Superposition Principle Research Articles

Kinetic Alfvén wave cascade in sub-ion range plasma turbulence

Kinetic Alfvén waves (KAWs) are simulated with a 3D particle-in-cell (PIC) code by using the eigenvector relations of density, velocity, electric, and magnetic field fluctuations derived from a two-fluid KAW model. Similar simulations are also performed with a whistler waves setup. The 2D two-fluid eigenvector relations are converted into 3D by using rotation of the reference frame. The initial condition for the simulations is a superposition of several waves at scales slightly larger than the ion skin depth. The nonlinear interactions produce a transfer of energy to smaller scales. The magnetic field perturbation ratios, velocity perturbation, and density perturbation ratios are calculated from the simulation at higher wavenumbers and compared with the analytically expected ratios for KAWs and whistler waves. We find that in both types of simulations, initialized either with an ensemble of KAWs or with whistlers, the observed polarization relations at later times match better with the KAW relations compared to whistlers. This indicates a preference for excitation of KAW fluctuations at smaller scales. The power spectrum in the perpendicular direction is calculated, and it shows similar indices as measured in the solar wind power spectrum in the transition (sub-ion) region. The power law extends to smaller scales when a higher ion-to-electron mass ratio is taken. The 2D magnetic power spectrum in magnetic field parallel and perpendicular directions shows typical anisotropy where the power spreads more in the perpendicular direction than in the parallel direction. This study shows that KAWs can explain features of the sub-ion range plasma turbulence in the solar wind.

Precision tests of bulk entanglement entropy

We consider linear superpositions of single particle excitations in a scalar field theory on AdS3 and evaluate their contribution to the bulk entanglement entropy across the Ryu-Takayanagi surface. We compare the entanglement entropy of these excitations obtained using the Faulkner-Lewkowycz-Maldacena formula to the entanglement entropy of linear superposition of global descendants of a conformal primary in a large c CFT obtained using the replica trick. We show that the closed form expressions for the entanglement entropy in the small interval expansion both in gravity and the CFT precisely agree. The agreement serves as a non-trivial check of the FLM formula for the quantum corrections to holographic entanglement entropy as well as the methods developed in the CFT to evaluate entanglement entropy of descendants. Our checks includes an example in which the state is time dependent and spatially in-homogenous as well another example involving a coherent state with a Bañados geometry as its holographic dual.

Dynamic strain distribution monitoring and fatigue damage analysis on a 100 kW wind turbine blade based on field aerodynamic measurements

Abstract Operation and maintenance (O&M) costs can account for 10%–20% of the total costs of electricity for a wind project. Structural health monitoring method is a form of preventive maintenance consisting of regular monitoring of the wind turbine components to detect potential faults. The strain measurements on the blades are typically used for load monitoring and damage detection, but only obtain a small amount of concentrated load information. In this work, a strain distribution monitoring method was proposed and validated based on aerodynamic measurements in the field. Then the contribution and evolution of the strain distribution from the aerodynamic load, gravity load, inertial load, and centrifugal load in the complex start-up process of the wind turbine were analyzed. The results shows that the mean value of the synthetic strain is mainly determined by the aerodynamic load and the centrifugal load, while the fluctuation amplitude is mainly determined by the gravity and the aerodynamic load. Furthermore, the fatigue damage of the blade root was evaluated based on strain extrapolation, rainflow cycle-counting algorithm, Goodman diagram and Miner’s linear superposition principle. It is found that the fatigue damage is generally greatest near the pressure side and suction side, and least near the leading edge and trailing edge. The strain distribution monitoring method can capture the location of maximum stress and the most severe fatigue damage on the blade, which are helpful for damage detection and load control, and further reduces O&M costs.

Realizing linear-polarization-decoupled quasi-perfect absorption through mirror-symmetric QR-code metasurfaces

Metamaterial absorbers (MAs) with irregular structures facilitate the attainment of unique absorption properties, leveraging the extensive geometric freedom. However, a challenge arises from the fact that polarization-dependent spectra do not coincide with cross-polarization. In this study, we introduce a MA featuring a mirror-symmetric quick response (QR)-code structure to achieve linear-polarization-decoupled absorption characteristics. We employ a direct binary search algorithm to reverse design the MA structure by specifying absorptivity for eigen-polarization states. Moreover, the absorptivity for arbitrary polarizations can be predicted through linear superposition of the two eigen-polarization states, opening up avenues for investigating polarization-controlled metasurfaces and metamaterials.

