Phase field study of precipitate growth: Effect of misfit strain and interface curvature

We have used phase field simulations to study the effect of misfit and interfacial curvature on diffusion-controlled growth of an isolated precipitate in a supersaturated matrix. Treating our simulations as computer experiments, we compare our simulation results with those based on the Zener–Frank and Laraia–Johnson–Voorhees theories for the growth of non-misfitting and misfitting precipitates, respectively. The agreement between simulations and the Zener–Frank theory is very good in one-dimensional systems. In two-dimensional systems with interfacial curvature (with and without misfit), we find good agreement between theory and simulations, but only at large supersaturations, where we find that the Gibbs–Thomson effect is less completely realized. At small supersaturations, the convergence of instantaneous growth coefficient in simulations towards its theoretical value could not be tracked to completion, because the diffusional field reached the system boundary. Also at small supersaturations, the elevation in precipitate composition matches well with the theoretically predicted Gibbs–Thomson effect in both misfitting and non-misfitting systems.

Long-range Coulomb interactions and nanoscale electronic inhomogeneities in correlated oxides

Electronic, magnetic, or structural inhomogeneities ranging in size from nanoscopic to mesoscopic scales seem endemic and are possibly generic to colossal magnetoresistance manganites and other transition metal oxides. They are hence of great current interest and understanding them is of fundamental importance. We show here that an extension, to include long-range Coulomb interactions, of a quantum two-fluid l-b model proposed recently for manganites [Phys. Rev. Lett. 92, 157203 (2004)] leads to an excellent description of such inhomogeneities. In the l-b model two very different kinds of electronic states, one localized and polaronic (l) and the other extended or broad band (b) coexist. For model parameters appropriate to manganites and even within a simple dynamical mean-field theory (DMFT) framework, it describes many of the unusual phenomena seen in manganites, including colossal magnetoresistance (CMR), qualitatively and quantitatively. However, in the absence of long-ranged Coulomb interaction, a system described by such a model would actually phase separate, into macroscopic regions of l and b electrons, respectively. As we show in this paper, in the presence of Coulomb interactions, the macroscopic phase separation gets suppressed and instead nanometer scale regions of polarons interspersed with band electron puddles appear, constituting a kind of quantum Coulomb glass. We characterize the size scales and distribution of the inhomogeneity using computer simulations. For realistic values of the long-range Coulomb interaction parameter V-0, our results for the thresholds for occupancy of the b states are in agreement with, and hence support, the earlier approach mentioned above based on a configuration averaged DMFT treatment which neglects V-0; but the present work has features that cannot be addressed in the DMFT framework. Our work points to an interplay of strong correlations, long-range Coulomb interaction, and dopant ion disorder, all inevitably present in transition metal oxides as the origin of nanoscale inhomogeneities rather than disorder frustrated phase competition as is generally believed. As regards manganites, it argues against explanations for CMR based on disorder frustrated phase separation and for an intrinsic origin of CMR. Based on this, we argue that the observed micrometer (meso) scale inhomogeneities owe their existence to extrinsic causes, e.g., strain due to cracks and defects. We suggest possible experiments to validate our speculation.

Effect of Polymer Grafting on the Bilayer Gel to Liquid-Crystalline Transition

Grafted polymers oil the surface of lipid membranes have potential applications in liposome-based drug delivery and Supported membrane systems. The effect of polymer grafting on the phase behavior of bilayers made up of single-tail lipids is investigated using dissipative particle dynamics. The bilayer is maintained in a tensionless state using a barostat. Simulations are carried Out by varying the grafting fraction, G(f), defined as the ratio of the number of polymer molecules to the number of lipid molecules, and the length of the lipid tails. At low G(f), the bilayer shows I sharp transition from the gel (L-beta) to the liquid-crystalline (L-alpha) phase. This main melting transition temperature is lowered as G(f) is increased, and above a critical value of G(f), the interdigitated L-beta I phase is observed prior to the main transition. The temperature range over which the intermediate phases are observed is a function of the lipid tail length and G(f). At higher grafting fractions, the presence of the L-beta I, phase is attributed to the increase in the area per head group due to the lateral pressure exerted by the polymer brush. The areal expansion and decrease in the melting temperatures as a function of G(f) were found to follow the scalings predicted by the self-consistent mean field theories for grafted polymer membranes. Our study shows that the grafted polymer density can be used to effectively control the temperature range and occurrence of a given bilayer phase.

