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Identifying the convective/absolute instability nature of a local base flow requires an analysis of its linear impulse response. One must find the appropriate singularity in the eigenvalue problem with complex frequencies and wavenumbers and prove causality. One way to do so is to show that the appropriate integration contour of this response, a steepest decent path through the relevant singularity, exists. Due to the inherent difficulties of such a proof, one often verifies instead whether this singularity satisfies the collision criterion. In other words, one must show that the branches involved in the formation of this singularity come from distinct halves of the complex wavenumber plane. However, this graphical search is computationally intensive in a single plane and essentially prohibitive in two planes. A significant computational cost reduction can be achieved when root finding procedures are applied instead of graphical ones to search for singularities. They focus on locating these points, with causality being verified graphically a posteriori for a small parametric sample size. The use of root-finding procedures require auxiliary equations, often derived by applying the zero group velocity conditions to the dispersion relation. This relation, in turn, is derived by applying matrix forming to the differential eigenvalue problem and taking the determinant of the resulting system of algebraic equations. Taking the derivative of the dispersion relation with respect to the wavenumbers generates the auxiliary equations. If the algebraic system is decoupled, this derivation is straightforward. However, its computational cost is often prohibitive when the algebraic system is coupled. Other methods exist, but often they can also be too costly and/or not reliable for two wavenumber plane searches. This paper describes an alternative methodology based on sensitivity analysis and adjoints that allow the zero group velocity conditions to be applied directly to the differential eigenvalue problem. In doing so, the direct and auxiliary differential eigenvalue problems can be solved simultaneously using standard shooting methods to directly locate singularities. Auxiliary dispersion relations no longer have to be derived, although it is shown that they are the algebraic equivalent of the auxiliary differential eigenvalue problems obtained by this alternative methodology. Using the latter dramatically reduces computational costs. The search for arbitrary singularities is then not only accelerated in single wavenumber planes but it also becomes viable in two wavenumber planes. Finally, the new method also allows group velocity calculations, greatly facilitating the verification of causality. Several test cases are presented to illustrate the capabilities of this new method.
Chemical constituents trapped within glacial ice provide a unique record of climate, as well as repositories for biological material such as pollen grains, fungal spores, viruses, bacteria and dissolved organic carbon. Past research suggests that the veins of polycrystalline ice may provide a liquid microenvironment for active microbial metabolism fueled by concentrated impurities in the veins. Despite these claims, no direct measurements of impurity concentration in ice veins have been made. Using micro-Raman spectroscopy, we show that sulfate and nitrate concentrations in the veins of glacial ice from Greenland (Greenland Ice Sheet Project 2) and Antarctic (Newall Glacier and a Dominion Range glacier) core samples were 104 and 105 times greater than the concentrations measured in melted (bulk) core water. Methanesulfonate was not found in the veins, consistent with its presence as particulate matter within the ice. The measured vein concentration of molecular anions implies a highly acidic (pH < 3) vein environment with high ionic strength (mM-M). We estimate that the vein volume provides 16.7 and 576 km3 of habitable space within the Greenland and Antarctic ice sheets, respectively, which could support the metabolism of organisms that are capable of growing in cold, high ionic strength solutions with low pH.
The existence of a non-trivial bounded solution to the Dirichlet problem is established for a class of nonlinear elliptic equations involving a fully anisotropic partial differential operator. The relevant operator depends on the gradient of the unknown through the differential of a general convex function. This function need not be radial, nor have a polynomial-type growth. Besides providing genuinely new conclusions, our result recovers and embraces, in a unified framework, several contributions in the existing literature, and augments them in various special instances.
