On the treatment of singularities of the Watson Hamiltonian for nonlinear molecules

The applicability of the Watson Hamiltonian for the description of nonlinear molecules—especially triatomic ones—has always been questioned, as the Jacobian of the transformation that leads to the Watson Hamiltonian, vanishes at the linear configuration. This results in singular behavior of the Watson Hamiltonian, giving rise to serious numerical problems in the computation of vibrational spectra, with unphysical, spurious vibrational states appearing among the physical vibrations, especially in the region of highly excited states. In this work, we analyze the problem and propose a simple way to confine the nuclear wavefunction in such a way that the spurious solutions are eliminated. We study the water molecule and observe an improvement compared with previous results. We also apply the method to the van der Walls molecule XeHe2.

Domain Bundle Boundaries in Single Crystal BaTiO3 Lamellae: Searching for Naturally Forming Dipole Flux-Closure / Quadrupole Chains

Naturally occurring boundaries between bundles of 90o stripe domains, which form in BaTiO3 lamellae on cooling through the Curie Temperature, have been characterised using both piezoresponse force microscopy (PFM) and scanning transmission electron microscopy (STEM). Detailed interpretation of the dipole configurations present at these boundaries (using data taken from PFM) shows that, in the vast majority of cases, they are composed of simple zigzag 180° domain walls. Topological information from STEM shows that, occasionally, domain bundle boundaries can support chains of dipole flux closure and quadrupole nanostructures, but these kinds of boundaries are comparatively rare; when such chains do exist, it is notable that singularities at the cores of the dipole structures are avoided. The symmetry of the boundary shows that diads and centres of inversion exist at positions where core singularities should have been expected.

Domain Bundle Boundaries in Single Crystal BaTiO3 Lamellae: Searching for Naturally Forming Dipole Flux-Closure/Quadrupole Chains

Naturally occurring boundaries between bundles of 90° stripe domains, which form in BaTiO3 lamellae on cooling through the Curie Temperature, have been characterized using both piezoresponse force microscopy (PFM) and scanning transmission electron microscopy (STEM). Detailed interpretation of the dipole configurations present at these boundaries (using data taken from PFM) shows that in the vast majority of cases they are composed of simple zigzag 180° domain walls. Topological information from STEM shows that occasionally domain bundle boundaries can support chains of dipole flux closure and quadrupole nanostructures, but these kinds of boundaries are comparatively rare; when such chains do exist, it is notable that singularities at the cores of the dipole
structures are avoided. The symmetry of the boundary shows that diads and centers of inversion exist at positions where core singularities should have been expected.

Wavelet analysis of bender element signals

Accurate determination of shear wave arrival time using bender elements may be severely affected by a combination of near-field effects and reflected waves. These may mask the first arrival of the shear wave, making its detection difficult in the time domain. This paper describes an approach for measuring the shear wave arrival time through analysis of the output signal in the time-scale domain using a multi-scale wavelet transform. The local maxima lines of the wavelet transform modulus are observed at different scales, and all singularities are mathematically characterised, allowing subsequent detection of the singularity relating to the first arrival. Examples of the use of this approach on typical synthetic and experimental bender element signals are also supplied, and these results are compared with those from other time and frequency domain approaches. The wavelet approach is not affected by near-field effects, but instead is characterised by a relatively consistent singularity related to the shear wave arrival time, across a range of frequencies and noise levels.

Relativistic High Harmonic Generation In Gas Jet Targets

We experimentally demonstrate a new regime of high-order harmonic generation by relativistic-irradiance lasers in gas jet targets. Bright harmonics with both odd and even orders, generated by linearly as well as circularly polarized pulses, are emitted in the forward direction, while the base harmonic frequency is downshifted. A 9 TW laser generates harmonics up to 360 eV, within the 'water window' spectral region. With a 120 TW laser producing 40 uJ/sr per harmonic at 120 eV, we demonstrate the photon number scalability. The observed harmonics cannot be explained by previously suggested scenarios. A novel high-order harmonics generation mechanism [T. Zh. Esirkepov et al., AIP Proceedings, this volume], which explains our experimental findings, is based on the phenomena inherent in the relativistic laser - underdense plasma interactions (self-focusing, cavity evacuation, and bow wave generation), mathematical catastrophe theory which explains formation of electron density singularities (cusps), and collective radiation due to nonlinear oscillations of a compact charge.

An investigation into the acceleration response of a damaged beam-type structure to a moving force

In recent years there have been a growing number of publications on procedures for damage detection in beams from analysing their dynamic response to the passage of a moving force. Most of this research demonstrates their effectiveness by showing that a singularity that did not appear in the healthy structure is present in the response of the damaged structure. This paper elucidates from first principles how the acceleration response can be assumed to consist of ‘static’ and ‘dynamic’ components, and where the beam has experienced a localised loss in stiffness, an additional ‘damage’ component. The combination of these components establishes how the damage singularity will appear in the total response. For a given damage severity, the amplitude of the ‘damage’ component will depend on how close the damage location is to the sensor, and its frequency content will increase with higher velocities of the moving force. The latter has implications for damage detection because if the frequency content of the ‘damage’ component includes bridge and/or vehicle frequencies, it becomes more difficult to identify damage. The paper illustrates how a thorough understanding of the relationship between the ‘static‘ and ‘damage’ components contributes to establish if damage has occurred and to provide an estimation of its location and severity. The findings are corroborated using accelerations from a planar finite element simulation model where the effects of force velocity and bridge span are examined.

New techniques for enhanced medial axis based decompositions in 2-D

New techniques are presented for using the medial axis to generate high quality decompositions for generating block-structured meshes with well-placed mesh singularities away from the surface boundaries. Established medial axis based meshing algorithms are highly effective for some geometries, but in general, they do not produce the most favourable decompositions, particularly when there are geometry concavities. This new approach uses both the topological and geometric information in the medial axis to establish a valid and effective arrangement of mesh singularities for any 2-D surface. It deals with concavities effectively and finds solutions that are most appropriate to the geometric shapes. Methods for directly constructing the corresponding decompositions are also put forward.

Enhanced medial-axis-based block-structured meshing in 2-D

New techniques are presented for using the medial axis to generate decompositions on which high quality block-structured meshes with well-placed mesh singularities can be generated. Established medial-axis-based meshing algorithms are effective for some geometries, but in general, they do not produce the most favourable decompositions, particularly when there are geometric concavities. This new approach uses both the topological and geometric information in the medial axis to establish a valid and effective arrangement of mesh singularities for any 2-D surface. It deals with concavities effectively and finds solutions that are most appropriate to the geometric shapes. Resulting meshes are shown for a number of example models.

Common Themes in Multi-block Structured Quad/Hex Mesh Generation

The automatic generation of structured multi-block quadrilateral (quad) and hexahedral (hex) meshes has been researched for many years without definitive success. The core problem in quad / hex mesh generation is the placement of mesh singularities to give the desired mesh orientation and distribution [1]. It is argued herein that existing approaches (medial axis, paving / plastering, cross / frame fields) are actually alternative views of the same concept. Using the information provided by the different approaches provides additional insight into the problem.