64 research outputs found
Effective order strong stability preserving RungeâKutta methods
We apply the concept of effective order to strong stability preserving (SSP) explicit RungeâKutta methods. Relative to classical RungeâKutta methods, effective order methods are designed to satisfy a relaxed set of order conditions, but yield higher order accuracy when composed with special starting and stopping methods. The relaxed order conditions allow for greater freedom in the design of effective order methods. We show that this allows the construction of four-stage SSP methods with effective order four (such methods cannot have classical order four). However, we also prove that effective order five methodsâlike classical order five methodsârequire the use of non-positive weights and so cannot be SSP. By numerical optimization, we construct explicit SSP RungeâKutta methods up to effective order four and establish the optimality of many of them. Numerical experiments demonstrate the validity of these methods in practice
Strong stability preserving explicit linear multistep methods with variable step size
Strong stability preserving (SSP) methods are designed primarily for time integration of nonlinear hyperbolic PDEs, for which the permissible SSP step size varies from one step to the next. We develop the first SSP linear multistep methods (of order two and three) with variable step size, and prove their optimality, stability, and convergence. The choice of step size for multistep SSP methods is an interesting problem because the allowable step size depends on the SSP coefficient, which in turn depends on the chosen step sizes. The description of the methods includes an optimal step-size strategy. We prove sharp upper bounds on the allowable step size for explicit SSP linear multistep methods and show the existence of methods with arbitrarily high order of accuracy. The effectiveness of the methods is demonstrated through numerical examples
Metalâferroelectric supercrystals with periodically curved metallic layers
Simultaneous manipulation of multiple boundary conditions in nanoscale heterostructures offers a versatile route to stabilizing unusual structures and emergent phases. Here, we show that a stable supercrystal phase comprising a three-dimensional ordering of nanoscale domains with tailored periodicities can be engineered in PbTiO3âSrRuO3 ferroelectricâmetal superlattices. A combination of laboratory and synchrotron X-ray diffraction, piezoresponse force microscopy, scanning transmission electron microscopy and phase-field simulations reveals a complex hierarchical domain structure that forms to minimize the elastic and electrostatic energy. Large local deformations of the ferroelectric lattice are accommodated by periodic lattice modulations of the metallic SrRuO3 layers with curvatures up to 107âmâ1. Our results show that multidomain ferroelectric systems can be exploited as versatile templates to induce large curvatures in correlated materials, and present a route for engineering correlated materials with modulated structural and electronic properties that can be controlled using electric fields
Charge Symmetry Breaking in 500 MeV Nucleon-Trinucleon Scattering
Elastic nucleon scattering from the 3He and 3H mirror nuclei is examined as a
test of charge symmetry violation. The differential cross-sections are
calculated at 500 MeV using a microsopic, momentum-space optical potential
including the full coupling of two spin 1/2 particles and an exact treatment of
the Coulomb force. The charge-symmetry-breaking effects investigated arise from
a violation within the nuclear structure, from the p-nucleus Coulomb force, and
from the mass-differences of the charge symmetric states. Measurements likely
to reveal reliable information are noted.Comment: 5 page
Nuclear muon capture by 3He: meson exchange currents for the triton channel
Exchange current corrections are calculated using currents found from the
hard-pion model and AV14+3BF wavefunctions. Results are given for the rate and
spin observables. Their sensitivity to g_P, the nucleon pseudoscalar form
factor, is reported.Comment: 35 pages, uuencoded gz-compressed tar file 42 Kbyte
Intrinsic magnetism in superconducting infinite-layer nickelates
The discovery of superconductivity in NdSrNiO [1]
introduced a new family of layered nickelate superconductors that has now been
extended to include a range of Sr-doping [2, 3], Pr or La in place of Nd [4-6],
and the 5-layer NdNiO [7]. A number of studies indicate that
electron correlations are strong in these materials [8-14], and hence a central
question is whether or not magnetism is present as a consequence of these
interactions. Here we report muon spin rotation/relaxation studies of a series
of superconducting infinite-layer nickelates. In all cases we observe an
intrinsic magnetic ground state, regardless of the rare earth ion or doping,
arising from local moments on the nickel sublattice. The coexistence of
magnetism - which is likely to be antiferromagnetic and short-range ordered -
with superconductivity is reminiscent of some iron pnictides [15] and heavy
fermion compounds [16], and qualitatively distinct from the doped cuprates
[17]
Quark-model study of few-baryon systems
We review the application of non-relativistic constituent quark models to
study one, two and three non-strange baryon systems. We present results for the
baryon spectra, potentials and observables of the NN, N,
and NN systems, and also for the binding energies of three
non-strange baryon systems. We make emphasis on observable effects related to
quark antisymmetry and its interplay with quark dynamics.Comment: 82 pages, 36 figures, 18 tables. Accepted for publication in Reports
on Progress in Physic
Validation of patient determined disease steps (PDDS) scale scores in persons with multiple sclerosis
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