Analytical approach to viscous fingering in a cylindrical Hele-Shaw cell

We report analytical results for the development of the viscous fingering instability in a cylindrical Hele-Shaw cell of radius a and thickness b. We derive a generalized version of Darcy's law in such cylindrical background, and find it recovers the usual Darcy's law for flow in flat, rectangular cells, with corrections of higher order in b/a. We focus our interest on the influence of cell's radius of curvature on the instability characteristics. Linear and slightly nonlinear flow regimes are studied through a mode-coupling analysis. Our analytical results reveal that linear growth rates and finger competition are inhibited for increasingly larger radius of curvature. The absence of tip-splitting events in cylindrical cells is also discussed.Comment: 14 pages, 3 ps figures, Revte

Self-Assembly Behavior of Amphiphilic Janus Dendrimers in Water: A Combined Experimental and Coarse-Grained Molecular Dynamics Simulation Approach

Indexación: Scopus.Acknowledgments: M.E.E.G. thank the Ph. D. scholarship (251115) from CONACyT. The authors would like to thank: Luis Elizalde-Herrera (CIQA) for his help running the NMR spectra; Gloria Macedo-Raygoza and Miguel J. Beltrán-García (UAG), for their help in the measuring of MALDI-TOF mass spectra; and Maricela Rodríguez-Nieto and Jorge Luis Menchaca (UANL), for their help with the AFM measurements. FDGN thanks to the USA Air Force Office of Scientific Research Awards.Amphiphilic Janus dendrimers (JDs) are repetitively branched molecules with hydrophilic and hydrophobic components that self-assemble in water to form a variety of morphologies, including vesicles analogous to liposomes with potential pharmaceutical and medical application. To date, the self-assembly of JDs has not been fully investigated thus it is important to gain insight into its mechanism and dependence on JDs’ molecular structure. In this study, the aggregation behavior in water of a second-generation bis-MPA JD was evaluated using experimental and computational methods. Dispersions of JDs in water were carried out using the thin-film hydration and ethanol injection methods. Resulting assemblies were characterized by dynamic light scattering, confocal microscopy, and atomic force microscopy. Furthermore, a coarse-grained molecular dynamics (CG-MD) simulation was performed to study the mechanism of JDs aggregation. The obtaining of assemblies in water with no interdigitated bilayers was confirmed by the experimental characterization and CG-MD simulation. Assemblies with dendrimersome characteristics were obtained using the ethanol injection method. The results of this study establish a relationship between the molecular structure of the JD and the properties of its aggregates in water. Thus, our findings could be relevant for the design of novel JDs with tailored assemblies suitable for drug delivery systems. © 2018 by the authors.https://www.mdpi.com/1420-3049/23/4/96

Mode-coupling approach to non-Newtonian Hele-Shaw flow

The Saffman-Taylor viscous fingering problem is investigated for the displacement of a non-Newtonian fluid by a Newtonian one in a radial Hele-Shaw cell. We execute a mode-coupling approach to the problem and examine the morphology of the fluid-fluid interface in the weak shear limit. A differential equation describing the early nonlinear evolution of the interface modes is derived in detail. Owing to vorticity arising from our modified Darcy's law, we introduce a vector potential for the velocity in contrast to the conventional scalar potential. Our analytical results address how mode-coupling dynamics relates to tip-splitting and side branching in both shear thinning and shear thickening cases. The development of non-Newtonian interfacial patterns in rectangular Hele-Shaw cells is also analyzed.Comment: 14 pages, 5 ps figures, Revtex4, accepted for publication in Phys. Rev.

