Department of Mathematics
https://hdl.handle.net/1956/1065
Sun, 25 Jul 2021 19:44:42 GMT2021-07-25T19:44:42ZPractical approaches to study microbially induced calcite precipitation at the field scale
https://hdl.handle.net/11250/2761700
Practical approaches to study microbially induced calcite precipitation at the field scale
Marban, David Landa; Tveit, Svenn; Kumar, Kundan; Gasda, Sarah
Microbially induced calcite precipitation (MICP) is a new and sustainable technology which utilizes biochemical processes to create barriers by calcium carbonate cementation; therefore, this technology has a potential to be used for sealing leakage zones in geological formations. The complexity of current MICP models and present computer power limit the size of numerical simulations. We describe a mathematical model for MICP suitable for field-scale studies. The main mechanisms in the conceptual model are as follow: suspended microbes attach themselves to the pore walls to form biofilm, growth solution is added to stimulate the biofilm development, the biofilm uses cementation solution for production of calcite, and the calcite reduces the pore space which in turn decreases the rock permeability. We apply the model to study the MICP technology in two sets of reservoir properties including a well-established field-scale benchmark system for CO2 leakage. A two-phase flow model for CO2 and water is used to assess the leakage prior to and with MICP treatment. Based on the numerical results, this study confirms the potential for this technology to seal leakage paths in reservoir-caprock systems.
Fri, 01 Jan 2021 00:00:00 GMThttps://hdl.handle.net/11250/27617002021-01-01T00:00:00ZEffects of a parent-administered exercise program in the neonatal intensive care unit: Dose does matter-a randomized controlled trial
https://hdl.handle.net/11250/2756988
Effects of a parent-administered exercise program in the neonatal intensive care unit: Dose does matter-a randomized controlled trial
Øberg, Gunn Kristin; Girolami, Gay L; Campell, Suzann K.; Ustad, Tordis; Heuch, Ivar; Jacobsen, Bjarne K.; Kaaresen, Per Ivar; Aulie, Vibeke Smith; Jørgensen, Lone
Background
Despite the risk of delayed motor development in infants born preterm, knowledge about interventions in the neonatal intensive care unitt (NICU) and the effects of dosing is sparse.
Objective
The objectives of this study were to examine the effectiveness of a parent-administered exercise program in the NICU on motor outcome at 3 months corrected age (CA) and the effect of dosing on motor performance.
Design
This was a randomized clinical trial.
Setting
The study was conducted at 3 university hospitals in Tromsø, Trondheim, and Oslo, Norway.
Participants
A total of 153 infants with gestational age <32 weeks at birth were randomly assigned to intervention or control groups.
Intervention
A 3-week parent-administered intervention designed to facilitate movements in preterm infants was performed in the NICU. Parents were asked to administer the intervention 10 minutes twice a day.
Measurements
Test of Infant Motor Performance (TIMP) was used to assess short-term outcome at 3 months CA.
Results
No significant difference in the TIMP z-score was found between intervention and control groups at follow-up 3 months CA, but a significant positive relationship was found between total intervention dose and TIMP z-scores. The adjusted odds of having a clinical z-score < 0 at 3 months CA was about 6 times higher for infants with less than median intervention time than for infants with a longer intervention time.
Limitations
The number of infants born before 28 weeks was small. A spillover effect in favor of the control group was possible. We do not know if the infants received physical therapy after discharge from the hospital.
Conclusions
There was no difference in motor performance between the intervention group and the control group at 3 months CA. However, an increased intervention dose was positively associated with improved motor outcome.
Wed, 01 Jan 2020 00:00:00 GMThttps://hdl.handle.net/11250/27569882020-01-01T00:00:00ZObjective Priors in the Empirical Bayes Framework
https://hdl.handle.net/11250/2756432
Objective Priors in the Empirical Bayes Framework
Klebanov, Ilja; Sikorski, Alexander; Schütte, Christof; Röblitz, Susanna
When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the nonparametric case, the maximum likelihood estimate is known to overfit the data, an issue that is commonly tackled by regularization. However, the majority of regularizations are ad hoc choices which lack invariance under reparametrization of the model and result in inconsistent estimates for equivalent models. We introduce a nonparametric, transformation-invariant estimator for the prior distribution. Being defined in terms of the missing information similar to the reference prior, it can be seen as an extension of the latter to the data-driven setting. This implies a natural interpretation as a trade-off between choosing the least informative prior and incorporating the information provided by the data, a symbiosis between the objective and empirical Bayes methodologies.
