Seminarium "Modeling of Complex Systems"

The Monte Carlo (MC) approach is now an essential ingredient in many quantitative studies and branches of science including physics, finance-economics, biology, engineering, etc. The MC algorithm is the natural choice for studying the static properties of a system, where dynamical effects are not required. In the modified MC approach proposed here the probability of accepting the final state depends on the activation energy, not on the relativeenergy between the final and initial state [1]. However, the barrier height is calculated on an ongoing basis, by generating intermediate stateswith a predefined step Δ. Therefore, we name this method step Monte Carlo (sMC) [1]. Importantly, the sMC method correctly takes into account the presence of various local barriers and it obeys the detailed balance condition, even if the system is not in equilibrium. As a result, the appropriate dynamics of the tested system is simulated. The details of sMC algorithm areexplained for the case of magnetization process (see figure). To test the correctness of sMC, we compare its results with those obtained bystochastic Landau-Lifshitz-Gilbert approach.[1] D. Sztenkiel, “Introducing the step Monte Carlo method for simulating dynamic properties,” Adv. Theory Simul. 2300184 (2023).The work is supported by the National Science Center (Poland) through project OPUS 2018/31/B/ST3/03438 and by the Interdisciplinary Center for Mathematical and Computational Modelling at the University of Warsawthrough the access to the computing facilities.

The seminar will be held in hybrid mode: in room 1.40 (FUW) and will betransmitted via Zoom:https://uw-edu-pl.zoom.us/j/92019406157?pwd=bE9aKzI0Y2JuZXpaZ1RsR2NrMmFVUT09Meeting ID: 920 1940 6157Passcode: 036238