Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions

Excess contributions to the free energy due to interfaces occur for many problems encountered in the statistical physics of condensed matter when coexistence between different phases is possible (e.g. wetting phenomena, nucleation, crystal growth, etc.). This article reviews two methods to estimate both interfacial free energies and line tensions by Monte Carlo simulations of simple models, (e.g. the Ising model, a symmetrical binary Lennard-Jones fluid exhibiting a miscibility gap, and a simple Lennard-Jones fluid). One method is based on thermodynamic integration. This method is useful to study flat and inclined interfaces for Ising lattices, allowing also the estimation of line tensions of three-phase contact lines, when the interfaces meet walls (where "surface fields" may act). A generalization to off-lattice systems is described as well. The second method is based on the sampling of the order parameter distribution of the system throughout the two-phase coexistence region of the model. Both the interface free energies of flat interfaces and of (spherical or cylindrical) droplets (or bubbles) can be estimated, including also systems with walls, where sphere-cap shaped wall-attached droplets occur. The curvature-dependence of the interfacial free energy is discussed, and estimates for the line tensions are compared to results from the thermodynamic integration method. Basic limitations of all these methods are critically discussed, and an outlook on other approaches is given

TAMMiCol: Tool for analysis of the morphology of microbial colonies.

Many microbes are studied by examining colony morphology via two-dimensional top-down images. The quantification of such images typically requires each pixel to be labelled as belonging to either the colony or background, producing a binary image. While this may be achieved manually for a single colony, this process is infeasible for large datasets containing thousands of images. The software Tool for Analysis of the Morphology of Microbial Colonies (TAMMiCol) has been developed to efficiently and automatically convert colony images to binary. TAMMiCol exploits the structure of the images to choose a thresholding tolerance and produce a binary image of the colony. The images produced are shown to compare favourably with images processed manually, while TAMMiCol is shown to outperform standard segmentation methods. Multiple images may be imported together for batch processing, while the binary data may be exported as a CSV or MATLAB MAT file for quantification, or analysed using statistics built into the software. Using the in-built statistics, it is found that images produced by TAMMiCol yield values close to those computed from binary images processed manually. Analysis of a new large dataset using TAMMiCol shows that colonies of Saccharomyces cerevisiae reach a maximum level of filamentous growth once the concentration of ammonium sulfate is reduced to 200 μM. TAMMiCol is accessed through a graphical user interface, making it easy to use for those without specialist knowledge of image processing, statistical methods or coding

Freezing of Spinodal Decompostion by Irreversible Chemical Growth Reaction

We present a description of the freezing of spinodal decomposition in systems, which contain simultaneous irreversible chemical reactions, in the hydrodynamic limit approximation. From own results we conclude, that the chemical reaction leads to an onset of spinodal decomposition also in the case of an initial system which is completely miscible and can lead to an extreme retardation of the dynamics of the spinodal decomposition, with the probability of a general freezing of this process, which can be experimetally observed in simultaneous IPN formation.Comment: 10 page

Curvature Dependence of Surface Free Energy of Liquid Drops and Bubbles: A Simulation Study

We study the excess free energy due to phase coexistence of fluids by Monte Carlo simulations using successive umbrella sampling in finite LxLxL boxes with periodic boundary conditions. Both the vapor-liquid phase coexistence of a simple Lennard-Jones fluid and the coexistence between A-rich and B-rich phases of a symmetric binary (AB) Lennard-Jones mixture are studied, varying the density rho in the simple fluid or the relative concentration x_A of A in the binary mixture, respectively. The character of phase coexistence changes from a spherical droplet (or bubble) of the minority phase (near the coexistence curve) to a cylindrical droplet (or bubble) and finally (in the center of the miscibility gap) to a slab-like configuration of two parallel flat interfaces. Extending the analysis of M. Schrader, P. Virnau, and K. Binder [Phys. Rev. E 79, 061104 (2009)], we extract the surface free energy gamma (R) of both spherical and cylindrical droplets and bubbles in the vapor-liquid case, and present evidence that for R -> Infinity the leading order (Tolman) correction for droplets has sign opposite to the case of bubbles, consistent with the Tolman length being independent on the sign of curvature. For the symmetric binary mixture the expected non-existence of the Tolman length is confirmed. In all cases {and for a range of radii} R relevant for nucleation theory, gamma(R) deviates strongly from gamma (Infinity) which can be accounted for by a term of order gamma(Infinity)/gamma(R)-1 ~ 1/R^2. Our results for the simple Lennard-Jones fluid are also compared to results from density functional theory and we find qualitative agreement in the behavior of gamma(R) as well as in the sign and magnitude of the Tolman length.Comment: 25 pages, submitted to J. Chem. Phy

An evaluation of survey designs and model-based inferences of fish aggregations using active acoustics

