Schallgeschwindigkeitsmessungen in Schmelzen aus den Systemen Al−Mg,Al−Sn,Mg−Sn und Fe−C

The concentration dependency of sound velocity was measured in molten alloys of the three systems Al–Mg, Al–Sn, and Mg–Sn in the temperature region between liquidus and 1000°C. Furthermore it was measured in molten alloys of the system Fe–C in the temperature range between liquidus temperatureT _L andT _L+150°C. From the velocities the compressibilities were calculated, whose concentration dependency revealed changes in the structure of the melts.The structure of the three systems Al–Mg, Al–Sn, and Mg–Sn in the molten state was already investigated by X-Ray diffraction. These results were compared with the results of velocity measurements. Inhomogeneities in the melts yield increased values of compressibility compared with the values to be expected for statistical distribution of the atoms. This result was used for the discussion of the structure of molten Fe-C-alloys:The conclusion can be drawn, that within the melts of the system Fe–C above 3^w/0 C inhomogeneities are existent.From the values of sound velocity in the molten elements the temperature dependency of the structure factorsI(0) was calculated and compared with experimental values.

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Teil der Dissertation von U. Maier, Universität Stuttgart, 1972.     

Parametrically driven sine-Gordon equation and Painlevé test

The Painlevé test for the parametrically driven sine-Gordon equation $\text{u}{}_{\mathrm{tt}}\text{? u}{}_{\mathrm{xx}}\text{+ ?(t)}\text{sin}\text{u = 0}$ is performed. A new equation is derived which passes the Painlevé test. The connection with the integrability is discussed.     

Generalized liouville equation,entropy, and dynamic systems containing limit cycles

The relation between the generalized Liouville equation, entropy production rates and autonomous systems of differential equations containing limit cycles is investigated. Moreover, the connection between the generalized Liouville equation and the Lie derivative of a differential form with respect to a vector field is discussed.     

Fermi-Bose Systems, Macroscopic Quantum Superposition States and Entanglement

We study the entanglement of states of a simple Fermi-Bose system. The Hilbert space is C ² l₂ (N). An explicit expression is given for the entanglement. We consider number states, coherent states and macroscopic quantum superposition states in the product system. Explicit formulas for the entanglement are also given in each of these cases.     

Entanglement, Hubbard Model, and Symmetries

Entangled quantum states are an important component of quantum computing techniques such as quantum error-correction, dense coding, and quantum teleportation. We use the requirements for a state in the Hilbert space C ² C ² to be entangled to find when states evolving under the two-point Hubbard model become entangled. We also investigate the connection of entanglement and discrete symmetries of the two-point Hubbard model. Furthermore we discuss the inclusion of phonon coupling.     

A comment on the generalized Liouville equation

The generalized Liouville equation is studied in a new light using the Lie derivative of a differential form with respect to a vector field.     

Acoustics of gas-saturated foams: Modelling comparisons

We show results obtained by Biot's equations and a simple Theory of Porous Media-based hybrid model describing acoustical waves in a gas-saturated high-porous foam. The resulting dispersion relations for the longitudinal mode and phase velocities vs. porosity show the extraordinary effect of waves in gas-saturated porous media. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic analysis of porous materials: Numerical modeling with a space-time FEM

In the current work, we investigate the dynamic analysis of a two-phase porous material using the space-time discontinuous Galerkin method. The physical model is based on the Theory of Porous Media (TPM). The finite element approximation consists of continuous approximations in space but discontinuous ones in time. The continuity condition between the adjacent time intervals is weakly enforced by the upwind flux treatment. No artificial penalty function is involved. Moreover, the Embedded Velocity Integration technique is applied to reduce the second-order equation in time into a first order one without introducing an additional constraint. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)