Number Of Modes Research Articles

Full wave modeling of radio-frequency beams in tokamaks in the electron cyclotron frequency range

Simulation of full wave, without paraxial approximation, high-resolution solution of wave equations in frequency domain in the electron cyclotron resonance (ECR) frequency range for realistic Tokamak plasma parameters became possible by using recently formulated hybrid iterative algorithm [Svidzinski et al., Phys. Plasmas 25, 082509 (2018)] for numerically solving discretized wave equations. This approach combines time evolution and iterative relaxation techniques into iteration cycles. This algorithm is implemented in 2D code FullWave, solving wave equations in Tokamaks in cold and hot plasma models, and it has been tested in 3D full wave iterative RF beams simulation tool, which is presently being developed to model 3D ECRH RF beams in fusion devices using dynamic grid adaptation. The results of 2D full wave modeling, assuming specified toroidal mode number, of ECRH RF beams in DIII-D plasma, performed in the cold and hot plasma models for outboard and top launch scenarios using FullWave are presented. Nonlocal hot plasma response model, based on accurate numerical solution of linearized Vlasov equation, is used to model beam propagation and absorption in the 2nd electron cyclotron harmonic region. Demonstration of capability of the hybrid iterative algorithm to model ECRH RF beams in 3D is made by simulating a substantial part of realistic beam in DIII-D, launched from outboard side of the machine. All relevant physics of RF beam propagation, most of which is not captured in paraxial approximation, such as beam's divergence, interference between the X and O modes in the beam, X-O mode conversion, beam splitting into the X and O mode beams, transformation of beam's cross section, and absorption at the 2nd electron cyclotron harmonic, is captured in the simulations. A numerical technique to find an optimal beam polarization at the launcher to launch a nearly pure X or O mode beam in plasma is developed and tested.

Defect induced crystal lattice disorder and its effect on the electron-phonon coupling in Fe doped ZnO thin films

We established a strong correlation between the crystal lattice disorder in Fe doped ZnO (FexZn1-xO) thin films and its effect on the electron phonon (e-p) coupling strength (I2LO/I1LO) which decreased with Fe doping concentration, improved with annealing temperature and showed a mixed increasing/decreasing trend by the variation of the argon (Ar) to oxygen (O2) gas ratio (Ar + O2, Ar) in the deposition chamber. Fe doping raised the number of phonon modes, intensity and full width at half maximum (FWHM) of the 1LO phonon modes suggesting the confinement of phonons due to the increased crystal lattice disorder in the FexZn1-xO films. High temperature annealing enhanced the e-p coupling strength reaching a maximum at 500 °C indicating better crystal quality at high temperature. Furthermore, the e-p coupling strength dropped with the doping concentration for the films prepared in Ar + O2 atmosphere and that showed a mixed increasing/decreasing trend for films prepared in Ar atmosphere. This unique physical phenomena confirmed that the coupling strength not only depend on the dopant concentration but also the dopant induced micro/nano defects that modulate the crystal lattice disorder and the coupling strength in doped ZnO. The as prepared FexZn1-xO thin films were highly oriented along the c-axis displaying columnar nanorod (film) like morphology at low (high) Fe doping concentration with the co-existence of both Fe2+ and Fe3+ ions. Fe doping increased the band gap from 3.28 eV for un-doped ZnO to 3.35 eV (1.40 at.% of Fe) and 3.42 eV (3.5 at.% of Fe). Nearly forty (40) thin films were used for a detailed investigation.

Dalton's law of partial optical thermodynamic pressures in highly multimoded nonlinear photonic systems.

We show that in highly multimoded nonlinear photonic systems, the optical thermodynamic pressures emerging from different species of the optical field obey Dalton's law of partial pressures. In multimode settings, the optical thermodynamic pressure is defined as the conjugate to the extensive variable associated with the system's total number of modes and is directly related to the actual electrodynamic radiation forces exerted at the physical boundaries of the system. Here, we extend this notion to photonic configuration supporting different species of the optical field. Under thermal equilibrium conditions, we formally derive an equation that establishes a direct link between the partial thermodynamic pressures and the electrodynamic radiation pressures exerted by each polarization species. Our theoretical framework provides a straightforward approach for quantifying the total radiation pressures through the system's thermodynamic variables without invoking the Maxwell stress tensor formalism. In essence, we show that the total electrodynamic pressure in such arrangements can be obtained in an effortless manner from initial excitation conditions, thus avoiding time-consuming simulations of the utterly complex multimode dynamics. To illustrate the validity of our results, we carry out numerical simulations in multimoded nonlinear optical structures supporting two polarization species and demonstrate excellent agreement with the Maxwell stress tensor method.

