Set yogurt's physical characteristics are greatly affected by the homogenization and heat treatment processes. In our previous study, set yogurt treated at 130°C and with the fat particle size reduced to ≤0.6 μm had equivalent curd strength, less syneresis and smoother texture than yogurt treated at 95°C. When investigating the mechanisms underlying yogurt's physical properties, it is important to evaluate the yogurt's microstructure. We conducted electron microscopy evaluations to investigate the mechanisms of changes in yogurt's physical properties caused by 130°C heat treatment and by a reduction in the fat globule size. We prepared yogurt mixtures by combining heat treatment at 95 and 130°C and homogenization pressure at 10 + 5 and 35 + 5 MPa and then fermented the mixtures in a common yogurt starter. Scanning electron microscopy (SEM) and transmission electron microscopy (TEM) were used for the structural observations. Fine particles were observed on the surface of the casein micelles of the yogurt treated at 95°C, and the coalescence density between micelles was high. The surface of the yogurt treated at 130°C had few fine particles, and the coalescence density between micelles was low. The yogurt treated at 130°C with 35 + 5 MPa homogenization had low coalescence density between casein micelles, but smaller-particle-size fat globules increased the network density. Approximately 30% of the fat globules were estimated to be incorporated into the yogurt networks compared to the volume of casein micelles. We speculate that 130°C heat treatment alters the structure of whey protein on the surface of casein micelles and interferes with network formation, but reducing the size of fat globules reinforces the network as a pseudoprotein.

In this paper, we consider the convergence rate with respect to Wasserstein distance in the invariance principle for deterministic non-uniformly hyperbolic systems. Our results apply to uniformly hyperbolic systems and large classes of non-uniformly hyperbolic systems including intermittent maps, Viana maps, unimodal maps and others. Furthermore, as a non-trivial application to the homogenization problem, we investigate the Wasserstein convergence rate of a fast–slow discrete deterministic system to a stochastic differential equation.

We study the asymptotic behaviour of the periodically mixed Zaremba problem. We cover the part of the boundary by a chess board with a small period (square size) $\varepsilon$ and impose the Dirichlet condition on black and the Neumann condition on white squares. As $\varepsilon \to 0$, we get the effective boundary condition which is always of the Dirichlet type. The Dirichlet data on the boundary, however, depend on the ratio between the magnitudes of the two boundary values.

This paper deals with the periodic homogenization of nonlocal parabolic Hamilton–Jacobi equations with superlinear growth in the gradient terms. We show that the problem presents different features depending on the order of the nonlocal operator, giving rise to three different cell problems and effective operators. To prove the locally uniform convergence to the unique solution of the Cauchy problem for the effective equation we need a new comparison principle among viscosity semi-solutions of integrodifferential equations that can be of independent interest.

We consider a nonlinear Robin problem for the Poisson equation in an unbounded periodically perforated domain. The domain has a periodic structure, and the size of each cell is determined by a positive parameter δ. The relative size of each periodic perforation is determined by a positive parameter ε. Under suitable assumptions, such a problem admits a family of solutions which depends on ε and δ. We analyse the behaviour the energy integral of such a family as (ε, δ) tends to (0, 0) by an approach that represents an alternative to asymptotic expansions and classical homogenization theory.

For a family of elliptic operators with periodically oscillating coefficients, $-{\rm div}(A(\cdot /\varepsilon )\nabla )$ with tiny ε > 0, we comprehensively study the first-order expansions of eigenvalues and eigenfunctions (eigenspaces) for both the Dirichlet and Neumann problems in bounded, smooth and strictly convex domains (or more general domains of finite type). A new first-order correction term is introduced to derive the expansion of eigenfunctions in L2 or $H^1_{\rm loc}$. Our results rely on the recent progress on the homogenization of boundary layer problems.

We prove that, in the limit of vanishing thickness, equilibrium configurations of inhomogeneous, three-dimensional non-linearly elastic rods converge to equilibrium configurations of the variational limit theory. More precisely, we show that, as $h\searrow 0$, stationary points of the energy , for a rod $\Omega _h\subset {\open R}^3$ with cross-sectional diameter h, subconverge to stationary points of the Γ-limit of , provided that the bending energy of the sequence scales appropriately. This generalizes earlier results for homogeneous materials to the case of materials with (not necessarily periodic) inhomogeneities.

