Matematisk institutt
http://hdl.handle.net/10852/5
Mon, 18 Jun 2018 07:51:50 GMT
20180618T07:51:50Z

The characteristics of billows generated by internal solitary waves
http://hdl.handle.net/10852/61885
The characteristics of billows generated by internal solitary waves
Carr, Magda; Franklin, James; King, Stuart E.; Davies, Peter A.; Grue, John; Dritschel, David G
The spatial and temporal development of shearinduced overturning billows associated with breaking internal solitary waves is studied by means of a combined laboratory and numerical investigation. The waves are generated in the laboratory by a lock exchange mechanism and they are simulated numerically via a contouradvective semiLagrangian method. The properties of individual billows (maximum height attained, time of collapse, growth rate, speed, wavelength, Thorpe scale) are determined in each case, and the billow interaction processes are studied and classified. For broad flat waves, similar characteristics are seen to those in parallel shear flow, but, for waves not at the conjugate flow limit, billow characteristics are affected by the spatially varying waveinduced shear flow. Wave steepness and wave amplitude are shown to have a crucial influence on determining the type of interaction that occurs between billows and whether billow overturning can be arrested. Examples are given in which billows (i) evolve independently of one another, (ii) pair with one another, (iii) engulf/entrain one another and (iv) fail to completely overturn. It is shown that the vertical extent a billow can attain (and the associated Thorpe scale of the billow) is dependent on wave amplitude but that its value saturates once a given amplitude is reached. It is interesting to note that this amplitude is less than the conjugate flow limit amplitude. The number of billows that form on a wave is shown to be dependent on wavelength; shorter waves support fewer but larger billows than their longwave counterparts for a given stratification.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61885
20170101T00:00:00Z

Wave analysis of porous geometry with linear resistance law
http://hdl.handle.net/10852/61884
Wave analysis of porous geometry with linear resistance law
Dokken, Jorgen S.; Grue, John; Karstensen, Lasse
The wave diffractionradiation problem of a porous geometry of arbitrary shape located in the free surface of a fluid is formulated by a set of integral equations, assuming a linear resistance law at the geometry. The linear forces, the energy relation and the mean horizontal drift force are evaluated for nonporous and porous geometries. A geometry of large porosity has an almost vanishing added mass. The exciting forces are a factor of 5–20 smaller compared to a solid geometry. In the long wave regime, the porous geometry significantly enhances both the damping and the mean drift force, where the latter grows linearly with the wavenumber. The calculated mean drift force on a porous hemisphere and a vertical truncated cylinder, relevant to the construction of fish cages, is compared to available published results.
This research has been published in Journal of Marine Science and Application. ©2017 Springer Verlag
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61884
20170101T00:00:00Z

Ship generated minitsunamis
http://hdl.handle.net/10852/61883
Ship generated minitsunamis
Grue, John
Very long waves are generated when a ship moves across an appreciable depth change ∆h comparable to the average and relatively shallow water depth h at the location, with ∆h/h ≃ 1. The phenomenon is new and the waves are recently observed in the Oslofjord in Norway. The 0.51 km long waves, extending across the 23 km wide fjord, are observed as runups and rundowns along the shore, of periods of 3060 seconds, where a wave height up to 1.4 m has been measured. The waves travelling with the shallow water speed, found ahead of the ships moving at subcritical depth Froude number, behave like a minitsunami. A qualitative explanation of the linear generation mechanism is provided by an asymptotic analysis, valid for ∆h/h << 1 and long waves, expressing the generation in terms of a pressure impulse at the depth change. Complementary fully dispersive calculations for ∆h/h ≃ 1 document symmetries of the waves at positive or negative ∆h. The wave height grows with the ship speed U according to U n with n in the range 3 − 4, for ∆h/h ≃ 1, while the growth in U is only very weak for ∆h/h << 1 (the asymptotics). Calculations show good agreement with observations.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61883
20170101T00:00:00Z

Simulation of Greeks of financial claims in Markets with Memory.
http://hdl.handle.net/10852/61846
Simulation of Greeks of financial claims in Markets with Memory.
Thirumeny, Roxicca
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/61846
20180101T00:00:00Z

