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“Viscosity is the most ubiquitous dissipative mechanical behavior” (Maugin, 1999). Despite its ubiquity, even for those systems where the mechanisms causing viscous and other forms of dissipation are known there are only a few quantitative models that extract the macroscopic rheological response from these microscopic mechanisms. One such mechanism is the stochastic breaking and forming of bonds which is present in polymer networks with transient cross-links, strong inter-layer bonding between graphene sheets, and sliding dry friction. In this paper we utilize a simple yet flexible model to show analytically how stochastic bonds can induce an array of rheological behaviors at the macroscale. We find that varying the bond interactions induces a Maxwell-type macroscopic material behavior with Newtonian viscosity, shear thinning, shear thickening, or solid like friction when subjected to shear at constant rates. When bond rupture is independent of the force applied, Newtonian viscosity is the predominant behavior. When bond breaking is accelerated by the applied force, a shear thinning response becomes most prevalent. Further connections of the macroscopic response to the interaction potential and rates of bonding and unbonding are illustrated through phase diagrams and analysis of limiting cases. Finally, we apply this model to polymer networks and tomore »experimental data on “solid bridges” in polydisperse granular media. We imagine possible applications to material design through engineering bonds with specific interactions to bring about a desired macroscopic behavior.« less

Self-assembly of proteins on lipid membranes underlies many important processes in cell biology, such as, exo- and endo-cytosis, assembly of viruses, etc. An attractive force that can cause self-assembly is mediated by membrane thickness interactions between proteins. The free energy profile associated with this attractive force is a result of the overlap of thickness deformation fields around the proteins which can be calculated from the solution of a boundary value problem. Yet, the time scales over which two inclusions coalesce has not been explored, even though the evolution of particle concentrations on membranes has been modeled using phase-field approaches. In this paper we compute this time scale as a function of the initial distance between two inclusions by viewing their coalescence as a first passage time problem. The mean first passage time is computed using Langevin dynamics and a partial differential equation, and both methods are found to be in excellent agreement. Inclusions of three different shapes are studied and it is found that for two inclusions separated by about hundred nanometers the time to coalescence is hundreds of milliseconds irrespective of shape. An efficient computation of the interaction energy of inclusions is central to our work. We compute itmore »using a finite difference technique and show that our results are in excellent agreement with those from a previously proposed semi-analytical method based on Fourier–Bessel series. The computational strategies described in this paper could potentially lead to efficient methods to explore the kinetics of self-assembly of proteins on lipid membranes.« less

Abstract The mechanism of the scoliotic curve development in healthy adolescents remains unknown in the field of orthopedic surgery. Variations in the sagittal curvature of the spine are believed to be a leading cause of scoliosis in this patient population. Here, we formulate the mechanics of S-shaped slender elastic rods as a model for pediatric spine under physiological loading. Second, applying inverse mechanics to clinical data of the subtypes of scoliotic spines, with characteristic 3D deformity, we determine the undeformed geometry of the spine before the induction of scoliosis. Our result successfully reproduces the clinical data of the deformed spine under varying loads, confirming that the prescoliotic sagittal curvature of the spine impacts the 3D loading that leads to scoliosis.

The double-helical topology of DNA molecules observed at room temperature in the absence of any external loads can be disrupted by increasing the bath temperature or by applying tensile forces, leading to spontaneous strand separation known as DNA melting. Here, continuum mechanics of a 2D birod is combined with statistical mechanics to formulate a unified framework for studying both thermal melting and tensile force induced melting of double-stranded molecules: it predicts the variation of melting temperature with tensile load, provides a mechanics-based understanding of the cooperativity observed in melting transitions, and reveals an interplay between solution electrostatics and micromechanical deformations of DNA which manifests itself as an increase in the melting temperature with increasing ion concentration. This novel predictive framework sheds light on the micromechanical aspects of DNA melting and predicts trends that were observed experimentally or extracted phenomenologically using the Clayperon equation.

Sedimentation in active fluids has come into focus due to the ubiquity of swimming micro-organisms in natural and industrial processes. Here, we investigate sedimentation dynamics of passive particles in a fluid as a function of bacteria E. coli concentration. Results show that the presence of swimming bacteria significantly reduces the speed of the sedimentation front even in the dilute regime, in which the sedimentation speed is expected to be independent of particle concentration. Furthermore, bacteria increase the dispersion of the passive particles, which determines the width of the sedimentation front. For short times, particle sedimentation speed has a linear dependence on bacterial concentration. Mean square displacement data shows, however, that bacterial activity decays over long experimental (sedimentation) times. An advection-diffusion equation coupled to bacteria population dynamics seems to capture concentration profiles relatively well. A single parameter, the ratio of single particle speed to the bacteria flow speed can be used to predict front sedimentation speed.