arXiv subjects

Amaresh Sahu

Publications and source records attributed to Amaresh Sahu.

9 recordsLinked to original sources

arXiv2026

Molecular interfacial rheology: Lipid membrane shear viscosity

We develop a method to extract the shear viscosity of a lipid membrane from equilibrium molecular dynamics simulations. The method characterizes the rheology of general interfacial systems embedded in three-dimensional media; we term it molecular interfacial rheology. In our simulations the planar bilayer and surrounding water are confined between solid, parallel walls. Following Onsager's regression hypothesis, membrane and water fluctuations are assumed to relax according to the coupled continuum-mechanical equations governing the confined system---which predict that the membrane transverse velocity autocorrelation function (TVACF) decays exponentially, at a rate set by the membrane and water viscosities. The measured TVACF, however, exhibits damped oscillations followed by a slowly decaying tail. We reconcile these behaviors using the Mori--Zwanzig formalism, and extract the wavevector-dependent membrane viscosity from the time-integral of the TVACF. Results from theory and simulations agree over a decade of wavevectors, and extrapolating to long wavelengths yields shear viscosities ranging from 0.064 to 0.18 pN*us/nm across two representative single-component, fluid-phase bilayers. Our results are corroborated by nonequilibrium simulations where a spatially varying in-plane body force is applied to lipid molecules, thus validating the framework of molecular interfacial rheology.

cond-mat.soft↗

arXiv2026

Three-slab model for the dielectric permittivity of a lipid bilayer

A model for the tensorial dielectric permittivity of phospholipid membranes is presented here. The four-nanometer-thick membrane is treated as a composite made up of three dielectric slabs: one for each of the two phospholipid head-group regions, and one for the entire domain spanned by the lipid tails. Equal and opposite bound surface charge densities surround each head-group slab, and account for the membrane dipole potential. Three-slab model parameters are obtained from molecular dynamics simulations, and capture both the zero-field electric potential and the membrane response to applied electric fields. The tail region is well-approximated as having vacuum permittivity, while the head-group region is highly anisotropic due to the configurations of molecular dipoles. For the bilayers studied, the out-of-plane permittivity of the head-group region is 10--15 times that of the vacuum, while the in-plane permittivity is an order of magnitude larger. Membrane responses to applied electric fields up to 30 millivolts per nanometer are found to be in the linear regime. The model overcomes a fundamental limitation of microscopic theories---where the out-of-plane permittivity lacks a meaningful continuum interpretation in the head-group region due to large gradients in the local electric field---by averaging over slab widths, thereby introducing new length scales. Our approach can be extended to characterize general interfacial systems with similar microscopic permittivities.

cond-mat.soft↗

arXiv2025

Osmotic forces modify lipid membrane fluctuations

In hydrodynamic descriptions of lipid bilayers, the membrane is often approximated as being impermeable to the surrounding, solute-containing fluid. However, biological and in vitro lipid membranes are influenced by their permeability and the resultant osmotic forces -- whose effects remain poorly understood. Here, we study the dynamics of a fluctuating, planar lipid membrane that is ideally selective: fluid can pass through it, while the electrically-neutral solutes cannot. We find that the canonical membrane relaxation mode, in which internal membrane forces are balanced by fluid drag, no longer exists over all wavenumbers. Rather, this mode only exists when it is slower than solute diffusion -- corresponding to a finite range of wavenumbers. The well-known equipartition result quantifying the size of membrane undulations due to thermal perturbations is consequently limited in its validity to the aforementioned range. Moreover, this range shrinks as the membrane surface tension is increased, and above a critical tension the membrane mode vanishes. Our findings are relevant when interpreting experimental measurements of membrane fluctuations, especially in vesicles at moderate to high tensions.

cond-mat.soft↗

arXiv2024

Arbitrary Lagrangian--Eulerian finite element method for lipid membranes

An arbitrary Lagrangian--Eulerian finite element method and numerical implementation for curved and deforming lipid membranes is presented here. The membrane surface is endowed with a mesh whose in-plane motion need not depend on the in-plane flow of lipids. Instead, in-plane mesh dynamics can be specified arbitrarily. A new class of mesh motions is introduced, where the mesh velocity satisfies the dynamical equations of a user-specified two-dimensional material. A Lagrange multiplier constrains the out-of-plane membrane and mesh velocities to be equal, such that the mesh and material always overlap. An associated numerical inf--sup instability ensues, and is removed by adapting established techniques in the finite element analysis of fluids. In our implementation, the aforementioned Lagrange multiplier is projected onto a discontinuous space of piecewise linear functions. The new mesh motion is compared to established Lagrangian and Eulerian formulations by investigating a preeminent numerical benchmark of biological significance: the pulling of a membrane tether from a flat patch, and its subsequent lateral translation.

physics.comp-ph↗

arXiv2022

Absolute vs Convective Instabilities and Front Propagation in Lipid Membrane Tubes

