11,434 research outputs found
Galerkin and Runge–Kutta methods: unified formulation, a posteriori error estimates and nodal superconvergence
Abstract. We unify the formulation and analysis of Galerkin and Runge–Kutta methods for the time discretization of parabolic equations. This, together with the concept of reconstruction of the approximate solutions, allows us to establish a posteriori superconvergence estimates for the error at the nodes for all methods. 1
Conserved Matter Superenergy Currents for Orthogonally Transitive Abelian G2 Isometry Groups
In a previous paper we showed that the electromagnetic superenergy tensor,
the Chevreton tensor, gives rise to a conserved current when there is a
hypersurface orthogonal Killing vector present. In addition, the current is
proportional to the Killing vector. The aim of this paper is to extend this
result to the case when we have a two-parameter Abelian isometry group that
acts orthogonally transitive on non-null surfaces. It is shown that for
four-dimensional Einstein-Maxwell theory with a source-free electromagnetic
field, the corresponding superenergy currents lie in the orbits of the group
and are conserved. A similar result is also shown to hold for the trace of the
Chevreton tensor and for the Bach tensor, and also in Einstein-Klein-Gordon
theory for the superenergy of the scalar field. This links up well with the
fact that the Bel tensor has these properties and the possibility of
constructing conserved mixed currents between the gravitational field and the
matter fields.Comment: 15 page
Quaternionic Hyperbolic Function Theory
We are studying hyperbolic function theory in the skew-field of quaternions. This theory is connected to k-hyperbolic harmonic functions that are harmonic with respect to the hyperbolic Riemannian metric (Formula Presented) in the upper half space (Formula Presented). In the case k = 2, the metric is the hyperbolic metric of the Poincaré upper half-space. Hempfling and Leutwiler started to study this case and noticed that the quaternionic power function xm(m ε Z), is a conjugate gradient of a 2-hyperbolic harmonic function. They researched polynomial solutions. We find fundamental k-hyperbolic harmonic functions depending only on the hyperbolic distance and x3. Using these functions we are able to verify a Cauchy type integral formula. Earlier these results have been verified for quaternionic functions depending only on reduced variables (x0, x1, x2). Our functions are depending on four variables. © Springer Nature Switzerland AG 2019.Peer reviewe
The effect of multiple paternity on genetic diversity during and after colonisation
In metapopulations, genetic variation of local populations is influenced by
the genetic content of the founders, and of migrants following establishment.
We analyse the effect of multiple paternity on genetic diversity using a model
in which the highly promiscuous marine snail Littorina saxatilis expands from a
mainland to colonise initially empty islands of an archipelago. Migrant females
carry a large number of eggs fertilised by 1 - 10 mates. We quantify the
genetic diversity of the population in terms of its heterozygosity: initially
during the transient colonisation process, and at long times when the
population has reached an equilibrium state with migration. During
colonisation, multiple paternity increases the heterozygosity by 10 - 300 % in
comparison with the case of single paternity. The equilibrium state, by
contrast, is less strongly affected: multiple paternity gives rise to 10 - 50 %
higher heterozygosity compared with single paternity. Further we find that far
from the mainland, new mutations spreading from the mainland cause bursts of
high genetic diversity separated by long periods of low diversity. This effect
is boosted by multiple paternity. We conclude that multiple paternity
facilitates colonisation and maintenance of small populations, whether or not
this is the main cause for the evolution of extreme promiscuity in Littorina
saxatilis.Comment: 7 pages, 5 figures, electronic supplementary materia
Commentary : Disentangling the contributions of childhood and adult weight to cardiovascular disease risk
Non peer reviewe
Adsorption of Cu, Ag, and Au atoms on graphene including van der Waals interactions
We performed a systematic density functional study of the adsorption of
copper, silver, and gold adatoms on graphene, especially accounting for van der
Waals interactions by the vdW-DF and the PBE+D2 methods. In particular, we
analyze the preferred adsorption site (among top, bridge, and hollow positions)
together with the corresponding distortion of the graphene sheet and identify
diffusion paths. Both vdW schemes show that the coinage metal atoms do bind to
the graphene sheet and that in some cases the buckling of the graphene can be
significant. The results for silver are at variance with those obtained with
GGA, which gives no binding in this case. However, we observe some quantitative
differences between the vdW-DF and the PBE+D2 methods. For instance the
adsorption energies calculated with the PBE+D2 method are systematically higher
than the ones obtained with vdW-DF. Moreover, the equilibrium distances
computed with PBE+D2 are shorter than those calculated with the vdW-DF method
Single-electron quantum dot in Si/SiGe with integrated charge-sensing
Single-electron occupation is an essential component to measurement and
manipulation of spin in quantum dots, capabilities that are important for
quantum information processing. Si/SiGe is of interest for semiconductor spin
qubits, but single-electron quantum dots have not yet been achieved in this
system. We report the fabrication and measurement of a top-gated quantum dot
occupied by a single electron in a Si/SiGe heterostructure. Transport through
the quantum dot is directly correlated with charge-sensing from an integrated
quantum point contact, and this charge-sensing is used to confirm
single-electron occupancy in the quantum dot.Comment: 3 pages, 3 figures, accepted version, to appear in Applied Physics
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