A Dynamic Renormalization Group Study of Active Nematics

We carry out a systematic construction of the coarse-grained dynamical equation of motion for the orientational order parameter for a two-dimensional active nematic, that is a nonequilibrium steady state with uniaxial, apolar orientational order. Using the dynamical renormalization group, we show that the leading nonlinearities in this equation are marginally \textit{irrelevant}. We discover a special limit of parameters in which the equation of motion for the angle field of bears a close relation to the 2d stochastic Burgers equation. We find nevertheless that, unlike for the Burgers problem, the nonlinearity is marginally irrelevant even in this special limit, as a result of of a hidden fluctuation-dissipation relation. 2d active nematics therefore have quasi-long-range order, just like their equilibrium counterpartsComment: 31 pages 6 figure

Global parameter identification of stochastic reaction networks from single trajectories

We consider the problem of inferring the unknown parameters of a stochastic biochemical network model from a single measured time-course of the concentration of some of the involved species. Such measurements are available, e.g., from live-cell fluorescence microscopy in image-based systems biology. In addition, fluctuation time-courses from, e.g., fluorescence correlation spectroscopy provide additional information about the system dynamics that can be used to more robustly infer parameters than when considering only mean concentrations. Estimating model parameters from a single experimental trajectory enables single-cell measurements and quantification of cell--cell variability. We propose a novel combination of an adaptive Monte Carlo sampler, called Gaussian Adaptation, and efficient exact stochastic simulation algorithms that allows parameter identification from single stochastic trajectories. We benchmark the proposed method on a linear and a non-linear reaction network at steady state and during transient phases. In addition, we demonstrate that the present method also provides an ellipsoidal volume estimate of the viable part of parameter space and is able to estimate the physical volume of the compartment in which the observed reactions take place.Comment: Article in print as a book chapter in Springer's "Advances in Systems Biology

Dynamics of biomembranes with active multiple-state inclusions

Nonequilibrium dynamics of biomembranes with active inclusions is considered. The inclusions represent protein molecules which perform cyclic internal conformational motions driven by the energy brought with ATP ligands. As protein conformations cyclically change, this induces hydrodynamical flows and also directly affects the local curvature of a membrane. On the other hand, variations in the local curvature of the membrane modify the transitions rates between conformational states in a protein, leading to a feedback in the considered system. Moreover, active inclusions can move diffusively through the membrane so that surface concentration varies. The kinetic description of this system is constructed and the stability of the uniform stationary state is analytically investigated. We show that, as the rate of supply of chemical energy is increased above a certain threshold, this uniform state becomes unstable and stationary or traveling waves spontaneously develop in the system. Such waves are accompanied by periodic spatial variation of membrane curvature and inclusion density. For typical parameter values, their characteristic wavelengths are of the order of hundreds of nanometers. For traveling waves, the characteristic frequency is of the order of a thousand Hz or less.Comment: 31 page

Iontophoresis to enhance topical delivery of terbinafine to the nail

The aim of this study was to investigate the application of electric current to enhance the ungual permeation of terbinafine – an antifungal agent that is currently delivered systemically for the treatment of onychomycosis

Nonequilibrium steady states in a vibrated-rod monolayer: tetratic, nematic and smectic correlations

We study experimentally the nonequilibrium phase behaviour of a horizontal monolayer of macroscopic rods. The motion of the rods in two dimensions is driven by vibrations in the vertical direction. Aside from the control variables of packing fraction and aspect ratio that are typically explored in molecular liquid crystalline systems, due to the macroscopic size of the particles we are also able to investigate the effect of the precise shape of the particle on the steady states of this driven system. We find that the shape plays an important role in determining the nature of the orientational ordering at high packing fraction. Cylindrical particles show substantial tetratic correlations over a range of aspect ratios where spherocylinders have previously been shown by Bates et al (JCP 112, 10034 (2000)) to undergo transitions between isotropic and nematic phases. Particles that are thinner at the ends (rolling pins or bails) show nematic ordering over the same range of aspect ratios, with a well-established nematic phase at large aspect ratio and a defect-ridden nematic state with large-scale swirling motion at small aspect ratios. Finally, long-grain, basmati rice, whose geometry is intermediate between the two shapes above, shows phases with strong indications of smectic order.Comment: 18 pages and 13 eps figures, references adde

