Classical Plane Research Articles

Spectrum Broadening Due to Nonselective Linear Absorption

The position and linewidth of an emission spectrum reflect the physical properties of the luminophor. So, keeping the spectrum from distortion is very important in its measurement. However, we find that the spectrum linewidth will be broadened when the near-infrared radiation from a sodium lamp passes through a nonselective linear absorbing filter. This counterintuitive linewidth-broadening phenomenon is obvious when the residual light power after the filter is low enough, typically lower than 2.48×10−4 μW. This novel linewidth-broadening effect is different from the well-known Lorentzian, Doppler, and Voigt broadening, and is likely to be more independent evidence of the discrete wavelet structure of classical plane light waves. The effect is significant in high-sensitivity spectroscopy measurements, for example streak camera spectroscopy and Raman spectroscopy experiments. In addition, this effect may also be significant for cosmological research.

Semiclassical perturbations of single-degree–of–freedom Hamiltonian systems I: Separatrix splitting

We study semiclassical perturbations of single-degree-of-freedom Hamiltonian systems possessing hyperbolic saddles with homoclinic orbits, and provide a sufficient condition for the separatrices to split, using a Melnikov-type approach. The semiclassical systems give approximations of the expectation values of the positions and momenta to the semiclassical Schrödinger equations with Gaussian wave packets as the initial conditions. The occurrence of separatrix splitting explains a mechanism for the existence of trajectories to cross the separatrices on the classical phase plane in the expectation value dynamics. Such separatrix splitting does not occur in standard systems of Hagedorn and Heller for the semiclassical Gaussian wave packet dynamics as well as in the classical systems. We illustrate our theory for the potential of a simple pendulum and give numerical computations for the stable and unstable manifolds in the semiclassical system as well as solutions crossing the separatrices.

Hadamard Coded Multiplane Wave based Ultrafast Doppler for Rat Brain Imaging

Abstract This study explores the application of Hadamard multiplane-wave coding in ultrafast power and color Doppler imaging for enhanced visualization of rat brain vasculature. By implementing an 8-order Hadamard matrix, an approximate 10 dB improvement in signal-to-noise ratio was significantly achieved, particularly in deep brain regions and the hippocampus. The enhanced imaging technique, compared to classical plane wave coherent compounding, demonstrates its potential for applications requiring deep penetration and high sensitivity to small blood flow without compromising the ultrafast frame rate.

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AbstractFor , let be a two‐dimensional algebraically defined graph, that is, a bipartite graph where each partite set is a copy of and two vertices and are adjacent if and only if . It is known that has girth 6 and can be extended to the point‐line incidence graph of the classical real projective plane. However, it was unknown whether there exists such that has girth 6 and is nonisomorphic to . This paper answers this question affirmatively and thus provides a construction of a nonclassical real projective plane. This paper also studies the diameter and girth of for families of bivariate functions .

Epitrochoids and Hypotrochoids Together Again

Summary Two classic plane curves, the epitrochoid and hypotrochoid, can be placed together in an optimal nested form. We find the appropriate equations by way of complex variables, and we also get a surprising answer for the slope of a particular tangent line.

Limited Delamination Modifications to the Extended Deep Plane Rhytidectomy: An Anatomical Basis for Improved Outcomes.

Background: This study introduces variations of a limited delamination approach to the deep plane face- and necklift. Objectives: To report surgeons' perceptions of limited delamination deep plane rhytidectomy, define the anatomical basis to support these modifications, and report complication rates. Methods: This retrospective multi-institutional chart review study of patients undergoing a modified classical deep plane face- and necklift. Surgeons' perception of outcomes and self-reported complications were collected. Results: In total, 3964 patients having undergone face- and necklift with six surgeons being included. Most patients were female (87.9%) with an age range of 31-83 years (mean 58 years). Most were primary procedures (2672/3964; 67.4%) with a median follow-up of 425 days (range 21-5470). Preliminary surgeon experience demonstrated increased ease of flap management, improved biomechanics, smaller perceived rates of skin discoloration, and telangiectasia of the skin and lower revisions rate (n = 11; 0.8%). Complication rates were low for hematoma (n = 24; 1.9%) and seroma requiring needle aspiration (n = 26; 2%) and minor infection (n = 18; 1.4%). Conclusions: A multicenter surgeon experience with the limited delamination extended deep plane rhytidectomy is based on anatomical evidence and demonstrates low complication rates and surgeon-perceived improved long-term outcomes. Prospective comparative outcomes of these evolving techniques are warranted.