Local dissipation limits the dynamics of impacting droplets on smooth and rough substrates
http://hdl.handle.net/10852/61755
Local dissipation limits the dynamics of impacting droplets on smooth and rough substrates
Carlson, Andreas; Gustav, Amberg; Wang, Yuli
A droplet that impacts onto a solid substrate deforms in a complex dynamics. To extract the principal mechanisms that dominate this dynamics, we deploy numerical simulations based on the phase field method. Direct comparison with experiments suggests that a dissipation local to the contact line limits the droplet spreading dynamics and its scaled maximum spreading radius βmax. By assuming linear response through a drag force at the contact line, our simulations rationalize experimental observations for droplet impact on both smooth and rough substrates, measured through a single contact line friction parameter μf . Moreover, our analysis shows that dissipation at the contact line can limit the dynamics and we describe βmax by the scaling law βmax ∼ (Reμl/μf ) 1/2 that is a function of the droplet viscosity (μl) and its Reynolds number (Re).
This research was originally published in Physical Review E. © 2017 American Physical Society
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61755
20170101T00:00:00Z

Approximations of Fractional Brownian Motion
http://hdl.handle.net/10852/61664
Approximations of Fractional Brownian Motion
Kristensen, Jan Josef
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/61664
20180101T00:00:00Z

Cohomology of Projective Systems on Ranked Posets
http://hdl.handle.net/10852/61612
Cohomology of Projective Systems on Ranked Posets
Lodsby, Kari Lovise
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61612
20170101T00:00:00Z

On Subrecursive Representability of Irrational Numbers, Part II
http://hdl.handle.net/10852/61543
On Subrecursive Representability of Irrational Numbers, Part II
Kristiansen, Lars
The final publication is available at IOS Press through http://dx.doi.org/10.3233/COM170081
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61543
20170101T00:00:00Z

A Boussinesq type extension of the GeoClaw model  a study of wave breaking phenomena applying dispersive long wave models
http://hdl.handle.net/10852/61411
A Boussinesq type extension of the GeoClaw model  a study of wave breaking phenomena applying dispersive long wave models
Kim, Jihwan; Pedersen, Geir Kleivstul; Løvholt, Finn; LeVeque, Randall J.
The nonlinear shallow water model is widely used in the study of tsunami propagation, but an increasing number of studies are dedicated to the dispersion dynamics of tsunamis. If the wave dispersion becomes important, Boussinesqtype models are often used. In this work, a general purpose Boussinesq solver, BoussClaw, is introduced for modeling nonlinear dispersive tsunami propagation, taking into account inundation. The BoussClaw model is an extension of the GeoClaw tsunami model. It employs a hybrid of finite volume and finite difference methods to solve Boussinesq equations from the literature, which are based on the depthaveraged velocity and include enhanced dispersion properties. On the other hand, in the selected formulation only some nonlinearity is retained in the dispersion term. In order to validate BoussClaw, numerical results are compared to analytic solutions, solutions obtained by preexisting models, and laboratory experiments. Even though the equations of BoussClaw are not fully nonlinear they perform far better than standard Boussinesq equations with only linear dispersion terms. Furthermore, the wave steepening and breaking are carefully scrutinized, and we demonstrate that the point of wave breaking may be wrongly identified in many of the commonly used Boussinesq models.
Kim, Jihwan, et al. "A Boussinesq type extension of the GeoClaw modela study of wave breaking phenomena applying dispersive long wave models." Coastal Engineering 122 (2017): 7586.
© 2017. This manuscript version is made available under the CCBYNCND 4.0 license.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61411
20170101T00:00:00Z

Study tips  to beginner students in mathematicsheavy sciences
http://hdl.handle.net/10852/61410
Study tips  to beginner students in mathematicsheavy sciences
Borge, Inger Christin; Johansen, Nils Voje; Seland, Elisabeth Havsberg
Through our work with teaching and learning mathematics at university level, we experience that students can benefit from tips on how to study, and in particular how to study mathematics.
The Department of Mathematics at the University of Oslo (UiO) published in autumn 2016 a booklet entitled “Studietips – til begynnerstudenter i matematikktunge realfag” (Study tips – to beginner students in mathematicsheavy sciences). It was handed out to the beginner students at the Faculty for Mathematics and Natural Sciences (MN) and published on the web for anyone to use [1].
The booklet gives good advice on how to study, in particular how to study mathematics, and on life as a student. It is based on surveys conducted amongst older students, on our experiences teaching and supervising beginner students and earlier work on study tips and mathematical thinking.
We have also given a seminar on study tips for the students. Prior to this seminar we sent out a “study tips survey”, giving the students the opportunity to reflect upon how they work with mathematics. The answers to the survey revealed that many beginner students reflect very well and have good intentions about their studying. However, we were also able to make some students reconsider their thoughts.
In this paper we will discuss the study tips and the “study tips survey”. In particular, we will consider some of the challenges one faces in the transition between upper secondary school and university when it comes to teaching and learning mathematics.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61410
20170101T00:00:00Z

