Self-assembly in chains, rings, and branches: a single component system with two critical points

Agências financiadoras: FCT - PEstOE/FIS/UI0618/2011; PTDC/FIS/098254/2008 ERC-PATCHYCOLLOIDS e MIUR-PRIN

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.

Exciting dynamical behavior in a network of two coupled rings of Chen oscillators

We study exotic patterns appearing in a network of coupled Chen oscillators. Namely, we consider a network of two rings coupled through a “buffer” cell, with Z3×Z5 symmetry group. Numerical simulations of the network reveal steady states, rotating waves in one ring and quasiperiodic behavior in the other, and chaotic states in the two rings, to name a few. The different patterns seem to arise through a sequence of Hopf bifurcations, period-doubling, and halving-period bifurcations. The network architecture seems to explain certain observed features, such as equilibria and the rotating waves, whereas the properties of the chaotic oscillator may explain others, such as the quasiperiodic and chaotic states. We use XPPAUT and MATLAB to compute numerically the relevant states.

Generalization of Wertheim's theory for the assembly of various types of rings

We generalize Wertheim's first order perturbation theory to account for the effect in the thermodynamics of the self-assembly of rings characterized by two energy scales. The theory is applied to a lattice model of patchy particles and tested against Monte Carlo simulations on a fcc lattice. These particles have 2 patches of type A and 10 patches of type B, which may form bonds AA or AB that decrease the energy by epsilon(AA) and by epsilon(AB) = r epsilon(AA), respectively. The angle theta between the 2 A-patches on each particle is fixed at 601, 90 degrees or 120 degrees. For values of r below 1/2 and above a threshold r(th)(theta) the models exhibit a phase diagram with two critical points. Both theory and simulation predict that rth increases when theta decreases. We show that the mechanism that prevents phase separation for models with decreasing values of theta is related to the formation of loops containing AB bonds. Moreover, we show that by including the free energy of B-rings ( loops containing one AB bond), the theory describes the trends observed in the simulation results, but that for the lowest values of theta, the theoretical description deteriorates due to the increasing number of loops containing more than one AB bond.

Annular Lichen Planus in Association with Crohn Disease

BACKGROUND: Lichen planus is an idiopathic inflammatory disease of the skin and mucous membranes. Although the etiology is not established, it has been associated with autoimmune diseases, viral infections, drugs and dental restoration materials. However, the association with inflammatory bowel disease has been very rarely reported in the literature. CASE REPORT: A 19-year-old female patient presented with annular lesions on her upper body and limbs, with a sharply defined border and non-atrophic skin in the center. The lesions were hyperpigmented and had been stable for over one year. The histopathology confirmed the diagnosis of annular lichen planus. She had weight loss, occasional diarrhea, and a severe anemia. The investigation of these symptoms led to the diagnosis of Crohn disease and a sickle cell trait. Therapy with systemic corticosteroids and mesalazine controlled the intestinal disease, with concomitant improvement of the skin lesions. CONCLUSIONS: As lichen planus can be associated with other immunological disorders, the association with inflammatory bowel disease should be considered in the evaluation of the patient.

J. R. R. Tolkien, The Lord of the Rings; A Viagem e a Transformação

Este livro, agora publicado pelo INIC, é o resultado de um trabalho de investigação realizado entre 1985 e 1987 para a obtenção do grau de Mestre em Estudos Literários Comparados pela Faculdade de Ciências Sociais e Humanas da Universidade Nova de Lisboa. A literatura fantástica é uma área da literatura mundial que recebeu nas últimas décadas um grande interesse por parte da comunidade científica internacional. A multiplicação das associações, reuniões e congressos, a par da crescente produção teórica e científica, dão prova da vitalidade desta área da crítica literária. Parte deste movimento foi precisamente despoletado pelo interesse provocado pela obra de 1. R. R. Tolkien e de outros autores como C. S. Lewis, Charles Williams, etc. Este fenómeno internacional não teve ainda reais desenvolvimentos em Portugal. Cinco anos volvidos sobre a realização deste trabalho verificamos que ele é um dos primeiros (senão o primeiro) editado entre nós que, de uma forma sistemática e científica, analisa a obra de Tolkien, abordando ainda, embora de forma breve, a problemática da ficção fantástica contemporânea.

