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Game engine based auralization of airborne sound insulationForsman, Jimmy January 2018 (has links)
Describing planned acoustic design by single number ratings yields a weak link to the subjective event, especially when the single number ratings are interpreted by others than experienced acousticians. When developing infrastructure, tools for decision making needs to address visual and aural perception. Visual perception can be addressed using game engines and this has enabled the establishment of tools for visualizations of planned constructions in virtual reality. Audio engines accounting for sound propagation in the game engine environment are steadily developing and have recently been made available. The aim of this project is to simulate airborne sound insulation by extending the support of recently developed audio engines directed towards virtual reality applications. The case studied was airborne sound insulation between two adjacent rooms in a building, the sound transmitted to the receiving room through the building structure resulting from sound pressure exciting the structural elements in the adjacent source room into vibration. The receiving room composed modelled space in the game engine Unreal Engine and Steam Audio was the considered audio engine. Sound transmission was modelled by filtering based on calculations of transmission loss via direct and flanking paths using the model included in the standard EN 12354-1. It was verified that the filtering technique for modelling sound transmission reproduced attenuations in correspondence with the predicted transmission loss. Methodology was established to quantify the quality of the audio engine room acoustics simulations. A room acoustics simulation was evaluated by comparing the reverberation time derived from simulation with theoretical predictions and the simulated reverberation time showed fair agreement with Eyring’s formula above its frequency threshold. The quality of the simulation of airborne sound insulation was evaluated relating the sound field in simulation to insulation classification by the standardized level difference. The spectrum of the simulated standardized level difference was compared with the corresponding sound transmission calculation for a modelled scenario. The simulated data displayed noticeable deviations from the transmission calculation, caused by the audio engine room acoustics simulation. However, the simulated data exhibited cancellation of favourable and unfavourable deviations from the transmission calculation resulting in a mean difference across the spectrum below the just noticeable difference of about 1 dB. Single number ratings was compared and the simulated single number rating was within the standard deviation of how the transmission model calculates predictions for a corresponding practical scenario measured in situ. Thus, the simulated data shows potential and comparisons between simulated data, established room acoustics simulation software and in situ measurements should further be made to deduce whether the deviations entails defects in the airborne sound insulation prediction or is an error imposed by the audio engine room acoustics simulation.
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Market potential for using demand response from heat pumps in multi-family buildingsGrill, Rebecca January 2018 (has links)
More renewable energy leads to higher energy imbalances in the Swedish electric power system. In the same time, the grid capacity is almost reached in some regions which requires an extension of the current grids or a reduction of the power consumption. Demand response could be a key factor for both stabilizing the energy balances and reducing the grid congestion. The aim with this thesis is to analyze the potential incomes that demand response from heat pumps can generate for the balance responsibility parties and the grid operators and evaluate how it would affect the end-consumers. The investigated local grid that contains of 174 multi-family buildings with heat pumps could reduce its highest peak power with 2,9 MW. This peak power reduction generated a cost reduction of 483 000 SEK per year or 2800 SEK per building per year in reduced penalty fees and power subscription fees. The mFRR market and the power reserve market were determined to be the most suitable markets for using demand response from heat pumps on for the balance responsibility party in the electricity price region SE3. SE3 consists of 10146 multi-family buildings with heat pumps. The mFRR market generated an average income of 2 699 000 SEK per winter season whereas the power reserve market generated a yearly administrative compensation of 1 133 000 SEK per season and 104 000 SEK per call-off. It is important that end-consumers obtain demand-based tariffs or hourly based tariffs to enable a cost reduction from the control system.
