Solvating collisions between deuterons and light-water octamers

One hundred classical trajectories have been numerically generated for solvating collisions of D⁺ with the stable light-water cluster (H₂O)₈. Ten distinct open channels were discovered, with product-ion hydration numbers ranging from 1 to 6. The deuteron tends preferentially to be carried away in neutrals, particularly when large ions are formed. The results can be explained in terms of competition between charge transfer within, and decomposition of, the charged reaction complex.     

Unexpected density fluctuations in jammed disordered sphere packings

We computationally study jammed disordered hard-sphere packings as large as a million particles. We show that the packings are saturated and hyperuniform, i.e., that local density fluctuations grow only as a logarithmically augmented surface area rather than the volume of the window. The structure factor shows an unusual nonanalytic linear dependence near the origin, S(k) approximately |k|. In addition to exponentially damped oscillations seen in liquids, this implies a weak power-law tail in the total correlation function, h(r) approximately -r(-4), and a long-ranged direct correlation function c(r).     

Equilibrium concentration of point defects in crystalline4He at O K

We calculate the concentrations of vacancies and intersitials in the ground state of a Bose solid which models⁴He. Because ground-state boson wave functions are nodeless, their probability densities correspond to classical Boltzmann factors, and properties of Bose solids, such as the concentration of vacancies and interstitials, can be calculated using classical statistical mechanics. We model the ground-state wave function of⁴He with the product (Jastrow) form that corresponds to a classical 1/r ^b pair potential, and use a quasiharmonic approximation to calculate the concentrations of vacancies and interstitials in an fcc lattice with this potential. We find that the fractional concentration of vacancies at the melting point is 1.60×10^–5 for 1/r ⁹ and 6.36×10^–6 for 1/r ⁶, while the interstitial fractional concentrations are 1.32×10^–3 and 1.08×10^–5, respectively; the defect concentrations decrease by 7–16 orders of magnitude when the crystal density increases by 50%. At the same density, and with the same 1/r ⁹ potential, the concentration of vacancies in an hcp lattice is essentially the same as in an fcc lattice, but the interstitial concentration is much lower, apparently because the fcc lattice contains a more favorable split-interstitial site than does hcp. Therefore, our fcc vacancy results should be directly relevant for (hcp)⁴He, providing what we think is a lower bound on the vacancy concentration, while the interstitial concentration in⁴He is probably much lower than our results.     

Negative Poisson's ratio materials via isotropic interactions

We show that under tension a classical many-body system with only isotropic pair interactions in a crystalline state can, counterintuitively, have a negative Poisson's ratio, or auxetic behavior. We derive the conditions under which the triangular lattice in two dimensions and lattices with cubic symmetry in three dimensions exhibit a negative Poisson's ratio. In the former case, the simple Lennard-Jones potential can give rise to auxetic behavior. In the latter case, a negative Poisson's ratio can be exhibited even when the material is constrained to be elastically isotropic.     

Negative thermal expansion in single-component systems with isotropic interactions

We have devised an isotropic interaction potential that gives rise to negative thermal expansion (NTE) behavior in equilibrium many-particle systems in both two and three dimensions over a wide temperature and pressure range (including zero pressure). An optimization procedure is used in order to find a potential that yields a strong NTE effect. A key feature of the potential that gives rise to this behavior is the softened interior of its basin of attraction. Although such anomalous behavior is well-known in material systems with directional interactions (e.g., zirconium tungstate), to our knowledge, this is the first time that NTE behavior has been established to occur in single-component many-particle systems for isotropic interactions. Using constant-pressure Monte Carlo simulations, we show that as the temperature is increased, the system exhibits negative, zero, and then positive thermal expansion before melting (for both two- and three-dimensional systems). The behavior is explicitly compared to that of a Lennard-Jones system, which exhibits typical expansion upon heating for all temperatures and pressures.     

