This thesis describes a system for dealing with free surface fluid simulations, and the components needed in order to construct such a system. It builds upon recent research, but in a computer graphics context the amount of available literature is limited and difficult to implement. Because of this, the text aims at providing a solid foundation of the mathematics needed, at explaining in greater detail the steps needed to solve the problem, and lastly at improving some aspects of the animation process as it has been described in earlier works. The aim of the system itself is to provide visually plausible renditions of animated fluids in three dimensions in a manner that allows it to be usable in a visual effects production context. The novel features described include a generalized interaction layer providing greater control to artists, a new way of dealing with moving objects that interact with the fluid and a method for adding source and drain capabilities..

AbstractConsider a ?uid being heated from below. The heating leads to an upward convectiveforce that is counteracted by the viscous forces of the ?uid. If the convectiveforce is large enough in comparison to the viscous forces the ?uid will be put in anunstable state.

AbstractConsider a ?uid being heated from below. The heating leads to an upward convectiveforce that is counteracted by the viscous forces of the ?uid. If the convectiveforce is large enough in comparison to the viscous forces the ?uid will be put in anunstable state.

Vätskor känns självklara och naturliga i vår vardag men de kan vara ganska komplexa och svår att simulera i exempelvis ett datorspel. Ett verklighetstroget vattenstänk i ett spel kan absolut ge en ökad realism i spelet och ge en förhöjd spelupplevelse.Detta arbete undersöker en teknik för att få en mer verklighetstrogen rörelse/beteende hos en vätska. Metoden bygger på att lösa Navier-Stokes algoritm som beskriver vätskors beteende på molekylär nivå, och beräkna en interaktion mellan partiklarna som representerar vätskan.Resultaten visar att en mer realistisk rörelse går att få fram jämfört med vad man kan få med ett enklare partikelsystem, men att antalet partiklar blir mycket begränsade. Prestanda hos datorer ökar ständigt och inom en snar framtid genom en utveckling av teknikern och närliggande metoder så kan den bli helt klart aktuell i nästa generations datorspel..

Background: Cerebral Palsy is usually divided into three subgroups: ataxic, spastic and dyskinetic, where children and adolescents can, because of misestimation in nutrition and energy intake, suffer from weight problems.Aim: To compare calculations with equations with the individual's measured RMR in the subgroups, to see if any equation is more suitable. This could be used as a tool to calculate the resting metabolism at times when it is not possible to perform clinical measurements.Method: The RMR has been measured in 37 children and adolescents aged 3-15 years through indirect respiratory calorimetry. Those values have been compared with calculations from five equations. The results were then analyzed in order to find if any equation is better to apply for calculating resting metabolism for each subgroup.Results: The ataxic group was overestimated by 56.5% of the calculated values. WHO/FAO/UNU?s equation indicates a significantly strong correlation between the measured and calculated values (r=0.85, p<0.05).

Att lösa partiella differentialekvationer, PDE, med hjälp av numeriska metoder harblivit vitalt det senaste århundradet. Det finns flera metoder tillgängliga och latticeBoltzmanns metod, LBM, har visat sig vara ett kraftfullt verktyg för att lösa Navier-Stokes, N-S ekvation. Metoden är beräkningsmässigt effektiv i jämförelse med andranumeriska metoder under rätt förhållanden. Mängden datorkraft som behövs för attlösa en PDE är viktig och detta gör LBM intressant just på grund av dess beräkningseffektivitet.En studie om möjligheterna att använda LBM till att lösa andra sorters PDEän N-S ekvation är spännande och utbildande. I detta arbete tar vi reda på om LBMkan användas till att lösa och modellera diffusionsekvationen, och om fallet är sådantvalidera att resultatet är tillräckligt korrekt.

When investigating mechanical problems it is often more convenient to deal with scalars rather than vectors. In this project methods stemming from the field of analytical mechanics, which lets one derive the equations of motion using scalar quantities instead of vectors, have been used. Two mechanical problems were investigated, a double pendulum with a spring and particles orbit in a sphere. The equations of motion of the two systems were derived with the assistance of computer algebra, using Maple and the external package Sophia. The systems were investigated with regard to periodicity and conserved quantities..

