Committee:

Topics:

1. Astronomical observations in visible wavelengths. Photometry, photometric systems in astronomy. Types and construction of telescopes.
2. Spectroscopy in astrophysics. Observations in wavelengths outside the visible range. Tools and results of space astronomy.
3. Physics of stars: the Lane-Emden equation and the polytropic model. Energy production in stars (p-p chain and the CNO cycle). The HR diagram. Evolution of stars in the HR diagram.
4. End states of stellar evolution. Evolutionary phases of massive stars and nucleosynthesis in stars. Supernovae.
5. Types of galaxies and their morphological classification. The structure and components of different galaxies. Spiral arms in disc galaxies.
6. Galaxy clusters and superclusters in the Universe. The Abell and Zwicky catalogs.
7. The large-scale structure of the Universe. Surveys exploring the LSS of the Universe (CfA slice, pencil-beam, SDSS) and their results: the statistical description of the LSS.
8. A hierarchical model of formation and evolution of galaxies. The physics of quasars, observational results.
9. The basics of cosmological theory: the cosmological principle, the Friedmann equations, the expanding universe and the big bang, cosmological parameters.
10. Observations confirming the big bang theory, the questions left open by the theory, and the theory of cosmic inflation as a possible solution.
11. Precision cosmological measurements and their results: the fluctuation spectrum of the CMB, SN Ia observations, and the large-scale structure of the Universe.
12. Active galactic nuclei and their unified model: characteristics of different active galactic nucleus categories (Seyfert galaxies, quasars, blazars, radio galaxies), evidence for the presence of a supermassive black holes, and the unified model.
13. Gamma-ray bursts: observations of different types of GRBs, the fireball model and the afterglow.
14. The astrophysics of hot intergalactic gas in galaxy clusters: characteristics of the hot gas, cooling flows and AGN feedback, methods for exploring the hot gas (X-ray spectroscopy, Sunyaev-Zeldovich effect).
15. The characteristics of gravitational waves, fundamentals of gravitational-wave detection, observations at various wavelengths and with multiple detectors.
16. Gravitational waves in astrophysics: signal types, observations so far, multimessenger astronomy. The cosmological application of gravitational waves.

Committee:

Information for the defense: 15 minutes are available for the defense of the dissertation, as well as an additional 5 minutes for answering the questions of the committee and the audience. Using a projectable presentation (PowerPoint, PDF) is recommended, which can be uploaded to the notebook provided for the presentation in advance.

Topics:

1. Molecular scale biophysics
2. Reaction kinetics and thermodynamics
3. Structure and function of proteins and nucleic acids
4. Biological membranes
5. Membrane potential, ion transport, nerve signaling
6. Spectroscopic methods in biology
7. Biophysical experimental techniques
8. Biophysics of sensation

Committee:

Topics:

Solid State Physics

1. Bonding in solid states (van der Walls, ionic, covalent, and metallic bonding).
2. Crystalline structures, experimental determination of crystalline structures (basic structures, symmetry properties, direct and reciprocal lattice, X-ray-, electron-, and neutron-diffraction).
3. Disordered systems ( alloys, amorphous materials, liquid crystals, quasicrystals).
4. Lattice vibrations (classic and quantum description, acoustic and optic branches, experimental determination of phonon spectra).
5. Thermal properties of crystalline materials (heat capacity of phonon gas, anharmonicity, thermal expansion, heat conductivity by phonons).
6. Electron states in periodic systems (Bloch and Wannier functions, band structure and its relation to the symmetry of the crystal, experimental determination of band structure, metals, semiconductors, insulators).
7. Pure and doped semiconductors, (Fermi energy, donor and acceptor levels, excitons). Schottky barrier, p-n transition, transistor.
8. Semiclassical description of the dynamic of electrons. Experimental determination of Fermi surface (motion of the electron in electric and magnetic fields, cyclotron resonance).
9. Electron in strong magnetic field (Landau levels, de Haas-van Alphen effect, quantum Hall effect)
10. Electron-phonon interaction, (limits of adiabatic decoupling, obtaining the electron- phonon interaction).
11. Theory of conduction (Boltzmann equation, relaxation time approximation and its limitations, transport coefficients in metals and semiconductor, scattering of impurities, phonons and electrons.
12. Interaction of solid materials with photons and neutrons (optical properties, Brillouin and Raman scattering, neutron scattering). Experimental methods for studying the properties of solid materials (Mössbauer effect, NMR, ESR, positron annihilation). 
13. The phenomenological theory of superconductivity (thermodynamics of superconductors, I. and II. type superconductors, Ginzburg-Landau theory, superconducting vortex).
14. BCS theory of superconductivity, tunnel effect, Josephson effect.
15. Many electron systems, electron-electron interaction (Hartree-Fock approximation, correlations, dielectric constant, screening, density function theory).

