Matematisk institutt
http://hdl.handle.net/10852/5
Wed, 19 Jun 2019 08:48:11 GMT2019-06-19T08:48:11ZComponent importance in multistate directed network flow systems
http://hdl.handle.net/10852/67665
Component importance in multistate directed network flow systems
Kalinowska, Martyna
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/676652019-01-01T00:00:00ZAn investigation into the interaction between waves and ice
http://hdl.handle.net/10852/67624
An investigation into the interaction between waves and ice
Rabault, Jean
The polar regions are the focus of increased attention due to a combination of environmental, political and economic reasons. In order to help support human activities in the arctic and monitor the state of the ecosystem, detailed understanding and models of the state of sea ice are necessary. Sea ice is affected by incoming waves, and therefore studying wave-ice interaction is an important part of this effort. In my thesis work, I investigated how waves propagate through different types of ice covers.
More specifically, two phenomena of practical importance were studied. First, I looked at how waves attenuate as they propagate through sea ice. This, in turn, determines how much ice can be broken by incoming waves and should be part of waves and ice forecasts. Second, I investigated the currents created under the ice as a consequence of the propagation of the waves. There it was shown experimentally that mean currents can arise, which are expected to play a role in the dispersion of nutriments and pollutants.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/676242018-01-01T00:00:00ZExperiments on wave propagation in grease ice: combined wave gauges and particle image velocimetry measurements
http://hdl.handle.net/10852/67612
Experiments on wave propagation in grease ice: combined wave gauges and particle image velocimetry measurements
Rabault, Jean; Sutherland, Graig J.; Jensen, Atle; Christensen, Kai Håkon; Marchenko, Aleksey
Water wave attenuation by grease ice is a key mechanism for the polar regions, as waves in ice influence many phenomena such as ice drift, ice breaking and ice formation. However, the models presented so far in the literature are limited in a number of regards, and more insights are required from either laboratory experiments or fieldwork for these models to be validated and improved. Unfortunately, performing detailed measurements of wave propagation in grease ice, either in the field or in the laboratory, is challenging. As a consequence, laboratory data are relatively scarce, and often consist of only a couple of wave elevation measurements along the length of the wave tank. We present combined measurements of wave elevation using an array of ultrasonic probes, and water kinematics using particle image velocimetry (PIV), in a small-scale wave tank experiment. Experiments are performed over a wider frequency range than has been previously investigated. The wave elevation measurements are used to compute the wavenumber and exponential damping coefficient. In contrast to a previous study in grease ice, we find that the wavenumber is consistent with the mass loading model, i.e. it increases compared with the open water case. Wave attenuation is compared with a series of one-layer models, and we show that they satisfactorily describe the viscous damping occurring. PIV data are also consistent with exponential wave amplitude attenuation, and a proper orthogonal decomposition analysis reveals the existence of mean flows under the ice that are a consequence of the displacement and packing of the ice induced by the gradient in the wave-induced stress. Finally, we show that the dynamics of grease ice can generate eddy structures that inject eddy viscosity into the water under the grease ice, which would lead to enhanced mixing and participating in energy dissipation.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/676122019-01-01T00:00:00ZCurving to fly: Synthetic adaptation unveils optimal flight performance of whirling fruits
http://hdl.handle.net/10852/67611
Curving to fly: Synthetic adaptation unveils optimal flight performance of whirling fruits
Rabault, Jean; Fauli, Richard Andre; Carlson, Andreas