Analytical and numerical study of the electro-osmotic annular flow of viscoelastic fluids

In this work we present semi-analytical solutions for the electro-osmotic annular flow of viscoelastic fluids modeled by the Linear and Exponential PTT models. The viscoelastic fluid flows in the axial direction between two concentric cylinders under the combined influences of electrokinetic and pressure forcings. The analysis invokes the Debye-Hückel approximation and includes the limit case of pure electro-osmotic flow. The solution is valid for both no slip and slip velocity at the walls and the chosen slip boundary condition is the linear Navier slip velocity model. The combined effects of fluid rheology, electro-osmotic and pressure gradient forcings on the fluid velocity distribution are also discussed.

Annular flow of viscoelastic fluids: Analytical and numerical solutions

This work provides analytical and numerical solutions for the linear, quadratic and exponential Phan–Thien–Tanner (PTT) viscoelastic models, for axial and helical annular fully-developed flows under no slip and slip boundary conditions, the latter given by the linear and nonlinear Navier slip laws. The rheology of the three PTT model functions is discussed together with the influence of the slip velocity upon the flow velocity and stress fields. For the linear PTT model, full analytical solutions for the inverse problem (unknown velocity) are devised for the linear Navier slip law and two different slip exponents. For the linear PTT model with other values of the slip exponent and for the quadratic PTT model, the polynomial equation for the radial location (β) of the null shear stress must be solved numerically. For both models, the solution of the direct problem is given by an iterative procedure involving three nonlinear equations, one for β, other for the pressure gradient and another for the torque per unit length. For the exponential PTT model we devise a numerical procedure that can easily compute the numerical solution of the pure axial flow problem

Further results on the inverse along an element in semigroups and rings

In this paper, we introduce a new notion in a semigroup $S$ as an extension of Mary's inverse. Let $a,d\in S$. An element $a$ is called left (resp. right) invertible along $d$ if there exists $b\in S$ such that $bad=d$ (resp. $dab=b$) and $b\leq_\mathcal{L}d$ (resp. $b\leq_\mathcal{R}d$). An existence criterion of this type inverse is derived. Moreover, several characterizations of left (right) regularity, left (right) $\pi$-regularity and left (right) $*$-regularity are given in a semigroup. Further, another existence criterion of this type inverse is given by means of a left (right) invertibility of certain elements in a ring. Finally we study the (left, right) inverse along a product in a ring, and, as an application, Mary's inverse along a matrix is expressed.

Nickel(II) complexes of bidentate N-N′ ligands containing mixed pyrazole, pyrimidine and pyridine aromatic rings as catalysts for ethylene polymerisation

