Numerical Tools I: ODE Integration

2012 ◽  
pp. 131-146
Author(s):  
Bruno Cordani
Keyword(s):  
Numerical Tools

scholarly journals Hunting for Gravitational Quantum Spikes

Universe ◽  
2021 ◽  
Vol 7 (3) ◽  
pp. 49
Author(s):  
Andrzej Góźdź ◽  
Włodzimierz Piechocki ◽  
Grzegorz Plewa ◽  
Tomasz Trześniewski
Keyword(s):  
Initial Data ◽  
Fundamental Importance ◽  
Quantum Structures ◽  
Subtle Effect ◽  
Gravitational Systems ◽  
Numerical Tools ◽  
The Universe

We present the result of our examination of quantum structures called quantum spikes. The classical spikes that are known in gravitational systems, occur in the evolution of the inhomogeneous spacetimes. A different kind of spikes, which we name strange spikes, can be seen in the dynamics of the homogeneous sector of the Belinski–Khalatnikov–Lifshitz scenario. They can be made visible if the so-called inhomogeneous initial data are used. The question to be explored is whether the strange spikes may survive quantization. The answer is in the affirmative. However, this is rather a subtle effect that needs further examination using sophisticated analytical and numerical tools. The spikes seem to be of fundamental importance, both at classical and quantum levels, as they may serve as seeds of real structures in the universe.

scholarly journals Numerical Homogenization of Multi-Layered Corrugated Cardboard with Creasing or Perforation

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 3786
Author(s):  
Tomasz Garbowski ◽  
Anna Knitter-Piątkowska ◽  
Damian Mrówczyński
Keyword(s):  
Computational Models ◽  
Load Capacity ◽  
Torsional Stiffness ◽  
Numerical Homogenization ◽  
Corrugated Board ◽  
3D Geometry ◽  
Corrugated Cardboard ◽  
Numerical Tools ◽  
Packaging Industry ◽  
Theoretical Considerations

The corrugated board packaging industry is increasingly using advanced numerical tools to design and estimate the load capacity of its products. This is why numerical analyses are becoming a common standard in this branch of manufacturing. Such trends cause either the use of advanced computational models that take into account the full 3D geometry of the flat and wavy layers of corrugated board, or the use of homogenization techniques to simplify the numerical model. The article presents theoretical considerations that extend the numerical homogenization technique already presented in our previous work. The proposed here homogenization procedure also takes into account the creasing and/or perforation of corrugated board (i.e., processes that undoubtedly weaken the stiffness and strength of the corrugated board locally). However, it is not always easy to estimate how exactly these processes affect the bending or torsional stiffness. What is known for sure is that the degradation of stiffness depends, among other things, on the type of cut, its shape, the depth of creasing as well as their position or direction in relation to the corrugation direction. The method proposed here can be successfully applied to model smeared degradation in a finite element or to define degraded interface stiffnesses on a crease line or a perforation line.

scholarly journals Performance Analysis on the Use of Oscillating Water Column in Barge-Based Floating Offshore Wind Turbines

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 475
Author(s):  
Payam Aboutalebi ◽  
Fares M’zoughi ◽  
Izaskun Garrido ◽  
Aitor J. Garrido
Keyword(s):  
Wind Turbines ◽  
Positive Impact ◽  
Offshore Wind ◽  
Offshore Wind Turbines ◽  
Floating Offshore Wind Turbines ◽  
Water Columns ◽  
Numerical Tools ◽  
Oscillating Water Columns ◽  
The Given ◽  
The Waves

Undesired motions in Floating Offshore Wind Turbines (FOWT) lead to reduction of system efficiency, the system’s lifespan, wind and wave energy mitigation and increment of stress on the system and maintenance costs. In this article, a new barge platform structure for a FOWT has been proposed with the objective of reducing these undesired platform motions. The newly proposed barge structure aims to reduce the tower displacements and platform’s oscillations, particularly in rotational movements. This is achieved by installing Oscillating Water Columns (OWC) within the barge to oppose the oscillatory motion of the waves. Response Amplitude Operator (RAO) is used to predict the motions of the system exposed to different wave frequencies. From the RAOs analysis, the system’s performance has been evaluated for representative regular wave periods. Simulations using numerical tools show the positive impact of the added OWCs on the system’s stability. The results prove that the proposed platform presents better performance by decreasing the oscillations for the given range of wave frequencies, compared to the traditional barge platform.

