On some categorical-algebraic conditions in S-protomodular categories

In the context of protomodular categories, several additional conditions have been considered in order to obtain a closer group-like behavior. Among them are locally algebraic cartesian closedness and algebraic coherence. The recent notion of S-protomodular category, whose main examples are the category of monoids and, more generally, categories of monoids with operations and Jo\'{o}nsson-Tarski varieties, raises a similar question: how to get a description of S-protomodular categories with a strong monoid-like behavior. In this paper we consider relative versions of the conditions mentioned above, in order to exhibit the parallelism with the "absolute" protomodular context and to obtain a hierarchy among S-protomodular categories

Point-source scalar turbulence

The statistics of a passive scalar randomly emitted from a point source is investigated analytically. Our attention has been focused on the two-point equal-time scalar correlation function. The latter is indeed easily related to the spectrum, a statistical indicator widely used both in experiments and in numerical simulations. The only source of inhomogeneity/anisotropy is in the injection mechanism, the advecting velocity here being statistically homogeneous and isotropic. Our main results can be summarized as follows. 1) For a very large velocity integral scale, a pure scaling behaviour in the distance between the two points emerges only if their separation is much smaller than their distance from the point source. 2) The value we have found for the scaling exponent suggests the existence of a direct cascade, in spite of the fact that here the forcing integral scale is formally set to zero. 3) The combined effect of a finite inertial-range extension and of inhomogeneities causes the emergence of subleading anisotropic corrections to the leading isotropic term, that we have quantified and discussed.Comment: 10 pages, 1 figure, submitted to Journal of Fluid Mechanic

Renormalized transport of inertial particles in surface flows

Surface transport of inertial particles is investigated by means of the perturbative approach, introduced by Maxey (J. Fluid Mech. 174, 441 (1987)), which is valid in the case the deflections induced on the particle trajectories by the fluid flow can be considered small. We consider a class of compressible random velocity fields, in which the effect of recirculations is modelled by an oscillatory component in the Eulerian time correlation profile. The main issue we address here is whether fluid velocity fluctuations, in particular the effect of recirculation, may produce nontrivial corrections to the streaming particle velocity. Our result is that a small (large) degree of recirculation is associated with a decrease (increase) of streaming with respect to a quiescent fluid. The presence of this effect is confirmed numerically, away from the perturbative limit. Our approach also allows us to calculate the explicit expression for the eddy diffusivity, and to compare the efficiency of diffusive and ballistic transport.Comment: 18 pages, 13 figures, submitted to JF

Does multifractal theory of turbulence have logarithms in the scaling relations?

The multifractal theory of turbulence uses a saddle-point evaluation in determining the power-law behaviour of structure functions. Without suitable precautions, this could lead to the presence of logarithmic corrections, thereby violating known exact relations such as the four-fifths law. Using the theory of large deviations applied to the random multiplicative model of turbulence and calculating subdominant terms, we explain here why such corrections cannot be present.Comment: 7 pages, 1 figur

Stokes drift for inertial particles transported by water waves

We study the effect of surface gravity waves on the motion of inertial particles in an incompressible fluid. Using the multiple-scale technique, we perform an analytical calculation which allows us to predict the dynamics of such particles; results are shown for both the infinite- and finite-depth regimes. Numerical simulations based on the velocity field resulting from the second-order Stokes theory for the surface elevation have been performed, and an excellent agreement with the analytical predictions is observed. Such an agreement seems to hold even beyond the formal applicability of the theory. We find that the presence of inertia leads to a non-negligible correction to the well-known horizontal Stokes drift; moreover, we find that the vertical velocity is also affected by a drift. The latter result may have some relevant consequences on the rate of sedimentation of particles of finite size. We underline that such a drift would also be observed in the (hypothetical) absence of the gravitational force.Comment: 9 pages, 4 figure

