arXiv subjects

André Guerra

Publications and source records attributed to André Guerra.

At least 37 records · Page 2Linked to original sources

arXiv2024

Constraint maps: singularities vs free boundaries

Energy-minimizing constraint maps are a natural extension of the obstacle problem within a vectorial framework. Due to inherent topological constraints, these maps manifest a diverse structure that includes singularities similar to harmonic maps, branch points reminiscent of minimal surfaces, and the intricate free-boundary behavior of the obstacle problem. The complexity of these maps poses significant challenges to their analysis. In this paper, we first focus on constraint maps with uniformly convex obstacles and establish continuity (and therefore higher-order regularity) within a uniform neighborhood of the free boundary. More precisely, thanks to a new quantitative unique continuation principle near singularities (which is new even in the setting of classical harmonic maps), we prove that, in the uniformly convex setting, topological singularities can only lie in the interior of the contact set. We then establish the optimality of this result. Second, while exploring the structure of the free boundary, we investigate the presence of branch points and show how they lead to completely new types of singularities not present in the scalar case.

math.AP↗

arXiv2024

Molecular dynamics characterization of the interfacial structure and forces of the methane-ethane sII gas hydrate interface

The nucleation of gas hydrates is of great interest in flow assurance, global energy demand, and carbon capture and storage. A complex molecular understanding is critical to control hydrate nucleation and growth in the context of potential applications. Molecular dynamics is employed in this work combined with the mechanical definition of surface tension to assess the surface stresses that control some of the behavior at the interface. Ensuring careful sampling and simulation behavior, this work extracts meaningful results from molecular properties. We characterize the interfacial tension for sII methane/ethane hydrate and gas mixtures for different temperatures and pressures. We find that the surface tension trends positively with temperature in a balance of water-solid and water-gas interactions. The molecular dipole shows the complexities of water molecule behavior in small, compressed pre-melting layer that emerges as a quasi-liquid. These behaviors contribute to the developing knowledge base surrounding practical applications of this interface.

physics.app-ph↗

arXiv2024

Compensation phenomena for concentration effects via nonlinear elliptic estimates

We study compensation phenomena for fields satisfying both a pointwise and a linear differential constraint. This effect takes the form of nonlinear elliptic estimates, where constraining the values of the field to lie in a cone compensates for the lack of ellipticity of the differential operator. We give a series of new examples of this phenomenon for a geometric class of cones and operators such as the divergence or the curl. One of our main findings is that the maximal gain of integrability is tied to both the differential operator and the cone, contradicting in particular a recent conjecture from arXiv:2106.03077. This extends the recent theory of compensated integrability due to D. Serre. In particular, we find a new family of integrands that are Div-quasiconcave under convex constraints.

math.AP↗

arXiv2024

Regularity and compactness for critical points of degenerate polyconvex energies

We study Lipschitz critical points of the energy $\int_Ωg(\det D u) \, d x$ in two dimensions, where $g$ is a strictly convex function. We prove that the Jacobian of any Lipschitz critical point is constant, and that the Jacobians of sequences of approximately critical points converge strongly. The latter result answers in particular an open problem posed by Kirchheim, Müller and Šverák in 2003.

math.AP↗

arXiv2024

The local Burkholder functional, quasiconvexity and Geometric Function Theory

We show that the local Burkholder functional $\mathcal B_K$ is quasiconvex. In the limit of $p$ going to 2 we find a class of non-polyconvex functionals which are quasiconvex on the set of matrices with positive determinant. In order to prove the validity of lower semicontinuity arguments in this setting, we show that the Burkholder functionals satisfy a sharp extension of the classical function theoretic area formula. As a corollary, in addition to functionals in geometric function theory, one finds new classes of non-polyconvex functionals, degenerating as the determinant vanishes, for which there is existence of minimizers.

math.AP↗

arXiv2024

Optimal quantitative stability of the Möbius group of the sphere in all dimensions

