It is well known that in addition to the longitudinal modulus, viscoelastic liquids show a shear stiffness at sufficiently high probe frequencies due to structural relaxations. For probe frequencies that are large compared to the structural relaxation frequency, the measured elastic longitudinal and shear moduli become so-called clamped properties (c(11)(infinity) and c(44)(infinity), respectively). During freezing or polymerization of amorphous liquids, these clamped moduli behave in a strongly nonlinear fashion as a function of temperature or polymerization time. Based on Brillouin spectroscopy data we will show that there exists a linear relation between c(11)(infinity) and c(44)(infinity) over a large temperature or polymerization time range. Surprisingly, the parameters of this linear relation between the elastic moduli vary only little for different materials. Implications for the nonlinear elastic behavior at the glass transition will be discussed on the basis of mode Gruneisen parameters

We investigate the response of two-dimensional pattern-forming systems with a broken up-down symmetry, such as chemical reactions, to spatially resonant forcing and propose related experiments. The nonlinear behavior immediately above threshold is analyzed in terms of amplitude equations suggested for a 1:2 and 1:1 ratio between the wavelength of the spatial periodic forcing and the wavelength of the pattern of the respective system. Both sets of coupled amplitude equations are derived by a perturbative method from the Lengyel-Epstein model describing a chemical reaction showing Turing patterns, which gives us the opportunity to relate the generic response scenarios to a specific pattern-forming system. The nonlinear competition between stripe patterns and distorted hexagons is explored and their range of existence, stability, and coexistence is determined. Whereas without modulations hexagonal patterns are always preferred near onset of pattern formation, single-mode solutions (stripes) are favored close to threshold for modulation amplitudes beyond some critical value. Hence distorted hexagons only occur in a finite range of the control parameter and their interval of existence shrinks to zero with increasing values of the modulation amplitude. Furthermore, depending on the modulation amplitude, the transition between stripes and distorted hexagons is either subcritical or supercritical.

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