408 research outputs found
Graded extension of SO(2,1) Lie algebra and the search for exact solutions of Dirac equation by point canonical transformations
SO(2,1) is the symmetry algebra for a class of three-parameter problems that
includes the oscillator, Coulomb and Morse potentials as well as other problems
at zero energy. All of the potentials in this class can be mapped into the
oscillator potential by point canonical transformations. We call this class the
"oscillator class". A nontrivial graded extension of SO(2,1) is defined and its
realization by two-dimensional matrices of differential operators acting in
spinor space is given. It turns out that this graded algebra is the
supersymmetry algebra for a class of relativistic potentials that includes the
Dirac-Oscillator, Dirac-Coulomb and Dirac-Morse potentials. This class is, in
fact, the relativistic extension of the oscillator class. A new point canonical
transformation, which is compatible with the relativistic problem, is
formulated. It maps all of these relativistic potentials into the
Dirac-Oscillator potential.Comment: Replaced with a more potrable PDF versio
Terrestrial temperature evolution of southern Africa during the late Pleistocene and Holocene:Evidence from the Mfabeni Peatland
The scarcity of suitable high-resolution archives, such as ancient natural lakes, that span beyond the Holocene, hinders long-term late Quaternary temperature reconstructions in southern Africa. Here we target two cores from Mfabeni Peatland, one of the few long continuous terrestrial archives in South Africa that reaches into the Pleistocene, to generate a composite temperature record spanning the last ∼43 kyr. The Mfabeni Peatland has previously been proven suitable for temperature and hydrological reconstructions based on pollen and geochemical proxies. Here we use branched glycerol dialkyl glycerol tetraethers (brGDGTs) preserved in the Mfabeni peatland to derive a new quantitative air temperature record for south-east Africa. Our temperature record generally follows global trends in temperature and atmospheric CO2 concentrations, but is decoupled at times. Annual air temperatures during Marine Isotope Stage (MIS) 3 were moderately high (c. 20.5 °C), but dropped by c. 5 °C during the Last Glacial Maximum, reaching a minimum at c.16–15 ka. Asynchronous with local insolation, this cooling may have resulted from reduced sea surface temperatures linked to a northward shift in the Southern Hemisphere westerly winds. Concurrent with the southward retreat of the westerlies, and increasing sea surface temperatures offshore, warming from minimum temperatures (c. 15.0 °C) to average Holocene temperatures (c. 20.0 °C) occurred across the deglaciation. This warming was briefly but prominently interrupted by a millennial-scale cooling event of c. 3 °C at c. 2.4 ka, concurrent with a sudden change in hydrological conditions. The average Holocene temperatures of c. 20.0 °C were similar to those reconstructed for MIS 3, but after the 2.4 ka cooling period, air temperatures in the Mfabeni peat recovered and steadily increased towards the present. In summary, our record demonstrates that land temperature in eastern South Africa is highly sensitive to global drivers as well as nearby sea surface temperatures
L2 series solutions of the Dirac equation for power-law potentials at rest mass energy
We obtain solutions of the three dimensional Dirac equation for radial
power-law potentials at rest mass energy as an infinite series of square
integrable functions. These are written in terms of the confluent
hypergeometric function and chosen such that the matrix representation of the
Dirac operator is tridiagonal. The "wave equation" results in a three-term
recursion relation for the expansion coefficients of the spinor wavefunction
which is solved in terms of orthogonal polynomials. These are modified versions
of the Meixner-Pollaczek polynomials and of the continuous dual Hahn
polynomials. The choice depends on the values of the angular momentum and the
power of the potential.Comment: 13 pages, 1 Tabl
Resolving the backbone tilt of crystalline poly(3-hexylthiophene) with resonant tender X-ray diffraction
The way in which conjugated polymers pack in the solid state strongly affects the performance of polymer-based optoelectronic devices. However, even for the most crystalline conjugated polymers the precise packing of chains within the unit cell is not well established. Here we show that by performing resonant X-ray diffraction experiments at the sulfur K-edge we are able to resolve the tilting of the planar backbones of crystalline poly(3-hexylthiophene) (P3HT) within the unit cell. This approach exploits the anisotropic nature of the X-ray optical properties of conjugated polymers, enabling us to discern between different proposed crystal structures. By comparing our data with simulations based on different orientations, a tilting of the planar conjugated backbone with respect to the side chain stacking direction of 30 ± 5° is determined
Fundamental genomic unity of ethnic India is revealed by analysis of mitochondrial DNA
Mitochondrial DNA (mtDNA) profiles of 23 ethnic populations of India drawn from diverse cultural, linguistic and geographical backgrounds are presented. There is extensive sharing of a small number of mtDNA haplotypes, reconstructed on the basis of restriction fragment length polymorphisms, among the populations. This indicates that Indian populations were founded by a small number of females, possibly arriving on one of the early waves of out-of-Africa migration of modern humans; ethnic differentiation occurred subsequently through demographic expansions and geographic dispersal. The Asian-specific haplogroup M is in high frequency in most populations, especially tribal populations and Dravidian populations of southern India. Populations in which the frequencies of haplogroup M are relatively lower show higher frequencies of haplogroup U; such populations are primarily caste populations of northern India. This finding is indicative of a higher Caucasoid admixture in northern Indian populations. By examining the sharing of haplotypes between Indian and south-east Asian populations, we have provided evidence that south-east Asia was peopled by two waves of migration, one originating in India and the other originating in southern China. These findings have been examined and interpreted in the light of inferences derived from previous genomic and historical studies