This work describes the synthesis and characterisation of Ni(II) complexes of the following neutral bidentate nitrogen ligands containing pyrazole (pz), pyrimidine (pm) and pyridine (py) aromatic rings: 2-pyrazol-1-yl-pyrimidine (pzpm), 2-(4-methyl-pyrazol-1-yl)-pyrimidine (4-Mepzpm), 2-(4-bromo-pyrazol-1-yl)-pyrimidine (4-Brpzpm), 2-(3,5-dimethyl-pyrazol-1-yl)-pyrimidine (pz*pm), 2-pyrazol-1-yl-pyridine (pzpy) and bis(3,5-dimethylpyrazol-1-yl)phenylmethane (bpz*mph). The complexes [NiBr2(pzpm)] (1), [NiBr2(4-Mepzpm)] (2), [NiBr2(4-Brpzpm)] (3), [NiBr2(pz*pm)] (4), [NiBr2(pzpy)] (5) and [NiBr2(bpz*mph)] (6) were tested as catalysts for ethylene polymerisation, in the presence of the cocatalysts methylaluminoxane (MAO) or diethylaluminium chloride (AlEt2Cl), the catalyst systems 1-3/MAO showing moderate to high activities up to the temperature of 20 °C only in the presence of MAO, whereas 4-6/MAO revealed to be inactive. Other related Pd(II) complexes, already reported in previous works, such as [PdClMe(pzpm)], [PdClMe(pz*pm)], [PdClMe(pzpy)] and [PdClMe(bpz*mph)], also showed to be inactive in the polymerisation of ethylene, when activated by MAO or AlEt2Cl. Selected samples of polyethylene products were characterised by GPC/SEC, 1H and 13C NMR and DSC, showing to be low molecular weight polymers with Mn values ranging from ca. 550 to 1500 g mol−1 and unusually low dispersities of 1.2–1.7, with total branching degrees generally varying between 2 and 12%, melting temperatures from 40 to 120 °C and crystallinities from 40 to 70%.

Encryption methods using formal power series rings

Recently there has been a great deal of work on noncommutative algebraic cryptography. This involves the use of noncommutative algebraic objects as the platforms for encryption systems. Most of this work, such as the Anshel-Anshel-Goldfeld scheme, the Ko-Lee scheme and the Baumslag-Fine-Xu Modular group scheme use nonabelian groups as the basic algebraic object. Some of these encryption methods have been successful and some have been broken. It has been suggested that at this point further pure group theoretic research, with an eye towards cryptographic applications, is necessary.In the present study we attempt to extend the class of noncommutative algebraic objects to be used in cryptography. In particular we explore several different methods to use a formal power series ring R && x1; :::; xn && in noncommuting variables x1; :::; xn as a base to develop cryptosystems. Although R can be any ring we have in mind formal power series rings over the rationals Q. We use in particular a result of Magnus that a finitely generated free group F has a faithful representation in a quotient of the formal power series ring in noncommuting variables.

Fixed rings and strictures in Eosinophilic Esophagitis develop due to continuing inflammation over time

Background and Aims: Two distinct e ndoscopic phenotypes of E osinophilic Esophagitis (EoE) h ave been identified: t he inflammatory (IP) a nd the stenosing (SP) p henotype. I t is not known whether these EoE-associated phenotypes are reflective of different phases during disease course. We aimed to assess the phenotype a t initial EoE p resentation and d iagnosis and to evaluate if SP increases over time. Methods: R etrospective a nalysis of t he Swiss EoE Database (SEED) extended b y a review of p atients charts, endoscopy and pathology records. Results: F orty-four E oE p atients were a nalyzed (33 males, mean age at index visit 41 ± 14 years, all Caucasians). Median follow-up t ime was 3.1 years (IQR 1-4, r ange 1 -18 years). Median diagnostic delay w as 5 y ears (IQR 2-16, range 0-34 years). A t first diagnosis, 3 2% ( 14/44) o f EoE patients h ad already presented w ith a stenosis. T he mean d iameter o f the stenoses w as 1 0 ± 2 mm, and the mean length was 2 .8 ± 2 .9 cm. Peak e osinophil count d id n ot c hange over t ime (48 ± 39 eos/HPF at index visit vs. 59 ± 41 eos/HPF at end of follow-up, n=44). The risk of the presence of a stenosis at index visit was 0% f or a d isease duration of 0 -4 y ears, 37% f or a d isease duration between 5-10 years and 67% f or a d isease duration >10 years (p = 0.0035, trend test). Conclusions: T he frequency of e sophageal stenoses i s proportional to the disease duration, whereas the inflammatory activity does n ot s ignificantly c hange over t ime. O ur f indings underscore the necessity to reduce diagnostic delay in EoE and to control the underlying inflammatory processes to prevent esophageal remodeling.