scholarly journals Dynamic Susceptibility of Ferrofluids: The Numerical Algorithm for the Inverse Problem of Magnetic Granulometry

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2450
Author(s):  
Alexey O. Ivanov ◽  
Vladimir S. Zverev
Keyword(s):  
Inverse Problem ◽  
Numerical Algorithm ◽  
Magnetic Moments ◽  
Computer Experiments ◽  
Dynamic Susceptibility ◽  
Mathematical Methods ◽  
Frequency Spectra ◽  
Experimental Data Processing ◽  
Direct Measurements ◽  
Dynamic Magnetic Susceptibility

The size-dependent properties of magnetic nanoparticles (MNP) are the major characteristics, determining MNP application in modern technologies and bio-medical techniques. Direct measurements of the nanosized particles, involved in intensive Brownian motion, are very complicated; so the correct mathematical methods for the experimental data processing enable to successfully predict the properties of MNP suspensions. In the present paper, we describe the fast numerical algorithm allowing to get the distribution over the relaxation time of MNP magnetic moments in ferrofluids. The algorithm is based on numerical fitting of the experimentally measured frequency spectra of the initial dynamic magnetic susceptibility. The efficiency of the algorithm in the solution of the inverse problem of magnetic granulometry is substantiated by the computer experiments for mono- and bi-fractional ferrofluids.

scholarly journals Application of the topological sensitivity method to the reconstruction of plasma equilibrium domain in a tokamak

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohamed Abdelwahed ◽  
Nejmeddine Chorfi ◽  
Maatoug Hassine ◽  
Imen Kallel
Keyword(s):  
Inverse Problem ◽  
Asymptotic Expansion ◽  
Numerical Algorithm ◽  
Shape Function ◽  
Optimization Technique ◽  
Plasma Equilibrium ◽  
Topological Sensitivity ◽  
Sensitivity Method

AbstractThe topological sensitivity method is an optimization technique used in different inverse problem solutions. In this work, we adapt this method to the identification of plasma domain in a Tokamak. An asymptotic expansion of a considered shape function is established and used to solve this inverse problem. Finally, a numerical algorithm is developed and tested in different configurations.

scholarly journals Difference between Brownian and Néel relaxation mechanisms in a magnetizing field

2021 ◽  
pp. 14-20
Author(s):  
Alexander V. Lebedev ◽  
Keyword(s):  
Relaxation Time ◽  
Oleic Acid ◽  
High Frequency ◽  
Cobalt Ferrite ◽  
Magnetic Moments ◽  
Relaxation Mechanism ◽  
Dynamic Susceptibility ◽  
Magnetite Particles ◽  
Magnetizing Field ◽  
Néel Relaxation

Measurements of the dynamic susceptibility of a magnetic fluid based on cobalt ferrite particles stabilized in water by a double surfactant layer have been carried out. Cobalt ferrite, in comparison with magnetite, has a significantly higher energy of magnetic anisotropy. Therefore, for particles of cobalt ferrite, the Brownian mechanism of relaxation of magnetic moments is characteristic. The Debye (with a finite relaxation time) contribution to the dynamic susceptibility and the high-frequency (dispersionless) contribution are distinguished by constructing Cole-Cole diagrams. It was found that with an increase in the magnetizing field, the Debye contribution to the dynamic susceptibility decreases, while the high-frequency one (having a zero relaxation time) remains unchanged. The indicated property of the dynamic susceptibility of a fluid with a Brownian relaxation mechanism is radically different from the properties of the susceptibility of a fluid with Néel particles. Previously, measurements were made of the susceptibility of a fluid based on magnetite particles stabilized with oleic acid in kerosene. The magnetite particles have significantly lower anisotropy energy and are characterized by the predominance of the Néel relaxation mechanism. Turning on the magnetizing field caused a decrease in both the Debye part of the susceptibility and the high-frequency part of the susceptibility of magnetite particles.

A Novel Approach to Evaluation of Vibration Source Separation Based on Spatial Distribution of Sensors and Fourier Transforms

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Ali Mahvash ◽  
Aouni A. Lakis
Keyword(s):  
Spatial Distribution ◽  
Fourier Transforms ◽  
A Priori ◽  
Source Separation ◽  
Experimental Tests ◽  
Spatial Distance ◽  
Vibration Source ◽  
Mathematical Methods ◽  
Frequency Spectra ◽  
Multiple Sensors

