Intensity Distribution Research Articles

Applying the Adomian Method to Solve the Fokker–Planck Equation: A Case Study in Astrophysics

The objective of this study is to model astrophysical systems using the nonlinear Fokker–Planck equation, with the Adomian method chosen for its iterative and precise solutions in this context, applying boundary conditions relevant to data from the Rossi X-ray Timing Explorer (RXTE). The results include analysis of 156 X-ray intensity distributions from X-ray binaries (XRBs), exhibiting long-tail profiles consistent with Tsallis q-Gaussian distributions. The corresponding q-values align with the principles of Tsallis thermostatistics. Various diffusion hypotheses—classical, linear, nonlinear, and anomalous—are examined, with q-values further supporting Tsallis thermostatistics. Adjustments in the parameter α (related to the order of fractional temporal derivation) reveal the extent of the memory effect, strongly correlating with fractal properties in the diffusive process. Extending this research to other XRBs is both possible and recommended to generalize the characteristics of X-ray scattering and electromagnetic waves at different frequencies originating from similar astronomical objects.

Investigation of interfractional range variation owing to anatomical changes with beam directions based on water equivalent thickness in proton therapy for pancreatic cancer.

To assess the interfractional anatomical range variations (ARVs) with beam directions and their impact on dose distribution in intensity modulated proton therapy, we analyzed water equivalent thickness (WET) from 10 patients with pancreatic cancer. The distributions of the interfractional WET difference ($\Delta{\mathrm{WET}}^{\theta }$) across 360° were visualized using polar histograms. Interfractional ARVs were evaluated using the mean absolute error and ΔWET pass rate, indicating the percentage of $\Delta \mathrm{WE}{\mathrm{T}}^{\theta }$ < thresholds. The impact on dose distribution in proton therapy was evaluated based on two treatment plans for 40Gy(RBE)/5 fractions: 'Plan A', using two beam angles, in which the target was closest to the body surface among four perpendicular directions; and 'Plan B', using two beam angles with small ARVs. Analysis revealed individual variations in angular trends of interfractional ARVs. Three distinct trends were identified: Group 1 exhibited small ARVs around posterior directions; Group 2 exhibited small ARVs except ~60°; Group 3 demonstrated minimal ARVs only ~90°. In dose evaluation, while 150° and 210° were selected in Plan B for 9 out of 10 patients, for the remaining patient, 60° and 90° were chosen. Comparing dose volume histogram parameters for all patients, Plan B significantly reduced target coverage loss while maintaining organ-at-risk sparing comparable to Plan A. These results demonstrated that selecting beam angles with small interfractional ARVs for each patient enhances the robustness of dose distribution, reducing target coverage loss.

Non-uniform phase distribution of a tightly focused elliptically polarized vortex beam

Abstract Tight focusing of elliptically polarized vortex beams has been previously studied for optical manipulation, optical information encoding, and so on. Still, there is a lack of research on the status of the phase distribution on the focal plane. In this study, we found that the phase distribution of a tightly focused elliptically polarized vortex beam is non-uniform, i.e., the phase distribution exhibits flatter and steeper regions due to the elliptical polarization of the input vortex beam. It is mentioned that the phase non-uniformity was related to the ellipticity of the polarization of the incident beam. Furthermore, we analyzed the intensity and phase distribution of a tightly focused elliptically polarized vortex beam. We found that the spin angular momentum was converted to the orbital angular momentum because the topological charge of the output beam was greater than that of the input beam. The non-uniform phase distribution of a tightly focused elliptically polarized vortex beam enables control over light–matter interaction, leading to advancements in optical tweezers, quantum information processing, and super-resolution microscopy.

Statistical properties of circular and rectangular multi-sinc Schell-model beams propagating in uniaxial crystals

With the extended Huygens–Fresnel principle, we derive the expressions for the spectral intensity, coherence, and effective beam width of circular and rectangular multi-sinc Schell-model (MSSM) beams propagating through uniaxial crystals. Numerical simulations are employed to extensively explore how beam and crystal parameters modulate the optical field. The results reveal that the propagating field exhibits multiple ring-shaped and array-like intensity distributions, with adjustable features such as the number of concentric rings, central brightness, array dimensions, and the morphology and diversity of sub-beams. Additionally, the spectral coherence displays an oscillatory distribution that evolves into a Gaussian distribution as the transmission distance increases. The anisotropy of uniaxial crystals not only influences the morphology of intensity distribution but also affects the evolution rate of coherence and the expansion rate of effective beam width. Our work contributes to optimizing beam propagation through uniaxial crystals, potentially benefiting precision optical systems in laser technology.

