Projects

František Rublík

Project selection:

National projects

ECMeNaM – Efficient computation methods for nanoscale material characterization
Efektívne výpočtové metódy pre charakterizáciu materiálov v nano mierke
Program: SRDA
Duration: 1.7.2022 – 30.6.2025
Project leader: Doc. RNDr. Witkovský Viktor, CSc.
Annotation: The aim of the project is to design and implement effective calculation methods for evaluating the results of measuring the mechanical properties of materials at the nanoscale using instrumented indentation methods (IIT) and atomic force microscopy (AFM). Both of these methods are able to provide highly localized information on the mechanical properties of the material, such as Young\’s modulus of elasticity (both methods), hardness (IIT method), or point-to-surface adhesion (AFM method). The principle is the analysis of the recording of the position of the measuring tip and the force interaction between the tip and the sample surface. The determination of the resulting values on the basis of data recorded by the instrument in both of these methods is based on non-trivial mathematical-statistical methods and calculation procedures working with data subjected to relatively high uncertainty or random noise, where it is also necessary to quantify the uncertainty of the measurement result. Both of these methods work with data of a similar nature, but each has certain specifics. The results obtained for IIT can thus serve as a reference for AFM. The project partners are the Czech Metrology Ins titute (CMI is the national metrology institute of the Czech Republic with top infrastructure in the field), the Institute of Measurement Science SAS (IMS SAS), and the Mathematical Institute SAS (MI SAS), which are academic institutions with extensive experience in basic research and applications of mathematics statistics in the field of measurement and metrology. This combination of partners brings a natural synergy and a combination of the necessary competencies for this
Probability distributions and their applications in modelling and testing
Rozdelenia pravdepodobnosti a ich aplikácie v modelovaní a testovaní
Program: VEGA
Duration: 1.1.2021 – 31.12.2023
Project leader: Doc. RNDr. Witkovský Viktor, CSc.
Annotation: The project is focused on the research of complex problems related to probability distributions and their use in mathematical modeling and tests of statistical hypotheses, where it is necessary to know the distributions of test statistics. A new broad family of probability distributions will be investigated. Many commonly used distributionsare special cases of this family. New approaches to multivariate statistical problems will be developed (an error-in-variables linear model, nonparametric statistical inference about several populations, nonparametric independence tests, detection of causality). A new apparatus of mathematical statistics will be applied to mathematical models in metrology, linguistics, demography, and insurance mathematics.