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In this work, we consider the coupled systems of linear unsteady partial differential equations, which arise in the modeling of poroelasticity processes. Stability estimates of weighted difference schemes for the coupled system of equations…
Interfaces in two-dimensional systems exhibit unexpected complex dynamical behaviors, the dynamics of a border connecting a stripe pattern and a uniform state is studied. Numerical simulations of a prototype isotropic model, the subcritical…
Climate simulations, at all grid resolutions, rely on approximations that encapsulate the forcing due to unresolved processes on resolved variables, known as parameterizations. Parameterizations often lead to inaccuracies in climate models,…
In this paper, we consider Euler-like balance laws for mixture components that involve macroscopic velocities and temperatures for each different species. These laws are not conservative due to mutual interaction between species. In…
The Lindblad equation describes the dissipative time evolution of a density matrix that characterizes an open quantum system in contact with its environment. The widespread ensemble interpretation of a density matrix requires its time…
Data-driven modeling and control of temperature dynamics in mechatronics systems and industrial processes are challenging control engineering problems. This is mainly because the temperature dynamics is inherently infinite-dimensional,…
Models in which dark energy interacts with dark matter have been proposed in the literature to help explain why dark energy should only come to dominate in recent times. In this paper, we present a dynamical framework to calculate…
New results from the Coupled Model Inter-comparison Project phase 5 (CMIP5) and multiple global reanalysis datasets are used to investigate the relationship between the mean and standard deviation in the surface air temperature. A…
This article presents a new phase-field formulation for non-equilibrium interface conditions in rapid phase transformations. With a particular way of defining concentration fields, the classical sharp and diffuse (thick) interface theories…
We study a decoupling iterative algorithm based on domain decomposition for the time-dependent nonlinear Stokes-Darcy model, in which different time steps can be used in the flow region and in the porous medium. The coupled system is…
The deterministic equations describing the dynamics of the atmosphere (and of the climate system) are known to display the property of sensitivity to initial conditions. In the ergodic theory of chaos this property is usually quantified by…
We consider a kinetic model of two species of particles interacting with a reservoir at fixed temperature, described by two coupled Vlasov-Fokker-Plank equations. We prove that in the diffusive limit the evolution is described by a…
Phase field models are powerful tools to tackle free boundary problems. For phase transformations involving diffusion, the evolution of the non conserved phase field is coupled to the evolution of the conserved diffusion field. Introducing…
Motivated by dynamical experiments on cold atomic gases, we develop a quantum kinetic approach to weakly perturbed integrable models out of equilibrium. Using the exact matrix elements of the underlying integrable model we establish an…
The Met Office's weather and climate simulation code the Unified Model is used for both operational Numerical Weather Prediction and Climate modelling. The computational performance of the model running on parallel supercomputers is a key…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
We present a thermodynamic theory of plane coherent solid-solid interfaces in multicomponent systems subject to nonhydrostatic mechanical stresses. The interstitial and substitutional chemical components are treated separately using…
Thermodynamics entails a set of mathematical conditions on quantum Markovian dynamics. In particular, strict energy conservation between the system and environment implies that the dissipative dynamical map commutes with the unitary system…
We study systems with periodically oscillating parameters that can give way to complex periodic or non periodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal…
This article presents a multi-physics methodology for the numerical simulation of physical systems that involve the non-linear interaction of multi-phase reactive fluids and elastoplastic solids, inducing high strain-rates and high…