Related papers: Arctic curves of the T-system with Slanted Initial…
Denote by $\mathcal{K}_0^n$ the family of all closed convex sets $A\subset\mathbb{R}^n$ containing the origin $0\in\mathbb R^n$. For $A\in\mathcal{K}_0^n,$ its polar set is denoted by $A^\circ.$ In this paper, we investigate the topological…
Understanding how sea ice melts is critical to climate projections. In the Arctic, melt ponds that develop on the surface of sea ice floes during the late spring and summer largely determine their albedo -- a key parameter in climate…
The time evolution of linear fields of spin $s = \pm 1$ and $s = \pm 2$ on Kerr black hole spacetimes are investigated by solving the homogeneous Teukolsky equation numerically. The applied numerical setup is based on a combination of…
The six-vertex model with domain-wall boundary conditions is one representative of a class of two-dimensional lattice statistical mechanics models that exhibit a phase separation known as the arctic curve phenomenon. In the thermodynamic…
We develop a linear method for solving the nonlinear differential equations of a lumped-parameter thermal model of a spacecraft moving in a closed orbit. Our method, based on perturbation theory, is compared with heuristic linearizations of…
In this thesis, I study hydrodynamical models of slim accretion disks --- advective, optically thick disks which generalize the standard models of radiatively efficient thin disks to all accretion rates. I start with a general introduction…
We investigate the area-preserving mean-curvature-type motion of a two-dimensional lattice crystal obtained by coupling constrained minimizing movements scheme introduced by Almgren, Taylor and Wang with a discrete-to-continuous analysis.…
We study a discrete-time interacting particle system with continuous state space which is motivated by a mathematical model for turnover through branching in actin filament networks. It gives rise to transient clusters reminiscent of actin…
We establish a general link between integrable systems in algebraic geometry (expressed as Jacobian flows on spectral curves) and soliton equations (expressed as evolution equations on flat connections). Our main result is a natural…
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…
We use the consistency approach to classify discrete integrable 3D equations of the octahedron type. They are naturally treated on the root lattice $Q(A_3)$ and are consistent on the multidimensional lattice $Q(A_N)$. Our list includes the…
This paper is devoted to the multigrid convergence analysis for the linear systems arising from the conforming linear finite element discretization of the second order elliptic equations with anisotropic diffusion. The multigrid convergence…
This paper is on further development of discrete complex analysis introduced by R. Isaacs, J. Ferrand, R. Duffin, and C. Mercat. We consider a graph lying in the complex plane and having quadrilateral faces. A function on the vertices is…
Using the Boltzmann weights of classical Statistical Mechanics vertex models we define a new class of Tensor Product Ansatzs for 2D quantum lattice systems, characterized by a strong anisotropy, which gives rise to stripe like structures.…
We consider the mathematical model of gas trapping in deep polar ice (firns), which consists of a parabolic partial differential equation, that can degenerate at one boundary extreme. In [1], we considered all the coefficients to be…
For systems of coupled differential equations on a sequence of W-random graphs, we derive the continuum limit in the form of an evolution integral equation. We prove that solutions of the initial value problems (IVPs) for the discrete model…
Synthetic quantum systems with interacting constituents play an important role in quantum information processing and in elucidating fundamental phenomena in many-body physics. Following impressive advances in cooling and trapping…
Rapid changes in Earth's cryosphere caused by human activity can lead to significant environmental impacts. Computer models provide a useful tool for understanding the behavior and projecting the future of Arctic and Antarctic ice sheets.…
By solving analytically the various types of Lane-Emden equations with rotation, we have discovered two new coupled fundamental properties of rotating, self-gravitating, gaseous disks in equilibrium: Isothermal disks must, on average,…
Snow density estimates below the surface, used with airplane-acquired ice-penetrating radar measurements, give a site-specific history of snow water accumulation. Because it is infeasible to drill snow cores across all of Antarctica to…