Appendages of seeds, fruits and other diaspores (dispersal units) are essential for their wind dispersal, as they act as wings and enable them to fly. Whirling fruits generate an auto-gyrating motion from their sepals, a leaf like structure, which curve upwards and outwards, creating a lift force that counteracts gravitational force. The link of the fruit’s sepal shape to flight performance, however, is as yet unknown. We develop a theoretical model and perform experiments for doublewinged bio-mimetic 3D-printed fruits, where we assume that the plant has a limited amount of energy that it can convert into a mass to build sepals and, additionally, allow them to curve. Both hydrodynamic theory and experiments involving synthetic, double-winged fruits show that to produce a maximal flight time there is an optimal fold angle for the desiccated sepals. A similar sepal fold angle is found for a wide range of whirling fruits collected in the wild, highlighting that wing curvature can aid as an efficient mechanism for wind dispersal of seeds and may improve the fitness of their producers in the context of an ecological strategy.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/676112019-01-01T00:00:00ZArtificial neural networks trained through deep reinforcement learning discover control strategies for active flow control
http://hdl.handle.net/10852/67610
Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control
Rabault, Jean; Kuchta, Miroslav; Jensen, Atle; Reglade, Ulysse; Cerardi, Nicolas
We present the first application of an Artificial Neural Network trained through a Deep Reinforcement Learning agent to perform active flow control. It is shown that, in a 2D simulation of the Kármán vortex street at moderate Reynolds number (Re = 100), our Artificial Neural Network is able to learn an active control strategy from experimenting with the mass flow rates of two jets on the sides of a cylinder. By interacting with the unsteady wake, the Artificial Neural Network successfully stabilizes the vortex alley and reduces drag by about 8 %. This is performed while using small mass flow rates for the actuation, on the order of 0.5 % of the mass flow rate intersecting the cylinder cross section once a new pseudo-periodic shedding regime is found. This opens the way to a new class of methods for performing active flow control.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/676102019-01-01T00:00:00ZKinematikken i bølger over en grunne
http://hdl.handle.net/10852/67561
Kinematikken i bølger over en grunne
Jorde, Stian
Vi har sett på hvordan kinematikken i et irregulært, langkammet bølgefelt utvikler seg når bølgefeltet beveger seg over en grunne. Vi har funnet at den generelle oppførselen til skjevheten til hastighetsmålingene reflekterer den til overflatemålingene, men med mindre utslag. Vi har derimot ikke klart å finne noen sammenheng mellom kurtosene til hastighetsmålingene og overflatemålingene. Kurtosene ser ut til å oppnå maksimumer på forskjellige steder langs grunna. Resultatene våre betyr at i den grad økt kurtose antyder økt sannsynlighet for freake hendelser vil økte sannsynligheter for freake hendelser oppstå under forskjellige forhold for overflatehevninger og hastigheter i bølgefeltet.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/675612018-01-01T00:00:00ZModulational instability and rogue waves in crossing sea states
http://hdl.handle.net/10852/67534
Modulational instability and rogue waves in crossing sea states
Gramstad, Odin; Bitner-Gregersen, Elzbieta; Trulsen, Karsten; Nieto Borge, Jose Carlos
Wave statistical properties and occurrence of extreme and rogue waves in crossing sea states are investigated. Compared to previous studies a more extensive set of crossing sea states are investigated, both with respect to spectral shape of the individual wave systems and with respect to the crossing angle and separation in peak frequency of the two wave systems. It is shown that, because of the effects described by Piterbarg, for a linear sea state the expected maximum crest elevation over a given surface area depends on the crossing angle so that the expected maximum crest elevation is largest when two wave systems propagate with a crossing angle close to 90°. It is further shown by nonlinear phase-resolving numerical simulations that nonlinear effects have an opposite effect, such that maximum sea surface kurtosis is expected for relatively large and small crossing angles, with a minimum around 90°, and that the expected maximum crest height is almost independent of the crossing angle. The numerical results are accompanied by analysis of the modulational instability of two crossing Stokes waves, which is studied using the Zakharov equation so that, different from previous studies, results are valid for arbitrary-bandwidth perturbations. It is shown that there is a positive correlation between the value of kurtosis in the numerical simulations and the maximum unstable growth rate of two crossing Stokes waves, even for realistic broadband crossing sea states.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/675342018-01-01T00:00:00ZQuantitative Prediction of Multivalent Ligand-Receptor Binding Affinities for Influenza, Cholera, and Anthrax Inhibition
http://hdl.handle.net/10852/67514
Quantitative Prediction of Multivalent Ligand-Receptor Binding Affinities for Influenza, Cholera, and Anthrax Inhibition
Liese, Susanne; Netz, Roland R.
