Reduction of infinite dimensional systems to finite dimensions: Compact convergence approach

We consider parameter dependent semilinear evolution problems for which, at the limit value of the parameter, the problem is finite dimensional. We introduce an abstract functional analytic framework that applies to many problems in the existing literature for which the study of asymptotic dynamics can be reduced to finite dimensions via the invariant manifolds technique. Some practical models are considered to show wide applicability of the theory. © 2013 Society for Industrial and Applied Mathematics.

Continuity of the dynamics in a localized large diffusion problem with nonlinear boundary conditions

This paper is concerned with singular perturbations in parabolic problems subjected to nonlinear Neumann boundary conditions. We consider the case for which the diffusion coefficient blows up in a subregion Omega(0) which is interior to the physical domain Omega subset of R(n). We prove, under natural assumptions, that the associated attractors behave continuously as the diffusion coefficient blows up locally uniformly in Omega(0) and converges uniformly to a continuous and positive function in Omega(1) = (Omega) over bar\Omega(0). (C) 2009 Elsevier Inc. All rights reserved.

Some uniform stability and convergence results for integral equations on the real line and projection methods for their solution

The paper considers second kind equations of the form (abbreviated x=y + K2x) in which and the factor z is bounded but otherwise arbitrary so that equations of Wiener-Hopf type are included as a special case. Conditions on a set are obtained such that a generalized Fredholm alternative is valid: if W satisfies these conditions and I − Kz, is injective for each z ε W then I − Kz is invertible for each z ε W and the operators (I − Kz)−1 are uniformly bounded. As a special case some classical results relating to Wiener-Hopf operators are reproduced. A finite section version of the above equation (with the range of integration reduced to [−a, a]) is considered, as are projection and iterated projection methods for its solution. The operators (where denotes the finite section version of Kz) are shown uniformly bounded (in z and a) for all a sufficiently large. Uniform stability and convergence results, for the projection and iterated projection methods, are obtained. The argument generalizes an idea in collectively compact operator theory. Some new results in this theory are obtained and applied to the analysis of projection methods for the above equation when z is compactly supported and k(s − t) replaced by the general kernel k(s,t). A boundary integral equation of the above type, which models outdoor sound propagation over inhomogeneous level terrain, illustrates the application of the theoretical results developed.

A compact difference scheme for numerical solutions of second order dual-phase-lagging models of microscale heat transfer

Dual-phase-lagging (DPL) models constitute a family of non-Fourier models of heat conduction that allow for the presence of time lags in the heat flux and the temperature gradient. These lags may need to be considered when modeling microscale heat transfer, and thus DPL models have found application in the last years in a wide range of theoretical and technical heat transfer problems. Consequently, analytical solutions and methods for computing numerical approximations have been proposed for particular DPL models in different settings. In this work, a compact difference scheme for second order DPL models is developed, providing higher order precision than a previously proposed method. The scheme is shown to be unconditionally stable and convergent, and its accuracy is illustrated with numerical examples.

An extension of Lorentz's almost convergence and applications in Banach spaces

2000 Mathematics Subject Classification: Primary 40C99, 46B99.

SYSTEMS OF DIFFERENTIAL EQUATIONSTHAT ARE COMPETITIVE OR COOPERATIVE II:CONVERGENCE ALMOST EVERYWHERE*MORRIS W. HIRSCH

A vector field in n-space determines a competitive (or cooperative) system of differential equations provided all of the off-diagonal terms of its Jacobian matrix are nonpositive (or nonnegative). The main results in this article are the following. A cooperative system cannot have nonconstant attracting periodic solutions. In a cooperative system whose Jacobian matrices are irreducible the forward orbit converges for almost every point having compact forward orbit closure. In a cooperative system in 2 dimensions, every solution is eventually monotone.  Applications are made to generalizations of positive feedback loops.

Convergence Of A Specialized Root Trait In Plants From Nutrient-impoverished Soils: Phosphorus-acquisition Strategy In A Nonmycorrhizal Cactus.

In old, phosphorus (P)-impoverished habitats, root specializations such as cluster roots efficiently mobilize and acquire P by releasing large amounts of carboxylates in the rhizosphere. These specialized roots are rarely mycorrhizal. We investigated whether Discocactus placentiformis (Cactaceae), a common species in nutrient-poor campos rupestres over white sands, operates in the same way as other root specializations. Discocactus placentiformis showed no mycorrhizal colonization, but exhibited a sand-binding root specialization with rhizosheath formation. We first provide circumstantial evidence for carboxylate exudation in field material, based on its very high shoot manganese (Mn) concentrations, and then firm evidence, based on exudate analysis. We identified predominantly oxalic acid, but also malic, citric, lactic, succinic, fumaric, and malonic acids. When grown in nutrient solution with P concentrations ranging from 0 to 100 μM, we observed an increase in total carboxylate exudation with decreasing P supply, showing that P deficiency stimulated carboxylate release. Additionally, we tested P solubilization by citric, malic and oxalic acids, and found that they solubilized P from the strongly P-sorbing soil in its native habitat, when the acids were added in combination and in relatively low concentrations. We conclude that the sand-binding root specialization in this nonmycorrhizal cactus functions similar to that of cluster roots, which efficiently enhance P acquisition in other habitats with very low P availability.

