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Register a new userRealizations of Isostatic Material Frameworks
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This paper studies the set of equivalent realizations of isostatic frameworks in two dimensions, and algorithms for finding all such realizations. We show that an isostatic framework has an even number of equivalent realizations that preserve edge lengths and connectivity. We enumerate the complete set of equivalent realizations for a toy framework with pinned boundary in two dimensions and study the impact of boundary length on the emergence of these realizations. To ameliorate the computational complexity of finding a solution to a large multivariate quadratic system corresponding to the constraints; alternative methods - based on constraint reduction and distance-based covering map or Cayley parameterization of the search space - are presented. The application of these methods is studied on atomic clusters, a model two-dimensional glasses, and jamming.
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The nature of the amorphous state has been notably difficult to ascertain at the microscopic level. In addition to the fundamental importance of understanding the amorphous state, potential changes to amorphous structures as a result of radiation damage have direct implications for the pressing problem of nuclear waste encapsulation. Here, we develop new methods to identify and quantify the damage produced by high-energy collision cascades that are applicable to amorphous structures and perform large-scale molecular dynamics simulations of high-energy collision cascades in a model zircon system. We find that, whereas the averaged probes of order such as pair distribution function do not indicate structural changes, local coordination analysis shows that the amorphous structure substantially evolves due to radiation damage. Our analysis shows a correlation between the local structural changes and enthalpy. Important implications for the long-term storage of nuclear waste follow from our detection of significant local density inhomogeneities. Although we do not reach the point of convergence where the changes of the amorphous structure saturate, our results imply that the nature of this new converged amorphous state will be of substantial interest in future experimental and modelling work.
Transient responses in disordered systems typically show a heavy-tail relaxation behavior: the decay time constant increases as time increases, revealing a spectral distribution of time constants. The asymptotic value of such transients is notoriously difficult to experimentally measure due to the increasing decay time-scale. However, if the heavy-tail transient is plotted versus log-time, a reduced set of data around the inflection point of such a plot is sufficient for an accurate fit. From a derivative plot in log-time, the peak height, position, line width, and, most importantly, skewness are all that is needed to accurately predict the asymptotic value of various heavy-tail decay models to within less than a percent. This curve fitting strategy reduces by orders of magnitude the amount of experimental data required, and clearly identifies a threshold below which the amount of data is insufficient to distinguish various models. The skew normal spectral fit and dispersive diffusion transient fit are proposed as four-parameter fits, with the latter including the stretched exponential as a limiting case. The line fit and asymptotic prediction are demonstrated using experimental transient responses in previously published amorphous silicon and amorphous InGaZnO data.
Below the melting temperature $T_m$ crystals are the stable phase of typical elemental or molecular systems. However, cooling down a liquid below $T_m$, crystallization is anything but inevitable. The liquid can be supercooled, eventually forming a glass below the glass transition temperature $T_g$. Despite their long lifetimes and the presence of strong barriers that produces an apparent stability, supercooled liquids and glasses remain intrinsically metastable state and thermodynamically unstable towards the crystal. Here we investigated the isothermal crystallization kinetics of the prototypical strong glassformer GeO$_2$ in the deep supercooled liquid at 1100 K, about half-way between $T_m$ and $T_g$. The crystallization process has been observed through time-resolved neutron diffraction for about three days. Data show a continuous reorganization of the amorphous structure towards the alpha-quartz phase with the final material composed by crystalline domains plunged into a low-density, residual amorphous matrix. A quantitative analysis of the diffraction patterns allows determining the time evolution of the relative fractions of crystal and amorphous, that was interpreted through an empirical model for the crystallization kinetics. This approach provides a very good description of the experimental data and identifies a predator-prey-like mechanism between crystal and amorphous, where the density variation acts as blocking barrier.
The local order units of dense simple liquid are typically three dimensional (close packed) clusters: hcp, fcc and icosahedrons. We show that the fluid demonstrates the superstable tetrahedral local order up to temperatures several orders of magnitude higher than the melting temperature and down to critical density. While the solid-like local order (hcp, fcc) disappears in the fluid at much lower temperatures and far above critical density. We conclude that the supercritical fluid shows the temperature (density) driven two stage melting of the three dimensional local order. We also find that the structure relaxation times in the supercritical fluid are much larger than ones estimated for weakly interactive gas even far above the melting line.
Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a one dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.
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