Multivalency achieves strong, yet reversible binding by the simultaneous formation of multiple weak bonds. It is a key interaction principle in biology and promising for the synthesis of high-affinity inhibitors of pathogens. We present a molecular model for the binding affinity of synthetic multivalent ligands onto multivalent receptors consisting of n receptor units arranged on a regular polygon. Ligands consist of a geometrically matching rigid polygonal core to which monovalent ligand units are attached via flexible linker polymers, closely mimicking existing experimental designs. The calculated binding affinities quantitatively agree with experimental studies for cholera toxin (n = 5) and anthrax receptor (n = 7) and allow to predict optimal core size and optimal linker length. Maximal binding affinity is achieved for a core that matches the receptor size and for linkers that have an equilibrium end-to-end distance that is slightly longer than the geometric separation between ligand core and receptor sites. Linkers that are longer than optimal are greatly preferable compared to shorter linkers. The angular steric restriction between ligand unit and linker polymer is shown to be a key parameter. We construct an enhancement diagram that quantifies the multivalent binding affinity compared to monovalent ligands. We conclude that multivalent ligands against influenza viral hemagglutinin (n = 3), cholera toxin (n = 5), and anthrax receptor (n = 7) can outperform monovalent ligands only for a monovalent ligand affinity that exceeds a core-size dependent threshold value. Thus, multivalent drug design needs to balance core size, linker length, as well as monovalent ligand unit affinity.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/675142018-01-01T00:00:00ZRogue Waves in the Ocean, the Role of Modulational Instability, and Abrupt Changes of Environmental Conditions that Can Provoke Non Equilibrium Wave Dynamics
http://hdl.handle.net/10852/67513
Rogue Waves in the Ocean, the Role of Modulational Instability, and Abrupt Changes of Environmental Conditions that Can Provoke Non Equilibrium Wave Dynamics
Trulsen, Karsten
Modulational instability is an efficient mechanism for the generation of rogue waves in the limit of narrow-banded and long-crested wave fields. While such wave fields are easily achieved in laboratories, there appears to be lacking evidence that known occurrences of rogue waves in the ocean (e.g. Draupner “New Year” wave, Andrea wave) or ship accidents that could have been provoked by rogue waves (e.g. the Prestige accident) actually happened in sea states favorable for the modulational instability to have played an important role. The absence of modulational instability does not mean that nonlinear interactions are unimportant. Here we point out recent results that suggest large deviations from Gaussian statistics can happen due to nonlinearity in the absence of modulational instability, the key ingredient seems to be that the wave field is brought into a state of non-equilibrium.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/675132018-01-01T00:00:00ZStochastic systems with memory and jumps
http://hdl.handle.net/10852/67500
Stochastic systems with memory and jumps
Banos, David; Cordoni, Francesco; Di Nunno, Giulia; Di Persio, Luca; Røse, Elin Engen
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/675002018-01-01T00:00:00ZDivisibility and Information Flow Notions of Quantum Markovianity for Noninvertible Dynamical Maps
http://hdl.handle.net/10852/67415
Divisibility and Information Flow Notions of Quantum Markovianity for Noninvertible Dynamical Maps
Chruscinski, Dariusz; Rivas, Angel; Størmer, Erling
We analyze the relation between completely positive (CP) divisibility and the lack of information backflow for an arbitrary—not necessarily invertible—dynamical map. It is well known that CP divisibility always implies a lack of information backflow. Moreover, these two notions are equivalent for invertible maps. In this Letter, it is shown that for a map which is not invertible the lack of information backflow always implies the existence of a completely positive propagator which, however, needs not be trace preserving. Interestingly, for a wide class of image nonincreasing dynamical maps, this propagator becomes trace preserving as well, and hence, the lack of information backflow implies CP divisibility. This result sheds new light into the structure of the time-local generators giving rise to CP-divisible evolutions. We show that if the map is not invertible then positivity of dissipation/decoherence rates is no longer necessary for CP divisibility.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/674152018-01-01T00:00:00ZTurbulence Scaling Comparisons in the Ocean Surface Boundary Layer
http://hdl.handle.net/10852/67414
Turbulence Scaling Comparisons in the Ocean Surface Boundary Layer
Esters, Leonie; Breivik, Øyvind; Landwehr, Sebastian; ten Doeschate, Anneke; Sutherland, Graig; Christensen, Kai Håkon; Bidlot, Jean-Raymond; Ward, Brian
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/674142018-01-01T00:00:00ZCharacterization of flow dynamics and reduced-order description of experimental two-phase pipe flow