Semi-classical 2-dimensional Minkowski planes

AbstractSemi-classical geometries have been investigated in the context of 2-dimensional affine planes, projective planes, Möbius planes and Laguerre planes. Here we deal with the case of 2-dimensional Minkowski planes. Semi-classical 2-dimensional Minkowski planes are obtained by pasting together two halves of the classical real Minkowski plane along two circles or parallel classes. By solving some functional equations for the functions that describe the pasting we determine all semi-classical 2-dimensional Minkowski planes. In contrast to the rich variety of other semi-classical planes there are only very few models of such Minkowski planes.

Dispersion and attenuation relations in flexoelectricity

The dispersion relations in flexoelectricity are examined for plane time-harmonic waves that propagate in the flexoelectric materials. In contrast to classic elastodynamics, dispersion is observed in the displacement field due to two micro-structural and two micro-inertial lengths that emerge from the electromechanical coupling. In the absence of such coupling, we return to the classic elastodynamic results. The problem dissociates in longitudinal and transverse waves, as is the case in classic elastodynamics. The group velocity of the mechanical field is also the velocity of the energy transfer across the planes of the waves. An optical branch of the dispersion relation appears due to the polarization field that follows the mechanical field. The longitudinal and transverse velocities of the plane waves was found to depend on the corresponding microstructural lengths and are less than or equal to the classic plane wave velocities because the micro-inertial lengths are greater than or equal to the micro-structural length. The opposite effect is expected when we encounter flexoelectric metamaterials in which case the micro-inertial lengths are less than the micro-structural length.

A Quantum-Safe Software-Defined Deterministic Internet of Things (IoT) with Hardware-Enforced Cyber-Security for Critical Infrastructures

The next-generation “Industrial Internet of Things” (IIoT) will support “Machine-to-Machine” (M2M) communications for smart Cyber-Physical-Systems and Industry 4.0, and require guaranteed cyber-security. This paper explores hardware-enforced cyber-security for critical infrastructures. It examines a quantum-safe “Software-Defined-Deterministic IIoT” (SDD-IIoT), with a new forwarding-plane (sub-layer-3a) for deterministic M2M traffic flows. A “Software-Defined Networking” (SDN) control plane controls many “Software-Defined-Deterministic Wide-Area Networks” (SDD-WANs), realized with FPGAs. The SDN control plane provides an “Admission-Control/Access-Control” system for network-bandwidth, using collaborating Artificial Intelligence (AI)-based “Zero Trust Architectures” (ZTAs). Hardware-enforced access-control eliminates all congestion, BufferBloat, and DoS/DDoS attacks, significantly reduces buffer-sizes, and supports ultra-reliable-low-latency communications in the forwarding-plane. The forwarding-plane can: (i) Encrypt/Authenticate M2M flows using quantum-safe ciphers, to withstand attacks by Quantum Computers; (ii) Implement “guaranteed intrusion detection systems” in FPGAs, to detect cyber-attacks embedded within billions of IIoT packets; (iii) Provide guaranteed immunity to external cyber-attacks, and exceptionally strong immunity to internal cyber-attacks; (iv) Save USD 100s of billions annually by exploiting FPGAs; and (v) Enable hybrid Classical-Quantum networks, by integrating a “quantum key distribution” (QKD) network with a classical forwarding plane with exceptionally strong cyber-security, determined by the computational hardness of cracking Symmetric Key Cryptography. Extensive experimental results for an SDD-WAN over the European Union are reported.

