Sharp-Interface Limit of a Fluctuating Phase-Field Model

We present a derivation of the sharp-interface limit of a generic fluctuating phase-field model for solidification. As a main result, we obtain a sharp-interface projection which presents noise terms in both the diffusion equation and in the moving boundary conditions. The presented procedure does not rely on the fluctuation-dissipation theorem, and can therefore be applied to account for both internal and external fluctuations in either variational or non-variational phase-field formulations. In particular, it can be used to introduce thermodynamical fluctuations in non-variational formulations of the phase-field model, which permit to reach better computational efficiency and provide more flexibility for describing some features of specific physical situations. This opens the possibility of performing quantitative phase-field simulations in crystal growth while accounting for the proper fluctuations of the system.Comment: 21 pages, 1 figure, submitted to Phys. Rev.

Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. II. Numerical study

We implement a phase-field simulation of the dynamics of two fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. We demonstrate the use of this technique in different situations including the linear regime, the stationary Saffman-Taylor fingers and the multifinger competition dynamics, for different viscosity contrasts. The method is quantitatively tested against analytical predictions and other numerical results. A detailed analysis of convergence to the sharp interface limit is performed for the linear dispersion results. We show that the method may be a useful alternative to more traditional methods.Comment: 13 pages in revtex, 5 PostScript figures. changes: 1 reference added, figs. 4 and 5 rearrange

Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. I. Theoretical approach

We present a phase-field model for the dynamics of the interface between two inmiscible fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. With asymptotic matching techniques we check the model to yield the right Hele-Shaw equations in the sharp-interface limit and compute the corrections to these equations to first order in the interface thickness. We also compute the effect of such corrections on the linear dispersion relation of the planar interface. We discuss in detail the conditions on the interface thickness to control the accuracy and convergence of the phase-field model to the limiting Hele-Shaw dynamics. In particular, the convergence appears to be slower for high viscosity contrasts.Comment: 17 pages in revtex. changes: 1 reference adde

Dynamics of a faceted nematic-smectic B front in thin-sample directional solidification

We present an experimental study of the directional-solidification patterns of a nematic - smectic B front. The chosen system is C_4H_9-(C_6H_{10})_2CN (in short, CCH4) in 12 \mu m-thick samples, and in the planar configuration (director parallel to the plane of the sample). The nematic - smectic B interface presents a facet in one direction -- the direction parallel to the smectic layers -- and is otherwise rough, and devoid of forbidden directions. We measure the Mullins-Sekerka instability threshold and establish the morphology diagram of the system as a function of the solidification rate V and the angle theta_{0} between the facet and the isotherms. We focus on the phenomena occurring immediately above the instability threshold when theta_{0} is neither very small nor close to 90^{o}. Under these conditions we observe drifting shallow cells and a new type of solitary wave, called "faceton", which consists essentially of an isolated macroscopic facet traveling laterally at such a velocity that its growth rate with respect to the liquid is small. Facetons may propagate either in a stationary, or an oscillatory way. The detailed study of their dynamics casts light on the microscopic growth mechanisms of the facets in this system.Comment: 12 pages, 19 figures, submitted to Phys. Rev.

Viscous fingering in liquid crystals: Anisotropy and morphological transitions

We show that a minimal model for viscous fingering with a nematic liquid crystal in which anisotropy is considered to enter through two different viscosities in two perpendicular directions can be mapped to a two-fold anisotropy in the surface tension. We numerically integrate the dynamics of the resulting problem with the phase-field approach to find and characterize a transition between tip-splitting and side-branching as a function of both anisotropy and dimensionless surface tension. This anisotropy dependence could explain the experimentally observed (reentrant) transition as temperature and applied pressure are varied. Our observations are also consistent with previous experimental evidence in viscous fingering within an etched cell and simulations of solidification.Comment: 12 pages, 3 figures. Submitted to PR

Kinematic reduction of reaction-diffusion fronts with multiplicative noise: Derivation of stochastic sharp-interface equations

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated to the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-KPZ universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations, kinetic roughening, and the noise-induced pushed-pulled transition, which is predicted and observed for the first time. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.Comment: 17 pages, 6 figure

Non-isothermal model for the direct isotropic/smectic-A liquid crystalline transition

