On Minimal Subspaces in Tensor Representations

Agraïments: This work is partially supported by the PRCEU-UCH30/10 grant of the Universidad CEU Cardenal Herrera

Improved Algorithms for Simulating Crystalline Membranes

The physics of crystalline membranes, i.e. fixed-connectivity surfaces embedded in three dimensions and with an extrinsic curvature term, is very rich and of great theoretical interest. To understand their behavior, numerical simulations are commonly used. Unfortunately, traditional Monte Carlo algorithms suffer from very long auto-correlations and critical slowing down in the more interesting phases of the model. In this paper we study the performance of improved Monte Carlo algorithms for simulating crystalline membrane, such as hybrid overrelaxation and unigrid methods, and compare their performance to the more traditional Metropolis algorithm. We find that although the overrelaxation algorithm does not reduce the critical slowing down, it gives an overall gain of a factor 15 over the Metropolis algorithm. The unigrid algorithm does, on the other hand, reduce the critical slowing down exponent to z apprx. 1.7.Comment: 14 pages, 1 eps-figur

Alternative display and interaction devices

While virtual environment systems are typically thought to consist of a head mounted display and a flex-sensing glove, alternative peripheral devices are beginning to be developed in response to application requirements. Three such alternatives are discussed: fingertip sensing gloves, fixed stereoscopic viewers, and counterbalanced head mounted displays. A subset of commercial examples that highlight each alternative is presented as well as a brief discussion of interesting engineering and implementation issues

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

A Real-Space Full Multigrid study of the fragmentation of Li11+ clusters

We have studied the fragmentation of Li11+ clusters into the two experimentally observed products (Li9+,Li2) and (Li10+,Li) The ground state structures for the two fragmentation channels are found by Molecular Dynamics Simulated Annealing in the framework of Local Density Functional theory. Energetics considerations suggest that the fragmentation process is dominated by non-equilibrium processes. We use a real-space approach to solve the Kohn-Sham problem, where the Laplacian operator is discretized according to the Mehrstellen scheme, and take advantage of a Full MultiGrid (FMG) strategy to accelerate convergence. When applied to isolated clusters we find our FMG method to be more efficient than state-of-the-art plane wave calculations.Comment: 9 pages + 6 Figures (in gzipped tar file

Three real-space discretization techniques in electronic structure calculations

A characteristic feature of the state-of-the-art of real-space methods in electronic structure calculations is the diversity of the techniques used in the discretization of the relevant partial differential equations. In this context, the main approaches include finite-difference methods, various types of finite-elements and wavelets. This paper reports on the results of several code development projects that approach problems related to the electronic structure using these three different discretization methods. We review the ideas behind these methods, give examples of their applications, and discuss their similarities and differences.Comment: 39 pages, 10 figures, accepted to a special issue of "physica status solidi (b) - basic solid state physics" devoted to the CECAM workshop "State of the art developments and perspectives of real-space electronic structure techniques in condensed matter and molecular physics". v2: Minor stylistic and typographical changes, partly inspired by referee comment