The Random Batch Method proposed in our previous work(Jin et al.J Comput Phys,2020)is not only a numerical method for interacting particle systems and its mean-field limit,but also can be viewed as a model of the particle system in which particles interact,at discrete time,with randomly selected mini-batch of particles.In this paper,we investigate the mean-field limit of this model as the number of particles N→∞.Unlike the classical mean field limit for interacting particle systems where the law of large numbers plays the role and the chaos is propagated to later times,the mean field limit now does not rely on the law of large numbers and the chaos is imposed at every discrete time.Despite this,we will not only justify this mean-field limit(discrete in time)but will also show that the limit,as the discrete time intervalτ→0,approaches to the solution of a nonlinear Fokker-Planck equation arising as the mean-field limit of the original interacting particle system in the Wasserstein distance. 相似文献
Journal of Russian Laser Research - The zero-refractive-index metamaterials have excellent electromagnetic properties, which provide new ideas and methods to realize the control of electromagnetic... 相似文献
Journal of Algebraic Combinatorics - APR tilts for path algebra kQ can be realized as the mutation of the quiver Q in $${\mathbb Z}Q$$ with respect to the translation. In this paper, we show that... 相似文献
Fluorescence correlation spectroscopy (FCS) has been widely used to investigate molecular diffusion behavior in various samples. The use of the maximum entropy method (MEM) for FCS data analysis provides a unique means to determine multiple distinct diffusion coefficients without a priori assumption of their number. Comparison of the MEM-based FCS method (MEM-FCS) with another method will reveal its utility and advantage as an analytical tool to investigate diffusion dynamics. Herein, we measured diffusion of fluorescent probes doped into nanostructured thin films using MEM-FCS, and validated the results with single molecule tracking (SMT) data. The efficacy of the MEM code employed was first demonstrated by analyzing simulated FCS data for systems incorporating one and two diffusion modes with broadly distributed diffusion coefficients. The MEM analysis accurately afforded the number of distinct diffusion modes and their mean diffusion coefficients. These results contrasted with those obtained by fitting the simulated data to conventional two-component and anomalous diffusion models, which yielded inaccurate estimates of the diffusion coefficients. Subsequently, the MEM analysis was applied to FCS data acquired from hydrophilic dye molecules incorporated into microphase-separated polystyrene-block-poly(ethylene oxide) (PS-b-PEO) thin films characterized under a water-saturated N2 atmosphere. The MEM analysis revealed distinct fast and slow diffusion components attributable to molecules diffusing on the film surface and inside the film, respectively. SMT studies of the same materials yielded trajectories for mobile molecules that appear to follow the curved PEO microdomains. Diffusion coefficients obtained from the SMT data were consistent with those obtained for the slow diffusion component detected by MEM-FCS. These results highlight the utility of MEM-FCS and SMT for gaining complementary information on molecular diffusion processes in heterogeneous material systems.
Two-stage ignition exists in the low-temperature combustion process of n-heptane and the first-stage ignition also shows a negative temperature coefficient(NTC) phenomenon. To study key reactions and understand chemical principles affecting the first-stage ignition of n-heptane, a lumped skeletal mechanism with 62 species is obtained based on the detailed NUIGMech1.0 mechanism using the directed relation graph method assisted by sensitivity analysis and isomer lumping. The lumped mechanism shows good performance on ignition delay time under wide conditions. The study revealed that the temperature after the first-stage ignition is higher and a larger amount of fuel is consumed at lower initial temperatures. The temperature at the first-stage ignition is relatively insensitive to the initial temperature. Further sensitivity analysis and reaction path analysis carried out based on the lumped mechanism show that the decomposition of RO2 to produce alkene and HO2is the most important reaction to inhibit the first-stage ignitions. The chain branching explosion closely related to the first-stage ignition will be terminated when the rate constant for the RO2 decomposition is larger than that of the isomerization of RO2 to produce QOOH. The NTC behavior as well as other characteristics of the first-stage ignition can be rationalized from the competition between these two reactions. 相似文献