Open and closed boundaries in large-scale convective dynamos

Earlier work has suggested that large-scale dynamos can reach and maintain equipartition field strengths on a dynamical time scale only if magnetic helicity of the fluctuating field can be shed from the domain through open boundaries. To test this scenario in convection-driven dynamos by comparing results for open and closed boundary conditions. Three-dimensional numerical simulations of turbulent compressible convection with shear and rotation are used to study the effects of boundary conditions on the excitation and saturation level of large-scale dynamos. Open (vertical field) and closed (perfect conductor) boundary conditions are used for the magnetic field. The contours of shear are vertical, crossing the outer surface, and are thus ideally suited for driving a shear-induced magnetic helicity flux. We find that for given shear and rotation rate, the growth rate of the magnetic field is larger if open boundary conditions are used. The growth rate first increases for small magnetic Reynolds number, Rm, but then levels off at an approximately constant value for intermediate values of Rm. For large enough Rm, a small-scale dynamo is excited and the growth rate in this regime increases proportional to Rm^(1/2). In the nonlinear regime, the saturation level of the energy of the mean magnetic field is independent of Rm when open boundaries are used. In the case of perfect conductor boundaries, the saturation level first increases as a function of Rm, but then decreases proportional to Rm^(-1) for Rm > 30, indicative of catastrophic quenching. These results suggest that the shear-induced magnetic helicity flux is efficient in alleviating catastrophic quenching when open boundaries are used. The horizontally averaged mean field is still weakly decreasing as a function of Rm even for open boundaries.

Search on a hypercubic lattice using a quantum random walk. I. d > 2

Random walks describe diffusion processes, where movement at every time step is restricted to only the neighboring locations. We construct a quantum random walk algorithm, based on discretization of the Dirac evolution operator inspired by staggered lattice fermions. We use it to investigate the spatial search problem, that is, to find a marked vertex on a d-dimensional hypercubic lattice. The restriction on movement hardly matters for d > 2, and scaling behavior close to Grover's optimal algorithm (which has no restriction on movement) can be achieved. Using numerical simulations, we optimize the proportionality constants of the scaling behavior, and demonstrate the approach to that for Grover's algorithm (equivalent to the mean-field theory or the d -> infinity limit). In particular, the scaling behavior for d = 3 is only about 25% higher than the optimal d -> infinity value.

Investigations on the melting and bending modulus of polymer grafted bilayers using dissipative particle dynamics

Understanding the influence of polymer grafted bilayers on the physicomechanical properties of lipid membranes is important while developing liposomal based drug delivery systems. The melting characteristics and bending moduli of polymer grafted bilayers are investigated using dissipative particle dynamics simulations as a function of the amount of grafted polymer and lipid tail length. Simulations are carried out using a modified Andersen barostat, whereby the membrane is maintained in a tensionless state. For lipids made up of four to six tail beads, the transition from the low temperature L-beta phase to the L-alpha phase is lowered only above a grafting fraction of G(f)=0.12 for polymers made up of 20 beads. Below G(f)=0.12 small changes are observed only for the HT4 bilayer. The bending modulus of the bilayers is obtained as a function of G(f) from a Fourier analysis of the height fluctuations. Using the theory developed by Marsh Biochim. Biophys. Acta 1615, 33 (2003)] for polymer grafted membranes, the contributions to the bending modulus due to changes arising from the grafted polymer and bilayer thinning are partitioned. The contributions to the changes in kappa from bilayer thinning were found to lie within 11% for the lipids with four to six tail beads, increasing to 15% for the lipids containing nine tail beads. The changes in the area stretch modulus were also assessed and were found to have a small influence on the overall contribution from membrane thinning. The increase in the area per head group of the lipids was found to be consistent with the scalings predicted by self-consistent mean field results. (C) 2010 American Institute of Physics.

