We analyze the nonequilibrium 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 lengthscale and timescale 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 nonequilibrium 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.
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.
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 versus convective nature of the instability. Furthermore, nonlinear simulations of unstable tubes reveal an initially localized disturbance result 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.
This thesis is concerned with developing a wholistic description of biological membranes: fascinating materials that make up the boundary of the cell, as well as many of the cell’s internal ...organelles. Our formulation of the theory of such materials relies on two well-known concepts: differential geometry and irreversible thermodynamics. The setting of differential geometry allows us to describe curves and surfaces, which in this case are embedded in the three-dimensional Euclidean space, while irreversible thermodynamics provides a theoretical framework to develop constitutive relations between the various thermodynamic forces and fluxes in a system. Both concepts are well-known, and are reviewed in Part A. We build on these classic results in Part B, and develop the theory of irreversible thermodynamics for arbitrarily curved and deforming lipid membranes. In particular, we treat the membrane as a two-dimensional surface, in which lipids flow in-plane as a two-dimensional fluid while the membrane bends out-of-plane as an elastic shell. We then obtain the fundamental balance laws of mass, linear momentum, angular momentum, energy, and entropy, as well as the second law of thermodynamics. Finally, we apply the framework of irreversible thermodynamics to determine appropriate constitutive relations, and substitute them into the balance laws to obtain the equations governing membrane dynamics. Our main result is to present the equations of motion and appropriate boundary conditions for three systems of increasing complexity: (i) a compressible, inviscid membrane, (ii) a compressible, viscous membrane, and (iii) an incompressible, viscous membrane. Part C of this thesis focuses on applications of the single-component theory. We begin by specializing the general governing equations to three commonly observed geometries in biological systems: planar sheets, spherical vesicles, and cylindrical tubes. A scaling analysis of the resultant equations reveals membrane dynamics are governed by two dimensionless numbers. The well-known Föppl–von Kármán number, Γ, compares tension forces to the familiar elastic bending forces, while a new dimensionless quantity—which we name the Scriven–Love number, SL—compares out-of-plane forces arising from the in-plane, intramembrane viscous stresses to bending forces. 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, and can never be ignored in lipid membrane tubes. Moreover, a stability analysis indicates membrane tubes are unstable above a critical value of Γ, while SL governs the spatiotemporal evolution of the deforming membrane. We close by investigating a novel hydrodynamic instability in which an initially local disturbance to an unstable tube yields propagating fronts, which leave a thin atrophied tube in their wake. Depending on the value of the Föppl–von Kármán number 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.
In this paper a method to optimize the structure of neural network named as Adaptive Particle Swarm Optimization (PSO) has been proposed. In this method nested PSO has been used. Each particle in ...outer PSO is used for different network construction. The particles update themselves in each iteration by following the global best and personal best performances. The inner PSO isused for training the networks and evaluate the performance of the networks. The effectiveness of this method is tested on many benchmark datasets to find out their optimum structure and the results are compared with other population based methods and finally the optimum structure is implemented using Modified Teaching Learning Based Optimization(MTLBO)for classification using neural network in data mining.
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.
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