Finite size effects on the phase diagram of a binary mixture confined between competing walls

A symmetrical binary mixture AB that exhibits a critical temperature T_{cb} of phase separation into an A-rich and a B-rich phase in the bulk is considered in a geometry confined between two parallel plates a distance D apart. It is assumed that one wall preferentially attracts A while the other wall preferentially attracts B with the same strength (''competing walls''). In the limit $D\to \infty$, one then may have a wetting transition of first order at a temperature T_{w}, from which prewetting lines extend into the one phase region both of the A-rich and the B-rich phase. It is discussed how this phase diagram gets distorted due to the finiteness of D% : the phase transition at T_{cb} immediately disappears for D<\infty due to finite size rounding, and the phase diagram instead exhibit two two-phase coexistence regions in a temperature range T_{trip}<T<T_{c1}=T_{c2}. In the limit D\to \infty T_{c1},T_{c2} become the prewetting critical points and T_{trip}\to T_{w}. For small enough D it may occur that at a tricritical value D_{t} the temperatures T_{c1}=T_{c2} and T_{trip} merge, and then for D<D_{t} there is a single unmixing critical point as in the bulk but with T_{c}(D) near T_{w}. As an example, for the experimentally relevant case of a polymer mixture a phase diagram with two unmixing critical points is calculated explicitly from self-consistent field methods

Spatial modelling of Gully erosion using GIS and R programing: A comparison among three data mining algorithms

© 2018 by the authors. Gully erosion triggers land degradation and restricts the use of land. This study assesses the spatial relationship between gully erosion (GE) and geo-environmental variables (GEVs) using Weights-of-Evidence (WoE) Bayes theory, and then applies three data mining methods-Random Forest (RF), boosted regression tree (BRT), and multivariate adaptive regression spline (MARS)-for gully erosion susceptibility mapping (GESM) in the Shahroud watershed, Iran. Gully locations were identified by extensive field surveys, and a total of 172 GE locationsweremapped. Twelve gully-related GEVs: Elevation, slope degree, slope aspect, plan curvature, convergence index, topographic wetness index (TWI), lithology, land use/land cover (LU/LC), distance from rivers, distance from roads, drainage density, and NDVI were selected to model GE. The results of variables importance by RF and BRT models indicated that distance from road, elevation, and lithology had the highest effect on GE occurrence. The area under the curve (AUC) and seed cell area index (SCAI) methods were used to validate the three GE maps. The results showed that AUC for the three models varies from 0.911 to 0.927, whereas the RF model had a prediction accuracy of 0.927 as per SCAI values, when compared to the other models. The findings will be of help for planning and developing the studied region

Effect of Gravity and Confinement on Phase Equilibria: A Density Matrix Renormalization Approach

The phase diagram of the 2D Ising model confined between two infinite walls and subject to opposing surface fields and to a bulk "gravitational" field is calculated by means of density matrix renormalization methods. In absence of gravity two phase coexistence is restricted to temperatures below the wetting temperature. We find that gravity restores the two phase coexistence up to the bulk critical temperature, in agreement with previous mean-field predictions. We calculate the exponents governing the finite size scaling in the temperature and in the gravitational field directions. The former is the exponent which describes the shift of the critical temperature in capillary condensation. The latter agrees, for large surface fields, with a scaling assumption of Van Leeuwen and Sengers. Magnetization profiles in the two phase and in the single phase region are calculated. The profiles in the single phase region, where an interface is present, agree well with magnetization profiles calculated from a simple solid-on-solid interface hamiltonian.Comment: 4 pages, RevTeX and 4 PostScript figures included. Final version as published. To appear in Phys. Rev. Let

A symmetric polymer blend confined into a film with antisymmetric surfaces: interplay between wetting behavior and phase diagram

We study the phase behavior of a symmetric binary polymer blend which is confined into a thin film. The film surfaces interact with the monomers via short range potentials. We calculate the phase behavior within the self-consistent field theory of Gaussian chains. Over a wide range of parameters we find strong first order wetting transitions for the semi-infinite system, and the interplay between the wetting/prewetting behavior and the phase diagram in confined geometry is investigated. Antisymmetric boundaries, where one surface attracts the A component with the same strength than the opposite surface attracts the B component, are applied. The phase transition does not occur close to the bulk critical temperature but in the vicinity of the wetting transition. For very thin films or weak surface fields one finds a single critical point at $\phi_c=1/2$. For thicker films or stronger surface fields the phase diagram exhibits two critical points and two concomitant coexistence regions. Only below a triple point there is a single two phase coexistence region. When we increase the film thickness the two coexistence regions become the prewetting lines of the semi-infinite system, while the triple temperature converges towards the wetting transition temperature from above. The behavior close to the tricritical point, which separates phase diagrams with one and two critical points, is studied in the framework of a Ginzburg-Landau ansatz. Two-dimensional profiles of the interface between the laterally coexisting phases are calculated, and the interfacial and line tensions analyzed. The effect of fluctuations and corrections to the self-consistent field theory are discussed.Comment: Phys.Rev.E in prin

Interface localisation-delocalisation transition in a symmetric polymer blend: a finite-size scaling Monte Carlo study

Using extensive Monte Carlo simulations we study the phase diagram of a symmetric binary (AB) polymer blend confined into a thin film as a function of the film thickness D. The monomer-wall interactions are short ranged and antisymmetric, i.e, the left wall attracts the A-component of the mixture with the same strength as the right wall the B-component, and give rise to a first order wetting transition in a semi-infinite geometry. The phase diagram and the crossover between different critical behaviors is explored. For large film thicknesses we find a first order interface localisation/delocalisation transition and the phase diagram comprises two critical points, which are the finite film width analogies of the prewetting critical point. Using finite size scaling techniques we locate these critical points and present evidence of 2D Ising critical behavior. When we reduce the film width the two critical points approach the symmetry axis $\phi=1/2$ of the phase diagram and for $D \approx 2 R_g$ we encounter a tricritical point. For even smaller film thickness the interface localisation/delocalisation transition is second order and we find a single critical point at $\phi=1/2$. Measuring the probability distribution of the interface position we determine the effective interaction between the wall and the interface. This effective interface potential depends on the lateral system size even away from the critical points. Its system size dependence stems from the large but finite correlation length of capillary waves. This finding gives direct evidence for a renormalization of the interface potential by capillary waves in the framework of a microscopic model.Comment: Phys.Rev.