Driven Heisenberg Magnets: Nonequilibrium Criticality, Spatiotemporal Chaos and Control

We drive a $d$-dimensional Heisenberg magnet using an anisotropic current. The continuum Langevin equation is analysed using a dynamical renormalization group and numerical simulations. We discover a rich steady-state phase diagram, including a critical point in a new nonequilibrium universality class, and a spatiotemporally chaotic phase. The latter may be `controlled' in a robust manner to target spatially periodic steady states with helical order.Comment: 7 pages, 2 figures. Published in Euro. Phys. Let

Approach to equilibrium in adiabatically evolving potentials

For a potential function (in one dimension) which evolves from a specified initial form $V_{i}(x)$ to a different $V_{f}(x)$ asymptotically, we study the evolution, in an overdamped dynamics, of an initial probability density to its final equilibeium.There can be unexpected effects that can arise from the time dependence. We choose a time variation of the form $V(x,t)=V_{f}(x)+(V_{i}-V_{f})e^{-\lambda t}$. For a $V_{f}(x)$, which is double welled and a $V_{i}(x)$ which is simple harmonic, we show that, in particular, if the evolution is adiabatic, the results in a decrease in the Kramers time characteristics of $V_{f}(x)$. Thus the time dependence makes diffusion over a barrier more efficient. There can also be interesting resonance effects when $V_{i}(x)$ and $V_{f}(x)$ are two harmonic potentials displaced with respect to each other that arise from the coincidence of the intrinsic time scale characterising the potential variation and the Kramers time.Comment: This paper contains 5 page

Melting-freezing cycles in a relatively sheared pair of crystalline monolayers

The nonequilibrium dynamical behaviour that arises when two ordered two-dimensional monolayers of particles are sheared over each other is studied in Brownian dynamics simulations. A curious sequence of nonequilibrium states is observed as the driving rate is increased, the most striking of which is a sliding state with irregular alternation between disordered and ordered states. We comment on possible mechanisms underlying these cycles, and experiments that could observe them.Comment: 7 pages, 8 figures, minor changes in text and figures, references adde

Two-Component Fluid Membranes Near Repulsive Walls: Linearized Hydrodynamics of Equilibrium and Non-equilibrium States

We study the linearized hydrodynamics of a two-component fluid membrane near a repulsive wall, via a model which incorporates curvature- concentration coupling as well as hydrodynamic interactions. This model is a simplified version of a recently proposed one [J.-B. Manneville et al. Phys. Rev. E, 64, 021908 (2001)] for non-equilibrium force-centres embedded in fluid membranes, such as light-activated bacteriorhodopsin pumps incorporated in phospholipid (EPC) bilayers. The pump/membrane system is modeled as an impermeable, two-component bilayer fluid membrane in the presence of an ambient solvent, in which one component, representing active pumps, is described in terms of force dipoles displaced with respect to the bilayer midpoint. We first discuss the case in which such pumps are rendered inactive, computing the mode structure in the bulk as well as the modification of hydrodynamic properties by the presence of a nearby wall. We then discuss the fluctuations and mode structure in steady state of active two-component membranes near a repulsive wall. We find that proximity to the wall smoothens membrane height fluctuations in the stable regime, resulting in a logarithmic scaling of the roughness even for initially tensionless membranes. This explicitly non-equilibrium result, a consequence of the incorporation of curvature-concentration coupling in our treatment, also indicates that earlier scaling arguments which obtained an increase in the roughness of active membranes near repulsive walls may need to be reevaluated.Comment: 39 page Latex file, 3 encapsulated Postscript figure

Spectral Signatures of the Diffusional Anomaly in Water

Analysis of power spectrum profiles for various tagged particle quantities in bulk SPC/E water is used to demonstrate that variations in mobility associated with the diffusional anomaly are mirrored in the exponent of the \onebyf\ region. Monitoring of \onebyf behaviour is shown to be a simple and direct method for linking phenomena on three distinctive length and time scales: the local molecular environment, hydrogen bond network reorganisations and the diffusivity. The results indicate that experimental studies of supercooled water to probe the density dependence of $1/f^\alpha$ spectral features, or equivalent stretched exponential behaviour in time-correlation functions, will be of interest.Comment: 5 Pages, 4 Figure