Matrices and Their (Un)Faithful Fermi-quadratic Forms

International Journal of Theoretical Physics - We consider the algebra of n × n matrices over ℂ and their corresponding Fermi-quadratic forms. The properties of these operators are...     

Microscale Investigations of Highfrequency Wave Propagation Through Highly Porous Media

Wave propagation in highly porous materials has a well established theoretical background. Still there are parameters which require complex laboratory experimentation in order to find numerical values. This paper presents an effective method to calculate the tortuosity of aluminum foam using numerical simulations. The work flow begins with the acquisition of the foam geometry by means of a micro-CT scanner and further image segmentation and analysis. The elastodynamic wave propagation equation is solved using a velocity-stress rotated staggered finite-difference technique. The effective wave velocities are calculated and using the fluid and, aluminum effective properties, the tortuosity is determined. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An alternative separation procedure for 90Sr age dating using DGA Resin

Journal of Radioanalytical and Nuclear Chemistry - The likelihood of an attack by a terrorist organization using a radiological dispersal device (RDD) is much higher than that of an attack with an...     

Exact complexity of the logistic map

The relation between chaotic behavior and complexity for one-dimensional maps is discussed. The one-dimensional maps are mapped into a binary string via symbolic dynamics in order to evaluate the complexity. We apply the complexity measure of Lempel and Ziv to these binary strings. To characterize the chaotic behavior, we calculate the Liapunov exponent. We show that the exact normalized complexity for the logistic mapf: [0,1]→[0,1],f(x)=4x(1−x) is given by 1.     

Phase-coupled nonlinear dynamical systems, stability, first integrals, and Liapunov exponents

The stability of a class of coupled identical autonomous systems of first-order nonlinear ordinary differential equations is investigated. These couplings play a central role in controlling chaotic systems and can be applied in electronic circuits and laser systems. As applications we consider a coupled van der Pol equation and a coupled logistic map. When the uncoupled system admits a first integral we study whether a first integral exists for the coupled system. Gradient systems and the Painlevé property are also discussed. Finally, the relation of the Liapunov exponents of the uncoupled and coupled systems are discussed.     

Lax representation and Kronecker product

We show how the Kronecker product can be used to find new Lax representations.     

Impact of heterogeneously distributed solid particles in the transition zone between porous and free flow domain

We present a direct numerical simulation approach for the simulation of shallow water flow using the particle based meshfree Smoothed Particle Hydrodynamics (SPH) method. Simulations of single phase flow are done to characterize the occurring flow parameters on both macro-scale and pore-scale. More precisely, we examine initiation of motion and sediment transport as appearing at the interface between a free flow and porous flow domain under parallel flow conditions. Therefore we evaluate three theoretical models presenting analytical solutions for this coupled problem. Moreover, we discuss the influence of heterogeneities at the interface on forces on single grains by implementing and testing various microstructures into our numerical model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parametrically driven pendulum and exact solutions

The parametrically driven pendulumx +f ₁(t) x +f ₂(t) sinx = 0 cannot be solved in closed form for arbitrary functionvsf ₁,f ₂. We apply the Painlevé test to obtain the constraint on the functionsf ₁, andf ₂ for which the equation passes the test. The constraint onf ₁, andf ₂, a differential equation whichf ₁ andf ₂ obey, is discussed and solutions are given. The third Painlevé transcendent plays a central role.     

On a hierarchy of nonlinear dynamical systems and Painlevé test

A hierarchy of nonlinear dynamical systems is studied applying the Painlevé test. An interesting connection between a reduced self-dual Yang-Mills equation and a reduced Yang-Mills equation is given.     

Über die Interpretation der Röntgenbeugungsdiagramme von mehrkomponentigen Schmelzen

The final results of x-ray diffraction experiments in molten alloys are electron distribution curves. These are used to get a decision between statistical distribution of the atoms of different kinds in the melt, between ordering of the atoms or between segregation. The according equations are deduced and finally a simple graphical method for the evaluation of the results is given. Important fact for the evaluation of molten alloys with a great difference between the atomic numbers of the two components is the number of scattering electrons in the first coordination sphere. With molten alloys which show little difference between the atomic numbers of the components the radius of the first coordination sphere is deciding. Finally it is shown, that the short range order parameter, which until now only was used in regard to the ordering in solid solutions, also can be used to get valuable results of the degree of ordering in molten alloys.