Applied Mathematics and Stochastics (GAMS)

Aplikovane ms metody Ing 02 GAMS - Group of Applied Mathematics and Stochastics is involved in studies of physical, biological and social systems, methods of mathematical statistics, mathematical analysis and theory of probability, in particular statistical analysis of data, formulation of theoretical transport models and searching for relevant analytical solutions, mathematical methods in defectoscopy, probabilistic estimates of limited social areas, study of so called Φ-divergence, mathematical models of pedestrian movement, panic models and others.

Methods of Algebra and Functional Analysis in Applications (MAFIA)

Aplikovana algebra a analyza Ing 03 The MAFIA team of the Department of Mathematics does research in mathematical physics and is focused mainly on problems of interest both in terms of mathematics and physics. The main research topics include: Lie and Hopf algebras, Hilbert space linear operators, integrable systems, solvable models of quantum physics, time-dependent systems, or perturbative methods in both classical and quantum mechanics.

An example of one of the group’s excellent results is available here.


Mathematic Modelling (MMG)

The activities of the MMGroup at the Department of Mathematics are devoted to the development of advanced methods in scientific computing, mathematical modelling and numerical simulation of complex phenomena in high-tech design, protection of the environment and computer science. The group is active in research and development as well as training promising young experts in mathematical engineering. The group has entered worldwide cooperation with universities and institutes as well as industrial enterprises.

Theoretical Information Technology Group (TIGR)

Activities of the Theoretical Information Technology Group at the Department of Mathematics are concerned with current topics of discrete mathematics applied to information technology and physics, such as non-standard representation of real numbers, combinatorics on words, and aperiodic tilings of space. Currently, the focus is on combinatorial issues as well as algebra and number theory with applications in theoretical information technology.

Physics of Heavy Ion Collisions

During the nucleus-nucleus collisions the intention of the team is to create the state of matter at the particular moment of the so called Big Bang, when what is known as quark-gluon plasma is predicted to have appeared. In this area, the behaviour of nuclear matter is studied during and immediately after the collision of two nuclei, accompanied by a broad range of effects and phenomena, which are to be correctly described in a theoretical way. Another research team of the Department of Physics deals with issues of particles production and their interaction with dense and hot nuclear matter within the STAR experiments at Brookhaven National Laboratory in the USA, ALICE at the LHC accelerator in CERN, Genève, and CBM FAIR Darmstadt.

Elementary Particles Physics

The Department of Physics is actively engaged in the study of elementary particles production and their properties during collisions of protons (antiprotons) in the ATLAS experiment using the LHC accelerator in CERN, Geneva, and D0 using the Tevatron accelerator at Fermilab, USA. Collisions of protons create many particles known already from the previous decades. However, the new processes express themselves by extraordinary phenomena, such as the production of very short-lived heavy particles. We at the department are also involved in the development and testing of detectors for experiments as well as in data analysis and processing.

The Department of Dosimetry and Application of Ionizing Radiation continues to cooperate on experiments in the Fermilab laboratories (Chicago, USA), and CERN (Geneva, Switzerland). Currently, the focus is on neutrinos studies within the NOvA experiment, which is a two-detector experiment designed mainly for research into neutrino oscillations. The D0, DIRAC and COMPASS experiments are another field of interest for the department. The department members participate in testing parts of detectors, in data collection, their processing and their physical analysis.

Quantum Mechanics

The Department of Physics members study the use of symmetries in analytical and numerical solutions of differential equations or in the design of models in string theory. They also study related areas of differential geometry and algebra, i.e. mainly the structure and applications of Lie groups and their algebras and classify various special classes of Lie algebras, study them and use them in applications, for example, for the design of special functions or study of models in string theory. They search for symmetry groups of interesting differential equations and use them also for their solution. Conversely, they construct equations with selected symmetries and investigate their common properties. Using the symmetries of simple Lie algebras, the department members study properties of symmetrical functions of several more variables and related orthogonal polynomials, formulate their discrete Fourier analysis and test applications within digital data processing.

