Related papers: Nonsmooth frameworks for an extended Budyko model
We consider a simplified version of the Budyko diffusive energy balance climate model. We obtain the exact number of monotone stationary solutions of the associated discontinuous nonlinear elliptic with absorption. We show that the…
Collision of equilibria with a splitting manifold has been locally studied, but might also be a contributing factor to global bifurcations. In particular a boundary collision can be coincident with collision of a virtual equilibrium with a…
We present a new conceptual model of the Earth's glacial-interglacial cycles, one leading to governing equations for which the vector field has a hyperplane of discontinuities. This work extends the classic Budyko- and Sellers-type…
A dynamical system derived from a conceptual climate model is investigated. The model is often referred to as Budyko-Sellers type Energy Balance Model (EBM), or in short, the Budyko model. The focus of this study is on the mathematical…
Starting from a classical Budyko-Sellers-Ghil energy balance model for the average surface temperature of the Earth, a nonautonomous version is designed by allowing the solar irradiance and the cloud cover coefficients to vary with time in…
The supercritical state of matter is usually described as a continuous phase without sharp boundaries between liquid and gas regions. However, under non-equilibrium conditions, this view breaks down. Here we report an experimental…
We develop a three-timescale framework for modelling climate change and introduce a space-heterogeneous one-dimensional energy balance model. This model, addressing temperature fluctuations from rising carbon dioxide levels and the…
In this paper we perform a careful analysis of the forced PP04 model for climate change, in particular the behaviour of the ice-ages. This system models the transition from a glacial to an inter-glacial state through a sudden release of…
As Arctic sea ice extent decreases with increasing greenhouse gases, there is a growing interest in whether there could be a bifurcation associated with its loss, and whether there is significant hysteresis associated with that bifurcation.…
In [SIAM J. Appl. Dyn. Sys., 12(4):2068--2092, 2013], Widiasih proposed and analyzed a deterministic one-dimensional Budyko-Sellers energy-balance model with a moving ice-line. In this paper, we extend this model to the stochastic setting…
Liquid-gas phase coexistence in a boundary-driven diffusive system is studied by analyzing fluctuating hydrodynamics of a density field defined on a one-dimensional lattice with a space interval $\Lambda$. When an interface width $\ell$ is…
We investigate the influence of boundaries and spatial nonreciprocity on nonequilibrium driven-dissipative phase transitions. We focus on a one-dimensional lattice of nonlinear bosons described by a Lindblad master equation, where the…
The climate is a complex non-equilibrium dynamical system that relaxes toward a steady state under the continuous input of solar radiation and dissipative mechanisms. The steady state is not necessarily unique. A useful tool to describe the…
We study the global influence of curvature on the free energy landscape of two-dimensional binary mixtures confined on closed surfaces. Starting from a generic effective free energy, constructed on the basis of symmetry considerations and…
There is widespread agreement that ice sheets flowed into the ocean in tropical latitudes at sea level during the Earth's past. Whether these extreme ice ages were snowball Earth events, with the entire surface covered in ice, or whether…
We investigate a coupled atmosphere-ocean model including the mechanical and thermodynamical interaction between the two fluids for the mid-latitudes. The formulation combines a multilayer quasi-geostrophic dynamical framework with…
This article investigates an energy balance model coupled to the primitive equations by a dynamic boundary condition with and without noise on the boundary. It is shown that this system is globally strongly well-posed both in the…
In this work we consider a general non-autonomous hybrid system based on the integrate-and-fire model, widely used as simplified version of neuronal models and other types of excitable systems. Our unique assumption is that the system is…
In this paper, we solve a North-type Energy Balance Model (EBM) using an analytical method, the Boundary Integral Method. This approach is discussed in light of existing analytical techniques for this type of equation. We use the method to…
We consider a nonlinear, free boundary fluid-structure interaction model in a bounded domain. The viscous incompressible fluid interacts with a nonlinear elastic body on the common boundary via the velocity and stress matching conditions.…