Fatigue in asphalt mixtures – a summary to understand the complexity of its mathematical modeling

Based on the reviewed literature in relation to the phenomenon of fatigue in asphalt mixtures, the foregoing paper depicts and describes in summary, the main variables that impact in the generation of said phenomenon in asphalt pavements. This has the purpose of showing its complexity to mathematically model it. As a general conclusion obtained in the study, it was found that the calibration difficulty of the models is mainly since the mathematical equations must be in capacity of considering that fatigue resistance of asphalt mixtures depends on load mode (stress-controlled or strain- controlled), the type of load (haversine or sinusoidal) and the rest periods to which laboratory samples are subjected. Additionally, both in situ, as within the laboratory, this varies with stiffness, volumetric composition (type and content of asphalt and aggregate), the geometry of samples, with effects associated to mix durability and environmental conditions, with the type of test, border conditions and support layers (base, subbase, subgrade). If these physical parameters are not considered, the mathematical equations lose reliability.

MOMENTUM AND HAMILTONIAN IN COMPLEX ACTION THEORY

In the complex action theory (CAT) we explicitly examine how the momentum and Hamiltonian are defined from the Feynman path integral (FPI) point of view based on the complex coordinate formalism of our foregoing paper. After reviewing the formalism briefly, we describe in FPI with a Lagrangian the time development of a ξ-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator. Solving this eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led to the momentum relation again via the saddle point for p. This study confirms that the momentum and Hamiltonian in the CAT have the same forms as those in the real action theory. We also show the third derivation of the momentum relation via the saddle point for q.

Energy Gap and Line Shifts for H-Like Ions in Dense Plasmas

Based on the results of a foregoing paper (Z. Naturforsch. 44 a, 519 - 523 (1989)) the density-dependence of the discrete energy states and the continuum level is calculated with better accuracy. A static approximation to the line shifts is derived and discussed

Vapour-liquid equilibrium in the binary systems formed by ethylene glycol, diethylene glycol, and N-methylpyrrolidone

Vapour-liquid equilibrium data are given for the binary systems ethylene glycol (EG)-N-methylpyrrolidone (NMP), ethylene glycol-diethylene glycol (DEG), and N-methylpyrrolidone-diethylene glycol at 50°C. The measurement of vapour-liquid equilibrium was carried out in a modified version of semimicrostill from foregoing paper. This still makes it possible to measure even at the pressures of the order 101 Pa. The dependence of the excess Gibbs energy on composition was expressed by the 4th order Redlich-Kister, Wilson, and NRTL equations. The systems EG-NMP and DEG-NMP exhibit negative deviations from ideal behaviour, EG with DEG form practically ideal solution.

Zur Elektrodynamik turbulent bewegter leitender Medien

In a foregoing paper the foundations for an electrodynamics of mean fields in turbulently moving electrically conducting media were developed. With the method demonstrated there a special case is treated. The turbulence is supposed to deviate from a homogeneous isotropic one showing reflexion symmetry, only due to a gradient of intensity, i. e. of the mean square velocity. The calculations are carried out for small intensities. As a result, expressions for the modified conductivity introduced for homogeneous turbulence in the foregoing paper are given and discussed. The effect of the intensity gradient is illustrated by a simple example. Furthermore, a possibility is shown for describing the general result in terms of modified conductivity and permeability.