A note on the finite fractal dimension of the global attractors for dissipative nonlinear Schrödinger‐type equations

In this article, we present, throughout two basic models of damped nonlinear Schrödinger (NLS)–type equations, a new idea to bound from above the fractal dimension of the global attractors for NLS‐type equations. This could answer the following open issue: consider, for instance, the classical one‐dimensional cubic nonlinear Schrödinger equation $$u_t+i{u}_{xx}+i|u{|}^{2}u+\gamma u=f,f\in {\mathrm{??}}^2(?).$$ “How can we bound the fractal dimension of the associate global attractor without the need to assume that the external forcing term f has some decay at infinity (that is belonging to some weighted Lebesgue space)?”     

Uniform stabilization to equilibrium of a nonlinear fluid–structure interaction model

We consider uniform stability to a nontrivial equilibrium of a nonlinear fluid–structure interaction (FSI) defined on a two or three dimensional bounded domain. Stabilization is achieved via boundary and/or interior feedback controls implemented on both the fluid and the structure. The interior damping on the fluid combining with the viscosity effect stabilizes the dynamics of fluid. However, this dissipation propagated from the fluid alone is not sufficient to drive uniformly to equilibrium the entire coupled system. Therefore, additional interior damping on the wave component or boundary porous like damping on the interface is considered. A geometric condition on the interface is needed if only boundary damping on the wave is active. The main technical difficulty is the mismatch of regularity of hyperbolic and parabolic component of the coupled system. This is overcome by considering special multipliers constructed from Stokes solvers. The uniform stabilization result obtained in this article is global for the fully coupled FSI model.     

Gelation Kinetics-Structure Analysis of pH-triggered Low Molecular Weight Hydrogelators

Properties such as shear modulus, gelation time, structure of supramolecular hydrogels are strongly dependent on self-assembly, gelation triggering mechanism and processes used to form the gel. In our work we extend reported rheology analysis methodologies to pH-triggered supramolecular gels to understand structural insight using a model system based on N−N’ Dibenzoyl-L-Cystine pH-triggered hydrogelator and Glucono-δ-Lactone as the trigger. We observed that Avrami growth model when applied to time-sweep rheological data of gels formed at lower trigger concentrations provide estimates of fractal dimension which agree well compared with visualization of the microstructure as seen via Confocal Laser Scanning Microscopy, for a range of gelator concentrations.     

The minimal dimensions of faithful representations for Heisenberg Lie superalgebras

This paper aims to determine the minimal dimensions and super-dimensions of faithful representations for Heisenberg Lie superalgebras over an algebraically closed field of characteristic zero.     

初始状态对自组织演化过程的影响

从实验上系统研究了在强电场下处于介质中的大量金属小球从不同初始状态通过自组织演化为分形的过程;用Sandbox方法定量分析了最终形成的稳定树枝状分形的维数。结果表明:不同初始状态形成分形的过程完全不同,但最终的树枝状分形的维数基本相同。分析认为,小球之间的相互作用存在临界作用距离,不同初始状态相邻小球之间的平均间距不同,因而演化过程不同;而维数相同正是系统耗散相同的体现。     

基于概率密度演化的输电塔-线体系抗风可靠性分析

以三线两塔直线段输电塔-线体系为工程对象,应用有限元数值模拟,建立了基于概率密度演化的输电塔-线体系抗风可靠性分析方法。首先,应用谱表示-降维方法模拟结构脉动风场,生成风荷载的代表性样本集合。然后,结合概率密度演化理论,分析了输电塔-线体系考虑气弹效应的随机动力反应。最后,应用等价极值思想构建了风荷载作用下输电塔-线体系失效准则,进而对输电塔-线体系的抗风可靠性进行精细化分析。本文结合谱表示-降维方法与概率密度演化理论,实现了仅用较少数量的代表性样本来精细地分析结构的抗风可靠性,为工程实践提供参考。     

Surface properties of silica gel samples modified by selected proteins

The adsorption of a polar (water) and a non-polar (n-octane) liquid on silica gels, modified by adsorption of proteins, has been studied by thermal analysis. Silica gels with physically adsorbed BSA and ovalbumin layers were used. Thermodesorption energies were determined from Q-TG and Q-DTG curves recorded under quasi-equilibrium conditions. Significant differences in liquid desorption were observed from the surfaces due to heterogeneous changes (energetic and geometrical) as a result of modification. These results are compared with those obtained for the samples heated at 160°C for 1 h.     

Studies of heterogeneity properties of selected high-temperature superconductor surfaces

Nitrogen adsorption measured at 77 K was used to characterize the surface heterogeneity of high-temperature superconductor surfaces. Properties relating to adsorption and porosity of the solids (adsorption capacity, specific surface area, radii and volume of the pores, pore-size distribution function) were determined from nitrogen adsorption–desorption isotherms and atomic force microscopy (AFM) for a series of oxide superconductors. It is shown that the adsorption isotherms of all samples are S-shaped and belong to type II according to the IUPAC classification. On the basis of the nitrogen adsorption isotherms and AFM data, fractal dimensions were determined and correlations found with adsorption and porosity parameters.