Single chain elasticity and thermoelasticity of polyethylene

Single-chain elasticity of polyethylene at $\theta$ point up to 90% of stretching with respect to its contour length is computed by Monte-Carlo simulation of an atomistic model in continuous space. The elasticity law together with the free-energy and the internal energy variations with stretching are found to be very well represented by the wormlike chain model up to 65% of the chain elongation, provided the persistence length is treated as a temperature dependent parameter. Beyond this value of elongation simple ideal chain models are not able to describe the Monte Carlo data in a thermodynamic consistent way. This study reinforces the use of the wormlike chain model to interpret experimental data on the elasticity of synthetic polymers in the finite extensibility regime, provided the chain is not yet in its fully stretched regime. Specific solvent effects on the elasticity law and the partition between energetic and entropic contributions to single chain elasticity are investigated.Comment: 32 pages with 5 figures included. Accepted as a regular paper on The Journal of Chemical Physics, August 2002. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physic

Agent Behavior Prediction and Its Generalization Analysis

Machine learning algorithms have been applied to predict agent behaviors in real-world dynamic systems, such as advertiser behaviors in sponsored search and worker behaviors in crowdsourcing. The behavior data in these systems are generated by live agents: once the systems change due to the adoption of the prediction models learnt from the behavior data, agents will observe and respond to these changes by changing their own behaviors accordingly. As a result, the behavior data will evolve and will not be identically and independently distributed, posing great challenges to the theoretical analysis on the machine learning algorithms for behavior prediction. To tackle this challenge, in this paper, we propose to use Markov Chain in Random Environments (MCRE) to describe the behavior data, and perform generalization analysis of the machine learning algorithms on its basis. Since the one-step transition probability matrix of MCRE depends on both previous states and the random environment, conventional techniques for generalization analysis cannot be directly applied. To address this issue, we propose a novel technique that transforms the original MCRE into a higher-dimensional time-homogeneous Markov chain. The new Markov chain involves more variables but is more regular, and thus easier to deal with. We prove the convergence of the new Markov chain when time approaches infinity. Then we prove a generalization bound for the machine learning algorithms on the behavior data generated by the new Markov chain, which depends on both the Markovian parameters and the covering number of the function class compounded by the loss function for behavior prediction and the behavior prediction model. To the best of our knowledge, this is the first work that performs the generalization analysis on data generated by complex processes in real-world dynamic systems

The coherent scattering function of the reptation model: simulations compared to theory

We present results of Monte Carlo simulations measuring the coherent structure function of a chain moving through an ordered lattice of fixed topological obstacles. Our computer experiments use chains up to 320 beads and cover a large range of wave vectors and a time range exceeding the reptation time. -- We compare our results (i) to the predictions of the primitive chain model, (ii) to an approximate form resulting from Rouse motion in a coiled tube, and (iii) to our recent evaluation of the full reptation model. (i) The primitive chain model can fit the data for times t \gt 20 T_2, where T_2 is the Rouse time of the chain. Besides some phenomenological amplitude factor this fit involves the reptation time T_3 as a second fit parameter. For the chain lengths measured, the asymptotic behavior T_3 ~ N^3 is not attained. (ii) The model of Rouse motion in a tube, which we have criticized before on theoretical grounds, is shown to fail also on the purely phenomenological level. (iii) Our evaluation of the full reptation model yields an excellent fit to the data for both total chains and internal pieces and for all wave vectors and all times, provided specific micro-structure effects of the MC-dynamics are negligible. Such micro-structure effects show up for wave vectors of the order of the inverse segment size. For the dynamics of the total chain our data analysis based on the full reptation model shows the importance of tube length fluctuations. Universal (Rouse-type) internal relaxation is unimportant. It can be observed only in the form of the diffusive motion of a short central subchain in the tube. -- Finally we present a fit formula which in a large range of wave vectors and chain lengths reproduces the numerical results of our theory for the scattering from the total chain.Comment: 26 pages, 12 figure