Isomorphs in model molecular liquids

Isomorphs are curves in the phase diagram along which a number of static and dynamic quantities are invariant in reduced units. A liquid has good isomorphs if and only if it is strongly correlating, i.e., the equilibrium virial/potential energy fluctuations are more than 90% correlated in the NVT ensemble. This paper generalizes isomorphs to liquids composed of rigid molecules and study the isomorphs of two systems of small rigid molecules, the asymmetric dumbbell model and the Lewis-Wahnstrom OTP model. In particular, for both systems we find that the isochoric heat capacity, the excess entropy, the reduced molecular center-of-mass self part of the intermediate scattering function, the reduced molecular center-of-mass radial distribution function to a good approximation are invariant along an isomorph. In agreement with theory, we also find that an instantaneous change of temperature and density from an equilibrated state point to another isomorphic state point leads to no relaxation. The isomorphs of the Lewis-Wahnstrom OTP model were found to be more approximative than those of the asymmetric dumbbell model, which is consistent with the OTP model being less strongly correlating. For both models we find "master isomorphs", i.e., isomorphs have identical shape in the virial/potential energy phase diagram.Comment: 20 page

Spatially heterogeneous dynamics investigated via a time-dependent four-point density correlation function

Relaxation in supercooled liquids above their glass transition and below the onset temperature of “slow” dynamics involves the correlated motion of neighboring particles. This correlated motion results in the appearance of spatially heterogeneous dynamics or “dynamical heterogeneity.” Traditional two-point time-dependent density correlation functions, while providing information about the transient “caging” of particles on cooling, are unable to provide sufficiently detailed information about correlated motion and dynamical heterogeneity. Here, we study a four-point, time-dependent density correlation function g4(r,t)g4(r,t) and corresponding “structure factor” S4(q,t)S4(q,t) which measure the spatial correlations between the local liquid density at two points in space, each at two different times, and so are sensitive to dynamical heterogeneity. We study g4(r,t)g4(r,t) and S4(q,t)S4(q,t) via molecular dynamics simulations of a binary Lennard-Jones mixture approaching the mode coupling temperature from above. We find that the correlations between particles measured by g4(r,t)g4(r,t) and S4(q,t)S4(q,t) become increasingly pronounced on cooling. The corresponding dynamical correlation length ξ4(t)ξ4(t) extracted from the small-qq behavior of S4(q,t)S4(q,t) provides an estimate of the range of correlated particle motion. We find that ξ4(t)ξ4(t) has a maximum as a function of time t,t, and that the value of the maximum of ξ4(t)ξ4(t) increases steadily from less than one particle diameter to a value exceeding nine particle diameters in the temperature range approaching the mode coupling temperature from above. At the maximum, ξ4(t)ξ4(t) and the α relaxation time τατα are related by a power law. We also examine the individual contributions to g4(r,t),g4(r,t), S4(q,t),S4(q,t), and ξ4(t),ξ4(t), as well as the corresponding order parameter Q(t)Q(t) and generalized susceptibility χ4(t),χ4(t), arising from the self and distinct contributions to Q(t).Q(t). These contributions elucidate key differences between domains of localized and delocalized particles.© 2003 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70264/2/JCPSA6-119-14-7372-1.pd

NVU dynamics. II. Comparing to four other dynamics

In the companion paper [Ingebrigtsen et al., arXiv:1012.3447] an algorithm was developed for tracing out a geodesic curve on the constant-potential-energy hypersurface. Here simulations of this NVU dynamics are compared to results for four other dynamics, both deterministic and stochastic. First, NVU dynamics is compared to the standard energy-conserving Newtonian NVE dynamics by simulations of the Kob-Andersen binary Lennard-Jones liquid, its WCA version (i.e., with cut-off's at the pair potential minima), and the Gaussian Lennard-Jones liquid. We find identical results for all quantities probed: radial distribution functions, incoherent intermediate scattering functions, and mean-square displacement as function of time. Arguments are then presented for the equivalence of NVU and NVE dynamics in the thermodynamic limit; in particular to leading order in 1/N these two dynamics give identical time-autocorrelation functions. In the final section NVU dynamics is compared to Monte Carlo dynamics, to a diffusive dynamics of small-step random walks on the constant-potential-energy hypersurface, and to Nose-Hoover NVT dynamics. If time is scaled for the two stochastic dynamics to make their single-particle diffusion constants identical to those of NVE dynamics, the simulations show that all five dynamics are equivalent at low temperatures except at short times

Saddles in the energy landscape probed by supercooled liquids

We numerically investigate the supercooled dynamics of two simple model liquids exploiting the partition of the multi-dimension configuration space in basins of attraction of the stationary points (inherent saddles) of the potential energy surface. We find that the inherent saddles order and potential energy are well defined functions of the temperature T. Moreover, decreasing T, the saddle order vanishes at the same temperature (T_MCT) where the inverse diffusivity appears to diverge as a power law. This allows a topological interpretation of T_MCT: it marks the transition from a dynamics between basins of saddles (T>T_MCT) to a dynamics between basins of minima (T<T_MCT).Comment: 4 pages, 3 figures, to be published on PR

