Gjesteforelesninger og seminarer - Side 9

QOMBINE seminar by Håkon R. Fredheim (University of Oslo)

Qombine presentation by Delphine Martres (UiO): postponed to 5 March 2025

Recent advances in experimental techniques have enabled remarkable discoveries and insight into how the dynamics of thin gas/vapour films can profoundly influence the behaviour of liquid droplets: drops impacting solids can “skate on a film of air” [1], so that they can “bounce off walls” [2,3]; reductions in ambient gas pressure can suppress splashing [4] and initiate the merging of colliding droplets [5]; and evaporating droplets can levitate on their own vapour film [7] (the Leidenfrost effect). Despite these advances, the precise physical mechanisms governing these phenomena remain a topic of debate.  A theoretical approach would shed light on these issues, but due to the strongly multiscale nature of these processes brute force computation is infeasible.  Furthermore, when films reach the scale of the mean free path in the gas (i.e. ~100nm) and below, new nanoscale physics appears that renders the classical Navier-Stokes paradigm inaccurate.

In this talk, I will overview our development of efficient computational models for the aforementioned droplet dynamics in the presence of gas nanofilms into which gas-kinetic, van der Waals and/or evaporative effects can be easily incorporated [8,9].  It will be shown that these models can reproduce experimental observations – for example, the threshold between bouncing and wetting for drop impact on a solid is reproduced to within 5%, whilst a model excluding either gas-kinetic or van der Waals effects is ~170% off!  These models will then be exploited to make new experimentally-verifiable predictions, such as how we expect drops to behave in reduced pressure environments.  Finally, I will conclude with some exciting directions for future work.

[1] JM Kolinski et al, Phys. Rev. Lett.  108 (2012), 074503. [2] JM Kolinski et al, EPL.  108 (2014), 24001. [3] J de Ruiter et al, Nature Phys.  11 (2014), 48. [4] L Xu et al, Phys. Rev. Lett. 94 (2005), 184505. [5] J Qian & CK Law, J. Fluid. Mech. 331 (1997), 59.  [6] KL Pan J. Appl. Phys. 103 (2008), 064901. [7] D Quéré, Ann. Rev. Fluid Mech. 45 (2013), 197.  [8] JE Sprittles, Phys. Rev. Lett.  118 (2017), 114502.  [9] MV Chubynsky et al, Phys. Rev. Lett.. 124 (2020), 084501.
Much of this work is based on a recent Annual Review: JE Sprittles, Ann. Rev. Fluid Mech. 56 (2024), 91.

The internal waves in consideration are generated locally in combination by:
1) the North Atlantic Current (NAC) that flows along the Norwegian shelf (average speed 0.3 m/s),
2) the local tide (dominant 24 hr mode),
3) the particular shelf geometry,
4) the seasonal pycnocline (at 20 m depth). The typical amplitude is 50 m. The local depth where they exist is 100 m (approx.).
The local internal wave speed of 0.4 m/s is comparable to the current speed.

The wave generation process occurs in a sequence of:
A) locally large depressions of the internal tide occurring at the lee side of two shallow ridges,  
B) the depressions are orthogonal to the current,
C) the depressions move slowly against the current, and
D) eventually fission into nonlinear-dispersive wave groups,
E) they propagate upstream against the current,
F) they are recorded on satellite images and is visible by eye.
 

In a recent RCN-funded project (ECOPULSE) 2020-2023 including research groups at UiO, the Norwegian Meteorological Institute and the Institute of Marine Research in Bergen, field experiments of the mother wave in points A) and C) were undertaken during July-September 2021 and 2022. The measurements show that the waves break and mix in the entire water column by convective breaking in the upper part of the water column, shear instability within the pycnocline, and by a variant of a shear instability near the bottom. The field measurements document the local wave properties and the initial phase of the fission process. The Vesterålen-Lofoten area is of immense political interest because of a) its traditional fisheries and breeding ground for the North Atlantic and Barents Sea Cod and other species, where also a cold water coral reef is located right where these waves are generated.  The waves do also extend across NORDLAND VII, an oil / gas field which may be considered for exploitation. Preliminary results will be presented.

C*-algebra seminar by David Jaklitsch (University of Oslo).