Enhancing long-term river water quality prediction: Construction and validation of an improved hybrid model

To prevent eutrophication of river caused by excessive inputs of nutrients, accurately predicting these nutrient concentrations is of utmost importance. However, long-term accurate predictions of nutrients concentrations remain a challenge. In this study, an improved hybrid algorithm combining adaptive variational mode decomposition and multi-functional recurrent fuzzy neural network (AVMD-MFRFNN) was proposed. Firstly, whale optimization algorithm (WOA) was developed to identify the optimal number of modes for variational mode decomposition (VMD). Then VMD was employed to decompose input data into intrinsic mode fractions (IMFs), benefiting for reducing the noise effect and non-stationarity of data. Then, MFRFNN with the capability of characterizing complex data was developed to train and test the IMFs. The proposed AVMD-MFRFNN achieved impressive results with the root mean square errors (RMSEs) of 0.036 mg/L, 0.758 mg/L and 1.435 mg/L for predicting total phosphorus (TP), chemical oxygen demand (CODMn) and total nitrogen (TN) after 168 hours. These results signify a decrease of 5.3%, 14.1% and 30.1% compared to the second-best compared method. Moreover, this study demonstrates the potential that integrating the proposed AVMD with other methods can enhance the modeling performance of time series. Furthermore, sensitivity analysis results further validate the effectiveness of WOA in optimizing VMD parameter. Finally, the applicability of AVMD-MFRFNN was confirmed by the data from another river section. These results provide new insights and technical support into the management and preservation of river water environment.

Bounding the Rademacher complexity of Fourier neural operators

AbstractRecently, several types of neural operators have been developed, including deep operator networks, graph neural operators, and Multiwavelet-based operators. Compared with these models, the Fourier neural operator (FNO), a physics-inspired machine learning method, is computationally efficient and can learn nonlinear operators between function spaces independent of a certain finite basis. This study investigated the bounding of the Rademacher complexity of the FNO based on specific group norms. Using capacity based on these norms, we bound the generalization error of the model. In addition, we investigate the correlation between the empirical generalization error and the proposed capacity of FNO. We infer that the type of group norm determines the information about the weights and architecture of the FNO model stored in capacity. The experimental results offer insight into the impact of the number of modes used in the FNO model on the generalization error. The results confirm that our capacity is an effective index for estimating generalization errors.

Low‐sidelobe orbital angular momentum beam for donut‐shaped amplitude‐and‐phase metasurface based on Bayliss synthesis method

AbstractIn this letter, a method for generating low‐sidelobe orbital angular momentum (OAM) beam is presented using a donut‐shaped amplitude and phase metasurface (DS‐APM). Building upon conventional phase‐only metasurface, the Bayliss synthesis method is employed to adjust the amplitude distribution on the metasurface. Thereby, the amplitude and phase metasurface (APM) can reduce the sidelobe level of the OAM beam. Subsequently, considering the Nyquist conditions and momentum constraints, a hollow modification is implemented on the APM array aperture center. The adjustment of the hollow dimension renders the DS‐APM compatible with the corresponding OAM beam mode number. Furthermore, a modified I‐shaped element is proposed, which enables independent modulation of the amplitude and phase of reflected cross‐polarized waves. Utilizing the proposed elements, a DS‐APM applied to generate a second‐order OAM beam operating at 15 GHz was designed, fabricated, and measured. The measurement results align with the full‐wave simulations, thereby validating the rationality of the proposed method.

Branch error reduction criterion-based signal recursive decomposition and its application to wind power generation forecasting.