A First Global Oceanic Compilation of Observational Dissolved Aluminum Data With Regional Statistical Data Treatment
Large national and international observational efforts over recent decades have provided extensive and invaluable datasets of a range of ocean variables. Compiled large datasets, structured, or unstructured, are a powerful tool that allow scientists to access and synthesize data collected over large spatial and temporal scales. The data treatment approaches for any element in the ocean could lead to new global perspectives of their distribution patterns and to a better understanding of large-scale oceanic processes and their impact on other biogeochemical cycles, which may not be evident otherwise. Ocean chemistry Big Data analysis may not just be limited to distribution patterns, but may be used to assess how sampling efforts and analytical methodologies can be improved. Furthermore, a systematic global scale assessment of data is important to evaluate the gaps in knowledge and to provide avenues for future research. In this context, here we provide an extensive compilation of oceanic aluminum (Al) concentration data from global ocean basins, including data available in the GEOTRACES Intermediate Data product (Schlitzer et al., 2018), but also thus far unpublished data
Inference of population splits and mixtures from genome-wide allele frequency data
Many aspects of the historical relationships between populations in a species
are reflected in genetic data. Inferring these relationships from genetic data,
however, remains a challenging task. In this paper, we present a statistical
model for inferring the patterns of population splits and mixtures in multiple
populations. In this model, the sampled populations in a species are related to
their common ancestor through a graph of ancestral populations. Using
genome-wide allele frequency data and a Gaussian approximation to genetic
drift, we infer the structure of this graph. We applied this method to a set of
55 human populations and a set of 82 dog breeds and wild canids. In both
species, we show that a simple bifurcating tree does not fully describe the
data; in contrast, we infer many migration events. While some of the migration
events that we find have been detected previously, many have not. For example,
in the human data we infer that Cambodians trace approximately 16% of their
ancestry to a population ancestral to other extant East Asian populations. In
the dog data, we infer that both the boxer and basenji trace a considerable
fraction of their ancestry (9% and 25%, respectively) to wolves subsequent to
domestication, and that East Asian toy breeds (the Shih Tzu and the Pekingese)
result from admixture between modern toy breeds and "ancient" Asian breeds.
Software implementing the model described here, called TreeMix, is available at
http://treemix.googlecode.comComment: 28 pages, 6 figures in main text. Attached supplement is 22 pages, 15
figures. This is an updated version of the preprint available at
http://precedings.nature.com/documents/6956/version/
A basis for variational calculations in d dimensions
In this paper we derive expressions for matrix elements (\phi_i,H\phi_j) for
the Hamiltonian H=-\Delta+\sum_q a(q)r^q in d > 1 dimensions.
The basis functions in each angular momentum subspace are of the form
phi_i(r)=r^{i+1+(t-d)/2}e^{-r^p/2}, i >= 0, p > 0, t > 0. The matrix elements
are given in terms of the Gamma function for all d. The significance of the
parameters t and p and scale s are discussed. Applications to a variety of
potentials are presented, including potentials with singular repulsive terms of
the form b/r^a, a,b > 0, perturbed Coulomb potentials -D/r + B r + Ar^2, and
potentials with weak repulsive terms, such as -g r^2 + r^4, g > 0.Comment: 22 page
South African research in the Southern Ocean: New opportunities but serious challenges
South Africa has a long track record in Southern Ocean and Antarctic research and has recently invested considerable funds in acquiring new infrastructure for ongoing support of this research. This infrastructure includes a new base at Marion Island and a purpose-built ice capable research vessel, which greatly expand research opportunities. Despite this investment, South Africa's standing as a participant in this critical field is threatened by confusion, lack of funding, lack of consultation and lack of transparency. The research endeavour is presently bedevilled by political manoeuvring among groups with divergent interests that too often have little to do with science, while past and present contributors of research are excluded from discussions that aim to formulate research strategy. This state of affairs is detrimental to the country's aims of developing a leadership role in climate change and Antarctic research and squanders both financial and human capital
Quantum Dynamical Algebra SU(1,1) in One-Dimensional Exactly Solvable Potentials
We mainly explore the linear algebraic structure like SU(2) or SU(1,1) of the
shift operators for some one-dimensional exactly solvable potentials in this
paper. During such process, a set of method based on original diagonalizing
technique is presented to construct those suitable operator elements, J0, J_\pm
that satisfy SU(2) or SU(1,1) algebra. At last, the similarity between radial
problem and one-dimensional potentials encourages us to deal with the radial
problem in the same way.Comment: No figures, 9 Pages accepted by International Journal of Theoretical
Physic
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