The aim of this study was to evaluate different types of volume and taper equations that can be used to predict single-tree stem volume and stem diameter at any given height along the tree stem for plantation grown Sitka spruce (Picea sitchensis (Bong.) Carr.), Norway spruce (Picea abies (L.) Karst) and White spruce (Picea glauca (Mounch) Voss) in Iceland. A number of published tree volume equations were tested and modified to predict the total stem volumes over bark but three logarithmic equations were taken for more in-depth analysis. Three taper equations were tested. Two variable-exponent equations (Kozak 1997, Kozak 2004) and one exponential equation described by Biging (1984). Data from a total of 617 sample trees were used in this study, collected from stands in various parts of the country and present different types of stands growing in different soil types and cover most of the site conditions suitable for forestry in Iceland.

When investigating mechanical problems it is often more convenient to deal with scalars rather than vectors. In this project methods stemming from the field of analytical mechanics, which lets one derive the equations of motion using scalar quantities instead of vectors, have been used. Two mechanical problems were investigated, a double pendulum with a spring and particles orbit in a sphere. The equations of motion of the two systems were derived with the assistance of computer algebra, using Maple and the external package Sophia. The systems were investigated with regard to periodicity and conserved quantities..

Asymptotically flat spaces are widely studied because it is one natural way of describing an isolated system in general relativity. In this thesis we study what happens to the Lanczos potential at spacelike infinity in such spacetimes. By transformations of the Weyl-Lanczos equation, we derive expressions for the limiting equations on both the timelike unit hyperboloid, and the timelike unit cylinder. Finally the Newman-Penrose formalism is used to get a component version of the equations..

Stage-discharge equations for lakes without disharge measurementsSimon AnderssonIn 2015 all lakes, rivers, coastal water and groundwater should be of good ecological statusaccording to the water framework directive from the European Union. In the process ofimproving the quality of Swedish water bodies, knowledge of where problems occur isneeded in order to utilize the resources optimally. The ability of lakes to store water is animportant factor since it controls the flow of water through the country. A stage-dischargeequation is a mathematical relation between discharge from a lake and its water level. Bybetter understanding of stage-discharge equations for lakes, their storage capacity can bedescribed better in hydrological models.This master thesis aims to evaluate methods for determining stage-discharge equations forlakes where a variable amount of field measurements is available.

In this project we have used the theory of analytical mechanics to derive equations of motion for complex mechanical systems in order to study their behaviour over time. Even if the theory provides powerful tools to tackle tough problems which would be very hard to solve by methods of Newtonian mechanics, you are still relatively limited without running any computer simulations. One realises that in a faster rate it will be an incredibly difficult task to find an analytical solution when the degrees of freedom increases. Even if one would succeed to derive the equations, one still has to solve them to get the information of the systems behavior. Of experience one knows that the equations in general are nonlinear and hence must be integrated numericaly.

In this project we have used the theory of analytical mechanics to derive equations of motion for complex mechanical systems in order to study their behaviour over time. Even if the theory provides powerful tools to tackle tough problems which would be very hard to solve by methods of Newtonian mechanics, you are still relatively limited without running any computer simulations. One realises that in a faster rate it will be an incredibly difficult task to find an analytical solution when the degrees of freedom increases. Even if one would succeed to derive the equations, one still has to solve them to get the information of the systems behavior. Of experience one knows that the equations in general are nonlinear and hence must be integrated numericaly.

I fo?ljande arbete underso?ks en partikelbaserad simuleringsmetod som kallas Fluid-partikelmetoden, FPM. FPM a?r designad fo?r att simulera komplexa fluiders beteenden pa? mesoskalan, vilken sammanla?nkar kontinuumskalan med den molekyla?ra skalan. Metoden utvecklades av Pep Espan?ol i slutet av 1990-talet och a?r en vidareutveckling och generallisering av Dissipative Particle Dynamics som togs fram av Hoogerbrugge och Koelman under tidigt 1990-tal.

At the department of Electronic Warfare Assessments at the Swedish Defence Research Agency in Linköping one of the activities is modelling and simulation of the duel between a robot and a target. The aim with this Master's thesis is to develop a simulation model of an hovering helicopter. First a theoretical description of the forces and moments acting on an helicopter is given. Then the equations of motion are derived. These equations are simplified to be valid only for a hovering helicopter and the result is a mathematical model.