32,949 research outputs found
Difference Methods for Boundary Value Problems in Ordinary Differential Equations
A general theory of difference methods for problems of the form
Ny ≡ y' - f(t,y) = O, a ≦ t ≦ b, g(y(a),y(b))= 0,
is developed. On nonuniform nets, t_0 = a, t_j = t_(j-1) + h_j, 1 ≦ j ≦ J, t_J = b, schemes of the form
N_(h)u_j = G_j(u_0,•••,u_J) = 0, 1 ≦ j ≦ J, g(u_0,u_J) = 0
are considered. For linear problems with unique solutions, it is shown that the difference scheme is stable and consistent for the boundary value problem if and only if, upon replacing the boundary conditions by an initial condition, the resulting scheme is stable and consistent for the initial value problem. For isolated solutions of the nonlinear problem, it is shown that the difference scheme has a unique solution converging to the exact solution if (i) the linearized difference equations are stable and consistent for the linearized initial value problem, (ii) the linearized difference operator is Lipschitz continuous, (iii) the nonlinear difference equations are consistent with the nonlinear differential
equation. Newton’s method is shown to be valid, with quadratic convergence, for computing the numerical solution
Mechanisms of superconductivity investigated by nuclear radiation
Investigation focused on the behavior of superconducting magnet and its constituent materials during and after exposure to nuclear radiation. The results will indicate the feasibility of their use in diverse applications and various environments
Polaron Coherence as Origin of the Pseudogap Phase in High Temperature Superconducting Cuprates
Within a two component approach to high Tc copper oxides including polaronic
couplings, we identify the pseudogap phase as the onset of polaron ordering.
This ordering persists in the superconducting phase. A huge isotope effect on
the pseudogap onset temperature is predicted and in agreement with experimental
data. The anomalous temperature dependence of the mean square copper oxygen ion
displacement observed above, at and below Tc stems from an s-wave
superconducting component of the order parameter, whereas a pure d-wave order
parameter alone can be excluded.Comment: 7 pages, 2 figure
Oxygen-isotope effect on the superconducting gap in the cuprate superconductor Y_{1-x}Pr_xBa_2Cu_3O_{7-\delta}
The oxygen-isotope (^{16}O/^{18}O) effect (OIE) on the zero-temperature
superconducting energy gap \Delta_0 was studied for a series of
Y_{1-x}Pr_xBa_2Cu_3O_{7-\delta} samples (0.0\leq x\leq0.45). The OIE on
\Delta_0 was found to scale with the one on the superconducting transition
temperature. These experimental results are in quantitative agreement with
predictions from a polaronic model for cuprate high-temperature superconductors
and rule out approaches based on purely electronic mechanisms.Comment: 5 pages, 3 figure
Isotope effect on superconductivity in Josephson coupled stripes in underdoped cuprates
Inelastic neutron scattering data for YBaCuO as well as for LaSrCuO indicate
incommensurate neutron scattering peaks with incommensuration away
from the point. can be replotted as a linear function of
the incommensuration for these materials. This linear relation implies that the
constant that relates these two quantities, one being the incommensuration
(momentum) and another being (energy), has the dimension of velocity
we denote : . We argue that this
experimentally derived relation can be obtained in a simple model of Josephson
coupled stripes. Within this framework we address the role of the isotope effect on the . We assume that the incommensuration is
set by the {\em doping} of the sample and is not sensitive to the oxygen
isotope given the fixed doping. We find therefore that the only parameter that
can change with O isotope substitution in the relation
is the velocity . We predict an oxygen isotope effect on and expect
it to be .Comment: 4 pages latex file, 2 eps fig
^25Mg NMR study of the MgB_2 superconductor
^25Mg NMR spectra and nuclear spin-lattice relaxation time, T_1, have been
measured in polycrystalline ^25MgB_2 with a superconducting transition
temperature T_c = 39.0 K in zero magnetic field. From the first order and
second order quadrupole perturbed NMR spectrum a quadrupole coupling frequency
nu_Q = 222(1.5) kHz is obtained. T_1T = 1090(50) sK and Knight shift K_c =
242(4) ppm are temperature independent in the normal conducting phase. The
^25Mg Korringa ratio equals to 0.95 which is very close to the ideal value of
unity for s-electrons. The comparison of the experimental nu_Q, T_1T, and K_c
with the corresponding values obtained by LDA calculations shows an excellent
agreement for all three quantities.Comment: 4 pages including 4 eps-figures, revtex
Iron isotope effect on the superconducting transition temperature and the crystal structure of FeSe_1-x
The Fe isotope effect (Fe-IE) on the transition temperature T_c and the
crystal structure was studied in the Fe chalcogenide superconductor FeSe_1-x by
means of magnetization and neutron powder diffraction (NPD). The substitution
of natural Fe (containing \simeq 92% of ^{56}Fe) by its lighter ^{54}Fe isotope
leads to a shift of T_c of 0.22(5)K corresponding to an Fe-IE exponent of
\alpha_Fe=0.81(15). Simultaneously, a small structural change with isotope
substitution is observed by NDP which may contribute to the total Fe isotope
shift of T_c.Comment: 4 pages, 3 figure
Evolution of two-gap behavior of the superconductor FeSe_1-x
The superfluid density, \rho_s, of the iron chalcogenide superconductor,
FeSe_1-x, was studied as a function of pressure by means of muon-spin rotation.
The zero-temperature value of \rho_s increases with increasing transition
temperature T_c (increasing pressure) following the tendency observed for
various Fe-based and cuprate superconductors. The analysis of \rho_s(T) within
the two-gap scheme reveals that the effect on both, T_c and \rho_s(0), is
entirely determined by the band(s) where the large superconducting gap
develops, while the band(s) with the small gap become practically unaffected.Comment: 5 pages, 3 figure
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