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– The maximum matching problem on random graphs is studied analytically by the cavity method of statistical physics. When the average vertex degree c is larger than 2.7183, groups of max-matching patterns which differ greatly from each other gradually emerge. An analytical expression for the max-matching size is also obtained, which agrees well with(More)
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 et al. 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 = 4.70TPa,(More)
The classic Michaelis-Menten equation describes the catalytic activities for ensembles of enzyme molecules very well. But recent single-molecule experiments showed that the waiting time distribution and other properties of single enzyme molecules were not consistent with the prediction based on the ensemble viewpoint. They have contributed to the slow(More)
Using polymer elastic theory and known RNA free energies, we construct a Monte Carlo algorithm to simulate the single RNA folding and unfolding by mechanical force on the secondary structure level. For the constant force ensemble, we simulate the force-extension curves of the P5ab, P5abc deltaA, and P5abc molecules in equilibrium. For the constant extension(More)
Recently experiments showed that some biological noncovalent bonds increase their lifetimes when they are stretched by an external force, and their lifetimes will decrease when the force increases further. Several specific quantitative models have been proposed to explain the intriguing transitions from the "catch bond" to the "slip bond." In this work we(More)
We develop a continue time Monte Carlo algorithm to simulate single RNAs unfolded by a time-dependent external force on the secondary structure level. Two recent unfolding RNA experiments carried out by Bustamante group are mainly investigated. We find that, in contrast to popular two-state assumption about the RNAs free energy landscape along the molecular(More)
We study the general energy and shape of the two-dimensional solid monolayer domains with the dipole-dipole interactions. Compared with the domain energy without tilted dipole moments [M. Iwamoto and Z. C. Ou-Yang, Phys. Rev. Lett. 93, 206101 (2004)], the general dipolar energy is not only shape and size but also boundary orientation dependent. The general(More)
Using Feynman-Kac and Cameron-Martin-Girsanov formulas, we find a generalized integral fluctuation theorem (GIFT) for general diffusion processes by constructing a time-invariable integral. The existing integral fluctuation theorems can be derived as its specific cases. We interpret the origin of the GIFT in terms of time reversal of stochastic systems.
Using the continuous time Monte Carlo method, we simulated the translocation of a polynucleotide chain driven through a nanopore by an electric field. We have used two models of driven diffusion due to the electric field. The chain may have strong interaction with the pore, and depends on which end of the chain first enters the pore. Depending on this(More)
Using simple polymer elastic theory and known RNA free energies, we study the single RNA folding and unfolding on the secondary structure level under mechanical constant force by stochastic kinetic simulation. As a primary application, this method is used to simulate the experiment performed by Science 292, 733 (2001)]. The extension-force curves in(More)