
Integreret speciale  modelbyggervariant, 2. modul, Vinter 2012, id:444  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Ja 
English abstract
Altered levels of the steroid hormone cortisol has been observed in some melancholic depressed patients. The reason for this is not fully understood. The level of cortisol in the blood is regulated by the neuroendocrine system called the hypothalamicpituitaryadrenal(HPA)axis. By proposing mathematical models for cortisol's synthesis and transport in the blood parts of this system are being investigated. For the ACTHinduced cortisolsynthesis is established a comprehensive mechanismbased model. This model can be parted into submodels to investigate specific parts of the cortisolsynthesis. MatLab simulations of a submodel of the activation of protein kinase A (PKA) indicates the occurrence of a maximum activation of PKA, at the total concentration of cyclic adenosine monophosphate being four times the total concentration of the PKA tetrameric. Simulations of a submodel for the system from the concentration of cytosolic cholesterol (CC) to the secretion of cortisol shows that the concentration of cholesterol in the mitochondrial inner membrane and the synthesis of steroids is strongly influenced by the concentration of the cholesterol transport protein StAR and the degree of phosphorylation. Variations of CC are of importance only at concentrations being less than 1000 nM, which is half of the standard concentration estimated in the literature. Furthermore are set up models of activation of melanocortin 2 receptor and cortisol mobilization in the cell cytostol on the basis of the curent knowledge. Simulations of these models, however do not yet show operational results. The model developed in this project for cortisol transport in the blood describes the binding of the hormone to the carrier protein, corticosteroid binding globulin (CBG). Simulations of the model shows that CBG increases the total concentration of cortisol in the blood, while the concentration of cortisol on the free form remains the same. The output of the concentration of free cortisol, however, is at a high level compared with the literature. Changes in the rates of production and of elimination can approximate this picture, but maybe the reason for the high concentrations are to be found in the model's simplified construction, which as an example does not include an exchange of cortisol in the body's tissues.
Modelprojekt, Bachelor. modul, Vinter 2012, id:445  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb:  Ja 
The present work is a mathematical investigation of the insulin granule motility and the role of actin filaments in pancreatic (formel)cells. It is supported by numerical analysis based on computer simulations. It appears that one dimensional motion of insulin granules, along micro tubuli and actin filaments, does not favor rapid transportation, which may indicate a mean of exocytosis regulation. Unrestricted random walks in three dimensions due to thermal fluctuations of the cytoplasmic molecules are, mathematically, more likely to transport the granules to the periphery of the cell. These findings are based on a simplified (formel)cell model with neglected chemical, electric and electrostatic forces and are not decisive for the interaction between granules and actin filaments. Lastly, the actin filament network close to the cell membrane is hypothesised to cause a smallscale mass diffusion of insulin granules.
Modelprojekt, Bachelor. modul, Vinter 2012, id:446  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
English abstract
This project report explores the Slingshot Effect. The Slingshot Effect is an expression of the phenomenon that an object in space can be accelerated by the gravity of a given planet. The study is conducted by setting up a differential equation that describes the movement of a space probe within a solar system encompassing the sun, the Earth, and the space probe itself. The purpose of setting up a differential equation describing this movement is to find explanations that may clarify the ways in which the space probe moves when positioned far away from Earth. The explanations found are functions that describe speed and position over time. Since it is not possible to analytically determine the reciprocal movement of three objects in the future, the mass of the space probe must be considered in relation to the mass of the sun and the mass of the Earth. Upon considering this relation, it becomes evident that the mass of the space probe is very small when compared to the mass of the sun and the mass of Earth, and thus, it can be presumed that the space probe will not affect the sun or the Earth with any given force. As a result, the system encompassing the sun, the Earth and the space probe will not conserve its energy. To provide a critical view on this study of the Slingshot Effect, a system consisting of the space probe and the Earth is defined. From within this system, the Slingshot Effect can be examined, provided that one is at a distance between the sun and the Earth at which the Earth's field of gravity is affecting the trajectory of the space probe. By solving the differential equation explaining the movement of the space probe, and by comparing the results to the theoretical study of the Slingshot Effect, it is examined how exact a study of the Slingshot Effect one can perform. The project report concludes that it is possible to satisfactorily study the Slingshot Effect by setting up a differential equation explaining the movement in a system without energy conservation. The results of the study show that the effect on the Slingshot Effect is less significant than the theoretical effect, and that the desired effect can only be achieved at an unrealistic distance from the centre of the Earth.
Speciale  modelbyggervariant, 2. modul, Vinter 2011, id:430  
Vejleder:  
Findes på RUb:  Ja 
This master thesis researches probabilistic description logics with the aim of showing how the different probability interpretations are reflected in the existing formalisms. As an integrated thesis in Mathematics and Computer Science, this project focuses on the mathematical as well as the conceptual differences between the different probability interpretations first generally, then specifically in probabilistic description logics. Some decidability issues are addressed as well. The thesis centers on one particular article by Tao et al. (2007) as the only one that uses the belieftype probability for terminological axioms such as concept inclusions. Most other research is focused on the frequency interpretation, which is perceived to be more useful, since there is a simple method for acquiring the probability values. The approach of Tao et al. is less popular for practical reasons, however, it can help us fully understand the behaviour of probabilistic description logics. It is my aim to critically investigate this article in detail, fill in the gaps of their explanations and make it accessible for students of Mathematics and Computer Science who are unfamiliar with this topic.
Speciale  modelbyggervariant, 2. modul, Vinter 2011, id:431  
Vejleder:  Stig Andur Pedersen og Anders J. Hede Madsen 
Findes på RUb:  Ja 
In the present thesis, a theory of semantic competence is modeled using tools from epistemic logic. The resulting formal model is used to analyze a problem from the philosophy of language, namely Frege's Dilemma. There are two aims of the thesis: to construct a formal theory of semantic competence, and to show that the formal theory can be used as an useful analytical tool in uncovering the informational structure behind problems from the philosophy of language. The first aim is achieved by, first, deciding for which theory of meaning a theory of semantic competence is wanted. Due to its simplicity, Millianism is chosen. Then various nonformal theories of semantic competence are evaluated with respect to finding one which allows for an objective, intersubjective comparison of competence levels. It is argued that the conceptual theory of (Marconi, 1997) is the best choice: the theory has a clearly defined structure making modeling possible, and is based on empirical studies from cognitive neuropsychology. Following these initial choises, the modeling framework and its philosophical interpretation is presented. The framework used is epistemic logic, and both the propositional and quantified versions are introduced. As a more expressible logical language is required, manysorted quantified epistemic logic is presented, and a novel, general completeness result is shown for manysorted extensions of quantified modal logic. Having thus set the stage of achieving the first aim, a slightly simplified version of the theory of (Marconi, 1997) is modeled. A suitable modelclass is defined and a meaning function is added to capture Millian meaning. Based on the shown completeness result, a sound and complete axiom system is presented, and a logic representing the formal theory is thereby found. The model is then validated. It is shown that both the essential ontological properties as well as the competence types from Marconi's theory are present. It is further shown that the formal counterparts of the competence types from Marconi's theory adhere to the principles dictated by empirical studies. Thereby, the first aim is achieved. To accomplish the second aim, proof of concept is shown. This is done by analyzing an objection to the correctness of the Millian theory of meaning, namely Frege's Dilemma (Frege, 1892). The formal theory is used to analyze both disjuncts of the dilemma, while focusing on the epistemic situation of the agent, i.e. the agent's level of semantic competence. The formal theory of semantic competence allows for multiple notions of semantic competence, each resulting in a unique rendering of the dilemma. Based on these analyses, it it is concluded that once the underlying informational structure of the discussed situations is revealed, neither disjunct proves to be a problem for the Millian theory of meaning. Hereby, the second aim is accomplished. However, I raise an intuitive objection to one of the analyses. It is argued that the objection introduces an unaccounted for parameter, namely contexts. In order to show that this objection is not fatal for the proposed analysis, a chapter is devoted to the construction of a contextual theory of semantic competence. The notion of contexts is incorporated into the models for semantic competence, and the possibilities for finding a complete axiomatic system is discussed, but no completeness result is shown. Therefore, a formal theory, i.e. a logic, for contextual semantic competence is not presented. However, the modeltheoretic machinery is used to reanalyze the problematic case. It is shown that when the situation is modeled in a contextual model, the epistemic analysis of the disjunct again showed the Puzzle about Identity is unproblematic for the Millian view. Overall, the constructed formal theory of semantic competence is shown to elucidate informational aspects of the problems posed to the philosophy of language by Frege's Dilemma. In particular, once the informational structure of the problems is clear, it is shown that each argument is far from being as decisive against Millianism as has been the mainstream view in 20th century philosophy of language.
