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The field of mathematical modelling for pedestrian dynamics has attracted significant scientific attention, with various models proposed from perspectives such as kinetic theory, statistical mechanics, game theory and partial differential equations. Often such investigations are seen as being a part of a new branch of study in the domain of applied physics, called sociophysics. Our study proposes three models that are tailored to specific scenarios of crowd dynamics. Our research focuses on two primary issues. The first issue is centred around pedestrians navigating through a partially dark corridor that impedes visibility, requiring the calculation of the time taken for evacuation using a Markov chain model. The second issue is posed to analyse how pedestrians move through a T-shaped junction. Such a scenario is motivated by the 2022 crowd-crush disaster took place in the Itaewon district of Seoul, Korea. We propose a lattice-gas-type model that simulates pedestrians’ movement through the grid by obeying a set of rules as well as a parabolic equation with special boundary conditions. By the means of numerical simulations, we investigate a couple of evacuation scenarios by evaluating the mean velocity of pedestrians through the dark corridor, varying both the length of the obscure region and the amount of uncertainty induced by the darkness. Additionally, we propose an agent-based-modelling and cellular automata inspired model that simulates the movement of pedestrians through a T-shaped grid, varying the initial number of pedestrians. We measure the final density and time taken to reach a steady pedestrian traffic state. Finally, we propose a parabolic equation with special boundary conditions that mimic the dynamic of the pedestrian populations in a T-junction. We solve the parabolic equation using a random walk numerical scheme and compare it with a finite difference approximation. Furthermore, we prove rigorously the convergence of the random walk scheme to a corresponding finite difference scheme approximation of the solution.

The program COMSOL Multiphysics was used to simulate a flow of helium gas transporting ionized fission products out of an ion guide. Two important parameters to study from the simulation was the evacuation time and velocity of the ions. The mean evacuation time was shown to be 0.1173s, and the velocity of a single particle peaked at 2500m/s, 1000-1500m/s being more common.

Diploma thesis deals with the issue of terrrorism in relation to soft targets and subsequent assessment of the selected soft target in terms of possible terrorist attack. The objective is primary school Sirotkova in Brno. The assessment criteria was evacuation of the school as a whole and its individual parts. A risk analysis was performed for the object to determine real threats in which there were clasified the probability and extent of impacts of potential attacks. The most likely scenarios of the attack were identified, based on this analysis. These scenarios were subsequently implemented into an advanced numerical 3D model, where the evacuation was simulated within these scenarios. In the framework of the school assessment, the work focused on comparing three different approaches to the evacuation process. The evacuation process was compared according to parameters of experimental data obtained from the practise of evacuation of primary school with evacuation processes set acording to the parameters of fire standards CSN and international SFPE fire safety standards. The results of the individual simulations were processed with a statistically determined probability percentile. The outcome of the assessment was to determine the probable evacuation time of the school and its individual parts. Based on these results, there was performed a proposal to optimize the evacuation process of the school, which made the process more efective and shortened the evacuation time to minimalize the impact of a potential terrorist attack.