Electron scattering states at solid surfaces calculated with realistic potentials

Scattering states with LEED asymptotics are calculated for a general non-muffin tin potential, as e.g. for a pseudopotential with a suitable barrier and image potential part. The latter applies especially to the case of low lying conduction bands. The wave function is described with a reciprocal lattice representation parallel to the surface and a discretization of the real space perpendicular to the surface. The Schroedinger equation leads to a system of linear one-dimensional equations. The asymptotic boundary value problem is confined via the quantum transmitting boundary method to a finite interval. The solutions are obtained basing on a multigrid technique which yields a fast and reliable algorithm. The influence of the boundary conditions, the accuracy and the rate of convergence with several solvers are discussed. The resulting charge densities are investigated.Comment: 5 pages, 4 figures, copyright and acknowledgment added, typos etc. correcte

Finite elements on degenerate meshes: inverse-type inequalities and applications

In this paper we obtain a range of inverse-type inequalities which are applicable to finite-element functions on general classes of meshes, including degenerate meshes obtained by anisotropic refinement. These are obtained for Sobolev norms of positive, zero and negative order. In contrast to classical inverse estimates, negative powers of the minimum mesh diameter are avoided. We give two applications of these estimates in the context of boundary elements: (i) to the analysis of quadrature error in discrete Galerkin methods and (ii) to the analysis of the panel clustering algorithm. Our results show that degeneracy in the meshes yields no degradation in the approximation properties of these method

Effective Interactions for the Three-Body Problem

The three-body energy-dependent effective interaction given by the Bloch-Horowitz (BH) equation is evaluated for various shell-model oscillator spaces. The results are applied to the test case of the three-body problem (triton and He3), where it is shown that the interaction reproduces the exact binding energy, regardless of the parameterization (number of oscillator quanta or value of the oscillator parameter b) of the low-energy included space. We demonstrate a non-perturbative technique for summing the excluded-space three-body ladder diagrams, but also show that accurate results can be obtained perturbatively by iterating the two-body ladders. We examine the evolution of the effective two-body and induced three-body terms as b and the size of the included space Lambda are varied, including the case of a single included shell, Lambda hw=0 hw. For typical ranges of b, the induced effective three-body interaction, essential for giving the exact three-body binding, is found to contribute ~10% to the binding energy.Comment: 19 pages, 9 figures, submitted to PR

Sparse convolution quadrature for time domain boundary integral formulations of the wave equation

Many important physical applications are governed by the wave equation. The formulation as time domain boundary integral equations involves retarded potentials. For the numerical solution of this problem, we employ the convolution quadrature method for the discretization in time and the Galerkin boundary element method for the space discretization. We introduce a simple a priori cut-off strategy where small entries of the system matrices are replaced by zero. The threshold for the cut-off is determined by an a priori analysis which will be developed in this paper. This analysis will also allow to estimate the effect of additional perturbations such as panel clustering and numerical integration on the overall discretization error. This method reduces the storage complexity for time domain integral equations from O(M2N) to O(M2N½ logM), where N denotes the number of time steps and M is the dimension of the boundary element spac

Stochastic methods for solving high-dimensional partial differential equations

We propose algorithms for solving high-dimensional Partial Differential Equations (PDEs) that combine a probabilistic interpretation of PDEs, through Feynman-Kac representation, with sparse interpolation. Monte-Carlo methods and time-integration schemes are used to estimate pointwise evaluations of the solution of a PDE. We use a sequential control variates algorithm, where control variates are constructed based on successive approximations of the solution of the PDE. Two different algorithms are proposed, combining in different ways the sequential control variates algorithm and adaptive sparse interpolation. Numerical examples will illustrate the behavior of these algorithms

Tensor Product Approximation (DMRG) and Coupled Cluster method in Quantum Chemistry

