Outputs (6)

Estimating divergence‐free flows via neural networks (2021)
Presentation / Conference Contribution
Kabanov, D. I., Espath, L., Kiessling, J., & Tempone, R. F. (2022, August). Estimating divergence‐free flows via neural networks. Presented at 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Virtual conference

We apply neural networks to the problem of estimating divergence-free velocity flows from given sparse observations. Following the modern trend of combining data and models in physics-informed neural networks, we reconstruct the velocity flow by trai... Read More about Estimating divergence‐free flows via neural networks.

Statistical learning for fluid flows: Sparse Fourier divergence-free approximations (2021)
Journal Article
Espath, L., Kabanov, D., Kiessling, J., & Tempone, R. (2021). Statistical learning for fluid flows: Sparse Fourier divergence-free approximations. Physics of Fluids, 33(9), Article 097108. https://doi.org/10.1063/5.0064862

We reconstruct the velocity field of incompressible flows given a finite set of measurements. For the spatial approximation, we introduce the Sparse Fourier divergence-free approximation based on a discrete L2 projection. Within this physics-informed... Read More about Statistical learning for fluid flows: Sparse Fourier divergence-free approximations.

Extended Larché–Cahn framework for reactive Cahn–Hilliard multicomponent systems (2021)
Journal Article
Clavijo, S. P., Espath, L., & Calo, V. M. (2021). Extended Larché–Cahn framework for reactive Cahn–Hilliard multicomponent systems. Continuum Mechanics and Thermodynamics, 33(6), 2391-2410. https://doi.org/10.1007/s00161-021-01045-9

At high temperature and pressure, solid diffusion and chemical reactions between rock minerals lead to phase transformations. Chemical transport during uphill diffusion causes phase separation, that is, spinodal decomposition. Thus, to describe the c... Read More about Extended Larché–Cahn framework for reactive Cahn–Hilliard multicomponent systems.

A continuum theory for mineral solid solutions undergoing chemo-mechanical processes (2021)
Journal Article
Clavijo, S. P., Espath, L., Sarmiento, A., & Calo, V. M. (2022). A continuum theory for mineral solid solutions undergoing chemo-mechanical processes. Continuum Mechanics and Thermodynamics, 34(1), 17-38. https://doi.org/10.1007/s00161-021-01041-z

Recent studies on metamorphic petrology as well as microstructural observations suggest the influence of mechanical effects upon chemically active metamorphic minerals. Thus, the understanding of such a coupling is crucial to describe the dynamics of... Read More about A continuum theory for mineral solid solutions undergoing chemo-mechanical processes.

Phase-field gradient theory (2021)
Journal Article
Espath, L., & Calo, V. (2021). Phase-field gradient theory. Zeitschrift für Angewandte Mathematik und Physik, 72(2), Article 45. https://doi.org/10.1007/s00033-020-01441-2

We propose a phase-field theory for enriched continua. To generalize classical phase-field models, we derive the phase-field gradient theory based on balances of microforces, microtorques, and mass. We focus on materials where second gradients of the... Read More about Phase-field gradient theory.

On the control volume arbitrariness in the Navier-Stokes equation (2021)
Journal Article
Espath, L. (2021). On the control volume arbitrariness in the Navier-Stokes equation. Physics of Fluids, 33(1), Article 015110. https://doi.org/10.1063/5.0037468

We present a continuum theory to demonstrate the implications of considering general tractions developed on arbitrary control volumes where the surface enclosing it lacks smoothness. We then tailor these tractions to recover the Navier-Stokes-αβ equa... Read More about On the control volume arbitrariness in the Navier-Stokes equation.