Modelprojekt, 2. modul, Vinter 2010, id:410  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
English abstract
We look at social force models as a way to model the behaviour of human crowds, in order to evaluate how well these types of models simulate crowd behaviour, and what the models' strengths and weaknesses are. In order to do this evaluation, we implement a computer simulation of an exemplary social force model. In order to create this simulation, we pick an exemplary model that is well described in the article that presents it, and analyse it in detail, filling in details from other articles when necessary. Based on this analysis of the model, we go from the abstract model formulation to a concrete numerical simulation by filling in required details, sucs as how to approximate the movement of pedestrians, how to set initial conditions and values, and how to implement the interaction between pedestrians and walls in practice. From our results, it is clear that our simulation (with the right parameters) exhibits reasonable pedestrian behaviour upon visual inspection. While we successfully replicate some results from the litterature, other effects do nok manifest themselves. We discuss several resons for this discrepancy, including features that are missing from the model, parameter values, effects of using random numbers to generate the initial conditions and possible errors in our implementation of the model. Based on the results of our own simulations and our review of the social force modelling field, we assess social force models and their strengths and weaknesses. We conclude that social force models are not based on any theories for the behaviour of crowds, but are created to replicate a set of observations. As such, any confidence in their productions must come from a record of producing results fitting observations; and since the field is relatively new, they have not yet reached this state. Social force models do, however, provide a practical way to simulate something that would otherwise be impossible to simulate. As such, they are the best available way to provide e.g. guidance when designing facilities that must accommodate many pedestrians, and given time the accuracy of their predictions will probably increase.
Modelprojekt, 1. modul, v2009/10, id:397  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
English abstract
This project is based around the analysis of a mathematical description of V. cholerae epidemics in cities connected by a river system. The stability analysis is descriped step by step to give the reader a thourough understanding of the material. A Matlab package has been coded and is included in full in the appendix. The program is explained superficially in the project. The usefulness of the modelis discussed in regards to the parameters needed, and the results reaced by an artificial scenario calculated by the program. It becomes evident that there are some problems withe the current model, due to several parameters that needs to be calibrated to specific outbreaks after they occur. This is mainly caused by a lack of understanding of the bacteria. Some problems concerning the calculations in Matlab are uncovered, which will result in an error that grows over longer timespans.
Modelprojekt, Bachelor. modul, Sommer 2013, id:453  
Vejleder:  Mogens Allan Niss 
Findes på RUb:  Ja Ja 
English abstract
This paper details a study of the distinction between prescriptive and descriptive elements in mathematical modelling. Through preliminary definitions of prescription and description we thoroughly analyse the modelling process in four specific cases: Optimization of a can, the Gini coefficient, mandate allocation methods and perspective drawing. We identify where in these processes prescriptions and descriptions, respectively, are made and examine how they shape the particular model and its use. Finally we argue that our preliminary definitions are reasonable and conclude that it is definitely prudent to distinguish between prescriptive elements and descriptive elements in both the modelling process and in the use of models of a mathematical nature.
Modelprojekt, Bachelor. modul, Sommer 2011, id:414  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
This project is about mathematical models and the spread of cervical cancer. Cervical cancer develops from the human papillomavirus (HPV), which is a collection of nearly 200 different viruses that causes everything from warts on the feet to cervical cancer. There has in recent years been much focus on cervical cancer, partly because it's one of those cancers, which it is actually possible to limit the spread off in several ways. From a mathematical point of view, it is of particularly strong interest to develop mathematical models that can predict the development of cervical cancer, and assist in a more focused development of screening and vaccination programs. Although it is possible to get the vaccine against HPV 16 and 18, which causes most of the cases of cervical cancer, modeling results shows that there is still a need, for screening programs to catch those cases the vaccine fails to prevent. I have in this project looked at one article RUC project from 2010 both of which have mathematical models for the spread of cervical cancer, as well as looked at the effect of a vaccination program. Our main conclusion is that, it does have a small benefit to vaccinate men, however it is rather marginal, and it would be preferable to instead use the cost of this on other kinds of treatment.
Modelprojekt, Bachelor. modul, Sommer 2011, id:415  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
English abstract
Speciale  modelbyggervariant, 2. modul, Sommer 2011, id:419  
Vejleder:  Johnny T. Ottesen 
Findes på RUb:  Ja 
English abstract
In this thesis a model of the baroreflex as presented in Ottesen and Olufsen 2010 is modified and later optimized against experimental data. It is investigated if the model can describe the experimental data, the answer is inconclusive. The model takes the change in pressure as an input and provides a heart rate as output. In the thesis the model is made dimensionless and the original models discrete time delay funktion is replaced by a distributed delay function. The experimental data originates from a series of HUTexperiment sessions on a group of test persons, young healthy men in their mid twenties. The HUTsessions exposed the test subjects to a consecutive series of five HUT's. The first of the five HUT's took place after an injection with saltwater (placebo), and the following four HUT's each took place after an atropine injection. The mathematical model is optimized on data from a series of HUTexperiments on the test subject referred to as Jens. The model is solved using the CVODES solver, which applies a variable order and variable step size implementation of the backwards Difference method. The sensitivity analysis performed to lock parameters of the model is a direct method that runs parallel with the BDF method. The parameter estimation method is a Metropolis Markov Chain Monte Carlo method (MCMC). The model fits reasonably well on data from Jens held in supine position after the saltwater injection, and the parameters found by MCMC are not physiologically unreasonable. The parameter values are used as an initial guess for a model describing Jens during a tilt. This procedure of sensitivity analysis followed by MCMC optimization and then applying the most likely parameters as initial guess for the following experiment are repeated for all 5 tilts. None of the heart rate data in the tilts are captured well by the optimized parameters which attain physiologically unrealistic values. Another model optimization is done on a HUTexperiment on the test person Danny. The optimization attempts to fit parameters to a pre tilt supine phase, a tilt up phase and an upright phase. The optimization produces poor fits. Due to physiologically confusing behavior in pulse data of the test persons compared to measured pressure data. And the fact that the model at several of these points produces qualitatively more meaningful ouputt, it is concluded that more investigations on other HUT data must be undertaken in order to give a conclusive answer to the problem statement.
