There is growing concern that the worldwide loss in biodiversity will harm the stability of the ecosystems, and thereby, the carrying capacity and critical ecosystem services the biosphere provides. Phytoplankton (microalgae) in lakes and oceans are arguably the most important primary producers. They are responsible for approximately half of the earth's primary production. However, there is little research into what influences the biodiversity of phytoplankton communities and of those studies the mechanisms for coexistence of phytoplankton have so far almost exclusively been studied on ecological time scales. We, therefore, explored how biodiversity and biomass (a proxy to primary production) of phytoplankton communities respond to co-varied environmental drivers over evolutionary time scales. We model adaptive evolution of phytoplankton' resource use, with a non-dimensionalized model of negatively buoyant phytoplankton inhabiting a partially mixed one-dimensional water column using reaction-advection-diffusion equations. We show that a number of environmental drivers have novel effects on biodiversity and biomass on evolutionary timescales. In contrast with previous non-evolutionary work, we found that decreasing light attenuation or increasing resource use efficiency can result in decreased biomass of plankton communities and nutrient-poor environments. One novel driver of species diversity was the combination of low rates of diffusion with relatively intermediate rates of sinking promote species diversity. Furthermore, we show that the phytoplankton turnover rate affects environmental heterogeneity and is, therefore, a contributing driver to species diversity.The evolution of half saturation constants can produce a variety of biodiversity-ecosystem function patterns as two positive, one unimodal, and one negative association were found when comparing biodiversity-ecosystem function. Collectively, our analyses suggest that environmental drivers can have substantially different effects over evolutionary timescales than those effects ecological modeling has previously shown.

When underwater sensors are being deployed there is always some uncertainty about the actual position of the sensors. The most common way of determine the sensors position is the use of hydro-acoustic methods. However, for electric field sensors the most favourable would be to use the sensor system itself. The first question being answered in this report is whether it is possible to position electric field sensors with the sensor system itself, and the answer is yes. An algorithm has been developed which calculates the relative position of the sensors based on data measured by the sensors when a dipole passes the sensor group. The algorithm extracts zero crossings of the z-components of the electric field measured by each sensor from the data, which are converted to moments in time, multiplied by the speed and course of the vessel and finally calculated into relative position vectors between the sensors using vector algebra. The result of the predicted relative position is within 0.2 m from the sensors’ actual position, which answers the second question about how accurate the method is. However, the error estimation is within a couple of centimetres indicating that there are other sources of error than speed and course. The third question being answered is whether the method is better than acoustic methods, and the answer is no. Nonetheless, the methods are within the same order of magnitude. In conclusion, the method has acceptable performance, especially considering the fact that it can determine the position of the sensors with the sensor system itself which could be significant.

We introduce the formalism of categorical symmetries, and examine how these appear in quantum field theories. We discuss rational conformal field theories and their Verlinde lines, with the critical Ising model as an example. We introduce Wess Zumino Witten models and affine Lie algebras. An algorithm for the fusion rules is presented. We use bosonization to realise two dimensional adjoint SU(N) QCD as a WZW coset model plus a kinetic term for the gauge field. We argue that the infrared theory has degenerate vacua acted upon by a non-negative integer valued matrix representation of a categorical symmetry. We compute generators for these matrices for gauge groups SU(3) and SU(4).

Infrasound is undetectable by the human ear and excessive exposure may be a substantial health risk. Low frequency sound propagates through walls with minimal attenuation, making it difficult to avoid. This study interprets the results from both analytical calculations and simulations of pressure waves propagating through a wall in one dimension. The wall is thin compared to the wavelength; the model implements properties of three materials commonly used in walls. The results indicate that the geometry of the wall, most importantly the small ratio between wall width and wavelength, is the prime reason for the low levels of attenuation observed in transmitted amplitudes of low frequency sounds, and that damping is negligible for infrasound. Furthermore, a one-dimensional homogeneous wall model gives rise to periodicity in the transmitted amplitude, which is not observed in experiments. Future studies should prioritize the introduction of at least one more dimension to the model, to allow for variable angles of incidence.

