Holes and cracks in rigid foam films

The classical problem of foam film rupture dynamics has been investigated when surfaces exhibit very high rigidity due to the presence of specific surfactants. Two new features are reported. First a strong deviation to the well-known Taylor-Culick law is observed. Then, crack-like patterns can be visualized in the film; these patterns are shown to appear at a well defined deformation. The key role of surface active material on these features is quantitatively investigated, pointing the importance of surface elasticity to describe these fast dynamical processes, and thus providing an alternative tool to characterize surface elasticity in conditions extremely far from equilibrium. The origin of the cracks and their consequences on film rupturing dynamics are also discussed

Exploring disparities and similarities in European food consumption patterns

This paper investigates the heterogeneity of food consumption patterns in Europe. The analysis relies on a wide set of indicators, namely the structure of calorie, protein and fat consumption as well as the consumption of main foodstuffs. Clusters based on estimated income elasticity of calorie and protein demand are also reported. Income elasticities of animal products tend to exceed those corresponding to the total calorie demand. The same pattern holds true for the elasticity of demand for proteins. Main dimensions of consumption are identified based on factor analysis and used subsequently for the purpose of clustering countries. The hard core clusters are those that remain stable regardless of the algorithm used in classification or the indicators as a proxy of food consumption patterns. A limited number of hard core clusters of countries emerged. The paper concludes with a discussion of clusters with homogeneous patterns of consumption.food consumption patterns, Europe, factor analysis, cluster analysis, hard-core clusters

Cross-linking patterns and their images in swollen and deformed gels

Using the theory of elasticity of polymer gels we show that large-scale cross-link density patterns written into the structure of the network in the melt state, can be revealed upon swelling by monitoring the monomer density patterns. We find that while isotropic deformations in good solvent yield magnified images of the original pattern, anisotropic deformations distort the image (both types of deformation yield affinely stretched images in $\theta$ solvents). We show that in ordinary solids with spatially inhomogeneous profile of the shear modulus, isotropic stretching leads to distorted density image of this profile under isotropic deformation. Using simple physical arguments we demonstrate that the different response to isotropic stretching stems from fundamental differences between the theory of elasticity of solids and that of gels. Possible tests of our predictions and some potential applications are discussed.Comment: 16 pages, 3 figure

Unemployment, Factor Substitution, and Capital Formation

We incorporate a wage bargaining structure in a dynamic general equilibrium model and show how this feature changes short and long-run properties of equilibria compared with a perfectly competitive setting. We discuss how employment, capital, and income shares respond to wage setting shocks and show that adjustment dynamics depend decisively on the magnitude of the elasticity of substitution between labour and capital. Values of the elasticity below unity add persistence, tend to preserve stability, and lead to empirically plausible adjustment patterns. By contrast, values above unity introduce additional volatility, thereby making steady states potentially unstable.

Elasticity of Polydomain Liquid Crystal Elastomers

We model polydomain liquid-crystal elastomers by extending the neo-classical soft and semi-soft free energies used successfully to describe monodomain samples. We show that there is a significant difference between polydomains cross-linked in homogeneous high symmetry states then cooled to low symmetry polydomain states and those cross-linked directly in the low symmetry polydomain state. For example, elastomers cross-linked in the isotropic state then cooled to a nematic polydomain will, in the ideal limit, be perfectly soft, and with the introduction of non-ideality, will deform at very low stress until they are macroscopically aligned. The director patterns observed in them will be disordered, characteristic of combinations of random deformations, and not disclination patterns. We expect these samples to exhibit elasticity significantly softer than monodomain samples. Polydomains cross-linked in the nematic polydomain state will be mechanically harder and contain characteristic schlieren director patterns. The models we use for polydomain elastomers are spatially heterogeneous, so rather than solving them exactly we elucidate this behavior by bounding the energies using Taylor-like (compatible test strain fields) and Sachs (constant stress) limits extended to non-linear elasticity. Good agreement is found with experiments that reveal the supersoft response of some polydomains. We also analyze smectic polydomain elastomers and propose that polydomain SmC* elastomers cross-linked in the SmA monodomain state are promising candidates for low field electrical actuation.Comment: 13 pages, 11 figure

International Evidence on Food Consumption Patterns: An Update Using 2005 International Comparison Program Data

In a 2003 report, International Evidence on Food Consumption Patterns, ERS economists estimated income and price elasticities of demand for broad consumption categories and food categories across 114 countries using 1996 International Comparison Program (ICP) data. This report updates that analysis with an estimated two-stage demand system across 144 countries using 2005 ICP data. Advances in ICP data collection since 1996 led to better results and more accurate income and price elasticity estimates. Low-income countries spend a greater portion of their budget on necessities, such as food, while richer countries spend a greater proportion of their income on luxuries, such as recreation. Low-value staples, such as cereals, account for a larger share of the food budget in poorer countries, while high-value food items are a larger share of the food budget in richer countries. Overall, low-income countries are more responsive to changes in income and food prices and, therefore, make larger adjustments to their food consumption pattern when incomes and prices change. However, adjustments to price and income changes are not uniform across all food categories. Staple food consumption changes the least, while consumption of higher-value food items changes the most.ICP 2005, high-value food products, consumption patterns, marginal share, income elasticity, price elasticity, ERS, USDA, Demand and Price Analysis, Food Security and Poverty, International Development, Research Methods/ Statistical Methods,

Elastic Instability Triggered Pattern Formation

Recent experiments have exploited elastic instabilities in membranes to create complex patterns. However, the rational design of such structures poses many challenges, as they are products of nonlinear elastic behavior. We pose a simple model for determining the orientational order of such patterns using only linear elasticity theory which correctly predicts the outcomes of several experiments. Each element of the pattern is modeled by a "dislocation dipole" located at a point on a lattice, which then interacts elastically with all other dipoles in the system. We explicitly consider a membrane with a square lattice of circular holes under uniform compression and examine the changes in morphology as it is allowed to relax in a specified direction.Comment: 15 pages, 7 figures, the full catastroph

Supersoft elasticity in polydomain nematic elastomers

We consider the equilibrium stress-strain behavior of polydomain liquid crystal elastomers (PLCEs). We show that there is a fundamental difference between PLCEs cross-linked in the high temperature isotropic and low temperature aligned states. PLCEs cross-linked in the isotropic state then cooled to an aligned state will exhibit extremely soft elasticity (confirmed by recent experiments) and ordered director patterns characteristic of textured deformations. PLCEs cross-linked in the aligned state will be mechanically much harder and characterized by disclination textures