Oscillation-based methods for actuation and manipulation of nano-objects

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in AIP Conference Proceedings 1882, 020056 (2017) and may be found at https://doi.org/10.1063/1.5001635.We discuss how oscillations can be used for fixation or manipulation of nano-objects or producing nano-drives. The underlying principles are scale-invariant and principally can be scaled down up to the molecular scale. The main underlying principle of fixation and actuation occurs to be symmetry breaking of an oscillating system. From this unifying standpoint, a series of actuation principles are discussed as dragging, ratchets, micro walking, friction-inertia actuators, oscillation tweezers, flagella motors for propulsion in liquids as well as some recently proposed actuation principles

Generic algebras: rational parametrization and normal forms

For every algebraically closed field $\boldsymbol k$ of characteristic different from $2$, we prove the following: (1) Generic finite dimensional (not necessarily associative) $\boldsymbol k$-algebras of a fixed dimension, considered up to isomorphism, are parametrized by the values of a tuple of algebraically independent over $\boldsymbol k$ rational functions in the structure constants. (2) There exists an "algebraic normal form", to which the set of structure constants of every such algebra can be uniquely transformed by means of passing to its new basis, namely: there are two finite systems of nonconstant polynomials on the space of structure constants, $\{f_i\}_{i\in I}$ and $\{b_j\}_{j\in J}$, such that the ideal generated by the set $\{f_i\}_{i\in I}$ is prime and, for every tuple $c$ of structure constants satisfying the property $b_j(c)\neq 0$ for all $j\in J$, there exists a unique new basis of this algebra in which the tuple $c'$ of its structure constants satisfies the property $f_i(c')=0$ for all $i\in I$.Comment: 20 pages. Added details on separability in the proof of Theorems 2 and