Due to the ability of sidestepping mode aliasing and endpoint effects, variational mode decomposition (VMD) is usually used as the forecasting module of a hybrid model in time-series forecasting. However, the forecast accuracy of the hybrid model is sensitive to the manually set mode number of VMD; neither underdecomposition (the mode number is too small) nor over-decomposition (the mode number is too large) improves forecasting accuracy. To address this issue, a branch error reduction (BER) criterion is proposed in this study that is based on which a mode number adaptive VMD-based recursive decomposition method is used. This decomposition method is combined with commonly used single forecasting models and applied to the wind power generation forecasting task. Experimental results validate the effectiveness of the proposed combination.

Gain and mode purity filtering dual polarized OAM beam generation using cavity waveguide-based 3D transmitarray

A 3D transmitarray (TA) is proposed to generate dual-polarized orbital angular momentum (OAM) beams with gain and mode purity filtering responses. The TA units are realized by square cavity filters with the same passband and different orders and inner widths, resulting in different coupling cavity numbers. The evanescent modes in the coupling cavities will greatly decrease the propagation constant, thus generating a large phase variation. The square structure of the cavity filter makes it able to support dual-polarized wave propagation with the same phase delay and insert loss. Based on these transmission characteristics, eight different TA units are designed to realize a 3-bit phase gradient within the passband of 25.4–26.7 GHz. It should be emphasized that the dispersed transmission phase and magnitude of the eight TA units in the stopbands will deteriorate the purity of the OAM beam. Therefore, the gain and mode purity filtering responses can be realized simultaneously. In order to verify the performance of the proposed OAM TA design, a TA prototype with the mode number l = −1 is fabricated by 3D printing technology. The TA can realize the maximum gain of 25.9 dB in the passband, and the rejection level is below −15.0 dB within the main beam direction. The purities of dual-polarized OAM beams are over 0.5 in the passband, and the cross-polarization is below −16.5 dB. The advantages of the OAM TA, including gain-filtering and mode purity-filtering responses, dual-polarization, and high efficiency make it a promising solution for millimeter-wave OAM sensing and communication applications.

Fast CU size decision and intra-prediction mode decision method for H.266/VVC

AbstractH.266/Versatile Video Coding (VVC) is the most recent video coding standard developed by the Joint Video Experts Team (JVET). The quad-tree with nested multi-type tree (QTMT) architecture that improves the compression performance of H.266/VVC is introduced. Moreover, H.266/VVC contains a greater number of intra-prediction modes than H.265/High Efficiency Video Coding (HEVC), totalling 67. However, these lead to extremely the coding computational complexity. To cope with the above issues, a fast intra-coding unit (CU) size decision method and a fast intra-prediction mode decision method are proposed in this paper. Specifically, the trained Support Vector Machine (SVM) classifier models are utilized for determining CU partition mode in a fast CU size decision scheme. Furthermore, the quantity of intra-prediction modes added to the RDO mode set decreases in a fast intra-prediction mode decision scheme based on the improved search step. Simulation results illustrate that the proposed overall algorithm can decrease 55.24% encoding runtime with negligible BDBR.

Enhancing frequency stability and mode control in a Brillouin random fiber laser with a strongly scattering disordered grating

Random fiber lasers (RFLs) with disordered scattering feedback media provide a range of functionalities and properties. The primary drawback with weak Rayleigh scattering (RS)-based RFLs is their large frequency drift and mode hopping, which are caused by the random walk of photons at different round trips. Here, we present a technique to control the mode propagation of RFLs by using a narrow gain bandwidth from stimulated Brillouin scattering and photon localization from a strongly scattering disordered grating. Multiple scattering of light within the disordered grating leads to photon localization and narrow reflection peaks, which suppresses frequency drift and reduces the number of modes. The compact Brillouin random fiber laser (BRFL) with a 200 m strongly scattering disordered grating enables single-mode lasing with an ultra-narrow linewidth of ∼650 Hz. The results of the real-time spectral evolution obtained by the heterodyne method demonstrate long-term stability of the lasing frequency, confirming the capability of the strongly scattering disordered grating to control mode propagation of the BRFL. The BRFL exhibits an ultra-high frequency stability of 0.48 MHz and mode-hop-free operation up to 120 s. This work provides a perspective on the development of RFLs with high coherence and stability.

Nonunion scaphoid bone shape prediction using iterative kernel principal polynomial shape analysis.

