Error analysis of QR algorithms for computing Lyapunov exponents

Lyapunov exponents give valuable information about long term dynamics. The discrete and continuous QR algorithms are widely used numerical techniques for computing approximate Lyapunov exponents, although they are not yet supported by a general error analysis. Here, a rigorous convergence theory is developed for both the discrete and continuous QR algorithm applied to a constant coefficient linear system with real distinct eigenvalues. For the discrete QR algorithm, the problem essentially reduces to one of linear algebra for which the timestepping and linear algebra errors uncouple and precise convergence rates are obtained. For the continuous QR algorithm, the stability, rather than the local accuracy, of the timestepping algorithm is relevant, and hence the overall convergence rate is independent of the stepsize. In this case it is vital to use a timestepping method that preserves orthogonality in the ODE system. We give numerical results to illustrate the analysis. Further numerical experiments and a heuristic argument suggest that the convergence properties carry through to the case of complex conjugate eigenvalue pairs

Vegetation classification in a floristically complex area: the Agulhas Plain

The vegetation of the Agulhas Plain was classified and described using Campbell’s (1985) approach. Data collected included a subset of Campbell’s structural and higher taxon characters, as well as dominant (10% cover) species, which would enable the recognition of communities to at least the sub-series level in his hierarchy. The classification was produced using the Braun–Blanquet method of table sorting. Nine zonal communities, at various hierarchical levels, were recognized and mapped. Non-fynbos communities included Forest & Thicket, and Renoster Shrubland. Fynbos communities, which covered most of the study area, were Mesotrophic Asteraceous Fynbos, Dune Asteraceous Fynbos, Dry Restioid Fynbos, Protea repens Proteoid Fynbos, Protea obtusifolia–Leucadendron meridianum/P. susannae–L. coniferum Proteoid Fynbos, L. platyspermum–P. compacta–L. xanthoconus Proteoid Fynbos and Mesic Ericaceous Fynbos. It was not possible to classify Forest & Thicket below the group level while a new concept (Dune Asteraceous Fynbos) was developed at the sub-series level. In all other respects the largely lowland vegetation of the Agulhas Plain could be integrated with Campbell’s Fynbos Biome mountain vegetation concepts. This study therefore demolished any justification for retaining a lowland fynbos vegetation concept. Since we utilized the skills of a number of trained botanists in collecting easily recognizable structural, and limited floristic data, the entire study was completed in under 18months. The mapped communities are adequate for conservation planning and comprise an essential descriptive basis for future studies on the evolution and maintenance of species diversity on the Agulhas Plain. The efficiency and effectiveness of our approach makes it suitable as a model for rapid vegetation classification of the much-threatened vegetation of the fynbos biome lowlands

Growth of Inflaton Perturbations and the Post-Inflation Era in Supersymmetric Hybrid Inflation Models

It has been shown that hybrid inflation may end with the formation of non-topological solitons of inflaton field. As a first step towards a fully realistic picture of the post-inflation era and reheating in supersymmetric hybrid inflation models, we study the classical scalar field equations of a supersymmetric hybrid inflation model using a semi-analytical ansatz for the spatial dependence of the fields. Using the minimal D-term inflation model as an example, the inflaton field is evolved using the full 1-loop effective potential from the slow-rolling era to the U(1)_{FI} symmetry-breaking phase transition. Spatial perturbations of the inflaton corresponding to quantum fluctuations are introduced for the case where there is spatially coherent U(1)_{FI} symmetry breaking. The maximal growth of the dominant perturbation is found to depend only on the ratio of superpotential coupling \lambda to the gauge coupling g. The inflaton condensate fragments to non-topological solitons for \lambda/g > 0.09. Possible consequences of non-topological soliton formation in fully realistic SUSY hybrid inflation models are discussed.Comment: 27 pages LaTeX, 8 figures. Additional references and discussio

Late Pleistocene-Holocene alluvial stratigraphy of southern Baja California, Mexico

A late Pleistocene to Holocene alluvial stratigraphy has been established for the basins of La Paz and San José del Cabo, in the southern tip of the Baja California peninsula, Mexico. Six discrete alluvial units (Qt1 through Qt6) were differentiated across the region using a combination of geomorphologic mapping, sedimentological analysis, and soil development. These criteria were supported using radiocarbon, optically stimulated luminescence and cosmogenic depth-profile geochronology. Major aggradation started shortly after ∼70 ka (Qt2), and buildup of the main depositional units ended at ∼10 ka (Qt4). After deposition of Qt4, increasing regional incision of older units and the progressive development of a channelized alluvial landscape coincide with deposition of Qt5 and Qt6 units in a second, incisional phase. All units consist of multiple 1–3 m thick alluvial packages deposited as upper-flow stage beds that represent individual storms. Main aggradational units (Qt2-Qt4) occurred across broad (>2 km) channels in the form of sheetflood deposition while incisional stage deposits are confined to channels of ∼0.5–2 km width. Continuous deposition inside the thicker (>10 m) pre-Qt5 units is demonstrated by closely spaced dates in vertical profiles. In a few places, disconformities between these major units are nevertheless evident and indicated by partly eroded buried soils. The described units feature sedimentological traits similar to historical deposits formed by large tropical cyclone events, but also include characteristics of upper-regime flow sedimentation not shown by historical sediments, like long (>10 m) wavelength antidunes and transverse ribs. We interpret the whole sequence as indicating discrete periods during the late Pleistocene and Holocene when climatic conditions allowed larger and more frequent tropical cyclone events than those observed historically. These discrete periods are associated with times when insolation at the tropics was higher than the present-day conditions, determined by precessional cycles, and modulated by the presence of El Niño-like conditions along the tropical and northeastern Pacific. The southern Baja California alluvial record is the first to document a precession-driven alluvial chronology for the region, and it constitutes a strong benchmark for discrimination of direct tropical influence on any other alluvial record in southwestern North America