Compact Ag@fe3o4 Core-shell Nanoparticles By Means Of Single-step Thermal Decomposition Reaction.

A temperature pause introduced in a simple single-step thermal decomposition of iron, with the presence of silver seeds formed in the same reaction mixture, gives rise to novel compact heterostructures: brick-like Ag@Fe3O4 core-shell nanoparticles. This novel method is relatively easy to implement, and could contribute to overcome the challenge of obtaining a multifunctional heteroparticle in which a noble metal is surrounded by magnetite. Structural analyses of the samples show 4 nm silver nanoparticles wrapped within compact cubic external structures of Fe oxide, with curious rectangular shape. The magnetic properties indicate a near superparamagnetic like behavior with a weak hysteresis at room temperature. The value of the anisotropy involved makes these particles candidates to potential applications in nanomedicine.

Convergence Of Soil Nitrogen Isotopes Across Global Climate Gradients.

Quantifying global patterns of terrestrial nitrogen (N) cycling is central to predicting future patterns of primary productivity, carbon sequestration, nutrient fluxes to aquatic systems, and climate forcing. With limited direct measures of soil N cycling at the global scale, syntheses of the (15)N:(14)N ratio of soil organic matter across climate gradients provide key insights into understanding global patterns of N cycling. In synthesizing data from over 6000 soil samples, we show strong global relationships among soil N isotopes, mean annual temperature (MAT), mean annual precipitation (MAP), and the concentrations of organic carbon and clay in soil. In both hot ecosystems and dry ecosystems, soil organic matter was more enriched in (15)N than in corresponding cold ecosystems or wet ecosystems. Below a MAT of 9.8°C, soil δ(15)N was invariant with MAT. At the global scale, soil organic C concentrations also declined with increasing MAT and decreasing MAP. After standardizing for variation among mineral soils in soil C and clay concentrations, soil δ(15)N showed no consistent trends across global climate and latitudinal gradients. Our analyses could place new constraints on interpretations of patterns of ecosystem N cycling and global budgets of gaseous N loss.

Convergence of developmental mutants into a single tomato model system: 'Micro-Tom' as an effective toolkit for plant development research

Background: The tomato (Solanum lycopersicum L.) plant is both an economically important food crop and an ideal dicot model to investigate various physiological phenomena not possible in Arabidopsis thaliana. Due to the great diversity of tomato cultivars used by the research community, it is often difficult to reliably compare phenotypes. The lack of tomato developmental mutants in a single genetic background prevents the stacking of mutations to facilitate analysis of double and multiple mutants, often required for elucidating developmental pathways. Results: We took advantage of the small size and rapid life cycle of the tomato cultivar Micro-Tom (MT) to create near-isogenic lines (NILs) by introgressing a suite of hormonal and photomorphogenetic mutations (altered sensitivity or endogenous levels of auxin, ethylene, abscisic acid, gibberellin, brassinosteroid, and light response) into this genetic background. To demonstrate the usefulness of this collection, we compared developmental traits between the produced NILs. All expected mutant phenotypes were expressed in the NILs. We also created NILs harboring the wild type alleles for dwarf, self-pruning and uniform fruit, which are mutations characteristic of MT. This amplified both the applications of the mutant collection presented here and of MT as a genetic model system. Conclusions: The community resource presented here is a useful toolkit for plant research, particularly for future studies in plant development, which will require the simultaneous observation of the effect of various hormones, signaling pathways and crosstalk.

Searching for star formation outside galaxies: Multiwavelength analysis of the intragroup medium of Hickson Compact Group 100

We use multiwavelength data (H I, FUV, NUV, R) to search for evidence of star formation in the intragroup medium of the Hickson Compact Group 100. We find that young star-forming regions are located in the intergalactic H I clouds of the compact group which extend to over 130 kpc away from the main galaxies. A tidal dwarf galaxy (TDG) candidate is located in the densest region of the H I tail, 61 kpc from the brightest group member and its age is estimated to be only 3.3 Myr. Fifteen other intragroup H II regions and TDG candidates are detected in the Galaxy Evolution Explorer (GALEX) FUV image and within a field 10' x 10' encompassing the H I tail. They have ages <200 Myr, H I masses of 10(9.2-10.4) M(circle dot), 0.001

Equation of state for the magnetic-color-flavor-locked phase and its implications for compact star models

Using the solutions of the gap equations of the magnetic-color-flavor-locked (MCFL) phase of paired quark matter in a magnetic field, and taking into consideration the separation between the longitudinal and transverse pressures due to the field-induced breaking of the spatial rotational symmetry, the equation of state of the MCFL phase is self-consistently determined. This result is then used to investigate the possibility of absolute stability, which turns out to require a field-dependent ""bag constant"" to hold. That is, only if the bag constant varies with the magnetic field, there exists a window in the magnetic field vs bag constant plane for absolute stability of strange matter. Implications for stellar models of magnetized (self-bound) strange stars and hybrid (MCFL core) stars are calculated and discussed.

