Application of the comparison principle to analysis of nonlinear systems

A comparison principle based on a Kamke theorem and Lipschitz conditions is presented along with its possible applications and modifications. It is shown that the comparison lemma can be used in the study of such areas as classical stability theory, higher order trajectory derivatives, Liapunov functions, boundary value problems, approximate dynamic systems, linear and nonlinear systems, and bifurcation analysis

Spaceborne memory organization, an associative data acquisition system, phase II Final report, Apr. - Dec. 1966

Spaceborne memory organization, associative data acquisition system design, and data compression technique

A rapidly converging triangular plate element

Shear stress analysis of triangular plate element

Spontaneous Scalarization and Boson Stars

We study spontaneous scalarization in Scalar-Tensor boson stars. We find that scalarization does not occur in stars whose bosons have no self-interaction. We introduce a quartic self-interaction term into the boson Lagrangian and show that when this term is large, scalarization does occur. Strong self-interaction leads to a large value of the compactness (or sensitivity) of the boson star, a necessary condition for scalarization to occur, and we derive an analytical expression for computing the sensitivity of a boson star in Brans-Dicke theory from its mass and particle number. Next we comment on how one can use the sensitivity of a star in any Scalar-Tensor theory to determine how its mass changes when it undergoes gravitational evolution. Finally, in the Appendix, we derive the most general form of the boson wavefunction that minimises the energy of the star when the bosons carry a U(1) charge.Comment: 23 pages, 5 postscript figures. Typing errors corrected. Includes some new text that relates the paper to several previous results. Accepted for publication in PR

Dysfunctional stem and progenitor cells impair fracture healing with age

Successful fracture healing requires the simultaneous regeneration of both the bone and vasculature; mesenchymal stem cells (MSCs) are directed to replace the bone tissue, while endothelial progenitor cells (EPCs) form the new vasculature that supplies blood to the fracture site. In the elderly, the healing process is slowed, partly due to decreased regenerative function of these stem and progenitor cells. MSCs from older individuals are impaired with regard to cell number, proliferative capacity, ability to migrate, and osteochondrogenic differentiation potential. The proliferation, migration and function of EPCs are also compromised with advanced age. Although the reasons for cellular dysfunction with age are complex and multidimensional, reduced expression of growth factors, accumulation of oxidative damage from reactive oxygen species, and altered signaling of the Sirtuin-1 pathway are contributing factors to aging at the cellular level of both MSCs and EPCs. Because of these geriatric-specific issues, effective treatment for fracture repair may require new therapeutic techniques to restore cellular function. Some suggested directions for potential treatments include cellular therapies, pharmacological agents, treatments targeting age-related molecular mechanisms, and physical therapeutics. Advanced age is the primary risk factor for a fracture, due to the low bone mass and inferior bone quality associated with aging; a better understanding of the dysfunctional behavior of the aging cell will provide a foundation for new treatments to decrease healing time and reduce the development of complications during the extended recovery from fracture healing in the elderly

Towards a global sustainable development agenda built on social–ecological resilience

Non-technical summary. The United Nations’ sustainable development goals (SDGs) articulate societal aspirations for people and our planet. Many scientists have criticised the SDGs and some have suggested that a better understanding of the complex interactions between society and the environment should underpin the next global development agenda. We further this discussion through the theory of social–ecological resilience, which emphasises the ability of systems to absorb, adapt, and transform in the face of change. We determine the strengths of the current SDGs, which should form a basis for the next agenda, and identify key gaps that should be filled. Technical summary. The United Nations’ sustainable development goals (SDGs) are past their halfway point and the next global development agenda will soon need to be developed. While laudable, the SDGs have received strong criticism from many, and scholars have proposed that adopting complex adaptive or social–ecological system approaches would increase the effectiveness of the agenda. Here we dive deeper into these discussions to explore how the theory of social–ecological resilience could serve as a strong foundation for the next global sustainable development agenda. We identify the strengths and weaknesses of the current SDGs by determining which of the 169 targets address each of 43 factors affecting social–ecological resilience that we have compiled from the literature. The SDGs with the strongest connections to social–ecological resilience are the environment-focus goals (SDGs 2, 6, 13, 14, 15), which are also the goals consistently under-prioritised in the implementation of the current agenda. In terms of the 43 factors affecting social–ecological resilience, the SDG strengths lie in their communication, inclusive decision making, financial support, regulatory incentives, economic diversity, and transparency in governance and law. On the contrary, ecological factors of resilience are seriously lacking in the SDGs, particularly with regards to scale, crossscale interactions, and non-stationarity. Social media summary. The post-2030 agenda should build on strengths of SDGs 2, 6, 13, 14, 15, and fill gaps in scale, variability, and feedbacks

Biomineralisation in the Palaeozoic oceans: evidence for simultaneous crystallisation of high and low magnesium calcite by phacopine trilobites

