Chaotic Behaviour of Active Magnetic Bearing System by Time Series Analysis

Chaotic behaviour is one of the hardest problems that can happen in nonlinear dynamical systems with severe nonlinearities. It makes the system's responses unpredictable. It makes the system's responses to behave similar to noise. In some applications it should be avoided. One of the approaches to detect the chaotic behaviour is nding the Lyapunov exponent through examining the dynamical equation of the system. It needs a model of the system. The goal of this study is the diagnosis of chaotic behaviour by just exploring the data (signal) without using any dynamical model of the system. In this work two methods are tested on the time series data collected from AMB (Active Magnetic Bearing) system sensors. The rst method is used to nd the largest Lyapunov exponent by Rosenstein method. The second method is a 0-1 test for identifying chaotic behaviour. These two methods are used to detect if the data is chaotic. By using Rosenstein method it is needed to nd the minimum embedding dimension. To nd the minimum embedding dimension Cao method is used. Cao method does not give just the minimum embedding dimension, it also gives the order of the nonlinear dynamical equation of the system and also it shows how the system's signals are corrupted with noise. At the end of this research a test called runs test is introduced to show that the data is not excessively noisy.

Structure-related magnetic fabric studies : implications for deformed and undeformed Precambrian rocks

The aim of this thesis research was to gain a better understanding of the emplacement of rapakivi granite intrusions, as well as the emplacement of gold-bearing hydrothermal fluids in structurally controlled mineralizations. Based on investigations of the magnetic fabric, the internal structures could be analysed and the intrusion mechanisms for rapakivi granite intrusions and respectively different deformation stages within gold-bearing shear and fault zones identified. Aeromagnetic images revealed circular structures within the rapakivi granite batholiths of Wiborg, Vehmaa and Åland. These circular structures represent intrusions that eventually build up these large batholiths. The rapakivi granite intrusions of Vehmaa, Ruotsinpyhtää within the Wiborg batholith and Saltvik intrusions within the Åland batholith all show bimodal magnetic susceptibilities with paramagnetic and ferromagnetic components. The distribution of the bimodality is related to different magma batches of the studied intrusions. The anisotropy of magnetic susceptibility (AMS) reveals internal structures that cannot be studied macroscopically or by microscope. The Ruotsinpyhtää and Vehmaa intrusions represent similar intrusion geometries, with gently to moderately outward dipping magnetic foliations. In the case of Vehmaa, the magnetic lineations are gently plunging and trend in the directions of the slightly elongated intrusion. The magnetic lineations represent magma flow. The shapes of the AMS ellipsoids are also more planar (oblate) in the central part of the intrusion, whereas they become more linear (prolate) near the margin. These AMS results, together with field observations, indicate that the main intrusion mechanism has involved the subsidence of older blocks with successive intrusion of fractionated magma during repeated cauldron subsidence. The Saltvik area within the Åland batholith consists of a number of smaller elliptical intrusions of different rapakivi types forming a multiple intrusive complex. The magnetic fabric shows a general westward dipping of the pyterlite and eastward dipping of the contiguous even-grained rapakivi granite, which indicates a central inflow of magma batches towards the east and west resulting from a laccolitic emplacement of magma batches, while the main mechanism for space creation was derived from subsidence. The magnetic fabric of structurally controlled gold potential shear and fault zones in Jokisivu, Satulinmäki and Koijärvi was investigated in order to describe the internal structures and define the deformation history and emplacement of hydrothermal fluids. A further aim of the research was to combine AMS studies with palaeomagnetic methods to constrain the timing for the shearing event relative to the precipitation of ferromagnetic minerals and gold. All of the studied formations are dominated by monoclinic pyrrhotite. The AMS directions generally follow the tectonic structures within the formations. However, internal variations in the AMS direction as well as the shapes of the AMS ellipsoids are observed within the shear zones. In Jokisivu and Satulinmäki in particular, the magnetic signatures of the shear zone core differ from the margins. Furthermore, the shape of the magnetic fabric in the shear zone core of Jokisivu is dominated by oblate shapes, whereas the margins exhibit prolate shapes. These variations indicate a later effect of the hydrothermal fluids on the general shear event. The palaeo-magnetic results reveal a deflection from the original Svecofennian age geomagnetic direction. These results, coupled with correlations between the orientation of the NRM vectors and the magnetic and rock fabrics, imply that the gold-rich hydrothermal fluids were emplaced pre/syntectonically during the late stages of the Svecofennian orogeny.