Video production  mathematics for beginner students
http://hdl.handle.net/10852/61409
Video production  mathematics for beginner students
Kleppe, Johannes; Borge, Inger Christin
Beginner student courses in mathematics in higher education have had high failure rates across the country. A national study [1] conducted by the Norwegian Association of Higher Education Institutions (UHR) in 2013 showed that students need help with the transition from upper secondary school to university or college.
As one of the initiatives following this study, UHR joined forces with Centre for Research, Innovation and Coordination of Mathematics Teaching (MatRIC) financing the production of mathematics videos that would help students with the transition from upper secondary school to university or college.
A group of six people from four higher education institutions, all with experience from teaching mathematics to upper secondary school students and/or first year university students, formed the video production group. So far the group has produced over 100 videos with a total running time of over 1000 minutes. These videos are freely available to everyone at the MatRIC TV web site [2] as a national resource.
The production group has made several decisions about the presentation of the mathematical material and the design of the videos along the way. In this contribution to the MNT conference we will discuss these choices and our experiences with producing these videos, and also their impact.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61409
20170101T00:00:00Z

Computational Analysis of a Drag reducing Cone Grid
http://hdl.handle.net/10852/61358
Computational Analysis of a Drag reducing Cone Grid
Utnes, Anders
CFD analysis of a cone grid applied to a flat plate, with mesh generation script.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61358
20170101T00:00:00Z

Nodal finite element de Rham complexes
http://hdl.handle.net/10852/61204
Nodal finite element de Rham complexes
Christiansen, Snorre H; Hu, Jun; Hu, Kaibo
We construct 2D and 3D finite element de Rham sequences of arbitrary polynomial degrees with extra smoothness. Some of these elements have nodal degrees of freedom and can be considered as generalisations of scalar Hermite and Lagrange elements. Using the nodal values, the number of global degrees of freedom is reduced compared with the classical Nédélec and Brezzi–Douglas–Marini finite elements, and the basis functions are more canonical and easier to construct. Our finite elements for H(div) with regularity r=2 coincide with the nonstandard elements given by Stenberg (Numer Math 115(1):131–139, 2010). We show how regularity decreases in the finite element complexes, so that they branch into known complexes. The standard de Rham complexes of Whitney forms and their higher order version can be regarded as the family with the lowest regularity. The construction of the new families is motivated by finite element systems.
This is a postpeerreview, precopyedit version of an article published in Numerische Mathematik. The final authenticated version is available online at: http://dx.doi.org/10.1007/s002110170939x
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61204
20170101T00:00:00Z

Convergence of a Godunov scheme for conservation laws with a discontinuous flux lacking the crossing condition
http://hdl.handle.net/10852/61200
Convergence of a Godunov scheme for conservation laws with a discontinuous flux lacking the crossing condition
Karlsen, Kenneth Hvistendahl; Towers, John D.
stability for entropy solutions of nonlinear degenerate parabolic convection–diffusion equations with discontinuous coefficients, Skr. K. Nor. Vidensk. Selsk. 3 (2003) 1–49], singles out the vanishing viscosity solution whether or not the crossing condition is satisfied, and has a discrete version satisfied by the Godunov variant of the finite difference scheme of [S. Diehl, On scalar conservation laws with point source and discontinuous flux function, SIAM J. Math. Anal. 26(6) (1995) 1425–1451]. We show that the solutions produced by that scheme converge to the unique vanishing viscosity solution. The scheme does not require a Riemann solver for the discontinuous flux problem. This makes its implementation simple even when the flux is multimodal, and there are multiple flux crossings.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61200
20170101T00:00:00Z