Analgesic efficacy of classical thoracolumbar interfascial plane block versus modified thoracolumbar interfascial plane block in patients undergoing lumbar disc surgeries: A comparative, randomised controlled trial.

We compared classical (medial) and modified (lateral) thoracolumbar interfascial plane block (TLIP) with only general anaesthesia (GA) using multimodal analgesia in patients undergoing lumbar disc surgeries. In this study, 100 patients aged 18-70 years were randomised to Group cTLIP (conventional TLIP block with 20 mL of 0.25% ropivacaine with GA), Group mTLIP (modified TLIP block with 20 mL of 0.25% ropivacaine with GA), and Group C (only GA using multimodal analgesia). The primary outcome was to assess the total peri-operative opioid consumption in the first 24 h. The secondary outcomes were to assess pain score upon arriving in the post-anaesthesia care unit, time to first analgesic need after surgery, post-operative opioid consumption in 24 h, and incidence of nausea and vomiting. The total peri-operative opioid consumption in Group cTLIP (507.58 (258.55) μg) and Group mTLIP (491.67 (165.39) μg) was significantly lower than that in Group C (1225.4 (237.03) μg); (P < 0.001). However, it was comparable between groups cTLIP and mTLIP (P = 0.767). Pain score was comparable in groups cTLIP and mTLIP. It was significantly lower than Group C (P = 0.001). Rescue analgesia was needed in all (100%) patients of Group C but in only 15.2% of patients of the cTLIP and mTLIP groups. No patient in groups cTLIP and mTLIP complained of nausea and vomiting in the first 24 h, whereas it was significantly higher (61.8%) in Group C (P = 0.001). The analgesic effect of the modified TLIP block was not superior to the conventional TLIP block. Both techniques provided the same intra-operative and post-operative analgesia for lumbar disc surgeries.

THE FRACTIONAL DISEN–FISHER PLANE: AN EFFECTIVE APPROACH TO DISTINGUISH COMPLEX TIME SERIES

With the explosive growth of data quantity and rapid development of nonlinear dynamics as well as the growing demand for complex data classification in the field of artificial intelligence and machine learning, the research of complex time series, generated by complex systems, has attracted enormous interests. However, how to simultaneously distinguish different types of time series data and extract more accurate and detailed information from them in the light of localized and global scale perspectives remains significant and needs to be tackled. Thus, in this paper, we propose the fractional DisEn–Fisher plane, which is innovatively constructed by the fractional form of dispersion entropy and Fisher information measure. These are both effective tools to diagnose the essential properties of complex time series, to analyze the complexity of systems and to depict the contained statistical information with higher accuracy and effectiveness. Several classical entropy plane methods are selected as a comparison to design simulation experiments by simulated data and three real-world datasets. Comparative experimental results show that this method is a feasible and reliable improvement method, which will help to provide more additional information in time series recognition and dynamic characterization. It may not only provide new insights for further improvement of complex time series analysis, but also have important implications for developing complex data clustering methods.

Acoustic Modeling and Analysis of Automotive Air-Filters

Air filters are placed upstream of internal combustion engines to remove dust particles in the suction air. In this article, we examine the acoustic characterization of an air-filtering unit in the absence of mean flow. For this purpose, a circular air-filtering unit with an axial inlet and side outlet widely used in the automobile industry is considered. The air-filter element is modeled as an equivalent acoustic fluid with finite flow resistivity. The flow resistivity of the region is estimated from the permeability of the filter paper and the geometrical arrangement of the paper folds (pleats) inside the air-filter element using an electrical analogy. A numerical model based on the finite element method (FEM) and an analytical model using classical one-dimensional plane wave analysis (1-D PWA) was developed. Experiments were carried out using an impedance tube to estimate transmission loss. A good correlation is observed between the FEM model and the experiments. The results obtained from the 1-D PWA are in reasonable agreement with those obtained from the other two methods.

