Martin Trulsson

FAUNUS: An object oriented framework for molecular simulation

BackgroundWe present a C++ class library for Monte Carlo simulation of molecular systems, including proteins in solution. The design is generic and highly modular, enabling multiple developers to easily implement additional features. The statistical mechanical methods are documented by extensive use of code comments that – subsequently – are collected to automatically build a web-based manual.ResultsWe show how an object oriented design can be used to create an intuitively appealing coding framework for molecular simulation. This is exemplified in a minimalistic C++ program that can calculate protein protonation states. We further discuss performance issues related to high level coding abstraction.ConclusionC++ and the Standard Template Library (STL) provide a high-performance platform for generic molecular modeling. Automatic generation of code documentation from inline comments has proven particularly useful in that no separate manual needs to be maintained.

Nonlocal rheology of granular flows across yield conditions.

The rheology of dense granular flows is studied numerically in a shear cell controlled at constant pressure and shear stress, confined between two granular shear flows. We show that a liquid state can be achieved even far below the yield stress, whose flow can be described with the same rheology as above the yield stress. A nonlocal constitutive relation is derived from dimensional analysis through a gradient expansion and calibrated using the spatial relaxation of velocity profiles observed under homogeneous stresses. Both for frictional and frictionless grains, the relaxation length is found to diverge as the inverse square root of the distance to the yield point, on both sides of that point.

A Classical Density Functional Theory of Ionic Liquids

We present a simple, classical density functional approach to the study of simple models of room temperature ionic liquids. Dispersion attractions as well as ion correlation effects and excluded volume packing are taken into account. The oligomeric structure, common to many ionic liquid molecules, is handled by a polymer density functional treatment. The theory is evaluated by comparisons with simulations, with an emphasis on the differential capacitance, an experimentally measurable quantity of significant practical interest.

Weak- and strong-coupling electrostatic interactions between asymmetrically charged planar surfaces.

We compare weak- and strong-coupling theory of counterion-mediated electrostatic interactions between two asymmetrically charged plates with extensive Monte Carlo simulations. Analytical results in both weak- and strong-coupling limits compare excellently with simulations in their respective regimes of validity. The system shows a surprisingly rich structure in terms of interactions between the surfaces as well as fundamental qualitative differences in behavior in the weak- and the strong-coupling limits.

Some comments and corrections regarding the calculation of electrostatic potential derivatives using the Ewald summation technique

A review of the literature on the calculation of electrostatic potentials, fields, and field gradients in systems consisting of charges and dipoles using the Ewald summation technique is presented. Discrepancies between the previous formulas are highlighted, and an error in the derivation of the reciprocal contributions to the electrostatic field and field gradient is corrected. The new formulas for the field and field gradient are shown to exhibit a termwise identity with the ones for the electrostatic energy.

A new dipolar potential for numerical simulations of polar fluids on the 4D hypersphere

We present a new method for Monte Carlo or Molecular Dynamics numerical simulations of three-dimensional polar fluids. The simulation cell is defined to be the surface of the northern hemisphere of a four-dimensional (hyper)sphere. The point dipoles are constrained to remain tangent to the sphere and their interactions are derived from the basic laws of electrostatics in this geometry. The dipole-dipole potential has two singularities which correspond to the following boundary conditions: when a dipole leaves the northern hemisphere at some point of the equator, it reappears at the antipodal point bearing the same dipole moment. We derive all the formal expressions needed to obtain the thermodynamic and structural properties of a polar liquid at thermal equilibrium in actual numerical simulation. We notably establish the expression of the static dielectric constant of the fluid as well as the behavior of the pair correlation at large distances. We report and discuss the results of extensive numerical Monte Carlo simulations for two reference states of a fluid of dipolar hard spheres and compare these results with previous methods with a special emphasis on finite size effects.

A correlation-hole approach to the electric double layer with counter-ions only

ABSTRACT We study a classical system of identically charged counter-ions near a planar wall carrying a uniform surface charge density. The equilibrium statistical mechanics of the system depends on a single dimensionless coupling parameter. A new self-consistent theory of the correlation-hole type is proposed which leads to a modified Poisson–Boltzmann integral equation for the density profile, convenient for analytical progress and straightforward to solve numerically. The exact density profiles are recovered in the limits of weak and strong couplings. In contrast to previous theoretical attempts of the test-charge family, the density profiles fulfil the contact-value theorem at all values of the coupling constant and exhibit the mean-field decay at asymptotically large distances from the wall, as expected. We furthermore show that the density corrections at large couplings exhibit the proper dependence on coupling parameter and distance to the charged wall. The numerical results for intermediate values of the coupling provide accurate density profiles which are in good agreement with those obtained by Monte Carlo simulations. The crossover to mean-field behaviour at large distance is studied in detail. GRAPHICAL ABSTRACT

Direct summation of dipole-dipole interactions using the Wolf formalism

We present an expanded Wolf formalism for direct summation of long-range dipole-dipole interactions and rule-of-thumbs how to choose optimal spherical cutoff (Rc) and damping parameter (α). This is done by comparing liquid radial distribution functions, dipole-dipole orientation correlations, particle energies, and dielectric constants, with Ewald sums and the Reaction field method. The resulting rule states that ασ < 1 and αRc > 3 for reduced densities around ρ(∗) = 1 where σ is the particle size. Being a pair potential, the presented approach scales linearly with system size and is applicable to simulations involving point dipoles such as the Stockmayer fluid and polarizable water models.

Quasi-universality in mixed salt-free counterion systems

The screening of plate-plate interactions by counterions is an age-old problem. We revisit this classic question when counterions exhibit a distribution of charges. While it is expected that the long-distance regime of interactions is universal, the behaviour of the inter-plate pressure at smaller distances should a priori depend rather severely on the nature of the ionic mixture screening the plate charges. We show that this is not the case, and that for comparable Coulombic couplings, different systems exhibit a quasi-universal equation of state.