Early classification of time series using multi-objective optimization techniques

In early classification of time series the objective is to build models which are able to make class-predictions for time series as accurately and as early as possible, when only a part of the series is available. It is logical to think that accuracy and earliness are conflicting objectives, since the more we wait, more data points from the series are available, and it is easier to make accurate class-predictions. Con- sidering this, the problem can be very naturally formulated as a multi-objective optimization problem, and solved as such. However, the solutions proposed in the literature up to now, reduce the problem into a single-objective problem by com- bining both objectives somehow. In this paper, we present a novel multi-objective formulation of the problem of early classification, and we design a solution us- ing multi-objective optimization techniques. This method will provide a variety of solutions which find different trade-offs between both objectives, allowing the user to select the most suitable solution a-posteriori, depending on the accuracy and earliness requirements of the problem at hand. To prove the usefulness of our proposal, we carry out an extensive experimentation process using 45 benchmark databases and we present a case study in the financial domain

L^{2}-restriction bounds for eigenfunctions along curves in the quantum completely integrable case

We show that for a quantum completely integrable system in two dimensions,the $L^{2}$-normalized joint eigenfunctions of the commuting semiclassical pseudodifferential operators satisfy restriction bounds ofthe form $\int_{\gamma} |\phi_{j}^{\hbar}|^2 ds = {\mathcal O}(|\log \hbar|)$ for generic curves $\gamma$ on the surface. We also prove that the maximal restriction bounds of Burq-Gerard-Tzvetkov are always attained for certain exceptional subsequences of eigenfunctions.Comment: Correct some typos and added some more detail in section

The Saffman-Taylor problem on a sphere

The Saffman-Taylor problem addresses the morphological instability of an interface separating two immiscible, viscous fluids when they move in a narrow gap between two flat parallel plates (Hele-Shaw cell). In this work, we extend the classic Saffman-Taylor situation, by considering the flow between two curved, closely spaced, concentric spheres (spherical Hele-Shaw cell). We derive the mode-coupling differential equation for the interface perturbation amplitudes and study both linear and nonlinear flow regimes. The effect of the spherical cell (positive) spatial curvature on the shape of the interfacial patterns is investigated. We show that stability properties of the fluid-fluid interface are sensitive to the curvature of the surface. In particular, it is found that positive spatial curvature inhibits finger tip-splitting. Hele-Shaw flow on weakly negative, curved surfaces is briefly discussed.Comment: 26 pages, 4 figures, RevTex, accepted for publication in Phys. Rev.

Daily rhythms of body temperature around lambing in sheep measured non-invasively

Fifteen ewes had data-loggers affixed under the tail, programmed to record temperature (T) every 5 min, storing up to 72 h of data. Ewes were monitored to identify time of lambing (time 0). Lambing period lasted 5 d; thereafter seven ewes which yielded data for 24 h before and after lambing were selected. Mean T (±S.E.M.) was 39.03±0.02°C. Mean T in the 24 h preceding lambing (38.68±0.02°C) was lower than it was in the 24 h following parturition (39.38±0.03°C) (P< 0.0001). T was lower in the 12 h preceding lamb birth (38.56±0.10°C) than it was in the previous 12 h (-24 to -12, 38.76±0.02°C) (P<0.0001); thereafter, T was lowest precisely at parturition (mean T = 38.18±0.03°C) and increases rapidly and peaked (mean T = 39.70±0.04°C) 2 h after lambing. In the 12 h following delivery (39.28±0.02°C), T increased, especially in the window +12 to +24 h (39.51±0.03°C). In conclusion, T of ewes changed around parturition, with a reduction 12 h before lambing, followed by a rapid increase in the hours following parturition. The data-loggers used proved a high degree of sensitivity to detect physiological T changes, which confirmed that they are appropriate for use in sheep studies

Breakdown of the Kondo Effect in Critical Antiferromagnets

The breakdown of the Kondo effect may be the origin of the anomalous properties of the heavy-fermion compounds at low temperatures. We study the dynamics of one impurity embedded in an antiferromagnetic host at the quantum critical point and show that the impurity is not screened and develops a power law correlation function. This suggests that the breakdown of the Kondo effect can simply be a consequence of the system's proximity to the quantum critical point.Comment: To appear in Physical Review B (Brief Reports