This master thesis explores the application of Pumped-Storage Hydroelectricity (PSH) within an electricity market characterised by a substantial share of renewable and intermittent electricity production. The purpose of PSH is to enhance the alignment of supply with demand by storing energy at electricity surplus and releasing it during shortage. The Juktan Power Station, once the largest pumped hydro storage facility in Sweden with a storage capacity of about 25 GWh and maximum generation of 335 MW, serves as a case study. An in-depth analysis of the properties of the Swedish electricity market and its influencing factors is conducted. Wind speed data is successfully used to increase accuracy of price prediction. Furthermore, a model is developed to calculate potential profitability employing various operation methods. In conclusion, large-scale PSH provide significant benefit to the stability of the electricity system with a clear increase in value after 2020. However, concerns about grid tariff design, electricity market development and energy storage incentives means that investments are not obviously profitable. / Detta examensarbete utforskar tillämpningen av pumpkraftverk på en modern elmarknad med betydande andel förnyelsebar och intermittent electricitetsproduktion. Syftet med pumpkraft är att förbättra anpassningen av tillgång och efterfrågan genom att lagra energi vid elöverskott och frigöra den vid underskott. Juktan Kraftstation, tidigare Sveriges största pumpkraftverk med en lagringskapacitet på ca 25 GWh och maximal generatoreffekt på 335 MW, används som fallstudie. En analys av den svenska elmarknaden och dess påverkande faktorer genomförs. Vindhastighetsdata används framgångsrikt för att förbättra träffsäkerheten för elprisförutsägelser. Vidare utvecklas en modell för att beräkna potentiell lönsamhet med olika driftmetoder. Sammanfattningsvis visas att storskalig pumpkraft ger betydande fördelar för elsystemet med tydlig förstärkning efter 2020. Däremot identifieras potentiella problem såsom elnätsavgiften, svårigheten att långsiktigt förutspå elmarknadens utveckling samt incitament för energilagring, vilka sammantaget gör att pumpkraftinvesteringar inte är självklart lönsamma.

Integer programming can be used to provide solutionsto complex decision and planning problems occurring in a wide varietyof situations. Applying integer programming to a real life problembasically involves a first phase where a mathematical model isconstructed, and a second phase where the problem described by themodel is solved. While the nature of the challenges involved in therespective two phases differ, the strong relationship between theproperties of models, and which methods that are appropriate for theirsolution, links the two phases. This thesis constitutes of threepapers, of which the third one considers the modeling phase, while thefirst and second one consider the solution phase.   Many applications of column generation yield master problems of setpartitioning type, and the first and second papers presentmethodologies for solving such problems. The characteristics of themethodologies presented are that all successively found solutions arefeasible and integral, where the retention of integrality is a majordistinction from other column generation methods presented in theliterature.   The third paper concerns nurse scheduling and describes the results ofa pilot implementation of a scheduling tool at a Swedish nursing ward.This paper focuses on the practical aspects of modeling and thechallenges of providing a solution to a complex real life problem.

The main purpose of this project was to help Swedbank get a better understandingof how gross domestic product growth rate develops in the future froma data set of macroeconomic variables. Since GDP values are released long aftera quarter has ended Swedbank would like to have a model that could predictupcoming GDP from these data sets. This was solved by a combination ofgrowth rate predictions from a dynamic factor model, a vector autoregressivemodel and two machine learning models. The predictions were combined usinga weighting method called system averaging model where the model predictionwith least historical error receives the largest weight in the nal future prediction.In previous work a simple moving average model has been implementedto achieve this eect however there are several aws in a simple moving averagemodel. Most of these defects could in theory be avoided by using an exponentialweighting scheme instead. This resulted in the use of an exponentialweighting method that is used to calculate weights for future predictions. Themain conclusions from this project were that some predictions could get betterwhen removing bad performing models which had too large of a weight. Puttingtoo high weight on a single well performing model is also not optimal since thepredictions could get very unstable because of varying model performance. Theexponential weighting scheme worked well for some predictions however whenthe parameter , that controls how the weight is distributed between recent andhistorical errors, got too small a problem arose. Too few values were used toform the nal weights for the prediction and the estimate got unsteady results.

