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A program called SCSPG (Semi-Circle Segmented Path Generator) is presented in this report. How it works is described and an example of it is illustrated using a case of work of friction along a curved path. As a benchmark for the program, work of friction along straight path is calculated and then compared to theoretical prediction.
We propose a model for nanoscale supercapacitor consisting of two-dimensional insulating BN layers placed between two commensurate and metallic graphene layers. First-principles Density Functional calculations of structure optimized total energy and self-consistent field potential performed on these nanoscale capacitors for different levels of charging and different number of BN layers mark the values of capacitance per unit mass, which are larger than those measured values for the supercapacitors made from other carbon based materials. Our theoretical study also compares results obtained for the present nanoscale capacitor with those of classical Helmholtz model and reveals crucial differences. Our model allows the fabrication of series/parallel mixed combinations consisting of epitaxially grown, sequential and multiple graphene/BN sheets.
An interface between the UrQMD-1.3cr model (version 1.3 for cosmic air showers) and the Geant4 transport toolkit has been developed. Compared to the current Geant4 (hybrid) hadronic models, this provides the ability to simulate at the microscopic level hadron, nucleus, and anti-nucleus interactions with matter from 0 to 1 TeV with a single transport code. This document provides installation requirements and instructions, as well as class and member function descriptions of the software.
An efficient integral equation based solver is constructed for the electrostatic problem on domains with cuboidal inclusions. It can be used to compute the polarizability of a dielectric cube in a dielectric background medium at virtually every permittivity ratio for which it exists. For example, polarizabilities accurate to between five and ten digits are obtained (as complex limits) for negative permittivity ratios in minutes on a standard workstation. In passing, the capacitance of the unit cube is determined with unprecedented accuracy. With full rigor, we develop a natural mathematical framework suited for the study of the polarizability of Lipschitz domains. Several aspects of polarizabilities and their representing measures are clarified, including limiting behavior both when approaching the support of the measure and when deforming smooth domains into a non-smooth domain. The success of the mathematical theory is achieved through symmetrization arguments for layer potentials.
Shaped laser pulses are a powerful tool to induce population transfer between electronic molecular states, and time-dependent perturbation theory is suitable for a description of such a transfer in weak external fields. The application of perturbation theory in numerical simulations of field matter interactions can lead to divergences. In a recent paper [K. Renziehausen et. al., J. Phys. B: At. Mol. Opt. Phys., 42:195402, 2009] we explained that the arising error in the norm of the wave function can be split into two parts. The first part is related to numerical errors caused by the discretisation of time that is required in the simulation and can be suppressed for a sufficiently small time step or abolished for an adequate numerical implementation of perturbation theory. The second part may cause divergences and is associated with the perturbative expansion order. We presented numerical evidence without any analytical proof. Here we are focussing on the derivation of analytical expressions to interpret the behavior of what we have called in the above mentioned paper 'simple algorithm'. The derivation of analytical expressions for the interpretation of what we have called in the above mentioned paper 'improved algorithm' are given in another paper [K. Renziehausen. arXiv, in preparation, 2012]. Moreover, we introduce here a gedankenexperiment to illustrate the influence of the different orders on the field-molecule interaction.
We accelerated an {\it ab-initio} QMC electronic structure calculation by using GPGPU. The bottleneck of the calculation for extended solid systems is replaced by CUDA-GPGPU subroutine kernels which build up spline basis set expansions of electronic orbital functions at each Monte Carlo step. We achieved 30.8 times faster evaluation for the bottleneck, confirmed on the simulation of TiO$_2$ solid with 1,536 electrons. To achieve better performance in GPGPU we propose a new updating scheme for Monte Carlo sampling, quasi-simultaneous updating, which is in between the configuration-by-configuration updating and the widely-used particle-by-particle one. The energy deviation caused both by the single precision treatment and the new updating scheme is found to be within the accuracy required in the calculation, $\sim 10^{-3}$ hartree per primitive cell.
