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The discovery that blazars dominate the extra-galactic 
$\gamma$-ray sky is a triumph in the Fermi era. However, the exact location of 
$\gamma$-ray emission region still remains in debate. Low-synchrotron-peaked blazars (LSPs) are estimated to produce high-energy radiation through the external Compton process, thus their emission regions are closely related to the external photon fields. We employed the seed factor approach proposed by Georganopoulos et al. It directly matches the observed seed factor of each LSP with the characteristic seed factors of external photon fields to locate the 
$\gamma$-ray emission region. A sample of 1 138 LSPs with peak frequencies and peak luminosities was adopted to plot a histogram distribution of observed seed factors. We also collected some spectral energy distributions (SEDs) of historical flare states to investigate the variation of 
$\gamma$-ray emission region. Those SEDs were fitted by both quadratic and cubic functions using the Markov-chain Monte Carlo method. Furthermore, we derived some physical parameters of blazars and compared them with the constraint of internal 
$\gamma\gamma$-absorption. We find that dusty torus dominates the soft photon fields of LSPs and most 
$\gamma$-ray emission regions of LSPs are located at 1–10 pc. The soft photon fields could also transition from dusty torus to broad line region and cosmic microwave background in different flare states. Our results suggest that the cubic function is better than the quadratic function to fit the SEDs.
The numerical investigation focuses on the flow patterns around a rectangular cylinder with three aspect ratios (
$L/D=5$, 
$10$, 
$15$) at a Reynolds number of 
$1000$. The study delves into the dynamics of vortices, their associated frequencies, the evolution of the boundary layer and the decay of the wake. Kelvin–Helmholtz (KH) vortices originate from the leading edge (LE) shear layer and transform into hairpin vortices. Specifically, at 
$L/D=5$, three KH vortices merge into a single LE vortex. However, at 
$L/D=10$ and 
$15$, two KH vortices combine to form a LE vortex, with the rapid formation of hairpin vortex packets. A fractional harmonic arises due to feedback from the split LE shear layer moving upstream, triggering interaction with the reverse flow. Trailing edge (TE) vortices shed, creating a Kármán-like street in the wake. The intensity of wake oscillation at 
$L/D=5$ surpasses that in the other two cases. Boundary layer transition occurs after the saturation of disturbance energy for 
$L/D=10$ and 
$15$, but not for 
$L/D=5$. The low-frequency disturbances are selected to generate streaks inside the boundary layer. The TE vortex shedding induces the formation of a favourable pressure gradient, accelerating the flow and fostering boundary layer relaminarization. The self-similarity of the velocity defect is observed in all three wakes, accompanied by the decay of disturbance energy. Importantly, the decrease in the shedding frequency of LE (TE) vortices significantly contributes to the overall decay of disturbance energy. This comprehensive exploration provides insights into complex flow phenomena and their underlying dynamics.
