2,340 research outputs found
Siegert pseudostates: completeness and time evolution
Within the theory of Siegert pseudostates, it is possible to accurately
calculate bound states and resonances. The energy continuum is replaced by a
discrete set of states. Many questions of interest in scattering theory can be
addressed within the framework of this formalism, thereby avoiding the need to
treat the energy continuum. For practical calculations it is important to know
whether a certain subset of Siegert pseudostates comprises a basis. This is a
nontrivial issue, because of the unusual orthogonality and overcompleteness
properties of Siegert pseudostates. Using analytical and numerical arguments,
it is shown that the subset of bound states and outgoing Siegert pseudostates
forms a basis. Time evolution in the context of Siegert pseudostates is also
investigated. From the Mittag-Leffler expansion of the outgoing-wave Green's
function, the time-dependent expansion of a wave packet in terms of Siegert
pseudostates is derived. In this expression, all Siegert pseudostates--bound,
antibound, outgoing, and incoming--are employed. Each of these evolves in time
in a nonexponential fashion. Numerical tests underline the accuracy of the
method
Theory of x-ray absorption by laser-dressed atoms
An ab initio theory is devised for the x-ray photoabsorption cross section of
atoms in the field of a moderately intense optical laser (800nm, 10^13 W/cm^2).
The laser dresses the core-excited atomic states, which introduces a dependence
of the cross section on the angle between the polarization vectors of the two
linearly polarized radiation sources. We use the Hartree-Fock-Slater
approximation to describe the atomic many-particle problem in conjunction with
a nonrelativistic quantum-electrodynamic approach to treat the photon-electron
interaction. The continuum wave functions of ejected electrons are treated with
a complex absorbing potential that is derived from smooth exterior complex
scaling. The solution to the two-color (x-ray plus laser) problem is discussed
in terms of a direct diagonalization of the complex symmetric matrix
representation of the Hamiltonian. Alternative treatments with time-independent
and time-dependent non-Hermitian perturbation theories are presented that
exploit the weak interaction strength between x rays and atoms. We apply the
theory to study the photoabsorption cross section of krypton atoms near the K
edge. A pronounced modification of the cross section is found in the presence
of the optical laser.Comment: 13 pages, 3 figures, 1 table, RevTeX4, corrected typoe
Topology optimization of geometrically nonlinear structures using an evolutionary optimization method
Iso-XFEM method is an evolutionary optimization method developed in our previous studies to enable the generation of high resolution topology optimised designs suitable for additive manufacture. Conventional approaches for topology optimization require additional post-processing after optimization to generate a manufacturable topology with clearly defined smooth boundaries. Iso-XFEM aims to eliminate this time-consuming post-processing stage by defining the boundaries using isovalues of a structural performance criterion and an extended finite element method (XFEM) scheme. In this paper, the Iso-XFEM method is further developed to enable the topology optimization of geometrically nonlinear structures undergoing large deformations. This is achieved by implementing a total Lagrangian finite element formulation and defining a structural performance criterion appropriate for the objective function of the optimization problem. The Iso-XFEM solutions for geometrically nonlinear test-cases implementing linear and nonlinear modelling are compared, and the suitability of nonlinear modelling for the topology optimization of geometrically nonlinear structures is investigated
Properties of metastable alkaline-earth-metal atoms calculated using an accurate effective core potential
The first three electronically excited states in the alkaline-earth-metal
atoms magnesium, calcium, and strontium comprise the (nsnp) triplet P^o_J
(J=0,1,2) fine-structure manifold. All three states are metastable and are of
interest for optical atomic clocks as well as for cold-collision physics. An
efficient technique--based on a physically motivated potential that models the
presence of the ionic core--is employed to solve the Schroedinger equation for
the two-electron valence shell. In this way, radiative lifetimes, laser-induced
clock shifts, and long-range interaction parameters are calculated for
metastable Mg, Ca, and Sr.Comment: 13 pages, 9 table
Influence of preload and nonlinearity of railpads on vibration of railway tracks under stationary and moving harmonic loads
In railway track dynamics, the stiffness and damping properties of railpads have a significant effect on track vibration, decay rates as well forces transmitted to the track supporting structure. Many studies have shown that railpads exhibit pronounced nonlinear behaviour, with preload and frequency dependent properties. This paper presents a three parameter railpad model, together with its differential equation of motion and the required model parameters obtained from experimental data. A time domain model of a rail discretely supported on these railpads is then formulated using the finite element method. The model is subjected to static and dynamic loading in order to study the effects of preload and frequency on its dynamic behaviour. Results are shown as time histories and frequency spectra for the track displacements and reaction forces for various preload levels. They emphasise the necessity of accounting for nonlinear behaviour based on the large disparities (up to 20 dB) observed between the linear and nonlinear cases for the parameters used in this study