Quantum Information and Communication

Quantum theory has led to surprising applications in information transmission and processing. The Department of Physics also focuses research on various processes of quantum information, such as quantum walks, quantum optics, quantum teleportation, or quantum cryptography and their role within information processing.

An example of one of the group’s excellent results is available here.

Physics and Technology of Thermonuclear Fusion

The Group of Physics and Technology of Thermonuclear Fusion is involved in coordinated fusion research at the Czech tokamak COMPASS and at the common European tokamak JET. This research is directly related to the planned research topics of the international experimental reactor ITER that is currently under construction. The tokamak GOLEM is obtaining a part of the coordinated research. in addition to the educational activities, we are involved in high-temperature superconductors in real tokamak environment, study of retention time the radiofrequency plasma induced by electromagnetic wave in magnetic field and mapping the poloidal asymmetry of plasma flow measured by Mach probes. The unique configuration of power coils and iron core of the GOLEM tokamak is used for testing and development of 3D models of ferromagnetic materials for characterisation of distribution change of the outer magnetic field near the unsaturated (or partially saturated) ferromagnetic materials. In the area of computer simulations, we are involved in the study of plasma interaction with electromagnetic wave complexes and issues of so called runaway electrons.

Solid State Lasers

Since 1964, the group of Solid State Lasers at the Department of Physical Electronic is involved in research into Solid State Lasers based on crystalline, glass, ceramic and fibre materials. Work is focused on research into and development of special laser systems generating radiation in visible, near and middle infra-red areas and research into short and ultra-short impulses and on characterisation of generated radiation at the level of the state-of-the-art knowledge of laser instrumentation and electronics. We are also involved in applications of laser radiation in medicine, sensor technology and in transfer of high-power laser radiation by special optic fibres. The group cooperates with ELI and HiLASE projects as well as with many foreign institutions.

Optical Physics

The group of optical physics at the Department of Physical Electronic is involved in the study of optical micro and nanostructures, their design and analysis, methods of realisation and selected applications. In the area of design and analysis; in addition to the synthetic diffraction elements and holograms, we are also pursuing, broad spectrum of photonic structures such as photonic crystals, metamaterials, plasmonic structures and substrates and other periodic or quazi-periodic optical systems. We are trying to create and develop various models and algorithms for numerical analysis, design and optimisation of these elements. In the experimental area, we have been involved for a long time in a broad spectrum of methods and techniques for the realisation of optical micro and nanostructures, mainly laser and electron lithography, interference lithography and related techniques. We use and study also methods for preparation of nanoparticles and their constitution into periodic systems. We solve applications of above mentioned micro-structures in areas such as shaping the optical beams, optical communications, optical micromanipulation, various forms of optical sensors, medical applications and others. For a long time, the group has also been involved in the field of holography and in the research into optical recording materials.

Computational Physics

Under the auspices of the Computational Physics group at the Department of the Physical Electronic physical processes are modelled and methods for the solution of partial differential equations are developed. Numerical methods developed are applied mainly in the fluid simulations of laser radiation interactions with targets. Using the particle simulations, we study interactions of ultra-short intensive laser pulses with matter. Numerical simulations are used for design and interpretation of experiments. We closely cooperate with ELI-Beamlines, and HiLASE projects, and with laboratory PALS and foreign workplaces (Los Alamos National Laboratory, USA; CELIA, Univ. Bordeaux, Francie; Utsunomiya Univ., Japan). The group also operates the femtosecond laser laboratory at the DPE.

An example of one of the group’s excellent results is available here.

Molecular Physics and Spectroscopy

The group of Molecular Physics and Spectroscopy at the Department of Physical Electronic is involved in the study of photo-induced processes in organic molecules, which include, for example, photoluminescence or photoinduced transfer of electron or electron excitation energy, and the influence on them of intensively localised electromagnetic field near plasmonic structures. These processes are the foundation of organic optoelectronics, photovoltaic or artificial photosynthesis. For clarification of their mechanism a synthesis of specifically designed polychromophoric compounds is used as well as spectroscopy (static as well as with time resolution) and quantum chemistry calculations.