http://hdl.handle.net/10852/67413
Characterization of flow dynamics and reduced-order description of experimental two-phase pipe flow
Viggiano, Bianca; Skjæraasen, Olaf; Schümann, Heiner; Tutkun, Murat; Cal, Raúl Bayoán
Two-phase dispersed and slug flows in a pipe are investigated using proper orthogonal decomposition (POD). The data are acquired through tomographic reconstruction of X-ray measurements, where holdup, cross-sectional phase distributions and phase interface characteristics are obtained. Instantaneous phase fractions of the flow fields are analyzed and reduced-order descriptions of the flow are achieved. The dispersed flow displays coherent features for the first few modes near the center of the pipe, representing the liquid-liquid interface location while the slug flow case shows coherent features that correspond to the cyclical formation of the slug in the first ten modes. For slug flow, the first two modes capture the liquid-dominated slug body region and the Taylor bubble/liquid film region, respectively. The reconstructions of the fields indicate that main features are observed in the low order descriptions utilizing less than one percent of the degrees of freedom of the full order descriptions. POD temporal coefficients a1, a2 and a3 show interdependence for the slug flow case. The coefficients also describe the phase fraction holdup as a function of time for both dispersed and slug flow.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/674132018-01-01T00:00:00ZA proposed tandem mechanism for memory storage in neurons involving magnetite and prions
http://hdl.handle.net/10852/67412
A proposed tandem mechanism for memory storage in neurons involving magnetite and prions
Alfsen, Erik; Størmer, Fredrik; Njå, Arild; Walløe, Lars
Knowledge about how information is stored in neurons of animals and in the human brain is still incomplete. A hypothesis related to long-term changes in synaptic efficiency has strong experimental support, but does not seem to be able to explain all observations. It has recently been proposed that magnetite together with a prionlike protein could be involved in a tandem mechanism for storage of memory in neurons in which electric impulses are received and reshaped by the magnetite to a form which can be accepted by the protein. The magnetite crystals can be magnetized by an electrical impulse, but they cannot hold the magnetism, which drops to zero after each impulse. Therefore, magnetite cannot be the substance in which information is stored. In the present paper we explain how a tandem mechanism could function in a neuron in which magnetite is situated together with a prion-like protein close to the cell surface membrane of the axon. We assume in addition that the information is stored in special storage neurons. With this, we propose a new hypothesis for information storage in neurons which could operate in addition to synaptic plasticity, but perhaps in different neurons.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/674122018-01-01T00:00:00ZStochastic functional differential equations and sensitivity to their initial path
http://hdl.handle.net/10852/67108
Stochastic functional differential equations and sensitivity to their initial path
Baños, David; Di Nunno, Giulia; Haferkorn, Hannes Hagen; Proske, Frank Norbert
We consider systems with memory represented by stochastic functional differential equations. Substantially, these are stochastic differential equations with coefficients depending on the past history of the process itself. Such coefficients are hence defined on a functional space. Models with memory appear in many applications ranging from biology to finance. Here we consider the results of some evaluations based on these models (e.g. the prices of some financial products) and the risks connected to the choice of these models. In particular we focus on the impact of the initial condition on the evaluations. This problem is known as the analysis of sensitivity to the initial condition and, in the terminology of finance, it is referred to as the Delta. In this work the initial condition is represented by the relevant past history of the stochastic functional differential equation. This naturally leads to the redesign of the definition of Delta. We suggest to define it as a functional directional derivative, this is a natural choice. For this we study a representation formula which allows for its computation without requiring that the evaluation functional is differentiable. This feature is particularly relevant for applications. Our formula is achieved by studying an appropriate relationship between Malliavin derivative and functional directional derivative. For this we introduce the technique of randomisation of the initial condition.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/671082018-01-01T00:00:00ZJoin of hexagons and Calabi-Yau threefolds
http://hdl.handle.net/10852/66817
Join of hexagons and Calabi-Yau threefolds
Meyer, Fredrik
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10852/668172017-01-01T00:00:00ZImproved Method for Calculating Exceedance Probabilities of Environmental Contours
