相关论文: Application of Polynomial Algorithms to a Random E…
Multiple polymer networks, such as double-network elastomers comprising a sacrificial and a matrix network, exhibit exceptional mechanical resilience, commonly attributed to the formation of an extended damage zone before a crack can grow.…
We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with…
The effect of disorder on flux lattices at equilibrium is studied quantitatively in the absence of free dislocations using both the Gaussian variational method and the renormalization group. Our results for the mean square relative…
We consider a class of elasticity equations in ${\mathbb R}^d$ whose elastic moduli depend on $n$ separated microscopic scales, are random and expressed as a linear expansion of a countable sequence of random variables which are…
A phase field model is presented to investigate dislocation formation (coherency loss) and workhardening in two-phase binary alloys. In our model the elastic energy density is a periodic function of the shear and tetragonal strains, which…
Discovering relationships between materials' microstructures and mechanical properties is a key goal of materials science. Here, we outline a strategy exploiting Bayesian optimization to efficiently search the multidimensional space of…
Motivated by anomalously large conductivity anisotropy in layered materials, we propose a simple model of randomly spaced potential barriers (mimicking stacking faults) with isotropic impurities in between the barriers. We solve this model…
We consider a continuum model of active viscoelastic matter, whereby an active nematic liquid-crystal is coupled to a minimal model of polymer dynamics with a viscoelastic relaxation time $\tau_C$. To explore the resulting interplay between…
The vortex lattice in a Type II superconductor provides a versatile model system to investigate the order-disorder transition in a periodic medium in the presence of random pinning. Here, using scanning tunnelling spectroscopy in a weakly…
A discrete model describing defects in crystal lattices and having the standard linear anisotropic elasticity as its continuum limit is proposed. The main ingredients entering the model are the elastic stiffness constants of the material…
We consider a two-dimensional Ising model with random i.i.d. nearest-neighbor ferromagnetic couplings and no external magnetic field. We show that, if the probability of supercritical couplings is small enough, the system admits a…
The theory of the depinning transition of elastic manifolds in random media provides a framework for the statistical dynamics of dislocation systems at yield. We consider the case of a single flexible dislocation gliding through a random…
We investigate the dynamics of a particle moving randomly along a disordered hetero-polymer subjected to rapid conformational changes which induce superdiffusive motion in chemical coordinates. We study the antagonistic interplay between…
Using the non-interacting Anderson tight-binding model on the Bethe lattice as a toy model for the many-body quantum dynamics, we propose a novel and transparent theoretical explanation of the anomalously slow dynamics that emerges in the…
We investigate the scattering of elastic waves off a disordered region described by a one-dimensional random-phase sine-Gordon model. The collective pinning results in an effective static disorder potential with universal and non-Gaussian…
Understanding how topological constraints affect the dynamics of polymers in solution is at the basis of any polymer theory and it is particularly needed for melts of rings. These polymers fold as crumpled and space-filling objects and,…
It has become increasingly clear that a full understanding of the physics of electrons in disordered systems requires an approach in which both disorder and interactions are taken into account. Work on small numbers of electrons has…
We revisit the classical problem of optimal experimental design (OED) under a new mathematical model grounded in a geometric motivation. Specifically, we introduce models based on elementary symmetric polynomials; these polynomials capture…
This paper presents a framework for abstracting uncertain or non-polynomial components of dynamical systems using polynomial constraints. This enables the application of polynomial-based analysis tools, such as sum-of-squares programming,…
We have studied the aging effect on the dynamics of unbinding of a double stranded directed polymer in a random medium. By using the Monte Carlo dynamics of a lattice model in two dimensions, for which disorder is known to be relevant, the…