Topological localization in out-of-equilibrium dissipative systems

In this paper we report that notions of topological protection can be applied to stationary configurations that are driven far from equilibrium by active, dissipative processes. We show this for physically two disparate cases : stochastic networks governed by microscopic single particle dynamics as well as collections of driven, interacting particles described by coarse-grained hydrodynamic theory. In both cases, the presence of dissipative couplings to the environment that break time reversal symmetry are crucial to ensuring topologically protection. These examples constitute proof of principle that notions of topological protection, established in the context of electronic and mechanical systems, do indeed extend generically to processes that operate out of equilibrium. Such topologically robust boundary modes have implications for both biological and synthetic systems.Comment: 11 pages, 4 figures (SI: 8 pages 3 figures

Protein-induced membrane curvature changes membrane tension

Adsorption of proteins onto membranes can alter the local membrane curvature. This phenomenon has been observed in biological processes such as endocytosis, tubulation and vesiculation. However, it is not clear how the local surface properties of the membrane, such as membrane tension, change in response to protein adsorption. In this paper, we show that the classical elastic model of lipid membranes cannot account for simultaneous changes in shape and membrane tension due to protein adsorption in a local region, and a viscous-elastic formulation is necessary to fully describe the system. Therefore, we develop a viscous-elastic model for inhomogeneous membranes of the Helfrich type. Using the new viscous-elastic model, we find that the lipids flow to accommodate changes in membrane curvature during protein adsorption. We show that, at the end of protein adsorption process, the system sustains a residual local tension to balance the difference between the actual mean curvature and the imposed spontaneous curvatures. This change in membrane tension can have a functional impact in many biological phenomena where proteins interact with membranes.Comment: 15 pages, 5 figure

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.Comment: 62 pages, 4 figure

Damping Estimation of Plates for Statistical Energy Analysis

The Power Input Method (P.I.M.) and the Impulse Response Decay Method (I.R.D.M.) are used to evaluate how the accuracy of damping loss factor estimation for plates is affected with respect to various processing parameters, such as the frequency resolution, the frequency bandwidth, the number of measurement locations, and the signal to noise ratio. In several computational experiments, accuracy is assessed for a wide range of damping loss factors from low (0.1%) to moderate (1%) to high (10%). A wide range of frequency is considered, including "low frequencies" for which modal density is less than one per band. The Power Input Method (P.I.M.) is first validated with computational studies of an analytical single degree of freedom oscillator. Experimental loss factor estimates for plates (multiple degree of freedom systems) are also computed using the P.I.M. algorithm. The P.I.M. is shown to estimate loss factors with reasonable accuracy for highly damped plates in the 300 Hz - 4000 Hz, wherein modal density exceeds unit value. In this case "reasonable accuracy" means the estimated loss factors are within 10% of those predicted by the impulse response decay method. For lower damping levels the method fails. The analytical Impulse Response Decay Method (I.R.D.M.) is validated by the use of two computational models: a single degree of freedom oscillator and a uniform rectangular panel. The panel computational model is a finite element model of a rectangular plate mechanically excited at a single point. The computational model is used to systematically evaluate the effect of frequency resolution, frequency bandwidth, the number of measurement points used in the computations, and noise level for all the three levels of damping. The "optimized" I.R.D.M. is shown to accurately estimate damping in plate simulations with low to moderate levels of damping with a deviation of no more than 2% from the known damping value. For highly damped plates the I.R.D.M. tends to under-estimate loss factors at high frequency. Experimental loss factor estimation for an aluminum plate with full constrained layer damping treatment, classified as a highly damped plate, and an undamped steel plate, classified as a lightly damped plate are computed using the "optimized" I.R.D.M. algorithm. Statistical Energy Analysis (S.E.A.), which is a natural extension of the Power Input Method, is used to evaluate coupling loss factors for two sets of plates, one set joined along a line and the other set joined at a point. Two alternative coupling loss factor estimation algorithms are studied, one using individual plate loss factor estimations, and the other using the loss factors of the plates estimated when the plates are coupled. The modal parameters (modal density and coupling loss factors) for both sets of plates are estimated experimentally and are compared with theoretical results. The estimations show reasonable agreement between agreement and theory that is, within 5 % for the damped system of plates. For the undamped system of plates the results are less accurate with deviations of more than 100% at low modal density and approximately 30% variation at higher frequencies

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 F\"oppl--von K\'arm\'an 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 F\"oppl--von K\'arm\'an 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 F\"oppl--von K\'arm\'an 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.Comment: 16 pages, 7 figures, 5 table