Normal heat conductivity in two-dimensional scalar lattices

The paper revisits recent counterintuitive results on divergence of heat conduction coefficient in two-dimensional lattices. It was reported that in certain lattices with on-site potential, for which one-dimensional chain has convergent conductivity, for the 2D case it turns out to diverge. We demonstrate that this conclusion is an artifact caused by insufficient size of the simulated system. To overcome computational restrictions, a ribbon of relatively small width is simulated instead of the square specimen. It is further demonstrated that the heat conduction coefficient in the "long" direction of the ribbon ceases to depend on the width, as the latter achieves only 10 to 20 interparticle distances. So, one can consider the dynamics of much longer systems, than in the traditional setting, and still can gain a reliable information regarding the 2D lattice. It turns out that for all considered models, for which the conductivity is convergent in the 1D case, it is indeed convergent in the 2D case. In the same time, however, the length of the system, necessary to reveal the convergence in the 2D case, may be much bigger than in its 1D counterpart.Comment: 6 pages, 6 figure

The Fermi-Pasta-Ulam problem: 50 years of progress

A brief review of the Fermi-Pasta-Ulam (FPU) paradox is given, together with its suggested resolutions and its relation to other physical problems. We focus on the ideas and concepts that have become the core of modern nonlinear mechanics, in their historical perspective. Starting from the first numerical results of FPU, both theoretical and numerical findings are discussed in close connection with the problems of ergodicity, integrability, chaos and stability of motion. New directions related to the Bose-Einstein condensation and quantum systems of interacting Bose-particles are also considered.Comment: 48 pages, no figures, corrected and accepted for publicatio

Melting-freezing cycles in a relatively sheared pair of crystalline monolayers

The nonequilibrium dynamical behaviour that arises when two ordered two-dimensional monolayers of particles are sheared over each other is studied in Brownian dynamics simulations. A curious sequence of nonequilibrium states is observed as the driving rate is increased, the most striking of which is a sliding state with irregular alternation between disordered and ordered states. We comment on possible mechanisms underlying these cycles, and experiments that could observe them.Comment: 7 pages, 8 figures, minor changes in text and figures, references adde

Stable Frank-Kasper phases of self-assembled, soft matter spheres

Single molecular species can self-assemble into Frank Kasper (FK) phases, finite approximants of dodecagonal quasicrystals, defying intuitive notions that thermodynamic ground states are maximally symmetric. FK phases are speculated to emerge as the minimal-distortional packings of space-filling spherical domains, but a precise quantitation of this distortion and how it affects assembly thermodynamics remains ambiguous. We use two complementary approaches to demonstrate that the principles driving FK lattice formation in diblock copolymers emerge directly from the strong-stretching theory of spherical domains, in which minimal inter-block area competes with minimal stretching of space-filling chains. The relative stability of FK lattices is studied first using a diblock foam model with unconstrained particle volumes and shapes, which correctly predicts not only the equilibrium {\sigma} lattice, but also the unequal volumes of the equilibrium domains. We then provide a molecular interpretation for these results via self-consistent field theory, illuminating how molecular stiffness regulates the coupling between intra-domain chain configurations and the asymmetry of local packing. These findings shed new light on the role of volume exchange on the formation of distinct FK phases in copolymers, and suggest a paradigm for formation of FK phases in soft matter systems in which unequal domain volumes are selected by the thermodynamic competition between distinct measures of shape asymmetry.Comment: 40 pages, 22 figure