Orbital angular momentum superimposed mode recognition based on multi-label image classification

Orbital angular momentum (OAM) multiplexing technology has great potential in high capacity optical communication. OAM superimposed mode can extend communication channels and thus enhance the capacity, and accurate recognition of multi-OAM superimposed mode at the receiver is very crucial. However, traditional methods are inefficient and complex for the recognition task. Machine learning and deep learning can offer fast, accurate and adaptable recognition, but they also face challenges. At present, the OAM mode recognition mainly focus on single OAM mode and ±l superimposed dual-OAM mode, while few researches on multi-OAM superimposed mode, due to the limitations of single-object image classification techniques and the diversity of features to recognize. To this end, we develop a recognition method combined with multi-label image classification to accurately recognize multi-OAM superimposed mode vortex beams. Firstly, we create datasets of intensity distribution map of three-OAM and four-OAM superimposed mode vortex beams based on numerical simulations and experimental acqusitions. Then we design a progressive channel-spatial attention (PCSA) model, which incorporates a progressive training strategy and two weighted attention modules. For the numerical simulation datasets, our model achieves the highest average recognition accuracy of 94.9% and 91.2% for three-OAM and four-OAM superimposed mode vortex beams with different transmission distances and noise strengths respectively. The highest experimental average recognition accuracy for three-OAM superimposed mode achieves 92.7%, which agrees with the numerical result very well. Furthermore, our model significantly outperforms in most metrics compared with ConvNeXt, and all experiments are within the affordable range of computational cost.

Scenario-based stochastic optimization on the variability of solar and wind for component sizing of integrated energy systems

The inherent intermittency and variability of renewable energy sources present significant challenges to the optimal design and implementation of integrated energy systems (IES). This paper introduces a novel stochastic optimization model that integrates advanced scenario generation and clustering algorithm for renewable energy sources within a multi-objective, bi-level optimization framework. Specifically, the clearness index is employed to represent the stochastic distribution of solar radiation intensity by beta distribution, while wind speed uncertainty is modeled seasonally using the Weibull distribution. Monte Carlo sampling with synchronous back substitution is applied for scenario generation and reduction of solar radiation and wind speed. To address the multi-objective evaluation, the analytic hierarchy process is utilized, and the joint optimization is achieved by combining a region contraction algorithm with stochastic programming. The proposed methodology is validated on an IES featuring various heating devices, incorporating uncertainties in both wind and solar energy. The results indicate that the absorption heat pump-based scheme achieves superior energy-saving performance, achieving an energy rate of 0.4724. Additionally, the compression heat pump-based scheme exhibits excellent economic efficiency and environmental sustainability, with a cost of energy of 0.3639 and a renewable fraction of 0.5536.

Spatially distributed low-cross talk vector beams.

A spatially distributed low-cross talk vector beam refers to a vector beam that exhibits different intensities, phases, and polarization states along the propagation direction. This type of vector beam features low-cross talk between beams on different planes and finds extensive applications in optical communications and related fields. However, current technologies face challenges such as intensity interference at different imaging planes and difficulties in the precise control of phases and polarization states, which affect beam quality. In this study, we investigated the beam propagation process and employed a global optimization strategy to precisely control the intensity and phase distribution of the beam fields. This approach ensures that the beam forms the desired complex amplitude distribution in the target region while effectively suppressing cross talk in non-target regions. We utilized the method to generate two beams with complementary intensities and phases. Subsequently, through an interference optical path, we separated these two beams and converted them into orthogonal polarization states. Finally, by superimposing these two beams, we obtained a spatially varying low-cross talk vector beam. We experimentally validated the beam's different optical characteristics and low-cross talk properties on three planes. Our work opens up new prospects, to the best of our knowledge, for holographic technology with capabilities for ultra-fine depth control and polarization multiplexing.