The chemical composition and microstructure of the calcite cuticles of eleven species of phacopine trilobites have been investigated by electron beam imaging, diffraction, and microanalysis, and results reveal that the lenses of their schizochroal eyes differed significantly in chemical composition from the rest of the cuticle in vivo. Apart from the eye lenses, most cuticles are inferred to have escaped extensive recrystallisation because their constituent crystals are sub-micrometre in size and have a preferred orientation that is consistent between species. Their current compositions of ~1.4 to 2.4 mol% MgCO3 are likely to be close to original values, although as they commonly luminesce and contain detectable manganese and iron, some diagenetic alteration has taken place. The associated lenses have a microstructure that is suitable for focusing light, yet are optically turbid owing to the presence within calcite of micropores and crystals of microdolomite, apatite, celestite and pyrite. The microdolomite indicates that lenses recrystallised from an original high-Mg calcite composition and this is supported by the presence of nanometre-scale modulated microstructures in both the calcite and dolomite. These lenses currently contain ~1 to 6 mol% MgCO3, and by comparison with the proportion of magnesium lost from echinoderm stereom in the same thin sections, may have contained ~7.5 mol% MgCO3 in vivo. In some samples, more extensive diagenetic alteration is evidenced by recrystallisation of the cuticle including lenses to coarse equant calcite or enrichment of the cuticle, but not necessarily the lenses, in magnesium accompanying replacement by a Mg–Fe phyllosilicate. The phacopine trilobites had to modify partition coefficients for magnesium considerably in order to grow lenses with contrasting compositions to the rest of their cuticles, and such a strong vital effect on biomineralisation suggests that incorporation of magnesium was essential for functioning of their calcite optical s

On the feasibility of N2 fixation via a single-site FeI/FeIV cycle: Spectroscopic studies of FeI(N2)FeI, FeIV=N, and related species

The electronic properties of an unusually redox-rich iron system, [PhBPR 3]FeNx (where [PhBPR 3] is [PhB(CH2PR2)3]−), are explored by Mössbauer, EPR, magnetization, and density-functional methods to gain a detailed picture regarding their oxidation states and electronic structures. The complexes of primary interest in this article are the two terminal iron(IV) nitride species, [PhBPiPr 3]FeN (3a) and [PhBPCH2Cy 3]FeN (3b), and the formally diiron(I) bridged-Fe(μ-N2)Fe species, {[PhBPiPr 3]Fe}2(μ-N2) (4). Complex 4 is chemically related to 3a via a spontaneous nitride coupling reaction. The diamagnetic iron(IV) nitrides 3a and 3b exhibit unique electronic environments that are reflected in their unusual Mössbauer parameters, including quadrupole-splitting values of 6.01(1) mm/s and isomer shift values of −0.34(1) mm/s. The data for 4 suggest that this complex can be described by a weak ferromagnetic interaction (J/D < 1) between two iron(I) centers. For comparison, four other relevant complexes also are characterized: a diamagnetic iron(IV) trihydride [PhBPiPr 3]Fe(H)3(PMe3) (5), an S = 3/2 iron(I) phosphine adduct [PhBPiPr 3]FePMe3 (6), and the S = 2 iron(II) precursors to 3a, [PhBPiPr 3]FeCl and [PhBPiPr 3]Fe-2,3:5,6-dibenzo-7-aza bicyclo[2.2.1]hepta-2,5-diene (dbabh). The electronic properties of these respective complexes also have been explored by density-functional methods to help corroborate our spectral assignments and to probe their electronic structures further

Charged Scalar-Tensor Boson Stars: Equilibrium, Stability and Evolution

We study charged boson stars in scalar-tensor (ST) gravitational theories. We analyse the weak field limit of the solutions and analytically show that there is a maximum charge to mass ratio for the bosons above which the weak field solutions are not stable. This charge limit can be greater than the GR limit for a wide class of ST theories. We numerically investigate strong field solutions in both the Brans Dicke and power law ST theories. We find that the charge limit decreases with increasing central boson density. We discuss the gravitational evolution of charged and uncharged boson stars in a cosmological setting and show how, at any point in its evolution, the physical properties of the star may be calculated by a rescaling of a solution whose asymptotic value of the scalar field is equal to its initial asymptotic value. We focus on evolution in which the particle number of the star is conserved and we find that the energy and central density of the star decreases as the cosmological time increases. We also analyse the appearance of the scalarization phenomenon recently discovered for neutron stars configurations and, finally, we give a short discussion on how making the correct choice of mass influences the argument over which conformal frame, the Einstein frame or the Jordan frame, is physical.Comment: RevTeX, 27 pages, 9 postscript figures. Minor revisions and updated references. Accepted for publication in Phys. Rev.

A Suborbital Payload for Soft X-ray Spectroscopy of Extended Sources

We present a suborbital rocket payload capable of performing soft X-ray spectroscopy on extended sources. The payload can reach resolutions of ~100(lambda/dlambda) over sources as large as 3.25 degrees in diameter in the 17-107 angstrom bandpass. This permits analysis of the overall energy balance of nearby supernova remnants and the detailed nature of the diffuse soft X-ray background. The main components of the instrument are: wire grid collimators, off-plane grating arrays and gaseous electron multiplier detectors. This payload is adaptable to longer duration orbital rockets given its comparatively simple pointing and telemetry requirements and an abundance of potential science targets.Comment: Accepted to Experimental Astronomy, 12 pages plus 1 table and 17 figure