Integreret speciale, modelbyggervariant, 3. modul, Sommer 2010, id:407  
Vejleder:  
Findes på RUb:  Ja 
English abstract
Speciale modelbyggervarianten, 2. modul, 2014, id:411  
Vejleder:  
Findes på RUb:  Ja 
English abstract
The purpose of this thesis is to investigate how the spectral signal from an agricultural field is influenced by the vertical distribution of chlorophyll through the canopy. In particular it is examined whether a uniform vertical distribution of chlorophyll improves the results of two types of models using satellitebased remote sensing data. Analysis of variance and simple linear regression is used to characterise the vertical chlorophyll profile in a canopy for field plots in five different European countries with a variety of crops. Out of a total of 68 fields, 28 fields are found to be characterised by a uniform vertical chlorophyll distribution while 16 fields have either a decreasing or increasing vertical distribution of chlorophyll. The vertical chlorophyll profile for 6 fields cannot be characterised by either of these models. 18 fields are not classified as observations lack homogeneity of variances. Biophysical conditions can be estimated by an empiricalstatistical model where spectral vegetation indices are related to field measurements of biophysical variables such as leaf area index (LAI) or leaf chlorophyll content. The empirical relation cannot be generalised as it depends on crop species, context and time. A physicallybased model such as PROSAIL can be used to estimate biophysical variables. PROSAIL uses input regarding the geometry and architecture of the canopy as well as leaf pigment content to simulate the spectral signal. The Matlab code for PROSAIL was adjusted to compensate for an error in the implentation of the ellipsoidal leaf angle distribution. Simulated reflectance data is used to evaluate the sensitivity of the vegetation indices. They are shown to be responsive of changes in leaf angle and LAI and the chlorophyll index in particular is shown to be sensitive of the leaf chlorophyll content. The empirical relation between the vegetation indices and LAI as well as (formel) is improved for fields with a uniform vertical chlorophyll profile but remains highly contextdependent. PROSAIL is used to simulate the reflectance from a number of Danish wheat and barley fields from 2008 and 2009. The deviation between measured and simulated reflectance is evaluated in relation to LAI, plant type, landscape and vertical distribution of chlorophyll. It is shown that the deviation regarding red reflectance is influenced by the vertical chlorophyll profile, however, the simulation of reflectance of visible light is generally improved at low LAI. The simulation of near infrared reflectance is improved at higher LAI levels.
Modelprojekt, 1. modul, 2014, id:468  
Vejleder:  
Findes på RUb:  Ja 
English abstract
The main focus of this article is to observe and describe how a population will change in time as a function determined by another population. More accurately there has been constructed a simple and a modified dynamical system used to describe the change in the number of users on facebook on both PC and Mac as a function of time. The simple model (formel) simply says that either you already have facebook  or you do not. If you do not, you are in a population where everyone without facebook has the same probability of creating an account on facebook  the only difference is whether you own a PC or a Maccomputer. If you already have facebookaccount, you have the same probability of deleting your account as the other users on your given system. This results in a state of equilibrium. When analyzing the parameters it became obvious that the rate of people deleting facebook will determine the number of constant users, while the rate of people signing up will determine how fast you reach the equilibrium. The modified model (formel) is essentially the same. It, however, has one small factor changed: Once you have deleted your facebook account, you will not be interested in signing up again. This small change alters the entire result as there no longer will be a state of equilibrium. The amount of facebook users will climb to a global maximum before declining slowly  but steadily. There will still be new people creating accounts, but it cannot match the amount of profiles being deleted. It has been impossible to get accurate parameters  which is why they have been determined as good as was possible. This, however, means that the graphs and predictions might not be accurate, but they should still give a good indication of how the amount of facebook users should climb and fall as time goes by. Essentially facebook will eventually lose popularity if this model has a shed of truth in its prediction. The only question remaining is how long facebook can remain the monarch of social media and who will eventually take over.
Fagmodelprojekt, 1. modul, 2013, id:464  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 2013, id:466  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb:  Ja 
English abstract
Colony Collapse Disorder (CCD) is a syndrome affecting the European honeybee (Apis mellifera). Affected hives lose their worker bees, but very few dead workers can be found in and around the hive. The syndrome has many suspected causes. Notable suspects are Varroa destructor, Nosema ceranae, American foulbrood and neonicotinoids. Earlier analyses have given no final conclusion about the main cause of CCD. Therefore, this study proposes a novel method for examining the main cause that is, by analyzing the spreading of the syndrome in space and time, rather than symptoms in the individual hive. We demonstrate that this is an applicable method of assessing whether the syndrome is transmitted through direct contact, spread via airborne spores, or distributed randomly. As a concrete example of this, we examine the spreading pattern of a disease transmitted via contact, both through mathematical analysis and through a simulation in GNU Octave. From this examination it is apparent that patterns can be easily told apart if a pathogen is transmitted from a point source in an area and the wind has a prevalent direction. For pathogens endemic in an area, our method has a more limited application. This report is a pilot study on inverse problem solving, directed at both human and veterinary epidemiology, aiming to identify diseases from their pattern of spreading.
Modelprojekt, 1. modul, 2010, id:400  
Vejleder:  Eksaminator Anders Madsen 
Findes på RUb:  Ja 
English abstract
In the present paper syntax, constant domain semantics with nonriged constants and an axiom system for nagent systems with identity for a termmodal logic is presented. This allows operator indices to be terms of the firstorder language resulting in poerators doubling as predicates. Quantification over agents is possible and the agents are reflected in the semantic structure. It is shown how classic epistemic axioms af S5 can be added to the core system. Examples of expressibility are given, and venues of further research addressed.
Model, 1. modul, 2010, id:401  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
This project is about mathematical models and the spread of cervical cancer. Cervical cancer develops from the human papillomavirus (HPV), which is a collection of nearly 200 different viruses that causes everything from warts on the feet to cervical cancer. There has in recent years been much focus on cervical cancer, partly because it's the cancer which in the developing world kills more women than any other, and partly because it's one of those cancers, which it is actually possible to limit the spread off in several ways. From a mathematical point of view, it is of particularly strong interest to develop mathematical models that can predict the development of cervical cancer, and assist in a more focused development of screening and vaccination programs. Although it is possible to get the vaccine against HPV 16 and 18, which causes most of the cases of cervical cancer, modeling results shows that there is still a need, for screening programs to catch those cases the vaccine fails to prevent. We have in this project looked at two articles, both of which have mathematical models for the spread of cervical cancer, as well as looked at the effect of a vaccination program. Since one of the articles already have been the subject of a thorough study of a former RUC project from 2009, we have in this project, chosen to focus more on the model developed in the Finnish article. In light of both a general description of HPV and a review of the Finnish model, we have formulated and discussed our own model, which have been adapted to Danish conditions, with a special emphasis on whether the conclusions in the article by Barnabas et.al. can be applied to Denmark. Our main conclusion is that, it does have a small benefit to vaccinate men, however it is rather marginal, and it would be preferable to instead use the cost of this on other kinds of treatment.
