Phase diagrams of binary mixtures of patchy colloids with distinct numbers and types of patches: Theempty fluid regime

We investigate the effect of distinct bonding energies on the onset of criticality of low functionality fluid mixtures. We focus on mixtures ofparticles with two and three patches as this includes the mixture where "empty" fluids were originally reported. In addition to the number of patches, thespecies differ in the type of patches or bonding sites. For simplicity, we consider that the patches on each species are identical: one species has threepatches of type A and the other has two patches of type B. We have found a rich phase behavior with closed miscibility gaps, liquid-liquid demixing, and negative azeotropes. Liquid-liquid demixing was found to pre-empt the "empty" fluid regime, of these mixtures, when the AB bonds are weaker than the AA or BB bonds. By contrast, mixtures in this class exhibit "empty" fluid behavior when the AB bonds are stronger than at least one of the other two. Mixtureswith bonding energies epsilon(BB) = epsilon(AB) and epsilon(AA) < epsilon(BB), were found to exhibit an unusual negative azeotrope. (C) 2011 American Institute of Physics. [doi:10.1063/1.3561396]

Synthesis and Coordination Chemistry of a New N-4-Polydentate Class of Pyridyl-Functionalized Scorpionate Ligands: Complexes of Fe-II, Zn-II, V-IV, Pd-II and Use for Heterobimetallic Systems

The new potentially N-4-multidentate pyridyl-functionalized scorpionates 4-((tris-2,2,2-(pyrazol-1-ypethoxy)methyl)pyridine (TpmPy, (1)) and 4-((tris-2,2,2-(3-phenylpyrazol-1-yl)ethoxy)methyl)pyridine (TpmPy(Ph), (2)) have been synthesized and their coordination behavior toward Fe-II, Ni-II, Zn-II, Cu-II, Pd-II, and V-III centers has been studied. Reaction of (1) with Fe(BF4)(2)center dot 6H(2)O yields [Fe(TpmPy)(2)](BF4)(2) (3), that, in the solid state, shows the sandwich structure with trihapto ligand coordination via the pyrazolyl arms, and is completely low spin (LS) until 400 K. Reactions of 2 equiv of (1) or (2) with Zn-II or Ni-II chlorides give the corresponding metal complexes with general formula [MCl2(TpmPy*)(2)] (M = Zn, Ni; TpmPy* = TpmPy, TpmPy(Ph)) (4-7) where the ligand is able to coordinate through either the pyrazolyl rings (in case of [Ni(TpmPy)(2)Cl-2 (5)) or the pyridyl-side (for [ZnCl2(TpmPy)(2)] (4), [ZnCl2(TpmPy(Ph))(2)] (6) and [NiCl2(TpmPy(Ph))(2)] (7)). The reaction of (1) with VCl3 gives [VOCl2(TpmPy)] (8) that shows the N-3-pyrazolyl coordination-mode. Moreover, (1) and react with cis-[PdCl2(CH3CN)(2)] to give the disubstituted complexes [PdCl2(TprnPy)(2)] (9) and [PdCl2(TpmPy(Ph))(2)] (10), respectively, bearing the scorpionate coordinated via the pyridyl group. Compounds (9) and (10) react with Fe(BF4)(2) to give the heterobimetallic Pd/Fe systems [PdCl2(mu-TpmPy)(2)-Fe](BF4)(2) (11) and [PdCl2(mu-TpmPy(Ph))(2)Fe-2(H2O)(6)]BF4)(4) (13), respectively. Compound (11) can also be formed from reaction of (3) with cis-[PdCl2(CH3CN)(2)], while reaction of (3) with Cu(NO3)(2).2.5H(2)O generates [Fe(mu-TpmPy)(2)-Cu(NO3)(2)](BF4)(2) (12), confirming the multidentate ability of the new chelating ligands. The X-ray diffraction analyses of compounds (1), (3), (4), (5), and (9) are also reported.

