arXiv subjects

Liming Xiong

Publications and source records attributed to Liming Xiong.

10 recordsLinked to original sources

arXiv2026

Oxygen Vacancies at Dislocation Core Modulate Plasticity in Strontium Titanate

Dislocation core chemistry in oxides critically influences mechanical behavior and functionality; yet the evolution of core chemistry during the dislocation motion in them has not been directly observed. Here, using SrTiO3 as a model material, we combine aberration-corrected scanning transmission electron microscopy and electron energy-loss spectroscopy with atomic-level molecular dynamics (MD) simulations to correlate the <110>{1-10} dislocation core structure, oxygen vacancy density, charge state, and mobility with each other. We find that the mechanically induced dislocation loops exhibit dissociated cores, whose oxygen vacancy density depends on the gliding distance: short loops are Ti-reduced and oxygen-deficient at the edge dislocation core, whereas longer loops remain close to stoichiometry in both the edge and screw components. MD simulations reveal that kink-assisted edge dislocation glide in SrTiO3 leaves oxygen-deficient trails behind, modulating the oxygen content inside the edge core. These results demonstrate that oxygen-vacancy evolution at the dislocation core intrinsically couples with plasticity in ionic crystals, suggesting a mechanism for oxygen vacancy-dependent dislocation mobility in plastically deformed oxides.

cond-mat.mtrl-sci↗

arXiv2026

Chv\'{a}tal-Erd\H{o}s condition for 2-factors with at most two components in graphs

It is well-known that Chv\'{a}tal and Erd\H{o}s stated that any graph of order at least three whose independence number is no greater than its connectivity is Hamiltonian; that any graph whose independence number is no greater than its connectivity minus one is Hamilton-connected; and that any graph whose independence number is no greater than its connectivity plus one is traceable. Kaneko and Yoshimoto [J. Graph Theory 43 (2003) 269--279] showed that every 4-connected graph of order at least six has a 2-factor with two components if its independence number is no greater than its connectivity. In this paper, we show that any connected graph of order at least three times its connectivity plus three has a 2-factor with at most two components, except for one exceptional class, if its independence number is no greater than its connectivity plus one. Our result is best possible.

math.CO↗

arXiv2024

Upper bound for the number of maximal dissociation sets in trees

Let $G$ be a simple graph. A dissociation set of $G$ is defined as a set of vertices that induces a subgraph in which every vertex has a degree of at most 1. A dissociation set is maximal if it is not contained as a proper subset in any other dissociation set. We introduce the notation $\Phi(G)$ to represent the number of maximal dissociation sets in $G$. This study focuses on trees, specifically showing that for any tree $T$ of order $n\geq4$, the following inequality holds: \[\Phi(T)\leq 3^{\frac{n-1}{3}}+\frac{n-1}{3}.\] We also identify the extremal tree that attains this upper bound. Additionally, to establish the upper bound on the number of maximal dissociation sets in trees of order $n$, we also determine the second largest number of maximal dissociation sets in forests of order $n$.

math.CO↗

arXiv2022

Effect of a Micro-scale Dislocation Pileup on the Atomic-Scale Multi-variant Phase Transformation and Twinning

In this paper, we perform concurrent atomistic-continuum (CAC) simulations to (i) characterize the internal stress induced by the microscale dislocation pileup at an atomically structured interface; (ii) decompose this stress into two parts, one of which is from the dislocations behind the pileup tip according to the Eshelby model and the other is from the dislocations at the pileup tip according to a super-dislocation model; and (iii) assess how such internal stresses contribute to the atomic-scale phase transformations (PTs), reverse PTs, and twinning. The main novelty of this work is to unify the atomistic description of the interface and the coarse-grained (CG) description of the lagging dislocations away from the interface within one single framework. Our major findings are: (a) the interface dynamically responds to a pileup by forming steps/ledges, the height of which is proportional to the number of dislocations arriving at the interface; (b) when the pre-sheared sample is compressed, a direct square-to-hexagonal PT occurs ahead of the pileup tip and eventually grows into a wedge shape; (c) upon a further increase of the loading, part of the newly formed hexagonal phase transforms back to the square phase. The square product phase resulting from this reverse PT forms a twin with respect to the initial square phase. All phase boundaries (PBs) and twin boundaries (TBs) are stationary and correspond to zero thermodynamic Eshelby driving forces; and (d) the stress intensity induced by a pileup consisting of 16 dislocations reduces the stress required for initiating a PT by a factor of 5.5, comparing with that in the sample containing no dislocations. This work is the first characterization of the behavior of PTs/twinning resulting from the reaction between a microscale dislocation slip and an atomically structured interface.

