arXiv subjects

Yuan Xiang

Publications and source records attributed to Yuan Xiang.

4 recordsLinked to original sources

arXiv2026

The co-directional overtaking collision problem between a dispersive shock wave and a rarefaction wave for the Hirota equation

In this paper, we mainly investigate the overtaking collision problem between a dispersive shock wave (DSW) and a rarefaction wave (RW) propagating in the same direction in the defocusing Hirota equation framework. Based on the Whitham theory, the zero-phase and single-phase modulation systems corresponding to the defocusing Hirota equation are given, along with explicit expressions of Riemann invariants. For step-type initial conditions with left-side DSW and right-side RW propagating identically, the global initial configuration is constructed.~The modulation solution within the nonlinear collision domain is obtained via the generalized hodograph transformation and solutions of the Euler-Poisson-Darboux equation. Thus, by matching the Riemann invariants at the boundaries of DSW and RW, we can provide a detailed analytical description for the dynamical behaviors of the collision across all evolutionary stages. The accuracy of theoretical predictions is verified by comparison with direct numerical simulations.

math-ph↗

arXiv2020

Counting generalized Schröder paths

A Schröder path is a lattice path from $(0,0)$ to $(2n,0)$ with steps $(1,1)$, $(1,-1)$ and $(2,0)$ that never goes below the $x-$axis. A small Schröder path is a Schröder path with no $(2,0)$ steps on the $x-$axis. In this paper, a 3-variable generating function $R_L(x,y,z)$ is given for Schröder paths and small Schröder paths respectively. As corollaries, we obtain the generating functions for several kinds of generalized Schröder paths counted according to the order in a unified way.

math.CO↗

arXiv2020

Ultrafast Photoinduced Band Splitting and Carrier Dynamics in Chiral Tellurium Nanosheets

Trigonal tellurium (Te) is a chiral semiconductor that lacks both mirror and inversion symmetries, resulting in complex band structures with Weyl crossings and unique spin textures. Detailed time-resolved polarized reflectance spectroscopy is used to investigate its band structure and carrier dynamics. The polarized transient spectra reveal optical transitions between the uppermost spin-split H4 and H5 and the degenerate H6 valence bands (VB) and the lowest degenerate H6 conduction band (CB) as well as a higher energy transition at the L-point. Surprisingly, the degeneracy of the H6 CB (a proposed Weyl node) is lifted and the spin-split VB gap is reduced upon photoexcitation before relaxing to equilibrium as the carriers decay. Using ab initio density functional theory (DFT) calculations we conclude that the dynamic band structure is caused by a photoinduced shear strain in the Te film that breaks the screw symmetry of the crystal. The band-edge anisotropy is also reflected in the hot carrier decay rate, which is a factor of two slower along c-axis than perpendicular to it. The majority of photoexcited carriers near the band-edge are seen to recombine within 30 ps while higher lying transitions observed near 1.2 eV appear to have substantially longer lifetimes, potentially due to contributions of intervalley processes in the recombination rate. These new findings shed light on the strong correlation between photoinduced carriers and electronic structure in anisotropic crystals, which opens a potential pathway for designing novel Te-based devices that take advantage of the topological structures as well as strong spin-related properties.

cond-mat.mtrl-sci↗

arXiv2017

Computational Simulations of Solvation Force and Squeeze Out of Dodecane Chain Molecules in Atomic Force Microscopy

There is a growing interest since the 1990s to understand the squeezing and shear behaviors of liquid films at nanometer scale by the atomic force microscope (AFM) measurement. We carry out all-atom contact-mode AFM simulations in a liquid-vapor molecular dynamics ensemble to investigate the solvation force oscillation and squeeze out mechanisms of a confined linear dodecane fluid between a gold AFM tip and a mica substrate. Solvation force oscillations are found to be associated with the layering transition of liquid film and unstable jumps of AFM tip position. Detailed structural analyses and molecular animations show that the local permeation of chain molecules and the squeeze out of molecules near the edge of contact promote the layering transition under compression. The confinement-induced slow down dynamics is manifested by the decrease in diffusivity and increase in rotational relaxation times. However, the persistent diffusive behavior of dodecane chain molecules even in the single-monolayer film is attributed to the chain sliding motions, given the fact that substantial vacancy space exists in the film due to thermal fluctuations.

cond-mat.soft↗