An Inverse recursive algorithm to retrieve the shape of the inaccessible dielectric objects

A regularized electromagnetic iterative inverse algorithm is formulated and implemented to reconstruct the shape of 2D dielectric objects using the far-field pattern of the scattered field data. To achieve this, an integral operator that maps the unknown boundary of the object onto the far-field pattern of the scattered field is defined and solved for the unknown boundary. The addressed inverse problem has an ill-posed nature and inherits nonlinearity. To overcome these, the proposed solution is linearized via Newton and regularized by Tikhonov in the sense of least squares. Besides, the dominance of the shadow region in the inverse-imaging process is exceeded by considering the superposition of multi-incoming plane waves, leading to less computational cost and a very fast inversion process. Comprehensive numerical analyses are carried out to ascertain the algorithm's feasibility, revealing that it is very efficient and promising.

Short-Period Skyrmion Crystals in Itinerant Body-Centered Tetragonal Magnets

In this study, we investigate the stability of a magnetic skyrmion crystal with short-period magnetic modulations in a centrosymmetric body-centered tetragonal system. By performing the simulated annealing for the spin model, incorporating the effects of the biquadratic interaction and high-harmonic wave–vector interaction in momentum space, we find that the double-Q square skyrmion crystal consisting of two spin density waves is stabilized in an external magnetic field. We also show that double-Q states appear in both low- and high-field regions; the low-field spin configuration is characterized by an anisotropic double-Q modulation consisting of a superposition of the spiral wave and sinusoidal wave, while the high-field spin configuration is characterized by an isotropic double-Q modulation consisting of a superposition of two sinusoidal waves. Furthermore, we show that the obtained multiple-Q instabilities can be realized for various ordering wave vectors. The results provide the possibility of realizing the short-period skyrmion crystals under the body-centered tetragonal lattice structure.

Resonant multi-wave, positive multi-complexiton, nonclassical Lie symmetries, and conservation laws to a generalized Hirota bilinear equation

This paper explores the evolutionary behavior of some specific waves for a Generalized Hirota Bilinear (GHB) equation with applications in modern sciences. More precisely, the linear superposition principle is first adopted to construct the resonant multi-wave of the GHB equation. Through the resonant N-wave and some particular computations, positive multi-complexiton to the governing model is then extracted with the use of computational packages. Furthermore, after deriving nonclassical Lie symmetries and their corresponding invariant solutions, Conservation Laws (CLs) for the GHB equation are formally constructed based on a general method developed by Ibragimov. The propagation dynamics of resonant double- and triple-waves as well as positive single- and double-complexitons are examined in detail by considering several case studies. The present results demonstrate how adjusting the nonlinear parameter can be used to control specific waves in nonlinear systems.

Thermogravimetric study on thermal degradation kinetics and polymer interactions in mixed thermoplastics

AbstractPotential interactions during thermal degradation of polymer blends significantly influence product yields and their composition. Therefore, chemical recycling of plastic waste requires fundamental understanding of feedstock dependency for effective process design. This study investigates the pyrolysis of polymer blends (HDPE, LDPE, PP, PS, ABS, PET, PA6, PVC) through thermogravimetric experiments at different heating rates. Sample homogeneity’s impact on interactions is analyzed using particles, powder, coextruded blends, and samples in crucibles with separated compartments. A kinetic model is presented to support the experimental findings, assuming linear superposition of individual polymer kinetics. A proposed grouping of thermoplastics, reflecting their degradation behavior and potential interactions, correlates with the polymer structure. Observed interactions, particularly in blends of heteroatom-containing polymers (N, O, Cl), are accelerated reactions and coke formation. Hence, the model accurately predicts the degradation of heteroatom-free polymer mixtures but encounters challenges with more complex blends. This comprehensive study emphasizes the importance of feedstock composition for future pyrolytic polymer recycling. Graphical abstract

Predicting lifetime of adhesive bonds for naval steel by time-temperature superposition

