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Register a new userEffect of physical aging on the low-frequency vibrational density of states of a glassy polymer
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The effects of the physical aging on the vibrational density of states (VDOS) of a polymeric glass is studied. The VDOS of a poly(methyl methacrylate) glass at low-energy (<15 meV), was determined from inelastic neutron scattering at low-temperature for two different physical thermodynamical states. One sample was annealed during a long time at temperature lower than Tg, and another was quenched from a temperature higher than Tg. It was found that the VDOS around the boson peak, relatively to the one at higher energy, decreases with the annealing at lower temperature than Tg, i.e., with the physical aging.
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We investigate the high-frequency behavior of the density of vibrational states in three-dimensional elasticity theory with spatially fluctuating elastic moduli. At frequencies well above the mobility edge, instanton solutions yield an exponentially decaying density of states. The instanton solutions describe excitations, which become localized due to the disorder-induced fluctuations, which lower the sound velocity in a finite region compared to its average value. The exponentially decaying density of states (known in electronic systems as the Lifshitz tail) is governed by the statistics of a fluctuating-elasticity landscape, capable of trapping the vibrational excitations.
We study a recently introduced and exactly solvable mean-field model for the density of vibrational states $mathcal{D}(omega)$ of a structurally disordered system. The model is formulated as a collection of disordered anharmonic oscillators, with random stiffness $kappa$ drawn from a distribution $p(kappa)$, subjected to a constant field $h$ and interacting bilinearly with a coupling of strength $J$. We investigate the vibrational properties of its ground state at zero temperature. When $p(kappa)$ is gapped, the emergent $mathcal{D}(omega)$ is also gapped, for small $J$. Upon increasing $J$, the gap vanishes on a critical line in the $(h,J)$ phase diagram, whereupon replica symmetry is broken. At small $h$, the form of this pseudogap is quadratic, $mathcal{D}(omega)simomega^2$, and its modes are delocalized, as expected from previously investigated mean-field spin glass models. However, we determine that for large enough $h$, a quartic pseudogap $mathcal{D}(omega)simomega^4$, populated by localized modes, emerges, the two regimes being separated by a special point on the critical line. We thus uncover that mean-field disordered systems can generically display both a quadratic-delocalized and a quartic-localized spectrum at the glass transition.
Individuals often develop reluctance to change their social relations, called secondary homebody, even though their interactions with their environment evolve with time. Some memory effect is loosely present deforcing changes. In other words, in presence of memory, relations do not change easily. In order to investigate some history or memory effect on social networks, we introduce a temporal kernel function into the Heider conventional balance theory, allowing for the quality of past relations to contribute to the evolution of the system. This memory effect is shown to lead to the emergence of aged networks, thereby perfectly describing and the more so measuring the aging process of links (social relations). It is shown that such a memory does not change the dynamical attractors of the system, but does prolong the time necessary to reach the balanced states. The general trend goes toward obtaining either global (paradise or bipolar) or local (jammed) balanced states, but is profoundly affected by aged relations. The resistance of elder links against changes decelerates the evolution of the system and traps it into so named glassy states. In contrast to balance
Glasses possess more low-frequency vibrational modes than predicted by Debye theory. These excess modes are crucial for the understanding the low temperature thermal and mechanical properties of glasses, which differ from those of crystalline solids. Recent simulational studies suggest that the density of the excess modes scales with their frequency $omega$ as $omega^4$ in two and higher dimensions. Here, we present extensive numerical studies of two-dimensional model glass formers over a large range of glass stabilities. We find that the density of the excess modes follows $D_text{exc}(omega)sim omega^2 $ up to around the boson peak, regardless of the glass stability. The stability dependence of the overall scale of $D_text{exc}(omega)$ correlates with the stability dependence of low-frequency sound attenuation. However, we also find that in small systems, where the first sound mode is pushed to higher frequencies, at frequencies below the first sound mode there are excess modes with a system size independent density of states that scales as $omega^3$.
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-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), the dielectric relaxation is perfectly consistent with stretched-exponential behaviour with Kohlrausch exponents $0.56 < beta < 0.65$, 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.
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