Disappearance of stretch-induced wrinkles of thin sheets: a study of orthotropic films

A recent paper (Healey et al., J. Nonlin. Sci., 2013, 23:777-805.) predicted the disappearance of the stretch-induced wrinkled pattern of thin, clamped, elastic sheets by numerical simulation of the F\"oppl-von K\'arm\'an equations extended to the finite in-plane strain regime. It has also been revealed that for some aspect ratios of the rectangular domain wrinkles do not occur at all regardless of the applied extension. To verify these predictions we carried out experiments on thin 20 micrometer thick adhesive covered), previously prestressed elastomer sheets with different aspect ratios under displacement controlled pull tests. On one hand the the adjustment of the material properties during prestressing is highly advantageous as in targeted strain regime the film becomes substantially linearly elastic (which is far not the case without prestress). On the other hand a significant, non-ignorable orthotropy develops during this first extension. To enable quantitative comparisons we abandoned the assumption about material isotropy inherent in the original model and derived the governing equations for an orthotropic medium. In this way we found good agreement between numerical simulations and experimental data. Analysis of the negativity of the second Piola-Kirchhoff stress tensor revealed that the critical stretch for a bifurcation point at which the wrinkles disappear must be finite for any aspect ratio. On the contrary there is no such a bound for the aspect ratio as a bifurcation parameter. Physically this manifests as complicated wrinkled patterns with more than one highly wrinkled zones on the surface in case of elongated rectangles. These arrangements have been found both numerically and experimentally. These findings also support the new, finite strain model, since the F\"oppl-von K\'arm\'an equations based on infinitesimal strains do not exhibit such a behavior.Comment: 16 pages, 5 figure

On the financial sustainability of earnings-related pension schemes with"pay-as-you-go"financing and the role of government indexed bonds

In this paper the authors reconsider the idea of an earnings-related pension system with reserves invested in indexed government bonds as a mechanism to both ensure financial sustainability and improve security. They start by reviewing the characterization of the sustainable rate of return of an earnings-related pension system with pay-as-you-go financing. The authors show that current proxies for the sustainable rate, including the Swedish"gyroscope,"are not stable and propose an alternative measure that depends on the growth of the buffer-stock and the pay-as-you-go asset. Using a simple one-sector macroeconomic model that embeds a notional account pension system they then show how GDP indexed government bonds, if combined with the right measure for the sustainable rate of return on contributions, could be used to generate a sustainable and secure earnings-related pension system, without becoming a fiscal burden. The proposal is particularly attractive for countries considering reforms to earnings-related systems that have accumulated a large implicit pension debt. In this case, the government bonds allow the financing of this debt in a transparent way. The proposed mechanism can also facilitate the transition to a fully-funded pension system when the government bonds are allowed to be traded.Economic Theory&Research,Technology Industry,Pensions&Retirement Systems,Economic Growth,Population Policies

The Mullins effect in the wrinkling behavior of highly stretched thin films

Recent work demonstrates that finite-deformation nonlinear elasticity is essential in the accurate modeling of wrinkling in highly stretched thin films. Geometrically exact models predict an isola-center bifurcation, indicating that for a bounded interval of aspect ratios only, stable wrinkles appear and then disappear as the macroscopic strain is increased. This phenomenon has been verified in experiments. In addition, recent experiments revealed the following striking phenomenon: For certain aspect ratios for which no wrinkling occurred upon the first loading, wrinkles appeared during the first unloading and again during all subsequent cyclic loading. Our goal here is to present a simple pseudo-elastic model, capturing the stress softening and residual strain observed in the experiments, that accurately predicts wrinkling behavior on the first loading that differs from that under subsequent cyclic loading. In particular for specific aspect ratios, the model correctly predicts the scenario of no wrinkling during first loading with wrinkling occurring during unloading and for all subsequent cyclic loading.Comment: 15 pages, 9 figure

Reactivity of pi-complexes of Ti, V, and Nb towards dithioacetic acid: Synthesis and structure of novel metal sulfur-containing complexes

