An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay

An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function V to be positive in some bounded sets of the state space while the classical invariance principle assumes that. V <= 0. As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets.

Possible states in the flow around two circular cylinders in tandem with separations in the vicinity of the drag inversion spacing

The possible states in the flow around two identical circular cylinders in tandem arrangements are investigated for configurations in the vicinity of the drag inversion separation. By means of numerical simulations, the hysteresis in the transition between the shedding regimes is studied and the relationship between (three-dimensional) secondary instabilities and shedding regime determination is addressed. The differences observed in the behavior of two- and three-dimensional flows are analyzed, and the regions of bistable flow are delimited. Very good agreement is found between the proposed scenario and results available in the literature. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3420111]

The viscosity parameter's dependence on the profile of the disk scale height

It is shown that, for accretion disks, the height scale is a constant whenever hydrostatic equilibrium and the subsonic turbulence regime hold in the disk. In order to have a variable height scale, processes are needed that contribute an extra term to the continuity equation. This contribution makes the viscosity parameter much greater in the outer region and much smaller in the inner region. Under these circumstances, turbulence is the presumable source of viscosity in the disk.

TURBULENCE AND THE FORMATION OF FILAMENTS, LOOPS, AND SHOCK FRONTS IN NGC 1275

NGC 1275, the central galaxy in the Perseus cluster, is the host of gigantic hot bipolar bubbles inflated by active galactic nucleus (AGN) jets observed in the radio as Perseus A. It presents a spectacular H alpha-emitting nebulosity surrounding NGC 1275, with loops and filaments of gas extending to over 50 kpc. The origin of the filaments is still unknown, but probably correlates with the mechanism responsible for the giant buoyant bubbles. We present 2.5 and three-dimensional magnetohydrodynamical (MHD) simulations of the central region of the cluster in which turbulent energy, possibly triggered by star formation and supernovae (SNe) explosions, is introduced. The simulations reveal that the turbulence injected by massive stars could be responsible for the nearly isotropic distribution of filaments and loops that drag magnetic fields upward as indicated by recent observations. Weak shell-like shock fronts propagating into the intracluster medium (ICM) with velocities of 100-500 km s(-1) are found, also resembling the observations. The isotropic outflow momentum of the turbulence slows the infall of the ICM, thus limiting further starburst activity in NGC 1275. As the turbulence is subsonic over most of the simulated volume, the turbulent kinetic energy is not efficiently converted into heat and additional heating is required to suppress the cooling flow at the core of the cluster. Simulations combining the MHD turbulence with the AGN outflow can reproduce the temperature radial profile observed around NGC 1275. While the AGN mechanism is the main heating source, the SNe are crucial to isotropize the energy distribution.

PARTITIONED ANALYSIS FOR DIMENSIONALLY-HETEROGENEOUS HYDRAULIC NETWORKS

In this work an iterative strategy is developed to tackle the problem of coupling dimensionally-heterogeneous models in the context of fluid mechanics. The procedure proposed here makes use of a reinterpretation of the original problem as a nonlinear interface problem for which classical nonlinear solvers can be applied. Strong coupling of the partitions is achieved while dealing with different codes for each partition, each code in black-box mode. The main application for which this procedure is envisaged arises when modeling hydraulic networks in which complex and simple subsystems are treated using detailed and simplified models, correspondingly. The potentialities and the performance of the strategy are assessed through several examples involving transient flows and complex network configurations.

Finite-size particles, advection, and chaos: A collective phenomenon of intermittent bursting

We consider finite-size particles colliding elastically, advected by a chaotic flow. The collisionless dynamics has a quasiperiodic attractor and particles are advected towards this attractor. We show in this work that the collisions have dramatic effects in the system's dynamics, giving rise to collective phenomena not found in the one-particle dynamics. In particular, the collisions induce a kind of instability, in which particles abruptly spread out from the vicinity of the attractor, reaching the neighborhood of a coexisting chaotic saddle, in an autoexcitable regime. This saddle, not present in the dynamics of a single particle, emerges due to the collective particle interaction. We argue that this phenomenon is general for advected, interacting particles in chaotic flows.