Identifying the protein content in a cell in a fast and reliable manner has become a relevant goal in the field of proteomics. This thesis computationally explores the potential for silicon nitride nanopores to sense and distinguish single miniproteins, which are small domains that promise to facilitate the systematic study of larger proteins. Sensing and identification of these biomolecules using nanopores happens by studying modulations in ionic current during translocation. The approach taken in this work was to study two miniproteins of similar geometry, using a cylindrical-shaped pore. I employed molecular mechanics to compare occupied pore currents computed based on the trajectory of ions. I further used density functional theory along with relative surface accessibility values to compute changes in interaction energies for single amino acids and obtain relative dwell times. While the protein remained inside the nanopore, I found no noticeable differences in the occupied pore currents of the two miniproteins for systems subject to 0.5 and 1.0 V bias voltages. Dwell times were estimated based on the translocation time of a protein that exhibits no interaction with the pore walls. I found that both miniproteins feel an attractive force to the pore wall and estimated their relative dwell times to differ by one order of magnitude. This means even in cases where two miniproteins are indistinguishable by magnitude changes in the ionic current, the dwell time might still be used to identify them. This work was an initial investigation that can be further developed to increase the accuracy of the results and be expanded to assess other miniproteins with the goal to aid future experimental work.

In this thesis we derive a coupled system of Cahn-Hilliard equations posed in a domain with moving boundary using arguments from thermodynamics. The physical setting we have in mind is a ternary solution observed during one species evaporation as a moving boundary problem. The mixture is made of two types of polymers blended in a solvent that is allowed to evaporate at part of the surface of the domain. After formulating the evolution system as a moving-boundary problem with kinetic interface condition, we fix the moving boundary to facilitate a suitable numerical approximation. We project the resulting model equations on a finite element space and then integrate the obtained system in Python using FEniCS. We show numerically the formation of morphologies and track the evolution of the remaining solvent and of the moving boundary position. The conjecture is that such a system would produce phase separation and that the resulting morphologies are mappable to the observations of organic solar cells. Finally, we study the effect of the most relevant parameters on the output of our Cahn-Hilliard system, particularly on the speed of the moving boundary and of the morphology formation. / I denna tes härleder vi ett kopplat system av Cahn-Hilliard ekvationer fomulerad i en tidsberoende domän med hjälp av termodynamiska argument. Den fysiska miljön vi tänker oss är en trekomponents lösning observerad under avdunstning med hänsyn till en tidsberoende domän. Blandningen består av två polymerer utspädda i ett lösningsmedel som tillåts förånga vid en av domänens gränser. Efter att vi formulerat evolutions ekvationerna i en tidsberoende domän med kinetiska gränsvillkor så utförs en transformation till en tidsoberoende domän för att underlätta en lösning med finita elementmetoden. Vi projicerar de resulterande ekvationerna på ett diskret rum skapat m.h.a. finita elementmetoden för att sedan integrera systemet med hjälp av FEniCS platformen skrivet i Python. Vi visar nummeriska lösningar för morfologiformationen och följer evolutionen av lösningsmedlet samt positionen för den rörliga gränsen. Vår förmodan är att ett sådant system kommer producera fas-seperation och den resulterande morfologin kommer vara jämnförbar med det som observeras hos organiska solceller. Slutligen studerar vi hur variationer av dom mest relevanta parametrarna påverkar på vårt Cahn-Hilliard system, i synnerhet positionen som en funktion av tid hos den rörliga gränsen samt morfologiformationen.

