Disclinations, dislocations and continuous defects: a reappraisal

Disclinations, first observed in mesomorphic phases, are relevant to a number of ill-ordered condensed matter media, with continuous symmetries or frustrated order. They also appear in polycrystals at the edges of grain boundaries. They are of limited interest in solid single crystals, where, owing to their large elastic stresses, they mostly appear in close pairs of opposite signs. The relaxation mechanisms associated with a disclination in its creation, motion, change of shape, involve an interplay with continuous or quantized dislocations and/or continuous disclinations. These are attached to the disclinations or are akin to Nye's dislocation densities, well suited here. The notion of 'extended Volterra process' takes these relaxation processes into account and covers different situations where this interplay takes place. These concepts are illustrated by applications in amorphous solids, mesomorphic phases and frustrated media in their curved habit space. The powerful topological theory of line defects only considers defects stable against relaxation processes compatible with the structure considered. It can be seen as a simplified case of the approach considered here, well suited for media of high plasticity or/and complex structures. Topological stability cannot guarantee energetic stability and sometimes cannot distinguish finer details of structure of defects.Comment: 72 pages, 36 figure

Elliptic Phases: A Study of the Nonlinear Elasticity of Twist-Grain Boundaries

We develop an explicit and tractable representation of a twist-grain-boundary phase of a smectic A liquid crystal. This allows us to calculate the interaction energy between grain boundaries and the relative contributions from the bending and compression deformations. We discuss the special stability of the 90 degree grain boundaries and discuss the relation of this structure to the Schwarz D surface.Comment: 4 pages, 2 figure

Pre-LGM Northern Hemisphere ice sheet topography

We here reconstruct the paleotopography of Northern Hemisphere ice sheets during the glacial maxima of marine isotope stages (MIS) 5b and 4.We employ a combined approach, blending geologically based reconstruction and numerical modeling, to arrive at probable ice sheet extents and topographies for each of these two time slices. For a physically based 3-D calculation based on geologically derived 2-D constraints, we use the University of Maine Ice Sheet Model (UMISM) to calculate ice sheet thickness and topography. The approach and ice sheet modeling strategy is designed to provide robust data sets of sufficient resolution for atmospheric circulation experiments for these previously elusive time periods. Two tunable parameters, a temperature scaling function applied to a spliced Vostok–GRIP record, and spatial adjustment of the climatic pole position, were employed iteratively to achieve a good fit to geological constraints where such were available. The model credibly reproduces the first-order pattern of size and location of geologically indicated ice sheets during marine isotope stages (MIS) 5b (86.2 kyr model age) and 4 (64 kyr model age). From the interglacial state of two north–south obstacles to atmospheric circulation (Rocky Mountains and Greenland), by MIS 5b the emergence of combined Quebec–central Arctic and Scandinavian–Barents-Kara ice sheets had increased the number of such highland obstacles to four. The number of major ice sheets remained constant through MIS 4, but the merging of the Cordilleran and the proto-Laurentide Ice Sheet produced a single continent-wide North American ice sheet at the LGM

Kramers rate theory of ionization and dissociation of bound states

Calculating the microscopic dissociation rate of a bound state, such as a classical diatomic molecule, has been difficult so far. The problem was that standard theories require an energy barrier over which the bound particle (or state) escapes into the preferred low-energy state. This is not the case when the long-range repulsion responsible for the barrier is either absent or screened (as in Cooper pairs, ionized plasma, or biomolecular complexes). We solve this classical problem by accounting for entropic memory at the microscopic level. The theory predicts dissociation rates for arbitrary potentials and is successfully tested on the example of plasma, where it yields an estimate of ionization in the core of Sun in excellent agreement with experiments. In biology, the new theory accounts for crowding in receptor-ligand kinetics and protein aggregation

Points, Walls and Loops in Resonant Oscillatory Media

In an experiment of oscillatory media, domains and walls are formed under the parametric resonance with a frequency double the natural one. In this bi-stable system, %phase jumps $\pi$ by crossing walls. a nonequilibrium transition from Ising wall to Bloch wall consistent with prediction is confirmed experimentally. The Bloch wall moves in the direction determined by its chirality with a constant speed. As a new type of moving structure in two-dimension, a traveling loop consisting of two walls and Neel points is observed.Comment: 9 pages (revtex format) and 6 figures (PostScript

Structure, Stresses and Local Dynamics in Glasses

The interrelations between short range structural and elastic aspects in glasses and glass forming liquids pose important and yet unresolved questions. In this paper these relations are analyzed for mono-atomic glasses and stressed liquids with a short range repulsive-attractive pair potentials. Strong variations of the local pressure are found even in a zero temperature glass, whereas the largest values of pressure are the same in both glasses and liquids. The coordination number z(J) and the effective first peak radius depend on the local pressures J's. A linear relation was found between components of site stress tensor and the local elastic constants. A linear relation was also found between the trace of the squares of the local frequencies and the local pressures. Those relations hold for glasses at zero temperature and for liquids. We explain this by a relation between the structure and the potential terms. A structural similarity between liquids and solids is manifested by similar dependencies of the coordination number on the pressures.Comment: 7 pages, 11 figure

Defect generation and deconfinement on corrugated topographies

We investigate topography-driven generation of defects in liquid crystals films coating frozen surfaces of spatially varying Gaussian curvature whose topology does not automatically require defects in the ground state. We study in particular disclination-unbinding transitions with increasing aspect ratio for a surface shaped as a Gaussian bump with an hexatic phase draped over it. The instability of a smooth ground state texture to the generation of a single defect is also discussed. Free boundary conditions for a single bump are considered as well as periodic arrays of bumps. Finally, we argue that defects on a bump encircled by an aligning wall undergo sharp deconfinement transitions as the aspect ratio of the surface is lowered.Comment: 24 page

Topological defects in spinor condensates

We investigate the structure of topological defects in the ground states of spinor Bose-Einstein condensates with spin F=1 or F=2. The type and number of defects are determined by calculating the first and second homotopy groups of the order-parameter space. The order-parameter space is identified with a set of degenerate ground state spinors. Because the structure of the ground state depends on whether or not there is an external magnetic field applied to the system, defects are sensitive to the magnetic field. We study both cases and find that the defects in zero and non-zero field are different.Comment: 10 pages, 1 figure. Published versio

Computer investigation of the energy landscape of amorphous silica

The multidimensional topography of the collective potential energy function of a so-called strong glass former (silica) is analyzed by means of classical molecular dynamics calculations. Features qualitatively similar to those of fragile glasses are recovered at high temperatures : in particular an intrinsic characteristic temperature $T_c\simeq 3500$K is evidenced above which the system starts to investigate non-harmonic potential energy basins. It is shown that the anharmonicities are essentially characterized by a roughness appearing in the potential energy valleys explored by the system for temperatures above $T_c$.Comment: 5 pages; accepted for publication in PR