Scaling law in Saddle-node bifurcations for one-dimensional maps: A complex variable approach

The study of transient dynamical phenomena near bifurcation thresholds has attracted the interest of many researchers due to the relevance of bifurcations in different physical or biological systems. In the context of saddle-node bifurcations, where two or more fixed points collide annihilating each other, it is known that the dynamics can suffer the so-called delayed transition. This phenomenon emerges when the system spends a lot of time before reaching the remaining stable equilibrium, found after the bifurcation, because of the presence of a saddle-remnant in phase space. Some works have analytically tackled this phenomenon, especially in time-continuous dynamical systems, showing that the time delay, tau, scales according to an inverse square-root power law, tau similar to (mu-mu (c) )(-1/2), as the bifurcation parameter mu, is driven further away from its critical value, mu (c) . In this work, we first characterize analytically this scaling law using complex variable techniques for a family of one-dimensional maps, called the normal form for the saddle-node bifurcation. We then apply our general analytic results to a single-species ecological model with harvesting given by a unimodal map, characterizing the delayed transition and the scaling law arising due to the constant of harvesting. For both analyzed systems, we show that the numerical results are in perfect agreement with the analytical solutions we are providing. The procedure presented in this work can be used to characterize the scaling laws of one-dimensional discrete dynamical systems with saddle-node bifurcations.

Topological entropy of catalytic sets: Hypercycles revisited

The dynamics of catalytic networks have been widely studied over the last decades because of their implications in several fields like prebiotic evolution, virology, neural networks, immunology or ecology. One of the most studied mathematical bodies for catalytic networks was initially formulated in the context of prebiotic evolution, by means of the hypercycle theory. The hypercycle is a set of self-replicating species able to catalyze other replicator species within a cyclic architecture. Hypercyclic organization might arise from a quasispecies as a way to increase the informational containt surpassing the so-called error threshold. The catalytic coupling between replicators makes all the species to behave like a single and coherent evolutionary multimolecular unit. The inherent nonlinearities of catalytic interactions are responsible for the emergence of several types of dynamics, among them, chaos. In this article we begin with a brief review of the hypercycle theory focusing on its evolutionary implications as well as on different dynamics associated to different types of small catalytic networks. Then we study the properties of chaotic hypercycles with error-prone replication with symbolic dynamics theory, characterizing, by means of the theory of topological Markov chains, the topological entropy and the periods of the orbits of unimodal-like iterated maps obtained from the strange attractor. We will focus our study on some key parameters responsible for the structure of the catalytic network: mutation rates, autocatalytic and cross-catalytic interactions.

Quantitative description of the self-assembly of patchy particles into chains and rings

We numerically study a simple fluid composed of particles having a hard-core repulsion complemented by two patchy attractive sites on the particle poles. An appropriate choice of the patch angular width allows for the formation of ring structures which, at low temperatures and low densities, compete with the growth of linear aggregates. The simplicity of the model makes it possible to compare simulation results and theoretical predictions based on the Wertheim perturbation theory, specialized to the case in which ring formation is allowed. Such a comparison offers a unique framework for establishing the quality of the analytic predictions. We find that the Wertheim theory describes remarkably well the simulation results.

Reply to "Comment on 'Effect of polydispersity on the ordering transition of adsorbed self- assembled rigid rods'"

We comment on the nature of the ordering transition of a model of equilibrium polydisperse rigid rods on the square lattice, which is reported by Lopez et al. to exhibit random percolation criticality in the canonical ensemble, in sharp contrast to (i) our results of Ising criticality for the same model in the grand canonical ensemble [Phys. Rev. E 82, 061117 (2010)] and (ii) the absence of exponent(s) renormalization for constrained systems with logarithmic specific-heat anomalies predicted on very general grounds by Fisher [Phys. Rev. 176, 257 (1968)].

The nature of the ordered phase of the confined self-assembled rigid Rod model

We investigate the nature of the ordered phase and the orientational correlations between adjacent layers of the confined three-dimensional self-assembled rigid rod model, on the cubic lattice. We find that the ordered phase at finite temperatures becomes uniaxial in the thermodynamic limit, by contrast to the ground state (partial) order where the orientation of the uncorrelated layers is perpendicular to one of the three lattice directions. The increase of the orientational correlation between layers as the number of layers increases suggests that the unconfined model may also exhibit uniaxial ordering at finite temperatures.