Oilseeds offer some protection to the access of ruminal microorganisms and may be an alternative to calcium salts of fatty acids (FA), which are not fully inert in the ruminal environment. This study aimed to evaluate the effects of different sources of FA supplementation on apparent total tract nutrient digestibility, milk yield and composition, and energy balance (EB) of cows during the transition period and early lactation. We compared diets rich in C18:2 and C18:3 FA. Multiparous Holstein cows were randomly assigned to receive one of the four diets: control (n=11); whole flaxseed (WF, n=10), 60 and 80 g/kg (diet dry matter (DM) basis) of WF during the prepartum and postpartum periods, respectively; whole raw soybeans (WS, n=10), 120 and 160 g/kg (diet DM basis) of WS during the prepartum and postpartum periods, respectively; and calcium salts of unsaturated fatty acids (CSFA, n=11), 24 and 32 g/kg (diet DM basis) of CSFA during the prepartum and postpartum periods, respectively. Dry cows fed WF had higher DM and net energy of lactation (NEL) intake than those fed WS or CSFA. The FA supplementation did not alter DM and NDF apparent total tract digestibility, dry cows fed WF exhibited greater NDF total tract digestion than cows fed WS or CSFA. Feeding WS instead of CSFA did not alter NEL intake and total tract digestion of nutrients, but increased milk fat yield and concentration. Calculated efficiency of milk yield was not altered by diets. FA supplementation increased EB during the postpartum period. Experimental diets increased long-chain FA (saturated and unsaturated FA) in milk. In addition, cows fed WS and CSFA had higher C18:1 trans-11 FA and C18:2 cis, and lower C18:3 FA in milk than those fed WF. Furthermore, cows fed CSFA had higher C18:1 trans-11 and cis-9, trans-11 FA than cows fed WS. Although supplemental C18:2 and C18:3 FA did not influence the milk yield of cows, they positively affected EB and increased unsaturated long-chain FA in milk fat.
This paper presents a stability analysis of a mixed convection problem in an inclined parallel-plate channel with uniform heating (or cooling) from the top and bottom. The channel is filled with a saturated homogeneous porous medium and the momentum equation is given by Darcy’s model. A forced through-flow is prescribed across the channel. Linear stability analysis is thus employed to determine the onset of thermoconvective instability. The channel inclination is shown to play an important role in the stability of the problem, where two different regimes can be present: a buoyancy-assisted regime and a buoyancy-opposed regime. The analysis of the problem leads to a differential eigenvalue problem composed of a system of four complex-valued equations that are used to determine the critical values of the Rayleigh number leading to an instability under different problem configurations. This eigenproblem is solved by employing the generalised integral transform technique (GITT), in which simpler real eigenfunction bases are used to expand the complex eigenproblem. The results indicate that the longitudinal rolls are always more unstable than oblique and transverse rolls. For a buoyancy-opposed regime, even with a very small channel inclination angle, the basic through-flow is always unstable. This result has an important implication for experimental research, as it shows that a perfect alignment must be employed for horizontal mixed-convection experiments to avoid instabilities that arise in the buoyancy-opposed regime.
The stability of the natural convection parallel flow in a vertical porous slab is reconsidered, by reformulating the problem originally solved in Gill’s classical paper of 1969 (J. Fluid Mech., vol. 35, pp. 545–547). A comparison is made between the set of boundary conditions where the slab boundaries are assumed to be isothermal and impermeable (Model A), and the set of boundary conditions where the boundaries are modelled as isothermal and permeable (Model B). It is shown that Gill’s proof of linear stability for Model A cannot be extended to Model B. The question about the stability/instability of the basic flow is examined by carrying out a numerical solution of the stability eigenvalue problem. It is shown that, with Model B, the natural convection parallel flow in the basic state becomes unstable when the Darcy–Rayleigh number is larger than 197.081. The normal modes selected at onset of instability are transverse rolls. Direct numerical simulations of the nonlinear regime of instability are carried out.
We study the existence and multiplicity of solutions for a parametric equation driven by the p-Laplacian operator on unbounded intervals. Precisely, by using a recent local minimum theorem we prove the existence of a non-trivial non-negative solution to an equation on the real line, without assuming any asymptotic condition either at 0 or at ∞ on the nonlinear term. As a special case, we note the existence of a non-trivial solution for the problem when the nonlinear term is sublinear at 0. Moreover, under a suitable superlinear growth at ∞ on the nonlinearity we prove a multiplicity result for such a problem.