Effects of polarized and pyramidal training, with or without mindfulness, on race time and performance in amateur runners: Protocol for a randomized controlled trial

Problem: Road races in athletics has increased worldwide in recent years, leading to a growth in amateur runners (AR). Despite this growth, research aimed at this population is scarce and has methodological weaknesses. One topic of recent interest in AR is the effects of training intensity distribution (TID) and mindfulness on race time (RT); however, there is not enough evidence to establish a consensus among scientists, trainers, and athletes. Objective: To compare the effects of four training programs with polarized and pyramidal TID models on 10 km RT, ventilatory thresholds one and two, maximum aerobic speed, maximum oxygen consumption and body composition in AR. Method: A randomized controlled clinical trial with four parallel arms. The study groups include two with a polarized TID model and two with a pyramidal TID model, both combined with and without a mindfulness program over 12 weeks. Mindfulness practice will consist of 65 minutes per week through individual sessions and group workshops. Discussion: The practice of recreational athletics is increasing; however, the effect of TID and mindfulness on RT in this population have not been extensively studied. Keywords: Training intensity distribution, mindfulness, amateur runners, race time, body composition, polarized training, pyramidal training.

Revealing the influence of ring-shaped beam profiles in high-speed laser beam microwelding by synchrotron x-ray imaging

Laser beam microwelding is a precise technique for joining miniature metal components with high feed rates, which is crucial for productivity. However, high feed rates provoke humping formation—periodic beadlike protuberances along the weld seam—that compromise weld integrity. While humping has been associated with the keyhole transition from a narrow to an elongated shape using standard laser intensity distributions (e.g., Gaussian, top-hat), the impact of complex beam profiles, like ring-shaped intensity distributions, remains less understood. In this work, the influence of core-only, ring-only, and superimposed core-ring intensity distributions on humping formation during laser beam microwelding is investigated by means of synchrotron x-ray imaging. Single-track experiments on stainless steel (1.4404) at 1000 mm/s reveal that the keyhole geometry shifts from deep and narrow with core-only power input to shallow and elongated with ring-only power input. Using a superimposed core-ring intensity distribution (Pc = 300 W, Pr = 600 W) results in a U-shaped capillary and the reduction of the humping amplitude by nearly 80% (from 45.61 μm with core-only to 10.29 μm). The additional laser power comes with the tripling of the melt pool width (from 81 μm with core-only to 263 μm) likely decreasing the melt flow velocity. The reduced variability of the capillary length present for the superimposed intensity distribution further indicates a stabilized evaporation behavior. This work provides valuable insights into mitigating humping formation during laser beam microwelding of stainless steel at elevated feed rates using core-ring intensity distributions.

Training for Elite Team-Pursuit Track Cyclists-Part I: A Profile of General Training Characteristics.

To profile the training characteristics of an elite team pursuit cycling squad and assess variations in training intensity and load accumulation across the 36-week period prior to a world-record performance at the 2018 Commonwealth Games. Training data of 5 male track endurance cyclists (mean [SD]; age 21.9 [3.52]y; 4.4 [0.16]W·kg-1 at anaerobic threshold; 6.2 [0.28]W·kg-1 maximal oxygen uptake 68.7 [2.99]mL kg·min-1) were analyzed with weekly total training volume and heart rate, power output, and torque intensity distributions calculated with reference to their 3:49.804min:s.ms performance requirements for a 4-km team pursuit. Athletes completed 543 (37)h-1 of training across 436 (16) sessions. On-bike activities accounted for 69.9% of all training sessions, with participants cycling 11,246 (1139)km-1 in the training period of interest, whereas 12.7% of sessions involved gym/strength training. A pyramidal intensity distribution was evident with over 65% and 70% of training, respectively, performed at low-intensity zone heart rate and power output, whereas 5.3% and 7.7% of training was performed above anaerobic threshold. The athletes accumulated 4.4% of total training volume at, or above, their world-record team pursuit lead position torque (55N·m). These data provide updated and novel insight to the power and torque demands and load accumulation contributing to world-record team pursuit performance. Although the observed pyramidal intensity distribution is common in endurance sports, the lack of shift toward a polarized intensity distribution during taper and competition peaking differs from previous research.

