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Our ability to predict the future of Arctic sea ice is limited by ice's sensitivity to detailed surface conditions such as the distribution of snow and melt ponds. Snow on top of the ice decreases ice's thermal conductivity, increases its…
Sea ice is a mushy layer, a porous material whose properties depend on the relative proportions of solid and liquid. The growth of sea ice is governed by heat transfer through the ice together with appropriate boundary conditions at the…
Travelling and rotating waves are ubiquitous phenomena observed in time dependent PDEs modelling the combined effect of dissipation and non-linear interaction. From an abstract viewpoint they appear as relative equilibria of an equivariant…
Wave-sea ice interactions shape the transition zone between open ocean and pack ice in the polar regions. Most theoretical paradigms, implemented in coupled wave-sea ice models, predict exponential decay of the wave energy but some recent…
Coupled climate model simulations designed to isolate the effects of Arctic sea-ice loss often apply artificial heating, either directly to the ice or through modification of the surface albedo, to constrain sea-ice in the absence of other…
A new continuum-mechanical formulation is proposed which encompasses all material processes within and surrounding an ice sheet. Using this formulation, the balance of mass and free-surface relations for ice sheets are derived and…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is performed to study the conditions for stability of a suspension of solid particles immersed in a viscous gas. The dissipation in such…
In this paper, we introduce a data-driven modeling approach for dynamics problems with latent variables. The state-space of the proposed model includes artificial latent variables, in addition to observed variables that can be fitted to a…
The Arctic sea ice cover has significantly declined over the recent decades. The debate on whether this decline is caused by anthropogenic activity or internal cycles is still ongoing. However, despite this uncertainty, some physical…
We study the seasonal changes in the thickness distribution of Arctic sea ice, $g(h)$, under climate forcing. Our analytical and numerical approach is based on a Fokker-Planck equation for $g(h)$ (Toppaladoddi \& Wettlaufer \emph{Phys. Rev.…
The premelting of ice is well known, but little is known about how the premelted and solid surfaces convert to each other. In this work, the transition dynamics between two phases are revealed with large-scale molecular dynamics…
This manuscript investigates the deformation of ice layers under a moving block, focusing on the theoretical framework and mathematical models that describe the mechanical and thermal properties of ice and its interaction with underlying…
The stochastic Arctic sea ice model described as a single periodic non-autonomous stochastic ordinary differential equation (ODE) is useful in explaining the seasonal variability of Arctic sea ice. However, to be nearer to realistic…
The fluctuation statistics of the observed sea ice extent during the satellite era are compared with model output from CMIP5 models using a multi-fractal time series method. The two robust features of the observations are that on annual to…
We first establish existence for all positive time near equilibrium for the moving interface problem between the Navier-Stokes equations for the evolving fluid phase (moved by the fluid velocity) and an elastic body modelled by the linear…
As Arctic conditions rapidly change, human activity in the Arctic will continue to increase and so will the need for high-resolution observations of sea ice. While satellite imagery can provide high spatial resolution, it is temporally…
Sea ice profoundly influences the polar environment and the global climate. Traditionally, Sea ice has been modeled as a continuum under Eulerian coordinates to describe its large-scale features, using, for instance, viscous-plastic…
Sea ice, or frozen ocean water, freezes and melts every year in the Arctic. Forecasts of where sea ice will be located weeks to months in advance have become more important as the amount of sea ice declines due to climate change, for…
A mechanism connecting ice algal ecodynamics with the buildup of organic macromolecules in brine channels is tested offline in a reduced model of pack geochemistry. Driver physical quantities are extracted from the global sea ice dynamics…