Point-source inertial particle dispersion

The dispersion of inertial particles continuously emitted from a point source is analytically investigated in the limit of small inertia. Our focus is on the evolution equation of the particle joint probability density function p(x,v,t), x and v being the particle position and velocity, respectively. For finite inertia, position and velocity variables are coupled, with the result that p(x,v,t) can be determined by solving a partial differential equation in a 2d-dimensional space, d being the physical-space dimensionality. For small inertia, (x,v)-variables decouple and the determination of p(x,v,t) is reduced to solve a system of two standard forced advection-diffusion equations in the space variable x. The latter equations are derived here from first principles, i.e. from the well-known Lagrangian evolution equations for position and particle velocity.Comment: 10 pages, submitted to JF

Relação jurídica entre agências de turismo e turistas-consumidores. Problemas e conflitos em Porto Alegre, Rio Grande do Sul

Este estudo exploratório-descritivo destaca os problemas e conflitos oriundos da Relação Jurídica entre Agências de Turismo (prestador de serviços turísticos) e Turistas- Consumidores (consumidor) em Porto Alegre (RS). Nos fundamentos teóricos, aborda inicialmente aspectos marcantes da legislação turística brasileira ao longo dos tempos, mais precisamente àquelas que dispõem sobre agências de turismo. Em seguida, aborda a Relação Jurídica e Turismo, referindo-se às partes envolvidas, à caracterização e às conseqüências dessa relação. Desenvolve-se a pesquisa de campo, cujos dados foram levantados junto aos cartórios das varas cíveis e juizados especiais cíveis do Fórum Central de Porto Alegre. Os resultados obtidos são descritos e analisados a partir da caracterização geral dos processos bem como das ações judiciais em andamento entre agências de turismo e turistas-consumidores. Por meio deste estudo foi possível analizar os problemas e conflitos existentes nesta relação e propor medidas para a minimização desses conflitos.This study concerns problems and conflicts in the juridical relations between travel agencies (provider of tourism services) and tourists (consumer) in Porto Alegre/RS, Brazil. This study begins with an evolutionary synthesis of tourism-related laws, specifically to those regarding travel agencies. Next, it examines the Juridical Relations and Tourism referring to the parties involved in this relation, that is, the travel agency and the tourist and the juridical relation between travel agencies and tourists, its characteristics and consequences. After this theoretical study, afield research was conducted in the Central Civil Court of Porto Alegre. This research allowed a general description of lawsuits including travel agencies as one of the parties, to then establish which disputes include travel agencies and tourists-consumers. With this study it was possible to analyze the existing problems in this relation and also to develop measures to minimize these conflicts.Fil: Silva, Andrea Monlleo Martins da. Universidade de São Paulo; Brasil.Fil: Rejowski, Mirian. Universidade de São Paulo; Brasil

Eddy diffusivities of inertial particles under gravity

The large-scale/long-time transport of inertial particles of arbitrary mass density under gravity is investigated by means of a formal multiple-scale perturbative expansion in the scale-separation parametre between the carrier flow and the particle concentration field. The resulting large-scale equation for the particle concentration is determined, and is found to be diffusive with a positive-definite eddy diffusivity. The calculation of the latter tensor is reduced to the resolution of an auxiliary differential problem, consisting of a coupled set of two differential equations in a (6+1)-dimensional coordinate system (3 space coordinates plus 3 velocity coordinates plus time). Although expensive, numerical methods can be exploited to obtain the eddy diffusivity, for any desirable non-perturbative limit (e.g. arbitrary Stokes and Froude numbers). The aforementioned large-scale equation is then specialized to deal with two different relevant perturbative limits: i) vanishing of both Stokes time and sedimenting particle velocity; ii) vanishing Stokes time and finite sedimenting particle velocity. Both asymptotics lead to a greatly simplified auxiliary differential problem, now involving only space coordinates and thus easy to be tackled by standard numerical techniques. Explicit, exact expressions for the eddy diffusivities have been calculated, for both asymptotics, for the class of parallel flows, both static and time-dependent. This allows us to investigate analytically the role of gravity and inertia on the diffusion process by varying relevant features of the carrier flow, as e.g. the form of its temporal correlation function. Our results exclude a universal role played by gravity and inertia on the diffusive behaviour: regimes of both enhanced and reduced diffusion may exist, depending on the detailed structure of the carrier flow.Comment: 8 figures (12 plots), submitted to JF