Mechanical design and analysis of modular active magnetic bearing test rig

Tässä työssä on tutkittu modulaarisen aktiivimagneettilaakeroidun koelaitteen mekaanista suunnittelua ja analysointia. Suurnopeusroottorin suunnittelun teoria on esitelty. Lisäksi monia analyyttisiä mallinnusmenetelmiä mekaanisten kuormitusten mallintamiseksi on esitelty. Koska kyseessä on suurnopeussähkökone, roottoridynamiikka ja sen soveltuvuus suunnittelussa on esitelty. Magneettilaakerien rakenteeseen ja toimintaan on tutustuttu osana tätä työtä. Kirjallisuuskatsaus nykyisistä koelaitteista esimerkiksi komponenttien ominaisuuksien tunnistamiseen ja roottoridynamiikan tutkimuksiin on esitelty. Työn rajauksena on konseptisuunnittelu muunneltavalle magneettilaakeroidulle (AMB) koelaitteelle ja suunnitteluprosessin dokumentointi. Muunneltavuuteen päädyttiin, koska se mahdollistaa erilaisten komponenttiasetteluiden testaamisen erilaisille magneettilaakerikokoonpanoille ja roottoreille. Pääpaino tässä työssä on suurnopeus induktiokoneen roottorin suunnittelussa ja mallintamisessa. Modulaaristen toimilaitteiden kuten magneettilaakerien ja induktiosähkömoottorin rakenne on esitelty ja modulaarisen rakenteen käytettävyyden hyödyistä koelaitekäytössä on dokumentoitu. Analyyttisiä ja elementtimenetelmään perustuvia tutkimusmenetelmiä on käytetty tutkittaessa suunniteltua suurnopeusroottoria. Suunnittelun ja analysoinnin tulokset on esitelty ja verrattu keskenään eri mallinnusmenetelmien välillä. Lisäksi johtopäätökset sähkömagneettisten osien liittämisen monimutkaisuudesta ja vaatimuksista roottoriin ja toimilaitteisiin sekä mekaanisten että sähkömagneettisten ominaisuuksien optimoimiseksi on dokumentoitu.

Brain tissue segmentation using q-entropy in multiple sclerosis magnetic resonance images

The loss of brain volume has been used as a marker of tissue destruction and can be used as an index of the progression of neurodegenerative diseases, such as multiple sclerosis. In the present study, we tested a new method for tissue segmentation based on pixel intensity threshold using generalized Tsallis entropy to determine a statistical segmentation parameter for each single class of brain tissue. We compared the performance of this method using a range of different q parameters and found a different optimal q parameter for white matter, gray matter, and cerebrospinal fluid. Our results support the conclusion that the differences in structural correlations and scale invariant similarities present in each tissue class can be accessed by generalized Tsallis entropy, obtaining the intensity limits for these tissue class separations. In order to test this method, we used it for analysis of brain magnetic resonance images of 43 patients and 10 healthy controls matched for gender and age. The values found for the entropic q index were 0.2 for cerebrospinal fluid, 0.1 for white matter and 1.5 for gray matter. With this algorithm, we could detect an annual loss of 0.98% for the patients, in agreement with literature data. Thus, we can conclude that the entropy of Tsallis adds advantages to the process of automatic target segmentation of tissue classes, which had not been demonstrated previously.

Calculation of the magnetic field penetration depth for high-Tc cuprate superconductors based on the Interlayer Pair Tunneling model /

In this work, the magnetic field penetration depth for high-Tc cuprate superconductors is calculated using a recent Interlayer Pair Tunneling (ILPT) model proposed by Chakravarty, Sudb0, Anderson, and Strong [1] to explain high temperature superconductivity. This model involves a "hopping" of Cooper pairs between layers of the unit cell which acts to amplify the pairing mechanism within the planes themselves. Recent work has shown that this model can account reasonably well for the isotope effect and the dependence of Tc on nonmagnetic in-plane impurities [2] , as well as the Knight shift curves [3] and the presence of a magnetic peak in the neutron scattering intensity [4]. In the latter case, Yin et al. emphasize that the pair tunneling must be the dominant pairing mechanism in the high-Tc cuprates in order to capture the features found in experiments. The goal of this work is to determine whether or not the ILPT model can account for the experimental observations of the magnetic field penetration depth in YBa2Cu307_a7. Calculations are performed in the weak and strong coupling limits, and the efi"ects of both small and large strengths of interlayer pair tunneling are investigated. Furthermore, as a follow up to the penetration depth calculations, both the neutron scattering intensity and the Knight shift are calculated within the ILPT formalism. The aim is to determine if the ILPT model can yield results consistent with experiments performed for these properties. The results for all three thermodynamic properties considered are not consistent with the notion that the interlayer pair tunneling must be the dominate pairing mechanism in these high-Tc cuprate superconductors. Instead, it is found that reasonable agreement with experiments is obtained for small strengths of pair tunneling, and that large pair tunneling yields results which do not resemble those of the experiments.

