Sheldon B. Opps

Discontinuous molecular dynamics for semiflexible and rigid bodies

A general framework for performing event-driven simulations of systems with semiflexible or rigid bodies interacting under impulsive forces is outlined. The method consists of specifying a means of computing the free evolution of constrained motion, evaluating the times at which interactions occur, and determining the consequences of interactions on subsequent motion. Algorithms for computing the times of interaction events and carrying out efficient event-driven simulations are discussed. The semiflexible case and the rigid case differ qualitatively in that the free motion of a rigid body can be computed analytically and need not be integrated numerically.

The nematic-isotropic phase transition in semiflexible fused hard-sphere chain fluids

A density-functional theory of the isotropic–nematic phase transition in both rigid and semiflexible hard-sphere chain fluids is described. The theory is based on an exact analytical evaluation of the excluded volume and second virial coefficient B2 for rigid chain molecules, which demonstrates that B2 in these cases is equivalent to that of a binary mixture of hard spheres and hard diatomic molecules. It is assumed that the same binary-mixture representation applies to semiflexible chains, while scaled particle theory is used to obtain the properties of the fluid at arbitrary densities. The results of the theory are in very good agreement with Monte Carlo (MC) simulation data for rigid tangent hard-sphere chains, but in lesser agreement with available MC studies of rigid fused hard-sphere chains. We find that there is reasonable agreement between the theory and MC data for semiflexible tangent chains, which improves with increasing chain length. The behavior predicted by the theory for semiflexible chain...

Recursion formulas for Appell’s hypergeometric function F2 with some applications to radiation field problems

Abstract Using some contiguous function relations for the classical Gauss hypergeometric series 2 F 1 , we establish a number of new recursion formulas for the Appell functions F 2 ( σ , α 1 , α 2 ± n ; β 1 , β 2 ; x , y ) and F 2 ( σ , α 1 , α 2 ; β 1 , β 2 ± n ; x , y ) , where n ∈ N 0 ≔ { 0 , 1 , 2 , … } = N ∪ { 0 } . Some important applications of our results to the evaluation of radiation field integrals are discussed and a listing of some useful reduction (and transformation) formulas is provided.

The nematic–isotropic phase transition in linear fused hard-sphere chain fluids

We present a modification of the generalized Flory dimer theory to investigate the nematic (N) to isotropic (I) phase transition in chain fluids. We focus on rigid linear fused hard-sphere (LFHS) chain molecules in this study. A generalized density functional theory is developed, which involves an angular weighting of the dimer reference fluid as suggested by decoupling theory, to accommodate nematic ordering in the system. A key ingredient of this theory is the calculation of the exact excluded volume for a pair of molecules in an arbitrary relative orientation, which extends the recent work by Williamson and Jackson for linear tangent hard-sphere chain molecules to the case of linear fused hard-sphere chains with arbitrary intramolecular bondlength. The present results for the N–I transition are compared with previous theories and with computer simulations. In comparison with previous studies, the results show much better agreement with simulations for both the coexistence densities and the nematic order parameter at the transition.

Discontinuous molecular dynamics simulation study of polymer collapse

Discontinuous molecular dynamics simulations were used to study the coil-globule transition of a polymer in an explicit solvent. Two different versions of the model were employed, which are differentiated by the nature of monomer-solvent, solvent-solvent, and nonbonded monomer-monomer interactions. For each case, a model parameter lambda determines the degree of hydrophobicity of the monomers by controlling the degree of energy mismatch between the monomers and solvent particles. We consider a lambda-driven coil-globule transition at constant temperature. The simulations are used to calculate average static structure factors, which are then used to determine the scaling exponents of the system in order to determine the theta-point values lambda(theta) separating the coil from the globule state. For each model we construct coil-globule phase diagrams in terms of lambda and the particle density rho. Additionally, we explore for each model the effects of varying the range of the attractive interactions on the phase boundary separating the coil and globule phases. The results are analyzed in terms of a simple Flory-type theory of the collapse transition.

Habitat use and home range size of red foxes in Prince Edward Island (Canada) based on snow-tracking and radio-telemetry data

There is a lack of information regarding the ecology and behaviour of red foxes that can be used to elaborate effective management programs for this species on Prince Edward Island (Canada). The main goal of this study was to provide baseline information on habitat selection and home range size of red foxes on Prince Edward Island. Data were collected from snow-tracking and radio-telemetry sessions conducted in two study sites (including one site within Prince Edward Island National Park). Our results indicated that red foxes selected for roads and human-use areas during both the breeding and the kit-rearing seasons in the park. Outside the park, however, the data failed to conclusively show that foxes have a unique preference for human-use habitats or roads. Forests were selected against in both study sites. Although roads are frequently visited by foxes during the kit-rearing season in the park, each individual fox typically stays in this habitat only for short periods of time (< 15 min). This finding suggests that foraging efficiency along the roads is very high possibly reflecting the abundance of anthropogenic food sources. Overall, we present the largest amount of data on habitat selection ever collected for red foxes in Prince Edward Island, Canada. Our results show that food sources in human-use areas and roads are altering the selection and/or use of habitats of red foxes in some areas of Prince Edward Island.

