Steady state dynamic dependence between local mobility and non-affine fluctuations in two-dimensional aggregates.

Motivated by qualitative experimental observations in collective behavior of self-propelled camphor particles at air-water interfaces, we study a generic aggregate forming system in two dimensions using canonical ensemble constant temperature molecular dynamics simulation. The aggregates form due to the competition between short-range attraction and long-range repulsion of pair-wise interactions as a generic proxy for the specific case of short-range capillary attraction competing with long-range Marangoni-assisted repulsion in camphor boat systems. Choosing the appropriate set of interaction parameters, we focus on characterising the local dynamics in two specific limiting morphologies, viz. compact and string-like aggregates. We focus on the temporal evolution of the mobility of an individual particle and the dynamic change in its nearest neighbourhood, measured in terms of the Debye-Waller factor ([Formula: see text]) and the non-affine parameter ([Formula: see text]), respectively (both defined in the text), and their interrelation over several lengths of observation time [Formula: see text]. The distribution for both measures are found to follow the relation: [Formula: see text] for the measured quantity x. The exponent [Formula: see text] is equal to two and one respectively, for the compact and string-like morphologies following the respective ideal fractal dimension of these aggregates. A functional dependence between these two observables is determined from a detailed statistical analysis of their joint and conditional distributions. The results obtained can readily be used and verified by experiments on aggregate forming systems more generic than the specific camphor boat system that motivated us, such as globular proteins, nanoparticle self-assembly etc. Further, the insights gained from this study might be useful to understand the evolution of collective dynamics in diverse glass-forming systems.

Quantifying structural dynamic heterogeneity in a dense two-dimensional equilibrium liquid.

We investigate local structural fluctuations in a model equilibrium fluid with the aim of better understanding the structural basis of locally heterogeneous dynamics identified in recent simulations and experimental studies of glass-forming liquids and other strongly interacting particle systems, such as lipid membranes, dusty plasmas, interfacial dynamics of crystals, the internal dynamics of proteins, etc. In particular, we utilize molecular dynamics simulation methods to study a single component Lennard-Jones condensed material at constant temperature in two dimensions over a range of densities covering both liquid and crystalline phase regimes. We identify three distinct structural classes of particles by examining the immediate neighborhood of individual particles relying on a solid-angle based tessellation technique. The area distribution of the neighborhoods reveals cages having hexagonal, pentagonal, and square symmetries. Pentagonal cells appear to be the predominant motif in the liquid phase, while the solid phase is dominated by hexagonal cells, as in the case of a perfect crystal. An examination of the spatial organization of particles belonging to each structural class further indicates that finite-size clusters of the hexagonal and pentagonal particle populations arise within both liquids and solids, and the size of these clusters grows in a complementary way as a function of density. Both particle populations form percolation clusters in the liquid-crystal coexistence regime. Interestingly, the populations of particles with different local structures, defined by the arrangement of neighboring particles, are found to maintain different diffusivities, as computed from the velocity autocorrelation function for each type of particle for all densities studied. Our analysis provides a new conceptual framework for understanding the structural origin of dynamical heterogeneity in soft materials.

Quantum discord and its allies: a review of recent progress.

We review concepts and methods associated with quantum discord and related topics. We also describe their possible connections with other aspects of quantum information and beyond, including quantum communication, quantum computation, many-body physics, and open quantum dynamics. Quantum discord in the multiparty regime and its applications are also discussed.

Morphology dictated heterogeneous dynamics in two-dimensional aggregates.

Particulate aggregates occur in a variety of non-equilibrium steady-state morphologies ranging from finite-size compact crystalline structures to non-compact string-like conformations. This diversity is due to the competition between pair-wise short range attraction and long range repulsion between particles. We identify different microscopic mechanisms in action by following the simulated particle trajectories for different morphologies in two dimensions at a fixed density and temperature. In particular, we show that the compact clusters are governed by symmetric caging of particles by their nearest neighbors while sidewise asymmetric binding of particles leads to non-compact aggregates. The measured timescales for these two mechanisms are found to be distinctly different providing phenomenological evidence of a relation between microstructure and dynamics of particulate aggregates. Supporting these findings, the time dependent diffusivity is observed to differ across the morphological hierarchy, while the average long-time dynamics is, in general, sub-diffusive at 'low' temperatures. Finally, one generic relation between diffusivity and structural randomness, applicable to simple equilibrium systems, is validated for complex aggregate forming systems through further analysis of the same system at different temperatures.

A minimal description of morphological hierarchy in two-dimensional aggregates.

A dimensionless parameter Λ is proposed to describe a hierarchy of morphologies in two-dimensional (2D) aggregates formed due to varying competition between short-range attraction and long-range repulsion. Structural transitions from finite non-compact to compact to percolated structures are observed in the configurations simulated by molecular dynamics at a constant temperature and density. Configurational randomness across the transition, measured by the two-body excess entropy S2, exhibits data collapse with the average potential energy [small epsilon, Greek, macron] of the systems. Independent master curves are presented among S2, the reduced second virial coefficient B2* and Λ, justifying this minimal description. This work lays out a coherent basis for the study of 2D aggregate morphologies relevant to diverse nano- and bio-processes.

Pre-yield non-affine fluctuations and a hidden critical point in strained crystals.

A crystalline solid exhibits thermally induced localised non-affine droplets in the absence of external stress. Here we show that upon an imposed shear, the size of these droplets grow until they percolate at a critical strain, well below the value at which the solid begins to yield. This critical point does not manifest in most thermodynamic or mechanical properties, but is hidden and reveals itself in the onset of inhomogeneities in elastic moduli, marked changes in the appearance and local properties of non-affine droplets and a sudden enhancement in defect pair concentration. Slow relaxation of stress and an-elasticity appear as observable dynamical consequences of this hidden criticality. Our results may be directly verified in colloidal crystals with video microscopy techniques but are expected to have more general validity.

Nonaffine heterogeneities and droplet fluctuations in an equilibrium crystalline solid.

We show, using molecular-dynamics simulations, that a two-dimensional Lennard-Jones solid exhibits droplet fluctuations characterized by nonaffine deviations from local crystallinity. The fraction of particles in these droplets increases as the mean density of the solid decreases and approaches ≈20% of the total number in the vicinity of the fluid-solid phase boundary. We monitor the geometry, local equation of state, density correlations, and Van Hove functions of these droplets. We provide evidence that these nonaffine heterogeneities should be interpreted as being droplet fluctuations from nearby metastable minima. The local excess pressure of the droplets plotted against the local number density shows a van der Waal loop with distinct branches corresponding to fluidlike compact and stringlike glassy droplets. The distinction between fluidlike and glassy droplets disappears above a well-defined temperature.

Structural transitions in a crystalline bilayer: the case of Lennard-Jones and Gaussian core models.

We study structural transitions in a system of interacting particles arranged as a crystalline bilayer, as a function of the density ρ and the distance d between the layers. As d is decreased a sequence of transitions involving triangular, rhombic, square and centred rectangular lattices is observed. The sequence of phases and the order of transitions depends on the nature of the interactions.