Theses - Applied Mathematics and Theoretical PhysicsNo Descriptionhttps://www.repository.cam.ac.uk/handle/1810/2064462024-07-23T21:07:29Z2024-07-23T21:07:29Z3181Modelling turbulence and transport of buoyant material in the ocean surface mixed layerDingwall, Jenniferhttps://www.repository.cam.ac.uk/handle/1810/3705482024-07-05T00:44:20Zdc.title: Modelling turbulence and transport of buoyant material in the ocean surface mixed layer
dc.contributor.author: Dingwall, Jennifer
dc.description.abstract: The ocean mixed layer (OML) is a significant and dynamically active part of the ocean which plays an important role in climate variability. Here, atmospheric processes such as winds, heat fluxes or density differences drive the generation of small-scale, three-dimensional turbulence and mixing of oceanic waters. These turbulent flows govern the distribution of buoyant materials including oil droplets and microplastics, which have significant implications for marine life and safety. However, turbulent flow structures are often too small to be resolved by global or regional circulation models, and observations at these scales remain limited. The focus of this thesis is to use numerical simulations to improve our understanding of the small-scale, three-dimensional turbulent processes in the OML and examine their role on transporting and accumulating buoyant material.
We use high resolution large eddy simulations (LES) and direct numerical simulations (DNS), and model non-inertial, buoyant particles using a combination of buoyant tracers and three-dimensional Lagrangian particles. Surface cooling drives convection, and under this regime persistent convective vortices form which trap and accumulate buoyant particles. We test the resilience of convective vortices under the additional presence of wind, and find that in weak winds, convective vortices survive but are less effective at trapping buoyant material. With sufficiently strong wind forcing, convective vortices are no longer visible, but some clustering occurs in downwelling regions associated with longitudinal wind rolls.
Despite their small size, the convective vortices exhibit a bias towards cyclonic vorticity which has not been reported previously. We independently vary the Coriolis acceleration and surface buoyancy flux, and using Lagrangian particles, we find that the large convective vortices develop through the merger of many small unbiased convective vortices. We propose a statistical theory to predict the cyclonic bias of large convective vortices and test the theory using LES results. We apply the theory to typical convective conditions and find that convective vortices in OML are expected to exhibit a bias, but convective vortices in the terrestrial and Martian atmospheres are expected to be largely unbiased.
Finally, motivated by accumulation of buoyant material observed at surface fronts in the SUNRISE field campaign in the Gulf of Mexico, we run simulations of a highly idealised front under geostrophic adjustment. By varying the balanced Rossby number, we show that strong fronts develop a three-dimensional instability which generates turbulence near the top and bottom boundaries. We describe the physical mechanisms at play and the energy pathways as the front evolves over time. In the case of the most turbulent dynamics, we additionally model the movement of buoyant particles. Shear instabilities drive turbulence which enhances mixing, and strongly buoyant particles are carried out of the front during the first inertial period, which segregates the particles and leaves a large void in the centre of the front. In contrast, weakly buoyant particles are quickly subducted into the interior, and subsequently move according to the inertial oscillations of the front.
Riemannian geometry for inverse problems in cryogenic electron microscopyDiepeveen, Willemhttps://www.repository.cam.ac.uk/handle/1810/3699102024-06-21T00:41:01Zdc.title: Riemannian geometry for inverse problems in cryogenic electron microscopy
dc.contributor.author: Diepeveen, Willem
dc.description.abstract: This thesis develops theory and algorithms for a Riemannian geometric approach to inverse problems in cryogenic electron microscopy (Cryo-EM). It is divided into two parts, motivated by the sub problem of orientation estimation and that of modelling of protein dynamics. The thesis is concluded with a discussion on how to bring these pieces together to solve the so-called continuous heterogeneous reconstruction problem and a reflection on the general implications and new opportunities that a Riemannian geometry-based approach has for and brings to signal processing and recovery problems.
In the first part of the thesis we consider how to use ideas from global optimisation on Riemannian manifolds to regularise the orientation estimation sub problem. Our approach is motivated by the two main challenges in orientation estimation: the high noise levels present in Cryo-EM data and the non-convexity of typical variational problems for estimating orientations. To overcome these challenges jointly, we construct a new regularised global optimisation scheme to solve a variational problem for orientation estimation in a more noise-robust fashion.