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Flipped Classroom och Digitala Materiel : En Karaktärisering av Tre Naturvetenskapliga Ämneslärares Användning av Digitala HjälpmedelGaleano, Victor January 2018 (has links)
IT- och IKT-kompetens utgör en stor del av såväl internationell som svensk utbildningsforskning och enda sedan 60-talet har regeringen gjort satsningar med ändamål att förbättra lärares och elevers kompetens inom dessa områden. Den internationella strävan är att läroplaner införlivar mål för förbättrad IT- och IKT-kompetens, för att förbereda elever inför en arbetsmarknad som alltmer kräver teknologiska kompetenser. I den svenska forskningen har det visat sig att användningen av IT i den svenska skolan har ökat märkbart de senaste åren. PISA-undersökningen har visat att Sverige har låga resultat i problemlösning och att dessa resultat samvarierar med hög användning av IT. Vidare kompetensutveckling behövs och lärare bör anpassa sin undervisning utefter de teknologiska verktygens närvaro i den svenska skolan. Flipped Classroom är en undervisningsmetodik som innebär en betydande omordning av aktiviteter i den klassiska undervisningen, med avseende på vad som sker i klassrummet och vad som sker utanför klassrummet. Vidare ämnar metodiken att tydligt integrera digitala materiel i undervisningen. Framtida forskning bör undersöka hur Flipped Classroom-lärare väljer att utforma deras videoföreläsningar och övriga datorbaserade instruktioner. Detta examensarbete söker finna svar på hur och i vilket syfte Flipped Clasroom-lärare i de naturvetenskapliga ämnena använder digitala materiel i sin flippade undervisning samt ge en överblick av dessa. Tre naturvetenskapliga ämneslärare som använder Flipped Classroom har intervjuats. Det är alltså intervjuerna som utgör den empiriska grunden för detta arbete. Vidare innefattar detta arbete en konstruktion av en lämplig modell för att karaktärisera Flipped Classroom-lärares användning av digitala materiel. Karaktäriseringen indikerar att övervägande del av de digitala materielen används för datorbaserad instruktion utanför klassrummet. Totalt sett utgör 57 % datorbaserad instruktion och 30 % elev-centrerade aktiviteter i klassrummet. Resterande 13 % består av digitala materiel som till övervägande del består i mjukvaror för automatisk rättning av prov. För de intervjuade lärarna gäller att övervägande del av samtliga materiel används för att förmedla det centrala innehållet i respektive kurser. Men individuella skillnader finns. Totalt sett så utgör ungefär 52 % av samtliga materiel, användingsområden som ämnar att elever antingen ska återge kunskap eller lagra den i långtidsminnet. Det visar sig också att större delen av dessa användningsområden samtidigt innebär omfattande förändringar av undervisningsmoment.
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A motion cueing model for mining and forestry simulator platforms based on Model Predictive Control / En modell för rörelsesignaler till simulatorplattformar inom gruv- och skogsindustri baserad på Model Predictive ControlWalker, Jens January 2015 (has links)
Oryx Simulations produce simulators for mining and forestry machinery used for educational and promotional purposes. The simulators use motion platforms to reflect how the vehicle moves within the simulator. This platform tilts and accelerates the driver in order to enhance the experience. Previously a classical washout filter algorithm has been used to control the platform which leaves something to be desired regarding how well it reflects the vehicles movement, how easy it is to tune and how it handles the limits of the platform. This thesis aims to produce a model that accurately reflects angles, velocities and accelerations while in the mean time respecting the limits of the platform. In addition to this the developed model should be easy to modify and tune. This is achieved using so-called Model Predictive Control which achieves the wanted behaviour by predicting how the platform will move based on its current state while implementing the constraints of the platform directly into the model. Since all of the parameters in the model are actual physical quantities, this makes the model easier to tune. A key component in this solution is the so-called tilt coordination which consists of substituting a lateral/longitudinal acceleration with the acceleration of gravity by tilting the driver. Constructing and implementing this model in Matlab we verify it by using data extracted from the simulator environment. We see that the parameters consisting of angles, rotational velocities and linear accelerations are tracked very well while respecting the constraints for the platform, constraints that can be easily changed to fit the current simulator.We also see that the model successfully implements tilt coordination into the behaviour of the platform. This model performs extraordinarily well in theory, what remains is to implement this to the motion platform and fine-tune it. / Oryx Simulations tillverkar simulatorer i huvudsak för gruv- och skogsindustrinvilket används i utbildnings- och marknadsföringssyfte. Simulatorerna använder en röorelseplattform för att spegla hur fordonet i simulatormiljön rör sig. Denna plattform lutar och accelererar föraren för att förstarka upplevelsen. Tidigare har ett så kallat klassiskt washout-filter använts för att kontrollera plattformen som lämnar en del i övrigt att onska vad gäller hur väl fordonets rörelser speglas, hur lätt det ar att justera samt hur det hanterar plattformens begränsningar. Detta projekt ämnar producera en modell som väl speglar vinklar,hastigheter och accelerationer samtidigt som den respekterar plattformens gränser. I tillägg till detta bör modellen vara enkel att modifiera och justera. Detta uppnås genom så kallad Model Predictive Control som förutsager hur plattformen kommer röra sig utifrån dess aktuella tillstånd samtidigt som den respekterar de tvång som finns på plattformen direkt i modellen. Då alla parametrar i modellen är faktiska fysiska kvantiteter blir modellen märkbart lättare att justera. En viktig komponent i denna lösning är så kallad tilt coordination vilket består i att substituera lateral/longtudinell acceleration med en komposant av tyngdaccelerationen genom att luta föraren. Denna modell konstrueras och implementeras i Matlab och verifieras genom att använda extraherat data från den simulerade miljön. Vi kan se att parametrarna som består av vinklar, rotationella hastigheter och linjära accelerationer speglas väldigt väl, samtidigt som tvången på plattformen respekteras. Dessa tvång kan enkelt modieras for att passa den aktuella simulatorn. Vi ser även att modellen framgångsrikt implementerar tilt coordination i plattformens beteende. I teorin har denna modell väldigt bra prestanda; vad som kvarstår är att implementera den på en rörelseplattform och finjustera modellen.
