Kinetics of Ordering in Fluctuation-Driven First-Order Transitions: Simulations and Dynamical Renormalization

Many systems where interactions compete with each other or with constraints are well described by a model first introduced by Brazovskii. Such systems include block copolymers, alloys with modulated phases, Rayleigh-Benard Cells and type-I superconductors. The hallmark of this model is that the fluctuation spectrum is isotropic and has a minimum at a nonzero wave vector represented by the surface of a d-dimensional hyper-sphere. It was shown by Brazovskii that the fluctuations change the free energy structure from a $\phi ^{4}$ to a $\phi ^{6}$ form with the disordered state metastable for all quench depths. The transition from the disordered to the periodic, lamellar structure changes from second order to first order and suggests that the dynamics is governed by nucleation. Using numerical simulations we have confirmed that the equilibrium free energy function is indeed of a $\phi ^{6}$ form. A study of the dynamics, however, shows that, following a deep quench, the dynamics is described by unstable growth rather than nucleation. A dynamical calculation, based on a generalization of the Brazovskii calculations shows that the disordered state can remain unstable for a long time following the quench.Comment: 18 pages, 15 figures submitted to PR

A phase-field model of Hele-Shaw flows in the high viscosity contrast regime

A one-sided phase-field model is proposed to study the dynamics of unstable interfaces of Hele-Shaw flows in the high viscosity contrast regime. The corresponding macroscopic equations are obtained by means of an asymptotic expansion from the phase-field model. Numerical integrations of the phase-field model in a rectangular Hele-Shaw cell reproduce finger competition with the final evolution to a steady state finger the width of which goes to one half of the channel width as the velocity increases

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.

Multivariable model to predict an ACTH stimulation test to diagnose adrenal insufficiency using previous test results

Context The adrenocorticotropin hormone stimulation test (AST) is used to diagnose adrenal insufficiency, and is often repeated in patients when monitoring recovery of the hypothalamo–pituitary–adrenal axis. Objective To develop and validate a prediction model that uses previous AST results with new baseline cortisol to predict the result of a new AST. Methods This was a retrospective, longitudinal cohort study in patients who had undergone at least 2 ASTs, using polynomial regression with backwards variable selection, at a Tertiary UK adult endocrinology center. Model was developed from 258 paired ASTs over 5 years in 175 adults (mean age 52.4 years, SD 16.4), then validated on data from 111 patients over 1 year (51.8, 17.5) from the same center, data collected after model development. Candidate prediction variables included previous test baseline adrenocorticotropin hormone (ACTH), previous test baseline and 30-minute cortisol, days between tests, and new baseline ACTH and cortisol used with calculated cortisol/ACTH ratios to assess 8 candidate predictors. The main outcome measure was a new test cortisol measured 30 minutes after Synacthen administration. Results Using 258 sequential ASTs from 175 patients for model development and 111 patient tests for model validation, previous baseline cortisol, previous 30-minute cortisol and new baseline cortisol were superior at predicting new 30-minute cortisol (R2 = 0.71 [0.49-0.93], area under the curve [AUC] = 0.97 [0.94-1.0]) than new baseline cortisol alone (R2 = 0.53 [0.22-0.84], AUC = 0.88 [0.81-0.95]). Conclusion Results of a previous AST can be objectively combined with new early-morning cortisol to predict the results of a new AST better than new early-morning cortisol alone. An online calculator is available at https://endocrinology.shinyapps.io/sheffield_sst_calculator/ for external validation

Computational performance of Free Mesh Method applied to continuum mechanics problems

The free mesh method (FMM) is a kind of the meshless methods intended for particle-like finite element analysis of problems that are difficult to handle using global mesh generation, or a node-based finite element method that employs a local mesh generation technique and a node-by-node algorithm. The aim of the present paper is to review some unique numerical solutions of fluid and solid mechanics by employing FMM as well as the Enriched Free Mesh Method (EFMM), which is a new version of FMM, including compressible flow and sounding mechanism in air-reed instruments as applications to fluid mechanics, and automatic remeshing for slow crack growth, dynamic behavior of solid as well as large-scale Eigen-frequency of engine block as applications to solid mechanics

Amine Containing Analogs of Sulindac for Cancer Prevention

Background: Sulindac belongs to the chemically diverse family of Non-Steroidal Anti-Inflammatory Drugs (NSAIDs) that effectively prevent adenomatous colorectal polyps and colon cancer, especially in patients with familial adenomatous polyposis. Sulindac sulfide amide (SSA), an amide analog of sulindac sulfide, shows insignificant COX-related activity and toxicity while enhancing anticancer activity in vitro and demonstrating in vivo xenograft activity. Objective: Develop structure-activity relationships in the sulindac amine series and identify analogs with promising anticancer activities. Method: A series of sulindac amine analogs were designed and synthesized and then further modified in a “libraries from libraries” approach to produce amide, sulfonamide and N,N-disubstituted sulindac amine sub-libraries. All analogs were screened against three cancer cell lines (prostate, colon and breast). Results: Several active compounds were identified viain vitro cancer cell line screening with the most potent compound (26) in the nanomolar range. Conclusion: Compound 26 and analogs showing the most potent inhibitory activity may be considered for further design and optimization efforts as anticancer hit scaffolds

Spinodal decomposition in multicomponent fluid mixtures: A molecular dynamics study

We have investigated the effect of the number p of components on the dynamics of phase separation in two-dimensional symmetric multicomponent fluids. In contrast to concentrated two-dimensional binary fluids, where the growth dynamics is controlled by the coupling of the velocity held to the order parameter, leading to large growth-exponent values, the dynamics in multicomponent fluids (p = 3, 4) is found to follow a t(1/3) growth law, where t is time, which we relate to a long-wavelength evaporation-condensation process. These findings, which are proposed to be consequences of the compact domain structure persisting in multicomponent fluids, imply that hydrodynamic modes do not affect the dynamics of the phase separation in these systems