Formação de alunos histórica e geograficamente competentes no ensino básico - contributo das imagens e dos mapas mentais

Relatório de investigação apresentado à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Ensino de 1º e 2º ciclo do Ensino Básico

Predictors of infant positive, negative and self-direct coping during face to face still-face in a Portuguese preterm sample

Past studies found three types of infant coping behaviour during Face-to-Face Still-Face paradigm (FFSF): a Positive Other-Directed Coping; a Negative Other-Directed Coping and a Self-Directed Coping. In the present study, we investigated whether those types of coping styles are predicted by: infants’ physiological responses; maternal representations of their infant’s temperament; maternal interactive behaviour in free play; and infant birth and medical status. The sample consisted of 46, healthy, prematurely born infants and their mothers. At one month, infant heart rate was collected in basal. At three months old (corrected age), infant heart-rate was registered during FFSF episodes. Mothers described their infants’ temperament using a validated Portuguese temperament scale, at infants three months of corrected age. As well, maternal interactive behaviour was evaluated during a free play situation using CARE-Index. Our findings indicate that positive coping behaviours were correlated with gestational birth weight, heart rate (HR), gestational age, and maternal sensitivity in free play. Gestational age and maternal sensitivity predicted Positive Other-Direct Coping behaviours. Moreover, Positive Other-Direct coping was negatively correlated with HR during Still-Face Episode. Self-directed behaviours were correlated with HR during Still-Face Episode and Recover Episode and with maternal controlling/intrusive behaviour. However, only maternal behaviour predicted Self-direct coping. Early social responses seem to be affected by infants’ birth status and by maternal interactive behaviour. Therefore, internal and external factors together contribute to infant ability to cope and to re-engage after stressful social events.

(E)xperimental study of the porosity and microstructure of self-compacting concrete (SCC) with binary and ternary mixes of fly ash and limestone filler

Self-compacting concrete (SCC) can soon be expected to replace conventional concrete due to its many advantages. Its main characteristics in the fresh state are achieved essentially by a higher volume of mortar (more ultrafine material) and a decrease of the coarse-aggregates. The use of over-large volumes of additions such as fly ash (FA) and/or limestone filler (LF) can substantially affect the concrete's pore structure and consequently its durability. In this context, an experimental programme was conducted to evaluate the effect on the concrete's porosity and microstructure of incorporating FA and LF in binary and ternary mixes of SCC. For this, a total of 11 SIX mixes were produced; 1 with cement only (C); 3 with C + FA in 30%, 60% and 70% substitution (fad); 3 with C + LF in 30%, 60% and 70% fad; 4 with C + FA + LF in combinations of 10-20%, 20-10%, 20-40% and 40-20% f(ad), respectively. The results enabled conclusions to be established regarding the SCC's durability, based on its permeability and the microstructure of its pore structure. The properties studied are strongly affected by the type and quantity of additions. The use of ternary mixes also proves to be extremely favourable, confirming the beneficial effect of the synergy between these additions. (C) 2015 Elsevier Ltd. All rights reserved.

Experimental study of the mechanical properties and durability of self-compacting mortars with nano materials (SiO2 and TiO2)

Resumo: Cement, as well as the remaining constituents of self-compacting mortars, must be carefully selected, in order to obtain an adequate composition with a granular mix as compact as possible and a good performance in the fresh state (self-compacting effect) and the hardened state (mechanical and durability-related behavior). Therefore in this work the possibility of incorporating nano particles in self-compacting mortars was studied. Nano materials are very reactive due mostly to their high specific surface and show a great potential to improve the properties of these mortars, both in mechanical and durability terms. In this work two nano materials were used, nano silica (nano SiO2) in colloidal state and nano titanium (nano TiO2) in amorphous state, in two types of self-compacting mortars (ratio binder:sand of 1:1 and 1:2). The self-compacting mortar mixes have the same water/cement ratio and 30% of replacement of cement with fly ashes. The influence of nano materials nano-SiO2 and nano-TiO2 on the fresh and hardened state properties of these self-compacting mortars was studied. The results show that the use of nano materials in repair and rehabilitation mortars has significant potential but still needs to be optimized. (C) 2015 Elsevier Ltd. All rights reserved.

Experimental study of the porosity and microstructure of self-compacting concrete (SCC) with binary and ternary mixes of fly ash and limestone filler

Abstract Self-compacting concrete (SCC) can soon be expected to replace conventional concrete due to its many advantages. Its main characteristics in the fresh state are achieved essentially by a higher volume of mortar (more ultrafine material) and a decrease of the coarse-aggregates. The use of over-large volumes of additions such as fly ash (FA) and/or limestone filler (LF) can substantially affect the concrete's pore structure and consequently its durability. In this context, an experimental programme was conducted to evaluate the effect on the concrete's porosity and microstructure of incorporating FA and LF in binary and ternary mixes of SCC. For this, a total of 11 SCC mixes were produced: 1 with cement only (C); 3 with C + FA in 30%, 60% and 70% substitution (fad); 3 with C + LF in 30%, 60% and 70% fad; 4 with C + FA + LF in combinations of 10-20%, 20-10%, 20-40% and 40-20% fad, respectively. The results enabled conclusions to be established regarding the SCC's durability, based on its permeability and the microstructure of its pore structure. The properties studied are strongly affected by the type and quantity of additions. The use of ternary mixes also proves to be extremely favourable, confirming the beneficial effect of the synergy between these additions. © 2015 Elsevier Ltd. All rights reserved.

