scholarly journals Mathematical model of crack diagnosis: inverse acoustic scattering problem and its high-precision numerical solution

2019 ◽  
Vol 22 ◽  
pp. 31-35 ◽  
Author(s):  
Victor A. Kovtunenko
2002 ◽  
Vol 10 (03) ◽  
pp. 349-384 ◽  
Author(s):  
FRANCESCA MARIANI ◽  
MARIA CRISTINA RECCHIONI ◽  
FRANCESCO ZIRILLI

In this paper we study a mathematical model to describe a three dimensional acoustic scattering problem associated to a "vibrating" obstacle that is a bounded simply connected domain contained in the three dimensional real Euclidean space whose shape changes in time. In particular we propose a numerical method based on a perturbation series and the operator expansion method to solve the mathematical model considered. This method makes possible to obtain highly parallelizable algorithms able to compute the solution of the problem considered order by order in perturbation theory, and able to obtain the required solution of the scattering problem summing up the perturbation series. Really impressive speed up factors are observed and reported when the algorithm is executed on the Chiba Cluster, a parallel machine of the Argonne National Laboratory, USA. We validate the mathematical model and the numerical method proposed solving some test problems. The quantitative character of the numerical results obtained is established. The results obtained on the test problems are discussed both from the numerical and the physical point of view. In particular we show that the Doppler spectrum associated to the far field patterns of the scattered acoustic fields depends mainly from the incoming wave and from the excited vibrational modes (Figs. 9–13). The website: shows some Applets relative to the numerical examples.


Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 705
Author(s):  
Fatemeh Rasouli ◽  
Kyle B. Reed

Dynamic models, such as double pendulums, can generate similar dynamics as human limbs. They are versatile tools for simulating and analyzing the human walking cycle and performance under various conditions. They include multiple links, hinges, and masses that represent physical parameters of a limb or an assistive device. This study develops a mathematical model of dissimilar double pendulums that mimics human walking with unilateral gait impairment and establishes identical dynamics between asymmetric limbs. It introduces new coefficients that create biomechanical equivalence between two sides of an asymmetric gait. The numerical solution demonstrates that dissimilar double pendulums can have symmetric kinematic and kinetic outcomes. Parallel solutions with different physical parameters but similar biomechanical coefficients enable interchangeable designs that could be incorporated into gait rehabilitation treatments or alternative prosthetic and ambulatory assistive devices.


1975 ◽  
Vol 30 (5) ◽  
pp. 656-671
Author(s):  
W. Bauhoff

AbstractThe mass eigenvalue equation for mesons in nonlinear spinor theory is derived by functional methods. In second order it leads to a spinorial Bethe-Salpeter equation. This is solved by a variational method with high precision for arbitrary angular momentum. The results for scalar mesons show a shift of the first order results, obtained earlier. The agreement with experiment is improved thereby. An excited state corresponding to the η' is found. A calculation of a Regge trajectory is included,too.


2012 ◽  
Vol 184-185 ◽  
pp. 789-792
Author(s):  
Bing Li ◽  
Yu Lan Wei ◽  
Meng Dan Jin ◽  
Ying Ying Fan

Put forward a method that use scatter points which got in different places to measure the involution cylindrical gears, give a mathematical model that use the discrete points to sure the total deviation of gear tooth profile. The experience results show that this way is of high precision in measurement points, measurement an error data processing less intervention, etc.


2013 ◽  
Vol 652-654 ◽  
pp. 2153-2158
Author(s):  
Wu Ji Jiang ◽  
Jing Wei

Controlling the tooth errors induced by the variation of diameter of grinding wheel is the key problem in the process of ZC1 worm grinding. In this paper, the influence of tooth errors by d1, m and z1 as the grinding wheel diameter changes are analyzed based on the mathematical model of the grinding process. A new mathematical model and truing principle for the grinding wheel of ZC1 worm is presented. The shape grinding wheel truing of ZC1 worm is carried out according to the model. The validity and feasibility of the mathematical model is proved by case studies. The mathematical model presented in this paper provides a new method for reducing the tooth errors of ZC1 worm and it can meet the high-performance and high-precision requirements of ZC1 worm grinding.


2001 ◽  
Author(s):  
Som Chattopadhyay

Abstract Positioning accuracy within the range of nanometers is required for high precision machining applications. The implementation of such a range is difficult through the slides because of (a) irregular nature of friction at the slider-guideway interface, and (b) complex motion characteristic at very low speeds. The complexity arises due to the local deformation at the interface prior to breakaway, which is known as microdynamics. In this work prior experimental results exhibiting microdynamics have been appraised, and mathematical model developed to understand this behavior.


Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 244 ◽  
Author(s):  
Vildan Yazıcı ◽  
Zahir Muradoğlu

This study examined the deformation problem of a plate system (formed side-by-side) composed of multi-structure plates. It obtained numerical approaches of the transmission conditions on the common border of plates that composed the system. Numerical examples were solved in different boundary and transmission conditions.


Author(s):  
Petro Martyniuk ◽  
Oksana Ostapchuk ◽  
Vitalii Nalyvaiko

The problem of pollution transfer by water flow in open channel was considered. The mathematical model of the problem was constructed. The numerical solution of the onedimensional boundary problem was obtained. The computational algorithm for solving the problem was programmed to implement. A series of numerical experiments with their further analysis was conducted.


Sensors ◽  
2022 ◽  
Vol 22 (2) ◽  
pp. 646
Author(s):  
Pietro Tedeschi ◽  
Gabriele Oligeri ◽  
Roberto Di Pietro

Jamming is a malicious radio activity that represents a dreadful threat when employed in critical scenarios. Several techniques have been proposed to detect, locate, and mitigate jamming. Similarly, counter-counter-jamming techniques have been devised. This paper belongs to the latter thread. In particular, we propose a new jammer model: a power-modulated jammer that defies standard localization techniques. We provide several contributions: we first define a new mathematical model for the power-modulated jammer and then propose a throughout analysis of the localization error associated with the proposed power-modulated jammer, and we compare it with a standard power-constant jammer. Our results show that a power-modulated jammer can make the localization process completely ineffective—even under conservative assumptions of the shadowing process associated with the radio channel. Indeed, we prove that a constant-power jammer can be localized with high precision, even when coupled with a strong shadowing effect (σ ≈ 6 dBm). On the contrary, our power-modulated jammer, even in the presence of a very weak shadowing effect (σ < 2 dBm), presents a much wider localization error with respect to the constant-power jammer. In addition to being interesting on its own, we believe that our contribution also paves the way for further research in this area.


Sign in / Sign up

Export Citation Format

Share Document