Model, 1. modul, 2010, id:404  
Vejleder:  
Findes på RUb:  Ja 
Speciale, modelbyggervariant, 3. modul, 2010, id:406  
Vejleder:  Johnny Ottesen og Mette S. Olufsen 
Findes på RUb:  Ja 
In this thesis we examined the phenomena caused by initial gravitational effects and short term neural control when the human body is subjected to a headuptilt (hut) test. This was done by constructing a simple mathematical model, which describes the systemic circulation of the cardiovascular system. The human body is divided into two parts; the lower and the upper body, which are further divided into venous and arterial compartments. The left heart isdescribed as a pump with timevarying elastance, thus making the model pulsatile. The system is modeled as an electrical analogue in which pressure is analogous to voltage. Flow to current, compliance to capacitance, and resistance is the same in both settings. The circuit can be represented by five nonlinear ordinary differential equations. To predict dynamics during hut, the neural control is included by defining timevarying peripheral resistance, venous compliance, and heart contractility. These regulating mechanisms were modeled by setpoint fuctions and sigmoidal functions, which resemble the behavior seen in experiments. We also developed an idealized cardiovascular model of the human body, where teh body is considered an elastic cylinder. We found the hydrostatic invariance point, and related this to the hut. The model was validated using data from a healthy 25 year old subject who underwent hut, and parameter estimation techniques were employed to estimate a set of parameters that minimized the least squares error between the model and the data. By identifying correlated parameter pairs and fixing insensitive parameters we were able to obtain reliable estimates for five model parameters during hut, and nine parameters in steady state. In steady state, we used three data sequences to obtain more reliable estimates. The constructed model was able to predict dynamics observed in the data both during steady state and during hut. There are fluctuations in the data which cannot be explained by the model, but we believe these originate from the respiration of the patient, something that is not included in the model. All model variables produce physiologicaly reasonable results during the hut: cardiac output drops the same amount as seen in the lterature, lower venous pressure is increased in agreement with other studies, and upper arteral pressure resembles the data obtained. These results show that the simple model can be used to predict responses from larger groups of subjects. Subsequent analysis of parameter estimates have potential to be used to predict differences within and between these groups of subjects. However, before using the model in a larger study, we suggest to include the following model improvements: 1) Include a simple model for the respiration of the patient. 2) The control of the lower venous compliance should be a strictly mechanical feature, and not part of the baroreflex system. 3) The upper peripheral resistance should also be controlled.
Model, 1. modul, 2009/10, id:392  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
English abstract
This project originates from the question of how come Mathematics is so effective, and hence is being used in so many other areas of the world, other than that of mathematics. Our question regards how come mathematics works in other discplines than mathematics itself. Our approach to the question was through three different cases, where mathematics could be assigned a great deal of the reasonfor the success. We tried to spread out in our choices af cases, both when it came to the way mathematics is interacting, but also when it came to what scientific fields, we were looking at. The three cases were the HardyWeinberg law on genetic populations, the JPEG algorithm used for compressing digital images, and a cardboard model of the Planetarium in Copenhagen. Through our analysis of these three cases, we found, firstly, that it is not possible to give a common description of what it means that the mathematics "works" in the case. The mathematics works in different ways in the different cases. Secondly, we found that the reason that mathematics can be used, is also different among the cases. Our assumption is that these results are general, that one cannot find one common reason that mathematics work.
Model, 1. modul, 2009/10, id:390  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb:  Ja 
English abstract
Mathematical modelling of isomorphs in IPLliquids The purpose of this project is to investigate, in part whether group theory, can be used as a model for isomorphic curves in IPLliquids, and in part whether the explanation of isomorphic behaviour can be found as symmetry in solutions to the, for this project unknown, differential equations that controls the dynamics in simulations of vicous liquids By analysing the IPLmodel with group theory a transformation group GIPL was suggested as a way of describing the equivalence relation r1n/3 /T1 = r2n/3/T2. From this it was shown, that isomorphic curves can be described as orbits in the (T, r)plane, where each of the orbits can be identified as elements in the quotient space by means of isochors and isotherms. From this it is concluded, that orbits can be used as a model for isomorphs, since these capture some of the isomorphic characteristics. As a frame of reference to the unknown differential equations, the heat equation is used as a simple example of a system of differential equations. Based on Olver [1993] a symmetry group Gi is established, for which the solution T(x, t) = je?(x?Kt) is group invariant. From the parameters (k, c, r), which define the contant K, an equivalence relation is created along with a group, Geq, that describes this relation. From this it is shown, that solutions to the heat equation are invariant to transformation by Geq. From the analysis of the heat equaiton in respect to symmetry groups, group invariant solutions and invariance towards transformations of the parameters in the heat equation it is postulatet, that the existence of isomorphs imply the presence of solutions that are invariant to the transformation of the underlying system of differential equations. Such an invariance should thus be pressent in all liquids that exhibit isomorphic behaviour. For IPLliquids it is surmised that the equivalence relation given by a constant ratio between r n/3 and T along isomophic curves has a relation to this invariance.
Speciale, Modelbyggervariant, 3. modul, 2009/10, id:395  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Ja 
Speciale, modelbyggervariant, 3. modul, 2009/10, id:396  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Ja 
We investigate a ODE model and appertaining claims from [PDG06]. A paradigmatic and fundamental discussion about continuity/discontinuity of the phenomena in question was undertaken. It was concluded that the standpoint taken in [PDG06], where they argue for discontinuity, is not entirely justified. In addition, it was shown that if discontinuity turns ourt to be true, a much more applicable methodology in the form af Kalman filtering, could be utilized instead of using stochastic differential equations as proposed in [PDG06]. Under the assumption of continuity of the phenomena in question, investigations was in turn undertaken. First of all, alternative parameter estimation techniques was tried out but with limeited results. It was hypothesized that glucagon had to be taken into account, and models extending the ODE model form [PDG06], was proposed. One of these actually attined enhanced physiologically reasonable model behaviour, but essential model deficiency is till present. Obvious problematic parts of the extended model, that could be responsible for the poor fitting results, was hypothesized for future work. This hypothesis also have physiological implications w.r.t. an increased understanding of the human glucose regulatory system.
Model, 1. modul, 2009, id:385  
Vejleder:  Viggo Andreasen 
Findes på RUb: 
English abstract
The present project propose a deterministic model for the replication of the bacterial chromosome based on the work by Mahaffy & Zyskind (1989). The main aim of this project is to examine how external factors influence on the stability of the model. In order to do this, we examine how the production of DnaA and the doubling rate of the cell mass, affects the models stability. This is done in an analytical analysis of the model near equilibrium, and further by a mumerical analysis of output values near equilibrium. Furthermore we propose and discuss extensions of the model. These extensions include modelling of RIDA, datA, Sequestration of the dnaAgene by SeqA and remodelling of oriC to contain multiple DnaAboxes. We conclude that there is a possibility for the existence of a transcritical bifucation, which resolves in a shift of stability.