QOMBINE seminar by Franz Fuchs and Ruben Bassa (UiO)

Positive geometry is a recent branch of mathematical physics which present exciting connections with real, complex and tropical algebraic geometry.

In this talk, we introduce the topic by developing the positive geometry of del Pezzo surfaces and their moduli spaces. 

We will analyze their connected components, likelihood equations and scattering amplitudes. 

The talk is based on joint work with Early, Geiger, Sturmfels and Yun. 

Abstract:  I will introduce a certain configuration space associated with a graph, and compute its cohomology ring.  It turns out to be related to internal zonotopal algebras, which were introduced in the context of approximation theory and show up in many different contexts.

This is joint work with Colin Crowley, Galen Dorpalen-Barry, and Andre Henriques.

Positroids are a class of matroids that were introduced by Postnikov in 2006 that index a certain stratification of the totally non-negative Grassmannian. These matroids are famously in bijection with a “zoo” of combinatorial objects including Grassmann necklaces and plabic graphs. We introduce a new family of positroids called rook matroids that arise from restricted rook placements on a skew shaped board and discuss it in terms of this zoo. We highlight the transversal structure of rook matroids and the slightly mysterious relationship they share with lattice path matroids. This is joint work with Per Alexandersson and ongoing work with Irem Portakal and Akiyoshi Tsuchiya. 

Gunnar Taraldsen is professor at Department of Mathematical  Sciences, NTNU. His current research interest focusses on the foundational principles of statistical inference including quantum probability, artificial intelligence, and machine learning. The aim is to bridge foundations for statistical inferences, to facilitate objective and replicable scientific learning, and to develop analytic and computing methodologies for data analysis.

Earlier research includes quantum mechanics, mathematical physics, measure theory, probability, medical ultrasound, non-linear wave propagation, numerical acoustics, medical statistics, outdoors sound propagation, community noise annoyance, acoustic noise mapping, underwater localization, underwater wave propagation, and spherical microphone arrays.

The Section 4 seminar for Spring 2025 will be held on Tuesdays at 09.10 am in room 1020.

Emil Aas Stoltenberg is assistant professor at BI Norwegian Business School, and associate professor (20%) at the University of Oslo (UiO). He holds a PhD in statistics from UiO (2020). From the first of June this year, he will be full-time at UiO.

Chebyshev varieties are algebraic varieties parametrized by Chebyshev polynomials or their multivariate generalizations. We determine the dimension, degree, singular locus and defining equations of these varieties. We explain how they play the role of toric varieties in sparse polynomial root finding, when monomials are replaced by Chebyshev polynomials. We present numerical root finding algorithms that exploit our results. Joint work with Zaïneb Bel-Afia and Chiara Meroni.

The amplituhedron is a semi-algebraic set given as the image of the positive Grassmannian under a linear map subject to a choice of additional parameters. We define the Infinituhedron as the limit of amplituhedra by sending one of the parameters to infinity. We derive its algebraic boundary in terms of Chow varieties and explain its geometric interpretation from the point of view of Positive Geometry in terms of secants of the rational normal curve. This discussion shows that the Infinituhedron is a positive geometry with a unique differential form. Joint work with Rainer Sinn.

Clara Bertinelli Salucci is a Postdoctoral Fellow at the Department of Mathematics, affiliated with the PLUMBIN' (Physics Learning Using Machines and Bayesian INference) project at the University of Oslo. She completed her PhD in Statistics and Machine Learning at the University of Oslo in April 2024, where she developed statistical and machine learning methods for diagnostics and prognostics of lithium-ion batteries for maritime applications. Currently, she is investigating the role of likelihood ratio test statistics for hypotheses tests in experimental and theoretical particle physics, focusing on deviations from Wilks' theorem in the search for new particles. Her postdoctoral research combines her expertise in statistics with her background in high-energy physics.

Note the non-standard time! 

In the first part of the talk, I will give an introductory talk to o-minimality, giving the definitions and some of intuition through understanding which Lie groups are amenable to being understood in o-minimal contexts. 

In the second part I will state the two theorems which have had the most important applications to algebra and give some intuition of how (at least one of them) has been used.