arXiv subjects

Zijie Lin

Publications and source records attributed to Zijie Lin.

20 records · Page 2Linked to original sources

arXiv2019

Bowen entropy of generic point for fixed-point free flows

Let $(X, ϕ)$ be a compact metric flow without fixed points. We will be concerned with the entropy of flows which takes into consideration all possible reparametrizations of the flows. In this paper, by establishing the Brin-Katok's entropy formula for flows without fixed points in non-ergodic case, we prove the following result: for an ergodic $ϕ$-invariant measure $μ$, $$ h_{top}^{B}(ϕ, G_μ(ϕ))=h_μ(ϕ_{1}),$$ where $G_μ(ϕ)$ is the set of generic points for $μ$ and $h_{top}^{B}(ϕ, G_μ(ϕ))$ is the Bowen entropy on $G_μ(ϕ)$. This extends the classical result of Bowen in 1973 to fixed-point free flows. Moreover, we show that the Bowen entropy can be determined via the local entropies of measures.

math.DS↗

arXiv2018

Polarization-insensitive space-selective etching in fused silica induced by picosecond laser irradiation

It is well known that when the fused silica is irradiated with focused femtosecond laser beams, space selective chemical etching can be achieved. The etching rate depends sensitively on the polarization of the laser. Surprisingly, we observe that by chirping the Fourier-transform-limited femtosecond laser pulses to picosecond pulses, the polarization dependence of the etching rate disappears, whereas an efficient etching rate can still be maintained. Observation with a scanning electron microscope reveals that the chirped pulses can induce interconnected nanocracks in the irradiated areas which facilitates efficient introduction of the etchant into the microchannel. The reported technology is of great use for fabrication of three-dimensional (3D) microfluidic systems and glass-based 3D printing.

physics.optics↗