In any dimension $n\geq 3$, we prove an optimal stability estimate for the Möbius group among maps $u\colon \mathbb S^{n-1} \to \mathbb R^n$, of the form $\inf_{λ>0,ϕ\in \mathrm{Möb}(\mathbb S^{n-1})} \int_{\mathbb S^{n-1}}\left|\frac 1λ\nabla_{T} u -\nabla_{ T}ϕ\right|^{n-1} d\mathcal H^{n-1} \leq C_n \mathcal E_{n-1}(u).$ Here, $\mathcal E_{n-1}(u)$ is a conformally invariant deficit which measures simultaneously lack of conformality and the deviation of $u(\mathbb S^{n-1})$ from being a round sphere in an isoperimetric sense. This entails in particular the following qualitative statement: sequences with vanishing deficit, once appropriately normalized by the action of the Möbius group, are compact. Both the qualitative and the quantitative results are new for all dimensions $n\geq 4$.

math.DG↗

arXiv2023

Unique continuation for differential inclusions

We consider the following question arising in the theory of differential inclusions: given an elliptic set $Γ$ and a Sobolev map $u$ whose gradient lies in the quasiconformal envelope of $Γ$ and touches $Γ$ on a set of positive measure, must $u$ be affine? We answer this question positively for a suitable notion of ellipticity, which for instance encompasses the case where $Γ\subset \mathbb R^{2\times 2}$ is an elliptic, smooth, closed curve. More precisely, we prove that the distance of $D u$ to $Γ$ satisfies the strong unique continuation property. As a by-product, we obtain new results for nonlinear Beltrami equations and recover known results for the reduced Beltrami equation and the Monge--Ampère equation: concerning the latter, we obtain a new proof of the $W^{2,1+\varepsilon}$-regularity for two-dimensional solutions.

math.AP↗

arXiv2023

Dynamics of Acoustically Levitated Ice Impacts on Smooth and Textured Surfaces: Effects of Surface Roughness, Elasticity, and Structure

Through acoustically levitated ice formation and subsequent release onto a controlled area, this study introduces a third class of ice-countering system beyond de- and anti-icing: ice-impacting. By subjecting stainless steel 316 (SS), epoxy resin-coated (ER), and laser-textured (LT) surfaces with known surface roughness, hardness, and structural characteristics to 40 ice droplet impacts each, the effect on surface properties and their effect on solid-solid interfacial impact dynamics, in turn, was examined using a novel analysis framework based on fundamental conservation laws. For the velocities experienced in this study, the impacts did not affect the surface properties; they were consistent after each impact. Elasticity was the most significant factor in droplet behavior: the ER surface exhibited rebounding for 78% of impacts (important for moving surfaces). Surface roughness also played a role, particularly for droplets with rotational motion, as immobilization occurred for 66% of impacts on the rougher LT surface. However, the nanostructures on that textured surface resulted in droplet redirection perpendicular to the surface directionality (critical for stationary surfaces). In contrast, the other surfaces saw no change or no consistent change in rebound angle. Elasticity also affected momentum retention, where the ER surface had a translational restitution coefficient of 0.32 compared to 0.17 for the two stainless steel surfaces. Surface roughness was the predominant aspect of energy retention: the LT surface had a translational-to-rotational energy transfer coefficient of 0.07 (0.23 for the smoother surfaces), resulting in an overall energy retention coefficient of 0.09 compared to 0.28 for the SS and ER surfaces on average.

