Equilibrium self-assembly of colloids with distinct interaction sites: Thermodynamics, percolation, and cluster distribution functions

We calculate the equilibrium thermodynamic properties, percolation threshold, and cluster distribution functions for a model of associating colloids, which consists of hard spherical particles having on their surfaces three short-ranged attractive sites (sticky spots) of two different types, A and B. The thermodynamic properties are calculated using Wertheim's perturbation theory of associating fluids. This also allows us to find the onset of self-assembly, which can be quantified by the maxima of the specific heat at constant volume. The percolation threshold is derived, under the no-loop assumption, for the correlated bond model: In all cases it is two percolated phases that become identical at a critical point, when one exists. Finally, the cluster size distributions are calculated by mapping the model onto an effective model, characterized by a-state-dependent-functionality (f) over bar and unique bonding probability (p) over bar. The mapping is based on the asymptotic limit of the cluster distributions functions of the generic model and the effective parameters are defined through the requirement that the equilibrium cluster distributions of the true and effective models have the same number-averaged and weight-averaged sizes at all densities and temperatures. We also study the model numerically in the case where BB interactions are missing. In this limit, AB bonds either provide branching between A-chains (Y-junctions) if epsilon(AB)/epsilon(AA) is small, or drive the formation of a hyperbranched polymer if epsilon(AB)/epsilon(AA) is large. We find that the theoretical predictions describe quite accurately the numerical data, especially in the region where Y-junctions are present. There is fairly good agreement between theoretical and numerical results both for the thermodynamic (number of bonds and phase coexistence) and the connectivity properties of the model (cluster size distributions and percolation locus).

Mathematical modelling of supercritical CO2 extraction of volatile oils from aromatic plants

The modelling of the experimental data of the extraction of the volatile oil from six aromatic plants (coriander, fennel, savoury, winter savoury, cotton lavender and thyme) was performed using five mathematical models, based on differential mass balances. In all cases the extraction was internal diffusion controlled and the internal mass transfer coefficienty (k(s)) have been found to change with pressure, temperature and particle size. For fennel, savoury and cotton lavender, the external mass transfer and the equilibrium phase also influenced the second extraction period, since k(s) changed with the tested flow rates. In general, the axial dispersion coefficient could be neglected for the conditions studied, since Peclet numbers were high. On the other hand, the solute-matrix interaction had to be considered in order to ensure a satisfactory description of the experimental data.

Dynamic equilibrium through reinforcement learning

Reinforcement Learning is an area of Machine Learning that deals with how an agent should take actions in an environment such as to maximize the notion of accumulated reward. This type of learning is inspired by the way humans learn and has led to the creation of various algorithms for reinforcement learning. These algorithms focus on the way in which an agent’s behaviour can be improved, assuming independence as to their surroundings. The current work studies the application of reinforcement learning methods to solve the inverted pendulum problem. The importance of the variability of the environment (factors that are external to the agent) on the execution of reinforcement learning agents is studied by using a model that seeks to obtain equilibrium (stability) through dynamism – a Cart-Pole system or inverted pendulum. We sought to improve the behaviour of the autonomous agents by changing the information passed to them, while maintaining the agent’s internal parameters constant (learning rate, discount factors, decay rate, etc.), instead of the classical approach of tuning the agent’s internal parameters. The influence of changes on the state set and the action set on an agent’s capability to solve the Cart-pole problem was studied. We have studied typical behaviour of reinforcement learning agents applied to the classic BOXES model and a new form of characterizing the environment was proposed using the notion of convergence towards a reference value. We demonstrate the gain in performance of this new method applied to a Q-Learning agent.

On the monoids of transformations that preserve the order and a uniform partition

In this article we consider the monoid O(mxn) of all order-preserving full transformations on a chain with mn elements that preserve a uniformm-partition and its submonoids O(mxn)(+) and O(mxn)(-) of all extensive transformations and of all co-extensive transformations, respectively. We determine their ranks and construct a bilateral semidirect product decomposition of O(mxn) in terms of O(mxn)(-) and O(mxn)(+).

Cork industry wastewater partition by ultra/nanofiltration: A biodegradation and valorisation study

Wastewater from cork processing industry present high levels of organic and phenolic compounds, such as tannins, with a low biodegradability and a significant toxicity. These compounds are not readily removed by conventional municipal wastewater treatment, which is largely based on primary sedimentation followed by biological treatment. The purpose of this work is to study the biodegradability of different cork wastewater fractions, obtained through membrane separation, in order to assess its potential for biological treatment and having in view its valorisation through tannins recovery, which could be applied in other industries. Various ultrafiltration and nanofiltration membranes where used, with molecular weight cut-offs (MWCO) ranging from 0.125 to 91 kDa. The wastewater and the different permeated fractions were analyzed in terms of Total Organic Carbon (TOC), Chemical Oxygen Demand (COD), Biochemical Oxygen Demand (BOD), Total Phenols (TP), Tannins, Color, pH and Conductivity. Results for the wastewater shown that it is characterized by a high organic content (670.5-1056.8 mg TOC/L, 2285-2604 mg COD/L, 1000-1225 mg BOD/L), a relatively low biodegradability (0.35-0.38 for BODs/COD and 0.44-0.47 for BOD20/COD) and a high content of phenols (360-410 mg tannic acid/L) and tannins (250-270 mg tannic acid/L). The results for the wastewater fractions shown a general decrease on the pollutant content of permeates, and an increase of its biodegradability, with the decrease of the membrane MWCO applied. Particularly, the permeated fraction from the membrane MWCO of 3.8 kDa, presented a favourable index of biodegradability (0.8) and a minimized phenols toxicity that enables it to undergo a biological treatment and so, to be treated in a municipal wastewater treatment plant. Also, within the perspective of valorisation, the rejected fraction obtained through this membrane MWCO may have a significant potential for tannins recovery. Permeated fractions from membranes with MWCO lower than 3.8 kDa, presented a particularly significant decline of organic matter and phenols, enabling this permeates to be reused in the cork processing and so, representing an interesting perspective of zero discharge for the cork industry, with evident environmental and economic advantages. (C) 2010 Elsevier Ltd. All rights reserved.

How foam-like is the shear-induced lamellar phase of an ionic liquid crystal?

Philosophical Magazine Letters Volume 88, Issue 9-10, 2008 Special Issue: Solid and Liquid Foams. In commemoration of Manuel Amaral Fortes

Equilibrium distributions of discrete non-autonomous graphs

We introduce the notions of equilibrium distribution and time of convergence in discrete non-autonomous graphs. Under some conditions we give an estimate to the convergence time to the equilibrium distribution using the second largest eigenvalue of some matrices associated with the system.

On the ranks of certain monoids of transformations that preserve a uniform partition

The rank of a semigroup, an important and relevant concept in Semigroup Theory, is the cardinality of a least-size generating set. Semigroups of transformations that preserve or reverse the order or the orientation as well as semigroups of transformations preserving an equivalence relation have been widely studied over the past decades by many authors. The purpose of this article is to compute the ranks of the monoid

The cardinal of various monoids of transformations that preserve a uniform partition

In this paper we give formulas for the number of elements of the monoids ORm x n of all full transformations on it finite chain with tun elements that preserve it uniform m-partition and preserve or reverse the orientation and for its submonoids ODm x n of all order-preserving or order-reversing elements, OPm x n of all orientation-preserving elements, O-m x n of all order-preserving elements, O-m x n(+) of all extensive order-preserving elements and O-m x n(-) of all co-extensive order-preserving elements.