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Lin Hu

Publications and source records attributed to Lin Hu.

24 records · Page 2Linked to original sources
arXiv2015

More bounds for the Grundy number of graphs

A coloring of a graph $G=(V,E)$ is a partition $\{V_1, V_2, \ldots, V_k\}$ of $V$ into independent sets or color classes. A vertex $v\in V_i$ is a Grundy vertex if it is adjacent to at least one vertex in each color class $V_j$ for every $j<i$. A coloring is a Grundy coloring if every vertex is a Grundy vertex, and the Grundy number $Γ(G)$ of a graph $G$ is the maximum number of colors in a Grundy coloring. We provide two new upper bounds on Grundy number of a graph and a stronger version of the well-known Nordhaus-Gaddum theorem. In addition, we give a new characterization for a $\{P_{4}, C_4\}$-free graph by supporting a conjecture of Zaker, which says that $Γ(G)\geq δ(G)+1$ for any $C_4$-free graph $G$.

math.CO↗
arXiv2014

Nano-scale displacement sensing based on Van der Waals interaction

We propose the nano-scale displacement sensor with high resolution for weak-force systems could be realized based on vertical stacked two-dimensional (2D) atomic corrugated layer materials bound through Van der Waals (VdW) interaction. Using first-principles calculations, we found the electronic structure of bi-layer blue phosphorus (BLBP) varies appreciably to both the lateral and vertical interlayer displacement. The variation of electronic structure due to the lateral displacement is attributed to the changing of the interlayer distance dz led by atomic layer corrugation, which is in a uniform picture with vertical displacement. Despite different stacking configurations, the change of in-direct band gap is proportional to dz-2. This stacking configuration independent dz-2 law is found also works for other graphene-like corrugated bi-layer materials, for example MoS2. By measuring the tunable electronic structure using absorption spectroscopy, the nano-scale displacement could be detected. BLBP represents a large family of bi-layer 2D atomic corrugated materials for which the electronic structure is sensitive to the interlayer vertical and lateral displacement, thus could be used for nano-scale displacement sensor. Since this kind of sensor is established on atomic layers coupled through VdW interaction, it provides unique applications in measurements of nano-scale displacement induced by tiny external force.

cond-mat.mtrl-sci↗
arXiv2009

Temperature dependence of circular DNA topological states

Circular double stranded DNA has different topological states which are defined by their linking numbers. Equilibrium distribution of linking numbers can be obtained by closing a linear DNA into a circle by ligase. Using Monte Carlo simulation, we predict the temperature dependence of the linking number distribution of small circular DNAs. Our predictions are based on flexible defect excitations resulted from local melting or unstacking of DNA base pairs. We found that the reduced bending rigidity alone can lead to measurable changes of the variance of linking number distribution of short circular DNAs. If the defect is accompanied by local unwinding, the effect becomes much more prominent. The predictions can be easily investigated in experiments, providing a new method to study the micromechanics of sharply bent DNAs and the thermal stability of specific DNA sequences. Furthermore, the predictions are directly applicable to the studies of binding of DNA distorting proteins that can locally reduce DNA rigidity, form DNA kinks, or introduce local unwinding.

q-bio.BM↗