cond-mat.mes-hall↗

arXiv2020

On traceable iterated line graph and hamiltonian path index

Xiong and Liu [L. Xiong and Z. Liu, Hamiltonian iterated line graphs, Discrete Math. 256 (2002) 407-422] gave a characterization of the graphs $G$ for which the $n$-th iterated line graph $L^n(G)$ is hamiltonian, for $n\ge2$. In this paper, we study the existence of a hamiltonian path in $L^n(G)$, and give a characterization of $G$ for which $L^n(G)$ has a hamiltonian path. As applications, we use this characterization to give several upper bounds on the hamiltonian path index of a graph.

math.CO↗

arXiv2017

Forbidden pairs for equality of edge-connectivity and minimum degree

Let $\mathcal{H}$ be a class of given graphs. A graph $G$ is said to be $\mathcal{H}$-free if $G$ contains no induced copies of $H$ for any $H \in \mathcal{H}$. In this article, we characterize all pairs $\{R,S\}$ of graphs such that every connected $\{R,S\}$-free graph has the same edge-connectivity and minimum degree.

math.CO↗

arXiv2017

Connected even factors in the square of essentially 2-edge connected graphs

In this paper we prove that the square of an essentially 2-edge connected graph with an additional property has a connected even factor with maximum degree at most 4. Moreover we show that, in general, the square of essentially 2-edge connected graph does not contain a connected even factor with bounded maximum degree.

math.CO↗

arXiv2017

Ballistic-diffusive Phonon Heat Transport across Grain Boundaries

The propagation of a heat pulse in a single crystal and across grain boundaries (GBs) is simulated using a concurrent atomistic-continuum method furnished with a coherent phonon pulse model. With a heat pulse constructed based on a Bose-Einstein distribution of phonons, this work has reproduced the phenomenon of phonon focusing in single and polycrystalline materials. Simulation results provide visual evidence that the propagation of a heat pulse in crystalline solids with or without GBs is partially ballistic and partially diffusive, i.e., there is a co-existence of ballistic and diffusive thermal transport, with the long-wavelength phonons traveling ballistically while the short-wavelength phonons scatter with each other and travel diffusively. To gain a quantitative understanding of GB thermal resistance, the kinetic energy transmitted across GBs is monitored on the fly and the time-dependent energy transmission for each specimen is measured; the contributions of coherent and incoherent phonon transport to the energy transmission are estimated. Simulation results reveal that the presence of GBs modifies the nature of thermal transport, with the coherent long-wavelength phonons dominating the heat conduction in materials with GBs. In addition, it is found the phonon-GB interaction can result in the reconstruction of the GBs.

cond-mat.mes-hall↗

arXiv2017

Passing Waves from Atomistic to Continuum

Progress in the development of coupled atomistic-continuum methods for simulations of critical dynamic material behavior has been hampered by a spurious wave reflection problem at the atomistic-continuum interface. This problem is mainly caused by the difference in material descriptions between the atomistic and continuum models, which results in a mismatch in phonon dispersion relations. In this work, we introduce a new method based on atomistic dynamics of lattice coupled with a concurrent atomistic-continuum method to enable a full phonon representation in the continuum description. This then permits the passage of short-wavelength, high-frequency phonon waves from the atomistic to continuum regions. The benchmark examples presented in this work demonstrate that the new scheme enables the passage of all allowable phonons through the atomistic-continuum interface; it also preserves the wave coherency and energy conservation after phonons transport across multiple atomistic-continuum interfaces. This work is the first step towards developing a concurrent atomistic-continuum simulation tool for non-equilibrium phonon-mediated thermal transport in materials with microstructural complexity.

cond-mat.mtrl-sci↗

arXiv2012

Star subdivisions and connected even factors in the square of a graph

For any positive integer $s$, a $[2,2s]$-factor in a graph $G$ is a connected even factor with maximum degree at most $2s$. We prove that if every induced $S(K_{1, 2s+1})$ in a graph $G$ has at least 3 edges in a block of degree at most two, then $G^2$ has a $[2,2s]$-factor. This extends the results of Hendry and Vogler and of Abderrezzak et al.

math.CO↗