The success of condensed matter physics in the 20th century is largely related to the deep understanding of matter organization, and following elaboration of physical concepts simplifying complex problems. Similar approach applied to the living matter reveals novel unique types of order at all scales, from individual molecules to biological tissues. At the scale typical for intracellular biomolecular assemblies, the peculiarities of the organization are mainly related to their unconventional topology and geometry, and to low dimensionality. Some of these unconventional types of order and their relation to biological functions will be illustrated : screw-like liquid-crystalline order of DNA in bacteriophages, chiral anticlinic liquid-crystalline state of nucleosomes in the chromatin fiber, 2D spherical crystals and 2D dodecahedral quasicrystals in capsids of small and medium viruses.

In this work, we experimentally investigate the ability of topological defects to guide interfacial assembly of spherical particles with homeotropic anchoring confined to nematic interfaces. We propose two different systems: In the first one, particles are trapped at an air/nematic interface where they spontaneously form various 2D patterns. We demonstrate that the phase transition between these patterns can be controlled by defects formed in the nematic bulk. In the second system, we explore the behavior of particles at the surface of bipolar nematic drops. We found that particles assemble into linear chains and interact with surface defects at the North and South poles of the drop, giving rise to the formation of star structures in a self-assembly process. We detail the mechanism that guides the behavior of particles and discuss the role of defects in the formation of the observed patterns.

We study the phase transition in a face-centered-cubic antiferromagnet with Ising spins as a function of the concentration $p$ of ferromagnetic bonds randomly introduced into the system. Such a model describes the spin-glass phase at strong bond disorder. Using the standard Monte Carlo simulation and the powerful Wang-Landau flat-histogram method, we carry out in this work intensive simulations over the whole range of $p$. We show that the first-order transition disappears with a tiny amount of ferromagnetic bonds, namely $p\sim 0.01$, in agreement with theories and simulations on other 3D models. The antiferromagnetic long-range order is also destroyed with a very small $p$ ($\simeq 5\%$). With increasing $p$, the system changes into a spin glass and then to a ferromagnetic phase when $p>0.65$. The phase diagram in the space ($T_c,p$) shows an asymmetry, unlike the case of the $\pm J$ Ising spin glass on the simple cubic lattice. We calculate the relaxation time around the spin-glass transition temperature and we show that the spin autocorrelation follows a stretched exponential relaxation law where the factor $b$ is equal to $\simeq 1/3$ at the transition as suggested by the percolation-based theory. This value is in agreement with experiments performed on various spin glasses and with Monte Carlo simulations on different SG models.

High resolution measurements reveal that condensation isotherms of $^4$He in a silica aerogel become discontinuous below a critical temperature. We show that this behaviour does not correspond to an equilibrium phase transition modified by the disorder induced by the aerogel structure, but to the disorder-driven critical point predicted for the athermal out-of-equilibrium dynamics of the Random Field Ising Model. Our results evidence the key role of non-equilibrium effects in the phase transitions of disordered systems.

We perform the complete canonical analysis of the tetrad formulation of bimetric gravity and confirm that it is ghost-free describing the seven degrees of freedom of a massless and a massive gravitons. In particular, we find explicit expressions for secondary constraints, one of which is responsible for removing the ghost, whereas the other ensures the equivalence with the metric formulation. Both of them have a remarkably simple form and, being combined with conditions on Lagrange multipliers, can be written in a covariant way.

This method comprises steps consisting in: injecting (100) a sample into a capillary tube; conveying (110) the sample along the capillary tube, under experimental conditions able to generate a Taylor dispersion effect; generating (120) a signal characterising the Taylor dispersion; processing (130) said signal to obtain the experimental Taylor signal Ŝ(t); and analysing (200) said experimental Taylor signal Ŝ(t). The analyzing step consists in obtaining an amplitude distribution P(G(c)) allowing said experimental Taylor signal Ŝ(t) to be decomposed into a sum of Gaussian functions by implementing a constraint-solving algorithm consisting in minimising a cost function Ha comprising at least one constraint term associated with a constraint that the amplitude distribution P(G(c)) must respect, this minimisation being carried out over a range of values of interest of a parameter G(c) characterising the Gaussian amplitude function P(G(c)).