Modeling and Analysis of Flexible Deployable Structure with Scissor-Like Elements Using a Novel Non-Locking Beam Element

The main goal of this paper is to develop a comprehensive dynamic modeling and analysis method based on the absolute node coordinate method to predict the impact of the member flexibility on the dynamic performance of scissor deployable structure under the framework of flexible multi-body dynamics. In the process, three locking problems in the classical plane shear beam element are reviewed and discussed. Then a novel non-locking planar beam element is proposed to solve the element locking problem, and the dynamic model of the scissor deployable structure is established. Next, the cantilever beam, simply supported beam and flexible simple pendulum are respectively used to verify the correctness of the proposed non-locking beam element from the static and dynamic perspectives. Finally, the simulation and experiment results show that the proposed new non-locking element and normal matrix modeling method can effectively evaluate the dynamic performance of deployable structure and improve the computational efficiency. This study not only provides theoretical guidance for the dynamic behavior analysis and prediction of scissor deployable structure, but also offers reference for the layout and design of same type mechanisms.

Theoretical model for investigating three-dimensional effect in integrity test of open-end pipe piles

An innovative theoretical model of non-axisymmetric vibration of pipe pile (NVPP) is proposed in this paper to investigate the three-dimensional effect in the pile integrity test (PIT) for open-end pipe piles. A new dynamic equilibrium equation of the pipe pile is established based on the stress simplification assumption. It overcomes the inaccuracies of existing three-dimensional models in predicting the longitudinal wave velocity of pile material. The surrounding soil and soil plug conform to the classical plane strain assumption, while the pile end soil is simulated by the fictitious soil annular pile developed from the traditional fictitious soil pile. Theoretical solutions for the velocity response of each point on the pipe pile top are deduced and validated against existing solutions and FEM results. The NVPP model is then applied to analyze the characteristics of testing signals of PITs for thick-wall and thin-wall pipe piles. Problems concerned in actual PITs for pipe piles are settled and practical recommendations for acquiring high-quality testing signals with minimal interference are provided.

Optimal plane curves of degree q − 1 over a finite field

Let q≥5 be a prime power. In this note, we prove that if a plane curve X of degree q−1 defined over Fq without Fq-linear components attains the Sziklai upper bound (d−1)q+1=(q−1)2 for the number of its Fq-rational points, then X is projectively equivalent over Fq to the curve C(α,β,γ):αXq−1+βYq−1+γZq−1=0 for some α,β,γ∈Fq⁎ such that α+β+γ=0. This completes the classification of curves that are extremal with respect to the Sziklai bound. Also, since the Sziklai bound is equal to the Stöhr-Voloch's bound for plane curves of degree q−1, our main result classifies the Fq-Frobenius extremal classical nonsingular plane curves of degree q−1.

Quantification of damage evolution in cross-ply polymer composites under longitudinal compression by fast computed tomography and semi-automated segmentation

Compressive failure in a notched cross-ply IM7/8552 carbon fiber reinforced polymer (CFRP) laminate is studied experimentally by time-lapse in-situ synchrotron radiation computed tomography (CT). The focus is on tracking and quantifying the fiber damage evolution in the 0° plies under compression for the first time via a specimen design that exhibits quasi-stable damage accumulation. A novel segmentation algorithm has been developed and applied to extract morphological features of interest including the kink band width, inclination angle, and the extent of propagation from the notch. In the four innermost 0∘ plies, shear-driven fiber fracture initiates from the notch tip and propagates as a single fracture plane inclined about 45° to the compression axis. This shear-driven fiber fracture transitions to a kink band at a distance of about 300μm from the notch, which propagates at a shallower angle. During the later stages of the test, the kink bands propagate in the reverse direction to areas that previously initiated by shear-driven fiber fracture, which may explain why post-mortem observations seldom reveal the fiber shear fracture mechanism. The fiber damage initiation and evolution appears distinctly different from the classical parallel plane kink bands formed by plastic microbuckling under uniaxial compression in that the dominant mechanism appears to be shear-driven fiber fracture.

