A 3D Nanostructured Hydrogel‐Framework‐Derived High‐Performance Composite Polymer Lithium‐Ion Electrolyte

Solid‐state electrolytes have emerged as a promising alternative to existing liquid electrolytes for next generation Li‐ion batteries for better safety and stability. Of various types of solid electrolytes, composite polymer electrolytes exhibit acceptable Li‐ion conductivity due to the interaction between nanofillers and polymer. Nevertheless, the agglomeration of nanofillers at high concentration has been a major obstacle for improving Li‐ion conductivity. In this study, we designed a three‐dimensional (3D) nanostructured hydrogel‐derived Li_0.35La_0.55TiO₃ (LLTO) framework, which was used as a 3D nanofiller for high‐performance composite polymer Li‐ion electrolyte. The systematic percolation study revealed that the pre‐percolating structure of LLTO framework improved Li‐ion conductivity to 8.8×10^?5 S cm^?1 at room temperature.     

Differentiable Functionals and Smoothed Bootstrap

The differentiability properties of statistical functionals have several interesting applications. We are concerned with two of them. First, we prove a result on asymptotic validity for the so-called smoothed bootstrap (where the artificial samples are drawn from a density estimator instead of being resampled from the original data). Our result can be considered as a smoothed analog of that obtained by Parr (1985, Stat. Probab. Lett., 3, 97-100) for the standard, unsmoothed bootstrap. Second, we establish a result on asymptotic normality for estimators of type generated by a density functional being a density estimator. As an application, a quick and easy proof of the asymptotic normality of , (the plug-in estimator of the integrated squared density ) is given.     

On the number of infinite geodesics and ground states in disordered systems

We study first-passage percolation models and their higher dimensional analogs—models of surfaces with random weights. We prove that under very general conditions the number of lines or, in the second case, hypersurfaces which locally minimize the sum of the random weights is with probability one equal to 0 or with probability one equal to +. As corollaries we show that in any dimensiond2 the number of ground states of an Ising ferromagnet with random coupling constants equals (with probability one) 2 or +. Proofs employ simple large-deviation estimates and ergodic arguments.     

Scaling of particle trajectories on a lattice

The scaling behavior of the closed trajectories of a moving particle generated by randomly placed rotators or mirrors on a square or triangular lattice is studied numerically. On both lattices, for most concentrations of the scatterers the trajectories close exponentially fast. For special critical concentrations infinitely extended trajectories can occur which exhibit a scaling behavior similar to that of the perimeters of percolation clusters.At criticality, in addition to the two critical exponents =15/7 andd _f=7/4 found before, the critical exponent =3/7 appears. This exponent determines structural scaling properties of closed trajectories of finite size when they approach infinity. New scaling behavior was found for the square lattice partially occupied by rotators, indicating a different universality class than that of percolation clusters.Near criticality, in the critical region, two scaling functions were determined numerically:f(x), related to the trajectory length (S) distributionn _s, andh(x), related to the trajectory sizeR _s (gyration radius) distribution, respectively. The scaling functionf(x) is in most cases found to be a symmetric double Gaussian with the same characteristic size exponent =0.433/7 as at criticality, leading to a stretched exponential dependence ofn _S onS, n_Sexp(–S ^6/7). However, for the rotator model on the partially occupied square lattice an alternative scaling function is found, leading to a new exponent =1.6±0.3 and a superexponential dependence ofn _S onS.h(x) is essentially a constant, which depends on the type of lattice and the concentration of the scatterers. The appearance of the same exponent =3/7 at and near a critical point is discussed.     

Duality Relations for Non-Ohmic Composites, with Applications to Behavior near Percolation

Keller, Dykhne, and others have exploited duality to derive exact results for the effective behavior of two-dimensional Ohmic composites. This paper addresses similar issues in the non-Ohmic context. We focus primarily on three different types of nonlinearity: (a) the weakly nonlinear regime; (b) power-law behavior; and (c) dielectric breakdown. We first make the consequences of duality explicit in each setting. Then we draw conclusions concerning the critical exponents and scaling functions of dual pairs of random non-Ohmic composites near a percolation threshold. These results generalize, unify, and simplify relations previously derived for nonlinear resistor networks. We also discuss some self-dual nonlinear composites. Our treatment is elementary and self-contained; however, we also link it with the more abstract mathematical discussions of duality by Jikov and Kozlov.     

Energy balance in dense microemulsions

A water-in-oil microemulsion composed of water, AOT and decane with volume fraction φ=0.50 and molar ratio X=40.8 was analysed by DSC. The percolation and the bicontinuous transitions as well as the melting endotherms and the freezing exotherms were measured. The main attention was focussed on the system energy balance. It was found that, by freezing the samples after the occurrence of the percolative transition, the total heat released is significantly less than the heat absorbed in the melting endotherms. A simple geometrical model was used as an analysis tool of the aforementioned energy difference. Since the system studied exhibits a percolative transition of dynamic type, on approaching the percolation threshold temperature (T≤T _p) and a static percolation for T≥T _p, the structural change from the connecting water-droplet-cluster to a connecting water channel was schematised in the model as a change from a sphere-necklace to a water-cylindrical channel of equal volume and equal length. The surface energy associated with the formation of the two different geometrical surfaces was evaluated and the amount of saved energy compared with the experimentally measured one.     

基于极大似然的异方差多正态总体均值的参数Bootstrap检验

本文考虑了异方差下多正态总体均值的检验问题。传统检验方法多为近似分布检验,且受总体数目及其样本量的影响较为严重,只有在总体数目较少、样本量适中或较大时才能很好的控制第一类错误。较近提出的参数bootstrap检验有效解决了在总体数目较多时检验的任意性,但在总体样本量都较小时,检验控制第一类错误倾向保守,或总体中存在个别样本量较少时犯第一类错误概率上升。本文从极大似然的角度推导出具有修正权重的极大似然检验统计量,并与bootstrap方法有效的结合,得到新的参数bootstrap检验方法。通过Monte Carlo模拟第一类错误和检验的势与Welch检验和广义F检验进行比较,结果表明本文提出的极大似然参数bootstrap检验在总体数目较多和存在小样本量时,均能很好地控制第一类错误,同时且有较好的势,适用范围更加广泛。     

A new universality for random sequential deposition of needles

Percolation and jamming phenomena are investigated for random sequential deposition of rectangular needles on d=2 square lattices. Associated thresholds and are determined for various needle sizes. Their ratios are found to be a constant for all sizes. In addition the ratio of jamming thresholds for respectively square blocks and needles is also found to be a constant . These constants exhibit some universal connexion in the geometry of jamming and percolation for both anisotropic shapes (needles versus square lattices) and isotropic shapes (square blocks on square lattices). A universal empirical law is proposed for all three thresholds as a function of a. Received 27 January 2000 and Received in final form 2 February 2000     

A Noise Temperature Analysis of the Electrical Degradation of Thin Nanostructured Films

Thermal noise measurements at proper biasing conditions are shown to represent a powerful tool for the characterization of the homogeneity of thin nanostructured films and their adhesion to the substrate. By modeling a thin-film as a two-dimensional random resistor network, we introduce a new type of excess-noise arising from local sources of Nyquist noise due to the presence of defective regions. The dishomogeneous Joule heating of the film is responsible for a thermal and electrical instability which is efficiently described by using a biased percolation model. The results of our simulations show that the Nyquist excess-noise temperature should provide a sensitive and non-destructive indicator of the packing density and of the quality of heat contact to the substrate of nanostructured films with grain size in the range 10–500 nm.