Magnetism 

16. Basic properties of magnetism (Hund’s rules, splitting of atomic levels in magnetic field, dia and para-magnetism, para-magnetic resonance, Pauli para-magnetism, exchange interaction).
17. Ordered magnetic materials (ferro- and antiferromagnets, mean-field theory, spin waves, magnetic anisotropy, magnetic domains).

Materials Physics

18. Defects in crystals, and their role in material properties, Point defects (equilibrium concentration, mixing entropy, evolution of point defects), dislocations (topological properties, continuum description, force acting on a dislocation), internal surfaces (grain boundary, phase boundary, energy of the boundaries, nanostructural materials).
19. Diffusion in solid states. Macroscopic and microscopic descriptions, Fick's laws, Important specific problems, Kirkendall-effect, generalized approach.
20. Mechanical properties, plasticity, work hardening, hardening by solid solution and precipitates.
21. Thermodynamic of multicomponent systems, phase rule, phase diagrams, calculating the phase diagram from free energy, homogeneous and heterogeneous nucleation. Irreversible thermodynamics, Onsager relations.
22. Molecular dynamics, empirical potentials, embedded potentials, first principle calculations, thermostats, barostat.
23. Phase field theories (Ginzburg-Landau, Cahn-Hilliard ), spinodal decomposition, superalloy, solidification.
24. Ceramics and composite materials (chemical structure of ceramics, properties, properties of composites, how to select materials for composites).

Committee:

Topics:

1. Ground state properties of nuclei and their measurements (binding energy, radius, magnetic moment, quadrupole moment)
2. Nuclear forces (the central potential, the mechanism of the interaction, the spin-dependent interaction, the tensor force)
3. Nuclear models (liquid drop model, Fermi-gas model, shell model, unified model)
4. Nuclear reactions (strong, electromagnetic, and weak processes of nuclei, charged-particle reactions)
5. Primordial nucleosynthesis (nuclear statistical equilibrium, the nucleosynthesis temperature, the primordial reaction network, results for the helium abundance, baryon-photon ratio, and baryon density parameter)
6. The nuclear physics of the Sun (the energy-generating reactions of the Sun, thermal reaction rate, reaction rate of charged particle reactions)
7. The nuclear physics of massive stars and supernova explosions (helium-, carbon-, neon-, oxygen- and silicon burning, the mechanisms of supernova explosions)
8. Basics of high-energy nuclear physics (high-energy particle accelerators, detectors, complex detector systems, timeline of the collisions, basic measurements and observables)
9. Processes in heavy-ion collisions (soft and hard processes, their physical ingredients and the relevant observables: jets, heavy quarks, photons, momentum distributions, anisotropies, viscosity, femtoscopy)
10. Strong interaction in heavy-ion collisions (basics of QCD, microscopic and effective theories, hydrodynamics, experimental and theoretical results on the QCD phase diagram)

Committee:

Topics:

1. Basic principles of particle detection, tracking, calorimetry.
2. Complex detector systems, particle identification.
3. Particle accelerators and their limitations, (anti)particle beams, focusing. Most important experimental discoveries at accelerators.
4. Characterization of elementary particles and their interactions, strangeness, barion and lepton numbers.
5. Geometrical symmetries, rotation group, Poincaré group, reflection symmetries.
6. Internal symmetry groups: SU(2), SU(3), particle multiplets, the basics of the quark model.
7. Quantization of free fields.
8. Interaction Lagrangians, Wick theorem, Feynman rules.
9. Non-abelian gauge theories, perturbative quantization, Feynman rules.
10. Basics of the electroweak theory: spontaneous symmetry breaking, Goldstone bosons, Higgs mechanism, masses and couplings of the W and Z bosons, lepton and quark multiplets.
11. Basics of quantum chromodynamics, one loop renormalization, running coupling, asymptotic freedom.

Committee:

Topics:

1. Universal properties of complex networks: Sparse and dense networks. Clustering coefficient. Small-world property. Scale independence and its implications. Quantities measuring centrality. Assortive and disassortive networks.
2. Network modeling: Erdős-Rényi model. Watts-Strogatz model. The Barabási-Albert model and its variations: the fitness models and the Holme-Kim model. The configuration model and randomization. The hidden parameter models.
3. Percolation properties of networks: Percolation transformation of the giant component and the Erdős-Rényi graph. Determining the critical point in generator function formalism. Resilience of networks in random node removal processes, targeted attacks on networks.
4. Propagation processes in networks: The SIS and SIR models. Behavior of the SIS model on homogeneous networks. The SIS model on scale-free networks.
5. Network motifs and groups: Triadic motifs of directed networks and the motif significance profile. The concept of network groups. The concept of the Girvan-Newman algorithm and modularity. Modularity optimization.
6. Dynamic foundations of statistical physics: Nonlinear dynamics and chaos in dissipative systems. One-dimensional mappings. Autocorrelation, Lyapunov exponent and Perron-Frobenius operator. Chaos in conservative systems and the Liouville operator.
7. Classical transport and fluctuation dissipation theorem: Classical linear response, classical Green-Kubo formula, relationship between diffusion and velocity autocorrelation.
8. Characterization of stochastic processes: Markov processes, Master equation, stability of stationary distribution, H-theorem, Fokker-Planck equation, stochastic differential equations, Brownian motion.
9. Open quantum systems: Open quantum systems, Markov approximation, Redfield equation and Lindblad equation.
10. Theory of linear response: Correlation and response functions. Quantum fluctuation-dissipation theorem.

