For the most up-to-date list, please see my Google scholar page.
2021
Directed force propagation in semiflexible networks
Grill, Maximilian J,
Kernes, Jonathan,
Slepukhin, Valentin M,
Wall, Wolfgang A,
and Levine, Alex J
Soft Matter,
2021
We consider the propagation of tension along specific filaments of a semiflexible filament network in response to the application of a point force using a combination of numerical simulations and analytic theory. We find the distribution of force within the network is highly heterogeneous, with a small number of fibers supporting a significant fraction of the applied load over distances of multiple mesh sizes surrounding the point of force application. We suggest that these structures may be thought of as tensile force chains, whose structure we explore via simulation. We develop self-consistent calculations of the point-force response function and introduce a transfer matrix approach to explore the decay of tension (into bending) energy and the branching of tensile force chains in the network.
Effects of curvature on the propagation of undulatory waves in lower dimensional elastic materials
Kernes, Jonathan,
and Levine, Alex J.
Phys. Rev. E,
2021
2020
Dynamics of undulatory fluctuations of semiflexible filaments in a network
Kernes, Jonathan,
and Levine, Alex J.
Phys. Rev. E,
2020
We study the dynamics of a single semiflexible filament coupled to a Hookean spring at its boundary. The spring produces a fluctuating tensile force on the filament, whose value depends on the filament’s instantaneous end-to-end length. The spring thereby introduces a nonlinearity, which mixes the undulatory normal modes of the filament and changes their dynamics. We study these dynamics using the Martin-Siggia-Rose-Janssen-de-Domincis formalism, and compute the time-dependent
correlation functions of transverse undulations and of the filament’s end-to-end distance. The relaxational dynamics of the modes below a characteristic wavelength p
κ/τR, set by the filament’s bending modulus κ and spring-renormalized tension τR, are changed by the boundary spring. This
occurs near the cross-over frequency between tension- and bending-dominated modes of the system. The boundary spring can be used to represent the linear elastic compliance of the rest of the filament network to which the filament is cross-linked. As a result, we predict that this nonlinear effect will be observable in the dynamical correlations of constituent filaments of networks and in the networks’ collective shear response. The system’s dynamic shear modulus is predicted to exhibit the well-known crossover with increasing frequency from ω 1/2 to ω 3/4 , but the inclusion of the the network’s compliance in the analysis of the individual filament dynamics shifts this transition to a
higher frequency
Equilibrium fluctuations of a semiflexible filament cross linked into a network
Kernes, Jonathan,
and Levine, Alex J.
Phys. Rev. E,
2020
We examine the equilibrium fluctuation spectrum of a semiflexible filament segment in a network. The effect of this cross linking is to modify the mechanical boundary conditions at the end of the filament. We consider the effect of both tensile stress in the network and its elastic compliance. Most significantly, the network’s compliance introduces a nonlinear term into the filament Hamiltonian even in the small-bending approximation. We analyze the effect of this nonlinearity upon the filament’s fluctuation profile. We also find that there are three principal fluctuation regimes dominated by one of the following:(i) network tension,(ii) filament bending stiffness, or (iii) network compliance. This work provides the theoretical framework necessary to analyze activity microrheology, which uses the observed filament fluctuations as a noninvasive probe of tension in the network.
Geometrically-induced localization of flexural waves on thin warped physical membranes
Kernes, Jonathan,
and Levine, Alex J
arXiv preprint arXiv:2011.07152
2020
We consider the propagation of flexural waves across a nearly flat, thin membrane, whose stress-free state is curved. The stress-free configuration is specified by a quenched height field, whose Fourier components are drawn from a Gaussian distribution with power law variance. Gaussian curvature couples the in-plane stretching to out-of-plane bending. Integrating out the faster stretching modes yields a wave equation for undulations in the presence of an effective random potential, determined purely by geometry. We show that at long times/lengths, the undulation intensity obeys a diffusion equation. The diffusion coefficient is found to be frequency dependent and sensitive to the quenched height field distribution...
Statistical mechanics and dynamics of semiflexible filaments, and the role of curvature in elastic low dimensional soft matter
Kernes, Jonathan Matthew
2020
In Part I, we examine both the statistical mechanics and dynamics of semiflexiblefilaments that are coupled to an external system. Chapters 2 and 3 look at semi-flexible filaments in network, where the external system is the elastic response ofthe filamentous network itself. The linear elastic compliance of the network is mod-eled by attaching a Hookean spring at the boundary of the filament, which in turn,introduces a nonlinearity into to the Hamiltonian. Chapter 2 uses this model to pro-pose a method for noninvasive microrheology measurements of semiflexible filamentnetworks based on thermal fluctuations of transverse undulations. The externalforce is seen to counteract bending strain, broadening fluctuations at the bound-aries. Chapter 3 considers ...