In the second (and main) part we focus on constructing a Riemannian manifold for protein conformations. In particular, we are interested in constructing Riemannian geometry for protein conformations such that physically realistic protein conformations live in low-dimensional geodesic subspaces. Before constructing a Riemannian manifold, we first consider how curvature causes a discrepancy between data only looking low-dimensional and data actually being low-dimensional, and also consider how to address such curvature effects. Next, we construct a Riemannian manifold of protein conformations with computationally feasible manifold mappings such that realistic protein dynamics data really are low-dimensional under the proposed Riemannian structure, i.e., not suffering from curvature effects. Thirdly, we argue that it could be beneficial to have additional structure on a Riemannian protein geometry to what we have so far. In particular, we consider pullback geometry as a candidate class of Riemannian geometries that comes with the structure of interest and in addition offers a large amount of geometries to choose from. However, instead of directly trying to approximate the target Riemannian geometry, we take a step back and consider how a pullback Riemannian structure affects downstream data processing first and consider how one should go about constructing proper pullback manifolds given a target geometry.
In the conclusions we see that the constructed individual parts can be combined into two variational problems for solving the continuous heterogeneous reconstruction problem, one of which being a new strategy for solving general inverse problems under a certain type of learned regulariser. Next, in the light of the findings in this thesis, we also advocate more generally for the development of methodology for processing data under data-driven Riemannian geometry. A key overall takeaway from this thesis is then that over time having a proper account of the Riemannian geometry of our data can change the way we go about handling them in any data analysis pipeline with classically Euclidean data.
Magic and Majorana Fermions in Quantum Computing, Topological Matter, and DynamicsMcLauchlan, Campbellhttps://www.repository.cam.ac.uk/handle/1810/3699772024-06-21T00:44:08Zdc.title: Magic and Majorana Fermions in Quantum Computing, Topological Matter, and Dynamics
dc.contributor.author: McLauchlan, Campbell
dc.description.abstract: This thesis explores the resource of “magic”, and the use of Majorana fermions, in quantum many-body physics and quantum computing. Along with other quantum resources, magic helps determine the advantage that a quantum circuit can display over classical computation. For the components of the quantum computer itself, Majorana fermions offer promising theoretical advantages, owing to their fermionic nature and noise characteristics.
A tool used throughout this thesis is the Pauli-based model of computation (PBC). We extend this model to the regime of fermionic computation, establishing the analogous “fermion-parity-based computation” (FPBC). We develop certain conceptual tools in fermionic computation, including the idea of a “logical Majorana fermion”, which is used throughout this thesis. We find several results that relate to the ease of implementing PBC or FPBC directly, and which relate the magic of (F)PBC to that of the original circuit.
We apply these insights to study the dynamics of magic in random quantum systems. We use PBC to identify a phase transition in the magic produced by (and its spread in) random quantum circuits. We relate this transition to previously found phase transitions in entanglement, providing further insight into the purported transition in classical simulability of these systems.
We then assess the capabilities of Majorana systems for implementing (F)PBC. We introduce a hardware model with which one can measure arbitrary fermion parities directly, within certain bounds of locality, thus removing an obstacle to (F)PBC present in existing designs.
To further investigate noise-reduction methods in large-scale Majorana-based quantum computing, we perform an in-depth investigation of “Majorana surface codes” as intriguing models of both quantum error-correcting codes and fermionic topological quantum matter. We provide a categorisation of anyonic excitations, boundaries and “twist defects” (lattice defects that can store quantum information) in these codes. Finding that twist defects can store logical Majorana fermions, as well as regular logical qubits expected, we introduce methods for computing with all topologically protected degrees of freedom in the code. We introduce new computing techniques. We finally discuss avenues towards improved quantum resource costs, potential implementations and connections to other codes.
Dualities and Categorical Structures from 2D UpPasquarella, Veronicahttps://www.repository.cam.ac.uk/handle/1810/3693722024-06-08T00:41:24Zdc.title: Dualities and Categorical Structures from 2D Up
dc.contributor.author: Pasquarella, Veronica
dc.description.abstract: String Theory is the most promising candidate unifying theory of fundamental interactions so far; however, the Standard Model (SM) still features many open questions.
