Condensed Matter Theory

Abstract:

A class of artificial microswimmers with combined translational and rotational self-propulsion is studied experimentally. The chemically fueled microswimmers are made of doublets of Janus colloidal beads with catalytic patches that are positioned at a fixed angle relative to one another. The mean-square displacement and the mean-square angular displacement of the active doublets are analyzed in the context of a simple Langevin description, using which the physical characteristics of the microswimmers such as the spontaneous translational and rotational velocities are extracted. Our work suggests strategies for designing microswimmers that could follow prescribed cycloidal trajectories.

Abstract:

A systematic analysis of B-DNA elasticity cross-terms was performed using molecular dynamics simulations of three different duplexes designed to contain all dinucleotide steps including a 6-mer A-tract. The influence of ionic strength was also evaluated by several trajectories of each molecule with different NaCl concentrations at physiological rank. Simulations show DNA flexibility is independent of salt, in agreement with the Odijk-Skolnick-Fixman model. In addition, our results demonstrate DNA asymmetry at this scale is more complex than predicted by long-scale DNA models, with the cross-terms relating twist, slide, roll, and twist on the one hand and tilt and shift on the other being most essential. We find the rest of the coupling terms can be generally discarded due to their lack of correlation, with the exception of purine-purine's rise-tilt and shift-tilt. More specifically, A-tracts do not present any specific features in terms of their flexibility and chirality properties within those expected for purine-purine steps. Finally, some hints about coupling mechanisms are provided; we suggest cup deformation is mostly responsible for the positive twist-rise correlation at step level, whereas roll-rise and tilt-rise correlations can be understood via changes in stagger.

Abstract:

We consider a hypothetical topological quantum computer composed of either Ising or Fibonacci anyons. For each case, we calculate the time and number of qubits (space) necessary to execute the most computationally expensive step of Shor's algorithm, modular exponentiation. For Ising anyons, we apply Bravyi's distillation method which combines topological and nontopological operations to allow for universal quantum computation. With reasonable restrictions on the physical parameters we find that factoring a 128-bit number requires approximately 103 Fibonacci anyons versus at least 3×109 Ising anyons. Other distillation algorithms could reduce the resources for Ising anyons substantially. © 2010 The American Physical Society.