Flow of evaporating, gravity-driven thin liquid films over topography

The effect of topography on the free surface and solvent concentration profiles of an evaporating thin film of liquid flowing down an inclined plane is considered. The liquid is assumed to be composed of a resin dissolved in a volatile solvent with the associated solvent concentration equation derived on the basis of the well-mixed approximation. The dynamics of the film is formulated as a lubrication approximation and the effect of a composition-dependent viscosity is included in the model. The resulting time-dependent, nonlinear, coupled set of governing equations is solved using a full approximation storage multigrid method. The approach is first validated against a closed-form analytical solution for the case of a gravity-driven, evaporating thin film flowing down a flat substrate. Analysis of the results for a range of topography shapes reveal that although a full-width, spanwise topography such as a step-up or a step-down does not affect the composition of the film, the same is no longer true for the case of localized topography, such as a peak or a trough, for which clear nonuniformities of the solvent concentration profile can be observed in the wake of the topography

Multigrid optimization for space-time discontinuous Galerkin discretizations of advection dominated flows

The goal of this research is to optimize multigrid methods for higher order accurate space-time discontinuous Galerkin discretizations. The main analysis tool is discrete Fourier analysis of two- and three-level multigrid algorithms. This gives the spectral radius of the error transformation operator which predicts the asymptotic rate of convergence of the multigrid algorithm. In the optimization process we therefore choose to minimize the spectral radius of the error transformation operator. We specifically consider optimizing h-multigrid methods with explicit Runge-Kutta type smoothers for second and third order accurate space-time discontinuous Galerkin finite element discretizations of the 2D advection-diffusion equation. The optimized schemes are compared with current h-multigrid techniques employing Runge-Kutta type smoothers. Also, the efficiency of h-, p- and hp-multigrid methods for solving the Euler equations of gas dynamics with a higher order accurate space-time DG method is investigated

A Fast Parallel Poisson Solver on Irregular Domains Applied to Beam Dynamic Simulations

We discuss the scalable parallel solution of the Poisson equation within a Particle-In-Cell (PIC) code for the simulation of electron beams in particle accelerators of irregular shape. The problem is discretized by Finite Differences. Depending on the treatment of the Dirichlet boundary the resulting system of equations is symmetric or `mildly' nonsymmetric positive definite. In all cases, the system is solved by the preconditioned conjugate gradient algorithm with smoothed aggregation (SA) based algebraic multigrid (AMG) preconditioning. We investigate variants of the implementation of SA-AMG that lead to considerable improvements in the execution times. We demonstrate good scalability of the solver on distributed memory parallel processor with up to 2048 processors. We also compare our SAAMG-PCG solver with an FFT-based solver that is more commonly used for applications in beam dynamics

Quantitative phase-field modeling of solidification at high Lewis number

A phase-field model of nonisothermal solidification in dilute binary alloys is used to study the variation of growth velocity, dendrite tip radius, and radius selection parameter as a function of Lewis number at fixed undercooling. By the application of advanced numerical techniques, we have been able to extend the analysis to Lewis numbers of order 10 000, which are realistic for metals. A large variation in the radius selection parameter is found as the Lewis number is increased from 1 to 10 000

Particle-Particle, Particle-Scaling function (P3S) algorithm for electrostatic problems in free boundary conditions

An algorithm for fast calculation of the Coulombic forces and energies of point particles with free boundary conditions is proposed. Its calculation time scales as N log N for N particles. This novel method has lower crossover point with the full O(N^2) direct summation than the Fast Multipole Method. The forces obtained by our algorithm are analytical derivatives of the energy which guarantees energy conservation during a molecular dynamics simulation. Our algorithm is very simple. An MPI parallelised version of the code can be downloaded under the GNU General Public License from the website of our group.Comment: 19 pages, 11 figures, submitted to: Journal of Chemical Physic

First-principles molecular dynamics simulations at solid-liquid interfaces with a continuum solvent