There is a lack of knowledge about the long-term behaviour of adhesive joints in the marine environment, and for hence, its reliability. The life cycle expected for a ship is twenty-five years and conduct duration tests would last decades. The importance and originality of this study are that it provides a methodology for predicting the durability of adhesive bonds. For this purpose, three adhesives for bonding naval steel were tested at several temperatures for determination of their shear strength on standard single-lap-joint specimens. Subsequently, using the time temperature superposition principle, these results were combined into one master curve for each adhesive that can be considered as a prediction method of the durability in a long-term period. The usual parametric models of Arrhenius and Williams-Landel-Ferry were used to obtain the master curve for each adhesive by manual shifting. The results were compared with those obtained applying an open-source software developed by the authors in R language, which specifically implements a non-parametric methodology based on the shift of the first derivative curves, following parameters of Explainable Artificial Intelligence. It was found a good correlation between both methodologies, supporting the durability lifetime obtained and therefore the applicability on ships of this adhesive technology.

A Method for the Coefficient Superposition Buckling Bearing Capacity of Thin-Walled Members

Axial compression tests were conducted on short rhombic tubes of different cross-sectional shapes. The deformation modes of the rhombic short tubes were obtained. To induce a finite element model with deformation modes consistent with the actual working conditions, buckling modes are introduced into the model as the initial imperfections of the structure. However, the buckling modes resulting from finite element buckling analyses often do not meet the needs of actual crushing modes. A coefficient superposition method of solution is proposed to derive modal characteristics consistent with the actual deformation modes by linear superposition of the buckling modes. Through the study of three aspects of theory, test, and simulation, and the comparison and verification of this method with the simulation results of related literature, the results show that the indexes derived from this method are closer to the actual circumstances and are more expandable, which provides a reference for the project.

Study on the composition and properties of EME-SBS-Nano ZnO high modulus asphalt material

The objective of this research is to address the rut problems in asphalt pavements and to resist the permanent plastic deformation with the increasing heavy traffic loads. In this paper, a new type materials of high modulus asphalt was developed by incorporating styrene–butadiene–styrene (SBS) and zinc oxide nanoparticles (nano ZnO) with an (EME)-type high modulus modifier, guided by the synergistic effects and the preparation methods of High-speed shear. The basic road performance, mechanical response and thermal stability of the new high modulus asphalt materials were analysed through basic physical indicator tests, dynamic shear rheometer tests, thermogravimetric analysis (TGA), the time–temperature superposition principle, the Refutas model, and the Christensen-Andersen-Marasteanu model. The optimal results demonstrate that the optimal blend ratio of the developed asphalt is 12% EME/8% SBS/1.5% ZnO. Under this composition, the road performance indicator values of softening point, penetration and ductility of the modified asphalt met the standard requirements. The dynamic shear rheometer tests demonstrates that the inclusion of SBS and nano ZnO considerably enhanced the shear resistance and recovery deformation capacity of EME, effectively improving the high-temperature deformation resistance of asphalt. Furthermore,the Refutas and the Christensen-Andersen-Marasteanu model fitting results showed that adding SBS and nano ZnO considerably improved the temperature sensitivity of the EME types high modulus modified asphalt and exhibiting low frequency sensitivity. Compared to PR Module-type high modulus modifier(PRM),TGA reveals that the maximum thermal weight loss of EME-SBS-ZnO decreased by 3.5441%, indicating better thermal stability and the major character of SBS,EME and asphalt is physical reaction. Moreover, EME-nano ZnO-SBS high modulus asphalt at 64 °C shows Jnr-diff = 9.5% and passes the "E" extreme traffic grade. Additionally, its cost is 4.67% lower than that of the PRM high modulus modified asphalt, presenting considerable economic benefits.

