Spectral analysis of the biharmonic operator subject to Neumann boundary conditions on dumbbell domains

We consider the biharmonic operator subject to homogeneous boundary conditions of Neumann type on a planar dumbbell domain which consists of two disjoint domains connected by a thin channel. We analyse the spectral behaviour of the operator, characterizing the limit of the eigenvalues and of the eigenprojections as the thickness of the channel goes to zero. In applications to linear elasticity, the fourth order operator under consideration is related to the deformation of a free elastic plate, a part of which shrinks to a segment. In contrast to what happens with the classical second order case, it turns out that the limiting equation is here distorted by a strange factor depending on a parameter which plays the role of the Poisson coefficient of the represented plate.Comment: To appear in "Integral Equations and Operator Theory

Domain Dependence of Elliptic Operators in Divergence Form

Domain Dependence of Elliptic Operators in Divergence For

On the flow separation mechanism in the inverse Leidenfrost regime

The inverse Leidenfrost regime occurs when a heated object in relative motion with a liquid is surrounded by a stable vapour layer, drastically reducing the hydrodynamic drag at large Reynolds numbers due to a delayed separation of the flow. To elucidate the physical mechanisms that control separation, here we report a numerical study of the boundary-layer equations describing the liquid-vapour flow around a solid sphere whose surface temperature is above the Leidenfrost point. Our analysis reveals that the dynamics of the thin layer of vaporised liquid controls the downstream evolution of the flow, which cannot be properly described substituting the vapour layer by an effective slip length. In particular, the dominant mechanism responsible for the separation of the flow is the onset of vapour recirculation caused by the adverse pressure gradient in the rearward half of the sphere, leading to an explosive growth of the vapour-layer thickness due to the accumulation of vapour mass. Buoyancy forces are shown to have an important effect on the onset of recirculation, and thus on the separation angle. Our results compare favourably with previous experiments.Comment: 17 pages, 5 figures, revised version submitted to J Fluid Mec

Comparison of hydrochar fractionation and composition in batch and continuous hydrothermal liquefaction

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Atmospheric-Pressure Non-thermal Plasma-JET effects on PS and PE surfaces

https://www.scopus.com/inward/record.url?eid=2-s2.0-84938125206&partnerID=40&md5=c2325a28f944e7e3e20b601b8d9a73efThe Atmospheric-Pressure Non-Thermal Plasma (APNTP) has become a topic of a great interest for a wide spectrum of applications in different industry branches, including the surface of treatment processes. In this work we evaluate the effect of an argon APNTP exposure to determine changes suffered by a polystyrene (PS) and polyethylene (PE) polymer surface through RAMAN spectroscopy and SEM. It was determined that the hydrophilic change in energetic terms, i.e. surface activation in the PS and PE polymers is addition of oxygen by surface activation when the samples with jet plasma are exposed with the inert argon gas. It was possible to characterize the hydrophilic shift based on the change in intensity of the spectra. © Published under licence by IOP Publishing Ltd.Ad Astra Rocket Company,Instituto Tecnologico de Costa Rica,International Atomic Energy Agency (IAEA),Universidad Nacional de Costa Ric

Coarsening Kinetics of Complex Macromolecular Architectures in Bad Solvent

This study reports a general scenario for the out-of-equilibrium features of collapsing polymeric architectures. We use molecular dynamics simulations to characterize the coarsening kinetics, in bad solvent, for several macromolecular systems with an increasing degree of structural complexity. In particular, we focus on: flexible and semiflexible polymer chains, star polymers with 3 and 12 arms, and microgels with both ordered and disordered networks. Starting from a powerful analogy with critical phenomena, we construct a density field representation that removes fast fluctuations and provides a consistent characterization of the domain growth. Our results indicate that the coarsening kinetics presents a scaling behaviour that is independent of the solvent quality parameter, in analogy to the time–temperature superposition principle. Interestingly, the domain growth in time follows a power-law behaviour that is approximately independent of the architecture for all the flexible systems; while it is steeper for the semiflexible chains. Nevertheless, the fractal nature of the dense regions emerging during the collapse exhibits the same scaling behaviour for all the macromolecules. This suggests that the faster growing length scale in the semiflexible chains originates just from a faster mass diffusion along the chain contour, induced by the local stiffness. The decay of the dynamic correlations displays scaling behavior with the growing length scale of the system, which is a characteristic signature in coarsening phenomena.This research was funded by projects PGC2018-094548-B-I00 (MCIU/AEI/FEDER, UE) and IT-1175-19 (GV, Spain