Double phase problems with variable growth

We consider a class of double phase variational integrals driven by nonhomogeneous potentials. We study the associated Euler equation and we highlight the existence of two different Rayleigh quotients. One of them is in relationship with the existence of an infinite interval of eigenvalues while the second one is associated with the nonexistence of eigenvalues. The notion of eigenvalue is understood in the sense of pairs of nonlinear operators, as introduced by Fu\v{c}ik, Ne\v{c}as, Sou\v{c}ek, and Sou\v{c}ek. The analysis developed in this paper extends the abstract framework corresponding to some standard cases associated to the $p(x)$-Laplace operator, the generalized mean curvature operator, or the capillarity differential operator with variable exponent. The results contained in this paper complement the pioneering contributions of Marcellini, Mingione et al. in the field of variational integrals with unbalanced growth

Nonequilibrium phase transition in surface growth

Conserved growth models that exhibit a nonlinear instability in which the height (depth) of isolated pillars (grooves) grows in time are studied by numerical integration and stochastic simulation. When this instability is controlled by the introduction of an infinite series of higher-order nonlinear terms, these models exhibit, as function of a control parameter, a non-equilibrium phase transition between a kinetically rough phase with self-affine scaling and a phase that exhibits mound formation, slope selection and power-law coarsening.Comment: 7 pages, 4 .eps figures (Minor changes in text and references.

Phase-ordering dynamics in itinerant quantum ferromagnets

The phase-ordering dynamics that result from domain coarsening are considered for itinerant quantum ferromagnets. The fluctuation effects that invalidate the Hertz theory of the quantum phase transition also affect the phase ordering. For a quench into the ordered phase a transient regime appears, where the domain growth follows a different power law than in the classical case, and for asymptotically long times the prefactor of the t^{1/2} growth law has an anomalous magnetization dependence. A quench to the quantum critical point results in a growth law that is not a power-law function of time. Both phenomenological scaling arguments and renormalization-group arguments are given to derive these results, and estimates of experimentally relevant length and time scales are presented.Comment: 6pp., 1 eps fig, slightly expanded versio

Simulation of spherulite growth using a comprehensive approach to modeling the first-order isotropic/smectic-A mesophase transition

A comprehensive modeling and simulation study of the first-order isotropic/smectic-A transition is presented and applied to phase diagram computation and two-dimensional spherulite growth. An approach based on nonlinear optimization, that incorporates experimental data (from 12CB, dodecyl-cyanobiphenyl), is used to determine physically realistic model parameters. These parameters are then used in conjunction with an optimized phase diagram computation method. Additionally, a time-dependent formulation is presented and applied to the study of two-dimensional smectic-A spherulite growth. These results show the growth kinematics and defect dynamics of nanoscale smectic-A spherulite growth in an isotropic phase with an initially radial layer configuration

Grain growth in ultrafine-grained Y-TZP ceramics

Grain growth in dense ultrafine-grained (120–600 nm) tetragonal ZrO2-Y2O3 ceramics is studied as a function of temperature. At all temperatures investigated both segregation and phase partitioning occur. It is argued that at temperatures ≤ 1150 °C grain growth is not significantly inhibited by solid solution drag or by phase partitioning. At higher temperatures the grain growth behaviour can be explained by the models of solid solution drag and/or phase partitioning depending on conditions.\u

Thermodynamics, transition dynamics, and texturing in polymer-dispersed liquid crystals with mesogens exhibiting a direct isotropic/smectic-A transition

Experimental and modeling/simulation studies of phase equilibrium and growth morphologies of novel polymer-dispersed liquid crystal (PDLC) mixtures of PS (polystyrene) and liquid crystals that exhibit a direct isotropic/smectic-A (lamellar) mesophase transition were performed for PS/10CB (decyl- cyanobiphenyl) and PS/12CB (dodecyl-cyanobiphenyl). Partial phase diagrams were determined using polarized optical microscopy (POM) and differential scanning calorimetry (DSC) for different compositions of both materials, determining both phase separation (liquid/liquid demixing) and phase ordering (isotropic/smectic-A transition) temperatures. The Flory-Huggins theory of isotropic mixing and Maier-Saupe-McMillan theory for smectic-A liquid crystalline ordering were used to computationally determine phase diagrams for both systems, showing good agreement with the experimental results. In addition to thermodynamic observations, growth morphology relations were found depending on phase transition sequence, quench rate, and material composition. Three stages of liquid crystal-rich domain growth morphology were observed: spherical macroscale domain growth ("stage I"), highly anisotropic domain growth ("stage II"), and sub-micron spheroid domain growth ("stage III"). Nano-scale structure of spheroidal and spherocylindrical morphologies were then determined via two-dimensional simulation of a high-order Landau-de Gennes model. Morphologies observed during stage II growth are typical of di- rect isotropic/smectic-A phase transitions, such as highly anisotropic "batonnets" and filaments. These morphologies, which are found to be persistent in direct isotropic/smectic-A PDLCs, could provide new functionality and applications for these functional materials.Comment: First Revision, 21 pages, 11 figures, submitted to Macromolecules as an article 17JUL200

The economic performance of cities: a Markov-switching approach

This paper examines the determinants of employment growth in metro areas. To obtain growth rates, we use a Markov-switching model that separates a city’s growth path into two distinct phases (high and low), each with its own growth rate. The simple average growth rate over some period is, therefore, the weighted average of the high-phase and low-phase growth rates, with the weight being the frequency of the two phases. We estimate the effects of a variety of factors separately for the high-phase and low-phase growth rates, along with the frequency of the low phase. We find that growth in the high phase is related to human capital, industry mix, and average firm size. In contrast, we find that growth in the low phase is mostly related to industry mix, specifically, the relative importance of manufacturing. Finally, the frequency of the low phase appears to be related to the level of non-education human capital, but to none of the other variables. Overall, our results strongly reject the notion that city-level characteristics influence employment growth equally across the phases of the business cycle.Business cycles ; Cities and towns

Phase Field Modelling of Submonolayer Epitaxial Growth

We report simulations of submonolayer epitaxial growth using a continuum phase field model. The island density and the island size distribution both show scaling behavior. When the capillary length is small, the island size distribution is consistent with irreversible aggregation kinetics. As the capillary length increases, the island size distribution reflects the effects of reversible aggregation. These results are in quantitative agreement with other simulation methods and with experiments. However, the scaling of the island total density does not agree with known results. The reasons are traced to the mechanisms of island nucleation and aggregation in the phase field model.Comment: 6 pages, 5 figure