Design and Experiments with a Low-Cost Single-Motor Modular Aquatic Robot

We present a novel design for a low-cost robotic boat powered by a single actuator, useful for both modular and swarming applications. The boat uses the conservation of angular momentum and passive flippers to convert the motion of a single motor into an adjustable paddling motion for propulsion and steering. We develop design criteria for modularity and swarming and present a prototype implementing these criteria. We identify significant mechanical sensitivities with the presented design, theorize about the cause of the sensitivities, and present an improved design for future work.Comment: Accepted to the International Conference on Ubiquitous Robots (UR 2020). 8 page

The Conformal Mode in 2D Simplicial Gravity

We verify that summing 2D DT geometries correctly reproduces the Polyakov action for the conformal mode, including all ghost contributions, at large volumes. The Gaussian action is reproduced even for c=10, well into the branched polymer phase, which confirms the expectation that the DT measure is indeed correct in this regime as well.Comment: 13 pages, 8 figure

Nonlinear MHD waves in a Prominence Foot

We study nonlinear waves in a prominence foot using 2.5D MHD model motivated by recent high-resolution observations with Hinode/SOT in Ca~II emission of a prominence on October 10, 2012 showing highly dynamic small-scale motions in the prominence material. Observations of H$\alpha$ intensities and of Doppler shifts show similar propagating fluctuations. However the optically thick nature of the emission lines inhibits unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity ($\delta I/I\sim \delta n/n$). The waves are evident as significant density fluctuations that vary with height, and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with typical period in the range of 5-11 minutes, and wavelengths $\sim <$2000 km. Recent Doppler shift observations show the transverse displacement of the propagating waves. The magnetic field was measured with THEMIS instrument and was found to be 5-14 G. For the typical prominence density the corresponding fast magnetosonic speed is $\sim$20 km s$^{-1}$, in qualitative agreement with the propagation speed of the detected waves. The 2.5D MHD numerical model is constrained with the typical parameters of the prominence waves seen in observations. Our numerical results reproduce the nonlinear fast magnetosonic waves and provide strong support for the presence of these waves in the prominence foot. We also explore gravitational MHD oscillations of the heavy prominence foot material supported by dipped magnetic field structure

Coulomb Gas Representation of the SU(2) WZW Correlators at Higher Genera

We express the correlation functions of the SU(2) WZW conformal field theory on Riemann surfaces of genus >1 by finite dimensional integrals.Comment: 9 pages, late

Measure in the 2D Regge quantum gravity

We propose a version of the 2D Regge calculus, in which the areas of all triangles are equal to each other. In this discretization Lund - Regge measure over link lengths is simplified considerably. Contrary to the usual Regge models with Lund - Regge measure, where this measure is nonlocal and rather complicated, the models based on our approach can be investigated using the numerical simulations in a rather simple way.Comment: Derivation of the basic result is reconsidered. Accepted for publication in Phys. Lett.

Singular vectors by Fusions in affine su(2)

Explicit expressions for the singular vectors in the highest weight representations of $A_1^{(1)}$ are obtained using the fusion formalism of conformal field theory.Comment: 7 page

Matrix models as conformal field theories: genus expansion

We obtain the topological expansion of the hermitian matrix model using its representation as a CFT on a hyperelliptic Riemann surface. To each branch point of the Riemann surface we associate an operator which represents a twist field dressed by the modes of the twisted boson. The partition function of the matrix model is computed as a correlation function of such dressed twist fields. The perturbative construction of the dressing operators yields a set of Feynman rules for evaluating the free energy and the loop observables at any genus.Comment: 17 pages, 4 figure

Nanotube-based scanning rotational microscope

A scheme of the scanning rotational microscope is designed. This scheme is based on using carbon nanotubes simultaneously as a probe tip and as a bolt/nut pair which converts translational displacements of two piezo actuators into pure rotation of the probe tip. First-principles calculations of the interaction energy between movable and rotational parts of the microscope confirms the capability for its operation. The scanning rotational microscope with a chemically functionalized nanotube-based tip can be used to study how the interaction between individual molecules or a molecule and a surface depends on their relative orientation.Comment: 4 pages, 3 figure