Phase Field Model for Three-Dimensional Dendritic Growth with Fluid Flow

We study the effect of fluid flow on three-dimensional (3D) dendrite growth using a phase-field model on an adaptive finite element grid. In order to simulate 3D fluid flow, we use an averaging method for the flow problem coupled to the phase-field method and the Semi-Implicit Approximated Projection Method (SIAPM). We describe a parallel implementation for the algorithm, using Charm++ FEM framework, and demonstrate its efficiency. We introduce an improved method for extracting dendrite tip position and tip radius, facilitating accurate comparison to theory. We benchmark our results for two-dimensional (2D) dendrite growth with solvability theory and previous results, finding them to be in good agreement. The physics of dendritic growth with fluid flow in three dimensions is very different from that in two dimensions, and we discuss the origin of this behavior

Subtropical Real Root Finding

We describe a new incomplete but terminating method for real root finding for large multivariate polynomials. We take an abstract view of the polynomial as the set of exponent vectors associated with sign information on the coefficients. Then we employ linear programming to heuristically find roots. There is a specialized variant for roots with exclusively positive coordinates, which is of considerable interest for applications in chemistry and systems biology. An implementation of our method combining the computer algebra system Reduce with the linear programming solver Gurobi has been successfully applied to input data originating from established mathematical models used in these areas. We have solved several hundred problems with up to more than 800000 monomials in up to 10 variables with degrees up to 12. Our method has failed due to its incompleteness in less than 8 percent of the cases

Using the interface Peclet number to select the maximum simulation interface width in phase-field solidification modelling

This study investigates the use of interface Peclet number P = w/(D-l/V-tip), to determine the interface width (w) used in phase-field simulations, where D-l is the liquid diffusivity and V-tip is the tip velocity. The maximum simulation interface width (w(max)) under varied growth conditions was analysed via convergence analysis and it was found that there is a limit of P for the maximum interface width at various velocities. Converged results can be obtained only when w < w(max) = 0.075D(l)/V-max where V-max is the maximum growth velocity during transient solidification. The effect of the inclusion of finite solid diffusivity on the P limit in selecting wmax was analysed, and little influence was observed. (C) 2013 Elsevier B. V. All rights reserved

Polyhedral Analysis using Parametric Objectives

The abstract domain of polyhedra lies at the heart of many program analysis techniques. However, its operations can be expensive, precluding their application to polyhedra that involve many variables. This paper describes a new approach to computing polyhedral domain operations. The core of this approach is an algorithm to calculate variable elimination (projection) based on parametric linear programming. The algorithm enumerates only non-redundant inequalities of the projection space, hence permits anytime approximation of the output

Phase transition for cutting-plane approach to vertex-cover problem

We study the vertex-cover problem which is an NP-hard optimization problem and a prototypical model exhibiting phase transitions on random graphs, e.g., Erdoes-Renyi (ER) random graphs. These phase transitions coincide with changes of the solution space structure, e.g, for the ER ensemble at connectivity c=e=2.7183 from replica symmetric to replica-symmetry broken. For the vertex-cover problem, also the typical complexity of exact branch-and-bound algorithms, which proceed by exploring the landscape of feasible configurations, change close to this phase transition from "easy" to "hard". In this work, we consider an algorithm which has a completely different strategy: The problem is mapped onto a linear programming problem augmented by a cutting-plane approach, hence the algorithm operates in a space OUTSIDE the space of feasible configurations until the final step, where a solution is found. Here we show that this type of algorithm also exhibits an "easy-hard" transition around c=e, which strongly indicates that the typical hardness of a problem is fundamental to the problem and not due to a specific representation of the problem.Comment: 4 pages, 3 figure

Can postoperative mean transprosthetic pressure gradient predict survival after aortic valve replacement?

BACKGROUND: In this study, we sought to determine the effect of the mean transprosthetic pressure gradient (TPG), measured at 6 weeks after aortic valve replacement (AVR) or AVR with coronary artery bypass grafting (CABG) on late all-cause mortality. METHODS: Between January 1998 and March 2012, 2,276 patients (mean age 68 ± 11 years) underwent TPG analysis at 6 weeks after AVR (n = 1,318) or AVR with CABG (n = 958) at a single institution. Mean TPG was 11.6 ± 7.8 mmHg and median TPG 11 mmHg. Based on the TPG, the patients were split into three groups: patients with a low TPG (<10 mmHg), patients with a medium TPG (10–19 mmHg) and patients with a high TPG (≥20 mmHg). Cox proportional-hazard regression analysis was used to determine univariate predictors and multivariate independent predictors of late mortality. RESULTS: Overall survival for the entire group at 1, 3, 5, and 10 years was 97, 93, 87 and 67 %, respectively. There was no significant difference in long-term survival between patients with a low, medium or high TPG (p = 0.258). Independent predictors of late mortality included age, diabetes, peripheral vascular disease, renal dysfunction, chronic obstructive pulmonary disease, a history of a cerebrovascular accident and cardiopulmonary bypass time. Prosthesis–patient mismatch (PPM), severe PPM and TPG measured at 6 weeks postoperatively were not significantly associated with late mortality. CONCLUSIONS: TPG measured at 6 weeks after AVR or AVR with CABG is not an independent predictor of all-cause late mortality and there is no significant difference in long-term survival between patients with a low, medium or high TPG

Linear Contraction Behavior of Low-Carbon, Low-Alloy Steels During and After Solidification Using Real-Time Measurements

A technique for measuring the linear contraction during and after solidification of low-alloy steel was developed and used for examination of two commercial low-carbon and low-alloy steel grades. The effects of several experimental parameters on the contraction were studied. The solidification contraction behavior was described using the concept of rigidity in a solidifying alloy, evolution of the solid fraction, and the microstructure development during solidification. A correlation between the linear contraction properties in the solidification range and the hot crack susceptibility was proposed and used for the estimation of hot cracking susceptibility for two studied alloys and verified with the real casting practice. The technique allows estimation of the contraction coefficient of commercial steels in a wide range of temperatures and could be helpful for computer simulation and process optimization during continuous casting. © 2013 The Minerals, Metals & Materials Society and ASM International

Action functionals for relativistic perfect fluids

Action functionals describing relativistic perfect fluids are presented. Two of these actions apply to fluids whose equations of state are specified by giving the fluid energy density as a function of particle number density and entropy per particle. Other actions apply to fluids whose equations of state are specified in terms of other choices of dependent and independent fluid variables. Particular cases include actions for isentropic fluids and pressureless dust. The canonical Hamiltonian forms of these actions are derived, symmetries and conserved charges are identified, and the boundary value and initial value problems are discussed. As in previous works on perfect fluid actions, the action functionals considered here depend on certain Lagrange multipliers and Lagrangian coordinate fields. Particular attention is paid to the interpretations of these variables and to their relationships to the physical properties of the fluid.Comment: 40 pages, plain Te