3D track extraction from a fluorescent nuclear track detector via machine learning and an application to diagnostics of laser-driven ions.

We have developed an ion diagnostic method for laser-driven ion acceleration experiments that uses fluorescent nuclear track detectors (FNTDs). An FNTD records the particle tracks as color centers and does not require chemical etching, unlike CR-39 track detectors. The color centers are observed using a confocal laser microscope, and 3D particle tracks can be obtained by changing its focal position. The intensity of the color centers corresponds to the energy deposited by the ions. The nuclides of the ions can be determined from the intensity distribution of the color centers as a function of depth and the distance between the stopping point and the surface of the detector. To extract the intensity distribution, we must track the same ion tracks in the depth-layered microscopic images from the surface to the stopping point, even if they overlap with those of other ions. In addition, since an FNTD is sensitive not only to ions but also to electrons and photons, we must identify ion tracks among those from the latter particles. To analyze a statistical number of ion tracks, it is necessary to automate these processes. We have thus developed a method for automated ion detection and 3D tracking that relies on a support vector classifier and a kernelized correlation filter. This method was tested on a laser ion acceleration experiment performed using the J-KAREN-P laser. The method automatically detects ion tracks on FNTDs and tracks them in the depth direction. The training data are sampled from the Heavy-Ion Medical Accelerator in Chiba.

Integration of multiple observations for validation of mechanisms of earthquake-triggered groundwater level Anomalies: 2016 Taiwan Meinong earthquake

This study analyzes multi-depth groundwater level data and integrated observation data to validate the previously proposed mechanisms of hydrological anomalies triggered by the 2016 M6.4 Meinong earthquake in Taiwan. The main influence area was northwest of the epicenter, which may be due to the blind fault rupture, intensity distribution, and hydrogeological properties. The step changes in groundwater level do not fit the concept of epicentral distance, static stress–strain theory, or the focal mechanism. The distribution of step changes in groundwater level have a pattern similar to that of horizontal peak ground velocity. The results imply that these changes may be driven by dynamic stress–strain, instead of static stress–strain. The minimum horizontal peak ground velocity and acceleration of the Meinong earthquake, which induced obvious step changes in groundwater level and soil liquefaction, are provided. The pressure dissipation ability of an aquifer (e.g., transmissivity) may affect the persistence of groundwater responses. Four wells located near the surface rupture area, which has cemented or partial cemented geological material, showed an obvious step decrease in the groundwater level at a deep depth and all wells showed an increase in the groundwater level at a shallow depth. These decreases and increases of the groundwater level at different depths have different mechanisms, which are discussed in this study. The integrated observations made during the Meinong earthquake show that ground motion and the hydraulic properties might be important factors in hydrological anomalies. The results of this study are an important reference for further studies on earthquake hydrology.

Training for Elite Team-Pursuit Track Cyclists-Part II: A Comparison of Preparation Phases in Consecutive World-Record-Breaking Seasons.

To compare the training characteristics of an elite team pursuit cycling squad in the 3-month preparation phases prior to 2 successive world-record (WR) performances. Training data of 5 male track endurance cyclists (mean [SD]; age 23.4 [3.46]y; body mass 80.2 [2.74]kg; 4.5 [0.17]W·kg-1 at LT2; maximal aerobic power6.2 [0.27]W·kg-1; maximal oxygen uptake 65.9 [2.89]mL·kg-1·min-1) were analyzed with weekly total training volume by training type and heart rate, power output, and torque intensity distributions calculated with reference to the respective WRs' performance requirements. Athletes completed 805 (82.81) and 725 (68.40)min·wk-1 of training, respectively, in each season. In the second season, there was a 32% increase in total track volume, although track sessions were shorter (ie,greater frequency) in the second season. A pyramidal intensity distribution was consistent across both seasons, with 81% of training, on average, performed below LT1 power output each week, whereas 6% of training was performed above LT2. Athletes accumulated greater volume above WR team pursuit lead power (2.4% vs 0.9%) and torque (6.2% vs 3.2%) in 2019. In one athlete, mean single-leg-press peak rate of force development was 71% and 46% higher at mid- and late-phases, respectively, during the preparation period. These findings provide novel insights into the common and contrasting methods contributing to successive WR team pursuit performances. Greater accumulation of volume above race-specific power and torque (eg,team pursuit lead), as well as improved neuromuscular force-generating capacities, may be worthy of investigation for implementation in training programs.