The existence of an infinite class of buoyant flows in a vertical porous channel with adiabatic and impermeable boundary walls, called adiabatic eigenflows, is discussed. A uniform heat source within the saturated medium is assumed, so that a stationary state is possible with a net vertical through-flow convecting away the excess heat. The simple isothermal flow with uniform velocity profile is a special adiabatic eigenflow if the power supplied by the heat source is zero. The linear stability analysis of the adiabatic eigenflows is carried out analytically. It is shown that these basic flows are unstable. The only exception, when the power supplied by the heat source is zero, is the uniform isothermal flow, which is stable. The existence of adiabatic eigenflows and their stability analysis is extended to the case of spanwise lateral confinement, viz. in the case of a vertical rectangular channel. A generalisation of this study to a vertical channel with an arbitrary cross-sectional shape is also presented.
Sea ice is a unique environment providing a vast habitat for a variety of life, including microscopic organisms. It accounts for roughly 5–6% of the surface area of the oceans. It is a complex porous structure of crystalline water, gas bubbles, and pockets of brine, as well as a connected structure composed of macro- and micro-porosity filled with concentrated aqueous liquids. Using micro-Raman spectroscopy, it is possible to characterise features of ice at a spatial resolution of a few to tens of micrometers, the scale of relevance to trapped microorganisms, by providing information concerning the presence and amount of molecular species present in the trapped liquids. We have applied this technique to determine the spatial distribution of sulphate, phosphate and carbonate anions in sea-ice veins using ice obtained from the vicinity of the Palmer Station, Antarctica. The observed sulphate concentrations were approximately 20–30% higher than nominal surface seawater concentrations, consistent with the concentration of brine in vein and inclusion liquids during the ice formation process. This concentration was lower than that in veins present in laboratory-prepared ice. Carbonate and dibasic phosphate anions were also observed in the sea ice. This speciation is consistent with an alkaline environment in the sea-ice aqueous system. The mean dibasic phosphate concentration found throughout the sample was 648 mM, while, for carbonate, it was 485 mM. However, these anions showed extremely high spatial variability. The high phosphate and carbonate enhancements observed relative to sulphate point to the influence of processes other than brine formation controlling the chemistry of these anions in sea ice.
In 1552 Portuguese humanist João de Barros published the first volume of his Décadas da Ásia, a historical account of the first half-century of Portugal's Asian empire modeled on Livy's History of Rome. In the introduction to this first volume, he speaks directly to the Portuguese king João III, offering the ailing monarch a dense and complex theorization of empire, praxis, language, the senses, and immortality. Speaking at length of the central place of historical narrative in the workings of empire, Barros weaves together three seemingly disparate threads. The first of these is an episode from the history of Alexander the Great as transmitted by Arrian and Plutarch that deals directly with the link between poetry, praxis (what Barros calls feitos), and immortality. The second involves a strategic reworking of philosophical ideas regarding immortality. The third is the theory of affatus developed at the end of the thirteenth century by the Mallorcan polymath Ramon Llull, according to which language (framed as speech) constitutes a sixth human sense.
Throughout his introduction, Barros moves adroitly from a more or less stock discussion of the role of the poet and historian in the preservation of imperial action to a fraught and tangled philosophical discussion of language itself as a tool of empire and immortality. Beginning with classical Greek notions of corruption and reproduction, Barros (turning to Llull) moves into a discussion of language as a bodily sense and then develops a theory of written language that links the latter at once to the divine and the sensible, imbuing it with the power to bestow immortality upon human actions.