Relativity of the event: examples in JT gravity and linearized GR

Observables in quantum gravity are famously defined asymptotically, at the boundary of AdS or Minkowski spaces. However, by gauge fixing a coordinate system or suitably dressing the field operators, an approximate, “quasi-local” approach is also possible, that can give account of the measurements performed by a set of observers living inside the spacetime. In particular, one can attach spatial coordinates to the worldlines of these observers and use their proper times as a time coordinate. Here we highlight that any such local formulation has to face the relativity of the event, in that changing frame (= set of observers) implies a reshuffling of the point-events and the way they are identified. As a consequence, coordinate transformations between different frames become probabilistic in quantum gravity. We give a concrete realization of this mechanism in Jackiw-Teitelboim gravity, where a point in the bulk can be defined operationally with geodesics anchored to the boundary. We describe different ways to do so, each corresponding to a different frame, and compute the variances of the transformations relating some of these frames. In particular, we compute the variance of the location of the black hole horizon, which appears smeared in most frames. We then suggest how to calculate this effect in Einstein gravity, assuming knowledge of the wavefunction of the metric. The idea is to expand the latter on a basis of semiclassical states. Each element of this basis enjoys standard/deterministic coordinate transformations and the result is thus obtained by superposition. As a divertissement, we sabotage Lorentz boosts by adding to Minkoswki space a quantum superposition of gravitational waves and compute the probabilistic coordinate transformation to a boosted frame at linear order. Finally, we attempt to translate the relativity of the event into the language of dressed operators.

Multi-component decompositions, linear superpositions, and new nonlinear integrable coupled KdV-type systems

Abstract In the realm of nonlinear integrable systems, the presence of decompositions facilitates the establishment of linear superposition solutions and the derivation of novel coupled systems exhibiting nonlinear integrability. By focusing on single-component decompositions within the potential BKP hierarchy, it has been observed that specific linear superpositions of decomposition solutions remain consistent with the underlying equations. Moreover, through the implementation of multi-component decompositions within the potential BKP hierarchy, successful endeavors have been undertaken to formulate linear superposition solutions and novel coupled KdV-type systems that resist decoupling via alterations in dependent variables.

Orthogonality of polarization superposition based on polarization holography.

We propose a polarization superposition orthogonal theory based on tensor polarization holography. Based on this theory, the holographic multiplexing capability can be improved measurably. The orthogonality of polarization waves is characterized by the null reconstruction in polarization holography, achieved through the superposition of multiple basic polarization reference waves. This paper analyzes the orthogonality of linear polarization wave superposition and circular polarization wave superposition using the tensor polarization holography theory. Using the polarized holography multiplexing technique, we experimentally verify the orthogonality of polarization wave superposition. Our experimental results align with the theoretical analysis, indicating potential applications in polarization encoding and decoding by this theory, thereby diversifying optical encryption technology Additionally, we demonstrate that polarization superposition orthogonality holds significant promise for optical control technology.

Night cooling by hybrid supply ventilation – analytical predictions of airflow rates and the ‘hybrid ventilation triangles’

Overheating in buildings can be mitigated during periods of excessively warm weather through the application of a night purge ventilation strategy. Building on the mathematical model of Waterson and Hunt (2024), we investigate the emerging field of hybrid ventilation – specifically the rates of airflow achieved by the simultaneous combination of ‘stack-driven’ natural displacement ventilation and a mechanical supply. Whilst the focus of Waterson and Hunt (2024) was specifically on predicting the time taken to complete a purge, herein we focus on airflow rates and in doing so elucidate the somewhat counter intuitive role that the mechanical supply has on the natural ventilation flow rates. Our results challenge the perception that a hybrid approach must be superior to both solely natural and mechanical strategies. Focusing on the variation in airflow rates during a hybrid purge, our model reveals: (i) a hybrid purge offers an improvement over a solely mechanical purge only during one of the two distinct flow regimes identified; and (ii) the manner in which the stack-driven and mechanical components combine is highly nuanced and cannot be predicted by the linear superposition of the constituent stack-driven and mechanical contributions.

Asymptotic solutions for heat transfer and stresses in functionally graded porous sandwich pipes subjected to nonuniform pressures and thermal loads

In this work, thermomechanical behaviors of temperature-dependent (TD) functionally graded porous (FGP) sandwich pipes subjected to nonuniform pressures and thermal loads are studied. Because the material properties are variable across the wall of the pipe, seeking exact solutions for the pipe is almost impossible. We use a slice model where the pipe is partitioned into plenty of annular slices and each slice is assumed to have uniform material properties. First, the nonlinear heat transfer along the pipe wall thickness is obtained by introducing an iterative procedure. Then, by using the Fourier series, the mechanical problem is decomposed into axisymmetric and nonaxisymmetric parts. Both the parts can be treated by the state space method and transfer matrix method, and then the superposition principle is used to obtain the displacement and stress distributions. The model results are in good consistency with those obtained from the numerical simulation and those reported in the literature. Finally, an FGP sandwich pipe is considered to discuss the effects of the temperature dependence of material properties (TDMP), power-law index, porosity, and pressure distribution on its thermomechanical behaviors.