physics.app-ph↗

arXiv2023

Non-Einsteinian Viscosity Reduction in Boron Nitride Nanotube Nanofluids

(1) Introduction: Nanoparticles have multiple applications, including drug delivery systems, biosensing, and carbon capture. Non-Einstein-like viscosity reduction has been reported in nanoparticle-polymer blends at low nanoparticle concentrations. More recently, a similar non-Einsteinian viscosity reduction effect has been observed in aqueous ultra-low concentration carbon-based nanofluids. (2) Methods: We use a boron nitride nanotube functionalized with hydrophilic groups in rheological experiments to investigate the viscosity reduction in ultra-low concentration nanofluids (0.1-10 ppm). We measure the dynamic viscosity in an air atmosphere and methane (0-5 MPag) at low temperatures (0-10 C). (3) Results: A negligible effect on the temperature dependence of viscosity was found. Ultra-low concentrations of BNNT reduced the viscosity of the nanofluid by up to 29% at 10 ppm in the presence of methane. The results presented here were compared to similar studies on O-GNF and O-MWCNT nanofluids, which also reported significant viscosity reductions. (4) Conclusions: This work identified a non-Einsteinian viscosity reduction in BNNT nanofluids, which was exacerbated by methane dissolved in the nanofluid.

cond-mat.mtrl-sci↗

arXiv2023

Stability of the Faber-Krahn inequality for the Short-time Fourier Transform

We prove a sharp quantitative version of the Faber--Krahn inequality for the short-time Fourier transform (STFT). To do so, we consider a deficit $δ(f;Ω)$ which measures by how much the STFT of a function $f\in L^2(\mathbb R)$ fails to be optimally concentrated on an arbitrary set $Ω\subset \mathbb R^2$ of positive, finite measure. We then show that an optimal power of the deficit $δ(f;Ω)$ controls both the $L^2$-distance of $f$ to an appropriate class of Gaussians and the distance of $Ω$ to a ball, through the Fraenkel asymmetry of $Ω$. Our proof is completely quantitative and hence all constants are explicit. We also establish suitable generalizations of this result in the higher-dimensional context.

math.CA↗

arXiv2023

Dynamic Viscosity of Methane Hydrate Systems from Non-Einsteinian, Plasma-Functionalized Carbon Nanotube Nanofluids

The viscosity of oxygen-functionalized multi-walled carbon nanotube (O-MWCNT) nanofluids was measured for concentrations from 0.1 to 10 ppm under conditions of 0 to 30 MPag pressures and 0 to 10 C temperatures. The presence of O-MWCNTs did not affect the temperature dependence of viscosity but did reduce the effective viscosity of solution due to cumulative hydrogen bond-disrupting surface effects, which overcame internal drag forces. O-MWCNTs added a weak pressure dependence to the viscosity of solution because of their ability to align more with the flow direction as pressure increased. In the liquid to hydrate phase transition, the times to reach the maximum viscosity were faster in O-MWCNT systems compared to the pure water baseline. However, the presence of O-MWCNTs limited the conditions at which hydrates formed as increased nanoparticle collisions in those systems inhibited the formation of critical clusters of hydrate nuclei. The times to viscosity values most relevant to technological applications were minimally 28.02 % (200 mPa s) and 21.08 % (500 mPa s) slower than the baseline, both in the 1 ppm system, even though all systems were faster to the final viscosity. This was attributed to O-MWCNT entanglement, which resulted in a hydrate slurry occurring at lower viscosity values.

physics.app-ph↗

arXiv2023

Sharp quantitative stability of the Möbius group among sphere-valued maps in arbitrary dimension

In this work we prove a sharp quantitative form of Liouville's theorem, which asserts that, for all $n\geq 3$, the weakly conformal maps of $\mathbb S^{n-1}$ with degree $\pm 1$ are Möbius transformations. In the case $n=3$ this estimate was first obtained by Bernand-Mantel, Muratov and Simon (Arch. Ration. Mech. Anal. 239(1):219-299, 2021), with different proofs given later on by Topping, and by Hirsch and the third author. The higher-dimensional case $n\geq 4$ requires new arguments because it is genuinely nonlinear: the linearized version of the estimate involves quantities which cannot control the distance to Möbius transformations in the conformally invariant Sobolev norm. Our main tool to circumvent this difficulty is an inequality introduced by Figalli and Zhang in their proof of a sharp stability estimate for the Sobolev inequality.

