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André Guerra

Publications and source records attributed to André Guerra.

50 records · Page 3Linked to original sources
arXiv2023

Non-Einsteinian Viscosity Behavior in Plasma-Functionalized Graphene Nanoflake Nanofluids and their Effect on the Dynamic Viscosity of Methane Hydrate Systems

Water's viscosity dependence on pressure was also not affected by O-GNFs, except at 10 ppm, where the shuttle effect may have increased the presence of hydrophobic methane bubbles in the solution. Under high pressure, the relative viscosity of the system remained non-Einsteinian at all temperatures except 2C. This may have been because the density anomaly of water was shifted to a colder temperature as the hydrogen bonding network was weaker. The phase transition from liquid to hydrate was identical to that of pure water, indicating that the presence of different stages of growth was not affected by the presence of O-GNF. However, the times to reach a maximum viscosity were faster in O-GNF systems compared to pure water. This said, the hydrate formation limitations inherent to the measurement system were not overcome by the presence of O-GNFs. The times to application-relevant viscosity values were maximized in the 1 ppm system at 49.75 % (200 mPa.s) and 31.93 % (500 mPa.s) faster than the baseline. Therefore, the presence of O-GNFs allowed for shorter times to desired viscosities and at lower driving forces than the baseline, improving the viability of the hydrate technologies to which they can be added.

physics.app-ph↗
arXiv2023

Dynamic Viscosity of Methane and Carbon Dioxide Hydrate Systems from Pure Water at High-Pressure Driving Forces

The viscosity of methane and carbon dioxide hydrate systems were measured using a high-pressure rheometer up to 30 MPag. Where hydrate formation was not detected, the effect of temperature on the viscosity was one order of magnitude higher than the pressure effect on viscosity in most of the experimental pressure range (-0.048 mPa s/C at 1 MPag and 0.009 mPa s/MPag at 2C). The pressure effect on the viscosity of carbon dioxide systems where no hydrate formation was observed was up to one order of magnitude higher than that of the methane systems, due to carbon dioxide's higher solubility in water. Novel rheological phases diagrams were developed to further characterize the gas hydrate systems. Several systems with high driving forces for hydrate formation (2.07 MPag to 4.1 MPag) did not form gas hydrates. System limitations to the formation of hydrates were categorized as kinetic, mass diffusion, and/or heat of crystallization effects.

physics.app-ph↗
arXiv2022

AEROS: Oceanographic Hyperspectral Imaging and Argos-Tracking CubeSat

AEROS is a 3U CubeSat pathfinder toward a future ocean-observing constellation, targeting the Portuguese Atlantic region. AEROS features a miniaturized, high-resolution Hyperspectral Imager (HSI), a 5MP RGB camera, and a Software Defined Radio (SDR). The sensor generated data will be processed and aggregated for end-users in a new web-based Data Analysis Center (DAC). The HSI has 150 spectrally contiguous bands covering visible to near-infrared with 10 nm bandwidth. The HSI collects ocean color data to support studies of oceanographic characteristics known to influence the spatio-temporal distribution and movement behavior of marine organisms. Usage of an SDR expands AEROS's operational and communication range and allows for remote reconfiguration. The SDR receives, demodulates, and retransmits short duration messages, from sources including tagged marine organisms, autonomous vehicles, subsurface floats, and buoys. The future DAC will collect, store, process, and analyze acquired data, taking advantage of its ability to disseminate data across the stakeholders and the scientific network. Correlation of animal-borne Argos platform locations and oceanographic data will advance fisheries management, ecosystem-based management, monitoring of marine protected areas, and bio-oceanographic research in the face of a rapidly changing environment. For example, correlation of oceanographic data collected by the HSI, geolocated with supplementary images from the RGB camera and fish locations, will provide researchers with near real-time estimates of essential oceanographic variables within areas selected by species of interest.

physics.ao-ph↗
arXiv2021

Automatic quasiconvexity of homogeneous isotropic rank-one convex integrands

We consider the class of non-negative rank-one convex isotropic integrands on $\mathbb{R}^{n\times n}$ which are also positively $p$-homogeneous. If $p \leq n = 2$ we prove, conditional on the quasiconvexity of the Burkholder integrand, that the integrands in this class are quasiconvex at conformal matrices. If $p \geq n = 2$, we show that the positive part of the Burkholder integrand is polyconvex. In general, for $p \geq n$, we prove that the integrands in the above class are polyconvex at conformal matrices. Several examples imply that our results are all nearly optimal.

math.AP↗
arXiv2021

Oscillations in wave map systems and homogenization of the Einstein equations in symmetry

In 1989, Burnett conjectured that, under appropriate assumptions, the limit of highly oscillatory solutions to the Einstein vacuum equations is a solution of the Einstein--massless Vlasov system. In a recent breakthrough, Huneau--Luk (arXiv:1907.10743) gave a proof of the conjecture in U(1)-symmetry and elliptic gauge. They also require control on up to fourth order derivatives of the metric components. In this paper, we give a streamlined proof of a stronger result and, in the spirit of Burnett's original conjecture, we remove the need for control on higher derivatives. Our methods also apply to general wave map equations.

