23,461 research outputs found
High-resolution 3D weld toe stress analysis and ACPD method for weld toe fatigue crack initiation
Weld toe fatigue crack initiation is highly dependent on the local weld toe stress-concentrating geometry including any inherent flaws. These flaws are responsible for premature fatigue crack initiation (FCI) and must be minimised to maximise the fatigue life of a welded joint. In this work, a data-rich methodology has been developed to capture the true weld toe geometry and resulting local weld toe stress-field and relate this to the FCI life of a steel arc-welded joint. To obtain FCI lives, interrupted fatigue test was performed on the welded joint monitored by a novel multi-probe array of alternating current potential drop (ACPD) probes across the weld toe. This setup enabled the FCI sites to be located and the FCI life to be determined and gave an indication of early fatigue crack propagation rates. To understand fully the local weld toe stress-field, high-resolution (5 mu m) 3D linear-elastic finite element (FE) models were generated from X-ray micro-computed tomography (mu-CT) of each weld toe after fatigue testing. From these models, approximately 202 stress concentration factors (SCFs) were computed for every 1 mm of weld toe. These two novel methodologies successfully link to provide an assessment of the weld quality and this is correlated with the fatigue performance
Strong-coupling asymptotic expansion for Schr\"odinger operators with a singular interaction supported by a curve in
We investigate a class of generalized Schr\"{o}dinger operators in
with a singular interaction supported by a smooth curve
. We find a strong-coupling asymptotic expansion of the discrete
spectrum in case when is a loop or an infinite bent curve which is
asymptotically straight. It is given in terms of an auxiliary one-dimensional
Schr\"{o}dinger operator with a potential determined by the curvature of
. In the same way we obtain an asymptotics of spectral bands for a
periodic curve. In particular, the spectrum is shown to have open gaps in this
case if is not a straight line and the singular interaction is strong
enough.Comment: LaTeX 2e, 30 pages; minor improvements, to appear in Rev. Math. Phy
Scattering by local deformations of a straight leaky wire
We consider a model of a leaky quantum wire with the Hamiltonian in , where is a compact
deformation of a straight line. The existence of wave operators is proven and
the S-matrix is found for the negative part of the spectrum. Moreover, we
conjecture that the scattering at negative energies becomes asymptotically
purely one-dimensional, being determined by the local geometry in the leading
order, if is a smooth curve and .Comment: Latex2e, 15 page
Jahn-Teller effect versus Hund's rule coupling in C60N-
We propose variational states for the ground state and the low-energy
collective rotator excitations in negatively charged C60N- ions (N=1...5). The
approach includes the linear electron-phonon coupling and the Coulomb
interaction on the same level. The electron-phonon coupling is treated within
the effective mode approximation (EMA) which yields the linear t_{1u} x H_g
Jahn-Teller problem whereas the Coulomb interaction gives rise to Hund's rule
coupling for N=2,3,4. The Hamiltonian has accidental SO(3) symmetry which
allows an elegant formulation in terms of angular momenta. Trial states are
constructed from coherent states and using projection operators onto angular
momentum subspaces which results in good variational states for the complete
parameter range. The evaluation of the corresponding energies is to a large
extent analytical. We use the approach for a detailed analysis of the
competition between Jahn-Teller effect and Hund's rule coupling, which
determines the spin state for N=2,3,4. We calculate the low-spin/high-spin gap
for N=2,3,4 as a function of the Hund's rule coupling constant J. We find that
the experimentally measured gaps suggest a coupling constant in the range
J=60-80meV. Using a finite value for J, we recalculate the ground state
energies of the C60N- ions and find that the Jahn-Teller energy gain is partly
counterbalanced by the Hund's rule coupling. In particular, the ground state
energies for N=2,3,4 are almost equal
Magnetic transport in a straight parabolic channel
We study a charged two-dimensional particle confined to a straight
parabolic-potential channel and exposed to a homogeneous magnetic field under
influence of a potential perturbation . If is bounded and periodic along
the channel, a perturbative argument yields the absolute continuity of the
bottom of the spectrum. We show it can have any finite number of open gaps
provided the confining potential is sufficiently strong. However, if
depends on the periodic variable only, we prove by Thomas argument that the
whole spectrum is absolutely continuous, irrespectively of the size of the
perturbation. On the other hand, if is small and satisfies a weak
localization condition in the the longitudinal direction, we prove by Mourre
method that a part of the absolutely continuous spectrum persists
Scattering through a straight quantum waveguide with combined boundary conditions
Scattering through a straight two-dimensional quantum waveguide Rx(0,d) with
Dirichlet boundary conditions on (-\infty,0)x{y=0} \cup (0,\infty)x{y=d} and
Neumann boundary condition on (-infty,0)x{y=d} \cup (0,\infty)x{y=0} is
considered using stationary scattering theory. The existence of a matching
conditions solution at x=0 is proved. The use of stationary scattering theory
is justified showing its relation to the wave packets motion. As an
illustration, the matching conditions are also solved numerically and the
transition probabilities are shown.Comment: 26 pages, 3 figure
Schroedinger operators with singular interactions: a model of tunneling resonances
We discuss a generalized Schr\"odinger operator in , with an attractive singular interaction supported by a
-dimensional hyperplane and a finite family of points. It can be
regarded as a model of a leaky quantum wire and a family of quantum dots if
, or surface waves in presence of a finite number of impurities if .
We analyze the discrete spectrum, and furthermore, we show that the resonance
problem in this setting can be explicitly solved; by Birman-Schwinger method it
is cast into a form similar to the Friedrichs model.Comment: LaTeX2e, 34 page
Unification of Dynamical Decoupling and the Quantum Zeno Effect
We unify the quantum Zeno effect (QZE) and the "bang-bang" (BB) decoupling
method for suppressing decoherence in open quantum systems: in both cases
strong coupling to an external system or apparatus induces a dynamical
superselection rule that partitions the open system's Hilbert space into
quantum Zeno subspaces. Our unification makes use of von Neumann's ergodic
theorem and avoids making any of the symmetry assumptions usually made in
discussions of BB. Thus we are able to generalize BB to arbitrary fast and
strong pulse sequences, requiring no symmetry, and to show the existence of two
alternatives to pulsed BB: continuous decoupling, and pulsed measurements. Our
unified treatment enables us to derive limits on the efficacy of the BB method:
we explicitly show that the inverse QZE implies that BB can in some cases
accelerate, rather than inhibit, decoherence.Comment: 6 pages. To appear in Phys. Rev.
Quantization of Dirac fields in static spacetime
On a static spacetime, the solutions of the Dirac equation are generated by a
time-independent Hamiltonian. We study this Hamiltonian and characterize the
split into positive and negative energy. We use it to find explicit expressions
for advanced and retarded fundamental solutions and for the propagator.
Finally, we use a fermion Fock space based on the positive/negative energy
split to define a Dirac quantum field operator whose commutator is the
propagator.Comment: LaTex2e, 17 page
Pseudospectra in non-Hermitian quantum mechanics
We propose giving the mathematical concept of the pseudospectrum a central
role in quantum mechanics with non-Hermitian operators. We relate
pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint
operators, and basis properties of eigenfunctions. The abstract results are
illustrated by unexpected wild properties of operators familiar from
PT-symmetric quantum mechanics.Comment: version accepted for publication in J. Math. Phys.: criterion
excluding basis property (Proposition 6) added, unbounded time-evolution
discussed, new reference
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