Statistical mechanics of two-dimensional Euler flows and minimum enstrophy states

A simplified thermodynamic approach of the incompressible 2D Euler equation is considered based on the conservation of energy, circulation and microscopic enstrophy. Statistical equilibrium states are obtained by maximizing the Miller-Robert-Sommeria (MRS) entropy under these sole constraints. The vorticity fluctuations are Gaussian while the mean flow is characterized by a linear $\bar{\omega}-\psi$ relationship. Furthermore, the maximization of entropy at fixed energy, circulation and microscopic enstrophy is equivalent to the minimization of macroscopic enstrophy at fixed energy and circulation. This provides a justification of the minimum enstrophy principle from statistical mechanics when only the microscopic enstrophy is conserved among the infinite class of Casimir constraints. A new class of relaxation equations towards the statistical equilibrium state is derived. These equations can provide an effective description of the dynamics towards equilibrium or serve as numerical algorithms to determine maximum entropy or minimum enstrophy states. We use these relaxation equations to study geometry induced phase transitions in rectangular domains. In particular, we illustrate with the relaxation equations the transition between monopoles and dipoles predicted by Chavanis and Sommeria [J. Fluid. Mech. 314, 267 (1996)]. We take into account stable as well as metastable states and show that metastable states are robust and have negative specific heats. This is the first evidence of negative specific heats in that context. We also argue that saddle points of entropy can be long-lived and play a role in the dynamics because the system may not spontaneously generate the perturbations that destabilize them.Comment: 26 pages, 10 figure

Statistical mechanics of Beltrami flows in axisymmetric geometry: Equilibria and bifurcations

We characterize the thermodynamical equilibrium states of axisymmetric Euler-Beltrami flows. They have the form of coherent structures presenting one or several cells. We find the relevant control parameters and derive the corresponding equations of state. We prove the coexistence of several equilibrium states for a given value of the control parameter like in 2D turbulence [Chavanis and Sommeria, J. Fluid Mech. 314, 267 (1996)]. We explore the stability of these equilibrium states and show that all states are saddle points of entropy and can, in principle, be destabilized by a perturbation with a larger wavenumber, resulting in a structure at the smallest available scale. This mechanism is therefore reminiscent of the 3D Richardson energy cascade towards smaller and smaller scales. Therefore, our system is truly intermediate between 2D turbulence (coherent structures) and 3D turbulence (energy cascade). We further explore numerically the robustness of the equilibrium states with respect to random perturbations using a relaxation algorithm in both canonical and microcanonical ensembles. We show that saddle points of entropy can be very robust and therefore play a role in the dynamics. We evidence differences in the robustness of the solutions in the canonical and microcanonical ensembles. A scenario of bifurcation between two different equilibria (with one or two cells) is proposed and discussed in connection with a recent observation of a turbulent bifurcation in a von Karman experiment [Ravelet et al., Phys. Rev. Lett. 93, 164501 (2004)].Comment: 25 pages; 16 figure

Assessment of Natural Resources Use for Sustainable Development - DPSIR Framework for Case Studies in Portsmouth and Thames Gateway, U.K.

This chapter reports on the uses of the DPSIR framework to assess the sustainability of the intertidal environments within the two UK case study areas, Portsmouth and Thames Gateway. It focuses on statutory conservation areas dominated by intertidal habitats. Two are located in Portsmouth (Portsmouth and Langstone Harbours) and four in the Thames Gateway (Benfleet Marshes, South Thames Estuary, Medway Estuary and the Swale in the Thames Gateway). Based on the reduction of a number of pressures and impacts observed in recent decades and the improvement of overall environmental quality, all six SSSIs are considered to be sustainable in the short and medium term. In the future, it is possible that the impacts of climate change, especially sea-level rise, might result in further reduction in the area and/or quality of intertidal habitats. Further integration between conservation and planning objectives (both for urban development and management of flood risk) at local level is needed to support the long-term sustainability of intertidal habitats

Simultaneous 3D measurement of the translation and rotation of finite size particles and the flow field in a fully developed turbulent water flow

We report a novel experimental technique that measures simultaneously in three dimensions the trajectories, the translation, and the rotation of finite size inertial particles together with the turbulent flow. The flow field is analyzed by tracking the temporal evolution of small fluorescent tracer particles. The inertial particles consist of a super-absorbent polymer that renders them index and density matched with water and thus invisible. The particles are marked by inserting at various locations tracer particles into the polymer. Translation and rotation, as well as the flow field around the particle are recovered dynamically from the analysis of the marker and tracer particle trajectories. We apply this technique to study the dynamics of inertial particles much larger in size (Rp/{\eta} \approx 100) than the Kolmogorov length scale {\eta} in a von K\'arm\'an swirling water flow (R{\lambda} \approx 400). We show, using the mixed (particle/fluid) Eulerian second order velocity structure function, that the interaction zone between the particle and the flow develops in a spherical shell of width 2Rp around the particle of radius Rp. This we interpret as an indication of a wake induced by the particle. This measurement technique has many additional advantages that will make it useful to address other problems such as particle collisions, dynamics of non-spherical solid objects, or even of wet granular matter.Comment: 18 pages, 7 figures, submitted to "Measurement Science and Technology" special issue on "Advances in 3D velocimetry