Model, 2. modul, 2009, id:386  
Vejleder:  
Findes på RUb: 
Model, 1. modul, 2009, id:387  
Vejleder:  Johnny Ottesen 
Findes på RUb: 
Speciale, modelbyggervariant, 3. modul, 2009, id:388  
Vejleder:  Michael Pedersen 
IMFUFAtekst:  469 
Findes på RUb: 
Speciale, modelbyggervariant, 3. modul, 2009, id:389  
Vejleder:  Johnny Ottesen 
IMFUFAtekst:  469 
Findes på RUb:  ja 
English abstract
In this thesis two mathematical models of the hypothalamicpituitaryadrenalaxis (HPAaxis) are build using well known physiological mechanisms. The HPAaxis controls the secretion of the hormones CRH, ACTH and cortisol. The regulation of these hormones are important to human health. These hormones are the variables in two systems of coupled nonlinear differential equations that constitute the models. The models includes a negative feedback of cortisol on ACTH. The first model has a negative feedback from cortisol on CRH corresponding to the "standard biology textsbook" description of the HPAaxis. The second model allows a feedback from cortisol on CRH to be positive og negative depending on the cortisol concentration by including mechanisms from hippocampus. For parameter values in a physiologically relevant range it is investigated if the models are capable of guaranteeing solutions with reasonable levels in hormone concentration. It is investigated if the models are capable of producing the ultradian oscillations that are observed in data of hormone concentrations. It is investigated if an external imposed function on the differential equation governing the CRH concentration can cause the circadian rhythm that is seen in the concentrations of ACTH and cortisol. Previous papers of the HPAaxis [1] and [2] claim to make models showing ultradian oscillations. We analyze the two models and find significant drawbacks that must be elaborated for a successful model taking care of the physiological mechanisms of the HPAaxis. Results of analytical investigation of our models For both models the results of the investigation is that all solutions end in a trapping region in the positive octant of (R3), thus guaranteeing reasonable levels in hormone concentration. Within this trapping region there exists at least on fixed point. The first model has a unique fixed point. The unique fixed point is locally stable for all physiological choices of parameters. Therefore no Hopf bifurcation is possible as an explanation for the ultradian oscillations in data. For the second model more than one fixed point is possible. The stability of a fixed point is categorized depending on the sign of the feedback on CRH at the fixed point. A sufficient, easily applicable criteria for a unique, globally stable fixed point is formulated for a more general model. This can be applied on the two specific models. Results of numerical investigation of our models In the case of a unique fixed point this is asymptotically stable for all reasonable parameter values and initial conditions. Perturbating the parameters in the second model makes the system undergo a bifurcation where two new fixed points emerge. In the case of three fixed points there is one unstable fixed point and two asymptotically stable fixed points. For all reasonable values of parameters and initial conditions the solutions converge towards one of the two stable fixed points. Thus for reasonable parameter values neither of the models are capable of producing the ultradian oscillations. The analytical criteria for a globally stable fixed point is fulfilled for some set of parameters within physiologically relevant ranges for both models. An external input in the differential equation governing CRH is capable of showing circadian oscillations in ACTH and cortisol concentration.
Model, 2. modul, 2008, id:371  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
English abstract
The project is about the status of Social Choice theory as mathematical model. The theory treats aggregations of individual preferences over a set of choices to a collective preference of the same choices. This is often used in economics and decision theory. The project presents the main notions of the theory, as they are formulated by Kenneth Arrow and Amartya Sen. As an example of results within the model, Arrows Impossibility Theorem is presented and proofed. To show the range of the model, som examples from the use in economics and decision theory is presented. There is also presented a discussion about the foundation of the theory, represented of a liberalist and Marxist inspired critique. The conslusion says among other things, that the impossibility theorem and the model is often used in situations not included by these.
Model, 1. modul, 2008, id:372  
Vejleder:  
Findes på RUb:  Nej 
English abstract
The starting point for the project is a mathematical model made by McBryde et al. (2007). The model simulates the hospital acquired spread of patient infection with Methicillinresistant Staphyloccocus aureus (MRSA) in an intensive care unit. We clarify the predictions and results of the model. The purpose of this is to infer on how to make recommendations for interventions against hospital acquired MRSA. We analyse and take a critical standpoint regarding the construction of the model and our results. Many assumptions regarding to the spread of MRSA lie in the foundation of the model which can also be recognized in the parameters it includes. We discuss the importance of the two versions of the model which is both stochastic and deterministic. Furthermore we find it important to put the model into a broader perspective by discussing the assumptions behind, measurements for the output of the results and overall applicability. The purpose of this discussion is to be able to place McBryde et al. (2007) in a wider context of research projects with a mathematical approach to hospital acquired infections by antibiotic resistant bacteria.
Model, 1. modul, 2008, id:373  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Ja 
English abstract
This report investigates a matemathical model for the severe blood poisoning sepsis. The model is developed by Zuev et al. (2006) as a patient specific model with one patient specific, dimensionless parameter, H, which is dependent of the patients BMI. In the paper by Zuev et al. (2006) it is not shown how the model is actually made patient specific by means of only one parameter, which is why the argument is made in the report. We perform an investigation consisting of stability analysis and sensitivity analysis. The stability analysis consists of a primarily algebraic analysis, where steady states and eigenvalues of the Jacobian matrix are investigated, and a numerical analysis where we focus on the general dynamics of the model. We find 3 different dynamics for the model where the patient recovers if H >0.86, while the patients at (XXX) will experience a periodic course of disease without either recovery nor death as an outcome. Finally patients with H < 0.52 will certainly die if treatment is not initiated. By including the sensitivity analysis, we furthermore find, that the model is somewhat accurate for H < 1, but at larger values of H, the output of the model are related with great incertainty. In total we conclude that the model by Zuev et al. (2006) is sufficient to describe sepsis. It will, however, demand further work before it can be implemented. We recommend significantly more empiric evidence and a more biological ivestigation. Our analyses recommend a discussion about whether it is suitable to make a model with only one patient specific parameter. This discussion gain further relevance since this parameter is also a bifurcation parameter, and the parameter which the variables ahs the highest sensitivity too. In the paper by Zuev et al. (2006), H is proposed to be dependent of variuos things; age, lung capacity etc. By means we find criticizable. We also suggest an expansion of the model, to incorporate antibiotic treatments. Finally we give a suggestion to implementation  which will need to wait for further validation of the model to take place.
Model, 1 og 2. modul, 2007/2008, id:363  
Vejleder:  Johnny Ottesen og Carsten Lunde Petersen 
Findes på RUb:  Ja 
English abstract
Profession  modelbygger, 3. modul, 2007/2008, id:366  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
English abstract
In this project I study the advantages and the disadvantage by the use of Spectralmethods for the solution of the NavierStokesequations. My case will be the formation and dynamics of rings of smoke. I conclude that the Spectralmethods are too dependent on good conditions. And therefore my model is not particularly suitable for the simulation of rings of smoke
Model, 2. modul, 2007/2008, id:367  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
Model, 1 og 2. modul, 2007, id:352  
Vejleder:  Anders Madsen 
Findes på RUb:  Ja 
English abstract
Model, 1. modul, 2007, id:354  
Vejleder:  Johnny T. Ottesen 
Findes på RUb:  Ja 
English abstract
The purpose of this project is to examine what influence the regulation of blood vessel compliance has on syncope during tilt experiments. This is accomplished by introducing a compartmentmodel of the circulation and introducing models of the effect of gravity, regulation of blood vessel compliance and seepage af fluid from the blood to the surrounding tissues. Teh equations of the model are solved numerically with ODE15s in MatLab. It is concluded that the limitation of regulation of vein compliance may be the cause of syncope during tilt experiments.