Glass Transition in the Density Functional Theory of Freezing

A mean-field description of the glass transition in the hard-sphere system is obtained by numerically locating "glassy" minima of a model free-energy functional. These minima, characterized by inhomogeneous but aperiodic density distributions, appear as the average density is increased above the value at which equilibrium crystallization takes place. Investigations of the density distribution and local bond-orientational order at these minima yield results similar to those obtained from simulations.

Thermal Stability of Spherical Nanoporous Aggregates and Formation of Hollow Structures by Sintering-A Phase-Field Study

Nanoporous structures are widely used for many applications and hence it Is important to investigate their thermal stability. We study the stability of spherical nanoporous aggregates using phase-field simulations that explore systematically the effect of grain boundary diffusion, surface diffusion, and grain boundary mobility on the pathways for microstructural evolution. Our simulations for different combinations of surface and GB diffusivity and GB mobility show four distinct microstructural pathways en route to 100% density: multiple dosed pores, hollow shells, hollow shells with a core, and multiple interconnected pores. The microstructures from our simulations are consistent with experimental observations in several different systems. Our results have important implications for rational synthesis of hollow nanostructures or aggregates with open pores, and for controlling the stability of nanoporous aggregates that are widely used for many applications.

Melting and mechanical properties of polymer grafted lipid bilayer membranes

The influence of polymer grafting on the phase behavior and elastic properties of two tail lipid bilayers have been investigated using dissipative particle dynamics simulations. For the range of polymer lengths studied, the L(c) to L(alpha) transition temperature is not significantly affected for grafting fractions, G(f) between 0.16 and 0.25. A decrease in the transition temperature is observed at a relatively high grafting fraction, G(f) = 0.36. At low temperatures, a small increase in the area per head group, a(h), at high G(f) leads to an increase in the chain tilt, inducing order in the bilayer and the solvent. The onset of the phase transition occurs with the nucleation of small patches of thinned membrane which grow and form continuous domains as the temperature increases. This region is the co-existence region between the L(beta)(thick) and the L(alpha)(thin) phases. The simulation results for the membrane area expansion as a function of the grafting density conform extremely well to the scalings predicted by self-consistent mean field theories. We find that the bending modulus shows a small decrease for short polymers (number of beads, N(p) = 10) and low G(f), where the influence of polymer is reduced when compared to the effect of the increased a(h). For longer polymers (N(p) > 15), the bending modulus increases monotonically with increase in grafted polymer. Using the results from mean field theory, we partition the contributions to the bending modulus from the membrane and the polymer and show that the dominant contribution to the increased bending modulus arises from the grafted polymer. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3631940]

Stochastic analysis of epidemics on adaptive time varying networks

Many studies investigating the effect of human social connectivity structures (networks) and human behavioral adaptations on the spread of infectious diseases have assumed either a static connectivity structure or a network which adapts itself in response to the epidemic (adaptive networks). However, human social connections are inherently dynamic or time varying. Furthermore, the spread of many infectious diseases occur on a time scale comparable to the time scale of the evolving network structure. Here we aim to quantify the effect of human behavioral adaptations on the spread of asymptomatic infectious diseases on time varying networks. We perform a full stochastic analysis using a continuous time Markov chain approach for calculating the outbreak probability, mean epidemic duration, epidemic reemergence probability, etc. Additionally, we use mean-field theory for calculating epidemic thresholds. Theoretical predictions are verified using extensive simulations. Our studies have uncovered the existence of an ``adaptive threshold,'' i.e., when the ratio of susceptibility (or infectivity) rate to recovery rate is below the threshold value, adaptive behavior can prevent the epidemic. However, if it is above the threshold, no amount of behavioral adaptations can prevent the epidemic. Our analyses suggest that the interaction patterns of the infected population play a major role in sustaining the epidemic. Our results have implications on epidemic containment policies, as awareness campaigns and human behavioral responses can be effective only if the interaction levels of the infected populace are kept in check.