math.AP↗
arXiv2020

Energy minimisers with prescribed Jacobian

We study the symmetry and uniqueness of maps which minimise the $np$-Dirichlet energy, under the constraint that their Jacobian is a given radially symmetric function $f$. We find a condition on $f$ which ensures that the minimisers are symmetric and unique. In the absence of this condition we construct an explicit $f$ for which there are uncountably many distinct energy minimisers, none of which is symmetric. Even if we prescribe the maps to be the identity on the boundary of a ball we show that the minimisers need not be symmetric. This gives a negative answer to a question of Hélein (Ann. Inst. H. Poincaré Anal. Non Linéaire 11 (1994), no. 3, 275-296).

math.AP↗
arXiv2020

Nonlinear open mapping principles, with applications to the Jacobian equation and other scale-invariant PDEs

For a nonlinear operator $T$ satisfying certain structural assumptions, our main theorem states that the following claims are equivalent: i) $T$ is surjective, ii) $T$ is open at zero, and iii) $T$ has a bounded right inverse. The theorem applies to numerous scale-invariant PDEs in regularity regimes where the equations are stable under weak$^*$ convergence. Two particular examples we explore are the Jacobian equation and the equations of incompressible fluid flow. For the Jacobian, it is a long standing open problem to decide whether it is onto between the critical Sobolev space and the Hardy space. Towards a negative answer, we show that, if the Jacobian is onto, then it suffices to rule out the existence of surprisingly well-behaved solutions. For the incompressible Euler equations, we show that, for any $p<\infty$, the set of initial data for which there are dissipative weak solutions in $L^p_t L^2_x$ is meagre in the space of solenoidal $L^2$ fields. Similar results hold for other equations of incompressible fluid dynamics.

math.AP↗
arXiv2020

Compensated compactness: continuity in optimal weak topologies

For $l$-homogeneous linear differential operators $\mathcal{A}$ of constant rank, we study the implication $v_j\rightharpoonup v$ in $X$ and $\mathcal{A} v_j\rightarrow \mathcal{A} v$ in $W^{-l}Y$ implies $F(v_j)\rightsquigarrow F(v)$ in $Z$, where $F$ is an $\mathcal{A}$-quasiaffine function and $\rightsquigarrow$ denotes an appropriate type of weak convergence. Here $Z$ is a local $L^1$-type space, either the space $\mathscr{M}$ of measures, or $L^1$, or the Hardy space $\mathscr{H}^1$; $X,\, Y$ are $L^p$-type spaces, by which we mean Lebesgue or Zygmund spaces. Our conditions for each choice of $X,\,Y,\,Z$ are sharp. Analogous statements are also given in the case when $F(v)$ is not a locally integrable function and it is instead defined as a distribution. In this case, we also prove $\mathscr{H}^p$-bounds for the sequence $(F(v_j))_j$, for appropriate $p<1$, and new convergence results in the dual of Hölder spaces when $(v_j)$ is $\mathcal{A}$-free and lies in a suitable negative order Sobolev space $W^{-β,s}$. The choice of these Hölder spaces is sharp, as is shown by the construction of explicit counterexamples. Some of these results are new even for distributional Jacobians.

math.AP↗
arXiv2020

Quasiconvexity, null Lagrangians, and Hardy space integrability under constant rank constraints

We present a systematic treatment of the theory of Compensated Compactness under Murat's constant rank assumption. We give a short proof of a sharp weak lower semicontinuity result for signed integrands, extending the results of Fonseca--Müller. The null Lagrangians are an important class of signed integrands, since they are the weakly continuous functions. We show that they are precisely the compensated compactness quantities with Hardy space integrability, thus proposing an answer to a question raised by Coifman-Lions-Meyer-Semmes. Finally we provide an effective way of computing the null Lagrangians associated with a given operator.

math.AP↗
arXiv2020

On the necessity of the constant rank condition for $L^p$ estimates

We consider a generalization of the elliptic $L^p$-estimate suited for linear operators with non-trivial kernels. A classical result of Schulenberger and Wilcox (Ann. Mat. Pura Appl. (4) 88: 229-305, 1971) shows that if the operator has constant rank then the estimate holds. We prove necessity of the constant rank condition for such an estimate.

math.CA↗
arXiv2019

Extremal rank-one convex integrands and a conjecture of Šverák

We show that in order to decide whether a given probability measure is laminate it is enough to verify Jensen's inequality in the class of extremal non-negative rank-one convex integrands. We also identify a subclass of these extremal integrands, consisting of truncated minors, thus proving a conjecture made by Šverák in (Arch. Ration. Mech. Anal. 119 293-300, 1992).

math.AP↗