相关论文: Theory of the sea ice thickness distribution
The Thorndike et al., (\emph{J. Geophys. Res.} {\bf 80} 4501, 1975) theory of the ice thickness distribution, $g(h)$, treats the dynamic and thermodynamic aggregate properties of the ice pack in a novel and physically self-consistent…
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.…
We use tools from statistical physics to develop a stochastic theory for the drift of a single Arctic sea-ice floe. Floe-floe interactions are modelled using a Coulomb friction term, with any change in the thickness or the size of the ice…
Sea ice is not continuous and homogeneous on large scales. Its morphology is inherently discrete and made of individual floes. In recent years, sea ice models have incorporated this horizontal heterogeneity. The modelling framework…
We outline a statistical theory of turbulence based on the Lagrangian formulation of fluid motion. We derive a hierarchy of evolution equations for Lagrangian N-point probability distributions as well as a functional equation for a suitably…
The hydrodynamic equation governing the homogeneous time evolution of the temperature in a model of confined granular gas is studied by means of the Enskog equation. The existence of a normal solution of the kinetic equation is assumed as a…
We derive a stochastic wave equation for an inflaton in an environment of an infinite number of fields. We study solutions of the linearized stochastic evolution equation in an expanding universe. The Fokker-Planck equation for the inflaton…
Sea ice is highly complex due to the inhomogeneity of the physical properties (e.g. temperature and salinity) as well as the permeability and mixture of water and a matrix of sea ice and/or sea ice crystals. Such complexity has proven…
Anomalous diffusion and power-law distributions are observed in various complex systems. To provide a consistent dynamical foundation for these phenomena, we present a geometric derivation of the nonlinear Fokker-Planck equation by…
We examine the nature of the ice-albedo feedback in a long standing approach used in the dynamic-thermodynamic modeling of sea ice. The central issue examined is how the evolution of the ice area is treated when modeling a partial ice cover…
We consider classical solutions to the kinetic Fokker-Planck equation on a bounded domain $\mathcal O \subset~\mathbb{R}^d$ in position, and we obtain a probabilistic representation of the solutions using the Langevin diffusion process with…
We formulate a model describing the evolution of thickness in a shallow ice sheet lying over a lithosphere. The model is thus governed by a set of variational inequalities that involve nonlinearities in the time derivative and in the…
We derive the exact evolution equation for the probability density function of particle displacements generated by arbitrary Gaussian velocity processes, when neither Markovianity and nor stationarity are assumed. Starting from the…
We study the formation and the evolution of velocity distribution tails for systems with long-range interactions. In the thermal bath approximation, the evolution of the distribution function of a test particle is governed by a…
We analyze the stability of a low-order coupled sea ice and climate model and extract the essential physics governing the time scales of response as a function of greenhouse gas forcing. Under present climate conditions the stability is…
Sea ice is a complex system, and observations have shown that ice segments (i.e., floes) have a wide range of sizes, with a floe size distribution that follows a power law. However, a theory for the power law and its exponent have remained…
This paper proves the local-in-time strong well-posedness of a parabolic-hyperbolic regularized version of Hibler's sea ice model. Hibler's model is the most frequently used sea ice model in climate science. Lagrangian coordinates are…
We develop a general approach for studying the cumulative probability distribution function of localized objects (particles) whose dynamics is governed by the first-order Langevin equation driven by superheavy-tailed noise. Solving the…
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 one-dimensional propagation of seismic waves with constant Q is shown to be governed by an evolution equation of fractional order in time, which interpolates the heat equation and the wave equation. The fundamental solutions for the…