The compositional zonation of both undeformed and plastically deformed tourmaline crystals from an amphibolite-facies mylonitic pegmatite from the Sierras Pampeanas (NW Argentina) has been investigated using electron microprobe analysis (EMPA). Undeformed tourmaline shows optical and compositional major and minor element growth zonation with a Ca- and Mg-rich rim zone and an Fe- rich core zone. The tourmaline population of the mylonite consists of crystals which appear undeformed at microscopic scale, and of weakly, moderately, and strongly deformed crystals. Depending on the intensity of plastic deformation, the optical zonation is blurred or absent, and the compositional zonation is less pronounced or destroyed. Plastic deformation mobilizes small cations (Fe2+, Mg2+) more efficiently and at lower deformation intensity than larger cations (Na+, Ca2+). In addition to intra-crystal homogenization, plastic deformation caused variable but generally minor Fe, Mg, Si, Al, Ca, and Na exchange between deformed tourmaline domains and co-existing fluid or solid phases. Dislocation creep is interpreted as the dominant deformation mechanism leading to the homogenization of the initial tourmaline growth zonation. The composition and the degree of homogeneity of deformed tourmaline domains depend on the initial composition of the growth zones, their initial volume ratio, the intensity and homogeneity of plastic deformation, and the size of the mobilized cation. Consequently, the composition of and the element distribution within plastically deformed crystals is not entirely controlled by intensive variables (P-T-X), and therefore not suitable for petrogenetic interpretation.

We study a competition-diffusion model while performing simultaneous homogenization and strong competition limits. The limit problem is shown to be a Stefan-type evolution equation with effective coefficients. We also perform some numerical simulations in one and two spatial dimensions that suggest that oscillations in motilities are detrimental to invasion behaviour of a species.

In this paper, we consider the Stokes equations in a perforated domain. When the number of holes increases while their radius tends to 0, it is proven in Desvillettes et al. [J. Stat. Phys. 131 (2008) 941–967], under suitable dilution assumptions, that the solution is well approximated asymptotically by solving a Stokes–Brinkman equation. We provide here quantitative estimates in $L^{p}$-norms of this convergence.

Kaolinite- and halloysite-potassium acetate complexes were synthesized by cogrinding with solid potassium acetate (mechanochemical intercalation). The efficiency of mechanochemical intercalation was compared to the intercalation in solution and by homogenization. The effects of ageing and grinding parameters (grinding time, sample:grinding body mass ratio (SGMR), rotational speed) and the humidity on the intercalation were studied. The degree of intercalation increased exponentially with ageing of the samples prepared by mechanochemical and homogenization techniques. For the mechanochemical and homogenization techniques the required amount of potassium acetate per gram of kaolin (∼0.4 g/g) was two orders of magnitude lower than that for the solution intercalation (78.6 g/g). The highest degree of intercalation (86%) and the lowest structural deformation were achieved by the mechanochemical method (¼ h of co-grinding with 1:2 SGMR at 300 rpm), followed by 16 h ageing at 57% relative humidity.

Determining the drag of a flowover a rough surface is a guiding example for the need to take geometric micro-scale effects into account when computing a macroscale quantity. A well-known strategy to avoid a prohibitively expensive numerical resolution of micro-scale structures is to capture the micro-scale effects through some effective boundary conditions posed for a problem on a (virtually) smooth domain. The central objective of this paper is to develop a numerical scheme for accurately capturing the micro-scale effects at essentially the cost of twice solving a problem on a (piecewise) smooth domain at affordable resolution. Here and throughout the paper “smooth” means the absence of any micro-scale roughness. Our derivation is based on a “conceptual recipe” formulated first in a simplified setting of boundary value problems under the assumption of sufficient local regularity to permit asymptotic expansions in terms of the micro-scale parameter.

The proposed multiscale model relies then on an upscaling strategy similar in spirit to previous works by Achdou et al. [1], Jäger and Mikelic [29, 31], Friedmann et al. [24, 25], for incompressible fluids. Extensions to compressible fluids, although with several noteworthy distinctions regarding e.g. the “micro-scale size” relative to boundary layer thickness or the systematic treatment of different boundary conditions, are discussed in Deolmi et al. [16,17]. For proof of concept the general strategy is applied to the compressible Navier-Stokes equations to investigate steady, laminar, subsonic flow over a flat plate with partially embedded isotropic and anisotropic periodic roughness imposing adiabatic and isothermal wall conditions, respectively. The results are compared with high resolution direct simulations on a fully resolved rough domain.