scholarly journals AN ALGORITHM FOR FINDING ALL ZEROS OF VECTOR FUNCTIONS

2008 ◽  
Vol 77 (3) ◽  
pp. 353-363 ◽  
Author(s):  
IBRAHEEM ALOLYAN

AbstractComputing a zero of a continuous function is an old and extensively researched problem in numerical computation. In this paper, we present an efficient subdivision algorithm for finding all real roots of a function in multiple variables. This algorithm is based on a simple computationally verifiable necessity test for the existence of a root in any compact set. Both theoretical analysis and numerical simulations demonstrate that the algorithm is very efficient and reliable. Convergence is shown and numerical examples are presented.

2021 ◽  
Vol 11 (4) ◽  
pp. 1960
Author(s):  
Naming Zhang ◽  
Ziang Wang ◽  
Jinhua Shi ◽  
Shuya Ning ◽  
Yukuo Zhang ◽  
...  

Previous research showed that pulsed functional magnetic stimulation can activate brain tissue with optimum intensity and frequency. Conventional stimulation coils are always set as a figure-8 type or Helmholtz. However, the magnetic fields generated by these coils are uniform around the target, and their magnetic stimulation performance still needs improvement. In this paper, a novel type of stimulation coil is proposed to shrink the irritative zone and strengthen the stimulation intensity. Furthermore, the electromagnetic field distribution is calculated and measured. Based on numerical simulations, the proposed coil is compared to traditional coil types. Moreover, the influential factors, such as the diameter and the intersection angle, are also analyzed. It was demonstrated that the proposed coil has a better performance in comparison with the figure-8 coil. Thus, this work suggests a new way to design stimulation coils for transcranial magnetic stimulation.


2013 ◽  
Vol 760-762 ◽  
pp. 2263-2266
Author(s):  
Kang Yong ◽  
Wei Chen

Beside the residual stresses and axial loads, other factors of pipe like ovality, moment could also bring a significant influence on pipe deformation under external pressure. The Standard of API-5C3 has discussed the influences of deformation caused by yield strength of pipe, pipe diameter and pipe thickness, but the factor of ovality degree is not included. Experiments and numerical simulations show that with the increasing of pipe ovality degree, the anti-deformation capability under external pressure will become lower, and ovality affecting the stability of pipe shape under external pressure is significant. So it could be a path to find out the mechanics relationship between ovality and pipe deformation under external pressure by the methods of numerical simulations and theoretical analysis.


1955 ◽  
Vol 22 (3) ◽  
pp. 355-360
Author(s):  
M. Morduchow ◽  
S. W. Yuan ◽  
H. Reissner

Abstract Based on a simplified model of the hub-fuselage structure, a theoretical analysis is made of the response of the hub and fuselage of a helicopter in flight to harmonic forces transmitted by the rotor blades to the hub both in, and normal to, the plane of rotation. The assumed structure is in the form of a plane framework with masses concentrated at the joints. Simple expressions are derived for the vibration amplitudes of the mass points as functions of the masses and natural frequencies of the hub and the fuselage. The pertinent nondimensional parameters are determined, and simple explicit conditions of resonance are derived. Numerical examples are given to illustrate the results.


2019 ◽  
Vol 35 (2) ◽  
pp. 147-152
Author(s):  
LARISA CHEREGI ◽  
VICUTA NEAGOS ◽  
◽  

We generalize the Pompeiu mean-value theorem by replacing the graph of a continuous function with a compact set.


