Finding the fundamental solution of the bi-axially symmetric Laplace–Beltrami equation using generalized shift operator

Many physical processes are described by partial differential equations. The relevance of this study is due to the need to solve applied problems of quantum mechanics, the theory of elasticity, and heat capacity. In this paper, an equation is considered that describes the field created by a contour with two axes of symmetry. The purpose of the study is to find a fundamental solution to this equation, which can later be used when solving boundary value problems.

Brain Injury Localization in Electromagnetic Imaging using Symmetric Crossing Lines Method

To avoid death or disability, patients with brain injury should undertake a diagnosis at the earliest time and accept frequent monitoring after starting any medical intervention. This paper presents a novel approach to localize brain injury using the intersection of pairs of signals from symmetrical antennas based on the hypothesis that healthy brains are approximately symmetric that the bleeding targets will lead to significantly different amplitude and phase changes if a pair of symmetrical transmit signals cross targets with the same distances. The scattered signals (S-parameters) across the band 0.5-2 GHz are acquired using 100 realistic brain models and 150 experimental data measurements. Each signal is divided into two frequency bands and then they are converted into two graphs. The neighbour pair signals from symmetric hemisphere are evaluated to detect and localize the potential abnormalities in the brain. The higher weighted pairs across the axes of symmetry are detected and used to localize any abnormal targets. The results indicate that crossing pairs of antenna signals from the hemisphere with a blood mass exhibit significantly different signal amplitude in the graph features compared to those without the target (p<0.003). The experiments show that our novel localization algorithm can achieve an accuracy of 0.85±0.08 Dice similarity coefficient based on 150 experimental measurements using an elliptical container, which is suitable for brain injury localization.

Backward Flux Re-Deposition Patterns during Multi-Spot Laser Ablation of Stainless Steel with Picosecond and Femtosecond Pulses in Air

We report on novel observations of directed re-deposition of ablation debris during the ultrafast laser micro-structuring of stainless steel in the air with multi-beams in close proximity on the surface. This interesting phenomenon is observed with both 10 ps and 600 fs NIR laser pulses at 5 kHz repetition rate. Ablation spot geometries could be altered with the use of beam splitting optics or a phase-only Spatial Light modulator. At low fluence (F ~ 1.0 J cm−2) and pulse exposure of a few hundred pulses, the debris appears as concentrated narrow “filaments” connecting the ablation spots, while at higher fluence, (F ~ 5.0 J cm−2) energetic jets of material emanated symmetrically along the axes of symmetry, depositing debris well beyond the typical re-deposition radius with a single spot. Patterns of backward re-deposition of debris to the surface are likely connected with the colliding shock waves and plasma plumes with the ambient air causing stagnation when the spots are in close proximity. The 2D surface debris patterns are indicative of the complex 3D interactions involved over wide timescales during ablation from picoseconds to microseconds.

Microrheology With an Anisotropic Optical Trap

Microrheology with optical tweezers (MOT) measurements are usually performed using optical traps that are close to isotropic across the plane being imaged, but little is known about what happens when this is not the case. In this work, we investigate the effect of anisotropic optical traps on microrheology measurements. This is an interesting problem from a fundamental physics perspective, but it also has practical ramifications because in 3D all optical traps are anisotropic due to the difference in the intensity distribution of the trapping laser along axes parallel and perpendicular to the direction of beam propagation. We find that attempting viscosity measurements with highly anisotropic optical traps will return spurious results, unless the axis with maximum variance in bead position is identified. However, for anisotropic traps with two axes of symmetry such as traps with an elliptical cross section, the analytical approach introduced in this work allows us to explore a wider range of time scales than those accessible with symmetric traps. We have also identified a threshold level of anisotropy in optical trap strength of ~30%, below which conventional methods using a single arbitrary axis can still be used to extract valuable microrheological results. We envisage that the outcomes of this study will have important practical ramifications on how all MOT measurements should be conducted and analyzed in future applications.

Students’ understanding of axial and central symmetry

The paper focuses on students’ understanding of the concepts of axial and central symmetries in a plane. Attention is paid to whether students of various ages identify a non-model of an axially symmetrical figure, know that a line segment has two axes of symmetry and a circle has an infinite number of symmetry axes, and are able to construct an image of a given figure in central symmetry. The results presented here were obtained by a quantitative analysis of tests given to nearly 1,500 Czech students, including pre-service mathematics teachers. The paper presents the statistics of the students’ answers, discusses the students’ thought processes and presents some of the students’ original solutions. The data obtained are also analysed with regard to gender differences and to the type of school that students attend. The results show that students have two principal misconceptions: that a rhomboid is an axially symmetrical figure and that a line segment has just one axis of symmetry. Moreover, many of the tested students confused axial and central symmetry. Finally, the possible causes of these errors are considered and recommendations for preventing these errors are given.

A closed form for the Stress Intensity Factor of a small embedded square-like flaw

In the present work, the stress intensity factor (SIF) of a small embedded square-like flaw is calculated by means of a procedure based on the Oore-Burns integral. An explicit equation is given to evaluate the SIF along the two axes of symmetry that correspond to the points where the SIF takes its maximum and minimum value on the contour crack. The SIF is calculated in accordance with FE numerical results.

Human antibodies neutralize enterovirus D68 and protect against infection and paralytic disease

Enterovirus D68 (EV-D68) causes outbreaks of respiratory illness, and there is increasing evidence that it causes outbreaks of acute flaccid myelitis (AFM). There are no licensed therapies to prevent or treat EV-D68 infection or AFM disease. We isolated a panel of EV-D68–reactive human monoclonal antibodies that recognize diverse antigenic variants from participants with prior infection. One potently neutralizing cross-reactive antibody, EV68-228, protected mice from respiratory and neurologic disease when given either before or after infection. Cryo–electron microscopy studies revealed that EV68-228 and another potently neutralizing antibody (EV68-159) bound around the fivefold or threefold axes of symmetry on virion particles, respectively. The structures suggest diverse mechanisms of action by these antibodies. The high potency and effectiveness observed in vivo suggest that antibodies are a mechanistic correlate of protection against AFM disease and are candidates for clinical use in humans with EV-D68 infection.