Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userReal Space Renormalization: A Generic Microscopic Theory for Low-Temperature Avalanches in Static Strained Insulating Glass
86
0
0.0
(
0
)
Authors
Di Zhou
Ask ChatGPT about the research
No Arabic abstract
We propose a microscopic model to study the avalanche problem of insulating glass deformed by external static uniform strain below $T=60$K. We use three-dimensional real-space renormalization procedure to carry out the glass mechanical susceptibility at macroscopic length scale. We prove the existence of irreversible stress drops in amorphous materials, corresponding to the steep positive-negative transitions in glass mechanical susceptibility. We also obtain the strain directions in which the glass system is brittle. The irreversible stress drops in glass essentially come from non-elastic stress-stress interaction which is generated by virtual phonon exchange process.
rate research
Read More
We study the glass and jamming transition of finite-dimensional models of simple liquids: hard- spheres, harmonic spheres and more generally bounded pair potentials that modelize frictionless spheres in interaction. At finite temperature, we study their glassy dynamics via field-theoretic methods by resorting to a mapping towards an effective quantum mechanical evolution, and show that such an approach resolves several technical problems encountered with previous attempts. We then study the static, mean-field version of their glass transition via replica theory, and set up an expansion in terms of the corresponding static order parameter. Thanks to this expansion, we are able to make a direct and exact comparison between historical Mode-Coupling results and replica theory. Finally we study these models at zero temperature within the hypotheses of the random-first-order-transition theory, and are able to derive a quantitative mean-field theory of the jamming transition. The theoretic methods of field theory and liquid theory used in this work are presented in a mostly self-contained, and hopefully pedagogical, way. This manuscript is a corrected version of my PhD thesis, defended in June, 29th, under the advisorship of Frederic van Wijland, and also contains the result of collaborations with Ludovic Berthier and Francesco Zamponi. The PhD work was funded by a CFM-JP Aguilar grant, and conducted in the Laboratory MSC at Universite Denis Diderot--Paris 7, France.
Glass sound velocity shift was observed to be longarithmically temperature dependent in both relaxation and resonance regimes: $Delta c/c=mathcal{C}ln T$. It does not monotonically increase with temperature from $T=0$K, but to reach a maximum around a few Kelvin. Different from tunneling-two-level-system (TTLS) which gives the slope ratio between relaxation and resonance regimes $mathcal{C}^{rm rel }:mathcal{C}^{rm res }=-frac{1}{2}:1$, we develop a generic coupled block model to give $mathcal{C}^{rm rel }:mathcal{C}^{rm res }=-1:1$, which agrees well with the majority of experimental measurements. We use electric dipole-dipole interaction to carry out a similar behavior for glass dielectric constant shift $Delta epsilon/epsilon=mathcal{C}ln T$. The slope ratio between relaxation and resonance regimes is $mathcal{C}^{rm rel}:mathcal{C}^{rm res}=1:-1$ which agrees with dielectric measurements quite well. By developing a renormalization procedure for non-elastic stress-stress and dielectric susceptibilities, we prove these universalities essentially come from $1/r^3$ long range interactions, independent of materials microscopic properties.
We study the spectrum of the Hessian of the Sherrington-Kirkpatrick model near T=0, whose eigenvalues are the masses of the bare propagators in the expansion around the mean-field solution. In the limit $Tll 1$ two regions can be identified. The first for $x$ close to 0, where $x$ is the Parisi replica symmetry breaking scheme parameter. In this region the spectrum of the Hessian is not trivial, and maintains the structure of the full replica symmetry breaking state found at higher temperatures. In the second region $Tll x leq 1$ as $Tto 0$, the bands typical of the full replica symmetry breaking state collapse and only two eigenvalues are found: a null one and a positive one. We argue that this region has a droplet-like behavior. In the limit $Tto 0$ the width of the full replica symmetry breaking region shrinks to zero and only the droplet-like scenario survives.
The spin glass behavior near zero temperature is a complicated matter. To get an easier access to the spin glass order parameter $Q(x)$ and, at the same time, keep track of $Q_{ab}$, its matrix aspect, and hence of the Hessian controlling stability, we investigate an expansion of the replicated free energy functional around its ``spherical approximation. This expansion is obtained by introducing a constraint-field and a (double) Legendre Transform expressed in terms of spin correlators and constraint-field correlators. The spherical approximation has the spin fluctuations treated with a global constraint and the expansion of the Legendre Transformed functional brings them closer and closer to the Ising local constraint. In this paper we examine the first contribution of the systematic corrections to the spherical starting point.
Mechanical deformation of amorphous solids can be described as consisting of an elastic part in which the stress increases linearly with strain, up to a yield point at which the solid either fractures or starts deforming plastically. It is well established, however, that the apparent linearity of stress with strain is actually a proxy for a much more complex behavior, with a microscopic plasticity that is reflected in diverging nonlinear elastic coefficients. Very generally, the complex structure of the energy landscape is expected to induce a singular response to small perturbations. In the athermal quasistatic regime, this response manifests itself in the form of a scale free plastic activity. The distribution of the corresponding avalanches should reflect, according to theoretical mean field calculations (Franz and Spigler, Phys. Rev. E., 2017, 95, 022139), the geometry of phase space in the vicinity of a typical local minimum. In this work, we characterize this distribution for simple models of glass forming systems, and we find that its scaling is compatible with the mean field predictions for systems above the jamming transition. These systems exhibit marginal stability, and scaling relations that hold in the stationary state are examined and confirmed in the elastic regime. By studying the respective influence of system size and age, we suggest that marginal stability is systematic in the thermodynamic limit.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
