arXiv subjects

Zhong-can Ou-Yang

Publications and source records attributed to Zhong-can Ou-Yang.

24 records · Page 2Linked to original sources

arXiv2003

Maximum matching on random graphs

The maximum matching problem on random graphs is studied analytically by the cavity method of statistical physics. When the average vertex degree \mth{c} is larger than \mth{2.7183}, groups of max-matching patterns which differ greatly from each other {\em gradually} emerge. An analytical expression for the max-matching size is also obtained, which agrees well with computer simulations. Discussion is made on this {\em continuous} glassy phase transition and the absence of such a glassy phase in the related minimum vertex covering problem.

cond-mat.dis-nn↗

arXiv2002

A constant extension ensembles model of double-stranded chain molecules

Because the constant extension ensemble of single chain molecule is not always equivalent with constant force ensemble, a model of double-stranded conformations, as in RNA molecules and $β$-sheets in proteins, with fixed extension constraint is built in this paper. Based on polymer-graph theory and the self-avoiding walks, sequence dependence and excluded-volume interactions are explicitly taken into account. Using the model, we investigate force-extension curves, contact distributions and force-temperature curves at given extensions. We find that, for the same homogeneous chains, the force-extension curves are almost consistent with the extension-force curves in the conjugated force ensembles. Especially, the consistence depends on chain lengths. But the curves of the two ensembles are completely different from each other if sequences are considered. In addition, contact distributions of homogeneous sequence show that the double-stranded regions in hairpin conformations tend to locate at two sides of the chain. We contribute the unexpected phenomena to the nonuniformity of excluded-volume interactions of the region and two tails with different lengths. This tendency will disappear if the interactions are canceled. Finally, in constant extension ensemble, the force-flipping transitions conjugated with re-entering phenomena in constant force ensemble are observed in hairpin conformations, while they do not present in secondary structure conformations.

cond-mat.soft↗

arXiv2002

A model for the force stretching double-stranded chain molecules

We modify and extend the recently developed statistical mechanical model for predicting the thermodynamic properties of chain molecules having noncovalent double-stranded conformations, as in RNA or ssDNA, and $β-$sheets in protein, by including the constant force stretching at one end of molecules as in a typical single-molecule experiment. The conformations of double-stranded regions of the chain are calculated based on polymer graph-theoretic approach [S-J. Chen and K. A. Dill, J. Chem. Phys. {\bf109}, 4602(1998)], while the unpaired single-stranded regions are treated as self-avoiding walks. Sequence dependence and excluded volume interaction are taken into account explicitly. Two classes of conformations, hairpin and RNA secondary structure are explored. For the hairpin conformations, all possible end-to-end distances corresponding to the different types of double-stranded regions are enumerated exactly. For the RNA secondary structure conformations, a new recursive formula incorporating the secondary structure and end-to-end distribution has been derived. Using the model, we investigate the extension-force curves, contact and population distributions and re-entering phenomena, respectively. we find that the force stretching homogeneous chains of hairpin and secondary structure conformations are very different: the unfolding of hairpins is two-state, while unfolding the latter is one-state. In addition, re-entering transitions only present in hairpin conformations, but are not observed in secondary structure conformations.

cond-mat.soft↗

arXiv2002

Maximum-entropy calculation of end-to-end distance distribution of force stretching chains

Using the maximum-entropy method, we calculate the end-to-end distance distribution of the force stretched chain from the moments of the distribution, which can be obtained from the extension-force curves recorded in single-molecule experiments. If one knows force expansion of the extension through the $(n-1)$th power of force, it is enough information to calculate the $n$ moments of the distribution. We examine the method with three force stretching chain models, Gaussian chain, free-joined chain and excluded-volume chain on two-dimension lattice. The method reconstructs all distributions precisely. We also apply the method to force stretching complex chain molecules: the hairpin and secondary structure conformations. We find that the distributions of homogeneous chains of two conformations are very different: there are two independent peaks in hairpin distribution; while only one peak is observed in the distribution of secondary structure conformations. Our discussion also shows that the end-to-end distance distribution may discover more critical physical information than the simpler extension-force curves can give.

cond-mat.soft↗

arXiv2002

Single- and multi-walled carbon nanotubes viewed as elastic tubes with Young's moduli dependent on layer number

The complete energy expression of a deformed single-walled carbon nanotube (SWNT) is derived in the continuum limit from the local density approximation model proposed by Lenosky {\it et al.} \lbrack Nature (London) {\bf 355}, 333 (1992)\rbrack and shows to be content with the classic shell theory by which the Young's modulus, the Poisson ratio and the effective wall thickness of SWNTs are obtained as $Y=4.70$TPa, $ν=0.34$, $h=0.75{\rm Å}$, respectively. The elasticity of a multi-walled carbon nanotube (MWNT) is investigated as the combination of the above SWNTs of layer distance $d=3.4 {\rm Å}$ and the Young's modulus of the MWNT is found to be an apparent function of the number of layers, $N$, varying from 4.70TPa to 1.04TPa for N=1 to $\infty$.

cond-mat.mtrl-sci↗

arXiv2000

Elastic property of single double-stranded DNA molecules: Theoretical study and comparison with experiments

This paper aims at a comprehensive understanding on the novel elastic property of double-stranded DNA (dsDNA) discovered very recently through single-molecule manipulation techniques. A general elastic model for double-stranded biopolymers is proposed and a new structural parameter called the folding angle $ϕ$ is introduced to characterize their deformations. The mechanical property of long dsDNA molecules is then studied based on this model, where the base-stacking interactions between DNA adjacent nucleotide basepairs, the steric effects of basepairs, and the electrostatic interactions along DNA backbones are taken into account. Quantitative results are obtained by using path integral method, and excellent agreement between theory and the observations reported by five major experimental groups are attained. The strong intensity of the base-stacking interactions ensures the structural stability of DNA, while the short-ranged nature of such interactions makes externally-stimulated large structural fluctuations possible. The entropic elasticity, highly extensibility, and supercoiling property of DNA are all closely related to this account. The present work also suggests the possibility that negative torque can induce structural transitions in highly extended DNA from right-handed B-form to left-handed configurations similar with Z-form configuration. Some formulae concerned with the application of path integral method to polymeric systems are listed in the Appendix.

cond-mat.soft↗