Gap functions and global error bounds for differential variational–hemivariational inequalities

This paper concerns with the study of a differential variational–hemivariational inequality (DVHVI, for short) in infinite-dimensional Banach spaces. We first introduce the new concept of gap functions for the variational control system of (DVHVI). Then, we consider two kinds of gap functions which are regularized gap function and Moreau–Yosida regularized gap function, respectively, and examine the relevant properties of the gap functions. Moreover, two global error bounds which depend implicitly on the regularized gap function and the Moreau–Yosida regularized gap function, accordingly, are obtained. Finally, in order to illustrate the applicability of the theoretical results, we investigate a coupled dynamic system which is formulated by a nonlinear reaction–diffusion equation described by a time-dependent nonsmooth semipermeability problem.     

Variational methods for fluid–structure interaction and porous media

In this work we consider a poroelastic, flexible material that may deform largely, which is situated in an incompressible fluid driven by the Navier–Stokes equations in two or three space dimensions. By a variational approach we show existence of weak solutions for a class of such coupled systems. We consider the unsteady case, this means that the PDE for the poroelastic solid involves the Fréchet-derivative of a non-convex functional as well as (second order in time) inertia terms.     

Detection on micro-Doppler effect based on 1550 nm laser coherent radar

A laser coherent detection system of 1550 nm wavelength was presented, and experimental research on detecting micro-Doppler effect in a dynamic target was developed. In this paper, the return signal in the time domain is decomposed into a set of components in different wavelet-scales by multi-resolution analysis, and the components are associated with the vibrational motions in a target. The micro-Doppler signatures are extracted by applying the reconstruction (inverse wavelet transform). During the course of the final data processing frequency analysis and time–frequency analysis are applied to analyze the vibrational signals and estimate the motion parameters successfully. The experimental results indicate that the micro-Doppler information in a moving can be effectively detected, and tiny vibrational signatures also can be acquired effectively by wavelet multi-resolution analysis and time–frequency analysis.     

Modeling emissivity of low-emissivity coating containing horizontally oriented metallic flake particles

The scattering and absorption cross sections of horizontally oriented metallic flake particles are estimated by extended geometric optics that includes diffraction and edge effects. Emissivity of the coating containing those particles is calculated using Kubelka–Munk theory. The dependence of emissivity of the coating on the radius, thickness, content of metallic flake particles and coating thickness is discussed. Finally, theoretical results are compared with the experimental measurements with Al/acrylic resin coating system and the results show that simulation values are in good agreement with experimental ones.     

The anomalous magnetic moment of the electron

The value of the electron's magnetic moment is a fundamental quantity in physics. Its deviation from the value expected from Dirac theory has given enormous impetus to the field of quantum theory and especially to quantum electrodynamics (QED) as the relativistic quantum field theory of electrodynamics. In fact, the measured values both for free and for bound electrons are explained by corresponding QED calculations on the part per trillion and part per billion level of accuracy, respectively. This agreement is amongst the best known in physics today. In turn, it allows highly precise determinations of related fundamental constants like the fine structure constant α or the electron mass. The present article discusses the application of the continuous Stern–Gerlach effect to the precise measurement of magnetic moments, especially of the electron bound in highly charged ions and possible tests of calculations in the framework of QED of bound states. Also, a test of QED in a more general approach by the comparison of values for the fine structure constant derived from different measurements, will be discussed.     

Concerning free volume quantities and the glass temperature

Free volume quantities proposed earlier by Boyer and Simha in connection with the glass transition are reformulated by taking into account the temperature dependence of the thermal expansivities α _l and α_g for the liquid and the glass, respectively. This necessitates an extrapolation of the liquid to temperatures below Tg which is performed by means of the reduced volume-temperature function established and given a theoretical foundation previously. For the glass, low temperature experimental data, encompassing all relaxations occuring below T_g, are required.

Two polymer series are examined in detail, namely, poly(methacrylates) and poly(vinyl) alkyl ethers, where α_g has been measured between at least 30°K and T_g. Results for poly(methylacrylate) and poly(styrene) are also given. The systematic decrease in the product (αl - αg) · T|_T=Tg with increasing length of the side chain noted previously is considerably reduced but not eliminated when the appropriately corrected expression is substituted instead. However, the free volume fraction related to the quantity αlT|_T=Tg remains more nearly invariant in the polymers analyzed.

An alternative treatment is discussed which considers an occupied volume expanding below T_g by a mechanism of thermal vibrations solely. Experimental and theoretical means of obtaining this quantity arc suggested.     

Effects of the Synergy of Hardness and Resilience on the Akron Abrasion Properties of SBR Vulcanizates

The hardness (H) and resilience (R) of rubber vulcanizates were combined together in this paper, named as hardness–resilience product (H⁴R), and its relationship with the Akron abrasion loss was investigated using various styrene-butadiene rubber (SBR) vulcanizates possessing specific hardness and resilience characteristics as samples. For the unfilled SBR vulcanizates with different chain microstructure, possessing high elastic resilience and low hardness, the results showed that their Akron abrasion loss had a good linear relationship with the log(H⁴100R). This linear relationship also occurred when these SBRs were filled with 50 phr carbon black. For two particular types of SBR, after being filled with different fractions of carbon black and aged for different times, all their Akron abrasion losses (including unaged, aged for 24 h, and aged for 48 h) also had a good linear relationship with the log(H⁴100R). However, this linear relationship weakened for one of the SBRs after being aged for 48 h. In the high H⁴R region (the carbon black fractions being 60 and 70 phr), the data obviously deviated from the fitting curve due to the high hardness of the aged vulcanizates. However, after being filled with 50 phr of various kinds of carbon blacks, the relationships between abrasion loss and log(H⁴100R) were also approximately linear, with the correlation coefficient of the fitting curves being 0.99966 and 0.99878, respectively, for the two types of SBR.