Energy landscape of a Lennard-Jones liquid: Statistics of stationary points

Molecular dynamics simulations are used to generate an ensemble of saddles of the potential energy of a Lennard-Jones liquid. Classifying all extrema by their potential energy u and number of unstable directions k, a well defined relation k(u) is revealed. The degree of instability of typical stationary points vanishes at a threshold potential energy, which lies above the energy of the lowest glassy minima of the system. The energies of the inherent states, as obtained by the Stillinger-Weber method, approach the threshold energy at a temperature close to the mode-coupling transition temperature Tc.Comment: 4 RevTeX pages, 6 eps figures. Revised versio

Invariants in the Yukawa system’s thermodynamic phase diagram

This paper shows that several known properties of the Yukawa system can be derived from the isomorph theory, which applies to any system that has strong correlations between its virial and potential-energy equilibrium fluctuations. Such "Roskilde-simple" systems have a simplified thermodynamic phase diagram deriving from the fact that they have curves (isomorphs) along which structure and dynamics in reduced units are invariant to a good approximation. We show that the Yukawa system has strong virial potential-energy correlations and identify its isomorphs by two different methods. One method, the so-called direct isomorph check, identifies isomorphs numerically from jumps of relatively small density changes (here 10%). The second method identifies isomorphs analytically from the pair potential. The curves obtained by the two methods are close to each other; these curves are confirmed to be isomorphs by demonstrating the invariance of the radial distribution function, the static structure factor, the mean-square displacement as a function of time, and the incoherent intermediate scattering function. Since the melting line is predicted to be an isomorph, the theory provides a derivation of a known approximate analytical expression for this line in the temperature-density phase diagram. The paper's results give the first demonstration that the isomorph theory can be applied to systems like dense colloidal suspensions and strongly coupled dusty plasmas.Comment: 12 pages, 12 figure

Growing Correlation Length on Cooling Below the Onset of Caging in a Simulated Glass-Forming Liquid

We present a calculation of a fourth-order, time-dependent density correlation function that measures higher-order spatiotemporall correlations of the density of a liquid. From molecular dynamics simulations of a glass-forming Lennard-Jones liquid, we find that the characteristic length scale of this function has a maximum as a function of time which increases steadily beyond the characteristic length of the static pair correlation function $g(r)$ in the temperature range approaching the mode coupling temperature from above

Different incidences of knee arthroplasty in the Nordic countries.

To access publisher's full text version of this article, please click on the hyperlink in Additional Links field or click on the hyperlink at the top of the page marked FilesBackground and purpose - The annual number of total knee arthroplasties (TKAs) has increased worldwide in recent years. To make projections regarding future needs for primaries and revisions, additional knowledge is important. We analyzed and compared the incidences among 4 Nordic countries Patients and methods - Using Nordic Arthroplasty Register Association (NARA) data from 4 countries, we analyzed differences between age and sex groups. We included patients over 30 years of age who were operated with TKA or unicompartmental knee arthroplasty (UKA) during the period 1997-2012. The negative binomial regression model was used to analyze changes in general trends and in sex and age groups. Results - The average annual increase in the incidence of TKA was statistically significant in all countries. The incidence of TKA was higher in women than in men in all 4 countries. It was highest in Finland in patients aged 65 years or more. At the end of the study period in 2012, Finland's total incidence was double that of Norway, 1.3 times that of Sweden and 1.4 times that of Denmark. The incidence was lowest in the youngest age groups (< 65 years) in all 4 countries. The proportional increase in incidence was highest in patients who were younger than 65 years. Interpretation - The incidence of knee arthroplasty steadily increased in the 4 countries over the study period. The differences between the countries were considerable, with the highest incidence in Finland. Patients aged 65 years or more contributed to most of the total incidence of knee arthroplasty.NordForsk gran

Feasibility of single-order parameter description of equilibrium viscous liquid dynamics

Molecular dynamics results for the dynamic Prigogine-Defay ratio are presented for two glass-forming liquids, thus evaluating the experimentally relevant quantity for testing whether metastable-equilibrium liquid dynamics to a good approximation are described by a single parameter. For the Kob-Andersen binary Lennard-Jones mixture as well as for an asymmetric dumbbell model liquid a single-parameter description works quite well. This is confirmed by time-domain results where it is found that energy and pressure fluctuations are strongly correlated on the alpha-time scale in the NVT ensemble; in the NpT ensemble energy and volume fluctuations similarly correlate strongly.Comment: Phys. Rev. E, in pres

Observation of Single Transits in Supercooled Monatomic Liquids

A transit is the motion of a system from one many-particle potential energy valley to another. We report the observation of transits in molecular dynamics (MD) calculations of supercooled liquid argon and sodium. Each transit is a correlated simultaneous shift in the equilibrium positions of a small local group of particles, as revealed in the fluctuating graphs of the particle coordinates versus time. This is the first reported direct observation of transit motion in a monatomic liquid in thermal equilibrium. We found transits involving 2 to 11 particles, having mean shift in equilibrium position on the order of 0.4 R_1 in argon and 0.25 R_1 in sodium, where R_1 is the nearest neighbor distance. The time it takes for a transit to occur is approximately one mean vibrational period, confirming that transits are fast.Comment: 19 pages, 8 figure