An extension to a high-order model for the direct isotropic/smectic-A liquid crystalline phase transition was derived to take into account thermal effects including anisotropic thermal diffusion and latent heat of phase-ordering. Multi-scale multi-transport simulations of the non-isothermal model were compared to isothermal simulation, showing that the presented model extension corrects the standard Landau-de Gennes prediction from constant growth to diffusion-limited growth, under shallow quench/undercooling conditions. Non-isothermal simulations, where meta-stable nematic pre-ordering precedes smectic-A growth, were also conducted and novel non-monotonic phase-transformation kinetics observed.Comment: First revision: 20 pages, 7 figure

New Electrocardiographic Algorithm for the Diagnosis of Acute Myocardial Infarction in Patients With Left Bundle Branch Block

Background Current electrocardiographic algorithms lack sensitivity to diagnose acute myocardial infarction (AMI) in the presence of left bundle branch block. Methods and Results A multicenter retrospective cohort study including consecutive patients with suspected AMI and left bundle branch block, referred for primary percutaneous coronary intervention between 2009 and 2018. Pre-2015 patients formed the derivation cohort (n=163, 61 with AMI); patients between 2015 and 2018 formed the validation cohort (n=107, 40 with AMI). A control group of patients without suspected AMI was also studied (n=214). Different electrocardiographic criteria were tested. A total of 484 patients were studied. A new electrocardiographic algorithm (BARCELONA algorithm) was derived and validated. The algorithm is positive in the presence of ST deviation ≥1 mm (0.1 mV) concordant with QRS polarity, in any lead, or ST deviation ≥1 mm (0.1 mV) discordant with the QRS, in leads with max (R|S) voltage (the voltage of the largest deflection of the QRS, ie, R or S wave) ≤6 mm (0.6 mV). In both the derivation and the validation cohort, the BARCELONA algorithm achieved the highest sensitivity (93%-95%), negative predictive value (96%-97%), efficiency (91%-94%) and area under the receiver operating characteristic curve (0.92-0.93), significantly higher than previous electrocardiographic rules (P<0.01); the specificity was good in both groups (89%-94%) as well as the control group (90%). Conclusions In patients with left bundle branch block referred for primary percutaneous coronary intervention, the BARCELONA algorithm was specific and highly sensitive for the diagnosis of AMI, leading to a diagnostic accuracy comparable to that obtained by ECG in patients without left bundle branch block

Renal Function Impact in the Prognostic Value of Galectin-3 in Acute Heart Failure

[Abstract] Introduction: Galectin-3 (Gal-3) is an inflammatory marker associated with the development and progression of heart failure (HF). A close relationship between Gal-3 levels and renal function has been observed, but data on their interaction in patients with acute HF (AHF) are scarce. We aim to assess the prognostic relationship between renal function and Gal-3 during an AHF episode. Materials and methods: This is an observational, prospective, multicenter registry of patients hospitalized for AHF. Patients were divided into two groups according to estimated glomerular filtration rate (eGFR): preserved renal function (eGFR ≥ 60 mL/min/1.73 m2) and renal dysfunction (eGFR <60 mL/min/1.73 m2). Cox regression analysis was performed to evaluate the association between Gal-3 and 12-month mortality. Results: We included 1,201 patients in whom Gal-3 values were assessed at admission. The median value of Gal-3 in our population was 23.2 ng/mL (17.3-32.1). Gal-3 showed a negative correlation with eGFR (rho = -0.51; p < 0.001). Gal-3 concentrations were associated with higher mortality risk in the multivariate analysis after adjusting for eGFR and other prognostic variables [HR = 1.010 (95%-CI: 1.001-1.018); p = 0.038]. However, the prognostic value of Gal-3 was restricted to patients with renal dysfunction [HR = 1.010 (95%-CI: 1.001-1.019), p = 0.033] with optimal cutoff point of 31.5 ng/mL, with no prognostic value in the group with preserved renal function [HR = 0.990 (95%-CI: 0.964-1.017); p = 0.472]. Conclusions: Gal-3 is a marker of high mortality in patients with acute HF and renal dysfunction. Renal function influences the prognostic value of Gal-3 levels, which should be adjusted by eGFR for a correct interpretation.Grant No. RD06-0003-0000 Grant No. RD12/0042/000