Modeling the Premium in NonLife Insurance  a Comparison of Generalized Linear and Generalized Linear Mixed Models
http://hdl.handle.net/10852/61164
Modeling the Premium in NonLife Insurance  a Comparison of Generalized Linear and Generalized Linear Mixed Models
Ha, Tam
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61164
20170101T00:00:00Z

Analysis of ContractforDifference with Vasicek Process and Cointegrated System in Stock Market and Nordic Electricity Market
http://hdl.handle.net/10852/61163
Analysis of ContractforDifference with Vasicek Process and Cointegrated System in Stock Market and Nordic Electricity Market
Huang, Bo
This thesis aims at pricing ContractforDifference (CFD) in stock market, and Electricity Price Area Differential (EPAD) in the Nord Pool. For CFD, our model consists of Geometric Brownian Motion and Vasicek process. For EPAD, we apply cointegrated system to build a model, with and without Vasicek process. Both parts claim calculable results. And they are given by a series of analysis and calculationwork. Reader will also encounter some figures of simulation by R.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61163
20170101T00:00:00Z

Bsplines in Machine Learning
http://hdl.handle.net/10852/61162
Bsplines in Machine Learning
Douzette, Andre Sevaldsen
In the recent decade, artificial intelligence and machine learning has become increasingly popular for solving complex realworld problems. In particular problems which was believed to be very hard or in some cases impossible by computers have seen a surge in interest from both academia but also the indus try. A recent example is the defeat of the worlds best Go player by Googles AlphaGo using deep neural networks. At the core of neural networks is the a part of the neurons called an activation function. This function is of mayor significance in how the network operates, but is often overlooked. One most often picks one of the commonly chosen nonadaptive functions as activation function. There have been research into using adaptive sigmoid or ReLU functions, but these have the drawbacks that the adaptations caused by data from one local region would effect the global domain. We therefore propose to use adaptive spline functions with free knots. Research into the field of spline networks have been limited in sophistication, with interpolating cubic splines being the most researched. The implementation in this thesis is using splines with Bsplines as a basis, and is therefore free to use any polynomial degree.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61162
20170101T00:00:00Z

Local Euler obstructions of toric varieties
http://hdl.handle.net/10852/61063
Local Euler obstructions of toric varieties
Utstøl Nødland, Bernt Ivar
We use Matsui and Takeuchi's formula for toric Adiscriminants to give algorithms for computing local Euler obstructions and dual degrees of toric surfaces and 3folds. In particular, we consider weighted projective spaces. As an application we give counterexamples to a conjecture by Matsui and Takeuchi. As another application we recover the wellknown fact that the only defective normal toric surfaces are cones.
Mon, 01 Jan 2018 00:00:00 GMT
http://hdl.handle.net/10852/61063
20180101T00:00:00Z

Invariance of the Cuntz splice
http://hdl.handle.net/10852/61045
Invariance of the Cuntz splice
Eilers, Søren; Restorff, Gunnar; Ruiz, Efren; Sørensen, Adam Peder Wie
We show that the Cuntz splice induces stably isomorphic graph C∗algebras. This result is a key step towards the recent complete classification of unital graph C∗algebras both with respect to Ktheoretical classification and with respect to geometrical classification in terms of an equivalence relation on the underlying graphs.
This is a postpeerreview, precopyedit version of an article published in Mathematische Annalen. The final authenticated version is available online at: http://dx.doi.org/10.1007/s002080171570y
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61045
20170101T00:00:00Z

Vanishing cotangent cohomology for Plücker algebras
http://hdl.handle.net/10852/61001
Vanishing cotangent cohomology for Plücker algebras
Christophersen, Jan Arthur; Ilten, Nathan Owen
We use representation theory and Bott’s theorem to show vanishing of higher cotangent cohomology modules for the homogeneous coordinate ring of Grassmannians in the Plücker embedding. As a byproduct, we answer a question of Wahl about the cohomology of the square of the ideal sheaf for the case of Plücker relations. We obtain slightly weaker vanishing results for the cotangent cohomology of the coordinate rings of isotropic Grassmannians.
This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in Algebra on 31 Jan 2017, available online: http://www.tandfonline.com/10.1080/00927872.2016.1249373
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10852/61001
20170101T00:00:00Z