An obstacle in diagnosis of multicomponent machinery using multiple sensors to acquire vibration data is firstly found in the data acquisition itself. This is due to the fact that vibration signals collected by each sensor are a mixture of vibration produced by different components and noise; it is not evident what signals are produced by each component. A number of research studies have been carried out in which this problem was considered a blind source separation (BSS) problem and different mathematical methods were used to separate the signals. One complexity with applying such mathematical methods to separate vibration sources is that no metric or standard measure exists to evaluate the quality of the separation. In this study, a method based on statistical energy analysis (SEA) is proposed using Fourier transforms and the spatial distance between sensors and components. The principle of this method is based on the fact that each sensor, with respect to its location in the system, collects a different version of the vibration produced in the system. By applying a short time Fourier transform to the signals collected by multiple sensors and making use of a priori knowledge of the spatial distribution of sensor locations with respect to the components, the source of the peaks on the frequency spectra of the signals can be identified and attributed to the components. The performance of the method was verified using a series of experimental tests on synthetic signals and real laboratory signals collected from different bearings and the results confirmed the efficacy of the method.

scholarly journals Incorrect inverse problem conected with the parameter identification of the heat and mass transfer models

2002 ◽  
Vol 6 (1) ◽  
pp. 23-28 ◽  
Author(s):  
Christo Boyadjiev
Keyword(s):  
Mass Transfer ◽  
Inverse Problem ◽  
Parameter Identification ◽  
Heat And Mass Transfer ◽  
Numerical Algorithm ◽  
Problem Solution ◽  
Iterative Regularization ◽  
Inverse Problem Solution ◽  
Transfer Models

A method for inverse problem solution by means of iterative regularization has been developed. A numerical algorithm for solving inverse incorrect problems based on the developed iterative regularization has been proposed.

About one numerical algorithm for the solution of the inverse problem with respect to potential

2018 ◽  
Vol 18 (4) ◽  
pp. 1035-1041
Author(s):  
Nargiz. Huseynova ◽  
Malahat Orujova ◽  
Nargiz Safarova ◽  
Nazile Hajiyeva
Keyword(s):  
Inverse Problem ◽  
Numerical Algorithm

Automatic quality detection system for structural objects using dynamic output method: Case study Vilnius bridges

2021 ◽  
pp. 147592172110615
Author(s):  
Vytautas Bucinskas ◽  
Andrius Dzedzickis ◽  
Nikolaj Sesok ◽  
Igor Iljin ◽  
Ernestas Sutinys ◽  
...  
Keyword(s):  
Resonant Frequency ◽  
Data Processing ◽  
Health Monitoring ◽  
Spectrum Analysis ◽  
Detection System ◽  
Detection Algorithm ◽  
Fast Fourier Transformation ◽  
Frequency Spectra ◽  
Similar Frequency ◽  
Experimental Data Processing

Paper provides an attempt to create a methodology for automated structure health monitoring procedures using vibration spectrum analysis. There is an option to use autoregressive (AR) spectral analysis to extract information from frequency spectra when conventional Fast Fourier transformation (FFT) analysis cannot give relevant information. An autoregressive spectrum analysis is widely used in optics and medicine; however, it can be applied for different purposes, such as spectra analysis in electronics or mechanical vibration. This paper presents an automated structural health monitoring approach based on the algorithm-driven definition of the first resonant frequency value from a noisy signal, acquired from traffic-created bridge vibrations. We implemented the AR procedure and developed a peak detection algorithm for experimental data processing. The functionality of the proposed methodology was evaluated by performing research on six bridges in Vilnius (Lithuania). We compared three methods of data processing: FFT, filtered FFT and AR. Bridges vibrations under different excitation conditions (wind, impulse and traffic) in normal direction were measured using accelerometers. AR provided one peak representing the lowest resonant frequency in all cases, while FFT and filtered FFT provided up to 12 peaks with similar frequency values. Such results allow implementing our method for remote automated structures health monitoring and ensure structures safety using a convenient and straightforward diagnostic method.

scholarly journals A numerical algorithm for solving the inverse problem of determining the low permeability zone

2016 ◽  
Vol 84 (4) ◽  
pp. 124-130
Author(s):  
M.A. Sultanov ◽  
◽  
G.B. Bakanov ◽  
I.E. Svetov ◽  
B.B. Ustemirova ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Numerical Algorithm ◽  
Low Permeability

The inverse problem for the vibrating beam

1984 ◽  
Vol 393 (1805) ◽  
pp. 277-295 ◽  
Keyword(s):  
Inverse Problem ◽  
Sufficient Conditions ◽  
Actual System ◽  
Frequency Spectra ◽  
System Parameters ◽  
Rigid Rods ◽  
The Right ◽  
Necessary And Sufficient ◽  
Resonant And Antiresonant Frequencies

The beam is modelled by a system of rigid rods joined together by rotational springs and with masses at the joints. The left end is clamped while the right end is subject to one of a number of conditions: it is free, pinned, sliding or clamped. It is shown that the resonant and antiresonant frequencies of the system may be almost completely ordered. Necessary and sufficient conditions are found that these frequencies must satisfy to correspond to an actual system, with positive parameters, and two stripping procedures are devised for the determination of these system parameters, from a knowledge of certain frequency spectra.

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