School of Science Department of Physics 62 The Structures and Motions of Novel Shaped Granular Particles Supervisor: HAN Yilong / PHYS Student: SINGH Aadit / PHYS Course: UROP 1000, Summer While experiments in the past have explored the relationship between granular chain length and entanglement probability, typically by shaking or agitating the chain, less attention has been paid to the role of the actual agitation that the chains undergo. This study explores the knotting behaviour of a granular chain placed inside a rotating container and investigates the effect of rotation speed on knotting probability and complexity. The results suggest that knotting probability initially increases with speed and seems to reduce at very high speeds, while being difficult to predict in the middle. It was found that the complexity of the knots increases steadily with speed but similarly begins to decrease at very high speeds. Development of Nanopositioning Stage and Electronics for High-Resolution Microscopy Applications Supervisor: Berthold JAECK / PHYS Student: BOLLAMPALLY Raghutheja / PHYS Course: UROP 1100, Fall UROP 2100, Spring UROP 3100, Summer This paper presents the design, implementation, and optimization of a two-layer PCB for an RP2040-based arbitrary waveform generator targeting nanopositioning applications. The work addresses critical limitations observed in the original breadboard prototype—including parasitic capacitances, intermittent connections, and thermal instability—through a meticulously engineered printed circuit board. Key aspects include a hybrid resistor footprint strategy (combining 1206 for precision networks and 0805 for general use), optimized power distribution with 40-mil traces, and strategic separation of analog/digital domains. The implemented design demonstrates a 75% reduction in output noise (from 48mVpp to 12mVpp). Challenges in power delivery, particularly the RP2040’s internal regulator failure under load, are analyzed with proposed solutions. The PCB’s performance validates the transition from prototype to reliable instrumentation, offering a cost-effective solution for high-resolution microscopy systems. Development of Nanopositioning Stage and Electronics for High-Resolution Microscopy Applications Supervisor: Berthold JAECK / PHYS Student: TUMENBAYAR Urtnasan / ELEC Course: UROP 1100, Summer This project presents the design and simulation of a relatively low cost high voltage amplifier for nanopositioning systems. The amplifier is designed to deliver output signals within a ±200V range and drive capacitive loads up to 200nF, addressing the requirements of piezoelectric actuators. The PA93 operational amplifier was selected for its high current and voltage capabilities, set in a positive feedback circuit. A dual output boost converter topology was employed with a LT1171HV to generate the bipolar supply voltages of the amplifier. Simulation results confirm the feasibility of the design, achieving near target performance with ±182V output and substantial current delivery. The design must be tested in practical applications and verified under load conditions.
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