Nonaxisymmetric magnetorotational instability in ideal and viscous plasmas

The excitation of magnetorotational instability (MRI) in rotating laboratory plasmas is investigated. In contrast to astrophysical plasmas, in which gravitation plays an important role, in laboratory plasmas it can be neglected and the plasma rotation is equilibrated by the pressure gradient. The analysis is restricted to the simple model of a magnetic confinement configuration with cylindrical symmetry, in which nonaxisymmetric perturbations are investigated using the local approximation. Starting from the simplest case of an ideal plasma, the corresponding dispersion relations are derived for more complicated models including the physical effects of parallel and perpendicular viscosities. The Friemann-Rotenberg approach used for ideal plasmas is generalized for the viscous model and an analytical expression for the instability boundary is obtained. It is shown that, in addition to the standard effect of radial derivative of the rotation frequency (the Velikhov effect), which can be destabilizing or stabilizing depending on the sign of this derivative in the ideal plasma, there is a destabilizing effect proportional to the fourth power of the rotation frequency, or, what is the same, to the square of the plasma pressure gradient, and to the square of the azimuthal mode number of the perturbations. It is shown that the instability boundary also depends on the product of the plasma pressure and density gradients, which has a destabilizing effect when it is negative. In the case of parallel viscosity, the MRI looks like an ideal instability independent of viscosity, while, in the case of strong perpendicular viscosity, it is a dissipative instability with the growth rate inversely proportional to the characteristic viscous decay rate. We point out, however, that the modes of the continuous range of the magnetohydrodynamics spectrum are not taken into account in this paper, and they can be more dangerous than those that are considered. (c) 2008 American Institute of Physics.

On the influence of non-thermal pressure on the mass determination of galaxy clusters

Aims. Given that in most cases just thermal pressure is taken into account in the hydrostatic equilibrium equation to estimate galaxy cluster mass, the main purpose of this paper is to consider the contribution of all three non-thermal components to total mass measurements. The non-thermal pressure is composed by cosmic rays, turbulence and magnetic pressures. Methods. To estimate the thermal pressure we used public XMM-Newton archival data of five Abell clusters to derive temperature and density profiles. To describe the magnetic pressure, we assume a radial distribution for the magnetic field, B(r) proportional to rho(alpha)(g). To seek generality we assume alpha within the range of 0.5 to 0.9, as indicated by observations and numerical simulations. Turbulent motions and bulk velocities add a turbulent pressure, which is considered using an estimate from numerical simulations. For this component, we assume an isotropic pressure, P(turb) = 1/3 rho(g)(sigma(2)(r) + sigma(2)(t)). We also consider the contribution of cosmic ray pressure, P(cr) proportional to r(-0.5). Thus, besides the gas (thermal) pressure, we include these three non-thermal components in the magnetohydrostatic equilibrium equation and compare the total mass estimates with the values obtained without them. Results. A consistent description for the non-thermal component could yield a variation in mass estimates that extends from 10% to similar to 30%. We verified that in the inner parts of cool core clusters the cosmic ray component is comparable to the magnetic pressure, while in non-cool core clusters the cosmic ray component is dominant. For cool core clusters the magnetic pressure is the dominant component, contributing more than 50% of the total mass variation due to non-thermal pressure components. However, for non-cool core clusters, the major influence comes from the cosmic ray pressure that accounts for more than 80% of the total mass variation due to non-thermal pressure effects. For our sample, the maximum influence of the turbulent component to the total mass variation can be almost 20%. Although all of the assumptions agree with previous works, it is important to notice that our results rely on the specific parametrization adopted in this work. We show that this analysis can be regarded as a starting point for a more detailed and refined exploration of the influence of non-thermal pressure in the intra-cluster medium (ICM).

Transition to chaotic scattering: Signatures in the differential cross section

We show that bifurcations in chaotic scattering manifest themselves through the appearance of an infinitely fine-scale structure of singularities in the cross section. These ""rainbow singularities"" are created in a cascade, which is closely related to the bifurcation cascade undergone by the set of trapped orbits (the chaotic saddle). This cascade provides a signature in the differential cross section of the complex pattern of bifurcations of orbits underlying the transition to chaotic scattering. We show that there is a power law with a universal coefficient governing the sequence of births of rainbow singularities and we verify this prediction by numerical simulations.

