Anomalous diffusion and stretched exponentials in heterogeneous glass-forming liquids: Low-temperature behavior

We propose a model of a heterogeneous glass forming liquid and compute the low-temperature behavior of a tagged molecule moving within it. This model exhibits stretched-exponential decay of the wavenumber-dependent, self intermediate scattering function in the limit of long times. At temperatures close to the glass transition, where the heterogeneities are much larger in extent than the molecular spacing, the time dependence of the scattering function crosses over from stretched-exponential decay with an index $b=1/2$ at large wave numbers to normal, diffusive behavior with $b = 1$ at small wavenumbers. There is a clear separation between early-stage, cage-breaking $\beta$ relaxation and late-stage $\alpha$ relaxation. The spatial representation of the scattering function exhibits an anomalously broad exponential (non-Gaussian) tail for sufficiently large values of the molecular displacement at all finite times.Comment: 9 pages, 6 figure

Goldstone-type fluctuations and their implications for the amorphous solid state

In sufficiently high spatial dimensions, the formation of the amorphous (i.e. random) solid state of matter, e.g., upon sufficent crosslinking of a macromolecular fluid, involves particle localization and, concommitantly, the spontaneous breakdown of the (global, continuous) symmetry of translations. Correspondingly, the state supports Goldstone-type low energy, long wave-length fluctuations, the structure and implications of which are identified and explored from the perspective of an appropriate replica field theory. In terms of this replica perspective, the lost symmetry is that of relative translations of the replicas; common translations remain as intact symmetries, reflecting the statistical homogeneity of the amorphous solid state. What emerges is a picture of the Goldstone-type fluctuations of the amorphous solid state as shear deformations of an elastic medium, along with a derivation of the shear modulus and the elastic free energy of the state. The consequences of these fluctuations -- which dominate deep inside the amorphous solid state -- for the order parameter of the amorphous solid state are ascertained and interpreted in terms of their impact on the statistical distribution of localization lengths, a central diagnostic of the the state. The correlations of these order parameter fluctuations are also determined, and are shown to contain information concerning further diagnostics of the amorphous solid state, such as spatial correlations in the statistics of the localization characteristics. Special attention is paid to the properties of the amorphous solid state in two spatial dimensions, for which it is shown that Goldstone-type fluctuations destroy particle localization, the order parameter is driven to zero, and power-law order-parameter correlations hold.Comment: 20 pages, 3 figure

Scaling of Entropic Shear Rigidity

The scaling of the shear modulus near the gelation/vulcanization transition is explored heuristically and analytically. It is found that in a dense melt the effective chains of the infinite cluster have sizes that scale sub-linearly with their contour length. Consequently, each contributes k_B T to the rigidity, which leads to a shear modulus exponent d\nu. In contrast, in phantom elastic networks the scaling is linear in the contour length, yielding an exponent identical to that of the random resistor network conductivity, as predicted by de Gennes'. For non-dense systems, the exponent should cross over to d\nu when the percolation length becomes much larger than the density-fluctuation length.Comment: 4 pages, 2 eps figure

The role of multiple marks in epigenetic silencing and the emergence of a stable bivalent chromatin state

We introduce and analyze a minimal model of epigenetic silencing in budding yeast, built upon known biomolecular interactions in the system. Doing so, we identify the epigenetic marks essential for the bistability of epigenetic states. The model explicitly incorporates two key chromatin marks, namely H4K16 acetylation and H3K79 methylation, and explores whether the presence of multiple marks lead to a qualitatively different systems behavior. We find that having both modifications is important for the robustness of epigenetic silencing. Besides the silenced and transcriptionally active fate of chromatin, our model leads to a novel state with bivalent (i.e., both active and silencing) marks under certain perturbations (knock-out mutations, inhibition or enhancement of enzymatic activity). The bivalent state appears under several perturbations and is shown to result in patchy silencing. We also show that the titration effect, owing to a limited supply of silencing proteins, can result in counter-intuitive responses. The design principles of the silencing system is systematically investigated and disparate experimental observations are assessed within a single theoretical framework. Specifically, we discuss the behavior of Sir protein recruitment, spreading and stability of silenced regions in commonly-studied mutants (e.g., sas2, dot1) illuminating the controversial role of Dot1 in the systems biology of yeast silencing.Comment: Supplementary Material, 14 page

Critical Properties of the Emergent Random Solid in Vulcanization / Gelation Transition

U of I OnlyPost 1923. No authorization form