scholarly journals Two-loop rational terms in Yang-Mills theories

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Jean-Nicolas Lang ◽  
Stefano Pozzorini ◽  
Hantian Zhang ◽  
Max F. Zoller
Keyword(s):  
Scattering Amplitudes ◽  
Gauge Theories ◽  
A Posteriori ◽  
Four Dimensions ◽  
Yang Mills ◽  
General Properties ◽  
Finite Set ◽  
Numerical Tools ◽  
Loop Amplitudes

Abstract Scattering amplitudes in D dimensions involve particular terms that originate from the interplay of UV poles with the (D − 4)-dimensional parts of loop numerators. Such contributions can be controlled through a finite set of process-independent rational counterterms, which make it possible to compute loop amplitudes with numerical tools that construct the loop numerators in four dimensions. Building on a recent study [1] of the general properties of two-loop rational counterterms, in this paper we investigate their dependence on the choice of renormalisation scheme. We identify a nontrivial form of scheme dependence, which originates from the interplay of mass and field renormalisation with the (D−4)-dimensional parts of loop numerators, and we show that it can be controlled through a new kind of one-loop counterterms. This guarantees that the two-loop rational counterterms for a given renormalisable theory can be derived once and for all in terms of generic renormalisation constants, which can be adapted a posteriori to any scheme. Using this approach, we present the first calculation of the full set of two-loop rational counterterms in Yang-Mills theories. The results are applicable to SU(N) and U(1) gauge theories coupled to nf fermions with arbitrary masses.

Stress analysis of finite orthotropic composite containing an elliptical hole

2021 ◽  
pp. 002199832110507
Author(s):  
Narin S. Fatima ◽  
Robert E. Rowlands
Keyword(s):  
Composite Structures ◽  
Elliptical Hole ◽  
External Loading ◽  
Finite Geometries ◽  
Orthotropic Composites ◽  
Numerical Tools ◽  
Design Type ◽  
Measured Displacement ◽  
Type Information ◽  
Important Design

Although the mechanical integrity of a member can be highly influenced by associated stresses, determining the latter can be very challenging for finite orthotropic composites containing cutouts. This is particularly so if the external loading is not well known, a common situation in practical situations. Acknowledging the above, a finite elliptically-perforated orthotropic tensile laminate is stress analyzed by combining measured displacement data with relevant analytical and numerical tools. Knowledge of the external loading is unnecessary. Results are verified independently and the concepts are applicable to other situations. The developed technology can provide important design-type information for orthotropic composites. In particular, the ability to apply analyses for perforated composite structures which assume infinite geometry to finite geometries is demonstrated.

scholarly journals Numerical Tools for the Bayesian Analysis of Stochastic Frontier Models

1997 ◽  
Author(s):  
Jacek Osiewalski ◽  
Mark F.J. Steel
Keyword(s):  
Bayesian Analysis ◽  
Stochastic Frontier ◽  
Stochastic Frontier Models ◽  
Numerical Tools

A Highly Accurate Beam Finite Element for Curved and Twisted Helicopter Blades

2011 ◽  
Author(s):  
Yan Skladanek ◽  
Paul Cranga ◽  
Guy Ferraris ◽  
Georges Jacquet ◽  
Re´gis Dufour
Keyword(s):  
Finite Element ◽  
Twist Angle ◽  
Experimental Investigations ◽  
Rotating Frame ◽  
Blade Design ◽  
Helicopter Blades ◽  
Performance Improvements ◽  
Blade Optimization ◽  
Model Reliability ◽  
Numerical Tools

Blade optimization is more than ever a crucial activity for helicopter manufacturers, always looking for performance improvements, noise reduction and vibratory comfort increase. Latest studies have led to design new blade concepts including a double swept plan shape, an evolutionary and increased twist angle at the tip and a new layout for internal components like roving spars. Such blades exhibit a highly coupled behavior between torsion, longitudinal and bending motions that should be accurately modeled for predictive numerical tools. In this research a highly accurate beam finite element is formulated in the rotating frame to improve the static deformation calculation under aerodynamic and centrifugal loads and thus enhance dynamic and stability analysis usually performed for a helicopter development. Numerical and experimental investigations are performed to demonstrate the model reliability both for academic beams with extreme shape and for actual blade design.

Numerical Tools for Improved Convergence of Meshfree Peridynamic Discretizations

2019 ◽  
pp. 1389-1415
Author(s):  
Pablo Seleson ◽  
David J. Littlewood
Keyword(s):  
Numerical Tools

Numerical tools to investigate mechanical and fatigue properties of additively manufactured MS1-H13 hybrid steels

2018 ◽  
Vol 23 ◽  
pp. 381-393 ◽  
Author(s):  
Alireza Ebrahimi ◽  
Mohsen Mohammadi
Keyword(s):  
Fatigue Properties ◽  
Numerical Tools
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