Search results for "Numerical"

Derivatives not first return integrable on a fractal set

2018

We extend to s-dimensional fractal sets the notion of first return integral (Definition 5) and we prove that there are s-derivatives not s-first return integrable.

Green’s function and existence of solutions for a third-order three-point boundary value problem

2019

The solutions of third-order three-point boundary value problem x‘‘‘ + f(t, x) = 0, t ∈ [a, b], x(a) = x‘(a) = 0, x(b) = kx(η), where η ∈ (a, b), k ∈ R, f ∈ C([a, b] × R, R) and f(t, 0) ≠ 0, are the subject of this investigation. In order to establish existence and uniqueness results for the solutions, attention is focused on applications of the corresponding Green’s function. As an application, also one example is given to illustrate the result. Keywords: Green’s function, nonlinear boundary value problems, three-point boundary conditions, existence and uniqueness of solutions.

Introducing a novel mesh following technique for approximation-free robotic tool path trajectories

2017

Abstract Modern tools for designing and manufacturing of large components with complex geometries allow more flexible production with reduced cycle times. This is achieved through a combination of traditional subtractive approaches and new additive manufacturing processes. The problem of generating optimum tool-paths to perform specific actions (e.g. part manufacturing or inspection) on curved surface samples, through numerical control machinery or robotic manipulators, will be increasingly encountered. Part variability often precludes using original design CAD data directly for toolpath generation (especially for composite materials), instead surface mapping software is often used to gener…

Resonances for nonanalytic potentials

2009

We consider semiclassical Schr"odinger operators on $R^n$, with $C^infty$ potentials decaying polynomially at infinity. The usual theories of resonances do not apply in such a non-analytic framework. Here, under some additional conditions, we show that resonances are invariantly defined up to any power of their imaginary part. The theory is based on resolvent estimates for families of approximating distorted operators with potentials that are holomorphic in narrow complex sectors around $R^n$.

On the accurate determination of nonisolated solutions of nonlinear equations

1981

A simple but efficient method to obtain accurate solutions of a system of nonlinear equations with a singular Jacobian at the solution is presented. This is achieved by enlarging the system to a higher dimensional one whose solution in question is isolated. Thus it can be computed e. g. by Newton's method, which is locally at least quadratically convergent and selfcorrecting, so that high accuracy is attainable.

Quadrature Formula Based on Interpolating Polynomials: Algorithmic and Computational Aspects

2007

The aim of this article is to obtain a quadrature formula for functions in several variables and to analyze the algorithmic and computational aspects of this formula. The known information about the integrand is {λi(f)}i=1n, where λi are linearly independent linear functionals. We find a form of the coefficients of the quadrature formula which can be easy used in numerical calculations. The main algorithm we use in order to obtain the coefficients and the remainder of the quadrature formula is based on the Gauss elimination by segments method. We obtain an expression for the exactness degree of the quadrature formula. Finally, we analyze some computational aspects of the algorithm in the pa…

1982

The molecular weight distribution (MWD) of a high polymer is calculated from a weakly perturbed Zimm-plot of the classical light scattering on dilute solutions of Gaussian polymer coils (theta state). A typical Zimm-plot is simulated corresponding to the measurements of high accuracy as would be obtained by using the laser photometer described by Hack and Meyerhoff. The accuracy as published by these authors for small dissymmetries is used. Two numerical methods for calculating the MWD are briefly described and tested, both using an empirical formula for the Laplace image of the calculated MWD.

Analytical and Numerical Investigation of 3D Multilayer Detachment Folding

2013

Multilayer detachment folding, in which a sequence of sedimentary layers is compressed above a weaker salt layer, is a common mode of deformation in thin-skinned fold-and-thrust belts. Here, we investigate the dynamics of multilayer detachment folding with three different viscosities: lower detachment or salt layer, overlying weak layers and competent layers. A semi-analytical solution, based on thick plate analysis of multilayer systems, is used to create mechanical phase diagrams of folding dominant wavelength and growth rate as a function of material parameters. The validity of the phase diagrams is tested and confirmed beyond the nucleation stages of folding by performing several 2D and…

Lattice quantum hadrodynamics on a CRAY Y-MP

1992

Quantum corrections to the mean-field equation of state for nuclear matter are estimated in a lattice simulation of quantum hadrodynamics on a CRAY Y-MP. In contrast with lattice quantum chromodynamics, where coordinate space methods are the standard, the calculations are carried out in momentum space and on nonhypercubic (irregular) lattices. The quantum corrections to the known, mean-field equation of state were found to be considerable. The time frame of the project and the large computational needs of the program required the use of powerful supercomputers, like the CRAY Y-MP, which are capable of performing at a very high computing speed by using both vector and parallel hardware, the …

Multiparton NLO corrections by numerical methods

2013

In this talk we discuss an algorithm for the numerical calculation of one-loop QCD amplitudes and present results at next-to-leading order for jet observables in electron-positron annihilation calculated with the above-mentioned method. The algorithm consists of subtraction terms, approximating the soft, collinear and ultraviolet divergences of QCD one-loop amplitudes, as well as a method to deform the integration contour for the loop integration into the complex plane to match Feynman's i delta rule. The algorithm is formulated at the amplitude level and does not rely on Feynman graphs. Therefore all ingredients of the algorithm can be calculated efficiently using recurrence relations. The…