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Tip vortex cavitation and diffused vorticity of propeller profiles: a modelling approach : Investigation of an implemented TVI model, and implementation and investigation of a DVH modelLundin, Lukas January 2017 (has links)
To predict fluid properties and interactions is an important task for the industry. It is plagued, however, by being close to impossible to predict analytically. Hence, it is customary to turn to numerical solutions. This in itself comes with many different methods and approaches suitable for different needs. This work focuses on two methods: Tip Vortex Index (TVI) and Diffused Vortex Hydrodynamics (DVH). TVI is a method to predict when a marine propeller will experience cavitation of tip vortices and is based on calculations from a Boundary Element Method (BEM). DVH is a particle method for simulating the circulation of a fluid in two dimensions and three dimensions. The aim is to investigate an implemented TVI model based on MPUF-3A for different marine propeller series, with different sub-designs for a total of 28 unique propellers, and implement the DVH method and test it for 3 different bodies. The results of this thesis show that the implemented TVI model is non-functional for the 28 different propellers, but the DVH method is successfully implemented and able to handle 2 different bodies. / Att förutspå fluid egenskaper och interaktioner är en viktig uppgift för industrin. Det plågas dock av att vara näst intil omöjligt att förutspå analytiskt. Det är därför vanligt att vända sig till numeriska lösningar. Detta kommer i sig med många olika metoder och tillvägagångssätt som passar olika behov. Detta arbete fokuserar på två metoder: Tip Vortex Index (TVI) och Diffused Vortex Hydrodynamics (DVH). TVI är en metod för att förutsäga när en marin propeller kommer att uppleva kavitation av spetsvirvlar och baseras på beräkningar från en Boundary Element Method (BEM). DVH är en partikelmetod för att simulera cirkulationen i fluid i två dimensioner och tre dimensioner. Syftet är att undersöka en implementerad TVI-modell baserad på MPUF-3A för olika marina propellerserier, med olika underdesigner, för totalt 28 unika propellrar, och implementera DVH-metoden och testa den för 3 olika kroppar. Resultaten av denna avhandling visar att den implementerade TVI-modellen är icke-funktionell för de 28 olika propellrarna, men DVH-metoden är framgångsrikt implementerad och kan hantera 2 olika kroppar
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Photoluminescence Characteristics of III-Nitride Quantum Dots and FilmsEriksson, Martin January 2017 (has links)
III-Nitride semiconductors are very promising in both electronics and optical devices. The ability of the III-Nitride semiconductors as light emitters to span the electromagnetic spectrum from deep ultraviolet light, through the entire visible region, and into the infrared part of the spectrum, is a very important feature, making this material very important in the field of light emitting devices. In fact, the blue emission from Indium Gallium Nitride (InGaN), which was awarded the 2014 Nobel Prize in Physics, is the basis of the common and important white light emitting diode (LED). Quantum dots (QDs) have properties that make them very interesting for light emitting devices for a range of different applications, such as the possibility of increasing device efficiency. The spectrally well-defined emission from QDs also allows accurate color reproduction and high-performance communication devices. The small size of QDs, combined with selective area growth allows for an improved display resolution. By control of the polarization direction of QDs, they can be used in more efficient displays as well as in traditional communication devices. The possibility of sending out entangled photon pairs is another QD property of importance for quantum key distribution used for secure communication. QDs can hold different exciton complexes, such as the neutral single exciton, consisting of one electron and one hole, and the biexciton, consisting of two excitons. The integrated PL intensity of the biexciton exhibits a quadratic dependence with respect to the excitation power, as compared to the linear power dependence of the neutral single exciton. The lifetime of the neutral exciton is 880 ps, whereas the biexciton, consisting of twice the number of charge carriers and lacks a dark state, has a considerably shorter lifetime of only 500 ps. The ratio of the lifetimes is an indication that the size of the QD is in the order of the exciton Bohr radius of the InGaN crystal making up these QDs in the InGaN QW. A large part of the studies of this thesis has been focused on InGaN QDs on top of hexagonal Gallium Nitride (GaN) pyramids, selectively grown by Metal Organic Chemical Vapor Deposition (MOCVD). On top of the GaN pyramids, an InGaN layer and a GaN capping layer were grown. From structural and optical investigations, InGaN QDs have been characterized as growing on (0001) facets on truncated GaN pyramids. These QDs exhibit both narrow photoluminescence linewidths and are linearly polarized in directions following the symmetry of the pyramids. In this work, the neutral single exciton, and