The scaphoid is an important mechanical stabilizer for both the proximal and distal carpal columns. The precise estimation of the complete scaphoid bone based on partial bone geometric information is a crucial factor in the effective management of scaphoid nonunion. Statistical shape model (SSM) could be utilized to predict the complete scaphoid shape based on the defective scaphoid. However, traditional principal component analysis (PCA) based SSM is limited by its linearity and the inability to adjust the number of modes used for prediction. This study proposes an iterative kernel principal polynomial shape analysis (iKPPSA)-based SSM to predict the pre-morbid shape of the scaphoid, aiming at enhancing the accuracy as well as the robustness of the model. Sixty-five sets of scaphoid images were used to train SSM and nine sets of scaphoid images were used for validation. For each validation image set, three defect types (tubercle, proximal pole, and avascular necrosis) were virtually created. The predicted shapes of the scaphoid by PCA, PPSA, KPCA, and iKPPSA-based SSM were evaluated against the original shape in terms of mean error, Hausdorff distance error, and Dice coefficient. The proposed iKPPSA-based scaphoid SSM demonstrates significant robustness, with a generality of 0.264mm and a specificity of 0.260mm. It accounts for 99% of variability with the first seven principal modes of variation. Compared to the traditional PCA-based model, the iKPPSA-based scaphoid model prediction demonstrated superior performance for the proximal pole type fracture, with significant reductions of 25.2%, 24.7%, and 24.6% in mean error, Hausdorff distance, and root mean square error (RMSE), respectively, and a 0.35% improvement in Dice coefficient. This study showed that the iKPPSA-based SSM exploits the nonlinearity of data features and delivers high reconstruction accuracy. It can be effectively integrated into preoperative planning for scaphoid fracture management or morphology-based biomechanical modeling of the scaphoid.

A high stability and low noise passively Q-switched yellow-green laser with a Ti3C2Tx-PVA saturable absorber

An 808 nm laser diode (LD) end-pumped passively Q-switched Nd: YAG ceramic yellow green laser at 561 nm with high stability and low noise has been demonstrated, for the first time to our knowledge based on passively Q-switching with a Ti3C2Tx-polyvinyl alcohol (Ti3C2Tx-PVA) film, frequency selection and filtering with a Brewster polarizer (BP) and a birefringent crystal (BC), and intracavity frequency doubling with a LiB3O5 (LBO) crystal. The 1112 nm and 1116 nm wavelengths from the Nd: YAG ceramic and the number of longitudinal modes of 1123 nm fundamental frequency light were effectively suppressed by adopting BP and BC. At 5.1 W of the 808 nm LD pump power, the 561 nm-PQYG laser with a maximum average power of 75.5 mW, a maximum repetition rate of 610 kHz, and a narrowest pulse width of 41 ns were obtained, corresponding to an average power instability of ±0.29%, a repetition rate instability ±7.08%, a pulse width instability of ±4.67%, and a laser noise of 0.49% over a period of 4 h.

Tailoring Single-Mode Random Lasing of Tin Halide Perovskites Integrated in a Vertical Cavity.

The development of random lasing (RL) with predictable and controlled properties is an important step to make these cheap optical sources stable and reliable. However, the design of tailored RL characteristics (emission energy, threshold, number of modes) is only obtained with complex photonic structures, while the simplest optical configurations able to tune the RL are still a challenge. This work demonstrates the tuning of the RL characteristics in spin-coated and inkjet-printed tin-based perovskites integrated into a vertical cavity with low quality factor. When the cavity mode is resonant with the photoluminescence (PL) peak energy, standard vertical lasing is observed. More importantly, single mode RL operation with the lowest threshold and a quality factor as high as 1000 (twenty times the quality factor of the resonator) is obtained if the cavity mode lies above the PL peak energy due to higher gain. These results can have important technological implications toward the development of low-cost RL sources without chaotic behavior.