Wed, 01 Jan 2020 00:00:00 GMThttps://hdl.handle.net/11250/27564322020-01-01T00:00:00ZTowards an understanding of ramified extensions of structured ring spectra
https://hdl.handle.net/11250/2756002
Towards an understanding of ramified extensions of structured ring spectra
Dundas, Bjørn Ian; Lindenstrauss, Ayelet; Richter, Birgit
We propose topological Hochschild homology as a tool for measuring ramification of maps of structured ring spectra. We determine second order topological Hochschild homology of the p-local integers. For the tamely ramified extension of the map from the connective Adams summand to p-local complex topological K-theory we determine the relative topological Hochschild homology and show that it detects the tame ramification of this extension. We show that the complexification map from connective topological real to complex K-theory shows features of a wildly ramified extension. We also determine relative topological Hochschild homology for some quotient maps with commutative quotients.
Wed, 01 Jan 2020 00:00:00 GMThttps://hdl.handle.net/11250/27560022020-01-01T00:00:00ZCyclic homology in a special world
https://hdl.handle.net/11250/2756000
Cyclic homology in a special world
Dundas, Bjørn Ian
In work of Connes and Consani, Γ-spaces have taken a new importance. Segal introduced Γ-spaces in order to study stable homotopy theory, but the new perspective makes it apparent that also information about the unstable structure should be retained. Hence, the question naturally presents itself: to what extent are the commonly used invariants available in this context? We offer a quick survey of (topological) cyclic homology and point out that the categorical construction is applicable also in an N -algebra (aka. semi-ring or rig) setup.
Under embargo until: 2022-01-14
Wed, 01 Jan 2020 00:00:00 GMThttps://hdl.handle.net/11250/27560002020-01-01T00:00:00ZA comparison of Monte Carlo sampling methods for metabolic network models
https://hdl.handle.net/11250/2755735
A comparison of Monte Carlo sampling methods for metabolic network models
Fallahi, Shirin; Skaug, Hans J.; Alendal, Guttorm
Reaction rates (fluxes) in a metabolic network can be analyzed using constraint-based modeling which imposes a steady state assumption on the system. In a deterministic formulation of the problem the steady state assumption has to be fulfilled exactly, and the observed fluxes are included in the model without accounting for experimental noise. One can relax the steady state constraint, and also include experimental noise in the model, through a stochastic formulation of the problem. Uniform sampling of fluxes, feasible in both the deterministic and stochastic formulation, can provide us with statistical properties of the metabolic network, such as marginal flux probability distributions. In this study we give an overview of both the deterministic and stochastic formulation of the problem, and of available Monte Carlo sampling methods for sampling the corresponding solution space. We apply the ACHR, OPTGP, CHRR and Gibbs sampling algorithms to ten metabolic networks and evaluate their convergence, consistency and efficiency. The coordinate hit-and-run with rounding (CHRR) is found to perform best among the algorithms suitable for the deterministic formulation. A desirable property of CHRR is its guaranteed distributional convergence. Among the three other algorithms, ACHR has the largest consistency with CHRR for genome scale models. For the stochastic formulation, the Gibbs sampler is the only method appropriate for sampling at genome scale. However, our analysis ranks it as less efficient than the samplers used for the deterministic formulation.
Wed, 01 Jan 2020 00:00:00 GMThttps://hdl.handle.net/11250/27557352020-01-01T00:00:00ZBrauer groups of bielliptic surfaces and classification of irregular surfaces in positive characteristic
https://hdl.handle.net/11250/2755245
Brauer groups of bielliptic surfaces and classification of irregular surfaces in positive characteristic
Ferrari, Eugenia
In this work we tackle three problems about surfaces.
In Part I (Chapter 2) we study the Brauer groups of bielliptic surfaces in characteristic zero. More precisely, given a bielliptic surface X, we give explicit generators for the torsion of the second cohomology group H^2(X,Z) of each type of bielliptic surface, and we determine the injectivity (and possibly the triviality) of the Brauer maps arising from canonical covers and bielliptic covers. This part is based on
E. Ferrari, S. Tirabassi, M. Vodrup, On the Brauer Group of Bielliptic Surfaces, with an appendix The Homomorphism Lattice of Two Elliptic Curves by J. Bergström and S. Tirabassi, preprint, arXiv:1910.12537, 2019.
In Part II (Chapter 3 and Chapter 4) we deal with two problems of characterisation of surfaces in positive characteristic.
In Chapter 3 we show that a smooth projective surface over an algebraically closed field of characteristic at least five is birational to an abelian surface if and only if P_1(S)=P_4(S)=1 and h^1(S,O_S)=2. This is based on
E. Ferrari, An Enriques Classification Theorem for Surfaces in Positive Characteristic, Manuscripta Mathematica 160, pp. 173–185, 2019.
Also, we discuss the fact that K3 surfaces are characterised by P_1(S)=P_2(S)=1 and h^1(S,O_S)=0.
In Chapter 4 we study surfaces of general type with p_g(S)=h^1(S,O_S)=3 in positive characteristic. We compare our results to those in characteristic zero that were obtained in
C.D. Hacon, R. Pardini, Surfaces with p_g=q=3, Transactions of the American Mathematical Society 354, No.7, pp.2631–2638, 2002.