The present work aims at providing a step further towards reconciling the two, analysing part of the richness that underlying mathematical structures and dualities are able to provide in, both, gravitating systems and Quantum Field Theories (QFTs) alike. In doing so, our approach will be of the top-down kind. In particular, we will be relying upon the key tools of holographic duality and categorical algebraic geometry. The use of the former is justified by the lack of a non-perturbative formulation of String Theory, whereas the latter is dictated by the great advancement there has been in the past decades in studying algebraic varieties associated to moduli spaces, specifically Higgs and Coulomb branches.
A fundamental step towards studying string theory vacua, and, ultimately their stability, is that of understanding the underlying mathematical structure of the QFT resulting from its dimensional reduction on Calabi-Yau (CY) manifolds, the latter being complex manifolds admitting a category theory description. In particular, the work of Kapustin, Rozansky and Saulina (KRS) has shown how this can be achieved in terms of a 3D TFT equipped with a 2-categorical structure.
Our analysis develops in two main directions, namely on the gravitational, and supersym metric quiver gauge theory side. In both cases, our treatment focuses on lower-dimensional structures necessitating extensions and generalisations of well-established dualities and correspondences, specifically, holographic duality, homological mirror symmetry, and 3D mirror symmetry. As we shall see, the common ground in between the two paths taken in this treatment is the role played by amplitutdes in studying fundamental interactions and the properties of the vacuum structure, as well as the role played by dualities in understanding analytic results.
Dynamics of Chiral FermionsOnder, Kaanhttps://www.repository.cam.ac.uk/handle/1810/3691472024-06-07T00:42:31Zdc.title: Dynamics of Chiral Fermions
dc.contributor.author: Onder, Kaan
dc.description.abstract: This thesis studies the dynamics of a variety of two and four dimensional quantum field theories containing Weyl fermions respecting some chiral symmetry. There are severe challenges in lattice regularising such theories and chiral gauge theories, where a non-anomolous chiral symmetry is gauged, can display interesting strong coupling dynamics such as confinement without chiral symmetry breaking. We explore such gauge dynamics in two and four dimensions using a variety of different techniques. Furthermore, we use tensor network methods to study chiral fermions on the lattice in two dimensions.
We start by studying the dynamics of chiral $SU(N)$ gauge theories in four dimensions. These contain Weyl fermions in the symmetric or anti-symmetric representation of the gauge group, together with further fermions in the fundamental and anti-fundamental. We revisit an old proposal of Bars and Yankielowicz who match the ‘t Hooft anomalies of this theory to free fermions. We show that there are novel and, in some cases, quite powerful constraints on the dynamics in the large $N$ limit. In addition, we study these $SU(N)$ theories with an extra Weyl fermion transforming in the adjoint representation. Here we show that all $21$ ‘t Hooft anomalies for global symmetries are matched with those of a Spin$(8)$ gauge theory. This suggests a non-supersymmetric extension of the duality of Pouliot and Strassler. We then discuss some non-supersymmetric dualities with vector-like matter content for $SO(N)$ and $Sp(N)$ gauge theories and the constraints imposed by Weingarten inequalities.
We then move on to study the dynamics of analogous chiral gauge theories in two dimensions which also contain Weyl fermions in the symmetric, antisymmetric, and fundamental representations. A consistent infrared limit of these theories consists of certain coset conformal field theories. There is also a free-fermion phase which shares the same central charge and ’t Hooft anomalies but does not coincide with the coset models. We show that these two theories sit on a conformal manifold of infrared theories and are related by a current-current deformation. We further consider extensions of these theories by adding Dirac fermions and comment on possible renormalization group flows.
Finally, we present matrix product state simulations of the 3450 lattice chiral fermion model in two dimensions. We consider a lattice setup introduced by Wang and Wen which realises two left and two right-moving fermions on one edge of a thin Chern insulator. The partner mirror fermions are localised on the opposing edge. We turn on symmetry preserving six-fermion gapping interactions on one edge of the Chern insulator to gap the doublers whilst preserving an anomaly free $U(1)$ chiral symmetry and leaving the opposing edge gapless. This provides a candidate lattice regularisation of chiral fermions. We present numerical results for the entanglement entropy scaling to extract the central charge and study excited states by using a quasi-particle ansatz. We observe a BKT transition at six-fermion coupling strength $g=7$ and a central charge $c=2$ scaling regime at $g=25$. We conclude by discussing subtleties of working with symmetric MPS at a fixed charge density.
