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F H Stillinger

Publications and source records attributed to F H Stillinger.

7 recordsLinked to original sources
PubMed2006

Exactly solvable disordered sphere-packing model in arbitrary-dimensional Euclidean spaces.

We introduce a generalization of the well-known random sequential addition (RSA) process for hard spheres in d-dimensional Euclidean space Rd. We show that all of the n-particle correlation functions of this nonequilibrium model, in a certain limit called the "ghost" RSA packing, can be obtained analytically for all allowable densities and in any dimension. This represents the first exactly solvable disordered sphere-packing model in an arbitrary dimension. The fact that the maximal density phi (infinity)=1/2d of the ghost RSA packing implies that there may be disordered sphere packings in sufficiently high d whose density exceeds Minkowski's lower bound for Bravais lattices, the dominant asymptotic term of which is 1/2d. Indeed, we report on a conjectural lower bound on the density whose asymptotic behavior is controlled by 2-(0.778,65...)d , thus providing the putative exponential improvement on Minkowski's 100-year-old bound. Our results suggest that the densest packings in sufficiently high dimensions may be disordered rather than periodic, implying the existence of disordered classical ground states for some continuous potentials.

Journal Article↗
PubMed2003

Lattice-based random jammed configurations for hard particles.

A nontrivial subset of the jammed packings for rigid disks and spheres are those that can be obtained by sequential removal of particles from periodic crystalline arrays. This paper considers the enumeration problems presented by such packings that are based on the close-packed triangular disk lattice, and the face-centered and body-centered cubic sphere lattices. Three distinct categories of packings have been distinguished, depending on their behavior with respect to nonoverlap geometric constraints and/or externally imposed virtual displacements: locally jammed, collectively jammed, and strictly jammed. Each of these possesses an upper limiting vacancy concentration beyond which no packings of the types considered can exist. For each of the three lattices, specific vacancy clusters have been identified whose presence would destroy local jamming, and some of the corresponding patterns that would destroy collective jamming in the triangular disk lattice have also been found. Within the allowable range of vacancy concentration for each case, the number of distinct jammed packings is expected to rise exponentially with system size. By using the concept of local attrition factors, approximate enumerations have been constructed for the three lattice classes of locally jammed packings. In the interests of later extension of this work, we stress that at least some aspects of these enumeration problems might benefit from the formal transcription to a lattice-gas/Ising-model representation with vacancy interactions chosen to enforce the packing category of interest.

Journal Article↗
PubMed2001

Supercooled liquids and the glass transition.

Glasses are disordered materials that lack the periodicity of crystals but behave mechanically like solids. The most common way of making a glass is by cooling a viscous liquid fast enough to avoid crystallization. Although this route to the vitreous state-supercooling-has been known for millennia, the molecular processes by which liquids acquire amorphous rigidity upon cooling are not fully understood. Here we discuss current theoretical knowledge of the manner in which intermolecular forces give rise to complex behaviour in supercooled liquids and glasses. An intriguing aspect of this behaviour is the apparent connection between dynamics and thermodynamics. The multidimensional potential energy surface as a function of particle coordinates (the energy landscape) offers a convenient viewpoint for the analysis and interpretation of supercooling and glass-formation phenomena. That much of this analysis is at present largely qualitative reflects the fact that precise computations of how viscous liquids sample their landscape have become possible only recently.

Journal Article↗
PubMed1992

Poly(L-alanine) as a universal reference material for understanding protein energies and structures.

We present a proposition, the "poly(L-alanine) hypothesis," which asserts that the native backbone geometry for any polypeptide or protein of M residues has a closely mimicking, mechanically stable, image in poly(L-alanine) of the same number of residues. Using a molecular mechanics force field to represent the relevant potential energy hypersurfaces, we have carried out calculations over a wide range of M values to show that poly(L-alanine) possesses the structural versatility necessary to satisfy the proposition. These include poly(L-alanine) representatives of minima corresponding to secondary and supersecondary structures, as well as poly(L-alanine) images for tertiary structures of the naturally occurring proteins bovine pancreatic trypsin inhibitor, crambin, ribonuclease A, and superoxide dismutase. The successful validation of the hypothesis presented in this paper indicates that poly(L-alanine) will serve as a good reference material in thermodynamic perturbation theory and calculations aimed at evaluating relative free energies for competing candidate tertiary structures in real polypeptides and proteins.

Algorithms↗
PubMed1991

A strategy for finding classes of minima on a hypersurface: implications for approaches to the protein folding problem.

Locating the native structure of a given protein is a task made difficult by the complexity of the potential energy hypersurface and by the huge number of local minima it contains. We have explored a strategy (the "antlion" method) for hypersurface modification that suppresses all minima but that of the native structure. Transferrable penalty functions with general applicability for modifying a hypersurface to retain the desired minimum are identified, and two blocked oligopeptides (alanine dipeptide and tetrapeptide) are used for specific numerical illustration of the dramatic simplification that ensues. In addition, an intermediary role for neural networks to manage some aspects of the antlion strategy applied to large polypeptides and proteins is introduced.

Alanine↗
PubMed1977

Theoretical approaches to the intermolecular nature of water.

A brief review is presented of recent advances in theoretical understanding of liquid water. These advances include detailed quantitative specification of water-molecule interaction potentials, and development of several techniques in statistical mechanics for predicting molecular order in the liquid. Specifically, computer simulation now plays a particularly important rôle. A labile, defective, random network picture for the liquid is the only consistently supported possibility. Implications of this picture for an explanation of hydrophobic solvation and bonding are mentioned. Furthermore, the apparent cooperative restructuring of the random network near the supercolling limit suggests that a dielectric anomaly might exist in this régime. Several areas for future development of water theory are suggested, bearing specifically on phenomena of biological interest.

Anesthetics↗