化学体系随机共振现象的理论研究

化学体系中随机共振现象的特性、机理、本质和应用的研究是非常重要的前沿课题。综述中国科学技术大学非线性化学实验室,在化学体系随机共振现象的理论研究中,所取得的主要成果,并阐述化学体系随机共振现象研究中所提出来的若干重要问题：非均相化学体系中随机共振;化学体系中内信号随机共振;化学体系中多重随机共振;化学体系中随机共振的调制;化学体系中色噪声作用下的随机共振;化学体系中时空随机共振;耦合化学体系中随机共振;化学体系中双参量随机共振。     

Stochastic simulation of reactive separations in capillary electrophoresis

A stochastic (Monte Carlo) simulation is used to investigate thermodynamic and kinetic contributions from the reversible A <--> B reaction in capillary electrophoresis (CE). The effects of equilibrium constant, rate constant, and electrophoretic mobility on the molecular zone profiles and the corresponding statistical moments are evaluated. As the reaction approaches steady state, the velocity of the zone is governed by the equilibrium constant and the electrophoretic mobilities of the reacting molecules. When the equilibrium constant is less than unity, the mean zone velocity is more similar to that of the reactant A. Conversely, when the equilibrium constant is greater than unity, the velocity is more similar to that of the product B. The extent of zone-broadening and asymmetry at steady state is dependent upon the equilibrium constant, the characteristic reaction lifetime, and the electrophoretic mobility difference between reacting molecules. If all other parameters are held constant, the plate height is greatest and skew is least when the equilibrium constant is unity. The plate height increases linearly with the characteristic reaction lifetime and electrophoretic mobility difference, whereas the skew is independent of these parameters. These conclusions have important implications for the elucidation of thermodynamic and kinetic information from experimental data.     

Stochastic resonance is applied to quantitative analysis for weak chromatographic signal of glyburide in plasma

Based on the theory of stochastic resonance, a new method carried on the quantitive analysis to weak chromatographic signal of glyburide in plasma, which was embedded in the noise background and the signal-to-noise ratio (SNR) of HPLC-UV is enhanced remarkably. This method enhances the quantification limit to 1 ng ml⁻¹, which is the same as HPLC-MS, and makes it possible to detect the weak signal accurately by HPLC-UV, which was not suitable before. The results showed good recovery and linear range from 1 to 50 ng ml⁻¹ of glyburide in plasma and the method can be used for quantitative analysis of glyburide.     

Low volatile monofunctional reactive diluents for radiation curable formulations

In the last decades the importance of UV curable formulations has increased continuously. Their fast curing speed, solvent-free polymerization conditions, and the formation of hard and highly crosslinked photopolymer networks represent major benefits. Commercial UV resins generally consist of multi-functional vinyl oligomers, photoinitiators, additives, and reactive diluents. Mono- and multi-functional reactive diluents serve as thinners to lower the overall resin viscosity and to improve processability. However, many monofunctional reactive diluents like isobornyl (meth)acrylate or benzyl (meth)acrylate exhibit high volatility, often already at room temperature. This causes adverse effects such as unpleasant odor, potential health risks, and changing resin composition during processing. A new group of monomers that show high potential for replacing traditional highly volatile reactive diluents are salicylate (meth)acrylates. In this work, salicylate-based thinners are synthesized, polymerized, and characterized with respect to their viscosity, volatility, thermal stability, photoreactivity, and thermomechanical properties of their homopolymers. Additionally, a first example of their diluting effect in a highly viscous difunctional polyester urethane methacrylate is demonstrated with 30 wt% of a cycloaliphatically and an aromatically substituted salicylate methacrylate. The polymers of the diluted resin exhibit similarly high glass transition temperatures of 110 and 126 °C, which are in the range of the polymers of the undiluted resin.     

Understanding Molecular Dynamics with Stochastic Processes via Real or Virtual Dynamics

Molecular dynamics with the stochastic process provides a convenient way to compute structural and thermodynamic properties of chemical, biological, and materials systems. It is demonstrated that the virtual dynamics case that we proposed for the Langevin equation[J. Chem. Phys. 147 , 184104 (2017)] in principle exists in other types of stochastic thermostats as well. The recommended "middle" scheme[J. Chem. Phys. 147 , 034109 (2017)] of the Andersen thermostat is investigated as an example. As shown by both analytic and numerical results, while the real and virtual dynamics cases approach the same plateau of the characteristic correlation time in the high collision frequency limit, the accuracy and efficiency of sampling are relatively insensitive to the value of the collision frequency in a broad range. After we compare the behaviors of the Andersen thermostat to those of Langevin dynamics, a heuristic schematic representation is proposed for understanding efficient stochastic thermostatting processes with molecular dynamics.     

Weak approximation of the stochastic wave equation

We investigate the accuracy of approximation of E[φ(u(t))], where {u(t):t∈[0,∞)} is the solution of the stochastic wave equation driven by the space-time white noise and φ is an R-valued function defined on the Hilbert space L²(R). The approximation is done by the leap-frog scheme. We show that, under certain conditions on φ, the approximation by the leap-frog scheme is of order two.     

The SC property of an expected residual function arising from stochastic complementarity problems

The stochastic nonlinear complementarity problem has been recently reformulated as an expected residual minimization problem which minimizes an expected residual function defined by an NCP function. In this work, we show that the expected residual function defined by the Fischer–Burmeister function is an function.     

Second phase spinodal decomposition for the Cahn-Hilliard-Cook equation

We consider the dynamics of a nonlinear partial differential equation perturbed by additive noise. Assuming that the underlying deterministic equation has an unstable equilibrium, we show that the nonlinear stochastic partial differential equation exhibits essentially linear dynamics far from equilibrium. More precisely, we show that most trajectories starting at the unstable equilibrium are driven away in two stages. After passing through a cylindrical region, most trajectories diverge from the deterministic equilibrium through a cone-shaped region which is centered around a finite-dimensional subspace corresponding to strongly unstable eigenfunctions of the linearized equation, and on which the influence of the nonlinearity is surprisingly small.

This abstract result is then applied to explain spinodal decomposition in the stochastic Cahn-Hilliard-Cook equation on a domain . This equation depends on a small interaction parameter  , and one is generally interested in asymptotic results as  . Specifically, we show that linear behavior dominates the dynamics up to distances from the deterministic equilibrium which can reach  with respect to the -norm.

     

Global stability and stochastic permanence of a non-autonomous logistic equation with random perturbation

This paper discusses a randomized non-autonomous logistic equation , where B(t) is a 1-dimensional standard Brownian motion. In [D.Q. Jiang, N.Z. Shi, A note on non-autonomous logistic equation with random perturbation, J. Math. Anal. Appl. 303 (2005) 164-172], the authors show that E[1/N(t)] has a unique positive T-periodic solution E[1/Np(t)] provided a(t), b(t) and α(t) are continuous T-periodic functions, a(t)>0, b(t)>0 and . We show that this equation is stochastically permanent and the solution Np(t) is globally attractive provided a(t), b(t) and α(t) are continuous T-periodic functions, a(t)>0, b(t)>0 and mint∈[0,T]a(t)>maxt∈[0,T]α²(t). By the way, the similar results of a generalized non-autonomous logistic equation with random perturbation are yielded.