Prompted by the success of heterotic line bundle model building on Complete Intersection Calabi Yau (CICY) manifolds and the new developments regarding a generalization thereof, I analyze the possibility of model building on generalized CICY (gCICY) manifolds.  Ultimately this is realized on two examples of gCICYs, one of which topologically equivalent to a CICY and one inequivalent to any previously studied examples.  The first chapter is dedicated to reporting background information on CICYs and gCICYs.  The mathematical machinery of CICYs and their generalizations are introduced alongside explicit constructions of two examples.  The second chapter introduces the reader to heterotic line bundle model building on CICYs and gCICYs.  In the setting of gCICYs, similar to regular CICYs, model building is accomplished in two steps: first the larger $E_{8}$ gauge group is broken to an $SU( 5 )$ grand unified theory  through a line bundle model.  Then the GUT is broken using Wilson line symmetry breaking, for which the presence of a freely acting discrete symmetry must be established.  To that end, I proceed to show that the two previous examples benefit from a $\mathbb{Z}_{2}$ freely acting discrete symmetry.  Utilizing this symmetry I construct 20 and 11 explicit models for the two gCICY examples respectively, by scanning over a finite range of line bundle charges. / Ett av de största problemen i modern teoretisk fysik är att hitta en teori för kvantgravitation.För en konsekvent kvantteori gravitation skulle vara en väsentlig del i fysikens pussel, och koppla samman gravitationsfysiken för planeter och galaxer, som beskrivs av allmänna relativitetsteorin, till fysiken för partiklar, beskrivet av kvantfältteori.Bland de mest lovande teorierna finns strängteorin som föreslår att ersätta partiklar med strängar som materiens grundläggande beståndsdel.Förutom att lösa kvantgravitationproblemet hoppas teoretiska fysiker genom strängteorin att förenkla beskrivningen av partikelfysik.Detta skulle ske genom att ersätta hela partikelzoo med ett enda objekt: strängen.Olika vibrationer i strängen skulle motsvara olika partiklar och interaktioner mellan strängar skulle motsvara interaktioner mellan partiklar.För att vara motsägelsefri kräver dock strängteori att det finns minst sex fler dimensioner än de vi kan uppleva.En av strategierna som för närvarande studeras för att förlika extra dimensioner med och moderna experiment kallas ``kompaktifiering'' eller ``compactification'' på engelska.Strategin föreslår att dessa extra dimensioner ska vara kompakta och så små att de är osynliga för observationer.Interesant nog påverkar geometrin i det sexdimensionella kompakta rummet i stor utsträckning fysiken som strängteorin producerar: olika rum skulle producera olika partiklar och olika grundläggande naturkrafter.I den här uppsatsen studerar jag två exempel på sådana sexdimensionella rum som kommer från en uppsättning av rum som kallas `` generaliserade CICYs'' som nyligen har upptäckts.Med hjälp av de tekniker som liknar de som har utvecklats för andra liknade rum, visar jag att vissa aspekter av en strängteori kompaktifierad på generaliserade CICY återspeglar de som mäts genom moderna partikelfysikexperiment.

The demand for computational tools that are capable to reliably predict the behavior of a nuclear reactor core in a variety of static and dynamic conditions does inevitably require a proper qualification of these tools for the intended purposes. One of the qualification methods is the verification of the code in question. Hereby, the correct implementation of the applied model as well as its flawless implementation in the code are scrutinized. The present work concerns with benchmarking as a substantial part of the verification of the three-dimensional, multigroup neutron kinetics model employed in the transient code POLCA-T. The benchmarking is done by solving some specified and widely used space-time kinetics benchmark problems and comparing the results to those of other, established and well-proven spatial kinetics codes. It is shown that the obtained results are accurate and consistent with corresponding solutions of other codes. In addition, a sensitivity analysis is carried out with the objective to study the sensitivity of the POLCA-T neutronics to variations in different numerical options. It is demonstrated that the model is numerically stable and provide reproducible results for a wide range of various numerical settings. Thus, the model is shown to be rather insensitive to significant variations in input, for example. The other consequence of this analysis is that, depending on the treated transient, the computing costs can be reduced by, for instance, employing larger time-steps during the time-integration process or using a reduced number of iterations. Based on the outcome of this study, one can finally conclude that the POLCA-T neutron kinetics is modeled and implemented correctly and thus, the model is fully capable to perform the assigned tasks.