Committee:

Topics:

1. Measurement data and measurement error - Errors and noise, their sources. Statistical and systematic error. Stochastic modelling of error. Data modelling - The basic problem of function fitting. Kernel function estimation.
2. Bootstrap methods. The maximum likelihood method. Hypothesis testing. Extreme statistics. Post hoc analysis. Regression. Independence test. Exact tests. Bayesian methods.
3. Random number generation. Numerical integration, Newton-type formulas, Gauss-type formulas. Monte-Carlo method, Markov chain Monte-Carlo. Hierarchical Bayesian networks.
4. Simulation of thermodynamic systems, Ising model, Metropolis algorithm. 
5. Fractal dimension, self-similar mathematical fractals, naturally occurring fractals, cellular automata. 
6. Numerical analysis of differential equations, Euler's method, Runge-Kutta method, stability, partial differential equations. 
7. Chaotic behaviour of dynamical systems. Population dynamics models, Strange attractor. Chaotic mappings, bifurcation, Lyapunov exponent. Quantum chaotic systems, distributions associated with eigenvalues of random matrices. 
8. Molecular dynamics, Verlet and velocity-Verlet algorithms. Determination of thermodynamic quantities and relaxation.
9. Signal processing and time series analysis - Fourier methods, FFT, spectra and spectrogram, transfer and window functions, Wiener filter. Correlation functions, Wiener-Hinchin theorem and power spectrum. Convolution and deconvolution. 
10. Machine learning - Prediction and classification methods. Supervised and unsupervised learning. The training set, validation and overfitting. K-means, Support Vector Machine, Random Forest, k-NN method.
11. Neural networks - fully connected neural nets, convolutional neural nets, backpropagation, optimizers (SGD, Adam), batch normalisation, autoencoders, word2vec.
12. Dimensionality reduction methods - Statistical properties of high dimensional data. 
13. Relational databases - the relational data model, logical and physical operators (seek, scan and variants of joins, aggregation), data storage models (row store, column store), indexes (clustered index, non-clustered index), the B-tree, keys and constraints, transactions. Query optimization. Data loading process. 
14. Multidimensional data, representation of geographic and spatial data. Basic search problems: interval search, spatial search, nearest neighbours. Spatial indices, spatial filling curves (Z-index, Peano-Hilbert-index), kD-tree, R-tree, role of bit coding. Spatial celling methods: Delaunay triangulation, Voronoi tessellation.
15. Image processing - Digital representation of images, colour models. Interpolation, convolution and deconvolution methods, homomorphic filtering. Edge, corner and speckle detection. Morphological analysis, feature extraction. Perspective correction, noise filtering methods.
16. Visualisation - Techniques for two and three dimensional visualisation of scientific data, representation of scalar, vector and tensor data. Use of colours, notation, Gestalt laws, Static and interactive visualisation techniques, Spatial data visualisation, Volumetric and level surface visualisation.

Committee:

Information for the defense: 15 minutes are available for the defense of the dissertation, as well as an additional 5 minutes for answering the questions of the committee and the audience. Using a projectable presentation (PowerPoint, PDF) is recommended, which can be uploaded to the notebook provided for the presentation in advance.

Topics:

1. Principles and biological aspects of thermodynamics and statistical physics (BP)
2. Structure and function of proteins (BP, BET, CB, IB)
3. Structure and function of DNA and RNA, classical and molecular genetics, gene technology (BP, CB, IB)
4. Biological membranes (BP, IB)
5. Bioenergetics: anaerobic and aerobic processes, chemiosmosis (BP, IB)
6. Bioenergetics: photosynthesis (BP, IB)
7. Membrane potential, ion transport (BP, IB)
8. Neurons and synapses, nerve signaling, Hodgkin-Huxley theory (BP, IB)
9. Spectroscopic methods in biology (BET)
10. Biophysical experimental techniques (BP, BET)
11. Biophysics of sensation (BP, IB)
12. Comparative and population genomics, molecular evolution (CB)
13. Collective behavior (synchronization, networks, motion) (BIS)

The topics are based on the following subjects:

BP:  Biophysics I. and II.
BET: Biophysical Experimental Techniques
CB:  Computational Biology
BIS: Bioinspired Systems
IB:  Introduction to Biology 1., 2., 3.