Dynamics of super-absorbent hydrogelsWebber, Josephhttps://www.repository.cam.ac.uk/handle/1810/3690452024-05-31T00:56:22Zdc.title: Dynamics of super-absorbent hydrogels
dc.contributor.author: Webber, Joseph
dc.description.abstract: This thesis explores the behaviour of hydrogels, a broad class of materials comprising a hydrophilic polymer scaffold surrounded by adsorbed water molecules, potentially comprising over 99% water by volume. In general, hydrogels are soft, elastic, porous materials that can swell or dry to a significant degree by imbibing or expelling water. Any modelling of their behaviour must take into account the interplay between elasticity, osmotic effects arising from the attraction of water to the polymer, the pressure-driven flow through their porous structure and conservation of water and polymer. Owing to the large swelling or drying strains seen in super-absorbent gels, linear theories fail to predict the dynamics seen in experiments, so we introduce a new `linear-elastic-nonlinear-swelling' theory that linearises with respect to small deviatoric shearing strains but allows for nonlinearity in the isotropic strains that result from volumetric change.
This theory is founded on three material parameters describing any gel (a shear modulus, an osmotic modulus and a permeability), all of which depend on the local polymer fraction and are macroscopically measurable, agnostic of the particular model used to describe the microscopic structure of the gel. In effect, modelling a gel in this manner is the same as treating a hydrogel swollen to any degree as its own distinct linear-elastic material. Swelling and drying are driven by the accumulation or expulsion of water within the matrix, with flows driven by gradients in pore pressure, and these gradients can be deduced by a momentum balance between pore pressures, osmotic pressures and elastic stresses.
Given these theoretical foundations, we can solve a number of gel swelling and drying problems, using the continuum-mechanical foundations introduced here to describe the physical processes describing the transient state as water flows through the matrix, and the dependence of the gel's behaviour on its material properties. This theory underlines the importance of deviatoric stresses in understanding the dynamics of hydrogels, showing how the dynamics of three-dimensional swelling is qualitatively different from simple one-dimensional models, and underlining a distinct difference between the dynamics of gels and other colloidal materials where such stresses do not arise. Furthermore, it is seen how differential swelling introduces shear stresses and sets the shape of hydrogels, forming curved interfaces and wrinkled surfaces.
It is also shown how our framework can be used to understand interfacial instabilities at the swelling front, with the patterns resulting from a complex interplay between elasticity and osmotic effects. Separating out the contributions of these two driving processes results in a rich range of phenomena exhibited at different stages during the swelling process, and can be used to explain the formation, development and healing of patterns seen in experiments.
Finally, two extensions to this modelling are illustrated, underlining the utility of our poroelastic approach. First, the freezing of hydrogels is discussed, which results in phase separation behaviour as water is driven out of the polymer matrix to form pure ice and a partially-dried hydrogel from which water has been expelled. Second, we incorporate surface tension effects at the interface between gels and water, an effect that can not only modify the behaviour discussed in earlier chapters, but also gives rise to novel qualitative phenomena including the bulk transport of interstitial fluid and the suppression of instabilities.
Parton Distributions in Beyond the Standard Model TheoriesMoore, Jameshttps://www.repository.cam.ac.uk/handle/1810/3672972024-05-16T00:57:54Zdc.title: Parton Distributions in Beyond the Standard Model Theories
dc.contributor.author: Moore, James
dc.description.abstract: Parton distributions are a key ingredient of precise predictions for collider experiments. They are usually determined from fits to experimental data under the assumption that the Standard Model (SM) of particle physics is complete; however, this can bias studies of beyond the Standard Model (BSM) physics if these SM-like PDFs are used in these analyses. It is important to quantify the extent to which this occurs, in order to avoid making incorrect conclusions about BSM physics.
We begin in Chapter 1 with a review of perturbative quantum chromodynamics (QCD) and parton distribution functions (PDFs), providing a definition of the PDFs at next- to-leading order in QCD perturbation theory. At the end of the Chapter, in Sect. 1.4, we introduce the main problem that this thesis aims to address in a variety of special cases, namely the simultaneous extraction of PDFs together with other theory parameters (specifically BSM theories).
