Estimate of the Cutoff Errors in the Ewald Summation for Dipolar Systems

Theoretical estimates for the cutoff errors in the Ewald summation method for dipolar systems are derived. Absolute errors in the total energy, forces and torques, both for the real and reciprocal space parts, are considered. The applicability of the estimates is tested and confirmed in several numerical examples. We demonstrate that these estimates can be used easily in determining the optimal parameters of the dipolar Ewald summation in the sense that they minimize the computation time for a predefined, user set, accuracy.Comment: 22 pages, 6 figures, Revtex style, submitted to J. Chem. Phy

How to mesh up Ewald sums (II): An accurate error estimate for the P3M algorithm

We construct an accurate estimate for the root mean square force error of the particle-particle-particle-mesh (P3M) algorithm by extending a single particle pair error measure which has been given by Hockney and Eastwood. We also derive an easy-to-use analytic approximation to the error formula. This allows a straightforward and precise determination of the optimal splitting parameter (as a function of system specifications and P3M parameters) and hence knowledge of the force accuracy prior to the actual simulation. The high quality of the estimate is demonstrated in several examples.Comment: 9 pages, 7 figures included, revtex styl

Polyelectrolytes in Solution - Recent Computer Simulations

We present a short overview over recent MD simulations of systems of fully flexible polyelectrolyte chains with explicitly treated counter ions using the full Coulomb potential. The main emphasis is given on the conformational properties of the polymers, with a short discussion on counter ion condensation.Comment: 10 pages, including 5 figures, to appear in the proceedings of the 50th Yamada Conference on Polyelectrolytes, Inuyama, Japan (1998

Fixed versus random triangulations in 2D simplicial Regge calculus

We study 2D quantum gravity on spherical topologies using the Regge calculus approach with the $dl/l$ measure. Instead of a fixed non-regular triangulation which has been used before, we study for each system size four different random triangulations, which are obtained according to the standard Voronoi-Delaunay procedure. We compare both approaches quantitatively and show that the difference in the expectation value of $R^2$ between the fixed and the random triangulation depends on the lattice size and the surface area $A$. We also try again to measure the string susceptibility exponents through a finite-size scaling Ansatz in the expectation value of an added $R^2$ interaction term in an approach where $A$ is held fixed. The string susceptibility exponent $\gamma_{str}'$ is shown to agree with theoretical predictions for the sphere, whereas the estimate for $\gamma_{str}$ appears to be too negative.Comment: 4 latex pages + 4 ps-figs. + espcrc2.sty, poster presented by W. Janke at LATTICE96(gravity

Strongly Charged, Flexible Polyelectrolytes in Poor Solvents -- Molecular Dynamics Simulations

We present a set of molecular dynamics (MD) simulations of strongly charged, flexible polyelectrolyte chains under poor solvent conditions in a salt free solution. Structural properties of the chains and of the solutions are reported. By varying the polymer density and the electrostatic interaction strength we study the crossover from a dominating electrostatic interaction to the regime of strong screening, where the hydrophobic interactions dominate. During the crossover a multitude of structures is observed. In the limit of low polymer density strongly stretched, necklace like conformations are found. In the opposite limit of high polymer density which is equivalent to strongly screened electrostatic interactions, we find that the chains are extremely collapsed, however we observe no agglomeration or phase separation. The investigations show that the density of free charges is one of the relevant parameters which rules the behavior of the system and hence should be used as a parameter to explain experimental results.Comment: 42 pages, including 22 figures and 2 table

Strong electrostatic interactions in spherical colloidal systems

We investigate spherical macroions in the strong Coulomb coupling regime within the primitive model in salt-free environment. We first show that the ground state of an isolated colloid is naturally overcharged by simple electrostatic arguments illustrated by the Gillespie rule. We furthermore demonstrate that in the strong Coulomb coupling this mechanism leads to ionized states and thus to long range attractions between like-charged spheres. We use molecular dynamics simulations to study in detail the counterion distribution for one and two highly charged colloids for the ground state as well as for finite temperatures. We compare our results in terms of a simple version of a Wigner crystal theory and find excellent qualitative and quantitative agreement.Comment: 30 pages and 17 PS figures. REVTEX. Minor changes. To appear in Phys Rev