In 1552 Portuguese humanist João de Barros published the first volume of his Décadas da Ásia, a historical account of the first half-century of Portugal's Asian empire modeled on Livy's History of Rome.1 In the introduction to this first volume, he speaks directly to the Portuguese king João III, offering the ailing monarch a dense and complex theorization of empire, praxis, language, the senses, and immortality. Speaking at length of the central place of historical narrative in the workings of empire, Barros weaves together three seemingly disparate threads. The first of these is an episode from the history of Alexander the Great as transmitted by Arrian and Plutarch that deals directly with the link between poetry, praxis (what Barros calls feitos), and immortality. The second involves a strategic reworking of philosophical ideas regarding immortality. The third is the theory of affatus developed at the end of the thirteenth century by the Mallorcan polymath Ramon Llull, according to which language (framed as speech) constitutes a sixth human sense.
Throughout his introduction, Barros moves adroitly from a more or less stock discussion of the role of the poet and historian in the preservation of imperial action to a fraught and tangled philosophical discussion of language itself as a tool of empire and immortality. Beginning with classical Greek notions of corruption and reproduction, Barros (turning to Llull) moves into a discussion of language as a bodily sense and then develops a theory of written language that links the latter at once to the divine and the sensible, imbuing it with the power to bestow immortality upon human actions. This last step, in which Barros links historiography to epic in a direct way, take us more or less full circle back to the question of immortality and links the writing of empire – or at least its narrative theorization – to the mortal anxieties that shaped Portuguese expansion into Muslim Africa and Asia at every turn.
Alexander and History
By the sixteenth century, there is a more or less standard historico-poetic conceit in place that revolves around Alexander the Great. In most extant versions, Portuguese poets and historians claimed that the Portuguese had essentially surpassed Alexander's achievements and that they thus served as a much more fitting subject for Homeric epic than the wanderings of Ulysses or the Trojan War.
The onset of thermoconvective instability in a horizontal porous layer with a basic Hadley flow is studied, under the assumption of weak vertical heterogeneity. Hadley flow is a single-cell convective circulation induced by horizontal linear changes of the layer boundary temperatures. When combined with heating from below, these thermal boundary conditions yield a temperature gradient inclined to the vertical, in the basic state. The linear stability of the basic state is studied by considering small-amplitude disturbances of the velocity field and the temperature field. The linearized governing equations for the disturbances are then solved both by Galerkin’s method of weighted residuals and by a combined use of the Runge–Kutta method and the shooting method. The effect of weak heterogeneity of the permeability and the effective thermal conductivity of the porous medium is studied with respect to neutral stability conditions. It is shown that, among the normal mode disturbances, the most unstable are longitudinal rolls, that is, plane waves with a wave vector perpendicular to the imposed horizontal temperature gradient. The effect of heterogeneity becomes important only for high values of the horizontal Rayleigh number, associated with the horizontal temperature gradient, approximately greater than 60. In this regime, the effect of heterogeneity is destabilizing. It is shown that heterogeneity with respect to thermal conductivity is of major importance in the onset of instability.
Tephra in glacial ice provide a method to obtain a depth vs chronology correlation within an ice core. Currently, core sections containing particulate must be sacrificially analysed to determine the nature of the particulate (e.g. aerosol, micrometeor, volcanic ash), and, in the case of volcanic ash, the event tied to the particle. Characterization through melting and chemical analysis precludes, de facto, its use for other purposes. A non-destructive technique to characterize particulates in ice cores prior to sectioning the samples, e.g. optical interrogation, would be useful, especially if chemical information specific to particular volcanic eruptions could be gleaned from such an analysis. We investigated the use of micro-Raman spectroscopy for this purpose. Spectra were obtained on samples of Antarctic blue ice tephra from different sources along with a reference ash sample of New Mexico Bandelier Tuff. Vitreous and crystalline particles in the samples were characterized. For vitreous material, a detailed analysis of the Raman-active vibrational bands of the glass structure was found to have the potential of being a unique identifier of the source of the glass, however, additional library development is needed for implementation.
