Yi-Chun Lee | Searcharxiv

arXiv2023

Evidence for spontaneous arrangement of two-way flow in water bridge via particle image velocimetry

By revisiting the century-old problem of water bridge, we demonstrate that it is in fact dynamic and comprises of two coaxial water currents that carry different charges and flow in opposite directions. This spontaneous separation is triggered by the different stages to construct the water bridge. Initially, a flow is facilitated by the cone jet that is powered by H+ and flows out of the positive-electrode beaker. An opposing cone-jet from negative beaker is established later and forced to take the outer route. This spontaneous arrangement of two-way flow is revealed by using fluorescein and carbon powder as tracers, and the Particle Image Velocimetry, These two opposing flows are found to carry non-equal flux that results in a net transport of water to the negative beaker. We manage to estimate the flow speed and cross-sectional area of these co-axial flows as a function of time and applied voltage. Note that the water on the outer layer functions as a millimeter tube that confines and interacts strongly with the flow inside. This provides a first natural and yet counter example to the recently reported near-frictionless flow in an equally miniatureized soft wall made from ferrofluid.

cond-mat.soft↗

arXiv2018

On Local Antimagic Vertex Coloring for Corona Products of Graphs

Let $G = (V, E)$ be a finite simple undirected graph without $K_2$ components. A bijection $f : E \rightarrow \{1, 2,\cdots, |E|\}$ is called a {\bf local antimagic labeling} if for any two adjacent vertices $u$ and $v$, they have different vertex sums, i.e. $w(u) \neq w(v)$, where the vertex sum $w(u) = \sum_{e \in E(u)} f(e)$, and $E(u)$ is the set of edges incident to $u$. Thus any local antimagic labeling induces a proper vertex coloring of $G$ where the vertex $v$ is assigned the color(vertex sum) $w(v)$. The {\bf local antimagic chromatic number} $χ_{la}(G)$ is the minimum number of colors taken over all colorings induced by local antimagic labelings of $G$. In this article among others we determine completely the local antimagic chromatic number $χ_{la}(G\circ \overline{K_m})$ for the corona product of a graph $G$ with the null graph $\overline{K_m}$ on $m\geq 1$ vertices, when $G$ is a path $P_n$, a cycle $C_n$, and a complete graph $K_n$.

math.CO↗