Lindemann measures for the solid-liquid phase transition

A set of Lindemann measures, based on positional deviations or return distances, defined with respect to mechanically stable inherent structure configurations, is applied to understand the solid-liquid phase transition in a Lennard-Jones-type system. The key quantity is shown to be the single-particle return distance-squared distribution. The first moment of this distribution is related to the Lindemann parameter which is widely used to predict the melting temperature of a variety of solids. The correlation of the single-particle return distance and local bond orientational order parameter in the liquid phase provides insights into mechanisms for melting. These generalized Lindemann measures, especially the lower order moments of the single-particle return distance distribution, show clear signatures of the transition of the liquid from the stable to the metastable, supercooled regime and serve as landscape-based indicators of the thermodynamic freezing transition for the Lennard-Jones-type system investigated.     

Patterns and Structures in Disk Packings

Using a computational procedure that imitates tightening of an assembly of billiard balls, we have generated a number of packings of n equal and non-equal disks in regions of various shapes. Our experiments are of three major types. In the first type, the values of n are in thousands, the initial disk configuration is random and a priori one expects the generated packings to be random. In fact, the packings turn out to display non-random geometric patterns and regular features, including polycrystalline textures with "rattlers" typically trapped along the grain boundaries. An experiment of the second type begins with a known or conjectured optimal disk packing configuration, which is then "frustrated" by a small perturbation such as variation of the boundary shape or a relative increase of the size of a selected disk with respect to the sizes of the other disks. We present such frustrated packings for both large n (~ 10, 000) and small n (~ 50 to 200). Motivated by applications in material science and physics, the first and second type of experiments are performed for boundary shapes rarely discussed in the literature on dense packings: torus, a strip cut from a cylinder, a regular hexagon with periodic boundaries. Experiments of the third type involve the shapes popular among mathematicians: circles, squares, and equilateral triangles the boundaries of which are hard reflecting walls. The values of n in these experiments vary from several tens to few hundreds. Here the obtained configurations could be considered as candidates for the densest packings, rather than random ones. Some of these conjecturally optimal packings look regular and the regularity often extends across different values of n. Specifically, as n takes on an increasing sequence of values, n = n(1), n(2), ...n(k), ..., the packings follow a well-defined pattern. This phenomenon is especially striking for packings in equilateral triangles, where (as far as we can tell from our finite computational experiments), not only are there an infinite number of different patterns, each with its own different sequence n(1), n(2), ...n(k), ..., but many of these sequences seem to continue indefinitely. For other shapes, notably squares and circles, the patterns either cease to be optimal or even cease to exist (as packings of non-overlapping disks) above some threshold value n(k0) (depending on the pattern). In these cases, we try to identify the values of n(k0).     

Quantum corrections for lattice gases

Classical lattice gases consisting of structureless particles (with spin) have been quantized by introducing a kinetic energy operator that produces nearest-neighbor hops. Systematic quantum corrections for the partition function and the particle distribution functions appear naturally as power series inX = ²/2ml ² ( ^–1 =k _B T,m is the mass,l is a distance related to lattice spacing). These corrections require knowledge of certain particle displacement probabilities in the corresponding classical lattice gases. Leading-order corrections have been derived in forms that should facilitate their use in computer simulation studies of lattice gases by the standard Monte Carlo method.     

Alternative view of self-diffusion and shear viscosity

By performing an elementary transformation, the conventional velocity autocorrelation function expression for the temperature and density dependent self-diffusion constant D(T,rho) has been reformulated to emphasize how initial particle momentum biases final mean displacement. Using collective flow variables, an analogous expression has been derived for 1/eta(T,rho), the inverse of shear viscosity. The Stokes-Einstein relation for liquids declares that D and T/eta should have a fixed ratio as T and rho vary, but experiment reveals substantial violations for deeply supercooled liquids. Upon analyzing the self-diffusion and viscous flow processes in terms of configuration space inherent structures and kinetic transitions between their basins, one possible mechanism for this violation emerges. This stems from the fact that interbasin transitions become increasingly Markovian as T declines, and though self-diffusion is possible in a purely Markovian regime, shear viscosity in the present formulation intrinsically relies on successive correlated transitions.