Continuum solvent models have become a standard technique in the context of electronic structure calculations, yet, no implementations have been reported capable to perform molecular dynamics at solid-liquid interfaces. We propose here such a continuum approach in a DFT framework, using plane-waves basis sets and periodic boundary conditions. Our work stems from a recent model designed for Car-Parrinello simulations of quantum solutes in a dielectric medium [J. Chem. Phys. 124, 74103 (2006)], for which the permittivity of the solvent is defined as a function of the electronic density of the solute. This strategy turns out to be inadequate for systems extended in two dimensions, by introducing new term in the Kohn-Sham potential which becomes unphysically large at the interfacial region, seriously affecting the convergence. If the dielectric medium is properly redefined as a function of the atomic coordinates, a good convergence is obtained and the constant of motion is conserved during the molecular dynamics simulations. Moreover, a significant gain in efficiency can be achieved if the simulation box is partitioned in two, solving the Poisson problem separately for the "dry" region using fast Fourier transforms, and for the solvated or "wet" region using a multigrid method. Eventually both solutions are combined in a self-consistent procedure, and in this way Car-Parrinello molecular dynamics simulations of solid-liquid interfaces can be performed at a very moderate computational cost. This scheme is employed to investigate the acid-base equilibrium at the TiO2-water interface.Comment: 36 pages, 7 figure

Prediction of the operating point of dendrites growing under coupled thermosolutal control at high growth velocity

We use a phase-field model for the growth of dendrites in dilute binary alloys under coupled thermosolutal control to explore the dependence of the dendrite tip velocity and radius of curvature upon undercooling, Lewis number (ratio of thermal to solutal diffusivity), alloy concentration, and equilibrium partition coefficient. Constructed in the quantitatively valid thin-interface limit, the model uses advanced numerical techniques such as mesh adaptivity, multigrid, and implicit time stepping to solve the nonisothermal alloy solidification problem for material parameters that are realistic for metals. From the velocity and curvature data we estimate the dendrite operating point parameter σ*. We find that σ* is nonconstant and, over a wide parameter space, displays first a local minimum followed by a local maximum as the undercooling is increased. This behavior is contrasted with a similar type of behavior to that predicted by simple marginal stability models to occur in the radius of curvature, on the assumption of constant σ*

Virtual photons in imaginary time: Computing exact Casimir forces via standard numerical-electromagnetism techniques

We describe a numerical method to compute Casimir forces in arbitrary geometries, for arbitrary dielectric and metallic materials, with arbitrary accuracy (given sufficient computational resources). Our approach, based on well-established integration of the mean stress tensor evaluated via the fluctuation-dissipation theorem, is designed to directly exploit fast methods developed for classical computational electromagnetism, since it only involves repeated evaluation of the Green's function for imaginary frequencies (equivalently, real frequencies in imaginary time). We develop the approach by systematically examining various formulations of Casimir forces from the previous decades and evaluating them according to their suitability for numerical computation. We illustrate our approach with a simple finite-difference frequency-domain implementation, test it for known geometries such as a cylinder and a plate, and apply it to new geometries. In particular, we show that a piston-like geometry of two squares sliding between metal walls, in both two and three dimensions with both perfect and realistic metallic materials, exhibits a surprising non-monotonic ``lateral'' force from the walls.Comment: Published in Physical Review A, vol. 76, page 032106 (2007

The Shapes of Dirichlet Defects

If the vacuum manifold of a field theory has the appropriate topological structure, the theory admits topological structures analogous to the D-branes of string theory, in which defects of one dimension terminate on other defects of higher dimension. The shapes of such defects are analyzed numerically, with special attention paid to the intersection regions. Walls (co-dimension 1 branes) terminating on other walls, global strings (co-dimension 2 branes) and local strings (including gauge fields) terminating on walls are all considered. Connections to supersymmetric field theories, string theory and condensed matter systems are pointed out.Comment: 24 pages, RevTeX, 21 eps figure