Polytypism and Silicon carbide : a solid state nuclear magnetic resonance study

A survey of predominantly industrial silicon carbide has been carried out using Magic Angle Spinning nuclear magnetic resonance (MAS nmr); a solid state technique. Three silicon carbide polytypes were studied; 3C, 6H, and 15R. The 13C and 29 Si MAS nmr spectra of the bulk SiC sample was identified on the basis of silicon (carbon) site type in the d iff ere n t pol Y t Y pes • Out to 5.00 A fro mac en t r a lsi 1 i con (0 r carbon) atom four types of sites were characterized using symmetry based calculations. This method of polytype analysis was also considered, in the prelminary stages, for applications with other polytypic material; CdBr 2 , CdI 2 , and PbI 2 " In an attempt to understand the minor components of silicon carbide, such as its surface, some samples were hydrofluoric acid washed and heated to extreme temperatures. Basically, an HF removable species which absorbs at -110 ppm (Si0 2 ) in the 29 Si MAS nmr spectrum is found in silicon carbide after heating. Other unidentified peaks observed at short recycle delays in some 29 Si MAS nmr spectra are considered to be impurities that may be within the lattice. These components comprise less than 5% of the observable silicon. A Tl study was carried out for 29 Si nuclei in a 3C ii polytype sample, using the Driven Equilibrium Single-Pulse Observation of T1 (DESPOT) technique. It appears as though there are a number of nuclei that have the same chemical shift but different T1 relaxation times. The T1 values range from 30 seconds to 11 minutes. Caution has to be kept when interpreting these results because this is the first time that DESPOT has been used for solid samples and it is not likely in full working order. MAS nmr indicates that the 13C and 29 Si ~sotropic chemical shifts of silicon carbide appear to have a reciprocal type of relationship_ Single crystal nmr analysis of a 6H sample is accordance with this finding when only the resultant isotropic shift is considered. However, single crystal nmr also shows that the actual response of the silicon and carbon nuclear environment to the applied magnetic field at various angles is not at all reciprocal. Such results show that much more single crystal nmr work is required to determine the actual behavior of the local magnetic environment of the SiC nuclei.

Simultaneous extraction of order parameters and orientational distribution fuctions from 31[superscript]P NMR spectra of magnetically partially oriented phospholipid bilayers

Order parameter profiles extracted from the NMR spectra of model membranes are a valuable source of information about their structure and molecular motions. To al1alyze powder spectra the de-Pake-ing (numerical deconvolution) ~echnique can be used, but it assumes a random (spherical) dist.ribution of orientations in the sample. Multilamellar vesicles are known to deform and orient in the strong magnetic fields of NMR magnets, producing non-spherical orientation distributions. A recently developed technique for simultaneously extracting the anisotropies of the system as well as the orientation distributions is applied to the analysis of partially magnetically oriented 31p NMR spectra of phospholipids. A mixture of synthetic lipids, POPE and POPG, is analyzed to measure distortion of multilamellar vesicles in a magnetic field. In the analysis three models describing the shape of the distorted vesicles are examined. Ellipsoids of rotation with a semiaxis ratio of about 1.14 are found to provide a good approximation of the shape of the distorted vesicles. This is in reasonable agreement with published experimental work. All three models yield clearly non-spherical orientational distributions, as well as a precise measure of the anisotropy of the chemical shift. Noise in the experimental data prevented the analysis from concluding which of the three models is the best approximation. A discretization scheme for finding stability in the algorithm is outlined

Magnetic field-induced cluster formation and variation of magneto-optical signals in zinc-substituted ferrofluids

Fine magnetic particles (size≅100 Å) belonging to the series ZnxFe1−xFe2O4 were synthesized by cold co-precipitation methods and their structural properties were evaluated using X-ray diffraction. Magnetization studies have been carried out using vibrating sample magnetometry (VSM) showing near-zero loss loop characteristics. Ferrofluids were then prepared employing these fine magnetic powders using oleic acid as surfactant and kerosene as carrier liquid by modifying the usually reported synthesis technique in order to induce anisotropy and enhance the magneto-optical signals. Liquid thin films of these fluids were prepared and field-induced laser transmission through these films was studied. The transmitted light intensity decreases at the centre with applied magnetic field in a linear fashion when subjected to low magnetic fields and saturate at higher fields. This is in accordance with the saturation in cluster formation. The pattern exhibited by these films in the presence of different magnetic fields was observed with the help of a CCD camera and was recorded photographically.

