We study the homogenization of Lagrangian functionals of Hamilton-Jacobi equations (HJ) with quadratic nonlinearity and unbounded stationary ergodic random potential in R, d≥1. We show that homogenization holds if and only if the potential is bounded from above. When the potential is unbounded from above, homogenization breaks down, due to the almost sure growth of the running maxima of the ran...

About 90% of the anthropogenic increase in heat stored in the climate system 6 is found the oceans. Therefore it is relevant to understand the details of ocean heat up7 take. Here we present a detailed, process-based analysis of ocean heat uptake (OHU) pro8 cesses in HiGEM1.2, an atmosphere-ocean general circulation model (AOGCM) with an 9 eddy-permitting ocean component of 1/3 resolution. Simi...

We develop a multiscale Eulerian–Lagrangian localized adjoint method for transient linear advection– diffusion equations with oscillatory coefficients, which arise in mathematical models for describing flow and transport through heterogeneous porous media, composite material design, and other applications.

In this paper we study time-periodic solutions to advection-diffusion equations of a scalar quantity u on a periodically moving n-dimensional hypersurface Γ(t) ⊂ Rn+1. We prove existence and uniqueness of solutions in suitable Hölder spaces.

In this paper, the exponential B-spline functions are used for the numerical solution of the advection-diffusion equation. Two numerical examples related to pure advection in a finitely long channel and the distribution of an initial Gaussian pulse are employed to illustrate the accuracy and the efficiency of the method. Obtained results are compared with some early studies.

The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional reaction-diffusion-advection equations, for the growth of a population on a heterogeneous habitat. Considering a number of models of increasing complexity we investigate the often con...

Integral representations are derived from a differential-type boundary value problem using a fundamental solution. A set of integral representations is equivalent to a set of differential equations. If the boundary conditions are substituted into the integral representations, the integral equations are obtained, and the unknown variables are determined by solving the integral equations. In othe...

In this paper we describe a general purpose, graphics processing unit (GP-GPU)-based approach for solving partial differential equations (PDEs) within advection-reactiondiffusion models. The GP-GPU-based approach provides a platform for solving PDEs in parallel and can thus significantly reduce solution times over traditional CPU implementations. This allows for a more efficient exploration of ...

In the past most diagnostic studies of frontal cyclone development have been carried out through use of quasigeostrophic models. In this paper we present the results of vertical motions obtained from a 5-level general balance model. Nongeostrophic effects such as deformation and beta term of the balance equations, divergence, vertical advection, and the twisting term of the complete vorticity e...