Water–propylene glycol sessile droplet shapes and migration: Marangoni mixing and separation of scales

New light is shed on morphological features of water–propylene glycol sessile droplets evaporating into ambient air at not too high relative humidity. Such droplets adopt a Marangoni-contracted shape even on perfectly wetting substrates, an effect well known since Cira et al. (Nature, 519, 2015). We here highlight a strong separation of scales normally occurring for such droplets. Namely, there is a narrow high-curvature zone localized at the foot of the droplet, where the apparent contact angle is formed, while the core of the droplet merely adheres to the classical (capillary–gravity) static shape. Experimentally, we rely upon interferometry to discern such fine key details. We detect a maximum of the droplet slope profile in the foot region, which amounts to the apparent contact angle. Theoretically, a local description of the foot region is devised. We indicate a crucial role of convective mixing by the solutal Marangoni flow, here accounted for by the Taylor dispersion, which proves to underlie the separation of scales and ensure self-consistency of the local model. Migration of such droplets in a humidity gradient is also approached within the same experimental and theoretical framework. It is considered that the resulting back–front asymmetry of the apparent contact angles drives the motion similarly to a wettability gradient, although the drag (‘Cox–Voinov’) factor is here found to be different. The predictions, comparing well with the measurements (our own and from the literature), are based on rigorous models, isothermal and as reduced as possible, without any fitting parameters or microphysics effects.

Combining Halo-EFT Descriptions of Nuclei and Precise Models of Nuclear Reactions

The clear separation of scales observed in halo nuclei between the extended halo and the compact core makes these exotic nuclei a perfect subject for effective field theory (EFT). Such description leads to a systematic expansion of the core-halo Hamiltonian, which naturally orders the nuclear-structure observables. In this short review, I show the advantages there are to include Halo-EFT descriptions within precise models of reactions. It helps identifying the nuclear-structure observables that matter in the description of the reactions, and enables us to easily bridge predictions of nuclear-structure calculations to reaction observables. I illustrate this on breakup, transfer and knockout reactions with $$^{11}$$ 11 Be, the archetypical one-neutron halo nucleus.

High Order Semi-implicit Multistep Methods for Time-Dependent Partial Differential Equations

We consider the construction of semi-implicit linear multistep methods that can be applied to time-dependent PDEs where the separation of scales in additive form, typically used in implicit-explicit (IMEX) methods, is not possible. As shown in Boscarino et al. (J. Sci. Comput. 68: 975–1001, 2016) for Runge-Kutta methods, these semi-implicit techniques give a great flexibility, and allow, in many cases, the construction of simple linearly implicit schemes with no need of iterative solvers. In this work, we develop a general setting for the construction of high order semi-implicit linear multistep methods and analyze their stability properties for a prototype linear advection-diffusion equation and in the setting of strong stability preserving (SSP) methods. Our findings are demonstrated on several examples, including nonlinear reaction-diffusion and convection-diffusion problems.

Learning dominant physical processes with data-driven balance models

Throughout the history of science, physics-based modeling has relied on judiciously approximating observed dynamics as a balance between a few dominant processes. However, this traditional approach is mathematically cumbersome and only applies in asymptotic regimes where there is a strict separation of scales in the physics. Here, we automate and generalize this approach to non-asymptotic regimes by introducing the idea of an equation space, in which different local balances appear as distinct subspace clusters. Unsupervised learning can then automatically identify regions where groups of terms may be neglected. We show that our data-driven balance models successfully delineate dominant balance physics in a much richer class of systems. In particular, this approach uncovers key mechanistic models in turbulence, combustion, nonlinear optics, geophysical fluids, and neuroscience.

Energy Localization through Locally Resonant Materials

Among the attractive properties of metamaterials, the capability of focusing and localizing waves has recently attracted research interest to establish novel energy harvester configurations. In the same frame, in this work, we develop and optimize a system for concentrating mechanical energy carried by elastic anti-plane waves. The system, resembling a Fabry-Pérot interferometer, has two barriers composed of Locally Resonant Materials (LRMs) and separated by a homogeneous internal cavity. The attenuation properties of the LRMs allow for the localization of waves propagating at particular frequencies. With proper assumptions on the specific ternary LRMs, the separation of scales (between the considered wave lengths and the characteristic dimension of the employed unit cells) enables the use of a two-scale asymptotic technique for computing the effective behavior of the employed LRMs. This leads to a complete analytic description of the motion of the system. Here we report the results achieved by optimizing the geometry of the system for obtaining a maximum focusing of the incoming mechanical energy. The analytic results are then validated through numerical simulations.

Model reduction in computational homogenization for transient heat conduction

This paper presents a computationally efficient homogenization method for transient heat conduction problems. The notion of relaxed separation of scales is introduced and the homogenization framework is derived. Under the assumptions of linearity and relaxed separation of scales, the microscopic solution is decomposed into a steady-state and a transient part. Static condensation is performed to obtain the global basis for the steady-state response and an eigenvalue problem is solved to obtain a global basis for the transient response. The macroscopic quantities are then extracted by averaging and expressed in terms of the coefficients of the reduced basis. Proof-of-principle simulations are conducted with materials exhibiting high contrast material properties. The proposed homogenization method is compared with the conventional steady-state homogenization and transient computational homogenization methods. Within its applicability limits, the proposed homogenization method is able to accurately capture the microscopic thermal inertial effects with significant computational efficiency.

Focusing of non-linear eccentric waves in astrophysical discs

ABSTRACT We develop a fully non-linear approximation to the short-wavelength limit of eccentric waves in astrophysical discs, based on the averaged Lagrangian method of Whitham. In this limit there is a separation of scales between the rapidly varying eccentric wave and the background disc. Despite having small eccentricities, such rapidly varying waves can be highly non-linear, potentially approaching orbital intersection, and this can result in strong pressure gradients in the disc. We derive conditions for the steepening of non-linearity and eccentricity as the waves propagate in a radially structured disc in this short-wavelength limit and show that the behaviour of the solution can be bounded by the behaviour of the WKB solution to the linearized equations.