnel Advance, Tunnelling and Underground Space Technology*, 80 (2018), 103-113.

It can be requested by email from guenter.hofstetter@uibk.ac.at.

*Supervisor: Hofstetter; Co-supervisor: Lackner/Ostermann*.

### Mathematics

*Admission requirement: Master's degree in mathematics (or equivalent).*

#### Dynamic low-rank approximations for kinetic models in plasma physics (NPM-1)

Solving kinetic problems directly is extremely expensive from a computational point of view. We consider the recently developed dynamic low-rank approximation, which has the potential to reduce the required effort by orders of magnitudes. We focus on developing algorithms and their implementation on HPC systems in the context of problems in plasma physics.

*Supervisor: Einkemmer; Co-supervisor: Kendl/Reimer*.

#### Semi-Lagrangian plasma simulation on modern computer architectures (NPM-2)

Large scale simulations on supercomputers are usually required to solve the various models for the nonlinear dynamics of magnetized fusion plasmas. Most of the algorithms currently available, however, do not fit very well to modern computer architectures (for example, GPUs). One approach to overcome this limitation are semi-Lagrangian discontinuous Galerkin methods. We will, in particular, further develop these algorithms, implement them on HPC systems, and demonstrate their efficiency for plasma simulation.

*Supervisor: Einkemmer; Co-supervisor: Kendl/Ostermann*.

#### Dynamic tomography of complex continua: Deep learning and regularization (NNA-1)

Solving dynamic inverse problems allows real-time imaging of many physiological processes, ranging from cardiovascular imaging to non-invasive surgery monitoring. Standard recovery methods accounting for rapid movements are only suitable for simple rigid motion. We develop and analyze efficient image reconstruction for complex motions, using tools from regularization theory, deep learning and neural networks to integrate suitable a-priori information.

*Supervisor: Haltmeier; Co-supervisor: Hofstetter/Probst*.

#### NETT deep learning for time dependent inverse problems with unknown forward operator (NNA-2)

Inverse problems arise in various applications ranging from medical imaging to non-destructive testing and remote sensing. Their characteristic feature is the inherent ill-posedness, requiring special techniques for its solution. We recently proposed network Tikhonov regularization (NETT) for inverse problems, which is based on generalized Tikhonov regularization using a neural network as learned regularizer. The aim of this project is to extend the NETT to inverse problems with partial unknown forward operators. In particular, appropriate networks and training strategies will be designed, a convergence analysis developed and an efficient numerical implementation established.

*Supervisor: Haltmeier; Co-supervisor: Kendl/Ostermann*.

### Nano- and Biophysics

*Admission requirement: Master's degree in physics (or equivalent).*

#### Non-equilibrium dynamics of colloidal suspensions under strong external driving (STP-1)

We will simulate the nonlinear dynamics of a colloidal suspension in response to an external perturbation in the form of a strong step-strain, and elucidate the evolution of shear stresses. New algorithms are needed to subtract thermal noises of the non-interacting systems for optimization of the signal-to-noise ratio.

*Supervisor: Franosch; Co-supervisor: Adam/Kendl*.

#### Disentangling the noise from the interactions in Brownian Dynamics (STP-2)

In a conventional Brownian Dynamics simulation interacting particles undergo an erratic motion due to thermal noise between collisions. A novel algorithm will be elaborated that allows to directly simulate only the difference between an interacting and freely evolving system thereby basically eliminating all noise and making the relevant physics accessible to simulation studies.

*Supervisor: Franosch; Co-supervisor: Adam/Kendl*.

### Material sciences

*Admission requirement: Master's degree in computational mechanics, civil/mechanical engineering, material sciences; Background knowledge in numerical methods beneficial. *

#### Multiscale framework for hierarchically-organized protective materials (MAS-1)

Impact processes take place frequently in daily life with e.g. protective materials reducing the severity of the occurring impact. In this project, the performance of protective materials shall be optimized aiming at specific industrial applications considering their microstructure within the multiscale framework, upscaling information from the finer scales towards the macroscale, and finally enabling simulation of the compaction behavior of protective materials when subjected to impact loading. For upscaling information from lower to higher scales analytical and/or numerical methods shall be employed. Finally, at the macroscale, the impact analyses shall be performed using the finite element method.

*Supervisor: Lackner; Co-supervisor: Harders/Hofstetter*.

#### Pore-space specific modeling of injection processes (MAS-2)

New numerical methods such as the smoothed particle hydrodynamics method enable the simulation of transport of reactive materials. Within this project, the injection process of viscous, reacting fluids into porous materials shall be modelled and simulated. The underlying porous material being injected shall be modelled considering its microstructure accessible from computer-tomography measurements. Potential applications of the developed method range from material strengthening in engineering towards medical applications such as e.g. injection of PMMA into porous bone.

*Supervisor: Lackner; Co-supervisor: Harders/Rauch*.

### Structural engineering

*Admission requirement: Master's degree in civil engineering (preferred) or mechanical engineering. A solid background in computational mechanics and structural dynamics as well as excellent computing skills are beneficial.*

#### Reliability analysis of high-speed railway bridges (SDY-1)

The objective is to assess the reliability of railway bridges subjected to high-speed trains. Models of dynamic vehicle-bridge-track-subsoil interaction at different scales will be developed. Analyses require the application of high-performance computing. Nonstandard stochastic methods such as subset simulation or line-sampling with small estimator variances will be used.

*Supervisor: Adam; Co-supervisor: Haltmeier/Rauch*.

#### Effect of soil-structure interaction on recorded vertical ground motion components (SDY-2)

Recent numerical studies have shown that earthquake excited regular steel-moment-resisting frames do not behave rigid in vertical direction, but show a significant peak acceleration response amplification. However, simulations based on recorded vertical free-field ground motions may overestimate this amplification. Aims of this project are to evaluate the impact of soil-structure interaction on recorded ground motion, develop soil-structure interaction models for HPC simulations, and derive seismic response on the free-field surface and at the base of the structure.

*Supervisor: Adam; Co-supervisor: Hofstetter/Rauch*.

##### Funding

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 847476.