Department of Mathematics
Recent Submissions
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Finite point blowup for the critical generalized Korteweg-de Vries equation
(Journal article; Peer reviewed, 2024)In the last twenty years, there have been significant advances in the study of the blow-up phenomenon for the critical generalized Korteweg-de Vries equation, including the determination of sufficient conditions for blowup, ... -
Stokes Graphs of the Rabi Problem with Real Parameters
(Journal article; Peer reviewed, 2024)We give a complete classification of generic topological types of domain configurations and Stokes graphs of the quadratic differential \({Q}_{0}\left(z\right)d{z}^{2}=-\frac{{z}^{4}+{c}_{3}{z}^{3}+{c}_{2}{z}^{2}+{c}_ ... -
Asymptotic stability of a finite sum of solitary waves for the Zakharov-Kuznetsov equation
(Journal article; Peer reviewed, 2024)We prove the asymptotic stability of a finite sum of well-ordered solitary waves for the Zakharov–Kuznetsov equation in dimensions two and three. We also derive a qualitative version of the orbital stability result, which ... -
Digitizing Fish Feeding Behaviour : A step towards feeding automation in aquaculture
(Doctoral thesis, 2025-05-14)Havbruksnæringen er i konstant utvikling. Det er da spesielt viktig å sørge for at næringen er bærekraftig og at endringsforslag er gjennomførbare og skalerbare. I det siste har mange avanserte teknologier som kunstig ... -
Advanced machine learning methods for multifrequency acoustic data
(Doctoral thesis, 2025-05-12)Lydbølgjer er effektive for kommunikasjon, navigasjon og avbilding under vatn, ettersom dei kan spreie seg over lange avstandar med minimal demping i vatn. Aktiv akustikk kan gje informasjon om fordeling og mengde av marine ... -
Accelerated ensemble optimization using momentum methods
(Journal article; Peer reviewed, 2024)We investigate the use of various momentum methods in combination with an ensemble approximation of gradients, for accelerated optimization. Although momentum gradient descent methods are popular in machine learning, it ... -
Justification of the Benjamin–Ono equation as an internal water waves model
(Journal article; Peer reviewed, 2024)In this paper, we give the first rigorous justification of the Benjamin-Ono equation: $$\begin{aligned} \hspace{3cm} \partial _t \zeta + (1 - \frac{\gamma }{2}\sqrt{\mu }|\textrm{D}|)\partial _x \zeta + \frac{3{\varepsilon ... -
Intermediate long wave equation in negative Sobolev spaces
(Journal article; Peer reviewed, 2024)We study the intermediate long wave equation (ILW) in negative Sobolev spaces. In particular, despite the lack of scaling invariance, we identify the regularity $s = -\frac 12$ as the critical regularity for ILW with any ... -
ATP dependence of decision-making capacity in a fine-grained model of gene regulatory networks
(Journal article; Peer reviewed, 2024)Cellular decision-making is fundamental to life, from developmental biology to environmental responses and antimicrobial resistance. Many regulatory processes that drive cellular decisions rely on gene expression, which ... -
Real-time ocean wave prediction in time domain with autoregression and echo state networks
(Journal article; Peer reviewed, 2024)This study evaluates the potential of applying echo state networks (ESN) and autoregression (AR) for dynamic time series prediction of free surface elevation for use in wave energy converters (WECs). The performance of ... -
(Uni)rational parametrizations of ℛ g,2 , ℛ g,4 and ℛ g,6 in low genera
(Journal article; Peer reviewed, 2024)The moduli space ℛ g,2n parametrizes double covers of smooth curves of genus g ramified at 2n points. We will prove the (uni)rationality of ℛ g,2 , ℛ g,4 and ℛ g,6 in low genera. -
Particle trajectories in the KP-II equation
(Journal article; Peer reviewed, 2024)In the current work, we consider particle trajectories beneath traveling soliton solutions described by the Kadomtsev–Petiviashvili-II (KP-II) equation, which is a model for small-amplitude water waves in shallow water. ... -
Dynamics of the Collision of Two Nearly Equal Solitary Waves for the Zakharov–Kuznetsov Equation
(Journal article; Peer reviewed, 2024)We study the dynamics of the collision of two solitary waves for the 2 and 3-dimensional Zakharov–Kuznetsov equation, a high-dimensional non-integrable version of the Korteweg-de Vries equation that appears as an asymptotic ... -
Infragravity waves and cross-shore motion–a conceptual study
(Journal article; Peer reviewed, 2024)It is widely known that Infragravity (IG) waves induce cross-shore fluid motion in the nearshore, and multiple recent observational studies have identified IG waves as the dominant factor for a range of nearshore processes ... -
Long time well-posedness and full justification of a Whitham-Green-Naghdi system
(Journal article; Peer reviewed, 2024)We establish the full justification of a ‘‘Whitham-Green-Naghdi’’ system modeling the propagation of surface gravity waves with bathymetry in the shallow water regime. It is an asymptotic model of the water waves equations ... -
Evolution and maintenance of mtDNA gene content across eukaryotes
(Journal article; Peer reviewed, 2024)Across eukaryotes, most genes required for mitochondrial function have been transferred to, or otherwise acquired by, the nucleus. Encoding genes in the nucleus has many advantages. So why do mitochondria retain any genes ... -
Rigorous derivation of weakly dispersive shallow-water models with large amplitude topography variations
(Journal article; Peer reviewed, 2024)We derive rigorously from the water waves equations new irrotational shallow-water models for the propagation of surface waves in the case of uneven topography in horizontal dimensions one and two. The systems are made to ... -
Refining the diffusive compressible Euler model
(Journal article; Peer reviewed, 2024)We revisit the molecular arguments underpinning the diffusive compressible Euler model (proposed in Svärd (2018)), and conclude that a heat diffusive term is not accounted for in the energy equation of the original model. ... -
Identifying codewords in general Reed-Muller codes and determining their weights
(Journal article; Peer reviewed, 2024)Determining the weight distribution of all Reed-Muller codes is a huge and exciting problem that has been around since the sixties. Some progress has been made very recently, but we are still far from a solution. In this ... -
A fixed-stress splitting method for nonlinear poroelasticity
(Journal article; Peer reviewed, 2024)In this paper we consider a nonlinear poroelasticity model that describes the quasi-static mechanical behaviour of a fluid-saturated porous medium whose permeability depends on the divergence of the displacement. Such ...
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