Five-Brane Configurations without a Strong Coupling Regime

Five-brane distributions with no strong coupling problems and high symmetry are studied. The simplest configuration corresponds to a spherical shell of branes with S^3 geometry and symmetry. The equations of motions with delta-function sources are carefully solved in such backgrounds. Various other brane distributions with sixteen unbroken supercharges are described. They are associated to exact world-sheet superconformal field theories with domain-walls in space-time. We study the equations of gravitational fluctuations, find normalizable modes of bulk 6-d gravitons and confirm the existence of a mass gap. We also study the moduli of the configurations and derive their (normalizable) wave-functions. We use our results to calculate in a controllable fashion using holography, the two-point function of the stress tensor of little string theory in these vacua.Comment: LateX, 32 pages, 4 figures; (v2) A reference adde

Discontinuous Galerkin Methods with Trefftz Approximation

We present a novel Discontinuous Galerkin Finite Element Method for wave propagation problems. The method employs space-time Trefftz-type basis functions that satisfy the underlying partial differential equations and the respective interface boundary conditions exactly in an element-wise fashion. The basis functions can be of arbitrary high order, and we demonstrate spectral convergence in the \Lebesgue_2-norm. In this context, spectral convergence is obtained with respect to the approximation error in the entire space-time domain of interest, i.e. in space and time simultaneously. Formulating the approximation in terms of a space-time Trefftz basis makes high order time integration an inherent property of the method and clearly sets it apart from methods, that employ a high order approximation in space only.Comment: 14 pages, 12 figures, preprint submitted at J Comput Phy

An adaptive, fully implicit multigrid phase-field model for the quantitative simulation of non-isothermal binary alloy solidification

Using state-of-the-art numerical techniques, such as mesh adaptivity, implicit time-stepping and a non-linear multi-grid solver, the phase-field equations for the non-isothermal solidification of a dilute binary alloy have been solved. Using the quantitative, thin-interface formulation of the problem we have found that at high Lewis number a minimum in the dendrite tip radius is predicted with increasing undercooling, as predicted by marginal stability theory. Over the dimensionless undercooling range 0.2–0.8 the radius selection parameter, σ*, was observed to vary by over a factor of 2 and in a non-monotonic fashion, despite the anisotropy strength being constant

Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations

This work derives a residual-based a posteriori error estimator for reduced models learned with non-intrusive model reduction from data of high-dimensional systems governed by linear parabolic partial differential equations with control inputs. It is shown that quantities that are necessary for the error estimator can be either obtained exactly as the solutions of least-squares problems in a non-intrusive way from data such as initial conditions, control inputs, and high-dimensional solution trajectories or bounded in a probabilistic sense. The computational procedure follows an offline/online decomposition. In the offline (training) phase, the high-dimensional system is judiciously solved in a black-box fashion to generate data and to set up the error estimator. In the online phase, the estimator is used to bound the error of the reduced-model predictions for new initial conditions and new control inputs without recourse to the high-dimensional system. Numerical results demonstrate the workflow of the proposed approach from data to reduced models to certified predictions

Incomplete Orthogonal Factorization Methods Using Givens Rotations II: Implementation and Results

We present, implement and test a series of incomplete orthogonal factorization methods based on Givens rotations for large sparse unsymmetric matrices. These methods include: column-Incomplete Givens Orthogonalization (cIGO-method), which drops entries by position only; column-Threshold Incomplete Givens Orthogonalization (cTIGO-method) which drops entries dynamically by both their magnitudes and positions and where the reduction via Givens rotations is done in a column-wise fashion; and, row-Threshold Incomplete Givens Orthogonalization (r-TIGO-method) which again drops entries dynamically, but only magnitude is now taken into account and reduction is performed in a row-wise fashion. We give comprehensive accounts of how one would code these algorithms using a high level language to ensure efficiency of computation and memory use. The methods are then applied to a variety of square systems and their performance as preconditioners is tested against standard incomplete LU factorization techniques. For rectangular matrices corresponding to least-squares problems, the resulting incomplete factorizations are applied as preconditioners for conjugate gradients for the system of normal equations. A comprehensive discussion about the uses, advantages and shortcomings of these preconditioners is given

Time dependent reliability model incorporating continuum damage mechanics for high-temperature ceramics

Presently there are many opportunities for the application of ceramic materials at elevated temperatures. In the near future ceramic materials are expected to supplant high temperature metal alloys in a number of applications. It thus becomes essential to develop a capability to predict the time-dependent response of these materials. The creep rupture phenomenon is discussed, and a time-dependent reliability model is outlined that integrates continuum damage mechanics principles and Weibull analysis. Several features of the model are presented in a qualitative fashion, including predictions of both reliability and hazard rate. In addition, a comparison of the continuum and the microstructural kinetic equations highlights a strong resemblance in the two approaches

Meshfree finite differences for vector Poisson and pressure Poisson equations with electric boundary conditions

We demonstrate how meshfree finite difference methods can be applied to solve vector Poisson problems with electric boundary conditions. In these, the tangential velocity and the incompressibility of the vector field are prescribed at the boundary. Even on irregular domains with only convex corners, canonical nodal-based finite elements may converge to the wrong solution due to a version of the Babuska paradox. In turn, straightforward meshfree finite differences converge to the true solution, and even high-order accuracy can be achieved in a simple fashion. The methodology is then extended to a specific pressure Poisson equation reformulation of the Navier-Stokes equations that possesses the same type of boundary conditions. The resulting numerical approach is second order accurate and allows for a simple switching between an explicit and implicit treatment of the viscosity terms.Comment: 19 pages, 7 figure

Effective actions of a Gauss-Bonnet brane world with brane curvature terms

We consider a warped brane world scenario with two branes, Gauss-Bonnet gravity in the bulk, and brane localised curvature terms. When matter is present on both branes, we investigate the linear equations of motion and distinguish three regimes. At very high energy and for an observer on the positive tension brane, gravity is four dimensional and coupled to the brane bending mode in a Brans-Dicke fashion. The coupling to matter and brane bending on the negative tension brane is exponentially suppressed. In an intermediate regime, gravity appears to be five dimensional while the brane bending mode remains four dimensional. At low energy, matter on both branes couple to gravity for an observer on the positive tension brane, with a Brans-Dicke description similar to the 2--brane Randall-Sundrum setup. We also consider the zero mode truncation at low energy and show that the moduli approximation fails to reproduce the low energy action.Comment: 14 page

Parallel, linear-scaling building-block and embedding method based on localized orbitals and orbital-specific basis sets

We present a new linear scaling method for the energy minimization step of semiempirical and first-principles Hartree-Fock and Kohn-Sham calculations. It is based on the self-consistent calculation of the optimum localized orbitals of any localization method of choice and on the use of orbital-specific basis sets. The full set of localized orbitals of a large molecule is seen as an orbital mosaic where each tessera is made of only a few of them. The orbital tesserae are computed out of a set of embedded cluster pseudoeigenvalue coupled equations which are solved in a building-block self-consistent fashion. In each iteration, the embedded cluster equations are solved independently of each other and, as a result, the method is parallel at a high level of the calculation. In addition to full system calculations, the method enables to perform simpler, much less demanding embedded cluster calculations, where only a fraction of the localized molecular orbitals are variational while the rest are frozen, taking advantage of the transferability of the localized orbitals of a given localization method between similar molecules. Monitoring single point energy calculations of large poly(ethylene oxide) molecules and three dimensional carbon monoxide clusters using an extended Huckel Hamiltonian are presented.Comment: latex, 15 pages, 10 figures, accepted for publication in J.Chem.Phy