Comparison of postoperative IL-6 and IL-10 levels following Erector Spinae Plane Block (ESPB) and classical Thoracolumbar Interfascial Plane (TLIP) block in a posterior lumbar decompression and stabilization procedure: a randomized controlled trial

Background and objectivesThe erector spinae plane block (ESPB) and classical thoracolumbar interfascial plane (TLIP) block can reduce postoperative pain in lumbar surgery. In this study, we compared the efficacy of ESPB and classical TLIP block in providing perioperative analgesia in patients undergoing lumbar posterior decompression and stabilization by comparing postoperative pain, opioid consumption, and IL-6 and IL-10 serum concentrations between ESPB and classical TLIP block.MethodThis was a prospective, double-blinded, randomized controlled trial in tertiary referral hospitals. Forty patients were randomized into two equal groups, each receiving either ESPB or classical TLIP block. The primary outcome was the difference in IL-6 and IL-10 serum concentrations at baseline and 6 h after lumbar posterior decompression and stabilization. The secondary outcome was total opioid consumption and pain score 24 h post-operatively.ResultThere were no significant differences between the ESPB and classical TLIP block groups in pain score, IL-6 and IL-10 concentration change, and total opioid consumption post-operatively. There was a significant difference in the time until the first dose of morphine was needed between the ESPB and classical TLIP block groups (300 min vs. 547.5 min; p = 0.002).ConclusionESPB and classical TLIP block performance during lumbar surgery have comparable pain scores, IL-6 and IL-10 concentration differences pre- and post-operation, and total opioid consumption post-operatively. However, classical TLIP block provides a prolonged duration of analgesia.Trial registrationClinicalTrials.gov NCT04951024.

A Study of the Movement of a Neutrosophic Material Point in the Neutrosophic Plane by Using a Neutrosophic AH-Isometry

This articles presents a new concept in mathematics according to a neutrosophic logic, which is the first of its kind in applied mathematics, which is the concept of the movement of a neutrosophic point in the neutrosophic plane and determining the path of this point, after determining Cartesian and polar neutrosophic coordinates of this point and also defining the neutrosophic local, velocity and acceleration vectors of these point. We have also determined the relationsships between the motion of a neutrosophic point and its equivalent in the classical plane, through an AH-isometry that connects the neutrosophic and classical plane. We conducted the previous study on three different examples, each example differs from the other in the form of a path and type of movement of the studied point.

Characterization of Intuitionistic Fuzzy Collineations in Intuitionistic Fuzzy Projective Planes

In this paper, the intuitionistic fuzzy counterparts of the collineations defined in classical projective planes are defined in intuitionistic fuzzy projective planes. The properties of the intuitionistic fuzzy projective plane left invariant under the intuitionistic fuzzy collineations are characterized depending on the base point, base line, membership degrees, and the non-membership degrees of the intuitionistic fuzzy projective plane.

Experimental observation of periodic Korteweg-de Vries solitons along a torus of fluid

We report on the experimental observation of solitons propagating along a torus of fluid. We show that such a periodic system leads to significant differences compared to the classical plane geometry. In particular, we highlight the observation of subsonic elevation solitons, and a nonlinear dependence of the soliton velocity on its amplitude. The soliton profile, velocity, collision, and dissipation are characterized using high-resolution space-time measurements. By imposing periodic boundary conditions onto the Korteweg-de Vries (KdV) equation, we recover these observations. A nonlinear spectral analysis of solitons (periodic inverse scattering transform) is also implemented and experimentally validated in this periodic geometry. Our work thus reveals the importance of periodicity for studying solitons and could be applied to other fields involving periodic systems governed by a KdV equation.