Efficient and accurate three dimensional Poisson solver for surface problems

We present a method that gives highly accurate electrostatic potentials for systems where we have periodic boundary conditions in two spatial directions but free boundary conditions in the third direction. These boundary conditions are needed for all kind of surface problems. Our method has an O(N log N) computational cost, where N is the number of grid points, with a very small prefactor. This Poisson solver is primarily intended for real space methods where the charge density and the potential are given on a uniform grid.Comment: 6 pages, 2 figure

Charge ordering induces a smectic phase in oblate ionic liquid crystals

We report a computer simulation study of an electroneutral mixture of oppositely charged oblate ellipsoids of revolution with aspect ratio A = 1/3. In contrast to hard or soft repulsive ellipsoids, which are purely nematic, this system exhibits a smectic-A phase in which charges of equal sign are counterintuitively packed in layers perpendicular to the nematic director

Exact solution of Riemann--Hilbert problem for a correlation function of the XY spin chain

A correlation function of the XY spin chain is studied at zero temperature. This is called the Emptiness Formation Probability (EFP) and is expressed by the Fredholm determinant in the thermodynamic limit. We formulate the associated Riemann--Hilbert problem and solve it exactly. The EFP is shown to decay in Gaussian.Comment: 7 pages, to be published in J. Phys. Soc. Jp

Non-conformal coarse-grained potentials for water

Water is a notoriously difficult substance to model both accurately and efficiently. Here, we focus on descriptions with a single coarse-grained particle per molecule using the so-called Approximate Non-Conformal (ANC) and generalized Stockmayer potentials as the starting points. They are fitted using the radial density function and the density of the atomistic SPC/E model by downhill simplex optimization. We compare the results with monatomic water (mW), ELBA, as well as with direct Iterative Boltzmann Inversion (IBI) of SPC/E. The results show that symmetrical potentials result in non-transferable models, that is, they need to be reparametrized for new state-points. This indicates that transferability may require more complex models. Furthermore, the results also show that the addition of a point dipole is not sufficient to make the potentials accurate and transferable to different temperatures (300 K-500 K) and pressures without an appropriate choice of properties as targets during model optimization

Particle linear theory on a self-gravitating perturbed cubic Bravais lattice

Discreteness effects are a source of uncontrolled systematic errors of N-body simulations, which are used to compute the evolution of a self-gravitating fluid. We have already developed the so-called "Particle Linear Theory" (PLT), which describes the evolution of the position of self-gravitating particles located on a perturbed simple cubic lattice. It is the discrete analogue of the well-known (Lagrangian) linear theory of a self-gravitating fluid. Comparing both theories permits to quantify precisely discreteness effects in the linear regime. It is useful to develop the PLT also for other perturbed lattices because they represent different discretizations of the same continuous system. In this paper we detail how to implement the PLT for perturbed cubic Bravais lattices (simple, body and face-centered) in a cubic simulation box. As an application, we will study the discreteness effects -- in the linear regime -- of N-body simulations for which initial conditions have been set-up using these different lattices.Comment: 9 pages, 4 figures and 4 tables. Minor corrections to match published versio

Self-Consistent Cosmological Simulations of DGP Braneworld Gravity

We perform cosmological N-body simulations of the Dvali-Gabadadze-Porrati braneworld model, by solving the full non-linear equations of motion for the scalar degree of freedom in this model, the brane bending mode. While coupling universally to matter, the brane-bending mode has self-interactions that become important as soon as the density field becomes non-linear. These self-interactions lead to a suppression of the field in high-density environments, and restore gravity to General Relativity. The code uses a multi-grid relaxation scheme to solve the non-linear field equation in the quasi-static approximation. We perform simulations of a flat self-accelerating DGP model without cosmological constant. The results of the DGP simulations are compared with standard gravity simulations assuming the same expansion history, and with DGP simulations using the linearized equation for the brane bending mode. This allows us to isolate the effects of the non-linear self-couplings of the field which are noticeable already on quasi-linear scales. We present results on the matter power spectrum and the halo mass function, and discuss the behavior of the brane bending mode within cosmological structure formation. We find that, independently of CMB constraints, the self-accelerating DGP model is strongly constrained by current weak lensing and cluster abundance measurements.Comment: 21 pages; 10 figures. Revised version matching published versio

Dipole Oscillations in Bose - Fermi Mixture in the Time-Dependent Grosspitaevskii and Vlasov equations

We study the dipole collective oscillations in the bose-fermi mixture using a dynamical time-dependent approach, which are formulated with the time-dependent Gross-Pitaevskii equation and the Vlasov equation. We find big difference in behaviors of fermion oscillation between the time-dependent approach and usual approaches such as the random-phase approximation and the sum-rule approach. While the bose gas oscillates monotonously, the fermion oscillation shows a beat and a damping. When the amplitude is not minimal, the dipole oscillation of the fermi gas cannot be described with a simple center-of-mass motion.Comment: 17 pages text, and 15 figure

Contact area of rough spheres: Large scale simulations and simple scaling laws

We use molecular simulations to study the nonadhesive and adhesive atomic-scale contact of rough spheres with radii ranging from nanometers to micrometers over more than ten orders of magnitude in applied normal load. At the lowest loads, the interfacial mechanics is governed by the contact mechanics of the first asperity that touches. The dependence of contact area on normal force becomes linear at intermediate loads and crosses over to Hertzian at the largest loads. By combining theories for the limiting cases of nominally flat rough surfaces and smooth spheres, we provide parameter-free analytical expressions for contact area over the whole range of loads. Our results establish a range of validity for common approximations that neglect curvature or roughness in modeling objects on scales from atomic force microscope tips to ball bearings.Comment: 2 figures + Supporting Materia

Charged Particles on Surfaces: Coexistence of Dilute Phases and Periodic Structures on Membranes

We consider a mixture of one neutral and two oppositely charged types of molecules confined to a surface. Using analytical techniques and molecular dynamics simulations, we construct the phase diagram of the system and exhibit the coexistence between a patterned solid phase and a charge-dilute phase. The patterns in the solid phase arise from competition between short-range immiscibility and long-range electrostatic attractions between the charged species. The coexistence between phases leads to observations of stable patterned domains immersed in a neutral matrix background.Comment: 5 pages, 3 figure

Potential flows in a core-dipole-shell system: numerical results

Numerical solutions for: the integral curves of the velocity field (streamlines), the density contours, and the accretion rate of a steady-state flow of an ideal fluid with p=K n^(gamma) equation of state orbiting in a core-dipole-shell system are presented. For 1 < gamma < 2, we found that the non-linear contribution appearing in the partial differential equation for the velocity potential has little effect in the form of the streamlines and density contour lines, but can be noticed in the density values. The study of several cases indicates that this appears to be the general situation. The accretion rate was found to increase when the constant gamma decreases.Comment: RevTex, 8 pages, 5 eps figures, CQG to appea