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We present a new technique for the design of transformation-optics devices based on large-scale optimization to achieve the optimal effective isotropic dielectric materials within prescribed index bounds, which is computationally cheap…
The linearized, compressible Navier-Stokes equations can be used to model acoustic wave propagation in the presence of viscous and thermal boundary layers. However, acoustic boundary layers are notorious for invoking prohibitively high…
Accurate modeling of boundary conditions is crucial in computational physics. The ever increasing use of neural networks as surrogates for physics-related problems calls for an improved understanding of boundary condition treatment, and its…
Accurate prediction of surrounding road users' trajectories is essential for safe and efficient autonomous driving. While deep learning models have improved performance, challenges remain in preventing off-road predictions and ensuring…
We consider the Navier-Stokes equations in a channel with a narrowing and walls of varying curvature. By applying the empirical interpolation method to generate an affine parameter dependency, the offline-online procedure can be used to…
In this paper, our aim is to analyse the generalization capabilities of first-order methods for statistical learning in multiple, different yet related, scenarios including supervised learning, transfer learning, robust learning and…
Multiscale modelling aims to systematically construct macroscale models of materials with fine microscale structure. However, macroscale boundary conditions are typically not systematically derived, but rely on heuristic arguments,…
In this article we prove highly improved and flexible Strichartz-type estimates allowing us to generalize the asymptotics we obtained for a stratified and rotating incompressible Navier-Stokes system: for large (and less regular) initial…
Rapid growth of constraints is often observed in free evolutions of highly gravitating systems. To alleviate this problem we investigate the effect of adding spatial derivatives of the constraints to the right hand side of the evolution…
Recent direct numerical simulations of the FENE-P model of non-Newtonian hydrodynamics revealed that the phenomenon of drag reduction by polymer additives exists (albeit in reduced form) also in homogeneous turbulence. We introduce here a…
Recent developments in neural networks have shown the potential of estimating drag on irregular rough surfaces. Nevertheless, the difficulty of obtaining a large high-fidelity dataset to train neural networks is deterring their use in…
Mathematical settings in which heterogeneous structures affect electron transport through a tube-shaped quantum waveguide are studied, highlighting the interaction between heterogeneities and geometric parameters like curvature and torsion.…
Purpose: This study aims to assess the accuracy of degree adaptive strategies in the context of incompressible Navier-Stokes flows using the high order hybridisable discontinuous Galerkin (HDG) method. Design/methodology/approach: The work…
Direct numerical simulation of turbulence at realistic Reynolds numbers is still beyond current computational capability, necessitating models that reduce the number of resolved spatial scales. Motivated by phenomenology and recent…
The present works is focused on studying bifurcating solutions in compressible fluid dynamics. On one side, the physics of the problem is thoroughly investigated using high-fidelity simulations of the compressible Navier-Stokes equations…
A procedure for evolving hyperbolic systems of equations on compact computational domains with no boundary conditions was recently described in [arXiv:1905.08657]. In that proposal, the computational grid is expanded in spacelike directions…
The objective of this work is to establish a systematic study of boundary value problems within the framework of differential forms and variable exponent spaces. Specifically, we investigate the Hodge Laplacian and related first order…
A fundamental problem in the field of turbulent skin-friction drag reduction is to determine the performance of the available control techniques at high values of the Reynolds number $Re$. We consider active, predetermined strategies based…
Performance of optimization on quadratic problems sensitively depends on the low-lying part of the spectrum. For large (effectively infinite-dimensional) problems, this part of the spectrum can often be naturally represented or approximated…
We consider the homogenization of the Navier-Stokes equation, set in a channel with a rough boundary, of small amplitude and wavelength $\epsilon$. It was shown recently that, for any non-degenerate roughness pattern, and for any reasonable…