23 research outputs found
Eutectic colony formation: A phase field study
Eutectic two-phase cells, also known as eutectic colonies, are commonly
observed during the solidification of ternary alloys when the composition is
close to a binary eutectic valley. In analogy with the solidification cells
formed in dilute binary alloys, colony formation is triggered by a
morphological instability of a macroscopically planar eutectic solidification
front due to the rejection by both solid phases of a ternary impurity that
diffuses in the liquid. Here we develop a phase-field model of a binary
eutectic with a dilute ternary impurity and we investigate by dynamical
simulations both the initial linear regime of this instability, and the
subsequent highly nonlinear evolution of the interface that leads to fully
developed two-phase cells with a spacing much larger than the lamellar spacing.
We find a good overall agreement with our recent linear stability analysis [M.
Plapp and A. Karma, Phys. Rev. E 60, 6865 (1999)], which predicts a
destabilization of the front by long-wavelength modes that may be stationary or
oscillatory. A fine comparison, however, reveals that the assumption commonly
attributed to Cahn that lamella grow perpendicular to the envelope of the
solidification front is weakly violated in the phase-field simulations. We show
that, even though weak, this violation has an important quantitative effect on
the stability properties of the eutectic front. We also investigate the
dynamics of fully developed colonies and find that the large-scale envelope of
the composite eutectic front does not converge to a steady state, but exhibits
cell elimination and tip-splitting events up to the largest times simulated.Comment: 18 pages, 18 EPS figures, RevTeX twocolumn, submitted to Phys. Rev.
Towards a quantitative phase-field model of two-phase solidification
We construct a diffuse-interface model of two-phase solidification that
quantitatively reproduces the classic free boundary problem on solid-liquid
interfaces in the thin-interface limit. Convergence tests and comparisons with
boundary integral simulations of eutectic growth show good accuracy for
steady-state lamellae, but the results for limit cycles depend on the interface
thickness through the trijunction behavior. This raises the fundamental issue
of diffuse multiple-junction dynamics.Comment: 4 pages, 2 figures. Better final discussion. 1 reference adde
On a linear programming approach to the discrete Willmore boundary value problem and generalizations
We consider the problem of finding (possibly non connected) discrete surfaces
spanning a finite set of discrete boundary curves in the three-dimensional
space and minimizing (globally) a discrete energy involving mean curvature.
Although we consider a fairly general class of energies, our main focus is on
the Willmore energy, i.e. the total squared mean curvature Our purpose is to
address the delicate task of approximating global minimizers of the energy
under boundary constraints.
The main contribution of this work is to translate the nonlinear boundary
value problem into an integer linear program, using a natural formulation
involving pairs of elementary triangles chosen in a pre-specified dictionary
and allowing self-intersection.
Our work focuses essentially on the connection between the integer linear
program and its relaxation. We prove that: - One cannot guarantee the total
unimodularity of the constraint matrix, which is a sufficient condition for the
global solution of the relaxed linear program to be always integral, and
therefore to be a solution of the integer program as well; - Furthermore, there
are actually experimental evidences that, in some cases, solving the relaxed
problem yields a fractional solution. Due to the very specific structure of the
constraint matrix here, we strongly believe that it should be possible in the
future to design ad-hoc integer solvers that yield high-definition
approximations to solutions of several boundary value problems involving mean
curvature, in particular the Willmore boundary value problem
Genome-wide association and Mendelian randomisation analysis provide insights into the pathogenesis of heart failure
Heart failure (HF) is a leading cause of morbidity and mortality worldwide. A small proportion of HF cases are attributable to monogenic cardiomyopathies and existing genome-wide association studies (GWAS) have yielded only limited insights, leaving the observed heritability of HF largely unexplained. We report results from a GWAS meta-analysis of HF comprising 47,309 cases and 930,014 controls. Twelve independent variants at 11 genomic loci are associated with HF, all of which demonstrate one or more associations with coronary artery disease (CAD), atrial fibrillation, or reduced left ventricular function, suggesting shared genetic aetiology. Functional analysis of non-CAD-associated loci implicate genes involved in cardiac development (MYOZ1, SYNPO2L), protein homoeostasis (BAG3), and cellular senescence (CDKN1A). Mendelian randomisation analysis supports causal roles for several HF risk factors, and demonstrates CAD-independent effects for atrial fibrillation, body mass index, and hypertension. These findings extend our knowledge of the pathways underlying HF and may inform new therapeutic strategies
A phase-field model with convection: sharp-interface asymptotics
We have previously developed a phase-field model of solidification that includes convection in the melt [Physica D 135 (2000) 175]. This model represents the two phases as viscous liquids, where the putative solid phase has a viscosity much larger than the liquid phase. The object of this paper is to examine in detail a simplified version of the governing equations for this phase-field model in the sharp-interface limit to derive the interfacial conditions of the associated free-boundary problem. The importance of this analysis is that it reveals the underlying physical mechanisms built into the phase-field model in the context of a free-boundary problem and, in turn, provides a further validation of the model. In equilibrium, we recover the standard interfacial conditions including the Young–Laplace and Clausius–Clapeyron equations that relate the temperature to the pressures in the two bulk phases, the interface curvature and material parameters. In nonequilibrium, we identify boundary conditions associated with classical hydrodynamics, such as the normal mass flux condition, the no-slip condition and stress balances. We also identify the heat flux balance condition which is modified to account for the flow, interface curvature and density difference between the bulk phases. The interface temperature satisfies a nonequilibrium version of the Clausius–Clapeyron relation which includes the effects of curvature, attachment kinetics and viscous dissipation
Abdominal aortic aneurysm and its correlation to plasma homocysteine, and vitamins
AbstractBackground. Hyperhomocysteinemia is a recognised independent risk factor in the genesis of atherosclerotic diseases. However, very little is known about the relationship between homocysteine and abdominal aortic aneurysm (AAA). Vitamins, namely B12 and folic acid have been implicated in the regulation of plasma homocysteine levels. However, there has been no prospective study that has analysed the relationship of AAA and plasma homocysteine in light of serum vitamin levels.Aims. To study the relationship between plasma homocysteine, serum B12 and folic acid levels, and AAA.Method. Case control study including 38 AAA patients and 36 controls. Fasting homocysteine, B12 and folic acid were determined in serum separated within 1 h of blood collection using a fluorescence polarisation immunoassay technique (FPIA).Results. Twenty-six (68%) of the AAA patients had elevated levels of homocysteine compared to 2 (6%) in the case control group. The mean homocysteine level in the AAA group was 19.4μmol/L (SE±1.1) (95% CI 17.17–21.65) and in the control group was 10.9μmol/L (SE±1) (95% CI 9.95–11.88) (p<0.001). Mean vitamin B12 levels in the AAA and the controls was 332.11pg/L (SE±16.44) and 414.33pg/L (SE±19.72), respectively (p<0.004). Mean folic acid in the AAA was 8.02 (SE±0.71) and the control was 9.8ηgm/L (SE±0.69), (ns).Conclusion. This study confirms significantly higher levels of plasma homocysteine in AAA patients but lower levels of B12. Use of supplemental vitamins that should lower plasma homocysteine may modify vascular disease progression. Clinical trials in this direction are warranted
Low order-value approach for solving VaR-constrained optimization problems
Optimization, Augmented Lagrangian, Order-value optimization, Low order-value optimization, Value at risk, Numerical algorithms, 65Kxx, 47N10,