Spin configurations in circular and rectangular vertical quantum dots in a magnetic field: Three-dimensional self-consistent simulation
The magnetic field dependence of the electronic properties of \textit{real}
single vertical quantum dots in circular and rectangular mesas is investigated
within a full three-dimensional multiscale self-consistent approach without any
{\it \'a priori} assumptions about the shape and strength of the confinement
potential. The calculated zero field electron addition energies are in good
agreement with available experimental data for both mesa geometries. Charging
diagrams in a magnetic field for number of electrons up to five are also
computed. Consistent with the experimental data, we found that the charging
curves for the rectangular mesa dot in a magnetic field are flatter and exhibit
less features than for a circular mesa dot. Evolution of the singlet-triplet
energy separation in the two electron system for both dot geometries in
magnetic field was also investigated. In the limit of large field, beyond the
singlet-triplet transition, the singlet-triplet energy difference continues to
become more negative in a circular mesa dot without any saturation within the
range of considered magnetic fields whilst it is predicted to asymptotically
approach zero for the rectangular mesa dot. This different behavior is
attributed to the symmetry "breaking" that occurs in the singlet wave-functions
in the rectangular mesa dot but not in the circular one.Comment: 12 pages, 8 gifure
Pseudo-dynamic method for structural analysis of automobile seats
This work describes the application of a pseudo-dynamic (PsD) method to the
dynamic analysis of passenger seats for the automotive industry. The project of such components
involves a structural test considering the action of dynamic forces arising from a
crash scenario. The laboratory certification of these automotive components consists essentially
on the inspection of the propagation and extension of plastic deformations zones in metallic
members of the seat structure as consequence of the mutual action between the seat and the
passenger fastened to the seat via seat belt anchorages. This work presents a relatively simple
experiment using PsD techniques as a novel method to performa test equivalent to the dynamic
model of a dummy-seat pair subjected to impulsive loads from a car crash.
Essentially, the PsD test method is a hybrid and hierarchic computer-driven testing procedure
where a numerical algorithm and experimental step are used and combined on-line in order to
solve a problem in the scope of structural dynamics. The implementation of the method is not
expensive and has the leading advantage of offering the operator a total control of any intermediate
structure state during the test still keeping the realism of a real dynamic testing.Project: NDT-AUTO Ref 13-02-2003-FDR-01281 (Agencia de Inovação
Development of Flutter Constraints for High-fidelity Aerostructural Optimization
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143080/1/6.2017-4455.pd
Mode tracking issues in structural optimization
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76633/1/AIAA-12747-342.pd
A Nonrigid Registration Method for Correcting Brain Deformation Induced by Tumor Resection
Purpose: This paper presents a nonrigid registration method to align preoperative MRI with intraoperative MRI to compensate for brain deformation during tumor resection. This method extends traditional point-based nonrigid registration in two aspects: (1) allow the input data to be incomplete and (2) simulate the underlying deformation with a heterogeneous biomechanical model.
Methods: The method formulates the registration as a three-variable (point correspondence, deformation field, and resection region) functional minimization problem, in which point correspondence is represented by a fuzzy assign matrix; Deformation field is represented by a piecewise linear function regularized by the strain energy of a heterogeneous biomechanical model; and resection region is represented by a maximal simply connected tetrahedral mesh. A nested expectation and maximization framework is developed to simultaneously resolve these three variables.
Results: To evaluate this method, the authors conducted experiments on both synthetic data and clinical MRI data. The synthetic experiment confirmed their hypothesis that the removal of additional elements from the biomechanical model can improve the accuracy of the registration. The clinical MRI experiments on 25 patients showed that the proposed method outperforms the ITK implementation of a physics-based nonrigid registration method. The proposed method improves the accuracy by 2.88 mm on average when the error is measured by a robust Hausdorff distance metric on Canny edge points, and improves the accuracy by 1.56 mm on average when the error is measured by six anatomical points.
Conclusions: The proposed method can effectively correct brain deformation induced by tumor resection. (C) 2014 American Association of Physicists in Medicine
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