Energy and Vorticity Spectra in Turbulent Superfluid 4^4He from T=0T=0 to TλT_\lambda

We discuss the energy and vorticity spectra of turbulent superfluid $^4$He in all the temperature range from $T=0$ up to the phase transition "$\lambda$ point", $T_\lambda\simeq 2.17\,$K. Contrary to classical developed turbulence in which there are only two typical scales, i.e. the energy injection $L$ and the dissipation scales $\eta$, here the quantization of vorticity introduces two additional scales, i.e the vortex core radius $a_0$ and the mean vortex spacing $\ell$. We present these spectra for the super- and normal-fluid components in the entire range of scales from $L$ to $a_0$ including the cross-over scale $\ell$ where the hydrodynamic eddy-cascade is replaced by the cascade of Kelvin waves on individual vortices. At this scale a bottleneck accumulation of the energy was found earlier at $T=0$. We show that even very small mutual friction dramatically suppresses the bottleneck effect due to the dissipation of the Kelvin waves. Using our results for the spectra we estimate the Vinen "effective viscosity" $\nu'$ in the entire temperature range and show agreement with numerous experimental observation for $\nu'(T)$.Comment: 20 pages, 5 figure

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

Temperature suppression of Kelvin-wave turbulence in superfluids

Kelvin waves propagating on quantum vortices play a crucial role in the phenomenology of energy dissipation of superfluid turbulence. Previous theoretical studies have consistently focused on the zero-temperature limit of the statistical physics of Kelvin-wave turbulence. In this letter, we go beyond this athermal limit by introducing a small but finite temperature in the form of non-zero mutual friction dissipative force; A situation regularly encountered in actual experiments of superfluid turbulence. In this case we show that there exists a new typical length-scale separating a quasi-inertial range of Kelvin wave turbulence from a far dissipation range. The letter culminates with analytical predictions for the energy spectrum of the Kelvin-wave turbulence in both of these regimes

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

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

Interplay between Polymer Chain Conformation and Nanoparticles Assembly in Model Industrial Silica/Rubber Nanocomposites

International audienceThe question of the influence of nanoparticles (NP) on chain dimensions in polymer nanocomposites(PNC) has been treated mainly through the fundamental way using theoretical or simulation tools andexperiments on well-defined model PNC. Here we present the first experimental study about theinfluence of NP on the polymer chain conformation for PNC designed to be as close as possible toindustrial systems employed in tire industry. PNC are silica nanoparticles dispersed into a Styrene-Butadiene-Rubber (SBR) matrix whose NP dispersion can be managed by NP loading with interfacialcoating or coupling additives usually employed in the manufacturing mixing process. We associatedspecific chain (d) labeling, and the so-called Zero Average Contrast (ZAC) method, with SANS, in-situSANS and SAXS/TEM experiments to extract the polymer chain scattering signal at rest for non-crosslinked and under stretching for cross-linked PNCs. NP loading, individual clusters or connectednetwork, as well as the influence of the type, the quantity of interfacial agent and the influence of theelongation rate have been evaluated on the chain conformation and on its related deformation. Weclearly distinguish the situations where the silica is perfectly matched from the unperfected matching bydirect comparison of SANS and SAXS structure factor. Whatever the silica matching situation, theadditive type and quantity and the filler content, there is no thus significant change in the polymerdimension for NP loading up to 15% v/v within a range of 5%. One can see an extra scatteringcontribution at low Q, as often encountered, enhanced for non-perfect silica matching but also visiblefor perfect filler matching. This contribution can be qualitatively attributed to specific h or d chainsadsorption onto the NP surface inside the NP cluster that modifying the average scattering neutroncontrast of the silica cluster. Under elongation, NP act as additional cross-linking junction preventingchain relaxation giving a deformation of the chain with NP closer to theoretical phantom networkprediction than for pure matrix