Modelbyggervariant, 3. modul, 2007, id:357  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
Model, 1 og 2. modul, 2007, id:358  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
Speciale  modelbyggervariant, 3. modul, 2007, id:360  
Vejleder:  
Findes på RUb:  Ja 
English abstract
In this thesis we present a population forecast for women in Denmark 50 years from now. We use mathematical modeling to produce the forecast. The mathematical model consists of an accounting model and separate submodels for fertility, death frequency, emigration frequency and number of immigrants. In the setup of each submodel we use statistical methods, and we focus on locating and describing possible soures of uncertainty. The resulting forecast shows both the uncertainty of the size of the total population and the uncertainty of oneyear age classes 50 years from now. The uncertainty grows quickly during the perod. We therefore conclude that the value of the forecast as a basis for making decisions is limited after 30 yeras and almost nonexistent after 50 years. The most certain mechanism of the population forecast is death, and the greatest source of uncertainty is linked to fertility. The strongest weakness of the forecast is the description of migration, which is based on ad hocassumptions. However, the forecast of the oldest agegroups makes sense throughout the entire time horizon, whereas the forecast of the youngest agegruoups loses its applicability after 30 years. The results of the forecast are compared with corresponding population projections from DREAM and Statistics Denmark. Their expected projections are in accordance with the median curves of our forecast. Since the forecast shows that the uncertainty grows rapidly throughout the period, we conclude that the uncertainty grows rapidly throughout the period, we conclude that population projections are of limited value on time durations more than 5 to 10 years, without considerations of uncertainty.
speciale  Modelbyggervariant, 3. modul, 2007, id:361  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
English abstract
Modelbygger, 3. modul, 2006/2007, id:350  
Vejleder:  Johnny T. Ottesen 
Findes på RUb:  ja 
English abstract
Model, 1. modul, 2006/2007, id:351  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
English abstract
This paper describes an experimental study in control of a forced damped pendulum. We add a linear control parameter to the equation of the pendulum and by creating and using a pendulum simulation program ("pendulspillet"), we gain knowledge about how this parameter affects the motion o the pendulum. Experimentally we obtain a control algorithm that stabilizes a set of orbits, into a small neighborhood of a saddle. We propose an analytical investigation of the reulting direction and magnitude of the control, by analysis of the stablre and unstable manifolds, since we believe this would contribute to improvements of stabilization speed and energy comsumption of the control. Furthermore we conclude that, although this is a linear control problem, The OGYmethod does not work for this particular kind of control.
Model, 1 + 2. modul, 2006, id:337  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb: 
English abstract
Interfaces and interfacial tension are interesting in many ways, one of the more peculiar things, which is unlike other things in science, is the thermodynamical dependence on the shape af the interface. When we consider a thermodynamical system of two or more phases the thermodynamical equilibrium is determined by the shape of the interface between the phases. The study of this interfacial shape is a perfect application for differential geometry since the interfaces can always be described with smooth curves with only countably many (often zero) points of discontinuity. The differentiability of these curves is very important to the study of interfaces and has the interesting application that the pressure difference across the interface is proportional to the normal curvature of the interface. In this respect, interfacial phenomena is a study which can be read about in a math book, it is a direct application of differential geometry. This makes interfacial phenomena interesting and special compared to other scientific fields of study. The idea in this project is to map out the characteristics of interfaces, interfacial tension, and their applications. The project is driven by the interest in these strange phenomena and seek to uncover how they should be described. Finally one should note that the authors of this report are at different stages of their education and consequently the status of this report differ among the authors. For Anatol this report is writen as part of the second module, and as such it is supposed to be a mathematical modelling project. For Jesper and Jon on the other hand, this project is their final mathematical project.
Model, 1. modul, 2006, id:340  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb: 
Model, 1. modul, 2006, id:343  
Vejleder:  Bernhelm Booss Bavnbek 
Findes på RUb:  Ja 
English abstract
Model, 2. modul, 2006, id:344  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
Profession  modelbygger, 3. modul, 2006, id:345  
Vejleder:  
Findes på RUb:  Ja 
English abstract
Developing epidemiological models extend an important scientitic field of research within mathematical populations biology. Some of the most highly applied models are the classical SIR and SEIRmodels that descripe the dynamical pattern in a population exposed to a given disease. This paper contains an expansion of the SIRmodel to a TSIRmodel that incorporates timeseries, and the model is used on a set of data consisting of births and easles infected individuals in the years 19001967 in Copenhagen county. The group of susceptibles is reconstructed from the number of births by statistical regression modelling, and the amount of measles infected individuals is reproduced from the reconstructed susceptibles. Due to lack of stationarity in the susceptible group it turns out that the model is not adequate in its way of reproducing measles infected individuals in the original timeperiod. Meanwhile it is to som extend possible to gain a reproduction of the measles infected individuals when the model is applied to an appropriate time interval where the susceptibles exposes a relatively great stationarity. Thereby it is concluded that the useability of the model presumes that it is employed on a set of data that exposes a great deal of stationarity in the susceptible group in the entire modelled period.
Model, 1. modul, 2006, id:346  
Vejleder:  Johnny T. Ottesen 
Findes på RUb:  Ja 
English abstract
In this report a mathematical model describing a physical system consisting of a rubber tube placed in a fluidfilled tank is formulated and analysed. This experiment is not subjected to empirical inquiry, but our experiment has clear analogy to previous works. A pump is compressing the tube periodically at a place of asymmetry. The report has two main purposes: To formulate a model that investigates if a mean flow is existent, and to find out which mechanisms are responsible for creating a mean flow. The model is formulated in accordance to the compartment principle and consists of 11 1st order interdependent differential equations. The equations are formulated according to conservation of mass and Newtons 2. law. When the size of each compartment approaches zero the differential equations approksimates the equation of continuity and the linearized Euler equation in one dimension with a frictional term. In the final model inertans, resistance and compliance varies with the radius of the tube. These three terms are thought to contribute to the mean flow and we wish to find out which of the three contributes the most. The equations in the model are solved numerically in MatLab to establish a mean flow. Afterwards the inertans, resistance and compliance are kept constant in pairs. The report concludes that it is possible to create a frequency dependent mean flow, and that the inertans contributes primarily to the frequency dependent mean flow.
Modelprojekt, 1. modul, 2006, id:458  
Vejleder:   
Findes på RUb:  Nej 
Model projekt, . modul, 2005, id:330  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
English abstract
In the report at hand the twocomponent flow af a lavalamp is simulated. The level set approach is being used to handle the free surface and to compute the surface tension to be used in NavierStokes equation. The implementation of the level set function in the modules of Femlab, a finite elemts based program, is described. We conclude that the level set approach os well fit to iterate the position of the dynamic surface and to compute its curvature. In the present imolemantation the level set function distributes the surface forces over a broad band in both sides of the free surface. However, the dynamics if the level set function does not secure constant width of the band, which give rise to nonphysical surface forces in i regions where the level set function is being seriously deformed.