Intrinsic profiles and capillary waves at homopolymer interfaces: a Monte Carlo study

A popular concept which describes the structure of polymer interfaces by ``intrinsic profiles'' centered around a two dimensional surface, the ``local interface position'', is tested by extensive Monte Carlo simulations of interfaces between demixed homopolymer phases in symmetric binary (AB) homopolymer blends, using the bond fluctuation model. The simulations are done in an LxLxD geometry. The interface is forced to run parallel to the LxL planes by imposing periodic boundary conditions in these directions and fixed boundary conditions in the D direction, with one side favoring A and the other side favoring B. Intrinsic profiles are calculated as a function of the ``coarse graining length'' B by splitting the system into columns of size BxBxD and averaging in each column over profiles relative to the local interface position. The results are compared to predictions of the self-consistent field theory. It is shown that the coarse graining length can be chosen such that the interfacial width matches that of the self-consistent field profiles, and that for this choice of B the ``intrinsic'' profiles compare well with the theoretical predictions.Comment: to appear in Phys. Rev.

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

Crowdsourcing, Citizen Science or Volunteered Geographic Information? The Current State of Crowdsourced Geographic Information

Citizens are increasingly becoming an important source of geographic information, sometimes entering domains that had until recently been the exclusive realm of authoritative agencies. This activity has a very diverse character as it can, amongst other things, be active or passive, involve spatial or aspatial data and the data provided can be variable in terms of key attributes such as format, description and quality. Unsurprisingly, therefore, there are a variety of terms used to describe data arising from citizens. In this article, the expressions used to describe citizen sensing of geographic information are reviewed and their use over time explored, prior to categorizing them and highlighting key issues in the current state of the subject. The latter involved a review of ~100 Internet sites with particular focus on their thematic topic, the nature of the data and issues such as incentives for contributors. This review suggests that most sites involve active rather than passive contribution, with citizens typically motivated by the desire to aid a worthy cause, often receiving little training. As such, this article provides a snapshot of the role of citizens in crowdsourcing geographic information and a guide to the current status of this rapidly emerging and evolving subject

A simple and efficient GIS tool for volume calculations of submarine landslides

A numeric tool is presented for calculating volumes of topographic voids such as slump scars of landslides, canyons or craters (negative/concave morphology), or alternatively, bumps and hills (positive/convex morphology) by means of digital elevation models embedded within a geographical information system (GIS). In this study, it has been used to calculate landslide volumes. The basic idea is that a (singular) event (landslide, meteorite impact, volcanic eruption) has disturbed an intact surface such that it is still possible to distinguish between the former (undisturbed) landscape and the disturbance (crater, slide scar, debris avalanche). In such cases, it is possible to reconstruct the paleo-surface and to calculate the volume difference between both surfaces, thereby approximating the volume gain or loss caused by the event. I tested the approach using synthetically generated land surfaces that were created on the basis of Shuttle Radar Topography Mission data. Also, I show the application to two real cases, (1) the calculation of the volume of the Masaya Slide, a submarine landslide on the Pacific continental slope of Nicaragua, and (2) the calculation of the void of a segment of the Fish River Canyon, Namibia. The tool is provided as a script file for the free GIS GRASS. It performs with little effort, and offers a range of interpolation parameters. Testing with different sets of interpolation parameters results in a small range of uncertainty. This tool should prove useful in surface studies not exclusively on earth

Assessing Predation Risk to Threatened Fauna from their Prevalence in Predator Scats: Dingoes and Rodents in Arid Australia

The prevalence of threatened species in predator scats has often been used to gauge the risks that predators pose to threatened species, with the infrequent occurrence of a given species often considered indicative of negligible predation risks. In this study, data from 4087 dingo (Canis lupus dingo and hybrids) scats were assessed alongside additional information on predator and prey distribution, dingo control effort and predation rates to evaluate whether or not the observed frequency of threatened species in dingo scats warrants more detailed investigation of dingo predation risks to them. Three small rodents (dusky hopping-mice Notomys fuscus; fawn hopping-mice Notomys cervinus; plains mice Pseudomys australis) were the only threatened species detected in <8% of dingo scats from any given site, suggesting that dingoes might not threaten them. However, consideration of dingo control effort revealed that plains mice distribution has largely retracted to the area where dingoes have been most heavily subjected to lethal control. Assessing the hypothetical predation rates of dingoes on dusky hopping-mice revealed that dingo predation alone has the potential to depopulate local hopping-mice populations within a few months. It was concluded that the occurrence of a given prey species in predator scats may be indicative of what the predator ate under the prevailing conditions, but in isolation, such data can have a poor ability to inform predation risk assessments. Some populations of threatened fauna assumed to derive a benefit from the presence of dingoes may instead be susceptible to dingo-induced declines under certain conditions