Newton's second law, Schrödinger's equation and Maxwell's equations are all theories composed of at most second-time derivatives. Indeed, it is not often we need to take the time derivative of the acceleration. So why are we not seeing more higher-order derivative theories? Although several studies present higher derivatives' usefulness in quadratic gravity and scalar-field theories, one will eventually encounter a problem. In 1850, the physicist Mikhail Ostrogradsky presented a theorem that stated that a non-degenerate Lagrangian composed of finite higher-order time derivatives results in a Hamiltonian unbounded from below. Explicitly, it was shown that the Hamiltonian of such a system includes linearity in physical momenta, often referred to as the ''Ostrogradsky ghost''. This thesis studies how one can avoid the Ostrogradsky ghost by considering degenerate Lagrangians to put constraints on the momenta. The study begins by showing the existence of the ghost and later cover the essential Hamiltonian formalism needed to conduct Hamiltonian constraint analyses of second-order time derivative systems, both single-variable and systems coupled to a regular one. Ultimately, the degenerate second-order Lagrangians successfully eliminate the Ostrogradsky ghost by generating secondary constraints restricting the physical momenta. Moreover, an outline of a Hamiltonian analysis of a general higher-order Lagrangian is presented at the end.

A significant portion of cancer patients receive radiotherapy as part of their curative or palliative treatment plan. Radiotherapy is however greatly limited by radiation induced toxicities in healthy tissue surrounding the tumour, which can lead to long-term or acute complications for a patient. In response to this issue, recent studies have considered a new technique called FLASH radiotherapy, where ultra-high dose rates have been shown to effectively reduce toxicity in normal cells whilst maintaining a tumour response equivalent to conventional dose rates. However, the exact mechanism for this effect is not yet well understood. This project seeks to investigate if certain dose delivery patterns exist where there is an increase or reduction of concentration of the toxic radical hydroxyl, which is known to play a key role in the damage of DNA in the cell, for unchanged total dose. This was done by simulating the chemical reactions which take place when water is irradiated with ionizing radiation using a simple model system consisting of water with free oxygen dissolved into it, called RadChemModel. Using basic reaction laws from chemistry, the concentration of each chemical species involved was solved for from a system of linear and non-linear ordinary differential equations. The concentration of hydroxyl was calculated as a function of time for a range of irradiation beam patterns. This model supports that there could be a difference in toxicity between FLASH and conventional beam parameters. Furthermore, a shift in the behaviour of hydroxyl suggesting reduced toxicity was observed at FLASH dose rates with very high beam pulse frequencies. However, the results obtained do not provide enough information to confirm that the concentration of hydroxyl is reduced with FLASH beam parameters. / En stor andel cancerpatienter får strålterapi som läkande eller palliativ behandling. Strålterapi kan ge upphov till allvarliga skador i den friska vävnaden i närheten av tumörområdet. För att förebygga omedelbara så väl som långsiktiga skadliga effekter av strålterapi, har nyligen pulicerade studier undersökt en ny teknik som kallas för FLASH strålterapi. Man har påvisat att ultra-höga doshastigheter kan minska strålskadorna i friska celler samtidigt som tumörkontrollen bevaras. Emellertid finns ännu ingen tillräcklig förklaring för den exakta mekanismen bakom fenomenet. Målet med detta projekt är att undersöka om en ökning eller minskning av koncentrationen hos radikalen hydroxyl, som är känd för att spela en kritisk roll i framkallandet av DNA skador, kunde upptäckas för särskilda doseringsmönster med en oförändrad total dos. Detta studerades med en enkel matematisk modell (RadChemModel) för vatten med upplöst syre. Med denna modell simulerades de kemiska reaktioner som äger rum när vatten bestrålas med joniserande strålning. Från fundamentala kemiska reaktionslagar, kunde koncentrationen av hydroxyl som funktion av tid fås genom att lösa ett system av linjära och icke-linjära ordinära differentialekvationer. Den här modellen visar att det kan finnas en skillnad i strålinducerade skador mellan FLASH och vanlig strålterapi. Resultaten från väldigt höga pulsfrekvenser med FLASH antydde också att mindre hydroxyl producerades och därmed att strålskador kan vara beroende av både doshastighet och pulsfrekvens. Däremot är resultaten inte tillräckliga för bekräfta att koncentrationen av hydroxyl är reducerad för FLASH.