math.AP↗

arXiv2023

On the optimal conformal capacity of linked curves

We investigate the following optimization problem: what is the least possible conformal capacity of a pair of linked curves in $S^3$? A natural conjecture, due to Gehring, Martin and Palka, is that the optimal value is attained by the standard Hopf link. We prove that this is the case under the assumption that each component of the link lies on a different side of a conformal image of the Clifford torus. In particular, this shows that the Hopf link is a local minimizer in a strong sense.

math.DG↗

arXiv2023

Effects of Poly(styrene/pentafluorostyrene-block-vinylpyrrolidone) Amphiphilic Kinetic Hydrate Inhibitors on the Dynamic Viscosity of Methane Hydrate Systems at High-Pressure Driving Forces

Reversible addition-fragmentation chain-transfer polymerization with a switchable chain-transfer agent was employed to synthesize amphiphilic block copolymers poly(styrene-b-vinylpyrrolidone) and poly(pentafluorostyrene-b-vinylpyrrolidone) at 10 wt.% hydrophobic content as kinetic hydrate inhibitors for methane hydrates. The dynamic viscosity of methane hydrate slurries was measured in a high-pressure rheometer up to 15 MPag. At 700 ppm of additives in aqueous media, the relative time for slurries to grow to 200 mPa s was 2.2-2.4 times longer than water reference values for the block copolymers. In contrast, it was only 1.3 for the poly(vinylpyrrolidone) homopolymer, demonstrating a reduced tendency for hydrate particle adhesion in block copolymer solutions. By increasing the concentration to 7000 ppm, however, the relative time only increased to 2.6-2.7. On the other hand, a block copolymer with 5 wt.% poly(pentafluorostyrene) block at 7000 ppm reached 3.5, which may indicate that the optimal hydrophobic content differs for each amphiphilic polymer and depends on monomer selection. No significant effect of polymer aggregation on hydrate growth was observed for the copolymers used in this study, which had the same hydrophobic percentage and molecular weights between 10,000 and 40,000 g/mol.

cond-mat.soft↗

arXiv2023

Molecular dynamics predictions of transport properties for carbon dioxide hydrates under pre-nucleation conditions using TIP4P/Ice water and EPM2, TraPPE, and Zhang carbon dioxide potentials

(1) Introduction: New technologies that leverage gas hydrates phenomena include carbon capture and sequestrations. These processes are often semi-continuous and require regulation of the system's flow properties for proper operation. Accurate computational models for the viscosity of carbon dioxide hydrate systems at pre-nucleation conditions can be important for process design and control of such technologies. (2) Methods: This work validates the viscosity predictions of molecular dynamics simulations using previously measured experimental data. The TIP4P/Ice force field was used to model water, while the EPM2, TraPPE, and Zhang force fields were used for carbon dioxide. The Green-Kubo and Einstein formulations of viscosity and diffusivity were used in this work. (3) Results: All force fields overpredicted viscosity when compared to experimental data, but EPM2 resulted in lower discrepancies. Additionally, EPM2 was determined to model molecular behavior expected from the macroscopic trends in viscosity with respect to temperature and pressure. (4) Conclusions: The EPM2 force field more accurately predicted the viscosity of carbon dioxide hydrates systems at pre-nucleation conditions relative to TraPPE and Zhang.

physics.app-ph↗

arXiv2023

TinyLev Acoustically Levitated Water: Direct Observation of Collective, Inter-Droplet Effects through Morphological and Thermal Analysis of Multiple Droplets

