Universality of the off-equilibrium response function in the kinetic Ising chain

The off-equilibrium response function $\chi (t,t_w)$ and autocorrelation function $C(t,t_w)$ of an Ising chain with spin-exchange dynamics are studied numerically and compared with the same quantities in the case of spin-flip dynamics. It is found that, even though these quantities are separately different in the two cases, the parametric plot of $\chi (t,t_w)$ versus $C(t,t_w)$ is the same. While this result could be expected in higher dimensionality, where $\chi (C)$ is related to the equilibrium state, it is far from trivial in the one dimensional case where this relation does not hold. The origin of the universality of $\chi(C)$ is traced back to the optimization of domains position with respect to the perturbing external field. This mechanism is investigated resorting to models with a single domain moving in a random environment.Comment: 24 pages, 7 figure

Static non-reciprocity in mechanical metamaterials

Reciprocity is a fundamental principle governing various physical systems, which ensures that the transfer function between any two points in space is identical, regardless of geometrical or material asymmetries. Breaking this transmission symmetry offers enhanced control over signal transport, isolation and source protection. So far, devices that break reciprocity have been mostly considered in dynamic systems, for electromagnetic, acoustic and mechanical wave propagation associated with spatio-temporal variations. Here we show that it is possible to strongly break reciprocity in static systems, realizing mechanical metamaterials that, by combining large nonlinearities with suitable geometrical asymmetries, and possibly topological features, exhibit vastly different output displacements under excitation from different sides, as well as one-way displacement amplification. In addition to extending non-reciprocity and isolation to statics, our work sheds new light on the understanding of energy propagation in non-linear materials with asymmetric crystalline structures and topological properties, opening avenues for energy absorption, conversion and harvesting, soft robotics, prosthetics and optomechanics.Comment: 19 pages, 3 figures, Supplementary information (11 pages and 5 figures

Efficient simulation of non-crossing fibers and chains in a hydrodynamic solvent

An efficient simulation method is presented for Brownian fiber suspensions, which includes both uncrossability of the fibers and hydrodynamic interactions between the fibers mediated by a mesoscopic solvent. To conserve hydrodynamics, collisions between the fibers are treated such that momentum and energy are conserved locally. The choice of simulation parameters is rationalised on the basis of dimensionless numbers expressing the relative strength of different physical processes. The method is applied to suspensions of semiflexible fibers with a contour length equal to the persistence length, and a mesh size to contour length ratio ranging from 0.055 to 0.32. For such fibers the effects of hydrodynamic interactions are observable, but relatively small. The non-crossing constraint, on the other hand, is very important and leads to hindered displacements of the fibers, with an effective tube diameter in agreement with recent theoretical predictions. The simulation technique opens the way to study the effect of viscous effects and hydrodynamic interactions in microrheology experiments where the response of an actively driven probe bead in a fiber suspension is measured.Comment: 12 pages, 2 tables, 5 figure

Protein-Mediated DNA Loops: Effects of Protein Bridge Size and Kinks

This paper focuses on the probability that a portion of DNA closes on itself through thermal fluctuations. We investigate the dependence of this probability upon the size r of a protein bridge and/or the presence of a kink at half DNA length. The DNA is modeled by the Worm-Like Chain model, and the probability of loop formation is calculated in two ways: exact numerical evaluation of the constrained path integral and the extension of the Shimada and Yamakawa saddle point approximation. For example, we find that the looping free energy of a 100 base pairs DNA decreases from 24 kT to 13 kT when the loop is closed by a protein of r = 10 nm length. It further decreases to 5 kT when the loop has a kink of 120 degrees at half-length.Comment: corrected typos and figures, references updated; 13 pages, 7 figures, accepted for publication in Phys. Rev.

Unexpected crossover dynamics of single polymer in a corrugated tube

We present molecular dynamics study of a generic (coarse-grained) model for single-polymer diffusion confined in a corrugated cylinder. For a narrow tube, i.e., diameter of the cylinder $\delta < 2.3$, the axial diffusion coefficient $D_{||}$ scales as $D_{||} \propto N^{-3/2}$, with chain length $N$, up to $N \approx 100$ then crosses over to Rouse scaling for the larger $N$ values. The $N^{-3/2}$ scaling is due to the large fluctuation of the polymer chain along its fully stretched equilibrium conformation. The stronger scaling, namely $N^{-3/2}$, is not observed for an atomistically smooth tube and/or for a cylinder with larger diameter.Comment: 10 pages, 3 figures, LaTeX, version accepted by J. Chem. Phy

Statics and Dynamics of the Wormlike Bundle Model

Bundles of filamentous polymers are primary structural components of a broad range of cytoskeletal structures, and their mechanical properties play key roles in cellular functions ranging from locomotion to mechanotransduction and fertilization. We give a detailed derivation of a wormlike bundle model as a generic description for the statics and dynamics of polymer bundles consisting of semiflexible polymers interconnected by crosslinking agents. The elastic degrees of freedom include bending as well as twist deformations of the filaments and shear deformation of the crosslinks. We show that a competition between the elastic properties of the filaments and those of the crosslinks leads to renormalized effective bend and twist rigidities that become mode-number dependent. The strength and character of this dependence is found to vary with bundle architecture, such as the arrangement of filaments in the cross section and pretwist. We discuss two paradigmatic cases of bundle architecture, a uniform arrangement of filaments as found in F-actin bundles and a shell-like architecture as characteristic for microtubules. Each architecture is found to have its own universal ratio of maximal to minimal bending rigidity, independent of the specific type of crosslink induced filament coupling; our predictions are in reasonable agreement with available experimental data for microtubules. Moreover, we analyze the predictions of the wormlike bundle model for experimental observables such as the tangent-tangent correlation function and dynamic response and correlation functions. Finally, we analyze the effect of pretwist (helicity) on the mechanical properties of bundles. We predict that microtubules with different number of protofilaments should have distinct variations in their effective bending rigidity