“Star” survey designs have become an increasingly popular alternative to parallel line designs in fisheries-independent sampling of areas with isolated fish aggregations, such as artificial reefs, seamounts, fish aggregating devices, and spawning aggregation sites. In this study, we simulated three scenarios of fish aggregating around a feature of interest with variations in the size and complexity of aggregations as well as their location relative to the habitat feature. Simulated and empirical data representing goliath grouper (Epinephalus itajara) spawning aggregations at artificial reefs were utilized as a case study, and scenarios were generated in relation to both a single habitat feature and a reef complex with multiple structures. Seven variations of survey design using both star and parallel transects were examined and compared by geostatistical and generalized additive models (GAMs) to identify the most robust approach to quantify fish aggregations in each scenario. In most scenarios, precision in the mean and variability of backscatter estimates is not significantly affected by the number of transects passing over the habitat feature as long as at least one pass is made. Estimation error is minimized using the GAM approach, and is further reduced when sampling variance is high, which was better accomplished by parallel designs overall. These results will help inform surveyors on the best overall approach to improve precision in quantifying fish aggregations given basic knowledge of their behavior around an established habitat feature and help them to adapt their survey designs based on common difficulties in sampling these populations simulated below

Pushing the limits of the reaction-coordinate mapping

This is the author accepted manuscript. The final version is available from AIP Publishing via the DOI in this recordThe reaction-coordinate mapping is a useful technique to study complex quantum dissipative dynamics into structured environments. In essence, it aims to mimic the original problem by means of an 'augmented system', which includes a suitably chosen collective environmental coordinate---the 'reaction coordinate'. This composite then couples to a simpler 'residual reservoir' with short-lived correlations. If, in addition, the residual coupling is weak, a simple quantum master equation can be rigorously applied to the augmented system, and the solution of the original problem just follows from tracing out the reaction coordinate. But, what if the residual dissipation is strong? Here we consider an exactly solvable model for heat transport---a two-node linear "quantum wire" connecting two baths at different temperatures. We allow for a structured spectral density at the interface with one of the reservoirs and perform the reaction-coordinate mapping, writing a perturbative master equation for the augmented system. We find that: (a) strikingly, the stationary state of the original problem can be reproduced accurately by a weak-coupling treatment even when the residual dissipation on the augmented system is very strong; (b) the agreement holds throughout the entire dynamics under large residual dissipation in the overdamped regime; (c) and that such master equation can grossly overestimate the stationary heat current across the wire, even when its non-equilibrium steady state is captured faithfully. These observations can be crucial when using the reaction-coordinate mapping to study the largely unexplored strong-coupling regime in quantum thermodynamics.European Research Council (ERC)London Mathematical SocietyUS National Science Foundatio

Heat Shock Protein 70 Prevents both Tau Aggregation and the Inhibitory Effects of Preexisting Tau Aggregates on Fast Axonal Transport

Aggregation and accumulation of the microtubule-associated protein tau are associated with cognitive decline and neuronal degeneration in Alzheimer's disease and other tauopathies. Thus, preventing the transition of tau from a soluble state to insoluble aggregates and/or reversing the toxicity of existing aggregates would represent a reasonable therapeutic strategy for treating these neurodegenerative diseases. Here we demonstrate that molecular chaperones of the heat shock protein 70 (Hsp70) family are potent inhibitors of tau aggregation in vitro, preventing the formation of both mature fibrils and oligomeric intermediates. Remarkably, addition of Hsp70 to a mixture of oligomeric and fibrillar tau aggregates prevents the toxic effect of these tau species on fast axonal transport, a critical process for neuronal function. When incubated with preformed tau aggregates, Hsp70 preferentially associated with oligomeric over fibrillar tau, suggesting that prefibrillar oligomeric tau aggregates play a prominent role in tau toxicity. Taken together, our data provide a novel molecular basis for the protective effect of Hsp70 in tauopathies

Diffusion-Limited Growth of Microbial Colonies.

The emergence of diffusion-limited growth (DLG) within a microbial colony on a solid substrate is studied using a combination of mathematical modelling and experiments. Using an agent-based model of the interaction between microbial cells and a diffusing nutrient, it is shown that growth directed towards a nutrient source may be used as an indicator that DLG is influencing the colony morphology. A continuous reaction-diffusion model for microbial growth is employed to identify the parameter regime in which DLG is expected to arise. Comparisons between the model and experimental data are used to argue that the bacterium Bacillus subtilis can undergo DLG, while the yeast Saccharomyces cerevisiae cannot, and thus the non-uniform growth exhibited by this yeast must be caused by the pseudohyphal growth mode rather than limited nutrient availability. Experiments testing directly for DLG features in yeast colonies are used to confirm this hypothesis

Steady free-surface flow at the stern of a ship

New solutions for steady two-dimensional free-surface flow past a curved plate are considered here. They can be interpreted as approximations to the flow locally at the stern of a ship. Weakly nonlinear solutions are derived analytically and nonlinear solutions are computed by boundary integral equation methods. Analysis in the phase plane provides a way to determine the geometries of hulls that give rise to wave-free stern flows. These waveless flows are desirable as they reduce ship-drag