http://hdl.handle.net/10852/66752
Improved Method for Calculating Exceedance Probabilities of Environmental Contours
Barbosa, Maria Hjelset
Environmental contours is commonly applied in e.g. ship design. The aim of this thesis is to study different methods of constructing environmental contours of sea states, and look at properties of these. Especially we will look at estimation of exceedance probabilities. Estimation of exceedance probabilities are done through Monte Carlo simulation. This is not a trivial task, since in principal we have to examine an unlimited amount of possible failure regions. In this thesis we use a new method of doing this. The method will be used on a number of examples where the joint distribution of the sea states is estimated from real data. We will also explore the case when the joint distribution is a mixture of distributions. This is of interest since it can model e.g, seasonal variations or variations of wave directions. For all examples we will compare the new method to former methods of estimating exceedance probabilities. Traditionally, environmental contours are constructed based on the well-known Rosenblatt transformation. There is, however, a challenge to this approach; due to the effects of the transformation, the probabilistic properties of the resulting environmental contour can be difficult to interpret. The tendency is for Rosenblatt contours to have exceedance probabilities higher than desired. In this thesis we will use our new method to evaluate the Rosenblatt contour and use the evaluation as basis to adjust the contours to the desired exceedance probability. Finally, we will compare the adjusted Rosenblatt contours to the contours constructed by Monte Carlo simulations, to see which contour is best in different applications.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/667522018-01-01T00:00:00ZOptimal reassuranse per portefølje
http://hdl.handle.net/10852/66749
Optimal reassuranse per portefølje
Torgersen, Linn Bui
Det forsikringsselskaper ønsker minst er stor risiko og høye erstatningsbeløp til kundene. For å unngå stor risiko, kan et forsikringsselskap reforsikre seg hos én eller flere reassurandører. Tilgjengjeld må de betale premie på reassuransen. Det er naturlig at dette foregår gjennom en reassuransekontrakt, hvor aktørene blir enige om hvor mye som skal erstattes når skader oppstår. Såkalte axb-kontrakter som vi skal se på i denne oppgaven, er de vanligste kontraktene som blir brukt. Disse kontraktene avhenger av nedre grense a og øvre grense b. Det vi er interessert i, er hva disse grensene bør ligge på for å oppnå en optimal reassuranse, gitt et kriterium som sier noe om avveiing mellom risiko og forventet gevinst. Vi skal i denne oppgaven optimere den nedre grensen a, ved hjelp av simuleringer. Deretter er vi interessert i hvordan denne nedre grensen er avhenger av parameterusikkerhet, som igjen avhenger av mengden tilgjengelige data, samt hvordan det avhenger av forholdet mellom marginen til henholdsvis cedent og reassurandør, og også hvor tunghalet fordelingen for skadestørrelsene er. Dette skal vi analyse ved hjelp av en simuleringstudie, hvor vi varierer størrelse på datasettet og parametere som inngår i modellen.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/667492018-01-01T00:00:00ZPricing of Unit-Linked Insurance Policies with respect to Turbulent Stock Markets
http://hdl.handle.net/10852/66748
Pricing of Unit-Linked Insurance Policies with respect to Turbulent Stock Markets
Liu, Wei
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/667482018-01-01T00:00:00ZUniversal base spaces and smoothability of face schemes of polyhedral manifolds
http://hdl.handle.net/10852/66634
Universal base spaces and smoothability of face schemes of polyhedral manifolds
Stavnes, Jarle
Teknikker og konsepter som er knyttet til kombinatorikk blir ofte brukt innenalgebraisk geometri. Et eksempel på dette er toriske degenerasjoner, som kanbrukes til å besvare visse klassifiseringsspørsmål. I denne avhandlingen har jeg regnet ut og undersøkt de universelle deformasjonsrommene til en klasse av slike toriske degenerasjoner.
I avhandlingen min har jeg undersøkt deformasjonsteorien til toriske degenerasjoner, og betraktet den underliggende kombinatorikken til deres tilhørende polyhedrale mangfoldigheter. Dette har også blitt knyttet opp mot klassiske resultater om Stanley-Reisner ringer.
Toriske degenerasjoner er en type singulære algebraiske varieteter som kan brukes til å komplementere modulirom tilhørende ulike typer av glatte algebraiske varieteter. Ved å bestemme deres universelle deformasjonsrom kan man si noe om strukturen til modulirommet de tilhører. Spesielt er spørsmålet om glattbarhet relevant for hvorvidt de befinner seg på komponenten som er av interesse, nemlig den som inneholder glatte varieteter.
Her vil deformasjonsrommet og deres glattingskomponenter bli beregnet for en klasse av toriske degenerasjoner som kombinatorisk svarer til 2-dimensjonale mangfoldigheter. Dette generaliserer tidligere analoge resultater for Stanley-Reisner skjemaer.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/666342019-01-01T00:00:00Z