X-Ray Photonics

The group of X-Ray photonics at the Department of Physical Electronic is involved in the study of generation and interaction of electromagnetic radiation in the energy range of photons from 50 eV to 420 keV. Specific attention is given to the range of 90 – 120 nm (applications in EUV lithography), the whole range of 200 – 2000 eV (satellite radio telescopes for astrophysics and in microscopy in the area of so called water window) and the range of 5 – 400 keV (X-Ray radiography and tomography). The group has the sources based on electron beam (XRT), capillary plasma source developed at the department (DPP) and the plasma source based on femtosecond laser interaction with solid state or gaseous target (LPP, HHG). The studies are focused on different X-ray optical systems and methods for displaying absorption, phase and diffuse radiation in the EUV / SXR / XR area for microscopy and diagnostics of high temperature plasmas.

Advanced Space Technologies

The group of Advanced Space Technologies at the Department of Physical Electronic is involved in development of measurement technologies for the detection of optical pulses and very accurate measurements of time and their applications in space science. The group is also involved in development and testing of methods for processing of signal from measurement and separation of useful signal from noise. The main area of development is focused on unique detectors of individual photons, fast electronic optical switches and time measuring instruments. All instruments developed enable extremely accurate measurements with accuracy of picoseconds fractions (10-12 s). Instruments developed are used and successfully operated at many existing cosmic projects both in earth-based measuring stations located on five continents, and on-board of five cosmic missions. Currently, the group is a backer of and leading executive manager of a cosmic project called European Laser Timing, which is prepared by the European Space Agency.

Ion Beams Application

The group of Ion Beam Applications at the Department of Physical Electronic is involved in the field of ion beams and their application mainly in the area of materials modification at the nanoscopic level. The group operates the Ion Beams Laboratory, where a device for ions implantation (energies up to 120 keV), ion analytical techniques (PIXE and RBS) using the high energy beam from van de Graaf accelerator and several smaller devices for production and use of low energy beams are available.

Radioactivity and Environment

The Department of Dosimetry and Application of Ionizing Radiation is involved in monitoring of environment by sampling (e.g. in surroundings of the NPP Temelín, and in mining areas of the uranium ore), monitoring of radionuclides deposition using the bioindicative samples analysis and in-situ gamma spectrometry. The department also contributes to the development of methods using the aerial gamma-ray spectrometric survey. Samples are processed using laboratory gamma spectrometry; this is a complex field of nuclear physics specialised especially in the development of detection methods and fast determination of activity during emergency radiation situations. Another integral part of natural radiation is radon. This field has also been addressed at the DDAIR for a long time. We focus especially on the measurement of radon in water, inhalation of radon workers underground, earthquake prediction using the occurrence of radon, mapping of radon resources and its distribution in building structures and working environments.

Computational methods and Monte Carlo modelling

For a long time, The Department of Dosimetry and Application of Ionizing Radiation has been involved in the development of computational methods and application of programmes for radiation transport through matter. Concerning the computational methods, the processing, analysis and evaluation of spectra, deconvolution of spectra, mathematical and statistical processing are the main field of our interest. Concerning the radiation transport simulations, the modelling calculations in the area of detection systems response, shielding, radiation protection, radioanalytical methods, nuclear safety and medical applications are our main fields of interest. Universal programmes for simulation of broad spectrum of particles MCNP, Penelope, geant4, Fluka are used as well as specific programmes such as SCALE, SRIM, visualisation programmes, tools for work with anthropomorphous phantoms for medicinal calculations etc. Calculations results are used in many practical applications.

