Abstract:
A doen a celíaca caracteriza-se pela intolerancia alimentar aos produtos que contêm glúten, o que leva a uma resposta imunológica com consequente atrofi a das vilosidades intestinais e prejuízo na absor o dos nutrientes. A baixa oferta de alimentos isentos de glúten no mercado brasileiro implica na necessidade do preparo caseiro desses alimentos com farinhas n o utilizadas usualmente. Desse modo, este trabalho teve como objetivo elaborar minipizzas isentas de glúten a partir de farinha de trigo sarraceno e em associa o às farinhas de soja e de arroz como alternativa para a n o priva o de certos tipos de alimentos à base de trigo. As minipizzas foram elaboradas seguindo a metodologia descrita em literatura específi ca e sendo avaliados os atributos aparência, sabor, odor e textura. Os atributos odor da minipizza trigo sarraceno + arroz e a textura da minipizza trigo sarraceno + soja foram considerados similares à amostra padr o. Constatou-se que existe a viabilidade da elabora o de minipizzas através da combina o entre diferentes tipos de farinhas sem glúten utilizadas neste estudo para pacientes celíacos.

Abstract:
We study the time scale T to equipartition in a 1D lattice of N masses coupled by quartic nonlinear (hard) springs (the Fermi-Pasta-Ulam beta model). We take the initial energy to be either in a single mode gamma or in a package of low frequency modes centered at gamma and of width delta-gamma, with both gamma and delta-gamma proportional to N. These initial conditions both give, for finite energy densities E/N, a scaling in the thermodynamic limit (large N), of a finite time to equipartition which is inversely proportional to the central mode frequency times a power of the energy density E/N. A theory of the scaling with E/N is presented and compared to the numerical results in the range 0.03 <= E/N <= 0.8.

Abstract:
We introduce a model of uncoupled pendula, which mimics the dynamical behavior of the Hamiltonian Mean Field (HMF) model. This model has become a paradigm for long-range interactions, like Coulomb or dipolar forces. As in the HMF model, this simplified integrable model is found to obey the Vlasov equation and to exhibit Quasi Stationary States (QSS), which arise after a "collisionless" relaxation process. Both the magnetization and the single particle distribution function in these QSS can be predicted using Lynden-Bell's theory. The existence of an extra conserved quantity for this model, the energy distribution function, allows us to understand the origin of some discrepancies of the theory with numerical experiments. It also suggests us an improvement of Lynden-Bell's theory, which we fully implement for the zero field case.

Abstract:
Long-lived quasistationary states, associated with stationary stable solutions of the Vlasov equation, are found in systems with long-range interactions. Studies of the relaxation time in a model of $N$ globally coupled particles moving on a ring, the Hamiltonian Mean Field model (HMF), have shown that it diverges as $N^\gamma$ for large $N$, with $\gamma \simeq 1.7$ for some initial conditions with homogeneously distributed particles. We propose a method for identifying exact inhomogeneous steady states in the thermodynamic limit, based on analysing models of uncoupled particles moving in an external field. For the HMF model, we show numerically that the relaxation time of these states diverges with $N$ with the exponent $\gamma \simeq 1$. The method, applicable to other models with globally coupled particles, also allows an exact evaluation of the stability limit of homogeneous steady states. In some cases it provides a good approximation for the correspondence between the initial condition and the final steady state.

Abstract:
The out-of-equilibrium dynamics of the Hamiltonian Mean Field (HMF) model is studied in presence of an externally imposed magnetic field h. Lynden-Bell's theory of violent relaxation is revisited and shown to adequately capture the system dynamics, as revealed by direct Vlasov based numerical simulations in the limit of vanishing field. This includes the existence of an out-of-equilibrium phase transition separating magnetized and non magnetized phases. We also monitor the fluctuations in time of the magnetization, which allows us to elaborate on the choice of the correct order parameter when challenging the performance of Lynden-Bell's theory. The presence of the field h removes the phase transition, as it happens at equilibrium. Moreover, regions with negative susceptibility are numerically found to occur, in agreement with the predictions of the theory.

Abstract:
objective this study assessed the concentration of potassium in raw and macerated raw vegetables and vegetables cooked by different methods - boiling, microwave and pressure-cooking - to verify if maceration and different cooking methods can effectively reduce the concentration of this mineral. methods this experiment had a random 3x5 factorial design (3 vegetables x 5 procedures) and the analyses were repeated 3 times. flame photometry was used to determine potassium concentration in raw, soaked, boiled, microwaved and pressure-cooked potatoes, carrots and broccoli. results potassium concentration in soaked (232.2mg/g), boiled (197.3mg/g), microwaved (170mg/g) and pressure-cooked (187.2mg/g) potatoes and soaked (315.0mg/g), boiled (309.9mg/g), microwaved (243.3mg/g) and pressure-cooked (210.6mg/g) carrots did not differ significantly. on the other hand, potassium concentration in microwaved (280.1mg/g) and pressure-cooked (167.3mg/g) broccoli was significantly different from that found in soaked and boiled broccoli. therefore, microwaving and pressure-cooking reduce the potassium concentration in broccoli more effectively. conclusion maceration and the different cooking methods were effective in reducing the concentration of potassium in the studied vegetables. however, other factors such as cooking length, temperature, type of container and microwave frequency and power level may also affect potassium concentration.

Abstract:
We study the phase diagram of two different Hamiltonians with competiting local, nearest-neighbour, and mean-field couplings. The first example corresponds to the HMF Hamiltonian with an additional short-range interaction. The second example is a reduced Hamiltonian for dipolar layered spin structures, with a new feature with respect to the first example, the presence of anisotropies. The two examples are solved in both the canonical and the microcanonical ensemble using a combination of the min-max method with the transfer operator method. The phase diagrams present typical features of systems with long-range interactions: ensemble inequivalence, negative specific heat and temperature jumps. Moreover, in a given range of parameters, we report the signature of phase reentrance. This can also be interpreted as the presence of azeotropy with the creation of two first order phase transitions with ensemble inequivalence, as one parameter is varied continuously.

Abstract:
We briefly review some equilibrium and nonequilibrium properties of systems with long-range interactions. Such systems, which are characterized by a potential that weakly decays at large distances, have striking properties at equilibrium, like negative specific heat in the microcanonical ensemble, temperature jumps at first order phase transitions, broken ergodicity. Here, we mainly restrict our analysis to mean-field models, where particles globally interact with the same strength. We show that relaxation to equilibrium proceeds through quasi-stationary states whose duration increases with system size. We propose a theoretical explanation, based on Lynden-Bell's entropy, of this intriguing relaxation process. This allows to address problems related to nonequilibrium using an extension of standard equilibrium statistical mechanics. We discuss in some detail the example of the dynamics of the free electron laser, where the existence and features of quasi-stationary states is likely to be tested experimentally in the future. We conclude with some perspectives to study open problems and to find applications of these ideas to dipolar media.

Abstract:
The Drinfel'd Lagrangian Grassmannian compactifies the space of algebraic maps of fixed degree from the projective line into the Lagrangian Grassmannian. It has a natural projective embedding arising from the canonical embedding of the Lagrangian Grassmannian. We show that the defining ideal of any Schubert subvariety of the Drinfel'd Lagrangian Grassmannian is generated by polynomials which give a straightening law on an ordered set. Consequentially, any such subvariety is Cohen-Macaulay and Koszul. The Hilbert function is computed from the straightening law, leading to a new derivation of certain intersection numbers in the quantum cohomology ring of the Lagrangian Grassmannian.