Existence of weak solutions for the generalized Navier-Stokes equations with damping

In this work we consider the generalized Navier-Stokes equations with the presence of a damping term in the momentum equation. The problem studied here derives from the set of equations which govern isothermal flows of incompressible and homogeneous non-Newtonian fluids. For the generalized Navier-Stokes problem with damping, we prove the existence of weak solutions by using regularization techniques, the theory of monotone operators and compactness arguments together with the local decomposition of the pressure and the Lipschitz-truncation method. The existence result proved here holds for any and any sigma > 1, where q is the exponent of the diffusion term and sigma is the exponent which characterizes the damping term.MCTES, Portugal [SFRH/BSAB/1058/2010]; FCT, Portugal [PTDC/MAT/110613/2010]info:eu-repo/semantics/publishedVersio

Rheology of vitreous humour and pharmacological substitutes used in the treatment of vitreoretinal pathologies

Vitreoretinal pathologies are the second leading cause of blindness worldwide. They can be caused by age-related changes in vitreous humour (VH) or as a consequence of some diseases that lead to rheological, biochemical and structural rearrangements. So far, the most effective treatment for these diseases is the injection of a VH substitute in the vitreous cavity. These substances can be used intra- operatively to push a detached retina into its normal position, to restore the volume of the vitreous cavity, and to help surgeons in membrane dissection. The major vitreous substitutes commercially available are silicone oils and perfluorocarbon liquids, but currently there is little information about the rheological properties of these fluids, that are intimately linked to their functionality. The aim of this work is to compare the rheological properties of the VH and five commercial vitreous substitutes currently used in vitreoretinal surgeries. Six fluids were analysed: VH extracted from New Zealand white rabbit specimen, three silicone oils (RS-Oil1000 and RS-Oil5000, Alchimia and Siluron 2000, Fluoron), two perfluorocarbon liquids (HPF8 and HPF10, Alchimia) and a mixture of silicone oil with perfluorocarbon (Densiron68, Fluoron). Extensional measurements were performed with a capillary break-up extensional rheometer (Haake CaBER1, ThermoElectron) and an in-house extensional rheometer. The steady shear and small amplitude oscillatory shear measurements (SAOS) were performed with a hybrid rheometer (DHR-2, TA Instruments). Our results show that VH substitutes used for same purpose exhibit significantly different rheological properties between them and when compared with the VH. Vitreous humour shows viscoelastic behaviour and all the pharmacological fluids tested display a Newtonian-like behaviour in steady shear flow with viscosities varying from 0.49 mPa s to 4.57 Pa s, at 37°C

Stopping a Viscous Fluid by a Feedback Dissipative Field: Thermal Effects without Phase Changing

We show how the action on two simultaneous effects (a suitable coupling about velocity and temperature and a low range of temperature but upper that the phase changing one) may be responsible of stopping a viscous fluid without any changing phase. Our model involves a system, on an unbounded pipe, given by the planar stationary Navier-Stokes equation perturbed with a sublinear term f(x, θ, u) coupled with a stationary (and possibly nonlinear) advection diffusion equation for the temperature θ.After proving some results on the existence and uniqueness of weak solutions we apply an energy method to show that the velocity u vanishes for x large enough

Which mechanism underlies the water-like anomalies in core-softened potentials?

Using molecular dynamics simulations we investigate the thermodynamic of particles interacting with a continuous and a discrete versions of a core-softened (CS) intermolecular potential composed by a repulsive shoulder. Dynamic and structural properties are also analyzed by the simulations. We show that in the continuous version of the CS potential the density at constant pressure has a maximum for a certain temperature. Similarly the diffusion constant, $D$, at a constant temperature has a maximum at a density $\rho_{\mathrm{max}}$ and a minimum at a density $\rho_{\mathrm{min}}<\rho_{\mathrm{max}}$, and structural properties are also anomalous. For the discrete CS potential none of these anomalies are observed. The absence of anomalies in the discrete case and its presence in the continuous CS potential are discussed in the framework of the excess entropy.Comment: 8 page

Frequency of occurrence of numbers in the World Wide Web

The distribution of numbers in human documents is determined by a variety of diverse natural and human factors, whose relative significance can be evaluated by studying the numbers' frequency of occurrence. Although it has been studied since the 1880's, this subject remains poorly understood. Here, we obtain the detailed statistics of numbers in the World Wide Web, finding that their distribution is a heavy-tailed dependence which splits in a set of power-law ones. In particular, we find that the frequency of numbers associated to western calendar years shows an uneven behavior: 2004 represents a `singular critical' point, appearing with a strikingly high frequency; as we move away from it, the decreasing frequency allows us to compare the amounts of existing information on the past and on the future. Moreover, while powers of ten occur extremely often, allowing us to obtain statistics up to the huge 10^127, `non-round' numbers occur in a much more limited range, the variations of their frequencies being dramatically different from standard statistical fluctuations. These findings provide a view of the array of numbers used by humans as a highly non-equilibrium and inhomogeneous system, and shed a new light on an issue that, once fully investigated, could lead to a better understanding of many sociological and psychological phenomena.Comment: 5 pages, 4 figure

Mean-field analysis of the q-voter model on networks

We present a detailed investigation of the behavior of the nonlinear q-voter model for opinion dynamics. At the mean-field level we derive analytically, for any value of the number q of agents involved in the elementary update, the phase diagram, the exit probability and the consensus time at the transition point. The mean-field formalism is extended to the case that the interaction pattern is given by generic heterogeneous networks. We finally discuss the case of random regular networks and compare analytical results with simulations.Comment: 20 pages, 10 figure

Towards the characterization of individual users through Web analytics

We perform an analysis of the way individual users navigate in the Web. We focus primarily in the temporal patterns of they return to a given page. The return probability as a function of time as well as the distribution of time intervals between consecutive visits are measured and found to be independent of the level of activity of single users. The results indicate a rich variety of individual behaviors and seem to preclude the possibility of defining a characteristic frequency for each user in his/her visits to a single site.Comment: 8 pages, 4 figures. To appear in Proceeding of Complex'0

A viscoelastic two-phase solver using a phase-field approach

In this work we discuss the implementation and the performance of an in-house viscoelastic two-phase solver, based on a diffuse interface approach. The Phase-Field method is considered and the Cahn-Hilliard equation is employed for describing the transport of a binary fluid system. The interface between the two fluids utilises a continuum approach, which is responsible for smoothing the inherent discontinuities of sharp interface models, facilitating studies that are related to morphological changes of the interface, such as droplet breakup and coalescence. The two-phase solver manages to predict the expected dynamics for all the cases investigated, and exhibits an overall good performance. The numerical implementation is able to predict the expected physical response of the oscillating drop case, while the performance is also validated by examining the droplet deformation case. The corresponding history of the deformation is predicted for several systems considering Newtonian fluids, viscoelastic fluids and combinations of both. Finally, we demonstrate the ability of the solver to capture the complex interfacial patterns of the Rayleigh-Taylor instability for different Atwood numbers when Newtonian fluids are considered. In the two regimes identified, the system is modified to consider viscoelastic fluids and the influence of elasticity is investigated