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A low-dimensional model (LDM) for turbulent Rayleigh-Benard convection in a Cartesian cell with square domain, based on the Galerkin projection of the Boussinesq equations onto a finite set of empirical eigenfunctions, is presented. The…
Vector modes represent the most general state of light in which, the spatial and polarisation degrees of freedom are coupled in a non-separable way. Crucially, while polarisation is limited to a bi-dimensional space, the spatial degree of…
A parametric reduced order model based on proper orthogonal decomposition with Galerkin projection has been developed and applied for the modeling of heat transport in T-junction pipes which are widely found in nuclear power plants. Thermal…
The transition to turbulence in Rayleigh-Benard convection with phase changes and the resulting convective patterns are studied in a three-dimensional Galerkin model. Our study is focused to the conditionally unstable regime of moist…
A relativistic diffusion model with cylindrical symmetry, which propagates an initial state based on quantum chromodynamics in time towards a thermal equilibrium limit, is derived from nonequilibrium-statistical considerations: Adapting an…
Plasmas are highly nonlinear and multi-scale, motivating a hierarchy of models to understand and describe their behavior. However, there is a scarcity of plasma models of lower fidelity than magnetohydrodynamics (MHD), although these…
The thermal dynamics in thermo-mechanical systems exhibits a much slower time scale compared to the structural dynamics. In this work, we use the method of multiple scales to reduce the thermo-mechanical structural models with a…
Many unsteady flows exhibiting complex dynamics are nevertheless characterized by emergent large-scale coherence in space and time. Reduced-order models based on Galerkin projection of the governing equations onto an orthogonal modal basis…
A coupled map lattice for convection is proposed, which consists of Eulerian and Lagrangian procedures. Simulations of the model not only reproduce a wide-range of phenomena in Rayleigh-B\'{e}nard convection experiments but also lead to…
The Galerkin method is used to derive a realistic model of plane Couette flow in terms of partial differential equations governing the space-time dependence of the amplitude of a few cross-stream modes. Numerical simulations show that it…
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by…
A ubiquitous arrangement in nature is a free-flowing fluid coupled to a porous medium, for example a river or lake lying above a porous bed. Depending on the environmental conditions, thermal convection can occur and may be confined to the…
The method of calculating the free energy and thermodynamic characteristics of the classical n-vector three-dimensional (3D) magnetic model at the microscopic level without any adjustable parameters is proposed. Mathematical description is…
Numerous study on natural and man made systems including rotating convection report the phenomena of supercritical and subcritical transitions from one state to another with the variation of relevant control parameters. However, the…
Reduced-order models were derived for plane Couette flow using Galerkin projection, with orthonormal basis functions taken as the leading controllability modes of the linearised Navier-Stokes system for a few low wavenumbers. Resulting…
The combined effectiveness of model reduction and the quasilinear approximation for the reproduction of the low-order statistics of oceanic surface boundary-layer turbulence is investigated. Idealized horizontally homogeneous problems of…
A visualization of three-dimensional incompressible flows by divergence-free quasi-two-dimensional projections of the velocity field on three coordinate planes was recently proposed. The projections were calculated using divergence-free…
We review different (reduced) models for thin structures using bending as principal mechanism to undergo large deformations. Each model consists in the minimization of a fourth order energy, potentially subject to a nonconvex constraint.…
Two Galerkin methods are applied to a problem of convection with uniform internal heat source are given. With each method analytical results are obtained and discussed. They concern the parameter representing the heating rate. Numerical…
Seismic imaging of the mantle has revealed large and small scale heterogeneities in the lower mantle; specifically structures known as large low shear velocity provinces (LLSVP) below Africa and the South Pacific. Most interpretations…