Analysis of Image Data Augmentation in Smart Agriculture

The demand for agricultural production automation in smart agriculture has made deep learning widely used in tasks, e.g., disease identification, weed-crop segment and fruit detection based on image processing. However, in agricultural production environments, there are limitations in data acquisition, so data enhancement technology has also been widely used. This study introduces two data enhancement methods commonly used in smart agriculture, namely image transformation and GAN-based, and analyzes their specific applications and roles in three common task scenarios: disease identification, weed-crop segment, and fruit detection. According to the analysis, the data enhancement is mainly used to deal with class imbalance problems and over-fitting problems, and can significantly improve model performance in specific scenarios; the complexity of tasks and image structures has an impact on the application effects of different methods, and image segmentation tasks. It is necessary to increase the number of image modes, so methods such as GAN-based are adopted. However, due to the complexity of the image, fruit detection uses simple transformation methods to achieve better results. In addition, data enhancement methods designed for specific tasks, such as simulating synthetic images, can also achieve good results. However, data augmentation technology still has mode collapse problems and is too cumbersome in its application, which points out the direction for subsequent research. Overall, this research sorts out the applications of common data enhancement methods, analyzes the characteristics and limitations of these methods, and hopes to provide guidance for subsequent research.

Modeling groundwater flow with random hydraulic conductivity using radial basis function partition of unity method

Simulating groundwater flows in heterogeneous aquifers is one of the most widely studied problems. The heterogeneity is modeled through random hydraulic conductivity fields log-normally distributed. In this paper, we aim to generate the realization of the log-normal hydraulic conductivity by summing up a finite number of random periodic modes with the Kraichnan algorithm. To address Neumann conditions, we propose a change of variables that results in Dirichlet boundary conditions along all boundaries of the computational domain. Then, we suggest using the radial basis function partition of unity method (RBFPUM) and RBFPUM with QR factorization (RBFPUM-QR) to analyze groundwater flow in the heterogeneous porous medium. We evaluate the performance of the proposed methods by increasing the number of random modes and the variance of the log-hydraulic conductivity fields using Gaussian and exponential correlation. In addition, we verify the effectiveness of the presented approaches in one and two dimensions using the method of manufactured solutions. Furthermore, we provide statistical inferences through Monte Carlo simulations. Numerical results demonstrate that RBFPUM-QR performs well in handling higher heterogeneity in both single realizations and Monte Carlo simulations.

The Puzzling of Stefan–Boltzmann Law: Classical or Quantum Physics

Stefan–Boltzmann law, stating the fourth power temperature dependence of the radiation emission by a black-body, was empirically formulated by Stefan in 1874 by fitting existing experiments and theoretically validated by Boltzmann in 1884 on the basis of a classical physical model involving thermodynamics principles and the radiation pressure predicted by Maxwell equations. At first sight the electromagnetic (EM) gas assumed by Boltzmann and following Rayleigh (1900) identifiable as an ensemble of N classical normal-modes, looks like an extension of the classical model of the massive ideal-gas. Accordingly, for this EM gas the internal total energy, U, was assumed to be function of volume V and temperature T as [Formula: see text], and the equation of state was given by [Formula: see text], with P the radiation pressure. In addition, Boltzmann implicitly assumed that, for given values of V and T, U and the number of modes N would take finite values. However, from one hand these assumptions are not justified by Maxwell equations and classical statistics since, in vacuum (i.e., far from the EM sources), the values of N and U diverge, the so-called ultraviolet catastrophe introduced by Ehrenfest in 1911. From another hand, Boltzmann derivation of Stefan law is found to be macroscopically compatible with its derivation from quantum statistics announced by Planck in 1901. In this paper, we present a justification of this puzzling classical/quantum compatibility by noticing that the implicit assumptions made by Boltzmann is fully justified by Planck quantum statistics. Furthermore, we shed new light on the interpretation of recent classical simulations of a black body carried out by Wang, Casati, and Benenti in 2022 who found an analogous puzzling consistency between Stefan–Boltzmann law and their simulations to induce speculations on classical physics and black body radiation that are claimed to require a critical reconsideration of the role of classical physics for the understanding of quantum mechanics.