The purpose of this qualitative study was to investigate how the progression appears in the teaching of subtraction between preschool class and grade 1. What was examined was whether the teaching in subtraction is interrelated be- tween these grades or whether it differs completely. In order to find this out, interviews were conducted with employed qualified teachers in pre-school class and grade 1. Through these interviews we got to learn about the teachers' stories about how they work and what influences their choices in their work on subtraction. A teaching media analysis was also carried out on the teaching materials that teachers stated they used in the teaching of subtraction. The re- sults show that teachers in pre-school class work very much with laboratory teaching materials in their teaching as well as in whole class or smaller groups, while teachers in grade 1 work less in whole class/groups but more with indi- vidual work. The work in grade 1 proves to be more focused on the fact that teachers want something to assess the students compared to the preschool class' work where much of the learning is done through play. The results show that preschool teachers work either very little with subtraction or not at all com- pared to primary school teachers in grade 1 where subtraction is practiced on a regular basis. In preschool the terminology that is used is both formal and informal, however, overall more informal words are used compared to grade 1 where more formal words are used. The results also show that preschool teach- ers prepare the subtraction strategy step-by-step calculations. In grade 1 the strategy step-by-step calculations are used as well as the numerical calculations strategy. / Syftet med denna kvalitativa studie var att undersöka hur progressionen ser ut i subtraktionsundervisning mellan förskoleklass och årskurs 1. Det som un- dersöktes var om undervisningen i subtraktion hänger samman mellan dessa årskurser eller om den ser helt olika ut. För att få reda på detta genomfördes intervjuer med verksamma behöriga lärare i förskoleklass samt årskurs 1. Ge- nom dessa intervjuer fick vi ta del av lärares berättelser om hur de arbetar och vad som påverkar deras val i sitt arbete med subtraktion. En läromedelsanalys genomfördes även på de läromedel som lärare uppgav att de använde sig av i subtraktionsundervisningen. Resultatet visar att lärare i förskoleklass arbetar väldigt mycket med laborativa läromedel i sin undervisning samt i helklasser eller mindre grupper medan lärare i årskurs 1 arbetar betydligt mindre del i helklass/grupper men desto mer med individuellt arbete. Arbetet i årskurs 1 visar sig vara mer inriktat på att lärare vill ha något som de kan bedöma ele- verna på jämfört med förskoleklassens arbete där stor del av lärandet sker ge- nom lek. Resultatet visar att lärare i förskoleklass arbetar väldigt lite eller inte alls med subtraktion till skillnad från årskurs 1 där subtraktion tränas regel- bundet. Terminologin som används i förskoleklass är en kombination av in- formella och formella ord, dock merparten informella ord till skillnad från årskurs 1 där det används mer formella ord. Resultatet visar att lärare i för- skoleklass förbereder subtraktionsstrategin stegvisa beräkningar och i årskurs 1 tränas strategierna stegvisa beräkningar samt talsortsvisa beräkningar.

Syftet med studien var att synliggöra hur lärande kan uppstå i arbete med problemlösningsuppgifter i årskurs tre samt om och i så fall hur användning av laborativt material kan bidra till detta lärande.   Studien bygger på observationer som bearbetades med hjälp av den sociokulturella teorin. Begreppen mediering, artefakter och elevers lärande är centrala i studien. Utöver detta behandlas även problemlösning och laborativt material i diskussionen.    Resultatet visade att användandet av laborativt material i samband med problemlösning kunde bidra till elevernas lärande. Vilket laborativt material som används för specifika uppgifter hade dock en påverkan på om och hur materialet användes. Dessutom visade resultatet att den kommunikation som skedde under tiden för lösningen också bidrog till elevernas lärande. Resultatet visade också att lärande kan synas på många olika sätt och att elever medierar och lär på olika sätt.

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The flow of blood in the human body is a very important component in un-derstanding a number of different ailments such as atherosclerosis and a falseaneurysm. In this thesis, we have utilized Poiseuille’s solution to Navier-Stokesequations with a Newtonian, incompressible fluid flowing laminar with zero ac-celeration in a pipe with non-flexible walls in order to study blood flow in anarterial tree. In order to study and simulate a larger arterial tree we have uti-lized a primitive building block, a bifurcation with one inlet and two outlets,joined together forming a tree. By prescribing an inlet flow and the pressureat every outlet at the bottom of the tree we have shown that we may solvethe system by fixed-point iteration, the Matlab functionfsolve, and Newton’smethod. This way of using primitive building blocks offers a flexible way to doanalysis as it makes it possible to easily change the shape of the tree as well asadding new building blocks such as a block that represents arteriosclerosis.

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abstract: A continuously and stably stratified fluid contained in a square cavity subjected to harmonic body forcing is studied numerically by solving the Navier-Stokes equations under the Boussinesq approximation. Complex dynamics are observed near the onset of instability of the basic state, which is a flow configuration that is always an exact analytical solution of the governing equations. The instability of the basic state to perturbations is first studied with linear stability analysis (Floquet analysis), revealing a multitude of intersecting synchronous and subharmonic resonance tongues in parameter space. A modal reduction method for determining the locus of basic state instability is also shown, greatly simplifying the computational overhead normally required by a Floquet study. Then, a study of the nonlinear governing equations determines the criticality of the basic state's instability, and ultimately characterizes the dynamics of the lowest order spatial mode by the three discovered codimension-two bifurcation points within the resonance tongue. The rich dynamics include a homoclinic doubling cascade that resembles the logistic map and a multitude of gluing bifurcations. The numerical techniques and methodologies are first demonstrated on a homogeneous fluid contained within a three-dimensional lid-driven cavity. The edge state technique and linear stability analysis through Arnoldi iteration are used to resolve the complex dynamics of the canonical shear-driven benchmark problem. The techniques here lead to a dynamical description of an instability mechanism, and the work serves as a basis for the remainder of the dissertation. / Dissertation/Thesis / Supplemental Materials Description File / zip file containing 10 mp4 formatted video animations, as well as a text readme and the previously submitted Supplemental Materials Description File / Doctoral Dissertation Mathematics 2019

We solve initial boundary value problems with information unavailable at random time-steps. The randomly unavailable information represents asynchrony between processing elements. To approximate the initial boundary value problem, finite difference operators with summation-by-parts proper-ties and weak boundary procedures are used. Utilizing the energy method, we derive energy estimates for synchronous and asynchronous problems. The simulations show that the solutions may remain accurate and stable, even in the asynchronous case.