Methods for research of historical monuments

In this field, the DDAIR is focused on two methods – X-ray fluorescence analysis of elements and thermoluminescent dating of subjects’ age. X-ray fluorescence analysis (RFA) is one of the non-destructive instrumental analytical methods that is used by DDAIR to survey precious items and historical monuments. A significant field of its application is the analysis of pigments in wall paintings, pictures, ceramics, or old illuminated writings. The method is further used for the analysis of geological samples or other type of samples from the environment. The thermoluminescent dating method is suitable for geological and archaeological materials with thermoluminescent response (containing quartz and feldspar) that have passed through burning or heating while created. The method is developed on brick samples whose age is known. The samples are prepared by means of the fine grains method. The goal is to optimize the method of bricks dating (hence the buildings) so that the results are reproducible and it would be possible to obtain them on a routine basis and use them in archaeological research.

Radiotherapy, Nuclear Medicine and Radiodiagnostics

Radiotherapy is used for the destruction of tumours using ionizing radiation, while protecting the surrounding tissue against damage as much as possible. The other two fields are used primarily for disease diagnoses. The latest research activities in this area - regarding the development of technical equipment used - are oriented towards the strategy and optimization of procedures of individual medical treatment methods. The DDAIR is especially focused on experimental verification of planned therapeutic doses in target volumes. In this respect, the department develops and optimizes special 3D gel dosimeters, which are made of tissue-equivalent materials and allow the spatial distribution of doses to be determined with sub-millimetre accuracy. Another area of interest is in-vivo dosimetry, which deals with the measurement of radiation doses in patients during irradiation. While measurement by means of point detectors to the skin is well established, transmission dosimetry is still waiting for its implementation in clinical practice. The transmission dosimetry is based on a measurement using a 2D detector located beneath the patient and the subsequent reconstruction of the 3D dose distribution in the patient. Because of this method, medical intention can be compared with the real therapeutic irradiation. Recently, our interest is focused on the use of in-vivo dosimetry in brachytherapy and special irradiation techniques, which are used with very high doses (Cyberknife, stereotactic radiotherapy, proton therapy). Further, new screening possibilities of magnetic resonance are tested as well as individual dosimetry of patients in nuclear medicine, or clinical dosimetry of proton beams.

Radiation Protection

Research in this area covers several subareas. The first of them is involved in in-vivo measurement methods that are used in the determination of internal irradiation on individuals. Here, our knowledge from computational methods is applied to refine and optimize the measurement geometry or improve the equipment itself. The second area covers mathematical models for the calculation of internal irradiation. The models contain both bio-kinetics of radionuclides in the human body, and calculation of dose values on anthropomorphic phantoms of human individuals. Both above-mentioned fields are brought together in the third area. This area is focused on the improvement of the treatment and minimization of patient doses within the therapy by open radionuclide sources in nuclear medicine.

X-Ray and Neutron Diffraction

The laboratory of structural radiography at the Department of Solid State Engineering is focused on X-ray diffraction study of residual stress in polycrystalline metallic and ceramic materials. In recent years, the equipment of the laboratory has been significantly innovated and allows both qualitative and quantitative phase composition and preferred orientation (textures) of polycrystalline materials to be explored. These characteristics of real crystalline structure of solid materials are one of the basic parameters, knowledge of which is essential for the design of new advanced materials.

The laboratory of neutron diffraction at the Department of Solid State Engineering uses diffraction properties of thermal neutrons for applications in structural and textural analysis and material research as well. Here, a quantitative neutrongraphical texture analysis is used that can provide crucial information for, for example, the technology involved in the preparation of oriented transformer steel sheets. For many years the laboratory has been involved in research into the properties of technically perspective materials (synthetic zeolites, perovskites, high temperature superconductors, fast ion conductors). It is the only school facility of this kind in the Czech Republic.