Deep-water ambient sound over the Atlantis II seamounts in the Northwest Atlantica).

Ambient sound was continuously recorded for 52 days by three synchronized, single-hydrophone, near-bottom receivers. The receivers were moored at depths of 2573, 2994, and 4443 m on flanks and in a trough between the edifices of the Atlantis II seamounts. The data reveal the power spectra and intermittency of the ambient sound intensity in a 13-octave frequency band from 0.5 to 4000 Hz. Statistical distribution of sound intensity exhibits much heavier tails than in the expected exponential intensity distribution throughout the frequency band of observations. It is established with high statistical significance that the data are incompatible with the common assumption of normally distributed ambient noise in deep water. Spatial variability of the observed ambient sound appears to be controlled by the seafloor properties, bathymetric shadowing, and nonuniform distribution of the noise sources on the sea surface. Temporal variability of ambient sound is dominated by changes in the wind speed and the position of the Gulf Stream relative to the experiment site. Ambient sound intensity increases by 4-10 dB when the Gulf Stream axis is within 25 km from the receivers. The sound intensification is attributed to the effect of the Gulf Stream current on surface wave breaking.

Investigation of thermal diffusivity measurement technique based on photoacoustic signal response under the influence of three-dimesional heat transfer

In this study, we investigated the feasibility of measuring the thermal diffusivity of thermally thick solid material using the photoacoustic (PA) signal response in a three-dimensional heat diffusion state. For this purpose, we developed a heat conduction simulation model based on cylindrical coordinates to replicate the PA effect on three-dimensional heat diffusion. By numerical analysis, it was found that the phase of PA signal deviates from one-dimensional theory prediction when the lateral heat diffusion of the solid sample reaches the chamber wall of PA cell. Specifically, it was found that the phase lag inflects at the frequency where the sample’s thermal diffusion length μs is 0.91 mm at a chamber radius of 3 mm. By utilizing this correlation, the infection frequency can potentially provide the thermal diffusivity of the thermally thick sample. The experimental validation qualitatively confirmed that the phenomena observed in the numerical analysis occur in practice. However, quantitatively, the experimental results showed discrepancies from the numerical analysis, which is likely due to the influence of the radial distribution of laser intensity. Nonetheless, this issue can be resolved in practical applications through calibration using a reference sample. Numerical analysis suggested that for materials with thermal diffusivity lower than that of air, measuring thermal diffusivity could be seemingly impossible. However, the experimental results demonstrated that calibration with a reference sample having sufficiently lower thermal diffusivity than that of air effectively compensates for the influence of air’s thermal diffusion. The significant factor affecting the accuracy of thermal diffusivity determination with the proposed method is identifying the inflection frequency. It will be necessary to explore an appropriate method for determining the frequency by integrating multiple sources of information, such as simultaneously observing the amplitude of the PA signal.

Total separation of multi-plastic wastes using magnetic levitation with adjustable sensitivity

Novel separation method with high efficiency is of great significance for mechanical recycling mixed waste plastics plays. However, the efficiency of most extant methods is restricted by their shortage that the methods can only deal with binary mixtures. In this paper, a novel magnetic levitation (MagLev) separation method based on scaled-up MagLev device is proposed to handle multi-plastics. A theoretical model on distribution of magnetic flux intensity and levitation conditions is established to guide the design of separation process. Based on the theoretical analysis, different processes for separation of multi-plastics with different purpose can be realized. The high sensitivity allows the separation of plastics with similar appearances (e.g. transparent plastics like polycarbonate and polymethyl methacrylate) and densities (difference with 0.01 g/cm3). The adjustable distribution of magnetic field changes the levitation condition of the waste plastics. Thus, the sequential separation of multi-plastics and extraction of target material from multi-plastics mixture are successfully addressed. The experiments demonstrate that the purities of separated multiple plastics reach to approx. 100 %. Furthermore, additional advantages of low cost and no energy consumed in separation process make the method a promising solution for economically-viable and environmentally-friendly mass production procedure.