The condensation and ordering of models of empty liquids

We consider a simple model consisting of particles with four bonding sites ("patches"), two of type A and two of type B, on the square lattice, and investigate its global phase behavior by simulations and theory. We set the interaction between B patches to zero and calculate the phase diagram as the ratio between the AB and the AA interactions, epsilon(AB)*, varies. In line with previous work, on three-dimensional off-lattice models, we show that the liquid-vapor phase diagram exhibits a re-entrant or "pinched" shape for the same range of epsilon(AB)*, suggesting that the ratio of the energy scales - and the corresponding empty fluid regime - is independent of the dimensionality of the system and of the lattice structure. In addition, the model exhibits an order-disorder transition that is ferromagnetic in the re-entrant regime. The use of low-dimensional lattice models allows the simulation of sufficiently large systems to establish the nature of the liquid-vapor critical points and to describe the structure of the liquid phase in the empty fluid regime, where the size of the "voids" increases as the temperature decreases. We have found that the liquid-vapor critical point is in the 2D Ising universality class, with a scaling region that decreases rapidly as the temperature decreases. The results of simulations and theoretical analysis suggest that the line of order-disorder transitions intersects the condensation line at a multi-critical point at zero temperature and density, for patchy particle models with a re-entrant, empty fluid, regime. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3657406]

Phase diagrams of particles with dissimilar patches: X-junctions and Y-junctions

We use Wertheim's first-order perturbation theory to investigate the phase behaviour and the structure of coexisting fluid phases for a model of patchy particles with dissimilar patches (two patches of type A and f(B) patches of type B). A patch of type alpha = {A, B} can bond to a patch of type beta = {A, B} in a volume nu(alpha beta), thereby decreasing the internal energy by epsilon(alpha beta). We analyse the range of model parameters where AB bonds, or Y-junctions, are energetically disfavoured (epsilon(AB) < epsilon(AA)/2) but entropically favoured (nu(AB) >> nu(alpha alpha)), and BB bonds, or X-junctions, are energetically favoured (epsilon(BB) > 0). We show that, for low values of epsilon(BB)/epsilon(AA), the phase diagram has three different regions: (i) close to the critical temperature a low-density liquid composed of long chains and rich in Y-junctions coexists with a vapour of chains; (ii) at intermediate temperatures there is coexistence between a vapour of short chains and a liquid of very long chains with X-and Y-junctions; (iii) at low temperatures an ideal gas coexists with a high-density liquid with all possible AA and BB bonds formed. It is also shown that in region (i) the liquid binodal is reentrant (its density decreases with decreasing temperature) for the lower values of epsilon(BB)/epsilon(AA). The existence of these three regions is a consequence of the competition between the formation of X- and Y-junctions: X-junctions are energetically favoured and thus dominate at low temperatures, whereas Y-junctions are entropically favoured and dominate at higher temperatures.

Measuring spatial interaction behavior in team sports using superimposed Voronoi diagrams

In team sports, the spatial distribution of players on the field is determined by the interaction behavior established at both player and team levels. The distribution patterns observed during a game emerge from specific technical and tactical methods adopted by the teams, and from individual, environmental and task constraints that influence players' behaviour. By understanding how specific patterns of spatial interaction are formed, one can characterize the behavior of the respective teams and players. Thus, in the present work we suggest a novel spatial method for describing teams' spatial interaction behaviour, which results from superimposing the Voronoi diagrams of two competing teams. We considered theoretical patterns of spatial distribution in a well-defined scenario (5 vs 4+ GK played in a field of 20x20m) in order to generate reference values of the variables derived from the superimposed Voronoi diagrams (SVD). These variables were tested in a formal application to empirical data collected from 19 Futsal trials with identical playing settings. Results suggest that it is possible to identify a number of characteristics that can be used to describe players' spatial behavior at different levels, namely the defensive methods adopted by the players.

A class of singular first order differential equations with applications in reaction-diffusion

Agências Financiadoras: FCT e MIUR

Big Bang bifurcations and allee effect in Blumberg’s dynamics

This paper concerns dynamics and bifurcations properties of a class of continuous-defined one-dimensional maps, in a three-dimensional parameter space: Blumberg's functions. This family of functions naturally incorporates a major focus of ecological research: the Allee effect. We provide a necessary condition for the occurrence of this phenomenon, associated with the stability of a fixed point. A central point of our investigation is the study of bifurcations structure for this class of functions. We verified that under some sufficient conditions, Blumberg's functions have a particular bifurcations structure: the big bang bifurcations of the so-called "box-within-a-box" type, but for different kinds of boxes. Moreover, it is verified that these bifurcation cascades converge to different big bang bifurcation curves, where for the corresponding parameter values are associated distinct attractors. This work contributes to clarify the big bang bifurcation analysis for continuous maps. To support our results, we present fold and flip bifurcations curves and surfaces, and numerical simulations of several bifurcation diagrams.