Magnetic phase separation in ordered alloys

We present a lattice model to study the equilibrium phase diagram of ordered alloys with one magnetic component that exhibits a low temperature phase separation between paramagnetic and ferromagnetic phases. The model is constructed from the experimental facts observed in Cu3-xAlMnx and it includes coupling between configurational and magnetic degrees of freedom that are appropriate for reproducing the low temperature miscibility gap. The essential ingredient for the occurrence of such a coexistence region is the development of ferromagnetic order induced by the long-range atomic order of the magnetic component. A comparative study of both mean-field and Monte Carlo solutions is presented. Moreover, the model may enable the study of the structure of ferromagnetic domains embedded in the nonmagnetic matrix. This is relevant in relation to phenomena such as magnetoresistance and paramagnetism

Elastic constants of Ni-Mn-Ga magnetic shape memory alloys

We have measured the adiabatic second order elastic constants of two Ni-Mn-Ga magnetic shape memory crystals with different martensitic transition temperatures, using ultrasonic methods. The temperature dependence of the elastic constants has been followed across the ferromagnetic transition and down to the martensitic transition temperature. Within experimental errors no noticeable change in any of the elastic constants has been observed at the Curie point. The temperature dependence of the shear elastic constant C' has been found to be very different for the two alloys. Such a different behavior is in agreement with recent theoretical predictions for systems undergoing multi-stage structural transitions.

Magnetic superelasticity and inverse magnetocaloric effect in Ni-Mn-In

Applying a magnetic field to a ferromagnetic Ni50Mn34In16 alloy in the martensitic state induces a structural phase transition to the austenitic state. This is accompanied by a strain which recovers on removing the magnetic field, giving the system a magnetically superelastic character. A further property of this alloy is that it also shows the inverse magnetocaloric effect. The magnetic superelasticity and the inverse magnetocaloric effect in Ni-Mn-In and their association with the first-order structural transition are studied by magnetization, strain, and neutron-diffraction studies under magnetic field.

Cooling and heating by adiabatic magnetization in Ni50Mn34In16 magnetic shape-memory alloy

We report on measurements of the adiabatic temperature change in the inverse magnetocaloric Ni50Mn34In16 alloy. It is shown that this alloy heats up with the application of a magnetic field around the Curie point due to the conventional magnetocaloric effect. In contrast, the inverse magnetocaloric effect associated with the martensitic transition results in the unusual decrease of temperature by adiabatic magnetization. We also provide magnetization and specific heat data which enable to compare the measured temperature changes to the values indirectly computed from thermodynamic relationships. Good agreement is obtained for the conventional effect at the second-order paramagnetic-ferromagnetic phase transition. However, at the first-order structural transition the measured values at high fields are lower than the computed ones. Irreversible thermodynamics arguments are given to show that such a discrepancy is due to the irreversibility of the first-order martensitic transition.

Evidence of extended orientational order in amorphous Fe/Sm thin films

Amorphous thin films of Fe/Sm, prepared by evaporation methods, have been magnetically characterized and the results were interpreted in terms of the random magnets theory. The samples behave as 2D and 3D random magnets depending on the total thickness of the film. From our data the existence of orientational order, which greatly influences the magnetic behavior of the films, is also clear.

Observation of phonon-induced magnetic deflagration in manganites

Very fast magnetic avalanches in (La, Pr)-based manganites are the signature of a phase transition from an insulating blocked charge-ordered antiferromagnetic state to a charge-delocalized ferromagnetic (CD-FM) state. We report here the experimental observation that this transition does not occur either simultaneously or randomly in the whole sample but there is instead a spatial propagation with a velocity of the order of tens of m/s. Our results show that avalanches originate from the inside of the sample, move to the outside, and occur at values of the applied magnetic field that depend on the CD-FM fraction in the sample. Moreover, upon application of surface acoustic waves at constant magnetic fields, we are able to trigger avalanches at very well-determined values of the temperature and magnetic field. Due to the interaction with the acoustic waves, the number of isolated ferromagnetic clusters in La0.225Pr0.40Ca0.375MnO3 starts to grow across the entire sample in the same way as if it were a magnetic deflagration.