The relation between stretched-exponential relaxation and the vibrational density of states in glassy disordered systems

Amorphous solids or glasses are known to exhibit stretched-exponential decay over broad time intervals in several of their macroscopic observables: intermediate scattering function, dielectric relaxation modulus, time-dependent elastic modulus, etc. This behaviour is prominent especially near the glass transition. In this Letter we show, on the example of dielectric relaxation, that stretched-exponential relaxation is intimately related to the peculiar lattice dynamics of glasses. By reformulating the Lorentz model of dielectric matter in a more general form, we express the dielectric response as a function of the vibrational density of states (DOS) for a random assembly of spherical particles interacting harmonically with their nearest-neighbours. Surprisingly we find that near the glass transition for this system (which coincides with the Maxwell rigidity transition in this model), the dielectric relaxation is perfectly consistent with stretched-exponential behaviour with Kohlrausch exponents 0.56<β<0.65, which is the range where exponents are measured in most experimental systems. Crucially, the root cause of stretched-exponential relaxation can be traced back to soft modes (boson-peak) in the DOS

Direct link between boson-peak modes and dielectric α-relaxation in glasses

We compute the dielectric response of glasses starting from a microscopic system-bath Hamiltonian of the Zwanzig-Caldeira-Leggett type and using an ansatz from kinetic theory for the memory function in the resulting generalized Langevin equation. The resulting framework requires the knowledge of the vibrational density of states (DOS) as input, which we take from numerical evaluation of a marginally stable harmonic disordered lattice, featuring a strong boson peak (excess of soft modes over Debye $\sim$ ω$^{2}_{p}$ law). The dielectric function calculated based on this ansatz is compared with experimental data for the paradigmatic case of glycerol at T $\lesssim$ T$_{g}$. Good agreement is found for both the reactive (real) part of the response and for the α-relaxation peak in the imaginary part, with a significant improvement over earlier theoretical approaches. On the low-frequency side of the α peak, the fitting supports the presence of $\sim$ ω$^{4}_{p}$ modes at vanishing eigenfrequency as recently shown [E. Lerner, G. During, and E. Bouchbinder, Phys. Rev. Lett. 117, 035501 (2016)]. α-wing asymmetry and stretched-exponential behavior are recovered by our framework, which shows that these features are, to a large extent, caused by the soft boson-peak modes in the DOS

First detection of stolbur phytoplasma in grapevines (Vitis vinifera cv. Chardonnay) affected with grapevine yellows in the Ukraine

Article first published online: 21 MAR 2005B. Milkus, D. Clair, S. Idir, N. Habili and E. Boudon-Padie

Derivation of nonlinear damping from viscoelasticity in case of nonlinear vibrations

Experiments show a strong increase in damping with the vibration amplitude during nonlinear vibrations of beams, plates and shells. This is observed for large size structures but also for micro- and nanodevices. The present study derives nonlinear damping from viscoelasticity by using a single-degree-of-freedom model obtained from standard linear solid material where geometric nonlinearity is inserted in. The solution of the problem is initially reached by a third-order harmonic balance method. Then, the equation of motion is obtained in differential form, which is extremely useful in applications. The damping model developed is nonlinear and the parameters are identified from experiments. Experimental and numerical results are compared for forced vibration responses measured for two different continuous structural elements: a free-edge plate and a shallow shell. The free-edge plate is interesting since it represents a case with no energy escape through the boundary

Grapevine phytoplasmas

The diseases associated with phytoplasmas in grapevine are collectively called yellows and occur in the majority of grapevine-growing regions over the world. At first, a short overview of symptoms and damage associated with the presence of grapevine phytoplasmas is reported. Then, vectors, alternative host plants, and epidemiological cycles, where known, are discussed for the main grapevine yellows in the different continents. Moreover, potential insect vectors and host plants, together with molecular characterization of the associated phytoplasmas, are reported