General protocol for predicting outbreaks of infectious diseases in social networks

Epidemic spreading on social networks with quenched connections is strongly influenced by dynamic correlations between connected nodes, posing theoretical challenges in predicting outbreaks of infectious diseases. The quenched connections introduce dynamic correlations, indicating that the infection of one node increases the likelihood of infection among its neighboring nodes. These dynamic correlations pose significant difficulties in developing comprehensive theories for threshold determination. Determining the precise epidemic threshold is pivotal for diseases control. In this study, we propose a general protocol for accurately determining epidemic thresholds by introducing a new set of fundamental conditions, where the number of connections between individuals of each type remains constant in the stationary state, and by devising a rescaling method for infection rates. Our general protocol is applicable to diverse epidemic models, regardless of the number of stages and transmission modes. To validate our protocol’s effectiveness, we apply it to two widely recognized standard models, the susceptible–infected–recovered-susceptible model and the contact process model, both of which have eluded precise threshold determination using existing sophisticated theories. Our results offer essential tools to enhance disease control strategies and preparedness in an ever-evolving landscape of infectious diseases.

Coverage extended MMF-based indoor OWC using overfilled launch and diversity reception

Speckle patterns generated as coherent optical beams are reflected by scattering elements. Multimode fibers (MMFs) can modify the transverse intensity distribution of speckle patterns with macro perturbations, i.e., pressures, providing a simple and low-cost way to achieve equivalent beam-steering for indoor optical wireless communications (OWCs) with divergent optical beams. However, the received optical power (ROP) variance severely limits the mobility of user terminals. In this paper, the issue is alleviated by using the overfilled launch of MMFs and the diversity gain of multi-receivers. By adjusting the axial spatial coupling distance between the MMF and the single mode fiber (SMF) emitting coherent laser, the number of excited modes of MMF can be significantly increased at 1550 nm with negligible coupling and bending losses. In addition, the signal-to-noise ratio (SNR) enhancement obtained by applying two receivers is theoretically analyzed for the case when either thermal noise or shot noise is dominant. The experimental results demonstrate that the proposed scheme can efficiently compensate for the ROP inhomogeneity, and at the same time it can extend the achievable full steering angle up to 12° at a 1.5-m free-space distance for bit error rate (BER) values of less than 3.8 × 10−3.

Spatiotemporal beating and vortices of van der Waals hyperbolic polaritons

In conventional thin materials, the diffraction limit of light constrains the number of waveguide modes that can exist at a given frequency. However, layered van der Waals (vdW) materials, such as hexagonal boron nitride (hBN), can surpass this limitation due to their dielectric anisotropy, exhibiting positive permittivity along one optic axis and negativity along the other. This enables the propagation of hyperbolic rays within the material bulk and an unlimited number of subdiffractional modes characterized by hyperbolic dispersion. By employing time-domain near-field interferometry to analyze ultrafast hyperbolic ray pulses in thin hBN, we showed that their zigzag reflection trajectories bound within the hBN layer create an illusion of backward-moving and leaping behavior of pulse fringes. These rays result from the coherent beating of hyperbolic waveguide modes but could be mistakenly interpreted as negative group velocities and backward energy flow. Moreover, the zigzag reflections produce nanoscale (60 nm) and ultrafast (40 fs) spatiotemporal optical vortices along the trajectory, presenting opportunities to chiral spatiotemporal control of light-matter interactions. Supported by experimental evidence, our simulations highlight the potential of hyperbolic ray reflections for molecular vibrational absorption nanospectroscopy. The results pave the way for miniaturized, on-chip optical spectrometers, and ultrafast optical manipulation.

Constrained Reweighting of Distributions: An Optimal Transport Approach.

We commonly encounter the problem of identifying an optimally weight-adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the moments, tail behavior, shapes, number of modes, etc., of the resulting weight-adjusted empirical distribution. In this article, we substantially enhance the flexibility of such a methodology by introducing a nonparametrically imbued distributional constraint on the weights and developing a general framework leveraging the maximum entropy principle and tools from optimal transport. The key idea is to ensure that the maximum entropy weight-adjusted empirical distribution of the observed data is close to a pre-specified probability distribution in terms of the optimal transport metric, while allowing for subtle departures. The proposed scheme for the re-weighting of observations subject to constraints is reminiscent of the empirical likelihood and related ideas, but offers greater flexibility in applications where parametric distribution-guided constraints arise naturally. The versatility of the proposed framework is demonstrated in the context of three disparate applications where data re-weighting is warranted to satisfy side constraints on the optimization problem at the heart of the statistical task-namely, portfolio allocation, semi-parametric inference for complex surveys, and ensuring algorithmic fairness in machine learning algorithms.