We study the statistical mechanics of a model describing the coevolution of species interacting in a random way. We find that at high competition replica symmetry is broken. We solve the model in the approximation of one step replica symmetry breaking and we compare our findings with accurate numerical simulations. Short title: RSB in the Random Replicant Model

Despite the fact that quantitative experimental data have been available for more than forty years now, nematoacoustics still poses intriguing theoretical and experimental problems. In this paper, we prove that the main observed features of acoustic wave propagation through a nematic liquid crystal cell - namely, the frequency-dependent anisotropy of sound velocity and acoustic attenuation - can be explained by properly accounting for two fundamental features of the nematic response: anisotropy and relaxation. The latter concept - new in liquid crystal modelling - provides the first theoretical explanation of the structural relaxation process hypothesised long ago by Mullen and co-workers [Mullen et al., Phys. Rev. Lett., 1972, 28, 799]. We compare and contrast our proposal with an alternative theory where the liquid crystal is modelled as an anisotropic second-gradient fluid.

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We consider the coupling between the local curvature tensor of a membrane and the local two-dimensional nematic order parameter, deriving it from a quasi-microscopic argument. This coupling makes the nematic director aligned along the lowest curvature eigenvector in a local metric. Local bending of a membrane may then generate nematic ordering. Alternatively, emerging nematic order leads to shape instabilities of closed vesicles. The theory is applied to a spherical isotropic vesicle, which turns into a prolate shape with two +1 disclinations on its poles as the nematic order sets in the membrane, described within the Landau-de Gennes continuum model.

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We show that nonlinear continuum elasticity can be effective in modeling plastic flows in crystals if it is viewed as Landau theory with an infinite number of equivalent energy wells whose configuration is dictated by the symmetry group GL (3, Z). Quasi-static loading can be then handled by athermal dynamics, while lattice based discretization can play the role of regularization. As a proof of principle we study in this Letter dislocation nucleation in a homogeneously sheared 2D crystal and show that the global tensorial invariance of the elastic energy foments the development of complexity in the configuration of collectively nucleating defects. A crucial role in this process is played by the unstable higher symmetry crystallographic phases, traditionally thought to be unrelated to plastic flow in lower symmetry lattices.Crystal plasticity is the simplest among yield phenomena in solids [1], and yet it has been compared in complexity to fluid turbulence [2,3]. The intrinsic irregularity of plastic flow in crystals [4] is due to short and long range interaction of crystal defects (dislocations) [5] dragged by the applied loading through a rugged energy landscape [6][7][8]. Fundamental understanding of plastic flow in crystals is crucial for improving hardening properties of materials [9], extending their fatigue life [10], controlling their forming at sub-micron scales [11] and building new materials [12].Macroscopic crystal plasticity relies on a phenomenological continuum description of plastic deformation in terms of a finite number of order parameters representing amplitudes of pre-designed mechanisms. These mechanisms are coupled elastically and operate according to friction type dynamics [13][14][15][16][17]. The alternative microscopic approaches, relying instead on molecular dynamics [18][19][20][21][22][23][24][25], can handle only macroscopically insignificant time and length scales [26]. An intermediate discrete dislocation dynamics approach focuses on long range interaction of few dislocations, while their short range interaction is still treated phenomenologically [27][28][29]. Collective dynamics of many dislocations can be also described by the dislocation density field, however, rigorous coarse-graining in such strongly interacting system still remains a major challenge [30][31][32][33][34][35][36][37].A highly successful computational bridge between microscopic and macroscopic approaches is provided by the quasi-continuum finite element method which uses adaptive meshing and employs ab initio approaches to guide the constitutive response at different mesh scales [38][39][40][41][42]. Its drawbacks, however, are spurious effects due to matching of FEM representations at different scales and a high computational cost of reconstructing the constitutive response at the smallest scales [43].In this Letter we propose a synthetic approach dea-Figure 1. Schematic representation of a lattice invariant shear and the associated energy barriers along the simple shear loading path ∇y = 1 + α(e1 ⊗ e ⊥ 1 ). Alt...

We propose a Landau-de Gennes variational theory fit to simultaneously describe isotropic, nematic, smectic- A , and smectic- C phases of a liquid crystal. The unified description allows us to deal with systems in which one, or all, of the order parameters develop because of the influence of defects, external fields and/or boundary conditions. We derive the complete phase diagram of the system, that is, we characterize how the homogeneous minimizers depend on the value of the constitutive parameters. The coupling between the nematic order tensor and the complex smectic order parameter generates an elastic potential which is a nonconvex function of the gradient of the smectic order parameter. This lack of convexity yields in turn a loss of regularity of the free-energy minimizers. We then consider the effect on an infinitesimal second-order regularization term in the free-energy functional, which fixes the optimal number of defects in the singular configurations.

We study experimentally the intermittent progress of the mechanically-induced martensitic transformation in a Cu-Al-Be single crystal through a full-field measurement technique: the grid method. We utilize an in-house especially designed gravity-based device, wherein a system controlled by water pumps applies a perfectly monotonic uniaxial load through very small force increments. The sample exhibits hysteretic superelastic behavior during the forward and reverse cubic-monoclinic transformation, produced by the evolution of the strain field of the phase microstructures. The in-plane linear strain components are measured on the sample surface during the loading cycle, and we characterize for the first time the strain intermittency in a number of ways, showing the emergence of power-law behavior for the strain avalanching over almost six decades of magnitude. We also describe the non-stationarity and the asymmetry observed in the forward vs. the reverse transformation. The present experimental approach, which allows for the monitoring of the reversible martensitic transformation both locally and globally in the crystal, proves useful and enhances our capabilities in the analysis and possible control of transition-related phenomena in shape-memory alloys.