Emergence of foams from the breakdown of the phase field crystal model

The phase field crystal (PFC) model captures the elastic and topological properties of crystals with a single scalar field at small undercooling. At large undercooling, new foam-like behavior emerges. We characterize this foam phase of the PFC equation and propose a modified PFC equation that may be used for the simulation of foam dynamics. This minimal model reproduces von Neumann's rule for two-dimensional dry foams, and Lifshitz-Slyozov coarsening for wet foams. We also measure the coordination number distribution and find that its second moment is larger than previously-reported experimental and theoretical studies of soap froths, a finding that we attribute to the wetness of the foam increasing with time.Comment: 4 pages, 4 figure

Equilibrium spherically curved 2D Lennard-Jones systems

To learn about basic aspects of nano-scale spherical molecular shells during their formation, spherically curved two-dimensional N-particle Lennard-Jones systems are simulated, studying curvature evolution paths at zero-temperature. For many N-values (N<800) equilibrium configurations are traced as a function of the curvature radius R. Sharp jumps for tiny changes in R between trajectories with major differences in topological structure correspond to avalanche-like transitions. For a typical case, N=25, equilibrium configurations fall on smooth trajectories in state space which can be traced in the E-R plane. The trajectories show-up with local energy minima, from which growth in N at steady curvature can develop.Comment: 10 pages, 2 figures, to be published in Journal of Chemical Physic

Use of genetic algorithms and gradient based optimization techniques for calcium phosphate precipitation

Phase equilibrium computations constitute an important problem for designing and optimizing crystallization processes. The Gibbs free energy is generally used as an objective function to find phase amount and composition at equilibrium. In such problems, the Gibbs free energy may be a quite complex function, with several local minima. This paper presents a contribution to handle this kind of problems by implementation of an optimization technique based on the successive use of a genetic algorithm (GA) and of a classical sequential quadratic programming (SQP) method: the GA is used to perform a preliminary search in the solution space for locating the neighborhood of the solution. Then, the SQP method is employed to refine the best solution provided by the GA. The basic operations involved in the design of the GA developed in this study (encoding with binary representation of real values, evaluation function, adaptive plan) are presented. Several test problems are first presented to demonstrate the validity of the approach. Then, calcium phosphate precipitation which is of major interest for P-recovery from wastewater, has been chosen as an illustration of the implemented algorithm

On the role of confinement on solidification in pure materials and binary alloys

We use a phase-field model to study the effect of confinement on dendritic growth, in a pure material solidifying in an undercooled melt, and in the directional solidification of a dilute binary alloy. Specifically, we observe the effect of varying the vertical domain extent ($\delta$) on tip selection, by quantifying the dendrite tip velocity and curvature as a function of $\delta$, and other process parameters. As $\delta$ decreases, we find that the operating state of the dendrite tips becomes significantly affected by the presence of finite boundaries. For particular boundary conditions, we observe a switching of the growth state from 3-D to 2-D at very small $\delta$, in both the pure material and alloy. We demonstrate that results from the alloy model compare favorably with those from an experimental study investigating this effect.Comment: 13 pages, 9 figures, 3 table

Duality, thermodynamics, and the linear programming problem in constraint-based models of metabolism

It is shown that the dual to the linear programming problem that arises in constraint-based models of metabolism can be given a thermodynamic interpretation in which the shadow prices are chemical potential analogues, and the objective is to minimise free energy consumption given a free energy drain corresponding to growth. The interpretation is distinct from conventional non-equilibrium thermodynamics, although it does satisfy a minimum entropy production principle. It can be used to motivate extensions of constraint-based modelling, for example to microbial ecosystems.Comment: 4 pages, 2 figures, 1 table, RevTeX 4, final accepted versio

Nonclassicality of pure two-qutrit entangled states

We report an exhaustive numerical analysis of violations of local realism by two qutrits in all possible pure entangled states. In Bell type experiments we allow any pairs of local unitary U(3) transformations to define the measurement bases. Surprisingly, Schmidt rank-2 states, resembling pairs of maximally entangled qubits, lead to the most noise-robust violations of local realism. The phenomenon seems to be even more pronounced for four and five dimensional systems, for which we tested a few interesting examples.Comment: 6 pages, journal versio

On the Axiomatics of the 5-dimensional Projective Unified Field Theory of Schmutzer

For more than 40 years E.Schmutzer has developed a new approach to the (5-dimensional) projective relativistic theory which he later called Projective Unified Field Theory (PUFT). In the present paper we introduce a new axiomatics for Schmutzer's theory. By means of this axiomatics we can give a new geometrical interpretation of the physical concept of the PUFT.Comment: 32 pages, 1 figure, LaTeX 2e, will be submitted to Genaral Relativity and Gravitatio

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

Flux networks in metabolic graphs

A metabolic model can be represented as bipartite graph comprising linked reaction and metabolite nodes. Here it is shown how a network of conserved fluxes can be assigned to the edges of such a graph by combining the reaction fluxes with a conserved metabolite property such as molecular weight. A similar flux network can be constructed by combining the primal and dual solutions to the linear programming problem that typically arises in constraint-based modelling. Such constructions may help with the visualisation of flux distributions in complex metabolic networks. The analysis also explains the strong correlation observed between metabolite shadow prices (the dual linear programming variables) and conserved metabolite properties. The methods were applied to recent metabolic models for Escherichia coli, Saccharomyces cerevisiae, and Methanosarcina barkeri. Detailed results are reported for E. coli; similar results were found for the other organisms.Comment: 9 pages, 4 figures, RevTeX 4.0, supplementary data available (excel