We consider a minimization scheme based on the Householder transport operator for the Grassman manifold, where a point on the manifold is represented by a m x n matrix with orthonormal columns. In particular, we consider the case where m >> n and present a method with asymptotic complexity mn^2. To avoid explicit parametrization of the manifold we use Householder transforms to move on the manifold, and present a formulation for simultaneous Householder reflections for S-orthonormal columns. We compare a quasi-Newton and nonlinear conjugate gradient implementation adapted to the manifold with a projected nonlinear conjugate gradient method, and demonstrate that the convergence rate is significantly improved if the manifold is taken into account when designing the optimization procedure.
We consider a direct optimization approach for ensemble density functional theory electronic structure calculations. The update operator for the electronic orbitals takes the structure of the Stiefel manifold into account and we present an optimization scheme for the occupation numbers that ensures that the constraints remain satisfied. We also compare sequential and simultaneous quasi-Newton and nonlinear conjugate gradient optimization procedures, and demonstrate that simultaneous optimization of the electronic orbitals and occupation numbers improve performance compared to the sequential approach.
Although memristive devices with threshold voltages are the norm rather than the exception in experimentally realizable systems, their SPICE programming is not yet common. Here, we show how to implement such systems in the SPICE environment. Specifically, we present SPICE models of a popular voltage-controlled memristive system specified by five different parameters for PSPICE and NGSPICE circuit simulators. We expect this implementation to find widespread use in circuits design and testing.
A formalism is introduced for the non-perturbative, purely numerical, solution of the reduced Rayleigh equation for the scattering of light from two-dimensional penetrable rough surfaces. As an example, we apply this formalism to study the scattering of p- or s-polarized light from two- dimensional dielectric or metallic randomly rough surfaces by calculating the full angular distribution of the co- and cross-polarized intensity of the scattered light. In particular, we present calculations of the mean differential reflection coefficient for glass and silver surfaces characterized by (isotropic or anisotropic) Gaussian and cylindrical power spectra. The proposed method is found, within the validity of the Rayleigh hypothesis, to give reliable results. For a non-absorbing metal surface the conservation of energy was explicitly checked, and found to be satisfied to within 0.03%, or better, for the parameters assumed. This testifies to the accuracy of the approach and a satisfactory discretization.
This paper identifies a new pathology that can be found for numerical simulations of nonlinear conservation law systems. Many of the difficulties already identified in the literature (rarefaction shocks, carbuncle phenomena, slowly moving shocks, wall heating, etc) can be traced to insufficient numerical dissipation, and the current case is no different. However, the details of the case we study here are somewhat unique in that the solution which is found by the numerics is very weak and can fail to have a derivative anywhere in the post-shock region.
In preparation to the exascale era, an alternative approach to calculate the electrostatic forces in Particle Mesh (PM) methods is proposed. While the traditional techniques are based on the calculation of the electrostatic potential by solving the Poisson equation, in the new approach the electric field is calculated by solving the Ampere's law. When the Ampere's law is discretized explicitly in time, the electric field values on the mesh are simply updated from the previous values. In this way, the electrostatic solver becomes an embarrassingly parallel problem, making the algorithm extremely scalable and suitable for exascale computing platforms. An implementation of a one dimensional PM code is presented to show that the proposed method produces correct results, and it is a very promising algorithm for exascale PM simulations.
The problem of estimating small transition probabilities for overdamped Langevin dynamics is considered. A simplification of Girsanov's formula is obtained in which the relationship between the infinitesimal generator of the underlying diffusion and the change of probability measure corresponding to a change in the potential energy is made explicit. From this formula an asymptotic expression for transition probability densities is derived. Separately the problem of estimating the probability that a small noise Langevin process excapes a potential well is discussed.