Two formation channels of ultra-compact dwarf galaxies in Hickson compact groups

Context. The formation of ultra-compact dwarf galaxies (UCDs) is believed to be driven by interaction, and UCDs are abundant in the cores of galaxy clusters, environments that mark the end-point of galaxy evolution. Nothing is known about the properties of UCDs in compact groups of galaxies, environments where most of galaxy evolution and interaction is believed to occur and where UCDs in an intermediate stage in their evolution may be expected. Aims. The main goal of this study is to detect and characterize, for the first time, the UCD population of compact groups of galaxies. For that, two nearby groups in different evolutionary stages, HCG22 and HCG90, were targeted. Methods. We selected about 40 UCD candidates from pre-existing photometry of both groups, and obtained spectra of these candidates using the VLT FORS2 instrument in MXU mode. Archival HST/ACS imaging was used to measure their structural parameters. Results. We detect 16 and 5 objects belonging to HCG22 and HCG90, respectively, covering the magnitude range -10.0 > M(R) > -11.5 mag. Their integrated colours are consistent with old ages covering a broad range in metallicities (metallicities confirmed by the spectroscopic measurements). Photometric mass estimates put 4 objects in HCG90 and 9 in HCG22 in the mass range of UCDs (> 2 x 10(6) M(circle dot)) for an assumed age of 12Gyr. These UCDs are on average 2-3 times larger than the typical size of Galactic GCs, covering a range of 2 less than or similar to r(h) less than or similar to 21 pc. The UCDs in HCG22 are more concentrated around the central galaxy than in HCG90, at the 99% confidence level. They cover a broad range in [alpha/Fe] abundances from sub-to super-solar. The spectra of 3 UCDs (2 in HCG22, 1 in HCG90) show tentative evidence of intermediate age stellar populations. The clearest example is the largest and most massive UCD (similar to 10(7) M(circle dot)) in our sample, which is detected in HCG22. Its properties are most consistent with a stripped dwarf galaxy nucleus. We calculate the specific frequency (S(N)) of UCDs for both groups, finding that HCG22 has about three times higher S(N) than HCG90. Conclusions. The ensemble properties of the detected UCDs supports two co-existing formation channels: a star cluster origin (low-luminosity, compact sizes, old ages, super-solar alpha/Fe), and an origin as tidally stripped dwarf nuclei (more extended and younger stellar populations). Our results imply that the UCDs detected in both groups do not, in their majority, originate from relatively recent galaxy interactions. Most of the detected UCDs have likely been brought into the group along with their host galaxies.

Kinematics of galaxies in compact groups Studying the B-band Tully-Fischer relation

We obtained new Fabry-Perot data cubes and derived velocity fields, monochromatic, and velocity dispersion maps for 28 galaxies in the Hickson compact groups 37, 40, 47, 49, 54, 56, 68, 79, and 93. We also derived rotation curves for 9 of the studied galaxies, 6 of which are strongly asymmetric. Combining these new data with previously published 2D kinematic maps of compact group galaxies, we investigated the differences between the kinematic and morphological position angles for a sample of 46 galaxies. We find that one third of the unbarred compact group galaxies have position angle misalignments between the stellar and gaseous components. This and the asymmetric rotation curves are clear signatures of kinematic perturbations, probably because of interactions among compact group galaxies. A comparison between the B-band Tully-Fisher relation for compact group galaxies and for the GHASP field-galaxy sample shows that, despite the high fraction of compact group galaxies with asymmetric rotation curves, these lay on the TF relation defined by galaxies in less dense environments, although with more scatter. This agrees with previous results, but now confirmed for a larger sample of 41 galaxies. We confirm the tendency for compact group galaxies at the low-mass end of the Tully-Fisher relation (HCG 49b, 89d, 96c, 96d, and 100c) to have either a magnitude that is too bright for its mass (suggesting brightening by star formation) and/or a low maximum rotational velocity for its luminosity (suggesting tidal stripping). These galaxies are outside the Tully Fisher relation at the 1 sigma level, even when the minimum acceptable values of inclinations are used to compute their maximum velocities. Including such galaxies with nu < 100 km s(-1) in the determination of the zero point and slope of the compact group B-band Tully-Fisher relation would strongly change the fit, making it different from the relation for field galaxies, which has to be kept in mind when studying scaling relations of interacting galaxies, especially at high redshifts.

Self-bound models of compact stars and recent mass-radius measurements

The exact composition of a specific class of compact stars, historically referred to as ""neutron stars,'' is still quite unknown. Possibilities ranging from hadronic to quark degrees of freedom, including self-bound versions of the latter, have been proposed. We specifically address the suitability of strange star models (including pairing interactions) in this work, in the light of new measurements available for four compact stars. The analysis shows that these data might be explained by such an exotic equation of state, actually selecting a small window in parameter space, but still new precise measurements and also further theoretical developments are needed to settle the subject.