Matematisk institutt
http://hdl.handle.net/10852/6
Mon, 22 Apr 2019 10:57:03 GMT
20190422T10:57:03Z

An 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 waveice 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 GMT
http://hdl.handle.net/10852/67624
20180101T00:00:00Z

Experiments 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 smallscale 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 onelayer 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 waveinduced 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 GMT
http://hdl.handle.net/10852/67612
20190101T00:00:00Z

Curving 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 autogyrating 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 biomimetic 3Dprinted 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, doublewinged 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 GMT
http://hdl.handle.net/10852/67611
20190101T00:00:00Z

Artificial 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 pseudoperiodic 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 GMT
http://hdl.handle.net/10852/67610
20190101T00:00:00Z

Modulational 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; BitnerGregersen, 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 phaseresolving 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 arbitrarybandwidth 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 GMT
http://hdl.handle.net/10852/67534
20180101T00:00:00Z

Quantitative Prediction of Multivalent LigandReceptor Binding Affinities for Influenza, Cholera, and Anthrax Inhibition
http://hdl.handle.net/10852/67514
Quantitative Prediction of Multivalent LigandReceptor 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 highaffinity 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 endtoend 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 coresize 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 GMT
http://hdl.handle.net/10852/67514
20180101T00:00:00Z

Rogue 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 narrowbanded and longcrested 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 nonequilibrium.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/67513
20180101T00:00:00Z

Stochastic 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 GMT
http://hdl.handle.net/10852/67500
20180101T00:00:00Z

Divisibility 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 timelocal generators giving rise to CPdivisible 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 GMT
http://hdl.handle.net/10852/67415
20180101T00:00:00Z

Turbulence 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, JeanRaymond; Ward, Brian
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/67414
20180101T00:00:00Z

Characterization of flow dynamics and reducedorder description of experimental twophase pipe flow
http://hdl.handle.net/10852/67413
Characterization of flow dynamics and reducedorder description of experimental twophase pipe flow
Viggiano, Bianca; Skjæraasen, Olaf; Schümann, Heiner; Tutkun, Murat; Cal, Raúl Bayoán
Twophase dispersed and slug flows in a pipe are investigated using proper orthogonal decomposition (POD). The data are acquired through tomographic reconstruction of Xray measurements, where holdup, crosssectional phase distributions and phase interface characteristics are obtained. Instantaneous phase fractions of the flow fields are analyzed and reducedorder 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 liquidliquid 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 liquiddominated 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 GMT
http://hdl.handle.net/10852/67413
20180101T00:00:00Z

A 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 longterm 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 prionlike 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 GMT
http://hdl.handle.net/10852/67412
20180101T00:00:00Z

Stochastic 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 GMT
http://hdl.handle.net/10852/67108
20180101T00:00:00Z

Join of hexagons and CalabiYau threefolds
http://hdl.handle.net/10852/66817
Join of hexagons and CalabiYau threefolds
Meyer, Fredrik
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/66817
20170101T00:00:00Z

Universal 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 StanleyReisner 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 2dimensjonale mangfoldigheter. Dette generaliserer tidligere analoge resultater for StanleyReisner skjemaer.
Tue, 01 Jan 2019 00:00:00 GMT
http://hdl.handle.net/10852/66634
20190101T00:00:00Z

Whitehead torsion of inertial hcobordisms
http://hdl.handle.net/10852/66249
Whitehead torsion of inertial hcobordisms
Jahren, Bjørn; Kwasik, Slawomir
We study the Whitehead torsion of inertial hcobordisms, continuing an investigation started in [12]. Of particular interest is a nested sequence of subsets of the Whitehead group, and a number of examples are given to show that these subsets are all different in general. The main new results are Theorem 2.5, Theorem 2.6, Theorem 2.7. Proposition 5.2 is a partial correction to [12, Lemma 8.1].
© 2018. This manuscript version is made available under the CCBYNCND 4.0 license http://creativecommons.org/licenses/byncnd/4.0/
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/66249
20180101T00:00:00Z