Gaseous and fluvial carbon export from an Amazon forest watershed

The transfer of carbon (C) from Amazon forests to aquatic ecosystems as CO(2) supersaturated in groundwater that outgases to the atmosphere after it reaches small streams has been postulated to be an important component of terrestrial ecosystem C budgets. We measured C losses as soil respiration and methane (CH(4)) flux, direct CO(2) and CH(4) fluxes from the stream surface and fluvial export of dissolved inorganic C (DIC), dissolved organic C (DOC), and particulate C over an annual hydrologic cycle from a 1,319-ha forested Amazon perennial first-order headwater watershed at Tanguro Ranch in the southern Amazon state of Mato Grosso. Stream pCO(2) concentrations ranged from 6,491 to 14,976 mu atm and directly-measured stream CO(2) outgassing flux was 5,994 +/- A 677 g C m(-2) y(-1) of stream surface. Stream pCH(4) concentrations ranged from 291 to 438 mu atm and measured stream CH(4) outgassing flux was 987 +/- A 221 g C m(-2) y(-1). Despite high flux rates from the stream surface, the small area of stream itself (970 m(2), or 0.007% of watershed area) led to small directly-measured annual fluxes of CO(2) (0.44 +/- A 0.05 g C m(2) y(-1)) and CH(4) (0.07 +/- A 0.02 g C m(2) y(-1)) per unit watershed land area. Measured fluvial export of DIC (0.78 +/- A 0.04 g C m(-2) y(-1)), DOC (0.16 +/- A 0.03 g C m(-2) y(-1)) and coarse plus fine particulate C (0.001 +/- A 0.001 g C m(-2) y(-1)) per unit watershed land area were also small. However, stream discharge accounted for only 12% of the modeled annual watershed water output because deep groundwater flows dominated total runoff from the watershed. When C in this bypassing groundwater was included, total watershed export was 10.83 g C m(-2) y(-1) as CO(2) outgassing, 11.29 g C m(-2) y(-1) as fluvial DIC and 0.64 g C m(-2) y(-1) as fluvial DOC. Outgassing fluxes were somewhat lower than the 40-50 g C m(-2) y(-1) reported from other Amazon watersheds and may result in part from lower annual rainfall at Tanguro. Total stream-associated gaseous C losses were two orders of magnitude less than soil respiration (696 +/- A 147 g C m(-2) y(-1)), but total losses of C transported by water comprised up to about 20% of the +/- A 150 g C m(-2) (+/- 1.5 Mg C ha(-1)) that is exchanged annually across Amazon tropical forest canopies.

Phosphorus kinetics in growing hair sheep

Kinetics modelling was used to study the effects of different dietary phosphorus (P) levels on P metabolism in young sheep. An experiment was conducted with 12 Santa Ines lambs receiving a basal diet of a hay-concentrate mixture. Different amounts of dicalcium phosphate were added to the basal diet, to give the following treatments levels of 0, 1.5, 3 and 4.5 g/animal/day. The isotopic dilution technique (32 p) was used for analyze four compartments: gastrointestinal tract, plasma, bone and soft tissues (liver, heart, kidney and muscle), as well as nutrient flows between them. All P flows showed a positive linear or exponential relationship with P intake. Both incorporation and reabsorption in bone and soft tissue increased with increasing P levels in the diet, with positive retention above 3 g/day. On the 4.5g P/day treatment, reduced P absorption and increased P in the faeces from dietary origin was noted. Three g/day of P treatment was sufficient to meet soft tissue requirements for young sheep. (C) 2008 Elsevier B.V. All rights reserved.

An environmentally friendly flow system for high-sensitivity spectrophotometric determination of free chlorine in natural waters

A green and highly sensitive analytical procedure was developed for the determination of free chlorine in natural waters, based on the reaction with N,N-diethyl-p-phenylenediamine (DPD). The flow system was designed with solenoid micro-pumps in order to improve mixing conditions by pulsed flows and to minimize reagent consumption as well as waste generation. A 100-cm optical path flow cell based on a liquid core waveguide was employed to increase sensitivity. A linear response was observed within the range 10.0 to 100.0 mu g L(-1), with the detection limit, coefficient of variation and sampling rate estimated as 6.8 mu g (99.7% confidence level), 0.9% (n = 20) and 60 determinations per hour, respectively. The consumption of the most toxic reagent (DPD) was reduced 20,000-fold and 30-fold in comparison to the batch method and flow injection with continuous reagent addition, respectively. The results for natural and tap water samples agreed with those obtained by the reference batch spectrophotometric procedure at the 95% confidence level. (C) 2010 Elsevier By. All rights reserved.