Fresh-state properties of self-compacting mortar and concrete with combined use of limestone filler and fly ash

This paper presents the results of a study on the behaviour of self-compacting concrete (SCC) in the fresh and hardened states, produced with binary and ternary mixes of fly ash (FA) and limestone filler (LF), using the method proposed by Nepomuceno. His method determines the SCC composition parameters in the mortar phase (self-compacting mortar - SCM) easily and efficiently, whilst guaranteeing the SCC properties in both the fresh and hardened states. For this, 11 SCMs were studied: one with cement (C) only; three with FA at 30%, 60% and 70% C substitution; three with LF at 30%, 60% and 70% C substitution; four with FA + LF in combinations of 10-20%, 20-10%, 20-40% and 40-20% C substitution. Once the composition of these mortars was defined, 18 SCC mixes were produced: 14 binary SCC mixes were produced with the seven binary mortar mixes, and four ternary SCC mixes were produced with the four ternary mortar mixes. In addition to the methodology proposed by Nepomuceno, the combined use of FA and LF in ternary mixtures was tested. The results confirmed that the method could yield SCC with adequate properties in both the fresh and hardened states. It was also possible to determine the SCC composition parameters in the mortar phase (self-compacting mortar - SCM) that will guarantee the SCC properties in both the fresh and hardened states, as confirmed through the optimized behaviour of the SCC in the fresh state and the promising results in the hardened state (compressive strength). The potential demonstrated by the joint use of LF and FA through the synergetic interaction of both additions is emphasized.

Study of the rheology of self-compacting concrete with fine recycled concrete aggregates

This work studies the effect of incorporating fine recycled aggregates on the rheology of self-compacting concrete over time (at 15,45 and 90 min). The fine fraction of the natural aggregates was replaced at 0%, 20%, 50% and 100% with recycled sand. The fresh-state properties were studied by empirical tests (slump-flow, J-Ring, L-Box) and fundamental ones in an ICAR rheometer. The mixes with 50% and 100% recycled sand lost their SCC characteristics at 90 min. Contrarily the mix with 20% replacement maintained suitable passing and filling ability. The causes of this trend were an initial increase of plastic viscosity and afterwards an increase of yield stress. The compressive strength of the 50% and 100% replacement mixes decreased significantly and that of the 20% replacement mix less than 10%. (C) 2015 Elsevier Ltd. All rights reserved.

On a self-start Darrieus wind turbine: blade design and field tests

This paper is about a design of an urban area Darrieus VAWT, having self-start ability due to an innovative profile design named EN0005, avoiding the need of extra components or external electricity feed-in. An approach is presented to study the ability of a blade profile to offer self-start ability. Methodologies applied for the blade body and for profile development are reported. Field tests and main conclusions are presented to persuade for the arrangement of this design. (C) 2015 Elsevier Ltd. All rights reserved.

Self-scheduling and bidding strategies of thermal units with stochastic emission constraints

This paper is on the self-scheduling problem for a thermal power producer taking part in a pool-based electricity market as a price-taker, having bilateral contracts and emission-constrained. An approach based on stochastic mixed-integer linear programming approach is proposed for solving the self-scheduling problem. Uncertainty regarding electricity price is considered through a set of scenarios computed by simulation and scenario-reduction. Thermal units are modelled by variable costs, start-up costs and technical operating constraints, such as: forbidden operating zones, ramp up/down limits and minimum up/down time limits. A requirement on emission allowances to mitigate carbon footprint is modelled by a stochastic constraint. Supply functions for different emission allowance levels are accessed in order to establish the optimal bidding strategy. A case study is presented to illustrate the usefulness and the proficiency of the proposed approach in supporting biding strategies. (C) 2014 Elsevier Ltd. All rights reserved.

Aryleneethynylene Trimers Bearing Calix[4]arenes: synthesis, optical properties and self-assembling studies

New homoditopic bis-calix[4]arene-carbazole conjugates, armed with hydrophilic carboxylic acid functions at their lower rims, are disclosed. Evidence for their self-association in solution was gathered from solvatochromic and thermochromic studies, as well as from gel-permeation chromatography analysis. Their ability to function as highly sensitive sensors toward polar electron-deficient aromatic compounds is demonstrated.