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Jeremiah Williams

Publications and source records attributed to Jeremiah Williams.

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Experiments and modeling of dust particle heating resulting from changes in polarity switching in the PK-4 microgravity laboratory

In the presence of gravity, the micron-sized charged dust particles in a complex (dusty) plasma are compressed into thin layers. However, under the microgravity conditions of the Plasma Kristall-4 (PK-4) experiment on the International Space Station (ISS), the particles fill the plasma, allowing us to investigate the properties of a three-dimensional (3D) multi-particle system. This paper examines the change in the spatial ordering and thermal state of the particle system created when dust particles are stopped by periodic oscillations of the electric field, known as polarity switching, in a dc glow discharge plasma. Data from the ISS is compared against experiments performed using a ground-based reference version of PK-4 and numerical simulations. Initial results show substantive differences in the velocity distribution functions between experiments on the ground and in microgravity. There are also differences in the motion of the dust cloud, in microgravity there is an expansion of the dust cloud at the application of polarity switching which is not seen in the ground-based experiments. It is proposed that the dust cloud in microgravity gains thermal energy at the application of polarity switching due to this expansion. Simulation results suggest that this may be due to a modification in the effective screening length of the dust at the onset of polarity switching, which arises from a configuration energy between the charged particles. Experimental measurements and simulations show that an extended time (much greater than the Epstein drag decay) is required to dissipate this energy.

physics.plasm-ph

Ergodic properties of one-dimensional incommensurate bilayer materials

We consider one-dimensional deterministic and random tight-binding Hamiltonians modeling electronic properties of twisted bilayer materials. When the twisted structure is incommensurate, we prove convergence of the density of states measure in the thermodynamic limit and Pastur's theorem on shift-invariance of the spectrum. Our results extend those of Massatt et al. and Canc\`es et al. in allowing for randomness. We provide numerical density of states computations for the operators we consider.

math-ph