the more rare negatively charged exciton, have been investigated. At low excitation power, the integrated intensity of the PL peak of the neutral exciton increases linearly with the excitation power. The negatively charged exciton, on the other hand, exhibits a quadratic power dependence, just like that of the biexciton. Upon increasing the temperature, the power dependence of the negatively charged exciton changes to linear, just like the neutral exciton. This change in power dependence is explained in terms of electrons in potential traps close to the QD escaping by thermal excitation, leading to a surplus of electrons in the vicinity of the QD. Consequently, only a single exciton needs to be created by photoexcitation in order to form a negatively charged exciton, while the extra electron is supplied to the QD by thermal excitation. Upon a close inspection of the PL of the neutral exciton, a splitting of the peak of just below 0.4 meV is revealed. There is an observed competition in the integrated intensity between these two peaks, similar to that between an exciton and a biexciton. The high energy peak of this split exciton emission is explained in terms of a remotely charged exciton. This exciton state consists of a neutral single exciton in the QD with an extra electron or hole in close vicinity of the QD, which screens the built-in field in the QD. The InGaN QDs are very small; estimated to be on the order of the exciton Bohr radius of the InGaN crystal, or even smaller. The lifetimes of the neutral exciton and the negatively charged exciton are approximately 320 ps and 130 ps, respectively. The ratio of the lifetimes supports the claim of the QD size being on the order of the exciton Bohr radius or smaller, as is further supported by power dependence results. Under the assumption of a spherical QD, theoretical calculations predict an emission energy shift of 0.7 meV, for a peak at 3.09 eV, due to the built-in field for a QD with a diameter of 1.3 nm, in agreement with the experimental observations. Studying the InGaN QD PL from neutral and charged excitons at elevated temperatures (4 K to 166 K) has revealed that the QDs are surrounded by potential fluctuations that trap charge carriers with an energy of around 20 meV, to be compared with the exciton trapping energy in the QDs of approximately 50 meV. The confinement of electrons close to the QD is predicted to be smaller than for holes, which accounts for the negative charge of the charged exciton, and for the higher probability of capturing free electrons. We have estimated the lifetimes of free electrons and holes in the GaN barrier to be 45 ps and 60 ps, in consistence with excitons forming quickly in the barrier upon photoexcitation and that free electrons and holes get trapped quickly in local potential traps close to the QDs. This analysis also indicates that there is a probability of 35 % to have an electron in the QD between the photoexcitation pulses, in agreement with a lower than quadratic power dependence of the negatively charged exciton. InN is an attractive material due to its infrared emission, for applications such as light emitters for communication purposes, but it is more difficult to grow with high quality and low doping concentration as compared to GaN. QDs with a higher In-composition or even pure InN is an interesting prospect as being a route towards increased quantum confinement and room temperature device operation. For all optical devices, p-type doping is needed. Even nominally undoped InN samples tend to be heavily n-type doped, causing problems to make pn-junctions as needed for LEDs. In our work, we present Mg-doped p-type InN films, which when further increasing the Mg-concentration revert to n-type conductivity. We have focused on the effect of the Mg-doping on the light emission properties of these films. The low Mg doped InN film is inhomogeneous and is observed to contain areas with n-type conductivity, so called n-type pockets in the otherwise p-type InN film. A higher concentration of Mg results in a higher crystalline quality and the disappearance of the n-type pockets. The high crystalline quality has enabled us to determine the binding energy of the Mg dopants to 64 meV. Upon further increase of the Mg concentration, the film reverts to ntype conductivity. The highly Mg doped sample also exhibits a red-shifted emission with features that are interpreted as originating from Zinc-Blende inclusions in the Wurtzite InN crystal, acting as quantum wells. The Mg doping is an important factor in controlling the conductivity of InN, as well as its light emission properties, and ultimately construct InN-based devices. In summary, in this thesis, both pyramidal InGaN QDs and InGaN QDs in a QW have been investigated. Novel discoveries of exciton complexes in these QD systems have been reported. Knowledge has also been gained about the challenging material InN, including a study of the effect of the Mg-doping concentration on the semiconductor crystalline quality and its light emission properties. The outcome of this thesis enriches the knowledge of the III-Nitride semiconductor community, with the long-term objective to improve the device performance of III-Nitride based light emitting devices.