In Chapters 2, 3 and 4, we describe the interplay between PDFs and the parameters of various BSM models. In more detail, in Chapter 2, we perform an approximate simultaneous extraction of PDFs together with the parameters of a dark photon model; in particular, we use projected high-luminosity LHC (HL-LHC) data to investigate the sensitivity of the HL-LHC to our particular class of light, leptophobic dark photons. Subsequently, in Chapter 3, we introduce the Standard Model Effective Field Theory (SMEFT), and carry out a simultaneous determination of PDFs together with two parameters drawn from the SMEFT; we show that at the HL-LHC, there will be significant interplay between extraction of PDFs and SMEFT parameters. In Chapter 4, we perform a much more comprehensive analysis of the PDF-SMEFT interplay in the top sector, using a new efficient methodology, SIMUnet. Importantly in Sect. 4.7, we also comment on the efficacy of the Monte Carlo replica method for error propagation, which forms the heart of the uncertainty calculation in both the NNPDF and SIMUnet methodologies.
In the second half of this thesis, we focus on future issues in PDF fitting, related to the work presented in the previous chapters. In Chapter 5, we explore how New Physics in the data might be inadvertently ‘fitted away’ into the PDFs, if the data is treated as SM-like. We also recommend strategies for disentangling PDFs and BSM effects. Finally, in Chapter 6, we discuss the Monte Carlo replica method used in many of the previous chapters, and discuss the need for its replacement in future PDF and BSM fits.
Modelling the propagation of subglacial floodsTobin, Sophiehttps://www.repository.cam.ac.uk/handle/1810/3681382024-05-11T15:21:49Zdc.title: Modelling the propagation of subglacial floods
dc.contributor.author: Tobin, Sophie
dc.description.abstract: Subglacial flooding, in which large volumes of water are suddenly released beneath a glacier, is a process which has the potential to significantly modify the dynamics of the overlying ice. The routing of the water beneath the glacier and the extent of its incorporation into existing drainage networks determines the response of the ice. As a result, modelling of subglacial flooding is both necessary for understanding the detailed dynamics of glaciers responding to meltwater and also a useful test case for investigating the properties of the contact between glacial ice and the bed on which it sits.
A number of studies have looked at the initial axisymmetric spreading of subglacial floodwater by considering the coupling between the flow of the water and the elastic deformation of the ice. Other studies have examined the movement of the water downstream, but without modelling the detailed, potentially elasticity-controlled dynamics at the flood front. In this thesis I combine these two approaches in order to model the processes which determine the propagation speeds of subglacial floods and their impact on the overlying ice.
In chapter 1 I discuss subglacial flooding in the broader context of subglacial drainage systems and review previous modelling approaches. In chapter 2 develop a model for flood propagation beneath glaciers by considering the behaviour of a blister of water trapped between a rigid sloping base and an elastic sheet. I use an asymptotic analysis to show that, by removing a jump in curvature otherwise present at the upslope edge, the presence of a sloping base results in a new, nearly-translating regime in which the body of the blister moves at an approximately constant speed, leaving behind a thin layer of fluid. In chapter 3 I compare this model to GPS observations of six different subglacial flooding events. The observed uplifts are compared to those predicted by the model and processes at the front of the blister which could regulate flood propagation speeds are discussed. Linking observations of ice acceleration to the hydraulic jacking of the ice caused by subglacial floods requires combining both viscous and elastic deformation, so in chapter 4 I investigate the impacts of viscoelasticity on ice dynamics. To explore potential effects, I investigate the impact of viscoelastic bending on the movement of grounding lines. I then develop a model for viscoelastic bending and stretching of ice which I discuss in the context of subglacial flooding. In chapter 5 I conclude and discuss future directions for this work.
Information and generative deep learning with applications to medical time-seriesEdinburgh, Tomhttps://www.repository.cam.ac.uk/handle/1810/3670922024-04-18T00:41:24Zdc.title: Information and generative deep learning with applications to medical time-series
dc.contributor.author: Edinburgh, Tom
dc.description.abstract: Physiological time-series data are a valuable but under-utilised resource in intensive care medicine. These data are highly-structured and contain a wealth of information about the patient state, but can be very high-dimensional and difficult to interpret. Understanding temporal relationships between time-series variables is crucial for many important tasks, in particular identifying patient phenotypes within large heterogeneous cohorts, and predicting and explaining physiological changes to a patient over time. There are wide- ranging complexities involved in learning such insights from longitudinal data, including a lack of a universal accepted framework for understanding causal influence in time-series, issues with poor quality data segments that bias downstream tasks, and important privacy concerns around releasing sensitive personal data. These challenges are by no means unique to this clinical application, and there are significant domain-agnostic elements within this thesis that have a broad scope to any research area that is centred around time-series monitoring (e.g. climate science, mathematical finance, signal processing).