Statistical mechanics of Fofonoff flows in an oceanic basin

We study the minimization of potential enstrophy at fixed circulation and energy in an oceanic basin with arbitrary topography. For illustration, we consider a rectangular basin and a linear topography h=by which represents either a real bottom topography or the beta-effect appropriate to oceanic situations. Our minimum enstrophy principle is motivated by different arguments of statistical mechanics reviewed in the article. It leads to steady states of the quasigeostrophic (QG) equations characterized by a linear relationship between potential vorticity q and stream function psi. For low values of the energy, we recover Fofonoff flows [J. Mar. Res. 13, 254 (1954)] that display a strong westward jet. For large values of the energy, we obtain geometry induced phase transitions between monopoles and dipoles similar to those found by Chavanis and Sommeria [J. Fluid Mech. 314, 267 (1996)] in the absence of topography. In the presence of topography, we recover and confirm the results obtained by Venaille and Bouchet [Phys. Rev. Lett. 102, 104501 (2009)] using a different formalism. In addition, we introduce relaxation equations towards minimum potential enstrophy states and perform numerical simulations to illustrate the phase transitions in a rectangular oceanic basin with linear topography (or beta-effect).Comment: 26 pages, 28 figure

Polychlorinated biphenyls and organochlorine pesticides in seafood from the Gulf of Naples (Italy).

Seven target polychlorinated biphenyls (PCBs; IUPAC nos. 28, 52, 101, 118, 138, 153, and 180) and the organochlorine pesticides (OCPs) hexachlorobenzene (HCB) and dichlorodiphenyltrichloroethane (DDT) and its related metabolites (p,p'-DDT, p,p'-DDE, and p,p'-DDD) were quantified in edible tissues from seven marine species (European hake, red mullet, blue whiting, Atlantic mackerel, blue and red shrimp, European flying squid, and Mediterranean mussel) from the Gulf of Naples in the southern Tyrrhenian Sea (Italy). PCBs 118, 138, and 153 were the dominant congeners in all the species examined. The concentrations of all PCBs (from not detectable to 15,427 ng g(-1) fat weight) exceeded those of all the DDTs (from not detectable to 1,769 ng g(-1) fat weight) and HCB (not detectable to 150.60 ng g(-1) fat weight) in the samples analyzed. The OCP concentrations were below the maximum residue limits established for fish and aquatic products by the Decreto Ministerale 13 May 2005 in all the samples analyzed; therefore the OCPs in the southern Tyrrhenian Sea species are unlikely to be a significant health hazard. Conversely, the mean concentrations of PCBs exceeded (greatly in some cases) the current limits (200 ng(-1) fat weight) set by the European Union for terrestrial foods. Although the manufacture and use of PCBs are banned or highly restricted, these compounds still are important persistent chemical contaminants in the Gulf of Naples

Design of polymer-based antimicrobial hydrogels through physico-chemical transition

The antimicrobial activity represents a cornerstone in the development of biomaterials: it is a leading request in many areas, including biology, medicine, environment and industry. Over the years, different polymeric scaffolds are proposed as solutions, based on the encapsulation of metal ions/particles, antibacterial agents or antibiotics. However, the compliance with the biocompatibility criteria and the concentration of the active principles to avoid under- and over-dosing are being debated. In this work, we propose the synthesis of a versatile hydrogel using branched polyacrylic acid (carbomer 974P) and aliphatic polyetherdiamine (elastamine\uae) through physico-chemical transition, able to show its ability to counteract the bacterial growth and infections thanks to the polymers used, that are not subjected to further chemical modifications. In particular, the antimicrobial activity is clearly demonstrated against Staphyloccoccus aureus and Candida albicans, two well-known opportunistic pathogens. Moreover, we discuss the hydrogel use as drug carrier to design a unique device able to combine the antibacterial/antimicrobial properties to the controlled drug delivery, as a promising tool for a wide range of biomedical applications

Effectiveness of rice germ supplementation on body composition, metabolic parameters, satiating capacity, and amino acid profiles in obese postmenopausal women: A randomized, controlled clinical pilot trial

Rice germ (RG) may be a safe and effective dietary supplement for obesity in menopause, considering its high protein content and considerable amounts of essential amino acids, good fatty acids, and fiber. This pilot randomized, blinded, parallel-group, placebo-controlled pilot trial investigated the effectiveness of 4-weeks RG supplementation (25 g twice a day) on body composition, as primary outcome, measured by Dual Energy X-Ray Absorptiometry (DXA), and metabolic parameters, as secondary outcomes, like amino acid profiles and satiating capacity, in obese postmenopausal women following a tailored hypocaloric diet (25–30% less than daily energy requirements). Twenty-seven women were randomly assigned to the supplemented group (14) or placebo group (13). There was a significant interaction between time and group for body mass index (BMI) (p < 0.0001), waist (p = 0.002) and hip circumferences (p = 0.01), total protein (0.008), albumin (0.005), Homeostasis Model Assessment index score (p = 0.04), glycine (p = 0.002), glutamine (p = 0.004), and histidine (p = 0.007). Haber’s means over time showed a clearly greater feeling of satiety for the supplemented compared to the placebo group. These findings indicate that RG supplementation in addition to a tailored diet counterbalanced the metabolic changes typical of menopause, with improvements in BMI, body composition, insulin resistance, amino acid profiles, and satiety