2021 ◽  
Vol 1 (1) ◽  
pp. 13-20
Author(s):  
Tao Bao ◽  
Mohammed Nabil EL KORSO

The co-centered orthogonal loop and dipole (COLD) array exhibits some interesting properties, which makes it ubiquitous in the context of polarized source localization. In the literature, one can find a plethora of estimation schemes adapted to the COLD array. Nevertheless, their ultimate performance in terms the so-called threshold region of mean square error (MSE), have not been fully investigated. In order to fill this lack, we focus, in this paper, on conditional and unconditional bounds that are tighter than the well known Cramér-Rao Bound (CRB). More precisely, we give some closed form expressions of the McAulay-Hofstetter, the Hammersley-Chapman-Robbins, the McAulaySeidman bounds and the recent Todros-Tabrikian bound, for both the conditional and unconditional observation model. Finally, numerical examples are provided to corroborate the theoretical analysis and to reveal a number of insightful properties.


Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Wei Chen ◽  
Bo Zhou

In this paper, we adapt the fractional derivative approach to formulate the flow-conservation transportation networks, which consider the propagation dynamics and the users’ behaviors in terms of route choices. We then investigate the controllability of the fractional-order transportation networks by employing the Popov-Belevitch-Hautus rank condition and the QR decomposition algorithm. Furthermore, we provide the exact solutions for the full controllability pricing controller location problem, which includes where to locate the controllers and how many controllers are required at the location positions. Finally, we illustrate two numerical examples to validate the theoretical analysis.


2021 ◽  
Vol 13 (2) ◽  
pp. 60
Author(s):  
Yuanyuan Yang ◽  
Gongsheng Li

We set forth a time-fractional logistic model and give an implicit finite difference scheme for solving of the model. The L^2 stability and convergence of the scheme are proved with the aids of discrete Gronwall inequality, and numerical examples are presented to support the theoretical analysis.


2021 ◽  
Author(s):  
N. González Díez ◽  
S. P. C. Belfroid ◽  
T. Iversen Solfeldt ◽  
C. Kristiansen

Abstract Flow-induced pulsations (FLIP) are pressure oscillations generated inside of flexibles used in dry gas applications that can cause unacceptable vibration levels and eventually failure of equipment. Because of the design of inner layer of the flexibles, the carcass, the frequency of the pulsations is high, potentially leading to fatigue failures of adjacent structures in a relatively short time. The traditional carcass is made of a steel strip formed into an interlocked s-shape in a series of preforming and winding steps. To enable bending of the pipe, gaps are present between each winding with a shape that can cause FLIP. The gaps can be reduced, and the profiles optimized, but they will always be able to generate FLIP at a certain gas velocity. To remove the risk of FLIP in dry gas projects and ensure that operator does not get operational constraints, an alternative carcass design has been developed. This is essentially a conventional agraff carcass but with an additional cover strip to close the gap, making the resulting carcass nearly smooth bore in nature. With a smooth bore this carcass can be used for flexibles which have a risk of FLIP or to produce pipes with a lower internal roughness. This alternative design can be manufactured and can therefore build on the large manufacturing and design experience of the traditional strip carcass. This alternative carcass technology is to undergo a full qualification process, in which the risk of flow induced pulsations is an essential component. With the investigated alternative carcass design, the cavities present in the traditional agraff designs are covered. It is expected that the risk due to the appearance of FLIP is therefore eliminated. Theoretical analysis, numerical simulations and scaled experiments are used to explore the risk for the alternative technology to create FLIP. The theoretical analysis is based on existing knowledge and literature. The numerical simulations and scaled tests are done to generate direct evidence for the end statements resulting from the qualification process. Numerical simulations follow the power balance method presented by the same authors in earlier papers. The same applies to the techniques used for the scaled tests. The main outcome of the qualification presented here are the pressure drop performance and the anti-FLIP capabilities of the design. The new design performs significantly better than the nominal design carcass for the same purpose. The pressure drop coefficients found are close to those expected for a normal, non-corrugated pipe, and thus the recommendation given by the API 17J standard does not apply to this design. The pressure drop coefficient is dependent on the installation direction of the flexible with respect to the flow. No signs of FLIP are found for the nominal design of the investigated carcass technology. This is the case for either installation direction. This is explained from a theoretical point of view, but also numerical and experimental evidence are provided.


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