Denis Melnikov | Searcharxiv

arXiv2022

Noisy Tree Data Structures and Quantum Applications

The paper presents a technique for constructing noisy data structures called a walking tree. We apply it for a Red-Black tree (an implementation of a Self-Balanced Binary Search Tree) and a segment tree. We obtain the same complexity of the main operations for these data structures as in the case without noise (asymptotically). We present several applications of the data structures for quantum algorithms. Finally, we suggest new quantum solution for strings sorting problem and show the lower bound. The upper and lower bounds are the same up to a log factor. At the same time, it is more effective than classical counterparts.

quant-ph↗

arXiv2011

Ordering of small particles in one-dimensional coherent structures by time-periodic flows

Small particles transported by a fluid medium do not necessarily have to follow the flow. We show that for a wide class of time-periodic incompressible flows inertial particles have a tendency to spontaneously align in one-dimensional dynamic coherent structures. This effect may take place for particles so small that often they would be expected to behave as passive tracers and be used in PIV measurement technique. We link the particle tendency to form one-dimensional structures to the nonlinear phenomenon of phase locking. We propose that this general mechanism is, in particular, responsible for the enigmatic formation of the `particle accumulation structures' discovered experimentally in thermocapillary flows more than a decade ago and unexplained until now.

physics.flu-dyn↗