Optical Spectroscopy

Research activities of the Laboratory of optical spectroscopy at the Department of Solid State Engineering are focused on optical diagnostics of bulk and thin-film dielectrical and semiconductor materials. Crystalline and ceramic materials that are studied are suitable for use in optoelectronics, production of lasers, luminescence detectors and scintillators for ionizing radiation. The aim of our research is to clarify and describe the electronic structure, formation and properties of point defects and properties of impurities in the studied materials. The results are used for optimization of crystal growth, preparation of ceramic and thin layers and to control the impurities contents in manufactured materials.

Computer Simulations of Solid Materials

The laboratory of material modelling at the Department of Solid State Engineering is focused on multiscale modelling of materials. This means both ab-initio quantum mechanical calculations of electronic structure (based on DFT), and simulations based on molecular mechanics (Forcefield theory) as well as selected problems of continuum thermodynamics. Currently, one of the most important projects includes computations of chemical stability of molecules suitable for the reprocessing of spent nuclear fuel, solutions of polymer elasticity and diffusivity of gaseous molecules in polymers depending on their crosslinking, and/or simulations of modulated martensitic structures in advanced metallic materials.

Applied Photonics

The laboratory of applied photonics at the Department of Solid State Engineering is involved in development and characterisation of polymeric structures used during constructions of chemical and physical waveguide sensors and active waveguide elements. For preparation of functional structures, we use methods of rotary thin film deposition from solution, vapour deposition of layers in vacuum, pulling from solution and chemical doping. For the testing of microstructures of developed materials there are the available methods of optical spectroscopy, light microscopy, attenuated total reflection spectroscopy, optical reflectometry and transmission electron microscopy.

Reactor Physics

The department of Nuclear Reactors is focused on theoretical and experimental physics. Using computational codes, the criticality of reactor systems can be analysed, dynamics of the reactor can be studied to determine the flow of neutrons and gamma radiation in different locations, the concentration of fission products and actinides can be determined and shielding can be analysed as well. Experiments from the field of reactor physics are carried out at the training reactor VR-1 that is operated by our department. These experiments cover the measurement of the neutron flux density and their diffusion parameters, the determination of the effects of different samples on reactivity and/or approaching the critical state.

Fuel Cycle

Optimisation of the middle part of the fuel cycle has a significant effect on economic efficiency of a nuclear power plant’s operation. In addition to the evaluation of uranium-plutonium fuel cycle, the department also studies potential applications of the thorium-uranium fuel cycle or the implementation of the MOX mixed fuels. The behaviour of uranium fuel in the nuclear reactor is known, but the implementation of thorium or plutonium to the fuel cycle changes the neutronic characteristics of the system and therefore it is necessary to analyse the effects of new fuel type on operation safety.

Research in the area of the fuel cycle back-end is focused on storage and final disposal of the spent fuel in cases when it will not be reprocessed. This relates to calculations of shielding containers for spent fuel, generation of residual heat and toxicity of disposed fuel and migration of radioisotopes in matter.


Sharing and transfer of the heat from the reactor to the turbine is an important part of the operation of nuclear power plants that is necessary for electricity generation. With the help of advanced computational codes (CFD codes) temperature profiles, flow rate of the coolant, the coefficients of heat conduction and material heat transfer coefficients are calculated. Knowledge of the system thermal model is also necessary to calculate the neutronic properties that are dependent on the temperature of individual components of the system. Attention is also paid to determining the thermomechanical properties of nuclear fuel in normal, abnormal and emergency conditions.

Control systems

Control and protection system is an important part of all nuclear facilities. The original control system of the reactor VR-1 was analogue. It was designed by FNSPE experts in collaboration with SKODA JS in the mid-80s of the 20th century. In 2001-2007, extensive reconstruction of the control devices and control systems was carried out with a significant contribution from the Department of Nuclear Reactors.

The Department is also engaged in the development of hardware and software equipment for programmable circuits and microprocessors, which are the basis of the control systems of nuclear facilities. An independent power safety circuit of the VR-1 reactor has been created at the department in frame of the development of control systems for research facilities. Another long-term project of the department is the implementation of detector electronic signal processing using the Campbell method.

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