Phase Field Simulation of Equiaxed Microstructure Formation during Semi-solid Processing of A380 Al Alloy

A phase field modelling approach is implemented in the present study towards simulation of microstructure evolution during cooling slope semi solid slurry generation process of A380 Aluminium alloy. First, experiments are performed to evaluate the number of seeds required within the simulation domain to simulate near spherical microstructure formation, occurs during cooling slope processing of the melt. Subsequently, microstructure evolution is studied employing a phase field method. Simulations are performed to understand the effect of cooling rate on the slurry microstructure. Encouraging results are obtained from the simulation studies which are validated by experimental observations. The results obtained from mesoscopic phase field simulations are grain size, grain density, degree of sphericity of the evolving primary Al phase and the amount of solid fraction present within the slurry at different time frames. Effect of grain refinement also has been studied with an aim of improving the slurry microstructure further. Insight into the process has been obtained from the numerical findings, which are found to be useful for process control.

Dynamics of history-dependent epidemics in temporal networks

The structural properties of temporal networks often influence the dynamical processes that occur on these networks, e.g., bursty interaction patterns have been shown to slow down epidemics. In this paper, we investigate the effect of link lifetimes on the spread of history-dependent epidemics. We formulate an analytically tractable activity-driven temporal network model that explicitly incorporates link lifetimes. For Markovian link lifetimes, we use mean-field analysis for computing the epidemic threshold, while the effect of non-Markovian link lifetimes is studied using simulations. Furthermore, we also study the effect of negative correlation between the number of links spawned by an individual and the lifetimes of those links. Such negative correlations may arise due to the finite cognitive capacity of the individuals. Our investigations reveal that heavy-tailed link lifetimes slow down the epidemic, while negative correlations can reduce epidemic prevalence. We believe that our results help shed light on the role of link lifetimes in modulating diffusion processes on temporal networks.

A method for coupling the phase-field model based on a grand-potential formalism to thermodynamic databases

In this paper we derive an approach for the effective utilization of thermodynamic data in phase-field simulations. While the most widely used methodology for multi-component alloys is following the work by Eiken et al. (2006), wherein, an extrapolative scheme is utilized in conjunction with the TQ interface for deriving the driving force for phase transformation, a corresponding simplistic method based on the formulation of a parabolic free-energy model incorporating all the thermodynamics has been laid out for binary alloys in the work by Folch and Plapp (2005). In the following, we extend this latter approach for multi-component alloys in the framework of the grand-potential formalism. The coupling is applied for the case of the binary eutectic solidification in the Cr-Ni alloy and two-phase solidification in the ternary eutectic alloy (Al-Cr-Ni). A thermodynamic justification entails the basis of the formulation and places it in context of the bigger picture of Integrated Computational Materials Engineering. (C) 2015 Elsevier Ltd. All rights reserved.

Damage Localization, Sensitivity of Energy Release and the Catastrophe Transition

Large earthquakes can be viewed as catastrophic ruptures in the earth’s crust. There are two common features prior to the catastrophe transition in heterogeneous media. One is damage localization and the other is critical sensitivity; both of which are related to a cascade of damage coalescence. In this paper, in an attempt to reveal the physics underlying the catastrophe transition, analytic analysis based on mean-field approximation of a heterogeneous medium as well as numerical simulations using a network model are presented. Both the emergence of damage localization and the sensitivity of energy release are examined to explore the inherent statistical precursors prior to the eventual catastrophic rupture. Emergence of damage localization, as predicted by the mean-field analysis, is consistent with observations of the evolution of damage patterns. It is confirmed that precursors can be extracted from the time-series of energy release according to its sensitivity to increasing crustal stress. As a major result, present research indicates that the catastrophe transition and the critical point hypothesis (CPH) of earthquakes are interrelated. The results suggest there may be two cross-checking precursors of large earthquakes: damage localization and critical sensitivity.

Coupling effects of heterogeneity and stress fluctuation on rupture

The coupling of mesoscopic strength distribution and stress fluctuation on damage evolution and rupture are examined. The numerical simulations show that there is only weak stress fluctuation at the initial damage stage when the mean field approximation is in effect. As the damage fraction becomes larger than the threshold value, the fluctuation is amplified significantly, and damage localization appears. The coupling between stress fluctuation, disordered heterogeneity and the damage localization may play an essential role in catastrophic rupture. (C) 2003 Elsevier Ltd. All rights reserved.