Initially, the acoustic field forced the droplets into an oblate spheroid shape, though the counteracting force of the cooling stream caused them to circularize. Droplet geometry was thus the net result of streaming forces and surface tension at the acoustic boundary layer/air-liquid interface. Nucleation was determined to be neither homogeneous nor heterogeneous but secondary, and thus dependent on the cooling rate and not on the degree of supercooling. It was likely initiated by aerosolized ice particles from the air or from droplets that had already nucleated and broken up. The latter secondary ice production process resulted in multi-drop systems with statistically identical nucleation times. Notably, this meant that the presence of interfacial rupture at an adjacent droplet could influence the crystallization behaviour of another. After the formation of an initial ice shell around the individual droplets, dendritic protrusions grew from the droplet surface, likely seeded by the same ice particles that caused nucleation, but at a quasi-liquid layer. When freezing was complete, it was determined that the frozen core had undergone a volumetric expansion of 30.75%, compared to 9% for pure, sessile water expansion. This significantly greater expansion may have resulted from entrained air bubbles at the inner solid-liquid interface and oscillations at the moving phase boundary caused by changes in local acoustic forces. Soon after melting began, acoustic streaming, the buoyancy of the remaining ice, and convective currents caused by an inner thermal gradient and thermocapillary effects along the air-liquid interface, all contributed to the droplet spinning about the horizontal axis.

physics.app-ph↗

arXiv2023

Effects of Poly(vinylpyrrolidone) on the Dynamic Viscosity of Methane Hydrate Systems at High-Pressure Driving Forces: Investigation of Concentration, Molecular Weight, and Shear Rate

The viscosity of methane hydrate slurries with poly(vinylpyrrolidone) (PVP) at 700 and 7000 ppm by weight, molecular weights of 40,000 (PVP40) and 360,000 (PVP360) Da, and shear rates of 400 and 80 1/s, were measured in a high-pressure rheometer with pressures up to 30 MPag and compared to pure water systems. The additives successfully reduced the formation of high-viscosity slurries, but at low concentrations were incapable of delaying hydrate agglomeration at the late growth stage. The average relative time required for PVP40 solutions at 700 ppm to grow to 50 mPa.s was 1.9 times the water reference value, but only 1.2 times to reach 200 mPa.s. Improved inhibition was observed for the higher concentration and higher molecular weight sets, where the relative time to reach 50 mPa.s were 8.2 and 2.6 times the water reference value, respectively. While the additives demonstrated anti-nucleation properties and suppressed crystal growth initially, they accelerated the hydrate clusters agglomeration rate, and potentially weakened the hydrate mechanical properties.

physics.app-ph↗

arXiv2023

Interfacial Effects during Phase Change in Multiple Levitated Tetrahydrofuran Hydrate Droplets

In this study, using direct digital and infrared imaging techniques, the freezing of up to three simultaneous THF hydrate droplets was investigated for the first time. Nucleation was initiated at the aqueous solution-air interface. Two pseudo-heterogeneous mechanisms created additional nucleation interfaces: one from cavitation effects entraining microbubbles and another from subvisible ice particles, also called hydrate nucleating particles (HNPs), impacting the droplet surface. For systems containing droplets in both the second and third positions, nucleation was statistically simultaneous between all droplets. This effect may have been caused by the high liquid-solid interfacial pressures that developed at nucleation, causing some cracking in the initial hydrate shell around the droplet and releasing additional HNPs (now of hydrate) into the air. During crystallization, the THF hydrate droplets developed a completely white opacity, termed optical clarity loss or OCL. It was suggested that high hydrate growth rates within the droplet resulted in the capture of tiny air bubbles within the solid phase. In turn, light refraction through many smaller bubbles resulted in the OCL. These bubbles created structural inhomogeneities, which may explain how the volumetric expansion of the droplets upon complete solidification was 23.6% compared with 7.4% in pure, stationary THF hydrate systems. Finally, the thermal gradient that developed between the top and bottom of the droplet during melting resulted in a surface tension gradient along the air-liquid interface. In turn, convective cells developed within the droplet, causing it to spin rapidly about the horizontal axis.

physics.app-ph↗