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

‘‘Lozenge’’ contour plots in scattering from polymer networks

We present a consistent explanation for the appearance of “lozenge” shapes in contour plots of the two dimensional scattering intensity from stretched polymer networks. By explicitly averaging over quenched variables in a tube model, we show that lozenge patterns arise as a result of chain material that is not directly deformed by the stretch. We obtain excellent agreement with experimental data

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

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

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

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

Comparing HARPS and Kepler surveys: The alignment of multiple-planet systems

Aims. We study a subset of the planetary population characterized both by HARPS and Kepler surveys. We compare the statistical properties of planets in systems with m.sin i >5-10 M_Earth and R>2 R_Earth. If we assume that the underlying population has the same characteristics, the different detection sensitivity to the orbital inclination relative to the line of sight allows us to probe the planets' mutual inclination. Methods. We considered the frequency of systems with one, two and three planets as dictated by HARPS data. We used Kepler's planetary period and host mass and radii distributions (corrected from detection bias) to model planetary systems in a simple yet physically plausible way. We then varied the mutual inclination between planets in a system according to different prescriptions (completely aligned, Rayleigh distributions and isotropic) and compared the transit frequencies with one, two or three planets with those measured by Kepler. Results. The results show that the two datasets are compatible, a remarkable result especially because there are no tunable knobs other than the assumed inclination distribution. For m.sin i cutoffs of 7-10 M_Earth, which are those expected to correspond to the radius cutoff of 2 R_Earth, we conclude that the results are better described by a Rayleigh distribution with mode of 1 deg or smaller. We show that the best-fit scenario only becomes a Rayleigh distribution with mode of 5 deg if we assume a rather extreme mass-radius relationship for the planetary population. Conclusions. These results have important consequences for our understanding of the role of several proposed formation and evolution mechanisms. They confirm that planets are likely to have been formed in a disk and show that most planetary systems evolve quietly without strong angular momentum exchanges (abridged).Comment: 10 pages, 6 figures, 4 tables, accepted for publication in Astronomy & Astrophysic

Examining the orbital decay targets KELT-9 b, KELT-16 b, and WASP-4b, and the transit-timing variations of HD 97658 b

Context. Tidal orbital decay is suspected to occur for hot Jupiters in particular, with the only observationally confirmed case of this being WASP-12b. By examining this effect, information on the properties of the host star can be obtained using the so-called stellar modified tidal quality factor Q*′, which describes the efficiency with which the kinetic energy of the planet is dissipated within the star. This can provide information about the interior of the star. Aims. In this study, we aim to improve constraints on the tidal decay of the KELT-9, KELT-16, and WASP-4 systems in order to find evidence for or against the presence of tidal orbital decay. With this, we want to constrain the Q*′ value for each star. In addition, we aim to test the existence of the transit timing variations (TTVs) in the HD 97658 system, which previously favoured a quadratic trend with increasing orbital period. Methods. Making use of newly acquired photometric observations from CHEOPS (CHaracterising ExOplanet Satellite) and TESS (Transiting Exoplanet Survey Satellite), combined with archival transit and occultation data, we use Markov chain Monte Carlo (MCMC) algorithms to fit three models to the data, namely a constant-period model, an orbital-decay model, and an apsidal-precession model. Results. We find that the KELT-9 system is best described by an apsidal-precession model for now, with an orbital decay trend at over 2 σ being a possible solution as well. A Keplerian orbit model with a constant orbital period provides the best fit to the transit timings of KELT-16 b because of the scatter and scale of their error bars. The WASP-4 system is best represented by an orbital decay model at a 5 σ significance, although apsidal precession cannot be ruled out with the present data. For HD 97658 b, using recently acquired transit observations, we find no conclusive evidence for a previously suspected strong quadratic trend in the data