In order to use sulfur-containing resources economically and with minimal environmental damage, it is important to understand the desulfurization processes. Hydrodesulfurization, for example, is carried out on the surface of a heterogeneous metal sulfide catalyst. Studies of simple, soluble inorganic systems provide information regarding the structure and reactivity of sulfur-containing compounds with metal complexes. Further, consistent with recent trends in materials chemistry, many model compounds warrant further study as catalyst precursors. The reactivity of low-valent organometallic sandwich pi-complexes toward dithiocarboxylic acids is described. For example, treatment of bisbenzene vanadium with CH3CSSH affords a divanadium tetrakis(dithioacetate) complex. The crystallographically determined V-V bond distance, 2.800(2), is nearly the same as the V-V bond distance in a V(mu-nu squared-S2)2V' unit in the mineral patonite (VS4)n. The stability of the V2S4 core in the dimer is demonstrated by evidence of V2S4(+) in the mass spectrum (70 eV, solid probe) of the vanadium dimer. Several other systems relevant to HDS catalysis are also discussed

Network formation of tissue cells via preferential attraction to elongated structures

Vascular and non-vascular cells often form an interconnected network in vitro, similar to the early vascular bed of warm blooded embryos. Our time-lapse recordings show that the network forms by extending sprouts, i.e., multicellular linear segments. To explain the emergence of such structures, we propose a simple model of preferential attraction to stretched cells. Numerical simulations reveal that the model evolves into a quasi-stationary pattern containing linear segments, which interconnect above the critical volume fraction of 0.2. In the quasi-stationary state the generation of new branches offset the coarsening driven by surface tension. In agreement with empirical data, the characteristic size of the resulting polygonal pattern is density-independent within a wide range of volume fractions

The first 40 million years of circumstellar disk evolution: the signature of terrestrial planet formation

We characterize the first 40 Myr of evolution of circumstellar disks through a unified study of the infrared properties of members of young clusters and associations with ages from 2 Myr up to ~ 40 Myr: NGC 1333, NGC 1960, NGC 2232, NGC 2244, NGC 2362, NGC 2547, IC 348, IC 2395, IC 4665, Chamaeleon I, Orion OB1a and OB1b, Taurus, the \b{eta} Pictoris Moving Group, \r{ho} Ophiuchi, and the associations of Argus, Carina, Columba, Scorpius-Centaurus, and Tucana-Horologium. Our work features: 1.) a filtering technique to flag noisy backgrounds, 2.) a method based on the probability distribution of deflections, P(D), to obtain statistically valid photometry for faint sources, and 3.) use of the evolutionary trend of transitional disks to constrain the overall behavior of bright disks. We find that the fraction of disks three or more times brighter than the stellar photospheres at 24 {\mu}m decays relatively slowly initially and then much more rapidly by ~ 10 Myr. However, there is a continuing component until ~ 35 Myr, probably due primarily to massive clouds of debris generated in giant impacts during the oligarchic/chaotic growth phases of terrestrial planets. If the contribution from primordial disks is excluded, the evolution of the incidence of these oligarchic/chaotic debris disks can be described empirically by a log-normal function with the peak at 12 - 20 Myr, including ~ 13 % of the original population, and with a post-peak mean duration of 10 - 20 Myr.Comment: accepted for publication, the Astrophysical Journal (2017

Cracking Patterns of Brittle Hemispherical Domes: an Experimental Study

Crack formation in hemispherical domes is a distinguished problem in structural mechanics. The safety of cracked domes has a long track record; the evolution of the cracking pattern received less attention. Here, we report displacement-controlled loading tests of brittle hemispherical dome specimens, including the evolution of the meridional cracking pattern. The 27 investigated specimens, 20 cm in diameter, were prepared in 3D printed molds, and their material is one of the three mixtures of gypsum and cement. We find that neither the (limited) tensile strength nor the exact value of the thickness significantly affects the statistical description of the cracking pattern, i.e., the cracking phenomenon is robust. The maximal number of the meridional cracks never exceeds seven before the fragments’ disintegration (collapse). We find that the size distribution of the fragments exhibits a lognormal distribution. The evolution is reflected in the load-displacement diagrams recorded in the test, too, as significant drops in the force are accompanied by an emergence of one or more new cracks, reflecting the brittle nature of the phenomenon. A simple, stochastic fragmentation model, in which a segment is fragmented at either in the middle or at the fourth point, fairly recovers the observed size distribution