Today's most popular techniques for accurately calculating the dynamics of the reduced density operator in an open quantum system, either require, or gain great computational benefits, from representing the bath response function a(t) in the form a(t)=Σ_k^K p_k e^{O_k t} . For some of these techniques, the number of terms in the series K plays the lead role in the computational cost of the calculation, and is therefore often a limiting factor in simulating open quantum system dynamics. We present an open source MATLAB program called BATHFIT 1, whose input is any spectral distribution functions J(w) or bath response function, and whose output attempts to be the set of parameters {p_k,w_k}_k=1^K such that for a given value of K, the series Σ_k^k p_k e^{O_k t} is as close as possible to a(t). This should allow the user to represent a(t) as accurately as possible with as few parameters as possible. The program executes non-linear least squares fitting, and for a very wide variety of spectral distribution functions, competent starting parameters are used for these fits. For most forms of J(w), these starting parameters, and the exact a(t) corresponding to the given J(w), are calculated using the recent Pade decomposition technique - therefore this program can also be used to merely implement the Pade decomposition for these spectral distribution functions; and it can also be used just to efficiently and accurately calculate a(t) for any given J(w) . The program also gives the J(w) corresponding to a given a(t), which may allow one to assess the quality (in the w-domain) of a representation of a(t) being used. Finally, the program can calculate the discretized influence functional coefficients for any J(w), and this is computed very efficiently for most forms of J(w) by implementing the recent technique published in [Quantum Physics Letters (2012) 1 (1) pg. 35].
Images of surface topography of ultrathin magnetic films have been used for Monte Carlo simulations in the framework of the ferromagnetic Ising model to study the hysteresis and thermal properties of nanomaterials. For high performance calculations was used super-scalable parallel algorithm for the finding of the equilibrium configuration. The changing of a distribution of spins on the surface during the reversal of the magnetization and the dynamics of nanodomain structure of thin magnetic films under the influence of changing external magnetic field was investigated.
A comparison of PGI OpenACC, FORTRAN CUDA, and Nvidia CUDA pseudospectral methods on a single GPU and GCC FORTRAN on single and multiple CPU cores is reported. The GPU implementations use CuFFT and the CPU implementations use FFTW. Porting pre-existing FORTRAN codes to utilize a GPUs is efficient and easy to implement with OpenACC and CUDA FORTRAN. Example programs are provided.
Quantitative understanding of the fracture toughness of metallic glasses, including the associated ductile-to-brittle transitions, is not yet available. Here we use a simple model of plastic deformation in glasses, coupled to an advanced Eulerian level set formulation for solving complex free boundary problems, to calculate the fracture toughness of metallic glasses as a function of the degree of structural relaxation corresponding to different annealing times near the glass temperature. Our main result indicates the existence of an elasto-plastic crack tip instability for sufficiently relaxed glasses, resulting in a marked drop in the toughness, which we interpret as a ductile-to-brittle transition similar to experimental observations.
Observed violations of Bell type inequalities exclude all relativistic micro causal ("local"), counterfactual definite ("real") hidden variable models of nature. This further relativization of our concept of reality triggers a growing pseudoscientific resistance against quantum mechanics (QM). I define Didactic Randi Challenges (DRC) via five characteristics. These are challenges which, according to the laws of nature, are impossible to meet. They effectively refute pseudoscientific claims according to which the challenge could easily be met. DRC work by being known to exist while never having been overcome, despite the large rewards which would follow from meeting the challenge. Pseudoscience exploits well meaning engagement in argument to create the appearance of an expert dispute (sowing doubt). DRC decline to discuss "until the challenge is met", without solidifying the perception of establishment conspiracy. This requires transparency, thus DRC are efficient didactic tools. The Quantum Randi Challenge (QRC) is a DRC designed to reject hidden variable models by simply teaching QM; there is no bet or interaction with challengers. The QRC is a computer game that anybody can modify. The present version includes a simulation of true QM behavior that violates Bell 99% of the time, hidden variables that violate the Bell and CHSH inequality with 50% probability, and ones which violate Bell 85% of the time when missing 13% anti-correlation. The DRC challenge is to modify the hidden variables so that the predicted QM behavior arises, including anti-correlation. If such were possible, the presented programs would make it trivial to meet the challenge. This fact and the whole QRC can be taught to a wide audience via the presented heuristics. Demanding anti-correlation is argued to be superior to employing CHSH.