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Theoretical prediction of properties of atomistic systems : Density functional theory and machine learningLindmaa, Alexander January 2017 (has links)
The prediction of ground state properties of atomistic systems is of vital importance in technological advances as well as in the physical sciences. Fundamentally, these predictions are based on a quantum-mechanical description of many-electron systems. One of the hitherto most prominent theories for the treatment of such systems is density functional theory (DFT). The main reason for its success is due to its balance of acceptable accuracy with computational efficiency. By now, DFT is applied routinely to compute the properties of atomic, molecular, and solid state systems. The general approach to solve the DFT equations is to use a density-functional approximation (DFA). In Kohn-Sham (KS) DFT, DFAs are applied to the unknown exchangecorrelation (xc) energy. In orbital-free DFT on the other hand, where the total energy is minimized directly with respect to the electron density, a DFA applied to the noninteracting kinetic energy is also required. Unfortunately, central DFAs in DFT fail to qualitatively capture many important aspects of electronic systems. Two prime examples are the description of localized electrons, and the description of systems where electronic edges are present. In this thesis, I use a model system approach to construct a DFA for the electron localization function (ELF). The very same approach is also taken to study the non-interacting kinetic energy density (KED) in the slowly varying limit of inhomogeneous electron densities, where the effect of electronic edges are effectively included. Apart from the work on model systems, extensions of an exchange energy functional with an improved KS orbital description are presented: a scheme for improving its description of energetics of solids, and a comparison of its description of an essential exact exchange feature known as the derivative discontinuity with numerical data for exact exchange. An emerging alternative route towards the prediction of the properties of atomistic systems is machine learning (ML). I present a number of ML methods for the prediction of solid formation energies, with an accuracy that is on par with KS DFT calculations, and with orders-of-magnitude lower computational cost. / Att kunna förutsäga egenskaper hos atomistiska system utgör en viktigdel av vår teknologiska utveckling, samt spelar en betydande roll i defysikaliska vetenskaperna. Sådana förutsägelser bygger på en kvantmekaniskbeskrivning av mångelektronsystem. En av de mest framståendeteorierna för att behandla den här typen av system är täthetsfunktionalteorin(DFT). Den främsta orsaken till dess framgång är attden lyckas kombinera skaplig noggrannhet med en bra beräkningseffektivitet.DFT används numera rutinmässigt för att beräkna storheterhos atomer, molekyler, och fasta kroppar. Generellt sett löses ekvationerna inom DFT genom att man inför entäthetsfunktionalapproximation (DFA). I Kohn-Sham (KS) DFT, användsDFAer för att approximera utbytes-korrelationsenergin. Inom orbitalfriDFT, där målet är att direkt minimera den totala energin med avseendepå elektrontätheten, så approximerar man också den icke-interageranderörelseenergin hos elektronerna. Dessvärre så fallerar många centralaDFAer att kvalitativt beskriva många viktiga aspekter hos elektronsystem.Två viktiga exempel är beskrivningen av lokaliserade elektroner,samt beskrivningen av system där det förekommer elektronytor. I denna avhandling använder jag modellsystem för att konstruera enDFAför elektronlokaliseringsfunktionen (ELF). Samma tillvägagångssättappliceras sedan för att studera den kinetiska energitätheten i gränsen avlångsamt varierande elektrontätheter, där effekten av elektronytor effektivtinkluderas. Förutom arbetet som berör modellsystem, så presenterasen utökad variant av en utbytes-energifunktional med en förbättrad KSorbitalbeskrivning: ett schema för att förbättra dess energiegenskaperför solida material, samt en jämförelse av dess beskrivning av en viktigegenskap hos den exakta utbytesenergin, vilket utgörs av diskontinuiteteri dess derivata. Ett mera nyligen uppkommet samt alternativt sätt att kunna förutsägaegenskaper hos atomistiska system utgörs av maskinlärning (ML).Jag presenterar ett antal ML-modeller för att kunna förutsäga formeringsenergierhos fasta material med en noggrannhet som är i linje medresultat som uppnås av beräkningar med hjälp av KS DFT, och med enberäkningseffektivitet som är flera storleksordningar snabbare.
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Adaptive Evolution of Resource Use, Phenotypic Diversity, and Productivity of Phytoplankton CommunitiesHellekant, Nils January 2019 (has links)
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.
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Positioning Electric Field Sensors in the Marine Environment Using Passage DataLangkilde, Maria January 2021 (has links)
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.
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A Primer to Categorical Symmetries and Their Application to QCD in Two DimensionsOlofsson, Rikard January 2021 (has links)
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).
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