Icy environments (glacial ice and sea ice) can be complex ecosystems, supporting a diversity of communities. In particular, the μ-environments in which bacteria and algae are found are poorly understood. One important habitat is the liquid trapped in the ice, either as veins and triple junctions inherent in the ice structure or as liquid inclusions. μ-Raman spectroscopy is an analytical tool with the potential to characterise qualitatively and quantitatively these liquid μ-environments especially with respect to molecular anions such as nitrate, sulphate, bisulphate and MSA. Using a model system for glacial ice, splat-cooled samples were prepared from aqueous solutions of these anions at varying concentrations (50–75 mM total sulphate, 30–200 mM nitrate, and 10–55 mM MSA). Concentrations of these anions in the vein liquid were measured directly and non-destructively at –15 °C using μ-Raman spectroscopy. In agreement with predicted concentrations in glacial ice veins, it was found that typical ionic concentrations in veins are quite high, with mean concentrations ranging from 0.23 M to 3.5 M depending on anion type and initial concentration. For sulphate solutions, it was also possible to measure vein pH's directly. The observed pH in these systems was extremely low, in some cases ~1. The results of these model studies as well as the implications for ice vein concentrations in natural systems of polycrystalline ice are discussed.
We report on our investigation into the use of III-V superlattice structures for thermoelectric (TE) applications. Preliminary review of III-V materials trends indicate that the GaSb/InAs superlattice system should offer one of the best potentials for high thermoelectric performance in the 500K-800K range. MOCVD growth of GaSb/InAs superlattice structures was carried out, and relevant structural, thermal, and electrical characterization has been performed. TEM and XRD results demonstrate a well-ordered superlattice structure. Thermal conductivity measurements reveal a reduction in the room-temperature thermal conductivity of GaSb/InAs superlattices (4.4-10.0 W/m-K), relative to either binary GaSb (32 W/m-K) or InAs (27 W/m-K). Additionally, we have worked to optimize the thermoelectric power factor (α2σ), studying both Se- and Te-doping of the superlattice structures, in an effort to demonstrate optimal thermoelectric performance. Our results demonstrate a maximum ZT of 0.36 at 400K for optimally doped n-type GaSb/InAs superlattice structures.
The thermal instability of the plane Poiseuille flow as a consequence of the effect of viscous dissipation is investigated. No external temperature difference is assumed in the environment; the lower boundary is considered adiabatic, while the upper boundary is isothermal. Thus, the sole cause of the unstable thermal stratification is the flow rate, through the volumetric heating induced by the viscous dissipation. A linear stability analysis is carried out numerically by the analysis of normal modes perturbing the basic flow with different inclinations. The study of cases with different Prandtl numbers and Gebhart numbers suggests that the most unstable perturbations are the longitudinal rolls, namely the normal modes with a wave vector perpendicular to the basic flow direction. A possible comparison with the hydrodynamic instability of the plane Poiseuille flow, described by the Orr–Sommerfeld eigenvalue problem is proposed. This comparison, when referred to high values of the Prandtl number, reveals that the dissipation instability may be effective at a Reynolds number smaller than that needed for the onset of the hydrodynamic instability.
The linear stability of a basic forced and free convection flow in an inclined porous channel is analysed by using the Darcy law and the Oberbeck–Boussinesq approximation. The basic velocity and temperature distributions are influenced by the effect of viscous dissipation, as well as by the boundary conditions. The boundary planes are assumed to be impermeable and isothermal, with a temperature of the lower boundary higher than that of the upper boundary. The instability against longitudinal rolls is studied by employing a second-order weighted residual solution and an accurate sixth-order Runge–Kutta solution of the disturbance equations. The instability against transverse rolls is also investigated. It is shown that these disturbances are in every case less unstable than the longitudinal rolls.
The incorporation of a high percentage of nitrogen in the GaAs lattice has been the subject of recent interest to reduce the bandgap while maintaining the nearly lattice matched condition to GaAs. We will report on the metalorganic chemical vapor deposition (MOCVD) of GaAsN using trimethylgallium (TMG), tertiarybutylarsine (TBA) and dimethylhydrazine (DMHy) organometallic sources in a hydrogen-free carrier gas. A nitrogen concentration as high as ∼8% in GaAsN was achieved. The effect of nitrogen concentration on the structural, optical and surface properties of GaAsN films will be discussed.