arXiv subjects

David Head

Publications and source records attributed to David Head.

5 recordsLinked to original sources

arXiv2026

Linear and Non-Linear Rheology of Single and Double Cross-Linked Biopolymer Networks under Viscous Shear Flow

In this research study, a numerical tool, which is based on a version of Slender Body theory, has been used and also modified to simulate the mechanical behaviour of single- and double-cross-linked biopolymer networks (hydrogel) under oscillatory shear flow. The hydrodynamic interactions among fibres of intertwined networks were considered. Then, the stress and Fourier coefficients (i.e. shear moduli) were evaluated for both linear and nonlinear regimes. It was found that the double peaks (two-step yielding) of two double network at 100% maximum strain amplitude (nonlinear regime) cannot happen due to changes in fibre alignments and seed numbers, although the crosslinkers between two subnetworks present, which was previously reported in the literature. In fact, we also observed two peaks for single network in nonlinear regime. Furthermore, it was shown that the stress-strain curve of double network is not predicted by just superimposing the results from the corresponding single networks at 5% maximum strain amplitude (linear regime), but this prediction can be provided at 100% maximum strain amplitude (nonlinear regime). The Fourier coefficients and corresponding amplitude (an indication of nonlinearity effects) for double network were quite considerable from zero to fifth modes in nonlinear regime, despite enough zero and first modes in linear regime. It was also shown that the nonlinearity effects can be related to the morphology of the initial structure, i.e. the seed number rather than the flow condition for the single network. These results can help scientists to better design enhance fibrous materials used in wound healing or tissue engineering.

cond-mat.soft↗

arXiv2022

Distinct viscoelastic scaling for isostatic spring networks of the same fractal dimension

Fractal structure emerges spontaneously from the chemical cross\-linking of monomers into hydrogels, and has been directly linked to power law visco\-elasticity at the gel transition, as recently demonstrated for isostatic (marginally--rigid) spring networks based on the Sierpinski triangle. Here we generalize the Sierpinski triangle generation rules to produce 4 fractals, all with the same dimension $d_{\rm f}=\log 3/\log 2$, with the Sierpinski triangle being one case. We show that spring networks derived from these fractals are all isostatic, but exhibit one of two distinct exponents for their power--law viscoelasticity. We conclude that, even for networks with fixed connectivity, power--law viscoelasticity cannot generally be a function of the fractal dimension alone.

cond-mat.soft↗

arXiv2022

Viscoelastic scaling regimes for marginally-rigid fractal spring networks

A family of marginally-rigid (isostatic) spring networks with fractal structure up to a controllable length was devised and the viscoelastic spectra $G^{*}(\omega)$ calculated. Two non-trivial scaling regimes were observed, (i)~$G^{\prime}\approx G^{\prime\prime}\propto\omega^{\Delta}$ at low frequencies, consistent with $\Delta=1/2$; (ii)~$G^{\prime}\propto G^{\prime\prime}\propto\omega^{\Delta^{\prime}}$ for intermediate frequencies corresponding to fractal structure, consistent with a theoretical prediction $\Delta^{\prime}=(\ln3-\ln2)/(\ln3+\ln2)$. The cross-over between these two regimes occurred at lower frequencies for larger fractals in a manner suggesting diffusive-like dispersion. Solid gels generated by introducing internal stresses exhibited similar behaviour above a low-frequency cut-off, indicating the relevance of these findings to real-world applications.

cond-mat.soft↗

arXiv2019

Non-affinity and fluid-coupled viscoelastic plateau for immersed fiber networks

We employ a matrix-based solver for the linear rheology of fluid-immersed disordered spring networks to reveal four distinct dynamic response regimes. One regime - completely absent in the known vacuum response - exhibits coupled fluid flow and network deformation, with both components responding non-affinely. This regime contains an additional plateau (peak) in the frequency-dependent storage (loss) modulus - features which vanish without full hydrodynamic interactions. The mechanical response of immersed networks such as biopolymers and hydrogels is thus richer than previously established, and offers additional modalities for design and control through fluid interactions.

cond-mat.soft↗

arXiv1999

Zero-temperature criticality in a simple glass model

We introduce the strongly-interacting trap model, a version of Bouchaud's trap model for glasses [Bouchaud J-P 1992 {\em J. Phys. I France {\bf 2}} 1705]. At finite temperatures the model exhibits glassy relaxation over intermediate timeframes but reaches a steady state at finite times. In limit of zero temperature and with a suitably renormalised timescale the model maps onto the Bak-Sneppen model, widely studied in the context of self-organised criticality [Bak P and Sneppen K 1993 {\em Phys. Rev. Lett. {\bf 71}} 4083]. Hence zero temperature is a critical point in all dimensions. These claims are supported by mean field analysis of the stationary solution and numerical simulations of a finite-dimensional lattice model.

cond-mat.stat-mech↗