Statistical distributions in the folding of elastic structures

The behaviour of elastic structures undergoing large deformations is the result of the competition between confining conditions, self-avoidance and elasticity. This combination of multiple phenomena creates a geometrical frustration that leads to complex fold patterns. By studying the case of a rod confined isotropically into a disk, we show that the emergence of the complexity is associated with a well defined underlying statistical measure that determines the energy distribution of sub-elements,``branches'', of the rod. This result suggests that branches act as the ``microscopic'' degrees of freedom laying the foundations for a statistical mechanical theory of this athermal and amorphous system

Energy Spectra of Superfluid Turbulence in 3^3He

In superfluid $^3$He turbulence is carried predominantly by the superfluid component. To explore the statistical properties of this quantum turbulence and its differences from the classical counterpart we adopt the time-honored approach of shell models. Using this approach we provide numerical simulations of a Sabra-shell model that allows us to uncover the nature of the energy spectrum in the relevant hydrodynamic regimes. These results are in qualitative agreement with analytical expressions for the superfluid turbulent energy spectra that were found using a differential approximation for the energy flux

First Order Phase Transition of a Long Polymer Chain

We consider a model consisting of a self-avoiding polygon occupying a variable density of the sites of a square lattice. A fixed energy is associated with each $90^\circ$-bend of the polygon. We use a grand canonical ensemble, introducing parameters $\mu$ and $\beta$ to control average density and average (total) energy of the polygon, and show by Monte Carlo simulation that the model has a first order, nematic phase transition across a curve in the $\beta$-$\mu$ plane.Comment: 11 pages, 7 figure

Statistical Mechanics of Two-dimensional Foams

The methods of statistical mechanics are applied to two-dimensional foams under macroscopic agitation. A new variable -- the total cell curvature -- is introduced, which plays the role of energy in conventional statistical thermodynamics. The probability distribution of the number of sides for a cell of given area is derived. This expression allows to correlate the distribution of sides ("topological disorder") to the distribution of sizes ("geometrical disorder") in a foam. The model predictions agree well with available experimental data

The Effective Temperature in Elasto-Plasticity of Amorphous Solids

An effective temperature $T_{\rm eff}$ which differs from the bath temperature is believed to play an essential role in the theory of elasto-plasticity of amorphous solids. The definition of a measurable $T_{\rm eff}$ in the literature on sheared solids suffers however from being connected to a fluctuation-dissipation theorem which is correct only in equilibrium. Here we introduce a natural definition of $T_{\rm eff}$ based on measurable structural features without recourse to any questionable assumption. The value of $T_{\rm eff}$ is connected, using theory and scaling concepts, to the flow stress and the mean energy that characterize the elasto-plastic flow.Comment: 4 pages, 5 figure

Did atmospheric thermal tides cause a daylength locking in the Precambrian? A review on recent results

After the initial suggestion by Zahnle and Walker (1987) that the torque accelerating the spin rate of the Earth and produced by the heating of the atmosphere by the Sun could counteract the braking lunir-solar gravitational torque in the Precambrian, several authors have recently revisited this hypothesis. In these studies, it is argued that the geological evidences of the past spin state of the Earth play in favor of this atmospheric tidal locking of the length of the day (LOD). In the present review of the recent literature, we show that the drawn conclusions depend crucially on the consideration of the stromatolite geological LOD estimates obtained by Pannella at 1.88 and 2.0 Ga, which are subject to large uncertainties. When only the most robust cyclostatigraphic estimates of the LOD are retained, the LOD locking hypothesis is not supported. Moreover, the consideration of the published General Circulation Model numerical simulations and of new analytical models for the thermal atmospheric tides suggest that the atmospheric tidal resonance, which is the crucial ingredient for the LOD locking in the Precambrian, was never of sufficiently large amplitude to allow for this tidal LOD lock.Comment: 16 pages, 9 figure

Energy distributions and effective temperatures in the packing of elastic sheets

The packing of elastic sheets is investigated in a quasi two-dimensional experimental setup: a sheet is pulled through a rigid hole acting as a container, so that its configuration is mostly prescribed by the cross-section of the sheet in the plane of the hole. The characterisation of the packed configuration is made possible by using refined image analysis. The geometrical properties and energies of the branches forming the cross-section are broadly distributed. We find distributions of energy with exponential tails. This setup naturally divides the system into two sub-systems: in contact with the container and within the bulk. While the geometrical properties of the sub-systems differ, their energy distributions are identical, indicating 'thermal' homogeneity and allowing the definition of effective temperatures from the characteristic scales of the energy distributions.Comment: 6 page

Multi-scale structural characterizations of fatty acid tubes with temperature tuneable diameter in bulk and at the air/water interface

International audienceThe use of agricultural resources for industrial purposes will undoubtedly be one of the major challenges of the 21st century, either from the energetic point of view by the progressive replacement of fossil fuels or with respect to non-energy uses by making available new organic “biosynthons” to the chemicals industry. In such a context, we demonstrate here the strong potential of dispersions of saturated fatty acids and their hydroxylated derivatives, extracted from biological compounds of plant origin, as a new class of green surfactants

Plastic Deformation of 2D Crumpled Wires

When a single long piece of elastic wire is injected trough channels into a confining two-dimensional cavity, a complex structure of hierarchical loops is formed. In the limit of maximum packing density, these structures are described by several scaling laws. In this paper it is investigated this packing process but using plastic wires which give origin to completely irreversible structures of different morphology. In particular, it is studied experimentally the plastic deformation from circular to oblate configurations of crumpled wires, obtained by the application of an axial strain. Among other things, it is shown that in spite of plasticity, irreversibility, and very large deformations, scaling is still observed.Comment: 5 pages, 6 figure

Last giant impact on the Neptunian system. Constraints on oligarchic masses in the trans-Saturnian region

Stochastic impacts by large bodies are, at present, the usually accepted mechanisms able to account for the obliquity of the ice giants. We attempt to set constraints on giant impacts as the cause of Neptune's current obliquity in the framework of modern theories. We also use the present orbital properties of the Neptunian irregular satellites (with the exception of Triton) to set constraints on the scenario of giant impacts at the end of Neptune formation. We model the angular momentum transfer to proto-Neptune and the impulse transfer to its irregular satellites by the last stochastic collision (GC) between the protoplanet and an oligarchic mass at the end of Neptune's formation. We obtain that an impactor mass greather than 4 Earth masses is not possible since it cannot reproduce the present rotational properties of the planet, unless the impact parameter of the collision were very small. On the other hand, if the impactor mass was greather than 1.4 Earth masses, the present Neptunian irregular satellites had to be formed or captured after the end of stochastic impacts. The upper bounds on the oligarchic masses (4 Earth masses from the obliquity of Neptune and 1.4 earth masses from the Neptunian irregular satellites) are independent of unknown parameters, such as the mass and distribution of the planetesimals, the location at which Uranus and Neptune were formed, the Solar Nebula initial surface mass density, and the growth regime. If stochastic impacts had occurred, these results should be understood as upper constraints on the oligarchic masses in the trans-Saturnian region at the end of ice planet formation and may be used to set constraints on planetary formation scenarios.Comment: Paper accepted for publication in Astronomy & Astrophysic