A VLA Study of Newly Discovered Southern Latitude Nonthermal Filaments in the Galactic Center: Polarimetric and Magnetic Field Properties

A population of structures unique to the Galactic Center (GC), known as the nonthermal filaments (NTFs), has been studied for over 40 yr, but much remains unknown about them. In particular, there is no widely accepted and unified understanding for how the relativistic electrons illuminating these structures are generated. One possibility is that there are compact and extended sources of cosmic rays, which then diffuse along magnetic flux tubes leading to the illumination of the NTFs through synchrotron emission. In this work, we present and discuss the polarimetric distributions associated with a set of faint NTFs in the GC that have only been studied in total intensity previously. We compare the derived polarized intensity, rotation measure, and intrinsic magnetic field distributions for these structures with the results obtained for previously observed GC NTFs. The results are then used to enhance our understanding of the large-scale polarimetric properties of the GC. We then use the derived polarimetric distributions to constrain models for the mechanisms generating the relativistic electrons that illuminate these structures.

Compact Partially End-Pumped Innoslab Laser Based on Micro-Cylindrical Lens Array Homogenizer

We demonstrate a compact, partially end-pumping Innoslab laser based on a micro-cylindrical lens array homogenizer. A dimension of 12 × 0.4 mm2 flat-top pumping line with a Gaussian intensity distribution across the line was simulated by the ray tracing technique. The rate equations considering the asymmetric transverse spatial distributions are theoretically developed. The simulation results are in good agreement with the experimental results. Preliminary data shows that for a pump power of 260 W, a maximum pulse energy of 15.7 mJ was obtained with a pulse width of 8.5 ns at a repetition frequency of 1 kHz. The beam quality M2 factors in the unstable and stable directions were 1.732 and 1.485, respectively. The technology has been successfully applied to temperature and humidity profiling lidar and ozone lidar and has been productized, yielding direct economic value.

High-efficiency generation of long-distance, tunable, high-order nondiffracting beams

Nondiffracting beams (NDBs) have presented significant utility across various fields for their unique properties of self-healing, anti-diffraction, and high-localized intensity distribution. We present a versatile and flexible method for generating high-order nondiffracting beams predicated on the Fourier transformation of polymorphic beams produced by the free lenses with tunable shapes. Based on the tunability of the digital free lenses, we demonstrate the experimental generation of various long-distance nondiffracting beams, including Bessel beams, polymorphic generalized nondiffracting beams, tilted nondiffracting beams, asymmetric nondiffracting beams, and specially structured beams generated by the superposition of Bessel beams. Our method achieves efficiency of up to about seven times compared with complex beam shaping methods. The generated NDBs exhibit characteristics of extended propagation distance and high-quality intensity profiles consistent with the theoretical predictions. The proposed method is anticipated to find applications in laser processing, optical manipulation, and other fields.

Starch-calcium inclusion complexes: Optimizing transparency, anti-fogging, and fluorescence in thermoplastic starch

With the increasing demand for anti-fogging transparent material and environmental concern, developing sustainable intrinsically hydrophilic and anti-fogging thermoplastic material is important. In this work, thermoplastic starch (TPS) films with good anti-fogging and optical properties were prepared via coordinative interactions with calcium chloride (CaCl2), zinc chloride (ZnCl2) and magnesium chloride (MgCl2). Among them, TPS with the incorporation of CaCl2 exhibited excellent anti-fogging and high optical transparency. Notably, the haze of TPS-0.2Ca just increased from 2.5 % to 3.8 %, with transparency remaining robust at 80 %. FTIR, XPS and 2D-WAXD results demonstrated the formation of inclusion complexes between Ca2+ and hydroxyl groups, which could modulate the hydrophobicity and hydrophilicity of TPS. Moreover, DMA, POM, and AFM results revealed that the formation of starch-calcium inclusion complex was crucial for achieving uniform intensity distribution, reduced crystalline areas, minimized light scattering, and decreased surface roughness, thereby contributing to the high transparency and low haze of TPS-Ca. Furthermore, TPS-Ca samples exhibited inherent fluorescent properties under UV light, showing the potential as disposable and eco-friendly fluorescence materials. This work provides new insights into design of sustainable TPS-based materials that combine robust antifogging performance with advanced optical property.