• Research of static magnetic field deformation due to the presence of magnetic nanoparticles using imaging methods based on magnetic resonance principles
• Class of the logarithmic Lambert W x F random variables and their applications
  
• Superconducting model of magnetic impurities in the diamagnetic matrix
  
• New methods of non-destructive volume analysis of rocks and minerals using X-ray microtomography
  

Result 1: Research of static magnetic field deformation due to the presence of magnetic nanoparticles using imaging methods based on magnetic resonance principles

Projects: VEGA 2/0013/14 a APVV-0513-10 (Institute of Measurement Science SAS)

Authors: I. Frollo, O. Štrbák, A. Krafčík, D. Gogola

Magnetic nanoparticles are widely used as a contrast agent in magnetic resonance imaging (MRI). Nanoparticles as contrast agents possess a magnetic moment which generates local inhomogeneities in the static magnetic field of the MR scanner. The goal of this study was to investigate the influence of the arrangement of magnetic nanoparticles on the final image contrast during MRI.

The magnetic field distortions of the near surroundings of the groups of magnetic nanoparticles Fe3O4, which are regarded as small magnetic dipoles were analyzed. The influence of saline and glucose molecules to contrast properties of clinically used MRI contrast agents were investigated. Because in general, circular samples were investigated as objects for imaging based on magnetic resonance, detailed mathematical models were developed. Resultant simulations were experimentally verified. The computer-aided analysis of magnetic nanoparticles deposition caused by magnetic field was carried out.
The methods find applications in research of physiologic and pathologic changes of metabolism in biological objects and could be used mainly in the clinical practice.

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Publications:

Result 2: Class of the logarithmic Lambert W x F random variables and their applications

Projects: APVV-0096-10, VEGA 1/0043/13, VEGA 2/0047/15 (Institute of Measurement Science SAS)

Authors: V. Witkovský (Institute of Measurement Science SAS)

Co-authors: G. Wimmer, T. Duby

We have defined a new class of log-linearly transformed random variables, the class of logarithmic Lambert W x F random variables. We have studied in detail the properties and the probability distribution of these random variables. The class of the log-Lambert W x F random variable is of particular interest, because the Lambert W function (special multivalued mathematical function known as the omega function or product logarithm) allows to calculate the exact probability distribution of the log-linearly transformed random variables with a known distribution F. An important role in this class belongs to be log-linearly transformed random variables with Chi-squared distribution. In particular, the probability distribution of the likelihood ratio test statistic in models with gaussian errors of measurement belongs to this type of probability distributions. In this work we have extensively characterized basic properties of that distribution, including the characteristic function of the distribution and its basic moments. Knowledge of the characteristic function allows to calculate the explicit distribution of linear combinations of such random variables, which is important for determining the critical values of the test statistics in linear models with normal (gaussian) errors.

Result 3: Supravodivý model magnetických prímesí v diamagnetickej matrici

Projects: APVV-0125-11, ASFEU projekt 26240220073 (Kompetenčné centrum pre nové materiály, pokročilé technológie a energetiku), ASFEU projekt 26240120019 (CENTE II).

Authors: A. Cigáň, A. Dvurečenskij, M. Škrátek, M. Majerová, P. Billik, J. Maňka

V oblasti vývoja magnetických nanokvapalín a nanočastíc pre priemyselné a biomedicínske aplikácie, ako je napr. čistenie odpadových vôd od ťažkých kovových iónov, MRI diagnostika, cielený transport liečiv, alebo liečba nádorových ochorení hypertermiou, je potrebné poznať ich magnetické vlastnosti, ktoré predstavujú jednu z ich projektovaných funkcionalít. Posledné je zvlášť významné pre nanočastice malých rozmerov alebo kompozitné nanočastice, skladajúce sa z jadra a viacerých obalových vrstiev, ktoré sú nositeľmi ich multifunkčných vlastností. Z pohľadu magnetických vlastnosti je potrebné riešiť otázku vzájomného ovplyvňovania jadra, jeho povrchovej vrstvy a jednotlivých obalových vrstiev na výsledné vlastnosti nanočastíc a v prípade magnetických nanokvapalín aj vzájomný vplyv kvapalného média, ktoré najčastejšie je diamagnetické a tuhých magnetických nanočastíc. V našich prácach sme študovali vplyv dopovania vysokoteplotného supravodiča Eu-123 ruténiom. Supravodič je model ideálnej diamagnetickej matrice a dopovanie s Ru vedie k tvorbe Ba3EuRu2O9 fázy obsahujúcej magnetické diméry Ru2O9. Získané výsledky naznačujú novú možnú cestu štúdia vzájomného ovplyvňovania sa diamagnetických a magnetických médií s využitím supravodičov a teploty ako kľúča na vypnutie ich diamagnetických vlastností.

Publications:

1. DVUREČENSKIJ, Andrej - CIGÁŇ, Alexander - BYSTRICKÝ, Roman - ŠKRÁTEK, Martin - BILLIK, Peter - MAJEROVÁ, Melinda - MAŇKA, Ján. Magnetic studies of EuBa2Cu3-xRuxO7-δ compounds. In Acta Physica Polonica A, 2015, vol. 127, no. 2, p. 300-302. ISSN 0587-4246. (0.530-IF2014)
2. ŠKRÁTEK, Martin - CIGÁŇ, Alexander - DVUREČENSKIJ, Andrej - MAJEROVÁ, Melinda - BYSTRICKÝ, Roman - BILLIK, Peter - MAŇKA, Ján. Effects of Ru addition on the superconducting properties of the Eu-123 system. In Acta Physica Polonica A, 2015, vol. 127, no. 2, p. 225-227. ISSN 0587-4246. (0.530-IF2014)

Result 4: New methods of non-destructive volume analysis of rocks and minerals using X-ray microtomography

Project: VEGA 2/0126/13 (Institute of Measurement Science SAS)

Author: M. Hain

Microtomographic methods used for non-destructive volume analysis of rocks and minerals in geology and mineralogy were developed and applied. In the frame of the methodology proposal, the microtomographic measurement conditions for these objects were optimized, including choice of optimal accelerating voltage and current of X-ray tube, signal accumulation time, number of repeated measurements, the relaxation time of the detector, choice of material of the targets and the number of X-ray projections. In the subsequent processing and visualization of results of microtomographic measurements, the methodology of 3D visualization of geological microstructures and defects with the application of methods for data filtering, rendering and image segmentation was elaborated. The results were applied in the collaboration with Dr. Ďurmeková and Dr. Ružička from the Faculty of Natural Sciences, Comenius University at the microtomographic analysis of a series of marble samples exposed to prolonged exposure of adverse chemical and physical agents.

Publication:

1. DURMEKOVÁ, T. - RUŽIČKA, P. - HAIN, Miroslav - ČAPLOVIČOVÁ, M. Changes in marble quality after sodium sulphate crystallization and long-lasting freeze-thaw testing. In Engineering Geology for Society and Territory - Volume 5 : Urban Geology, Sustainable Planning and Landscape Exploitation. Springer, 2015. ISBN 978-3-319-09047-4, p. 237-241.