UROP Proceedings 2020-21

School of Science Department of Physics 70 Quantum State Calculation of Two-dimensional Supramolecular Nanostructures Supervisor: LIN Nian / PHYS Student: CHAN Wai Ming / PHYS Course: UROP1100, Fall In this paper, a MATLAB program is used to simulate the physical system of a 2-dimensional supramolecular nanomolecule, by numerically solving the 2-dimensional Schrödinger equation. A four-layer hexagonal lattice cell was constructed in MATLAB. From the program, variables such as band structure, total density of states (TDOS) and local density of states (LDOS) can be measured. Then we would observe the variables’ response to the change of parameters, in this paper, mainly positions of potential pillars. Quantum State Calculation of Two-dimensional Supramolecular Nanostructures Supervisor: LIN Nian / PHYS Student: YUE Cheuk Kan Kelvin / PHYS-IRE Course: UROP1100, Summer In this paper, a physical system of a two-dimensional supramolecular nanostructure is simulated by a MATLAB program, which numerically solves a Schrödinger equation. Hexagonal and triangular potential pillars are constructed and put into the hexagonal lattice in the program. From the program, variables such as band structure, total density of states (TDOS), local density of states (LDOS) and effective mass of electron are calculated. These variables’ response to the change of parameters, including the size r and angle of rotation θ of the potential pillars are then observed. The ultimate goal of this project is to explore how the physical properties of supramolecules are affected by transformation of the structure. Application of Machine Learning in Physics Supervisor: LIU Junwei / PHYS Student: TRAN Duc Huy / PHYS-IRE Course: UROP1100, Fall The Ising model is a simple model which explains the phase transition of ferromagnetic materials. Although the analytical solutions for some simple cases of Ising model has been discovered, investigating more complicated cases still requires numerical simulations. The Metropolis-Hastings algorithm is a popular approach to this problem. Among the different implementations of this algorithm, the local update algorithm is the simplest one and could be generalized to many complex cases of Ising model. However, it faces the problem of auto-correlation. The Wolff-cluster update algorithm could reduce the auto-correlation, but is only valid for the case with two-spin interaction. The Self-Learning Monte Carlo method (SLMC), invented by Junwei Liu, Yang Qi et. al., could combine the advantage of the previous two methods and produce more efficient simulations.

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