Modelprojekt, . modul, 2005, id:333  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb: 
Model, 2. modul, 2004/05, id:316  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb: 
Model, 1. modul, 2004/05, id:317  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
Model, 1. modul, 2004/05, id:318  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 2004, id:292  
Vejleder:  Michael Danielsen 
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 2004, id:297  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
Modelprojekt, 2. modul, 2004, id:300  
Vejleder:  Per Gregersen 
Findes på RUb:  Ja 
English abstract
In the project a mathematical analysis is made of GTAP  an economic model for quantitative analyses of policy issues on a global basis. The equations of GTAP are presented, together with the economical and mathematical assumptions necessary. A numerical solution to the initial value problem of GTAP is presented. A combined analysis based on the mathematical modelling process, which is described in the beginning of the project. In the analysis it is concluded that the economical and mathematical assumptions and their consequences are hidden from the modeluser. A theoretical validation of the models is therfore impossible. Furthermore, the model assumptions demand that the database is fitted to equilibrium, which together with the models economical assumptions also makes an empirical validation of the model impossible. It is therefore impossible to either theoretically or empirically validate the model, yet it is still used in policy decisionmaking. We ask for a debate on the consequences and uncertainties involved with quantitative use of the model.
Modelprojekt, 1. modul, 2004, id:301  
Vejleder:  Michael Danielsen 
Findes på RUb:  Nej 
Modelprojekt, 2. modul, 2004, id:302  
Vejleder:  Jesper Larsen 
Findes på RUb:  Nej 
English abstract
Modelprojekt, 1 + 2. modul, 2004, id:303  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Ja 
English abstract
We wish to find the answer to the following question "How is the vascular system affected by the breating process?". We have created a model of the vascular system, by using energy band formalism and wish to determine how the change in pressure will affect the blood flow. We have used mechnical and electrical laws to create the model, and estimated the parameters of the model so that we would receive values of the pressure, flow and volume close to those of experimental data. Our model consists of (among other) two arteryvein branches, wich represent the chest and liver. The model contains two branches because the chest and the liver are affected in different ways by the breathing process. The breathing process itself is accounted for in a change in pressure in the elements of the model, and we have examined how big an effect the depth of the breath, the length of the breath and the ground pressure have on the vascular system. The ground pressure is the minimum pressure in the chest, which keeps the lungs from collapsing. Byh variation of the parameters that control the depth of the breath, the length of the breath and the ground pressure, we can examine their effects on the vascular system. We have found that the length of the breath has got no effect on the blood flow, while both the depth of the breath and the ground pressure has. Deep breathing and high ground pressure result in a bigger flow.
Modelbygger, 3.. modul, 2004, id:306  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
English abstract
Modelprojekt, 1. modul, 2004, id:307  
Vejleder:  Poul Winther Andersen og Jesper Larsen 
Findes på RUb:  Ja 
Speciale  modelbygger, 3. modul, 2004, id:311  
Vejleder:  Johnny T. Ottesen 
Findes på RUb:  Ja 
English abstract
Modelprojekt, 1 og 2. modul, 2003, id:281  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Ja 
Professionsprojekt, modelbygger, 3. modul, 2003, id:282  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Nej 
Modelprojekt, 1. modul, 2003, id:285  
Vejleder:  Bernhelm Booss Bavnbek 
Findes på RUb:  Ja 
English abstract
The focal point of this project is routing in mobile adhoc networks. The original purpose was, to make possible an analytic comparison of reallife routing algorithms. This turned out to be difficult, and we have therefore worked with a broader question: What can mathematical models express, concerning routing in mobile adhoc networks, and what deficiencies does these models have with regard to an assessment of reallife routing algorithms ? We treat models based on stochastic graph theory. In particular we treat in depth two models. One which describes the probability that a finite network is connected, and another which describes how utilization of multiple routes, can decrease routing overhead by delaying the time, at which point new routes must be searched for. The conclusion is, that it is limited what we at present moment can say about routing, with the aid of mathematical models. However, as a start, we can give a few limited partial results. The studied models have several deficiencies, among others, the lack of a time aspect, and lack of named nodes. Furthermore it is questionable whether some of the assumptions, used in the models, are too restrictive.
Modelprojekt, 1. modul, 2003, id:296  
Vejleder:  Johnny Ottesen 
IMFUFAtekst:  420 
Findes på RUb:  Ja 
Modelbyggervarianten, 3. modul, 2002, id:268  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 2002, id:271  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
English abstract
When a vertical jet hits a leveled surface, an equilibrium will arise. Within a radius r of the jet, the level of the liquid will be low. At a distance r from the jet this level will increase abruptly. This ring discontinuity is called the hydraulic jump. While preparing a thesis at the University og Copenhagen [4] in 1995, two students observed that the hydraulic jump could assume a polygonal form. In 1997, this peculiar discovery gave rise to a model, which had the purpose of describing which physical mechanisms are the governing of the existence of the polygonshaped jump. The basis of the model is an asserted linetension combined with a balance of forces extered on the exterior of the jump. The development of this model is not documented in detail in any publication. In this report the existing model is deployed and analysed. This is done to clarify if the mechanisms of the model gives sufficient conditions to verify the existence of the polygonal jumps. The report concludes that the model is capable of reflecting a numberof qualitative characteristics of the jump. The linetension, however, is not substantiated in any physical principle. Because of this a new model, which is better theoretically founded, is desirable. In this report the controlling equations of a new model is deduced from the physical principle of mass preservation (among others). The two models will be briefly compared and discussed.
Modelprojekt, 1. Modul + 2. Modul. modul, 2002, id:274  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb:  Nej 
Speciale, modelbyggervariant, 3. modul, 2002, id:276  
Vejleder:  Carsten Lunde Pedersen (Matematik) Keld Helsgaun (Datalogi) 
Findes på RUb:  Ja 
This Master Thesis deals with Fractal Image Compression, a lossy method for compressing digital images. Fractal Image Compression is based on image modelling with fractal structures known as iterated function systems (IFS). Compression of an image is done by constructing a iterated function system having the image as its fixed point. The system is composed of contractive affine mappings between self similar regions of the image. The parameters describing the function system serves as the compressed representation of the image. Decompression is done by iterating the function system from a random image, thus generating the fixed point of the system i.e. the original image. This thesis deals with three aspects of fractal compression, including mathematical foundation, implementation and useability of the method. The underlying mathematics is explored, covering traditional IFS, IFS with Probabilities and Recurrent IFS. Based on the mathematical theory, a prototype for fractal compression is implemented and then compared to both JPEG and an existing fractal compression application. We conclude that the most important mathematical results that makes fractal compression possible are the collage theorem for compression and the fixed point theorem for decompression. For the implementation of fractal compression methods, partitioned iterated function systems (PIFS) are used. These systems are not as mathematically well founded as the traditional IFS, but solves a number of problems that hinder implementation of traditional IFS in applications for image compression. Even though the prototype proves fractal compression to be a working method for lossy image compression, our tests show the quality vs. Compression ratio to be poor and not comparable to standard JPEG compression. Thus, fractal compression as implemented in the prototype is a poor substitute for common lossy image compression methods.