Spatial dynamics of team sports exposed by Voronoi diagrams

Team sports represent complex systems: players interact continuously during a game, and exhibit intricate patterns of interaction, which can be identified and investigated at both individual and collective levels. We used Voronoi diagrams to identify and investigate the spatial dynamics of players' behavior in Futsal. Using this tool, we examined 19 plays of a sub-phase of a Futsal game played in a reduced area (20 m(2)) from which we extracted the trajectories of all players. Results obtained from a comparative analysis of player's Voronoi area (dominant region) and nearest teammate distance revealed different patterns of interaction between attackers and defenders, both at the level of individual players and teams. We found that, compared to defenders, larger dominant regions were associated with attackers. Furthermore, these regions were more variable in size among players from the same team but, at the player level, the attackers' dominant regions were more regular than those associated with each of the defenders. These findings support a formal description of the dynamic spatial interaction of the players, at least during the particular sub-phase of Futsal investigated. The adopted approach may be extended to other team behaviors where the actions taken at any instant in time by each of the involved agents are associated with the space they occupy at that particular time.

A resource for signs and Feynman diagrams of the standart model

When performing a full calculation within the standard model (SM) or its extensions, it is crucial that one utilizes a consistent set of signs for the gauge couplings and gauge fields. Unfortunately, the literature is plagued with differing signs and notations. We present all SM Feynman rules, including ghosts, in a convention-independent notation, and we table the conventions in close to 40 books and reviews.

Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations

An improved class of nonlinear bidirectional Boussinesq equations of sixth order using a wave surface elevation formulation is derived. Exact travelling wave solutions for the proposed class of nonlinear evolution equations are deduced. A new exact travelling wave solution is found which is the uniform limit of a geometric series. The ratio of this series is proportional to a classical soliton-type solution of the form of the square of a hyperbolic secant function. This happens for some values of the wave propagation velocity. However, there are other values of this velocity which display this new type of soliton, but the classical soliton structure vanishes in some regions of the domain. Exact solutions of the form of the square of the classical soliton are also deduced. In some cases, we find that the ratio between the amplitude of this wave and the amplitude of the classical soliton is equal to 35/36. It is shown that different families of travelling wave solutions are associated with different values of the parameters introduced in the improved equations.

Exploiting the bin-class histograms for feature selection on discrete data

In machine learning and pattern recognition tasks, the use of feature discretization techniques may have several advantages. The discretized features may hold enough information for the learning task at hand, while ignoring minor fluctuations that are irrelevant or harmful for that task. The discretized features have more compact representations that may yield both better accuracy and lower training time, as compared to the use of the original features. However, in many cases, mainly with medium and high-dimensional data, the large number of features usually implies that there is some redundancy among them. Thus, we may further apply feature selection (FS) techniques on the discrete data, keeping the most relevant features, while discarding the irrelevant and redundant ones. In this paper, we propose relevance and redundancy criteria for supervised feature selection techniques on discrete data. These criteria are applied to the bin-class histograms of the discrete features. The experimental results, on public benchmark data, show that the proposed criteria can achieve better accuracy than widely used relevance and redundancy criteria, such as mutual information and the Fisher ratio.

Generation of high-affinity monoclonal antibodies of IgG class against native β-d-glucans from basidiomycete mushrooms

β-d-glucans from basidiomycete strains are powerful immunomodulatory agents in several clinical conditions. Therefore, their assay, purification and characterization are of great interest to understand their structure-function relationship. Hybridoma cell fusion was used to raise monoclonal antibodies (Mabs) against extracellular β-d-glucans (EBGs) from Pleurotus ostreatus. Two of the hybridoma clones (1E6-1E8-B5 and 3E8-3B4) secreting Mabs against EBGs were selected. This hybridoma cell line secreted Mabs of the IgG class which were then purified by hydroxyapatite chromatography to apparent homogeneity on native and SDS-PAGE. Mabs secreted by 1E6-1E8-B5 clone were found to recognize a common epitope on several β-d-glucans from different basidiomycete strains. This Mab exhibited high affinity constant (KA) for β-d-glucans from several mushroom strains in the range of 3.20 × 109 ± 3.32 × 103-1.51 × 1013 ± 3.58 × 107 L/mol. Moreover, they reacted to some heat-treated β-d-glucans in a different mode when compared with the native forms; these data suggest that this Mab binds to a conformational epitope on the β-d-glucan molecule. The epitope-binding studies of Mabs obtained from 1E6-1E8-B5 and 3E8-3B4 revealed that the Mabs bind to the same epitope on some β-d-glucans and to different epitopes in other antigen molecules. Therefore, these Mabs can be used to assay for β-d-glucan from basidiomycete mushrooms. © 2015 Elsevier Ltd. All rights reserved.