Mean-field limit of Non-exchangeable interacting diffusions with singular kernels

The mean-field limit of interacting diffusions without exchangeability, caused by weighted interactions and non-i.i.d. initial values, are investigated. The weights could be signed and unbounded. The result applies to a large class of singular kernels including the Biot-Savart law. We demonstrate a flexible type of mean-field convergence, in contrast to the typical convergence of $\frac{1}{N}\sum_{i=1}^N\delta_{X_i}$. More specifically, the sequence of signed empirical measure processes with arbitrary uniform $l^r$-weights, $r>1$, weakly converges to a coupled PDE's, such as the dynamics describing the passive scalar advected by the 2D Navier-Stokes equation. Our method is based on a tightness/compactness argument and makes use of the systems' uniform Fisher information. The main difficulty is to determine how to propagate the regularity properties of the limits of empirical measures in the absence of the DeFinetti-Hewitt-Savage theorem for the non-exchangeable case. To this end, a sequence of random measures, which merges weakly with a sequence of weighted empirical measures and has uniform Sobolev regularity, is constructed through the disintegration of the joint laws of particles.Comment: 34 page

Infrared image segmentation with 2-D maximum entropy method based on particle swarm optimization (PSO

Abstract The 2-D maximum entropy method not only considers the distribution of the gray information, but also takes advantage of the spatial neighbor information with using the 2-D histogram of the image. As a global threshold method, it often gets ideal segmentation results even when the imageÕs signal noise ratio (SNR) is low. However, its time-consuming computation is often an obstacle in real time application systems. In this paper, the image thresholding approach based on the index of entropy maximization of the 2-D grayscale histogram is proposed to deal with infrared image. The threshold vector (t, s), where t is a threshold for pixel intensity and s is another threshold for the local average intensity of pixels, is obtained through a new optimization algorithm, namely, the particle swarm optimization (PSO) algorithm. PSO algorithm is realized successfully in the process of solving the 2-D maximum entropy problem. The experiments of segmenting the infrared images are illustrated to show that the proposed method can get ideal segmentation result with less computation cost

Gaussian Fluctuations for Interacting Particle Systems with Singular Kernels

Wang Z, Zhao X, Zhu R. Gaussian Fluctuations for Interacting Particle Systems with Singular Kernels. Archive for Rational Mechanics and Analysis . 2023;247(5): 101.We consider the asymptotic behaviour of the fluctuations for the empirical measures of interacting particle systems with singular kernels. We prove that the sequence of fluctuation processes converges in distribution to a generalized Ornstein-Uhlenbeck process. Our result considerably extends classical results to singular kernels, including the Biot-Savart law. The result applies to the point vortex model approximating the 2D incompressible Navier-Stokes equation and the 2D Euler equation. We also obtain Gaussianity and optimal regularity of the limiting Ornstein-Uhlenbeck process. The method relies on the martingale approach and the Donsker-Varadhan variational formula, which transfers the uniform estimate to some exponential integrals. Estimation of those exponential integrals follows by cancellations and combinatorics techniques and is of the type of the large deviation principle

2016, 662−675 Physicochemical Problems of Mineral Processing

Abstract: Dry dense-medium fluidized bed separation provides a new alternative approach for coal beneficiation and cleaning. An indicator of segregation degree S ash was proposed to evaluate the stratified performance of coal samples by bed density. Fluidization stability of the bed was greatly enhanced by mixing a certain amount (21.53%) of fine magnetite powder (< 0.15 mm) into the fluidized media, which indicated a uniform density distribution as well as slight fluctuations in bed. It was found that the favorable density-segregation performance of 3-13 mm coarse coal occurred with a static bed height of 80 mm and a superficial gas velocity of 11.84 cm/s. The optimal segregation degree values of 0.67, 0.74 and 0.76 were obtained for 3-6, 6-10 and 10-13 mm coal samples, respectively. Low-ash clean coal with yields of 50.79, 56.83 and 61.24% were effectively acquired by the dry separation for various coal size fractions, respectively. Probable error values of 0.07, 0.055 and 0.05 g/cm 3 were achieved, indicating good separation performance

Intumescent Flame Retardant Mechanism of Lignosulfonate as a Char Forming Agent in Rigid Polyurethane Foam

Intumescent flame retardants (IFR) have been widely used to improve flame retardancy of rigid polyurethane (RPU) foams and the most commonly used char forming agent is pentaerythritol (PER). Lignosulfonate (LS) is a natural macromolecule with substantial aromatic structures and abundant hydroxyl groups, and carbon content higher than PER. The flame retardancy and its mechanism of LS as char forming agent instead of PER in IFR formulation were investigated by scanning electron microscopy, thermogravimetric analysis, limiting oxygen index testing and cone calorimeter test. The results showed LS as a char forming agent did not increase the density of RPU/LS foams. LOI value and char residue of RPU/LS foam were higher than RPU/PER and the mass loss of RPU/LS foam decreased 18%, suggesting enhanced thermal stability. CCT results showed LS as a char forming agent in IFR formulation effectively enhanced the flame retardancy of RPU foams with respect to PER. The flame retardancy mechanism showed RPU/LS foam presented a continuous and relatively compact char layer, acting as the effect of the flame retardant and heat insulation between gaseous and condensed phases. The efficiency of different LS ratio in IFR formulation as char forming agent was different, and the best flame retardancy and thermal stability was obtained at RPU/LS1

Surface functionalization of graphene oxide by amino acids for Thermomyces lanuginosus lipase adsorption

Graphene oxide (GO) with oxygen containing functional groups can be selectively modified by small biomolecules to achieve heterogeneous surface properties. To achieve a hyper-enzymatic activity, the surface functionality of GO should be tailored to the orientation adsorption of the Thermomyces lanuginosus (TL) lipase, and the active center can be covered by a relatively hydrophobic helical lid for protection. In this work, amino acids were used to interact with GO through reduction reaction, hydrophobic forces, electrostatic forces, or hydrogen bonding to alter the surface hydrophobicity and charge density. Characterization of the structure and surface properties confirmed that the GO samples decorated with phenylalanine (Phe) and glutamic acid (Glu) exhibited superior hydrophobicity than other modifications, whereas tryptophan (Trp) and cysteine (Cys) provided weaker reduction effects on GO. Moreover, the zeta potential of the samples modified by amino acids of lysine (Lys) and arginine (Arg) is higher than other modified samples. The adsorption amount of lipase on Glu-GO reached 172 mg/g and the relative enzymatic activity reached up to 200%. The thermodynamic data and the Freundlich isotherm model fitting showed that the lipase adsorption process on modified samples was spontaneous, endothermic and entropy increase