Dynamic ion shadows behind finitesized objects in collisionless magnetized plasma flows
http://hdl.handle.net/10852/66038
Dynamic ion shadows behind finitesized objects in collisionless magnetized plasma flows
Miloch, Wojciech Jacek; Jung, Hendrik; Darian, Diako; Greiner, Franko; Mortensen, Mikael; Piel, A.
The potential and density wake behind a finitesized object in a magnetized collisionless plasma flow is studied with selfconsistent numerical simulations. With increasing magnetization of the plasma, the standard picture of ion focusing in the wake for plasmas with large electron to ion temperature ratios becomes invalid. A strong magnetic field parallel to the flow direction leads to a chain of ion depletions in the wake and enhanced ion density at their envelopes. This is due to a novel mechanism of a dynamic ion shadow, which is not the geometrical shadow of the finitesized object. It corresponds to a change in topology of the wake potential. Complex ion trajectories resulting from electrostatic collisions with the object can lead to significant variations in electrical charging of other objects in the wake.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/66038
20180101T00:00:00Z

Parametric or nonparametric: The FIC approach
http://hdl.handle.net/10852/65861
Parametric or nonparametric: The FIC approach
Jullum, Martin; Hjort, Nils Lid
Should one rely on a parametric or nonparametric model when analysing a given data set? This classic question cannot be answered by traditional model selection criteria like AIC and BIC, since a nonparametric model has no likelihood. The purpose of the present paper is to develop a focused information criterion (FIC) for comparing general nonnested parametric models with a nonparametric alternative. It relies in part on the notion of a focus parameter, a population quantity of particular interest in the statistical analysis. The FIC compares and ranks candidate models based on estimated precision of the different modelbased estimators for the focus parameter. It has earlier been developed for several classes of problems, but mainly involving parametric models. The new FIC, including also nonparametrics, is novel also in the mathematical context, being derived without the local neighbourhood asymptotics underlying previous versions of FIC. Certain averageweighted versions, called AFIC, allowing several focus parameters to be considered simultaneously, are also developed. We concentrate on the standard i.i.d. setting and certain direct extensions thereof, but also sketch further generalisations to other types of data. Theoretical and simulationbased results demonstrate desirable properties and satisfactory performance.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/65861
20170101T00:00:00Z

Bifurcation Analysis of a Certain HodgkinHuxley Model Depending on Multiple Bifurcation Parameters
http://hdl.handle.net/10852/65821
Bifurcation Analysis of a Certain HodgkinHuxley Model Depending on Multiple Bifurcation Parameters
Erhardt, André Henrik
In this paper, we study the dynamics of a certain HodgkinHuxley model describing the action potential (AP) of a cardiac muscle cell for a better understanding of the occurrence of a special type of cardiac arrhythmia, the socalled early afterdepolarisations (EADs). EADs are pathological voltage oscillations during the repolarisation or plateau phase of cardiac APs. They are considered as potential precursors to cardiac arrhythmia and are often associated with deficiencies in potassium currents or enhancements in the calcium or sodium currents, e.g., induced by ion channel diseases, drugs or stress. Our study is focused on the enhancement in the calcium current to identify regions, where EADs related to enhanced calcium current appear. To this aim, we study the dynamics of the model using bifurcation theory and numerical bifurcation analysis. Furthermore, we investigate the interaction of the potassium and calcium current. It turns out that a suitable increasing of the potassium current adjusted the EADs related to an enhanced calcium current. Thus, one can use our result to balance the EADs in the sense that an enhancement in the potassium currents may compensate the effect of enhanced calcium currents.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/65821
20180101T00:00:00Z

Mode jumping MCMC for Bayesian variable selection in GLMM
http://hdl.handle.net/10852/65654
Mode jumping MCMC for Bayesian variable selection in GLMM
Hubin, Aliaksandr; Storvik, Geir Olve
Generalized linear mixed models (GLMM) are used for inference and prediction in a wide range of different applications providing a powerful scientific tool. An increasing number of sources of data are becoming available, introducing a variety of candidate explanatory variables for these models. Selection of an optimal combination of variables is thus becoming crucial. In a Bayesian setting, the posterior distribution of the models, based on the observed data, can be viewed as a relevant measure for the model evidence. The number of possible models increases exponentially in the number of candidate variables. Moreover, the space of models has numerous local extrema in terms of posterior model probabilities. To resolve these issues a novel MCMC algorithm for the search through the model space via efficient mode jumping for GLMMs is introduced. The algorithm is based on that marginal likelihoods can be efficiently calculated within each model. It is recommended that either exact expressions or precise approximations of marginal likelihoods are applied. The suggested algorithm is applied to simulated data, the famous U.S. crime data, protein activity data and epigenetic data and is compared to several existing approaches.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/65654
20180101T00:00:00Z