Object-oriented construction of a multigrid electronic-structure code with Fortran 90

We describe the object-oriented implementation of a higher-order finite-difference density-functional code in Fortran 90. Object-oriented models of grid and related objects are constructed and employed for the implementation of an efficient one-way multigrid method we have recently proposed for the density-functional electronic-structure calculations. Detailed analysis of performance and strategy of the one-way multigrid scheme will be presented.Comment: 24 pages, 6 figures, to appear in Comput. Phys. Com

Study of singular boundary value problems for second order impulsive differential equations

AbstractThis paper studies the existence of extremal solutions for a class of singular boundary value problems of second order impulsive differential equations. By using the method of upper and lower solutions and the monotone iterative technique, criteria of the existence of extremal solutions are established

Global bifurcation phenomena for singular one-dimensional p-Laplacian

AbstractIn this paper, we present global existence results for the following problem(Pλ){φp(u′(t))′+λh(t)f(u(t))=0,a.e. in(0,1),u(0)=u(1)=0, where φp(x)=|x|p−2x, p>1,λ a positive parameter and h a nonnegative measurable function on (0,1) which may be singular at t=0 and/or t=1, and f∈C(R+,R+) with R+=[0,∞). By applying the global bifurcation theorem and figuring the shape of unbounded subcontinua of solutions, we obtain many different types of global existence results of positive solutions. We also obtain existence results of sign-changing solutions for (Pλ) when f is an odd symmetric function

Stretching-induced conductance variations as fingerprints of contact configurations in single-molecule junctions

Molecule-electrode contact atomic structures are a critical factor that characterizes molecular devices, but their precise understanding and control still remain elusive. Based on combined first-principles calculations and single-molecule break junction experiments, we herein establish that the conductance of alkanedithiolate junctions can both increase and decrease with mechanical stretching and the specific trend is determined by the S-Au linkage coordination number (CN) or the molecule-electrode contact atomic structure. Specifically, we find that the mechanical pulling results in the conductance increase for the junctions based on S-Au CN two and CN three contacts, while the conductance is minimally affected by stretching for junctions with the CN one contact and decreases upon the formation of Au monoatomic chains. Detailed analysis unravels the mechanisms involving the competition between the stretching-induced upshift of the highest occupied molecular orbital-related states toward the Fermi level of electrodes and the deterioration of molecule-electrode electronic couplings in different contact CN cases. Moreover, we experimentally find a higher chance to observe the conductance enhancement mode under a faster elongation speed, which is explained by ab initio molecular dynamics simulations that reveal an important role of thermal fluctuations in aiding deformations of contacts into low-coordination configurations that include monoatomic Au chains. Pointing out the insufficiency in previous notions of associating peak values in conductance histograms with specific contact atomic structures, this work resolves the controversy on the origins of ubiquitous multiple conductance peaks in S-Au-based single-molecule junctions.Comment: 11 pages, 4 figures; to be published in J. Am. Chem. So

Superradiance in the Kerr-Taub-NUT spacetime

Superradiance is the effect of field waves being amplified during reflection from a charged or rotating black hole. In this paper, we study the low-energy dynamics of super-radiant scattering of massive scalar and massless higher spin field perturbations in a generic axisymmetric stationary Kerr-Taub-NUT (Newman-Unti-Tamburino) spacetime, which represents sources with both gravitomagnetic monopole moment (magnetic mass) and gravitomagnetic dipole moment (angular momentum). We obtain a generalized Teukolsky master equation for all spin perturbation fields. The equations are separated into their angular and radial parts. The angular equations lead to spin-weighted spheroidal harmonic functions that generalize those in Kerr spacetime. We identify an effective spin as a coupling between frequency (or energy) and the NUT parameter. The behaviors of the radial wave function near the horizon and at the infinite boundary are studied. We provide analytical expressions for low-energy observables such as emission rates and cross sections of all massless fields with spin, including scalar, neutrino, electromagnetic, Rarita-Schwinger, and gravitational waves.Comment: 42 pages, 2 figure