A flow-based procedure with solenoid micro-pumps for the spectrophotometric determination of uric acid in urine

The determination of uric acid in urine shows clinical importance, once it can be related to human organism dysfunctions, such as gout. An analytical procedure employing a multicommuted flow system was developed for the determination of uric acid in urine samples. Cu(II) ions are reduced by uric acid to Cu(I) that can be quantified by spectrophotometry in the presence of 2,2`-biquinoline 4,4`-dicarboxylic acid (BCA). The analytical response was linear between 10 and 100 mu mol L(-1) uric acid with a detection limit of 3.0 mu mol L(-1) (99.7% confidence level). Coefficient of variation of 1.2% and sampling rate of 150 determinations per hour were achieved. Per determination, 32 mu g of CuSO(4) and 200 mu g of BCA were consumed, generating 2.0 mL of waste. Recoveries from 91 to 112% were estimated and the results for 7 urine samples agreed with those obtained by the commercially available enzymatic kit for determination of uric acid. The procedure required 100-fold dilution of urine samples, minimizing sample consumption and interfering effects. In order to avoid the manual dilution step, on-line sample dilution was achieved by a simple system reconfiguration attaining a sampling rate of 95 h(-1). (C) 2009 Elsevier B.V. All rights reserved.

Runoff sources and land cover change in the Amazon: an end-member mixing analysis from small watersheds

The flowpaths by which water moves from watersheds to streams has important consequences for the runoff dynamics and biogeochemistry of surface waters in the Amazon Basin. The clearing of Amazon forest to cattle pasture has the potential to change runoff sources to streams by shifting runoff to more surficial flow pathways. We applied end-member mixing analysis (EMMA) to 10 small watersheds throughout the Amazon in which solute composition of streamwater and groundwater, overland flow, soil solution, throughfall and rainwater were measured, largely as part of the Large-Scale Biosphere-Atmosphere Experiment in Amazonia. We found a range in the extent to which streamwater samples fell within the mixing space determined by potential flowpath end-members, suggesting that some water sources to streams were not sampled. The contribution of overland flow as a source of stream flow was greater in pasture watersheds than in forest watersheds of comparable size. Increases in overland flow contribution to pasture streams ranged in some cases from 0% in forest to 27-28% in pasture and were broadly consistent with results from hydrometric sampling of Amazon forest and pasture watersheds that indicate 17- to 18-fold increase in the overland flow contribution to stream flow in pastures. In forest, overland flow was an important contribution to stream flow (45-57%) in ephemeral streams where flows were dominated by stormflow. Overland flow contribution to stream flow decreased in importance with increasing watershed area, from 21 to 57% in forest and 60-89% in pasture watersheds of less than 10 ha to 0% in forest and 27-28% in pastures in watersheds greater than 100 ha. Soil solution contributions to stream flow were similar across watershed area and groundwater inputs generally increased in proportion to decreases in overland flow. Application of EMMA across multiple watersheds indicated patterns across gradients of stream size and land cover that were consistent with patterns determined by detailed hydrometric sampling.

Evidences of turbulent mixing in multi-pumping flow systems

Multi-pumping flow systems exploit pulsed flows delivered by Solenoid pumps. Their improved performance rely on the enhanced radial mass transport inherent to the pulsed flow, which is a consequence of the establishment of vortices thus a tendency towards turbulent mixing. This paper presents several evidences of turbulent mixing in relation to pulsed flows. such as recorded peak shape, establishment of fluidized beds, exploitation of flow reversal, implementation of relatively slow chemical reactions and/or heating of the reaction medium. In addition, Reynolds number associated with the GO period of a pulsed flow is estimated and photographic images of dispersing samples flowing under laminar regime and pulsed flow conditions are presented. (C) 2009 Elsevier B.V. All rights reserved.