Polyharmonic Multiquadric Particular Solutions for Reissner/Mindlin Plate

Analytical particular solutions of the polyharmonic multiquadrics are derived for both the Reissner and Mindlin thick-plate models in a unified formulation. In the derivation, the three coupled second-order partial differential equations are converted into a product operator of biharmonic and Helmholtz operators using the Hörmander operator decomposition technique. Then a method is introduced to eliminate the Helmholtz operator, which enables the utilization of the polyharmonic multiquadrics. Then, the analytical particular solutions of displacements, shear forces, and bending or twisting moments corresponding to the polyharmonic multiquadrics are all explicitly derived. Numerical examples are carried out to validate these particular solutions. The results obtained by the present method are more accurate than those by the traditional multiquadrics and splines

Thermally-Switchable Metalenses Based on Quasi-Bound States in the Continuum

Dynamic wavefront shaping with optical metasurfaces has presented a major challenge and inspired a large number of highly elaborate solutions. Here, we experimentally demonstrate thermo-optically reconfigurable, nonlocal metasurfaces using simple device architectures and conventional CMOS-compatible dielectric materials. These metasurfaces support quasi-bound states in the continuum (q-BICs) derived from symmetry breaking and encoded with a spatially varying geometric phase, such that they shape optical wavefront exclusively on spectrally narrowband resonances. Due to the enhanced light-matter interaction enabled by the resonant q-BICs, a slight variation of the refractive index introduced by heating and cooling the entire device leads to a substantial shift of the resonant wavelength and a subsequent change to the optical wavefront associated with the resonance. We experimentally demonstrate a metalens modulator, the focusing capability of which can be thermally turned on and off, and reconfigurable metalenses, which can be thermo-optically switched to produce two distinct focal patterns. Our devices offer a pathway to realize reconfigurable, multifunctional meta-optics using established manufacturing processes and widely available dielectric materials that are conventionally not considered "active" materials due to their small thermo-optic or electro-optic coefficients

Meshfree Model for Wave-Seabed Interactions Around Offshore Pipelines

The evaluation of the wave-induced seabed instability around a submarine pipeline is particularly important for coastal engineers involved in the design of pipelines protection. Unlike previous studies, a meshfree model is developed to investigate the wave-induced soil response in the vicinity of a submarine pipeline. In the present model, Reynolds-Averaged Navier-Stokes (RANS) equations are employed to simulate the wave loading, while Biot&rsquo s consolidation equations are adopted to investigate the wave-induced soil response. Momentary liquefaction around an offshore pipeline in a trench is examined. Validation of the present seabed model was conducted by comparing with the analytical solution, experimental data, and numerical models available in the literature, which demonstrates the capacity of the present model. Based on the newly proposed model, a parametric study is carried out to investigate the influence of soil properties and wave characteristics for the soil response around the pipeline. The numerical results conclude that the liquefaction depth at the bottom of the pipeline increases with increasing water period (T) and wave height (H), but decreases as backfilled depth ( H b ), degree of saturation ( S r ) and soil permeability (K) increase. Document type: Articl

Small B cell lymphocytic lymphoma presenting as obstructive sleep apnea

BACKGROUND: Most lymphomas that involve the tonsil are large B cell lymphomas. Large B-cell lymphoma is a high grade malignancy which progresses rapidly. Tonsillar lymphoma usually presents as either a unilaterally enlarged palatine tonsil or as an ulcerative and fungating lesion over the tonsillar area. Small lymphocytic lymphomas (SLL) of the Waldeyer's ring are uncommon. CASE PRESENTATION: We report a 41-year-old male who presented with a ten-year history of snoring. Physical examination revealed smooth bilateral symmetrically enlarged tonsils without abnormal surface change or cervical lymphadenopathy. Palatal redundancy and a narrowed oropharyngeal airway were also noted. The respiratory disturbance index (RDI) was 66 per hour, and severe obstruction sleep apnea (OSA) was suspected. No B symptoms, sore throat, odynophagia or dysphagia was found. We performed uvulopalatopharyngoplasty (UPPP) and pathological examination revealed incidental small B-cell lymphocytic lymphoma (SLL). CONCLUSION: It is uncommon for lymphoma to initially present as OSA. SLL is an indolent malignancy and is not easy to detect in the early stage. We conclude that SLL may be a contributing factor of OSA in the present case