Note on the fractal dimension of hard sphere trajectories

Using Monte Carlo molecular dynamics, a new, careful study is made of the approach of the trajectory of a typical particle in a hard sphere fluid to that of a Brownian particle, discussed before by Powles and Quirke and Rapaport. The apparent fractal dimension of the trajectory, as a function of reduced length scale,(), characterizes the transition from mechanical to Brownian motion and differs markedly from 2 in all present computer simulations.     

应用普通扫描仪作薄层色谱定量分析的初步研究

尝试应用普通扫描仪作薄层色谱定量分析。样品通过硅胶板层析展开后，用碘蒸汽显色，再用普通扫描仪记录其图像，通过图像分析技术计算出斑点中样品的量。结果表明，对油醇、油酸、月桂胺和焦谷氨酸油酯等长碳链有机化合物，样点在nmol级的范围内时计算量与实际量有良好的线性相关性。     

Image analysis in the electron microscopy of cellulose protofibrils II. Digital correlation methods

Electron micrographs of parallel arrays of negatively stained ramie cellulose protofibrils were analyzed using the two-dimensional digital autocorrelation function (ACF). The method is based upon the statistical analysis of images in real space. The ACF shows strong parallel streaks of high correlation, and the lateral distance between adjacent streaks allows the mean interfibrillar distance to be estimated as 3.7 nm. The intensity profile along the streaks shows a weak modulation with peaks occurring at integral multiples of 3 or 6 nm. These results provide direct evidence that there is a regular axial texture in the protofibrils, and corroborate the conclusions previously drawn from optical diffraction analysis. Using the difference vectors found in the ACF it has been possible to reduce the picture noise level by linear integration, thereby obtaining an enhanced image. A preliminary result obtained in this way suggests that the projected protofibril morphology associated with the observed axial periodicity is a ribbon-like zigzag structure. Possible applications of the method for future work are discussed.     

Differential thermal analysis of the Al+20% (Fe-50%B) system

In the present study, aluminium and mechanically alloyed (36 h) Fe/B (50 wt%) are mixed. Al+20 (wt%) Fe/B mixture has been studied by differential thermal analysis to determine the aluminium quantity that is supposed to melt and afterwards does not solidify as it reacts with Fe/B powder. The different areas between endothermic reaction (melting peak) and exothermic reaction (solidification peak) allow in knowing the quantity of aluminium that reacts with Fe/B and the amount of intermetallic phases formed at high temperature. In order to follow the process, compacts were sintered at different temperatures (700, 800, 900, 1000 and 1200 °C), in N₂/10H₂/0.1CH₄ atmosphere. Microstructure was evaluated by image analysis and the results obtained by both techniques are compared.     

Extrapolated Smoothing Descent Algorithm for Constrained Nonconvex and Nonsmooth Composite Problems*

In this paper, the authors propose a novel smoothing descent type algorithm with extrapolation for solving a class of constrained nonsmooth and nonconvex problems,where the nonconvex term is possibly nonsmooth. Their algorithm adopts the proximal gradient algorithm with extrapolation and a safe-guarding policy to minimize the smoothed objective function for better practical and theoretical performance. Moreover, the algorithm uses a easily checking rule to update the smoothing parameter to ensure that any accumulation point of the generated sequence is an (affine-scaled) Clarke stationary point of the original nonsmooth and nonconvex problem. Their experimental results indicate the effectiveness of the proposed algorithm.     

Impact Responses of Prismatic Lithium-Ion Battery Based on the Membrane Factor Method北大核心CSCD

Aimed at the internal short circuit problem due to large deformation of the prismatic lithium-ion battery cell under impact loadings, a simplified battery model was first established. Then the motion equations of velocity and displacement based on the membrane factor method were proposed. With the effects of the face-sheet thickness and the densification region on the normalized final deflection, impact response characteristics of prismatic battery cells were investigated in detail. The results show that, the improved motion equations involving the membrane factor can reflect the dynamic response mechanisms of the prismatic battery cell under impact loadings, and the large deflection under high-speed impact can be predicted. With the increase of the face-sheet thickness, the deflection of the battery cell’s lower part decreases obviously. However, the densification region expands with the face-sheet thickness. The deflection and the densification region of the cell’s lower part both increase with the inner core density of the battery. This proposed impact model provides a theoretical guidance for the multi-functional integrated dynamic design of prismatic battery cells. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

The Regularity of Stochastic Convolution Driven by Tempered Fractional Brownian Motion and Its Application to Mean-field Stochastic Differential Equations

In this paper, some properties of a stochastic convolution driven by tempered fractional Brownian motion are obtained. Based on this result, we get the existence and uniqueness of stochastic mean-field equation driven by tempered fractional Brownian motion. Furthermore, combining with the Banach fixed point theorem and the properties of Mittag-Leffler functions, we study the existence and uniqueness of mild solution for a kind of time fractional mean-field stochastic differential equation driven by tempered fractional Brownian motion.     

Convergence of distorted Brownian motions and singular Hamiltonians

We prove a convergence theorem for sequences of Diffusion Processes corresponding to Dirichlet Forms of the kind .We obtain convergence in total variation norm of the corresponding probability measures on the path space C(₊;^d) under hypotheses which, for example, are satisfied in the case of H _loc ¹ ( ^d )-convergence of the 's, but we can allow more singular situations as regards the approximating sequences. We use then these results to give a criterion of convergence for generalized Schrödinger operators in which the potential function should not necessarily exists as a measurable function. We obtain convergence not only in strong resolvent sense, but we also obtain convergence in the uniform operator topology up to sets of arbitrarily small Lebesgue measure. Applications to the problem of the approximation of ordinary Schrödinger operators by generalized ones corresponding to zero-range interactions are given.     

Skew Brownian motion-type of extensions

We consider a class of possible extensions of a given symmetric Feller processZ _t fromR{0} to the entire real lineR, depending on a parameter [0, 1]. It is proved that the proposed extension exists if =1/2; for 1/2, exists if and only ifZ _t does not jump over 0 (e.g., ifZ _t is a diffusion).     

The uniform modulus of continuity of iterated Brownian motion

LetX be a Brownian motion defined on the line (withX(0)=0) and letY be an independent Brownian motion defined on the nonnegative real numbers. For allt0, we define theiterated Brownian motion (IBM),Z, by setting . In this paper we determine the exact uniform modulus of continuity of the process Z.Research supported by NSF grant DMS-9122242.