Search

We study the dynamics of the end monomers of a real chain confined in a spherical cavity to search for a small target on the cavity surface using Langevin dynamics simulation. The results are compared and contrasted with those of a Rouse chain to understand the influence of excluded volume interactions on the search dynamics, as characterized by the first passage time (FPT). We analyze how the mean FPT depends on the cavity size Rb, the target size a, and the degree of confinement quantified by Rg/Rb, with Rg being the polymer radius of gyration in free space. As a basic finding, the equilibrium distribution of the end monomers of a real chain in a closed spherical cavity differs from that of a Rouse chain at a given Rg/Rb, which leads to the differences between the mean FPTs of real and Rouse chains. Fitting the survival probability S(t) by a multi-exponential form, we show that the S(t) of real chains exhibits multiple characteristic times at large Rg/Rb. Our simulation results indicate that the search dynamics of a real chain exhibit three characteristic regimes as a function of Rg/Rb, including the transition from the Markovian to non-Markovian process at Rg/Rb ≈ 0.39, along with two distinct regimes at 0.39 < Rg/Rb < 1.0 and Rg/Rb > 1.0, respectively, where S(t) exhibits a single characteristic time and multiple characteristic times. [ABSTRACT FROM AUTHOR]

We develop a theory for the motion of a particle grafted with inhomogeneous bead-spring Rouse chains via the generalized Langevin equation (GLE), where individual grafted polymers are allowed to take different bead friction coefficients, spring constants, and chain lengths. An exact solution of the memory kernel K(t) is obtained for the particle in the time (t) domain in the GLE, which depends only on the relaxation of the grafted chains. The t-dependent mean square displacement g(t) of the polymer-grafted particle is then derived as a function of the friction coefficient γ0 of the bare particle and K(t). Our theory offers a direct way to quantify the contributions of the grafted chain relaxation to the mobility of the particle in terms of K(t). This powerful feature enables us to clarify the effect on g(t) of dynamical coupling between the particle and grafted chains, leading to the identification of a relaxation time of fundamental importance in polymer-grafted particles, namely, the particle relaxation time. This timescale quantifies the competition between the contributions of the solvent and grafted chains to the friction of the grafted particle and separates g(t) into the particle- and chain-dominated regimes. The monomer relaxation time and the grafted chain relaxation time further divide the chain-dominated regime of g(t) into subdiffusive and diffusive regimes. Analysis of the asymptotic behaviors of K(t) and g(t) provides a clear physical picture of the mobility of the particle in different dynamical regimes, shedding light on the complex dynamics of polymer-grafted particles. [ABSTRACT FROM AUTHOR]

The generalized Langevin equation (GLE) provides an attractive theoretical framework for investigating the dynamics of conformational fluctuations of polymeric systems. While the memory kernel is a central function in the GLE, explicit analytical forms for this function have been challenging to obtain, even for the simple models of polymer dynamics. Here, we achieve an explicit analytical expression for the memory kernel in the GLE for the end-to-end vector of Rouse chains in the overdamped limit. Our derivation takes advantage of the finding that the dynamics of the end-to-end vector of Rouse chains with both free ends are equivalent to those of Rouse chains with one free end and the other fixed. For the latter model, we first show that the equations of motion of the Rouse modes as well as their statistical properties can be obtained under the boundary conditions where the free end is held fixed temporarily. We then analytically solve the terms associated with intrachain interactions in the GLE. By formally comparing these terms with the GLE based on the Rouse modes, we obtain an explicit expression for the memory kernel, along with analytical forms for the potential field and the random colored noise force. Our analytical memory kernel is confirmed by numerical calculations in the Laplace space and is shown to yield asymptotic behaviors that are consistent with previous studies. Finally, we utilize our analytical result to simulate the cyclization dynamics of Rouse chains and discuss the scaling of the cyclization time with chain length. [ABSTRACT FROM AUTHOR]

Energy storage has a flexible regulatory effect, which is important for improving the consumption of new energy and sustainable development. The remaining useful life (RUL) forecasting of energy storage batteries is of significance for improving the economic benefit and safety of energy storage power stations. However, the low accuracy of the current RUL forecasting method remains a problem, especially the limited research on forecasting errors. In this paper, a method for forecasting the RUL of energy storage batteries using empirical mode decomposition (EMD) to correct long short-term memory (LSTM) forecasting errors is proposed. Firstly, the RUL forecasting model of energy storage batteries based on LSTM neural networks is constructed. The forecasting error of the LSTM model is obtained and compared with the real RUL. Secondly, the EMD method is used to decompose the forecasting error into many components. The time series of EMD components are forecasted by different LSTM models. The forecasting values of different time series are added to determine the corrected forecasting error and improve the forecasting accuracy. Finally, a simulation analysis shows that the proposed method can effectively improve the forecasting effect of the RUL of energy storage batteries. [ABSTRACT FROM AUTHOR]

Individual circular polyelectrolytes in simple shear flow are studied by means of mesoscale hydrodynamic simulations, revealing the complex coupling effects of shear rate, electrostatic interaction, and circular architecture on their conformational and dynamical properties. Shear flow deforms the polyelectrolyte and strips condensed counterions from its backbone. A decrease in condensed counterions alters electrostatic interactions among charged particles, affecting shear-induced polymer deformation and orientation. Circular architecture determines the features of deformation and orientation. At weak electrostatic interaction strengths, the polyelectrolyte changes its shape from an oblate ring at small shear rates to a prolate ring at large shear rates, whereas strong electrostatic interaction strengths are associated with a transition from a prolate coil to a prolate ring. Circular polyelectrolytes exhibit tumbling and tank-treading motions in the range of large shear rates. Further study reveals a similarity between the roles of intramolecular electrostatic repulsion and chain rigidity in shear-induced dynamics. [ABSTRACT FROM AUTHOR]