**Exercises**: Summer term 2020

**Timetable:** UFV/PSP/19C, Monday 08:00 – 09:30, Room: KNKTFA (PA9-PKn)

**Flyer:**

**Student projects**:

Year 2020:

**Maroš Jevočin** — Theoretical study of Ca^{2+} ion dependent cardiac thin filament activation using opened Ising chain with nearest-neighbor cooperative interaction (project proposal, pdf talk)

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The cardiac thin filament activation process is currently open problem in regard of theoretical description. Several studies have been made on the actin-myosin cross-bridges in myosin fiber. Yet only a few considered a dependency of myofilament activation on concentration of Ca 2+ ions. Presence of Ca 2+ ions in troponin-tropomyosin complex significantly improves chance of muscle filament contraction. 1D Ising model, which describes cardiac thin muscle fiber as a sequence made of 26 troponin-tropomyosin units was first time introduced by J. J. Rice et al.. Our aim is to improve the theoretical model by discarding periodic boundary approximation, which is in discrepancy with physiological description of cardiac muscle thin filament. We will show a method, which will allow us to calculate contraction force of cardiac muscle thin filament with open boundaries. With experimental data provided by work of D. P. Dobesh et al.. We will look for optimal set of parameters for our improved model.

The cardiac thin filament activation process is currently open problem in regard of theoretical description. Several studies have been made on the actin-myosin cross-bridges in myosin fiber. Yet only a few considered a dependency of myofilament activation on concentration of Ca 2+ ions. Presence of Ca 2+ ions in troponin-tropomyosin complex significantly improves chance of muscle filament contraction. 1D Ising model, which describes cardiac thin muscle fiber as a sequence made of 26 troponin-tropomyosin units was first time introduced by J. J. Rice et al.. Our aim is to improve the theoretical model by discarding periodic boundary approximation, which is in discrepancy with physiological description of cardiac muscle thin filament. We will show a method, which will allow us to calculate contraction force of cardiac muscle thin filament with open boundaries. With experimental data provided by work of D. P. Dobesh et al.. We will look for optimal set of parameters for our improved model.

**Matej Kecer** — Turbulence of compressible fluid with broken Galilean invariance (project proposal, pdf talk)

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In this proposed work we attempt to study field-theoretical model of fully developed turbulence, described by Navier-Stokes equation. We will consider random force with finite correlation time, the so called colored noise. This choice leads to more realistic and more general model. However, it also leads to breaking of Galilean invariance symmetry. Similar model was worked out in N. V. Antonov et al., however, authors here considered only incompressible fluids. We study such phenomena in compressible case. We approach the problem by means of field-theoretic renormalization group and our goal is to explore the model in one loop approximation.

In this proposed work we attempt to study field-theoretical model of fully developed turbulence, described by Navier-Stokes equation. We will consider random force with finite correlation time, the so called colored noise. This choice leads to more realistic and more general model. However, it also leads to breaking of Galilean invariance symmetry. Similar model was worked out in N. V. Antonov et al., however, authors here considered only incompressible fluids. We study such phenomena in compressible case. We approach the problem by means of field-theoretic renormalization group and our goal is to explore the model in one loop approximation.

Year 2018:

**Mária Džamová** — The physics of cooperative transport in groups of ants (pdf talk)

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*Collective behavior of biological systems (flock of birds, group of ants, …) is very complex phenomena and hard for mathematical description. Because in physics we are able to describe large systems of similar interacting particles, scientists take this physical tools and try to use them to understand collective biological groups. Feinerman at al., in their article, study cooperative transport of load provided by ants. They use statistical physics of interacting particles for mathematical description of their observations. When consider ants communicate through the forces by which they pull or lift the load, pull-lift decisions can be characterized as spin flips. Motion of ants transit between random and ballistic which is reminiscent of order–disorder transitions in statistical mechanics. Therefore they describe the system with Hamiltonian, map this problem to an Ising model and use the mean-field solution for this Hamiltonian, which is exact in thermodynamic limit (at temperature T=1). Model undergoes a second-order phase transition with divergence of susceptibility at the critical point. This requires including a small external field to Hamiltonian of system. In analytical solution for group of ants it can be implemented by including a single ant, which navigates others towards the nest.*

**Jozef Haniš** — Spatial carrier fringe pattern demodulation by use of a one-dimensional continuous wavelet transform (pdf talk)

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*One of the most popular options how to examine objects is to observe and capture their image by photons. For this favorite method is necessary to develop reconstruction algorithm to retrieve basic features of the objects as their height, phase or absorption, see also M. A. Gdeisat et al. It is possible to retrieve all these features (the information) with Continuous Wavelet Transform (CWT) applied on images with fringe patterns. At this seminar I will present basic knowledge, benefits of 1D CWT, as well as illumination of objects by the fringe patterns. You will hear how to use and implement 1D CWT, how to analyze objects, how to simulate illumination objects with fringe patterns and at the end of the seminar how to retrieve basic features from these objects via 1D CWT.*

**Michal Rončík** — EPR paradox (pdf talk)

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*The paper entitled — Can Quantum Mechanical Description of Physical Reality Be Considered Complete? — by the authors A. Einstein, B. Podolsky and N. Rosen is known as EPR paradox. Ranked by impact, EPR is among the top ten of all papers ever published in Physical Review journals and plays an important role in quantum information theory. However, the conclusion of this work stated that Quantum Mechanics is incomplete and raises many discussions persisting till today. The essence of their work is a logical connection between two statements (1) the quantum mechanical description of reality given by the wave function is not complete or (2) when the operators corresponding to two physical quantities do not commute the two quantities cannot have simultaneous reality. The whole problem is illustrated on a thought experiment in which we measure the position and momentum of two interacting particles which no longer interact. In fact, the presented proof is not straightforward. In my presentation, I will try to concentrate attention to central concerns and focus on the issue of entanglement which brings this article. I will also briefly mention the answers and reaction of the scientific community on this paper.*