G.P. Pirola, Surfaces with p_g=q=3, Manuscripta Mathematica 108, pp.163–170, 2002.
Thu, 27 May 2021 00:00:00 GMThttps://hdl.handle.net/11250/27552452021-05-27T00:00:00ZAn iterative staggered scheme for phase field brittle fracture propagation with stabilizing parameters
https://hdl.handle.net/11250/2754959
An iterative staggered scheme for phase field brittle fracture propagation with stabilizing parameters
Brun, Mats Kirkesæther; Wick, Thomas; Berre, Inga; Nordbotten, Jan Martin; Radu, Florin Adrian
This paper concerns the analysis and implementation of a novel iterative staggered scheme for quasi-static brittle fracture propagation models, where the fracture evolution is tracked by a phase field variable. The model we consider is a two-field variational inequality system, with the phase field function and the elastic displacements of the solid material as independent variables. Using a penalization strategy, this variational inequality system is transformed into a variational equality system, which is the formulation we take as the starting point for our algorithmic developments. The proposed scheme involves a partitioning of this model into two subproblems; phase field and mechanics, with added stabilization terms to both subproblems for improved efficiency and robustness. We analyze the convergence of the proposed scheme using a fixed point argument, and find that under a natural condition, the elastic mechanical energy remains bounded, and, if the diffusive zone around crack surfaces is sufficiently thick, monotonic convergence is achieved. Finally, the proposed scheme is validated numerically with several bench-mark problems.
Wed, 01 Jan 2020 00:00:00 GMThttps://hdl.handle.net/11250/27549592020-01-01T00:00:00ZMonolithic and splitting solution schemes for fully coupled quasi-static thermo-poroelasticity with nonlinear convective transport
https://hdl.handle.net/11250/2754950
Monolithic and splitting solution schemes for fully coupled quasi-static thermo-poroelasticity with nonlinear convective transport
Brun, Mats Kirkesæther; Ahmed, Elyes; Berre, Inga; Nordbotten, Jan Martin; Radu, Florin Adrian
This paper concerns monolithic and splitting-based iterative procedures for the coupled nonlinear thermo-poroelasticity model problem. The thermo-poroelastic model problem we consider is formulated as a three-field system of PDE’s, consisting of an energy balance equation, a mass balance equation and a momentum balance equation, where the primary variables are temperature, fluid pressure, and elastic displacement. Due to the presence of a nonlinear convective transport term in the energy balance equation, it is convenient to have access to both the pressure and temperature gradients. Hence, we introduce these as two additional variables and extend the original three-field model to a five-field model. For the numerical solution of this five-field formulation, we compare six approaches that differ by how we treat the coupling/decoupling between the flow and/from heat and/from the mechanics, suitable for varying coupling strength between the three physical processes. The approaches have in common a simultaneous application of the so-called -scheme, which works both to stabilize iterative splitting as well as to linearize nonlinear problems, and can be seen as a generalization of the Undrained and Fixed-Stress Split algorithms. More precisely, the derived procedures transform a nonlinear and fully coupled problem into a set of simpler subproblems to be solved sequentially in an iterative fashion. We provide a convergence proof for the derived algorithms, and demonstrate their performance through several numerical examples investigating different strengths of the coupling between the different processes.
Wed, 01 Jan 2020 00:00:00 GMThttps://hdl.handle.net/11250/27549502020-01-01T00:00:00ZLie groupoids of mappings taking values in a Lie groupoid
https://hdl.handle.net/11250/2754929
Lie groupoids of mappings taking values in a Lie groupoid
Amiri, Habib; Glöckner, Helge; Schmeding, Alexander
Endowing differentiable functions from a compact manifold to a Lie group with the pointwise group operations one obtains the so-called current groups and, as a special case, loop groups. These are prime examples of infinite-dimensional Lie groups modelled on locally convex spaces. In the present paper, we generalise this construction and show that differentiable mappings on a compact manifold (possibly with boundary) with values in a Lie groupoid form infinite-dimensional Lie groupoids which we call current groupoids. We then study basic differential geometry and Lie theory for these Lie groupoids of mappings. In particular, we show that certain Lie groupoid properties, like being a proper étale Lie groupoid, are inherited by the current groupoid. Furthermore, we identify the Lie algebroid of a current groupoid as a current algebroid (analogous to the current Lie algebra associated to a current Lie group). To establish these results, we study superposition operators \[ C^\ell (K,f)\colon C^\ell (K,M)\rightarrow C^\ell (K,N)\,,\;\, \gamma f\circ \gamma \] between manifolds of $C^\ell $-functions. Under natural hypotheses, $C^\ell (K,f)$ turns out to be a submersion (an immersion, an embedding, proper, resp., a local diffeomorphism) if so is the underlying map $f\colon M\rightarrow N$. These results are new in their generality and of independent interest.
Wed, 01 Jan 2020 00:00:00 GMThttps://hdl.handle.net/11250/27549292020-01-01T00:00:00Z