Nearshore Propagation and Amplification of the Tsunami Following the 2024 Noto Peninsula Earthquake, Japan

AbstractOn 1 January 2024, a massive earthquake struck the Noto Peninsula in Japan, and the resulting tsunami significantly damaged the nearby coasts. This study focuses on Iida Bay, located on the peninsula that suffered severe coastal damage. We observed a tsunami waveform in Iida Bay from video analysis owing to the lack of instrument data. This, combined with the waveform observed outside the bay, was used to correct the initial sea‐surface displacements produced by a prior source model. We successfully reproduced the observed waveforms with corrected displacements and investigated how the tsunami propagated and amplified in the bay. Alongshore wave propagation and superposition were identified as crucial factors in this tsunami event.

A modified noise prediction model based on vehicles’ random probability distribution for signalized and main road priority-controlled intersections

A modified noise prediction model based on vehicles’ random probability distribution is proposed to address the difficulty of noise prediction caused by various traffic characteristics of different types of intersections. Monte Carlo simulation is used to generate specific vehicle locations with the assumption of time headway is Burr distribution, and traffic noise can be calculated based on the energy superposition principle. The model has been validated as the average absolute error for Leq of 1.4 dB(A) at both signalized and main road priority-controlled intersections. Applications of two types of intersections are presented. Different noise impacts are indicated in the two intersection modes, as the signalized intersection reduces noise value by 2.1 dB compared with a 0.3 dB increase at priority-controlled intersections with speeds varying from 30 to 50 km/h. Higher speeds result in more concentrated noise values across flow ratios at signalized intersections, while the opposite trend is observed at priority-controlled intersections. Flow ratios of two axes, speed, and receiver locations play different roles in the noise effect of two intersection modes.

Experimental and theoretical study on axial compression behaviour of the modular combined column

Between the modular units of the modular steel building, there exists a combination of the adjacent modular columns. Due to the gaps between the modular columns and the lack of horizontal connections, the integrity of the modular steel structure is weak, which limits the use of modular steel structures in high-rise buildings. This paper proposes a kind of modular combined column realized the connection of modular single columns through the connectors and concrete, which can improve the integrity of the modular steel building. The assembly process of this new modular combined column is described. For axial compressive performance tests, four modular combined column specimens were designed, each with different height or different number of connecting plates. The axial compressive bearing capacity, ductility, stiffness, and other mechanical parameters of the specimens were analyzed according to the phenomena and load-displacement curves of the test. Then, the axial compression failure mode of the modular combined column specimens is compared and analyzed in conjunction with the finite element model. The results indicate that the axial compressive performance and ductility of the combined column suggested in this research are exceptional. The connector can enhance the overall mechanical qualities of the combined column by augmenting the restraining impact of concrete. Finally, the theoretical equation of the axial compression bearing capacity of the modular combined column is obtained by employing the superposition principle, and the equation's reliability is confirmed, along with the test results and the results of the numerical analysis.

Introduction of a free sound system design exchange format (SDE) for data from different sound systems for noise predictions with complex summation

To consider the correlated sources of sound systems from different manufacturers in noise predictions equally with complex summation, a free exchange format for sound system planning software on the one hand and environmental noise software on the other is being defined in a cooperation with d&b audiotechnik, L-Acoustics and SoundPLAN: SDE = Sound/System Design/Data Exchange/Export This paper introduces the SDE format, its motivation and structure. With increasing open-air events in urban areas, potential problems with noise also increase. Proactive noise predictions can help prevent noise from becoming a problem in the first place. Until now it has not been possible to use data from planned sound systems from different manufacturers for equivalent calculations with complex summation. Modern sound systems have high directivity, especially loudspeaker arrays. The directivity of arrays results from superposition of sound waves from all loudspeakers. This effect is used specifically with line arrays and subwoofer arrays to optimize sound and coverage in audience areas. However, the resulting emission of an entire sound system is not constant over distance. Time-of-flight and relative phase at the receiver points must be considered with complex summation.