In the first half of this thesis, I focused firstly on information and causal influence in time- series data and then on flexible time-series modelling and hierarchical model comparison using Bayesian methods. To aid these tasks, I reviewed and developed new statistical methodology, particularly using integrated likelihoods for model evidence estimation. Together, this provided a framework for evaluating trajectories of the information contained within and between physiological variables, and allowed a comparison between patient cohorts that showed evidence of impaired physiological regulation in Covid-19 patients. The second half of this thesis introduced generative deep learning models as a tool to address some of the key difficulties in clinical time-series data, including artefact detection, imputation and synthetic dataset generation. The latter is especially important in the future of critical care research, because of the inherent challenges in publishing clinical datasets. However, I showed that that there are many obstacles that must be addressed before large-scale synthetic datasets can be utilised fully, including preserving complex relationships between physiological time-series variables within the synthetic data.
Impact cratering with yield-stress fluidsIoannou, Georgiahttps://www.repository.cam.ac.uk/handle/1810/3669772024-04-13T00:45:55Zdc.title: Impact cratering with yield-stress fluids
dc.contributor.author: Ioannou, Georgia
dc.description.abstract: Impact cratering is the process where a moving object hits a deformable target, causing material to be ejected away from the impact point, at least most of the times, and opening a crater on the target surface. This process has been studied extensively to understand the dynamics of planetary impact cratering and other similar natural or industrial processes. Most of the relevant experimental works involve water and granular media, and very few yield-stress fluids like soft materials. Except for the common experiment of a water drop impacting a water pool, in most works the impactor is a solid, non-deformable sphere. However, in the relevant geological process, and in most other applications, both target and impactor are deformable. Also, the material used in lab experiments to mimic the relevant geological process must have rheological properties that allow for it to hold a shape at the end of the process so that the resulted crater does not vanish. Ideal experimental materials are the yield-stress fluids, which behave as solids when low stresses are applied, but deform as fluids when the applied stresses exceed a threshold value.
In this work, we conduct impact cratering experiments with a yield-stress fluid as both target and impactor. We explore many aspects of the time-dependent features of this highly transient process by recording the dynamics with high-speed cameras. The transient features we study are the transient cavity (air-gel interface) dimensions and shape, the spreading of the drop material upon impact, and the duration of the cavity growth. The dynamics of this transient process are considered using an energy balance. We find that only a small percentage of the impactor kinetic energy is converted into potential energy of the cavity, unlike Newtonian fluids. Here, most of the impactor kinetic energy is converted into elastic energy stored in the material.
A particle tracking method is employed to visualise the response of the target material upon impact. Interestingly, the cavity does not grow radially as a hemi-sphere, like in Newtonian fluids, but growth is faster in horizontal than in vertical direction. Additionally, growth in vertical direction ceases before that in the horizontal direction. After the crater is formed, the target material undergoes a damped oscillation for a time period 50 times greater than the duration of cavity growth. We explore the dependence of the period of oscillation on material properties and examine whether the material oscillates in phase everywhere in the target.
Our study of the transient features expands to the ejecta sheet that emerges from the target, which is primarily material expelled from the point of impact. We perform a qualitative study of sheet shapes, categorising the ejecta into regimes according to the instabilities that arise at the edge of the sheet. These regimes are determined by a single dimensionless number that compares the inertial stresses to the dissipative stresses of the flow. Additionally, we study the dimensions and shape of the ejecta sheet and how these quantities evolve with time and compare our findings with the ejecta emerging from water and granular impact cratering.
When the transient part of the process finishes, a final crater that has a static shape in time is formed on the surface of the target. Using laser profilometry, we acquire the three-dimensional shape of the crater formed from which we categorise the different morphological regimes and examine how the final dimensions of the crater are related to its transient conformation. Moreover, we compare the size and shape of our craters with those reported in the literature when the target is a granular bed or a planetary body.
We augment our experimental study of impact cratering with simulations that imitate the laboratory experiments. For the simulations we use OpenFOAM, an open-source software package, and investigate various constitutive models for non-Newtonian fluids. Only the cavity growth stage is studied, when the flow is presumed to be stable and axisymmetric. The size and shape of the transient cavity for the different models are compared with each other and with the experimental results.
We conclude with a summary of our findings and a discussion of future directions of research.