Related papers: Statistical Mechanical Model for a closed loop ple…
Presented here, is a technical manuscript that may form the basis of later published work. In it, we develop a statistical mechanical model to describe a closed loop plectoneme, applicable for when the closed loop is sufficiently…
Soft elastic filaments that can be stretched, bent and twisted exhibit a range of topologically and geometrically complex morphologies that include plectonemes, solenoids, knot-like and braid-like structures. We combine numerical…
The work in this article is inspired by a classical problem: the statistical physical properties of a closed polymer loop that is wound around a rod. Historically the preserved topology of this system has been addressed through…
A fundamental theory is presented for the mechanical response of polymer networks undergoing large deformation which seamlessly integrates statistical mechanical principles with macroscopic thermodynamic constitutive theory. Our formulation…
Braids composed of two interwoven polymer chains exhibit a buckling transition whose origin has been explained through the onset of plectonemic structures. Here we study, by a combination of simulation and analytics, the dynamics of…
Theoretical studies of nearly spherical vesicles and microemulsion droplets, that present typical examples for thermally-excited systems that are subject to constraints, are reviewed. We consider the shape fluctuations of such systems…
Loops undergoing thermal fluctuations are prevalent in nature. Ring-like or cross-linked polymers, cyclic macromolecules, and protein-mediated DNA loops all belong to this category. Stability of these molecules are generally described in…
We propose a mathematical model to describe the athermal fluctuations of thin sheets driven by the type of random driving that might be experienced prior to weak crumpling. The model is obtained by merging the F\"oppl-von K\'arm\'an…
We present a novel formalism to characterize elastic heterogeneities in amorphous solids. In particular, we derive high-order strain-energy expansions for pairwise energies under athermal quasistatic dynamics. We then use the presented…
We investigate the statistical mechanics of a torsionally constrained polymer. The polymer is modeled as a fluctuating rod with bend stiffness A kT and twist stiffness C kT. In such a model, thermal bend fluctuations couple geometrically to…
We introduce a random matrix framework for studying statistical-mechanical lattice systems through spectral observables. Equilibrium configurations sampled from a Boltzmann measure are mapped to matrix ensembles whose covariance structure…
Thermally fluctuating sheets and ribbons provide an intriguing forum in which to investigate strong violations of Hooke's Law: large distance elastic parameters are in fact not constant, but instead depend on the macroscopic dimensions.…
Variational methods are used to calculate structural and thermodynamical properties of a titrating polyelectrolyte in a discrete representation. The Coulomb interactions are emulated by harmonic repulsive forces, the force constants being…
We propose a simple and efficient scheme based on adaptive finite elements over conforming quadtree meshes for collapse plastic analysis of structures. Our main interest in kinematic limit analysis is concerned with both purely…
We present new rectangular mixed finite elements for linear elasticity. The approach is based on a modification of the Hellinger-Reissner functional in which the symmetry of the stress field is enforced weakly through the introduction of a…
We investigate the dynamics of elastic microstructures within a fluid that are subjected to thermal fluctuations. We perform analysis to obtain systematically simplified descriptions of the mechanics in the limiting regimes when (i) the…
A stress equilibration procedure for linear elasticity is proposed and analyzed in this paper with emphasis on the behavior for (nearly) incompressible materials. Based on the displacement-pressure approximation computed with a stable…
A novel variational framework to model the fatigue behavior of brittle materials based on a phase-field approach to fracture is presented. The standard regularized free energy functional is modified introducing a fatigue degradation…
A mathematical continuum limit of the interaction energy of a random particle chain is shown to yield new insight into the effect of microscopic heterogeneities on macroscopic fracture laws in brittle materials. We derive a formula which…
We consider the statistical mechanics of a classical particle in a one-dimensional box subjected to a random potential which constitutes a Wiener process on the coordinate axis. The distribution of the free energy and all correlation…