Numerical study of scars in a chaotic billiard

We study numerically the scaling properties of scars in stadium billiard. Using the semiclassical criterion, we have searched systematically the scars of the same type through a very wide range, from ground state to as high as the 1 millionth state. We have analyzed the integrated probability density along the periodic orbit. The numerical results confirm that the average intensity of certain types of scars is independent of $\hbar$ rather than scales with $\sqrt{\hbar}$. Our findings confirm the theoretical predictions of Robnik (1989).Comment: 7 pages in Revtex 3.1, 5 PS figures available upon request. To appear in Phys. Rev. E, Vol. 55, No. 5, 199

Supergravity Inflation on the Brane

We study N=1 Supergravity inflation in the context of the braneworld scenario. Particular attention is paid to the problem of the onset of inflation at sub-Planckian field values and the ensued inflationary observables. We find that the so-called $\eta$-problem encountered in supergravity inspired inflationary models can be solved in the context of the braneworld scenario, for some range of the parameters involved. Furthermore, we obtain an upper bound on the scale of the fifth dimension, M_5 \lsim 10^{-3} M_P, in case the inflationary potential is quadratic in the inflaton field, $\phi$. If the inflationary potential is cubic in $\phi$, consistency with observational data requires that $M_5 \simeq 9.2 \times 10^{-4} M_P$.Comment: 6 pages, 1 figure, to appear in Phys. Rev.

Large and Almost Maximal Neutrino Mixing within the Type II See-Saw Mechanism

Within the type II see-saw mechanism the light neutrino mass matrix is given by a sum of a direct (or triplet) mass term and the conventional (type I) see-saw term. Both versions of the see-saw mechanism explain naturally small neutrino masses, but the type II scenario offers interesting additional possibilities to explain large or almost maximal or vanishing mixings which are discussed in this paper. We first introduce ``type II enhancement'' of neutrino mixing, where moderate cancellations between the two terms can lead to large neutrino mixing even if all individual mass matrices and terms generate small mixing. However, nearly maximal or vanishing mixings are not naturally explained in this way, unless there is a certain initial structure (symmetry) which enforces certain elements of the matrices to be identical or related in a special way. We therefore assume that the leading structure of the neutrino mass matrix is the triplet term and corresponds to zero U_{e3} and maximal theta_{23}. Small but necessary corrections are generated by the conventional see-saw term. Then we assume that one of the two terms corresponds to an extreme mixing scenario, such as bimaximal or tri-bimaximal mixing. Deviations from this scheme are introduced by the second term. One can mimic Quark-Lepton Complementarity in this way. Finally, we note that the neutrino mass matrix for tri-bimaximal mixing can be -- depending on the mass hierarchy -- written as a sum of two terms with simple structure. Their origin could be the two terms of type II see-saw.Comment: 25 pages. Comments and references added, to appear in JHE

Electroweak phase diagram at finite lepton number density

We study the thermodynamics of the electroweak theory at a finite lepton number density. The phase diagram of the theory is calculated by relating the full 4-dimensional theory to a 3-dimensional effective theory which has been previously solved using nonperturbative methods. It is seen that the critical temperature increases and the value of the Higgs boson mass at which the first order phase transition line ends decreases with increasing leptonic chemical potential.Comment: 16 pages, 14 figures, RevTex4, v2: references added, minor corrections, v3: small changes, references added, published in Phys. Rev.

Impact of cooking on vitamin D-3 and 25(OH)D-3 content of pork products

Publication history: Accepted - 29 July 2022; Published online - 2 August 2022Little is known regarding the impact of cooking on vitamin D content in pork, despite meat being a major contributor to vitamin D intakes. This paper investigated the effect of household cooking (pan-fry/roast/grill/sous-vide/sauté), on the vitamin D3 and 25-hydroxyvitamin D3 (25(OH)D3) concentration/retention in pork loin, mince and sausages. We hypothesised that vitamin D concentrations would be higher in cooked vs raw pork, and retention would differ between products. Cooking significantly increased vitamin D3 (+49 %) and 25(OH)D3 (+33 %) concentrations. All cooked loin vitamin D3 concentrations were significantly lower than mince/sausage. Vitamin D3 retention was > 100 % for all samples (102–135 %), except sauté mince (99 %) which still did not differ significantly from 100 % retention. Sous-vide cooking resulted in the highest vitamin D3 retention (135 %). Likely owing to water/fat loss, household cooking of pork results in favourable retention of vitamin D3 and 25(OH)D3. The type of pork product has greater influence than cooking method.This work was funded as part of a Department for the Economy (DfE; Northern Ireland) Co-operative Awards in Science and Technology (CAST) PhD studentship, supported by Devenish Nutrition Limited

A Curvature Principle for the interaction between universes

We propose a Curvature Principle to describe the dynamics of interacting universes in a multi-universe scenario and show, in the context of a simplified model, how interaction drives the cosmological constant of one of the universes toward a vanishingly small value. We also conjecture on how the proposed Curvature Principle suggests a solution for the entropy paradox of a universe where the cosmological constant vanishes.Comment: Essay selected for an honorable mention by the Gravity Research Foundation, 2007. Plain latex, 8 page