Related papers: Generalized Deam-Edwards Approach to the Statistic…
We consider the gelation of particles which are permanently connected by random crosslinks, drawn from an ensemble of finite-dimensional continuum percolation. To average over the randomness, we apply the replica trick, and interpret the…
We consider a spring-block model with both dry and viscous frictions, subjected to a periodic driving allowing mechanically stable configurations to be sampled. We show that under strong driving, the scaling of the correlation length with…
The vulcanization transition - the crosslink-density-controlled equilibrium phase transition from the liquid to the amorphous solid state - is explored analytically from a renormalization group perspective. The analysis centers on a minimal…
Randomly crosslinked macromolecules undergo a liquid-to-amorphous solid phase transition at a critical crosslink concentration. This transition has two main signatures: the random localization of a fraction of the monomers and the emergence…
We propose a link prediction algorithm that is based on spring-electrical models. The idea to study these models came from the fact that spring-electrical models have been successfully used for networks visualization. A good network…
We obtain, using semi-analytical transfer operator techniques, the Edwards thermodynamics of a one-dimensional model of blocks connected by harmonic springs and subjected to dry friction. The theory is able to reproduce the linear…
A new first-principles statistical mechanics formulation is proposed to describe slow and dilated granular fluids, where prolonged intergranular contacts vitiate collision theory. The contacts, where all the important physics takes place,…
Signatures of the vulcanization transition--amorphous solidification induced by the random crosslinking of macromolecules--include the random localization of a fraction of the particles and the emergence of a nonzero static shear modulus. A…
A Landau theory is constructed for the vulcanization transition in cross-linked polymer systems with spontaneous nematic ordering. The neo-classical theory of the elasticity of nematic elastomers is derived via the minimization of this…
In this thesis the formation and properties of a polymer gel on and at a surface are investigated. The gel under investigation is defined as a three-dimensional network of "phantom" macromolecules that form permanent links with one another…
We present analytical results (up to a numerical diagonalization of a real symmetric matrix) for a set of time- and ensemble-average physical observables in the non-Hookean Gaussian Network Model (GNM) - a generalization of the Rouse model…
We study the rescaled probability distribution of the critical depinning force of an elastic system in a random medium. We put in evidence the underlying connection between the critical properties of the depinning transition and the extreme…
This study presents a Eulerian theory to elucidate the molecular kinematics in polymer networks and their connection to continuum deformation, grounded in fundamental statistical physics and thermodynamics. Three key innovations are…
In many interesting physical settings, such as the vulcanization of rubber, the introduction of permanent random constraints between the constituents of a homogeneous fluid can cause a phase transition to a random solid state. In this…
Spatial heterogeneity in the elastic properties of soft random solids is examined via vulcanization theory. The spatial heterogeneity in the \emph{structure} of soft random solids is a result of the fluctuations locked-in at their…
Under sufficient permanent random covalent bonding, a fluid of atoms or small molecules is transformed into an amorphous solid network. Being amorphous, local structural properties in such networks vary across the sample. A natural order…
The thermodynamics and dynamics of supercooled liquids correlate with their elasticity. In particular for covalent networks, the jump of specific heat is small and the liquid is {\it strong} near the threshold valence where the network…
We report on a novel approach to the Deam-Edwards model for interacting polymeric networks without using replicas. Our approach utilizes the fact that a network modelled from a single non-interacting Gaussian chain of macroscopic size can…
Systems which consist of many localized constituents interacting with each other can be represented by complex networks. Consistently, network science has become highly popular in vast fields focusing on natural, artificial and social…
The fluctuation-dissipation theorem is a cornerstone result in statistical mechanics that can be used to translate the statistics of the free natural variability of a system into information on its forced response to perturbations. By…