Dimensionality and design of isotropic interactions that stabilize honeycomb, square, simple cubic, and diamond lattices

We use inverse methods of statistical mechanics and computer simulations to investigate whether an isotropic interaction designed to stabilize a given two-dimensional (2D) lattice will also favor an analogous three-dimensional (3D) structure, and vice versa. Specifically, we determine the 3D ordered lattices favored by isotropic potentials optimized to exhibit stable 2D honeycomb (or square) periodic structures, as well as the 2D ordered structures favored by isotropic interactions designed to stabilize 3D diamond (or simple cubic) lattices. We find a remarkable `transferability' of isotropic potentials designed to stabilize analogous morphologies in 2D and 3D, irrespective of the exact interaction form, and we discuss the basis of this cross-dimensional behavior. Our results suggest that the discovery of interactions that drive assembly into certain 3D periodic structures of interest can be assisted by less computationally intensive optimizations targeting the analogous 2D lattices.Comment: 22 pages (preprint version; includes supplementary information), 5 figures, 3 table

Excess-entropy scaling of dynamics for a confined fluid of dumbbell-shaped particles

We use molecular simulation to study the ability of excess entropy scaling relationships to describe the kinetic properties of a confined molecular system. We examine a model for a confined fluid consisting of dumbbell-shaped molecules that interact with atomistically detailed pore walls via a Lennard-Jones potential. We obtain kinetic, thermodynamic, and structural properties of the system at three wall-fluid interaction strengths and over a temperature range that includes sub-and super-critical conditions. Four dynamic properties are considered: translational and rotational diffusivities, a characteristic relaxation time for rotational motion, and a collective relaxation time stemming from analysis of the coherent intermediate scattering function. We carefully consider the reference state used to define the excess entropy of a confined fluid. Three ideal-gas reference states are considered, with the cases differentiated by the extent to which one-body spatial and orientational correlations are accounted for in the reference state. Our results indicate that a version of the excess entropy that includes information related to the one-body correlations in a confined fluid serves as the best scaling variable for dynamic properties. When adopting such a definition for the reference state, to a very good approximation, bulk and confined data for a specified dynamic property at a given temperature collapse onto a common curve when plotted against the excess entropy.National Science Foundation CBET-0828979Welch Foundation F-1696David and Lucile Packard FoundationChemical Engineerin

Relationship between thermodynamics and dynamics of supercooled liquids

Diffusivity, a measure for how rapidly a fluid self-mixes, shows an intimate, but seemingly fragmented, connection to thermodynamics. On one hand, the "configurational" contribution to entropy (related to the number of mechanically-stable configurations that fluid molecules can adopt) has long been considered key for predicting supercooled liquid dynamics near the glass transition. On the other hand, the excess entropy (relative to ideal gas) provides a robust scaling for the diffusivity of fluids above the freezing point. Here we provide, to our knowledge, the first evidence that excess entropy also captures how supercooling a fluid modifies its diffusivity, suggesting that dynamics, from ideal gas to glass, is related to a single, standard thermodynamic quantity.Comment: to appear in Journal of Chemical Physic

Philopoemen: a study in Hellenistic history

The basis of the work is an examination of the ancient source material, in particular plutarch's 'Life of Philopoemen' and the fragments of polybius' Histories which deal with the Achaean League. An outline of the resultant interpretation of philopoemen's career is as follows. Until 222 B. C. he took no part in Achaean politics, but was involved solely with megalopolis. Between 222 and 211 philopoemen was in Crete representing the interests of Philip V of Macedon, from 210 to 200 in Achaea, where after attaining a military independence, of Macedonia with Philips encouragement, he used this attempt to join Rome. Defeated on this issue, in 200 he returned to Crete to help the Gortynians, Achean allies. In his absence his friend Aristaenus carried his policy and joined Achaea to Rome. On Philopoemen's return in 194 he first desired to cooperate with Flamininus; but when he discovered that flamininus was merely using Achaea for Roman policy Philopoemen began to press the letter of the law of the Achaean foedus with Rome at First misunderstanding , but finally exploiting Achaean olientela. He refused Rome any right of interference in Peloponnesian matters, although he himself was unable to find satisfactory solutions to many of the Achaens' problems, particularly those associated with exiles from Sparta and Messene. The Roman Senate, bound by its conventions could find no way round the impasse until after Philopoen's death in 182, when his party lost most of its influence in Achaea. This interplay of policies and purposes of the Senate and Philopoemen is worked out in the detail. The concluding chapter traces the developing weakness of his party after his death and attempts to correct some modern interpretation of Poybius' judgement of Philopoemen and his policies. Appendicies deal with source problems in the Achaean strategos list - and other pertinent problems

Tuning density profiles and mobility of inhomogeneous fluids

Density profiles are the most common measure of inhomogeneous structure in confined fluids, but their connection to transport coefficients is poorly understood. We explore via simulation how tuning particle-wall interactions to flatten or enhance the particle layering of a model confined fluid impacts its self-diffusivity, viscosity, and entropy. Interestingly, interactions that eliminate particle layering significantly reduce confined fluid mobility, whereas those that enhance layering can have the opposite effect. Excess entropy helps to understand and predict these trends.Comment: 5 pages, 3 figure