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.
Nonlinear Dynamics - In this paper, we study a delayed diffusive predator–prey model with nonlocal competition in prey and habitat complexity. The local stability of coexisting equilibrium is... 相似文献
Fluorescence probes in the NIR-IIa region show drastically improved imaging owing to the reduced photon scattering and autofluorescence in biological tissues. Now, NIR-IIa polymer dots (Pdots) are developed with a dual fluorescence enhancement mechanism. First, the aggregation induced emission of phenothiazine was used to reduce the nonradiative decay pathways of the polymers in condensed states. Second, fluorescence quenching was minimized by different levels of steric hindrance to further boost the fluorescence. The resulting Pdots displayed a fluorescence QY of ca. 1.7 % in aqueous solution, suggesting an enhancement of ca. 21 times in comparison with the original polymer in tetrahydrofuran (THF) solution. Small-animal imaging by using the NIR-IIa Pdots exhibited a remarkable improvement in penetration depth and signal to background ratio, as confirmed by through-skull and through-scalp fluorescent imaging of the cerebral vasculature of live mice. 相似文献