We present the Copupled Cluster (CC) method and the Density matrix Renormalization Grooup (DMRG) method in a unified way, from the perspective of recent developments in tensor product approximation. We present an introduction into recently developed hierarchical tensor representations, in particular tensor trains which are matrix product states in physics language. The discrete equations of full CI approximation applied to the electronic Schr\"odinger equation is casted into a tensorial framework in form of the second quantization. A further approximation is performed afterwards by tensor approximation within a hierarchical format or equivalently a tree tensor network. We establish the (differential) geometry of low rank hierarchical tensors and apply the Driac Frenkel principle to reduce the original high-dimensional problem to low dimensions. The DMRG algorithm is established as an optimization method in this format with alternating directional search. We briefly introduce the CC method and refer to our theoretical results. We compare this approach in the present discrete formulation with the CC method and its underlying exponential parametrization.Comment: 15 pages, 3 figure

Numerics of boundary-domain integral and integro-differential equations for BVP with variable coefficient in 3D

This is the post-print version of the article. The official published version can be accessed from the links below - Copyright @ 2013 Springer-VerlagA numerical implementation of the direct boundary-domain integral and integro-differential equations, BDIDEs, for treatment of the Dirichlet problem for a scalar elliptic PDE with variable coefficient in a three-dimensional domain is discussed. The mesh-based discretisation of the BDIEs with tetrahedron domain elements in conjunction with collocation method leads to a system of linear algebraic equations (discretised BDIE). The involved fully populated matrices are approximated by means of the H-Matrix/adaptive cross approximation technique. Convergence of the method is investigated.This study is partially supported by the EPSRC grant EP/H020497/1:"Mathematical Analysis of Localised-Boundary-Domain Integral Equations for Variable-Coefficients Boundary Value Problems"

Addition of platinum derivatives to neoadjuvant single-agent fluoropyrimidine chemoradiotherapy in patients with stage II/III rectal cancer: protocol for a systematic review and meta-analysis (PROSPERO CRD42017073064)

Background Neoadjuvant (chemo-)radiation has proven to improve local control compared to surgery alone, but this improvement did not translate into better overall or disease-specific survival. The addition of oxaliplatin to fluoropyrimidine-based neoadjuvant chemoradiotherapy holds the potential of positively affecting survival in this context since it has been proven effective in the palliative and adjuvant setting of colorectal cancer. Thus, the objective of this systematic review is to assess the efficacy, safety, and quality of life resulting from adding a platinum derivative to neoadjuvant single-agent fluoropyrimidine-based chemoradiotherapy in patients with Union for International Cancer Control stage II and III rectal cancer. Methods: MEDLINE, Web of Science, and Cochrane Central Register of Controlled Trials will be systematically searched to identify all randomized controlled trials comparing single-agent fluoropyrimidine-based chemoradiotherapy to combined neoadjuvant therapy including a platinum derivative. Predefined data on trial design, quality, patient characteristics, and endpoints will be extracted. Quality of included trials will be assessed according to the Cochrane Risk of Bias Tool, and the GRADE recommendations will be applied to judge the quality of the resulting evidence. The main outcome parameter will be survival, but also treatment toxicity, perioperative morbidity, and quality of life will be assessed. Discussion: The findings of this systematic review and meta-analysis will provide novel insights into the efficacy and safety of combined neoadjuvant chemoradiotherapy including a platinum derivative and may form a basis for future clinical decision-making, guideline evaluation, and research prioritization. Systematic review registration PROSPERO CRD4201707306

Application of Multicanonical Multigrid Monte Carlo Method to the Two-Dimensional ϕ4\phi^4-Model: Autocorrelations and Interface Tension

We discuss the recently proposed multicanonical multigrid Monte Carlo method and apply it to the scalar $\phi^4$-model on a square lattice. To investigate the performance of the new algorithm at the field-driven first-order phase transitions between the two ordered phases we carefully analyze the autocorrelations of the Monte Carlo process. Compared with standard multicanonical simulations a real-time improvement of about one order of magnitude is established. The interface tension between the two ordered phases is extracted from high-statistics histograms of the magnetization applying histogram reweighting techniques.Comment: 49 pp. Latex incl. 14 figures (Fig.7 not included, sorry) as uuencoded compressed tar fil