Related papers: Stiffest Elastic Networks
This is the second paper devoted to energetic rigidity, in which we apply our formalism to examples in two dimensions: underconstrained random regular spring networks, vertex models, and jammed packings of soft particles. Spring networks…
The relation between network structure and dynamics is determinant for the behavior of complex systems in numerous domains. An important long-standing problem concerns the properties of the networks that optimize the dynamics with respect…
The role of fixed degrees of freedom in soft/granular matter systems has broad applicability and theoretical interest. Here we address questions of the geometrical role that a scaffolding of fixed particles plays in tuning the threshold…
We formulate an effective medium (mean field) theory of a material consisting of randomly distributed nodes connected by straight slender rods, hinged at the nodes. Defining novel wavelength-dependent effective elastic moduli, we calculate…
We present general, computable, improvable, and rigorous bounds for the total energy of a finite heterogeneous volume element or a periodically distributed unit cell of an elastic composite of any known distribution of inhomogeneities of…
Networks of stiff fibers govern the elasticity of biological structures such as the extracellular matrix of collagen. These networks are known to stiffen nonlinearly under shear or extensional strain. Recently, it has been shown that such…
Intermediate filaments are cytoskeletal proteins that are key regulators of cell mechanics, a role which is intrinsically tied to their hierarchical structure and their unique ability to accommodate large axial strains. However, how the…
Cells actively probe and respond to the stiffness of their surroundings. Since mechanosensory cells in connective tissue are surrounded by a disordered network of biopolymers, their in vivo mechanical environment can be extremely…
The robustness of deep neural networks is crucial to modern AI-enabled systems and should be formally verified. Sigmoid-like neural networks have been adopted in a wide range of applications. Due to their non-linearity, Sigmoid-like…
The past decade has witnessed the development and success of coarse-grained network models of proteins for predicting many equilibrium properties related to collective modes of motion. Curiously, the results are usually robust towards the…
In this paper, we study the preferential stiffness and the crack-tip fields for an elastic porous solid of which material properties are dependent upon the density. Such a description is necessary to describe the failure that can be caused…
We review the physical properties of macromolecular networks, consisting of semiflexible polymers such as actin. We start by giving a theoretical analysis of the conformational statistics and mechanical response of single filaments.…
A new formalism is used for a Monte Carlo determination of the elastic constants of a two-dimensional net of fixed connectivity. The net is composed of point-like atoms each of which is tethered to six neighbors by a bond limiting the…
Complex networks are ubiquitous: a cell, the human brain, a group of people and the Internet are all examples of interconnected many-body systems characterized by macroscopic properties that cannot be trivially deduced from those of their…
Disordered fibrous networks are ubiquitous in nature as major structural components of living cells and tissues. The mechanical stability of networks generally depends on the degree of connectivity: only when the average number of…
We review the theoretical bounds on the effective properties of linear elastic inhomogeneous solids (including composite materials) in the presence of constituents having non-positive-definite elastic moduli (so-called negative-stiffness…
The non-linear stress-strain relation for crosslinked polymer networks is studied using molecular dynamics simulations. Previously we demonstrated the importance of trapped entanglements in determining the elastic and relaxational…
Phase separation has recently emerged as an important organizational principle in the dense and heterogeneous environment within living cells. Here, we use a synthetic system to show that compressive stresses in a polymer network suppress…
Complex networks grow subject to structural constraints which affect their measurable properties. Assessing the effect that such constraints impose on their observables is thus a crucial aspect to be taken into account in their analysis. To…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…