Development of a network based model to simulate the between-farm transmission of the porcine reproductive and respiratory syndrome virus.

Contact structure within a population can significantly affect the outcomes of infectious disease spread models. The objective of this study was to develop a network based simulation model for the between-farm spread of porcine reproductive and respiratory syndrome virus to assess the impact of contact structure on between-farm transmission of PRRS virus. For these farm level models, a hypothetical population of 500 swine farms following a multistage production system was used. The contact rates between farms were based on a study analyzing movement of pigs in Canada, while disease spread parameters were extracted from published literature. Eighteen distinct scenarios were designed and simulated by varying the mode of transmission (direct versus direct and indirect contact), type of index herd (farrowing, nursery and finishing), and the presumed network structures among swine farms (random, scale-free and small-world). PRRS virus was seeded in a randomly selected farm and 500 iterations of each scenario were simulated for 52 weeks. The median epidemic size by the end of the simulated period and percentage die-out for each scenario, were the key outcomes captured. Scenarios with scale-free network models resulted in the largest epidemic sizes, while scenarios with random and small-world network models resulted in smaller and similar epidemic sizes. Similarly, stochastic die-out percentage was least for scenarios with scale-free networks followed by random and small-world networks. Findings of the study indicated that incorporating network structures among the swine farms had a considerable impact on the spread of PRRS virus, highlighting the importance of understanding and incorporating realistic contact structures when developing infectious disease spread models for similar populations.

Theoretical study of solvent effects on the coil-globule transition

The coil-globule transition of a polymer in a solvent has been studied using Monte Carlo simulations of a single chain subject to intramolecular interactions as well as a solvent-mediated effective potential. This solvation potential was calculated using several different theoretical approaches for two simple polymer/solvent models, each employing hard-sphere chains and hard-sphere solvent particles as well as attractive square-well potentials between some interaction sites. For each model, collapse is driven by variation in a parameter which changes the energy mismatch between monomers and solvent particles. The solvation potentials were calculated using two fundamentally different methodologies, each designed to predict the conformational behavior of polymers in solution: (1) the polymer reference interaction site model (PRISM) theory and (2) a many-body solvation potential (MBSP) based on scaled particle theory introduced by Grayce [J. Chem. Phys. 106, 5171 (1997)]. For the PRISM calculations, two well-studied solvation monomer-monomer pair potentials were employed, each distinguished by the closure relation used in its derivation: (i) a hypernetted-chain (HNC)-type potential and (ii) a Percus-Yevick (PY)-type potential. The theoretical predictions were each compared to results obtained from explicit-solvent discontinuous molecular dynamics simulations on the same polymer/solvent model systems [J. Chem. Phys. 125, 194904 (2006)]. In each case, the variation in the coil-globule transition properties with solvent density is mostly qualitatively correct, though the quantitative agreement between the theory and prediction is typically poor. The HNC-type potential yields results that are more qualitatively consistent with simulation. The conformational behavior of the polymer upon collapse predicted by the MBSP approach is quantitatively correct for low and moderate solvent densities but is increasingly less accurate for higher densities. At high solvent densities, the PRISM-HNC and MBSP approaches tend to overestimate, while the PRISM-PY approach underestimates the tendency of the solvent to drive polymer collapse.

Discontinuous molecular dynamics for rigid bodies: Applications

Event-driven molecular dynamics simulations are carried out on two rigid-body systems which differ in the symmetry of their molecular mass distributions. First, simulations of methane in which the molecules interact via discontinuous potentials are compared with simulations in which the molecules interact through standard continuous Lennard-Jones potentials. It is shown that under similar conditions of temperature and pressure, the rigid discontinuous molecular dynamics method reproduces the essential dynamical and structural features found in continuous-potential simulations at both gas and liquid densities. Moreover, the discontinuous molecular dynamics approach is demonstrated to be between 3 and 100 times more efficient than the standard molecular dynamics method depending on the specific conditions of the simulation. The rigid discontinuous molecular dynamics method is also applied to a discontinuous-potential model of a liquid composed of rigid benzene molecules, and equilibrium and dynamical properties are shown to be in qualitative agreement with more detailed continuous-potential models of benzene. The few qualitative differences in the angular dynamics of the two models are related to the relatively crude treatment of variations in the discontinuous repulsive interactions as one benzene molecule rotates by another.

The ground-state phase behavior of model Langmuir monolayers

A coarse-grained model for surfactant molecules adsorbed at a water surface is studied at zero temperature to elucidate ground-state tilt ordering. The surfactants are modeled as rigid rods composed of head and tail segments, where the tails consist of effective monomers representing methylene CH2 groups. These rigid rods interact via site–site Lennard-Jones potentials with different interaction parameters for the tail–tail, head–tail, and head–head interactions. In this work, we study the effects due to variations in both the head diameter and bond length on transitions from untilted to tilted structures and from nearest-neighbor (NN) to next-nearest-neighbor (NNN) tilting. Coupling between tilt ordering and lattice distortion is also considered. We provide a molecular derivation of a scaling relation between tilt angles and distortion obtained previously by phenomenological arguments. Due to the discrete site–site nature of the model interactions, the predicted ground-state phase behavior is much richer...