Role of the first coordination shell in determining the equilibrium structure and dynamics of simple liquids

The traditional view that the physical properties of a simple liquid are determined primarily by its repulsive forces was recently challenged by Berthier and Tarjus, who showed that in some cases ignoring the attractions leads to large errors in the dynamics [L. Berthier and G. Tarjus, Phys. Rev. Lett. 103, 170601 (2009); J. Chem. Phys. 134, 214503 (2011)]. We present simulations of the standard Lennard-Jones liquid at several condensed-fluid state points, including a fairly low density state and a very high density state, as well as simulations of the Kob-Andersen binary Lennard-Jones mixture at several temperatures. By varying the range of the forces, results for the thermodynamics, dynamics, and structure show that the determining factor for getting the correct statics and dynamics is not whether or not the attractive forces {\it per se} are included in the simulations. What matters is whether or not interactions are included from all particles within the first coordination shell (FCS) - the attractive forces can thus be ignored, but only at extremely high densities. The recognition of the importance of a local shell in condensed fluids goes back to van der Waals; our results confirm this idea and thereby the basic picture of the old hole- and cell theories for simple condensed fluids

The instantaneous shear modulus in the shoving model

We point out that the instantaneous shear modulus of the shoving model for the non-Arrhenius temperature dependence of viscous liquids' relaxation time is the experimentally accessible high-frequency plateau modulus, not the idealized instantaneous affine shear modulus that cannot be measured. Data for a large selection of metallic glasses are compared to three different versions of the shoving model. The original shear-modulus based version shows a slight correlation to the Poisson ratio, which is eliminated by the energy-landscape formulation of the model in which the bulk modulus plays a minor role

NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface

An algorithm is derived for computer simulation of geodesics on the constant potential-energy hypersurface of a system of N classical particles. First, a basic time-reversible geodesic algorithm is derived by discretizing the geodesic stationarity condition and implementing the constant potential energy constraint via standard Lagrangian multipliers. The basic NVU algorithm is tested by single-precision computer simulations of the Lennard-Jones liquid. Excellent numerical stability is obtained if the force cutoff is smoothed and the two initial configurations have identical potential energy within machine precision. Nevertheless, just as for NVE algorithms, stabilizers are needed for very long runs in order to compensate for the accumulation of numerical errors that eventually lead to "entropic drift" of the potential energy towards higher values. A modification of the basic NVU algorithm is introduced that ensures potential-energy and step-length conservation; center-of-mass drift is also eliminated. Analytical arguments confirmed by simulations demonstrate that the modified NVU algorithm is absolutely stable. Finally, simulations show that the NVU algorithm and the standard leap-frog NVE algorithm have identical radial distribution functions for the Lennard-Jones liquid

A repulsive reference potential reproducing the dynamics of a liquid with attractions

A well-known result of liquid state theory is that the structure of dense fluids is mainly determined by repulsive forces. The WCA potential, which cuts intermolecular potentials at their minima, is therefore often used as a reference. However, this reference gives quite wrong results for the viscous dynamics of the Kob-Andersen binary Lennard-Jones liquid [Berthier and Tarjus, Phys. Rev. Lett. 103, 170601 (2009)]. We show that repulsive inverse-power law potentials provide a useful reference for this liquid by reproducing its structure, dynamics, and isochoric heat capacity

Exponential distributions of collective flow-event properties in viscous liquid dynamics

We study the statistics of flow events in the inherent dynamics in supercooled two- and three-dimensional binary Lennard-Jones liquids. Distributions of changes of the collective quantities energy, pressure and shear stress become exponential at low temperatures, as does that of the event "size" $S\equiv\sum {d_i}^2$. We show how the $S$-distribution controls the others, while itself following from exponential tails in the distributions of (1) single particle displacements $d$, involving a Lindemann-like length $d_L$ and (2) the number of active particles (with $d>d_L$).Comment: Accepter version (PRL

Investigation of the shear-mechanical and dielectric relaxation processes in two mono-alcohols close to the glass transition

Shear-mechanical and dielectric measurements on the two monohydroxy (mono-alcohol) molecular glass formers 2-ethyl-1-hexanol and 2-butanol close to the glass transition temperature are presented. The shear-mechanical data are obtained using the piezoelectric shear-modulus gauge method covering frequencies from 1mHz to 10kHz. The shear-mechanical relaxation spectra show two processes, which follow the typical scenario of a structural (alpha) relaxation and an additional (Johari-Goldstein) beta relaxation. The dielectric relaxation spectra are dominated by a Debye-type peak with an additional non-Debye peak visible. This Debye-type relaxation is a common feature peculiar to mono-alcohols. The time scale of the non-Debye dielectric relaxation process is shown to correspond to the mechanical structural (alpha) relaxation. Glass-transition temperatures and fragilities are reported based on the mechanical alpha relaxation and the dielectric Debye-type process, showing that the two glass-transition temperatures differ by approximately 10K and that the fragility based on the Debye-type process is a factor of two smaller than the structural fragility. If a mechanical signature of the Debye-type relaxation exists in these liquids, its relaxation strength is at most 1% and 3% of the full relaxation strength of 2-butanol and 2-ethyl-1-hexanol respectively. These findings support the notion that it is the non-Debye dielectric relaxation process that corresponds to the structural alpha relaxation in the liquid.Comment: 8 pages, 6 figures. Minor corrections, updated figures, more dielectric data show

Balanced exploitation and coexistence of interacting, size-structured, fish species

This paper examines some effects of exploitation on a simple ecosystem containing two interacting fish species, with life histories similar to mackerel (Scomber scombrus) and cod (Gadus morhua), using a dynamic, size-spectrum model. Such models internalize body growth and mortality from predation, allowing bookkeeping of biomass at a detailed level of individual predation and growth and enabling scaling up to the mass balance of the ecosystem. Exploitation set independently for each species with knife-edge, size-at-entry fishing can lead to collapse of cod. Exploitation to achieve a fixed ratio of yield to productivity across species can also lead to collapse of cod. However, harvesting balanced to the overall productivity of species in the exploited ecosystem exerts a strong force countering such collapse. If balancing across species is applied to a fishery with knife-edge selection, size distributions are truncated, changing the structure of the system and reducing its resilience to perturbations. If balancing is applied on the basis of productivity at each body size as well as across species, there is less disruption to size-structure, resilience is increased, and substantially greater biomass yields are possible. We note an identity between the body size at which productivity is maximized and the age at which cohort biomass is maximized. In our numerical results based on detailed bookkeeping of biomass, cohort biomass reaches its maximum at body masse

Aging effects manifested in the potential energy landscape of a model glass former

We present molecular dynamics simulations of a model glass-forming liquid (the binary Kob-Anderson Lennard-Jones model) and consider the distributions of inherent energies and metabasins during aging. In addition to the typical protocol of performing a temperature jump from a high temperature to a low destination temperature, we consider the temporal evolution of the distributions after an 'up-jump', i.e. from a low to a high temperature. In this case the distribution of megabasin energies exhibits a transient two-peak structure. Our results can qualitatively be rationalized in terms of a trap model with a Gaussian distribution of trap energies. The analysis is performed for different system sizes. A detailed comparison with the trap model is possible only for a small system because of major averging effects for larger systems.Comment: 16 pages, 14 figure