Is the Ewald summation still necessary? Pairwise alternatives to the accepted standard for long-range electrostatics

We investigate pairwise electrostatic interaction methods and show that there are viable computationally efficient (O(N)) alternatives to the Ewald summation for typical modern molecular simulations. These methods are extended from the damped and cutoff-neutralized Coulombic sum originally proposed by Wolf et al. [J. Chem. Phys. 110, 8255 (1999)]. One of these, the damped shifted force method, shows a remarkable ability to reproduce the energetic and dynamic characteristics exhibited by simulations employing lattice summation techniques. Comparisons were performed with this and other pairwise methods against the smooth particle-mesh Ewald summation to see how well they reproduce the energetics and dynamics of a variety of molecular simulations.     

Operator algebras and a theorem of Dieudonne

LetA be aC*-algebra with second dualA″. Let (φ _n)(n=1,...) be a sequence in the dual ofA such that limφ _n(a) exists for eacha εA. In general, this does not imply that limφ _n(x) exists for eachx εA″. But if limφ _n(p) exists whenever p is the range projection of a positive self-adjoint element of the unit ball ofA, then it is shown that limφ _n(x) does exist for eachx inA″. This is a non-commutative generalisation of a celebrated theorem of Dieudonné. A new proof of Dieudonné’s theorem, for positive measures, is given here. The proof of the main result makes use of Dieudonné’s original theorem.     

The Langevin Hull: Constant pressure and temperature dynamics for non-periodic systems

We have developed a new isobaric-isothermal (NPT) algorithm which applies an external pressure to the facets comprising the convex hull surrounding the system. A Langevin thermostat is also applied to the facets to mimic contact with an external heat bath. This new method, the "Langevin Hull", can handle heterogeneous mixtures of materials with different compressibilities. These systems are problematic for traditional affine transform methods. The Langevin Hull does not suffer from the edge effects of boundary potential methods, and allows realistic treatment of both external pressure and thermal conductivity due to the presence of an implicit solvent. We apply this method to several different systems including bare metal nanoparticles, nanoparticles in an explicit solvent, as well as clusters of liquid water. The predicted mechanical properties of these systems are in good agreement with experimental data and previous simulation work.     

Radial oscillations of neutron stars in strong magnetic fields

The eigen frequencies of radial pulsations of neutron stars are calculated in a strong magnetic field. At low densities we use the magnetic BPS equation of state (EOS) similar to that obtained by Lai and Shapiro while at high densities the EOS obtained from the relativistic nuclear mean field theory is taken and extended to include strong magnetic field. It is found that magnetized neutron stars support higher maximum mass whereas the effect of magnetic field on radial stability for observed neutron star masses is minimal.     

Size-dependent spontaneous alloying of Au-Ag nanoparticles

We report on systematic studies of size-dependent alloy formation of silver-coated gold nanoparticles (NPs) in aqueous solution at ambient temperature using X-ray absorption fine structure spectroscopy (XAFS). Various Au-core sizes (2.5-20 nm diameter) and Ag shell thicknesses were synthesized using radiolytic wet techniques. The equilibrium structures (alloy versus core-shell) of these NPs were determined in the suspensions. We observed remarkable size dependence in the room temperature interdiffusion of the two metals. The interdiffusion is limited to the subinterface layers of the bimetallic NPs and depends on both the core size and the total particle size. For the very small particles (< or =4.6 nm initial Au-core size), the two metals are nearly randomly distributed within the particle. However, even for these small Au-core NPs, the interdiffusion occurs primarily in the vicinity of the original interface. Features from the Ag shells do remain. For the larger particles, the boundary is maintained to within one monolayer. These results cannot be explained either by enhanced self-diffusion that results from depression of the melting point with size or by surface melting of the NPs. We propose that defects, such as vacancies, at the bimetallic interface enhance the radial migration (as well as displacement around the interface) of one metal into the other. Molecular dynamics calculations correctly predict the activation energy for diffusion of the metals in the absence of vacancies and show an enormous dependence of the rate of mixing on defect levels. They also suggest that a few percent of the interfacial lattice sites need to be vacant to explain the observed mixing.     

Dipolar ordering in the ripple phases of molecular-scale models of lipid membranes

Symmetric and asymmetric ripple phases have been observed to form in molecular dynamics simulations of a simple molecular-scale lipid model. The lipid model consists of an dipolar head group and an ellipsoidal tail. Within the limits of this model, an explanation for generalized membrane curvature is a simple mismatch in the size of the heads with the width of the molecular bodies. The persistence of a bilayer structure requires strong attractive forces between the head groups. One feature of this model is that an energetically favorable orientational ordering of the dipoles can be achieved by out-of-plane membrane corrugation. The corrugation of the surface stabilizes the long range orientational ordering for the dipoles in the head groups which then adopt a bulk anti-ferroelectric state. We observe a common feature of the corrugated dipolar membranes: the wave vectors for the surface ripples are always found to be perpendicular to the dipole director axis.