Waning Immunity and the Second Wave: Some Projections for SARS-COV-2

This paper offers projections of future transmission dynamics for SARS-CoV-2 in an SEIRS model with demographics and waning immunity. In a stylized optimal control setting calibrated to the USA, we show that the disease is endemic in steady state and that its dynamics are characterized by damped oscillations. The magnitude of the oscillations depends on how fast immunity wanes. The optimal social distancing policy both curbs peak prevalence and postpones the infection waves relative to the uncontrolled dynamics. Last, we perform sensitivity analysis with respect to the duration of immunity, the infection fatality rate and the planning horizon

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

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

Conductance Fluctuations of Generic Billiards: Fractal or Isolated?

We study the signatures of a classical mixed phase space for open quantum systems. We find the scaling of the break time up to which quantum mechanics mimics the classical staying probability and derive the distribution of resonance widths. Based on these results we explain why for mixed systems two types of conductance fluctuat ions were found: quantum mechanics divides the hierarchically structured chaotic component of phase space into two parts - one yields fractal conductance fluctuations while the other causes isolated resonances. In general, both types appear together, but on different energy scales.Comment: restructured and new figure

Molecular Dynamics Simulation of Spinodal Decomposition in Three-Dimensional Binary Fluids

Using large-scale molecular dynamics simulations of a two-component Lennard-Jones model in three dimensions, we show that the late-time dynamics of spinodal decomposition in concentrated binary fluids reaches a viscous scaling regime with a growth exponent $n=1$, in agreement with experiments and a theoretical analysis for viscous growth.Comment: 4 pages, 3 figure

The impact range for smooth wall–liquid interactions in nanoconfined liquids

Bulk and nanoconfined liquids have initially very different physics; for instance, nanoconfined liquids show stratification and position-dependent relaxation processes. A number of similarities between bulk and nanoconfined liquids have nevertheless been reported in computer simulations during the last decade. Inspired by these observations, we present results from molecular dynamics computer simulations of three nanoconfined liquids (i.e., single-component Lennard-Jones (LJ) liquid, Kob-Andersen binary LJ mixture, and an asymmetric dumbbell model) demonstrating also a microscopic similarity between bulk and nanoconfined liquids. The results show that the interaction range for the wall-liquid and liquid-liquid interactions of the nanoconfined liquid are identical to the bulk liquid as long as the liquid remains "Roskilde simple" in nanoconfinement, i.e., the liquid has strong correlations between virial and potential energy equilibrium fluctuations in the NVT ensemble.Comment: 8 page

NVU dynamics. II. Comparing to four other dynamics

In the companion paper [Ingebrigtsen et al., arXiv:1012.3447] an algorithm was developed for tracing out a geodesic curve on the constant-potential-energy hypersurface. Here simulations of this NVU dynamics are compared to results for four other dynamics, both deterministic and stochastic. First, NVU dynamics is compared to the standard energy-conserving Newtonian NVE dynamics by simulations of the Kob-Andersen binary Lennard-Jones liquid, its WCA version (i.e., with cut-off's at the pair potential minima), and the Gaussian Lennard-Jones liquid. We find identical results for all quantities probed: radial distribution functions, incoherent intermediate scattering functions, and mean-square displacement as function of time. Arguments are then presented for the equivalence of NVU and NVE dynamics in the thermodynamic limit; in particular to leading order in 1/N these two dynamics give identical time-autocorrelation functions. In the final section NVU dynamics is compared to Monte Carlo dynamics, to a diffusive dynamics of small-step random walks on the constant-potential-energy hypersurface, and to Nose-Hoover NVT dynamics. If time is scaled for the two stochastic dynamics to make their single-particle diffusion constants identical to those of NVE dynamics, the simulations show that all five dynamics are equivalent at low temperatures except at short times

Optimized intermolecular potential for nitriles based on Anisotropic United Atoms model

An extension of the Anisotropic United Atoms intermolecular potential model is proposed for nitriles. The electrostatic part of the intermolecular potential is calculated using atomic charges obtained by a simple Mulliken population analysis. The repulsion-dispersion interaction parameters for methyl and methylene groups are taken from transferable AUA4 literature parameters [Ungerer et al., J. Chem. Phys., 2000, 112, 5499]. Non-bonding Lennard-Jones intermolecular potential parameters are regressed for the carbon and nitrogen atoms of the nitrile group (–C≡N) from experimental vapor-liquid equilibrium data of acetonitrile. Gibbs Ensemble Monte Carlo simulations and experimental data agreement is very good for acetonitrile, and better than previous molecular potential proposed by Hloucha et al. [J. Chem. Phys., 2000, 113, 5401]. The transferability of the resulting potential is then successfully tested, without any further readjustment, to predict vapor-liquid phase equilibrium of propionitrile and n-butyronitrile