Modelprojekt, 1. modul, 2002, id:277  
Vejleder:  
Findes på RUb:  Ja 
Speciale, modelbyggervariant, 3. modul, 2002, id:280  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
English abstract
In this master thesis we present an agestructured school oriented epidemic model. The model is in two parts; one part describes a single epidemic season using a standard epidemic model, while the other part is a descrete seasontoseason map which describes the loss of susceptibles due to the epidemic. The analysis of the model focus on periodic solutions of the model. If a threshold value exceeds unity the map has an endemic stationary state. Without the introduction of an agedependent reduction in the susceptibility or infectiousness, the endemic stationary state is stable and possible oscilations of infected are of a size that does not correspond with data. With the introduction of an agedependent reduction in the infectibility, the model shows both stablre and unstable oscilations. For a limited choice of parameter values and stating points the existens of an attractor is established.
Model, 1. modul, 2001, id:261  
Vejleder:  Erik von Essen 
Findes på RUb:  Nej 
Model, 2. modul, 2001, id:262  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
Model, 1 og 2. modul, 2001, id:263  
Vejleder:  
Findes på RUb:  Ja 
Professionsprojekt, Modelbyggervarianten, 3. modul, 2000, id:240  
Vejleder:  Johnny Ottesen 
IMFUFAtekst:  380 
Findes på RUb:  Nej 
English abstract
In this report we present an extension of a mathematical model of pressure as a function of time and volume in the left ventricle of the heart. It is useful both at isovolumetric contraction and at ejection to the cardiovascular system. The model is an extension of a model originally proposed by J. P. Mulier. The goal of this extension is a possible scaling of the model so as to validate it at different heart rates. Additionally, this new model is implemented into a cardiovascular model.
Modelprojekt, 2. modul, 2000, id:245  
Vejleder:  Jesper Larsen 
IMFUFAtekst:  388 
Findes på RUb:  Ja 
English abstract
In the following paper we present the main results of a one term graduate student project. The entire work is presented, in Danish, in Jakobsen & Niss. We analyse the form of the fluiddynamical equation of motion, in a two dimensional model with distributed sources and periodic boundary conditions. We conclude that the form of the equation of motion depends on the assumptions about the fluid entering and leaving the model. Futher we look at the total kinetic energy in the model, and how it depends on the assumptions.
Professionsprojekt, Modelbyggervarianten, 3. modul, 2000, id:247  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
Modelprojekt, 2. modul, 19992000, id:246  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
English abstract
Modelprojekt, 1. modul, 1999, id:220  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
Modelprojekt, . modul, 1999, id:222  
Vejleder:  
Findes på RUb: 
Ingen projektrapport afleveret til MATSN.
Modelprojekt, 2. modul, 1999, id:224  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
Professionsprojekt, modelbyggervarianten, 3. modul, 1999, id:225  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
Modelprojekt, 2. modul, 1999, id:227  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 1999, id:228  
Vejleder:  Bernhelm BoossBavnbek 
IMFUFAtekst:  386 
Findes på RUb:  Nej 
Projektet behandler problemet om hvorvidt man v.h.a. formelle matematiske metoder kan sammenligne og kvalitetsvurdere forskellige mandatfordelingsmetoder, og derigennem evt. bestemme den mest neutrale.
Modelprojekt, 2. modul, 1999, id:230  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
Modelprojekt, 1 + 2. modul, 1999, id:231  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
Modelprojekt, 2. modul, 1999, id:232  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 1999, id:234  
Vejleder:  John Villumsen 
Findes på RUb:  Ja 
Projektrapporten omhandler matematiske modeller anvendt i kombinatorisk kemi.
Professionsprojekt, Modelbyggervarianten, 3. modul, 1999, id:236  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
English abstract
Professionsprojekt, Modelbyggervarianten, 3. modul, 1999, id:238  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
Modelprojekt, 1 + 2. modul, 1999, id:242  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
Modelprojekt, 2. modul, 1998, id:213  
Vejleder:  Johnny Ottesen 
IMFUFAtekst:  356 
Findes på RUb:  Ja 
Model og videnskabsfagsprojekt, 2. modul, 1998, id:214  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Ja 
Professionsprojekt, modelbyggervarianten, 3. modul, 1998, id:217  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 199798, id:207  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 1997, id:198  
Vejleder:  
Findes på RUb:  Ja 
In the following I have examined the use of a stochastic decision function in Bayesian sampling planning. More precisely I examined the problem of accepting or rejecting a batch of articles described by a normally distributed average weight. Such a decision can be made by using a polynomial loss function. If we let the loss function be linearly dependent on the size of the samlpe, we can find the optimal size of the sample. In this report I have examined the appliance of a stochastic decision function proposed by /Ho, 1995). The purpose of this decision function is to allow for the buyer to bargain after the sample have been tested. I have written a program in Mathematica that can find the optimal size of the sample and loss function. Results from this program show that the stochastic decision function does not have a great influcence on the minimizing sample size.
Modelprojekt, . modul, 1997, id:196  
Vejleder:  Johnny Ottesen og Jacob Jacobsen 
Findes på RUb:  Ja 
Model, 2. modul, 1997, id:193  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  nej 
Modelprojekt, 2. modul, 1997, id:188  
Vejleder:  
IMFUFAtekst:  337 
Findes på RUb:  Ja 
Modelbyggervariant, 3. Modul. modul, 1997, id:190  
Vejleder:  Mogens N. Olesen 
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 1997, id:202  
Vejleder:  Bernhelm BoossBavnbek 
IMFUFAtekst:  347 
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 1997, id:203  
Vejleder:  Erik von Essen 
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 1997, id:204  
Vejleder:  Jesper Larsen 
Findes på RUb:  Nej 
Modelprojekt, 2. modul, 1997, id:205  
Vejleder:  Stig Andur Pedersen 
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 1997, id:463  
Vejleder:  Stig Andur Pedersen 
Findes på RUb: 
Professionsprojekt  modelbyggervariant, 3. modul, 1996/97, id:186  
Vejleder:  Jacob M. Jacobsen og Jesper Larsen 
IMFUFAtekst:  331 
Findes på RUb:  Ja 
Model, 1. modul, 1996, id:192  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
Modelprojekt, 2. modul, 1996, id:176  
Vejleder:  Mogens Brun Heefelt 
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 1996, id:177  
Vejleder:  Jacob M. Jacobsen 
Findes på RUb:  Ja 
Modelprojekt, . modul, 1996, id:182  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
Model, 2. modul, 1996, id:191  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Ja 
Modelprojekt, 2. modul, 1996, id:165  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
Modelprojekt, 2. modul, 1996, id:166  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
Praksisprojekt modelbygning, . modul, 1996, id:172  
Vejleder:  Anders Hede Madsen 
Findes på RUb: 
Praktisk modelbyggerprojekt, 3. modul, 1995, id:158  
Vejleder:  Jesper Larsen 
IMFUFAtekst:  301 
Findes på RUb: 
Modelprojekt, . modul, 1995, id:159  
Vejleder:  
IMFUFAtekst:  299 
Findes på RUb: 
Modelprojekt, 1. modul, 1995, id:167  
Vejleder:  Erik von Essen 
Findes på RUb: 
Modelprojekt, 2. modul, 1994, id:130  
Vejleder:  Jesper Larsen 
Findes på RUb: 
Modelprojekt, . modul, 1991/92, id:104  
Vejleder:  Gestur Olafsson 
Findes på RUb: 