We analyze the stability of biological membrane tubes, with and without a base flow of lipids. Membrane dynamics are completely specified by two dimensionless numbers: the well-known Föppl--von Kármán number $Γ$ and the recently introduced Scriven--Love number $SL$, respectively quantifying the base tension and base flow speed. For unstable tubes, the growth rate of a local perturbation depends only on $Γ$, whereas $SL$ governs the absolute or convective nature of the instability. Furthermore, nonlinear simulations of unstable tubes reveal an initially localized disturbance results in propagating fronts, which leave a thin atrophied tube in their wake. Depending on the value of $Γ$, the thin tube is connected to the unperturbed regions via oscillatory or monotonic shape transitions -- reminiscent of recent experimental observations on the retraction and atrophy of axons. We elucidate our findings through a weakly nonlinear analysis, which shows membrane dynamics may be approximated by a model of the class of extended Fisher--Kolmogorov equations. Our study sheds light on the pattern selection mechanism in axonal shapes by recognizing the existence of two Lifshitz points, at which the front dynamics undergo steady-to-oscillatory bifurcations.

cond-mat.soft↗

arXiv2020

Geometry and dynamics of lipid membranes: The Scriven--Love number

The equations governing lipid membrane dynamics in planar, spherical, and cylindrical geometries are presented here. Unperturbed and first-order perturbed equations are determined and non-dimensionalized. In membrane systems with a nonzero base flow, perturbed in-plane and out-of-plane quantities are found to vary over different length scales. A new dimensionless number, named the Scriven--Love number, and the well-known Föppl--von Kármán number result from a scaling analysis. The Scriven--Love number compares out-of-plane forces arising from the in-plane, intramembrane viscous stresses to the familiar elastic bending forces, while the Föppl--von Kármán number compares tension to bending forces. Both numbers are calculated in past experimental works, and span a wide range of values in various biological processes across different geometries. In situations with large Scriven--Love and Föppl--von Kármán numbers, the dynamical response of a perturbed membrane is dominated by out-of-plane viscous and surface tension forces---with bending forces playing a negligible role. Calculations of non-negligible Scriven--Love numbers in various biological processes and in vitro experiments show in-plane intramembrane viscous flows cannot generally be ignored when analyzing lipid membrane behavior.

cond-mat.soft↗

arXiv2020

Active Contact Forces Drive Non-Equilibrium Fluctuations in Membrane Vesicles

We analyze the non-equilibrium shape fluctuations of giant unilamellar vesicles encapsulating motile bacteria. Owing to bacteria--membrane collisions, we experimentally observe a significant increase in the magnitude of membrane fluctuations at low wave numbers, compared to the well-known thermal fluctuation spectrum. We interrogate these results by numerically simulating membrane height fluctuations via a modified Langevin equation, which includes bacteria--membrane contact forces. Taking advantage of the length and time scale separation of these contact forces and thermal noise, we further corroborate our results with an approximate theoretical solution to the dynamical membrane equations. Our theory and simulations demonstrate excellent agreement with non-equilibrium fluctuations observed in experiments. Moreover, our theory reveals that the fluctuation--dissipation theorem is not broken by the bacteria; rather, membrane fluctuations can be decomposed into thermal and active components.

cond-mat.soft↗

arXiv2020

Arbitrary Lagrangian--Eulerian finite element method for curved and deforming surfaces. I. General theory and application to fluid interfaces

An arbitrary Lagrangian--Eulerian (ALE) finite element method for arbitrarily curved and deforming two-dimensional materials and interfaces is presented here. An ALE theory is developed by endowing the surface with a mesh whose in-plane velocity need not depend on the in-plane material velocity, and can be specified arbitrarily. A finite element implementation of the theory is formulated and applied to curved and deforming surfaces with in-plane incompressible flows. Numerical inf--sup instabilities associated with in-plane incompressibility are removed by locally projecting the surface tension onto a discontinuous space of piecewise linear functions. The general isoparametric finite element method, based on an arbitrary surface parametrization with curvilinear coordinates, is tested and validated against several numerical benchmarks. A new physical insight is obtained by applying the ALE developments to cylindrical fluid films, which are computationally and analytically found to be stable to non-axisymmetric perturbations, and unstable with respect to long-wavelength axisymmetric perturbations when their length exceeds their circumference. A Lagrangian scheme is attained as a special case of the ALE formulation. Though unable to model fluid films with sustained shear flows, the Lagrangian scheme is validated by reproducing the cylindrical instability. However, relative to the ALE results, the Lagrangian simulations are found to have spatially unresolved regions with few nodes, and thus larger errors.

physics.comp-ph↗

arXiv2018

The irreversible thermodynamics of curved lipid membranes

The theory of irreversible thermodynamics for arbitrarily curved lipid membranes is presented here. The coupling between elastic bending and irreversible processes such as intra-membrane lipid flow, intra-membrane phase transitions, and protein binding and diffusion is studied. The forms of the entropy production for the irreversible processes are obtained, and the corresponding thermodynamic forces and fluxes are identified. Employing the linear irreversible thermodynamic framework, the governing equations of motion along with appropriate boundary conditions are provided.

cond-mat.soft↗