Physical Applications Research Articles

A diffusion-based wind turbine wake model

Describing the evolution of a wind turbine's wake from a top-hat profile near the turbine to a Gaussian profile in the far wake is a central feature of many engineering wake models. Existing approaches, such as super-Gaussian wake models, rely on a set of tuning parameters that are typically obtained from fitting high-fidelity data. In the current study, we present a new engineering wake model that leverages the similarity between the shape of a turbine's wake normal to the streamwise direction and the diffusion of a passive scalar from a disk source. This new wake model provides an analytical expression for a streamwise scaling function that ensures the conservation of linear momentum in the wake region downstream of a turbine. The model also considers the different rates of wake expansion that are known to occur in the near- and far-wake regions. Validation is presented against high-fidelity numerical data and experimental measurements from the literature, confirming a consistent good agreement across a wide range of turbine operating conditions. A comparison is also drawn with several existing engineering wake models, indicating that the diffusion-based model consistently provides more accurate wake predictions. This new unified framework allows for extensions to more complex wake profiles by making adjustments to the diffusion equation. The derivation of the proposed model included the evaluation of analytical solutions to several mathematical integrals that can be useful for other physical applications.

All‐Sky Microwave Radiance Observation Operator Based on Deep Learning With Physical Constraints

AbstractSatellite data assimilation relies on the radiative transfer models (RTMs) to establish the relationships between model state variables and satellite radiances. However, atmospheric radiative transfer calculations are computationally expensive, especially when involving multiple‐scattering calculations in cloudy areas. In recent years, deep learning (DL) models have been increasingly applied to emulate and accelerate physical models. This study, for the first time, explores DL techniques to emulate all‐sky radiative transfer in microwave bands. The FengYun‐3E (FY‐3E) Microwave Humidity Sounder‐2 (MWHS‐2) was selected as the target instrument due to its comprehensive spectral coverage, with the radiative transfer for TOVS scattering module (RTTOV‐SCATT) serving as the reference model. Three DL architectures were trained and compared, including multilayer perceptron (MLP), Bidirectional Long Short‐Term Memory with Attention (BiLSTM‐Attention), and Transformer. The BiLSTM‐Attention architecture demonstrated superior performance in both clear‐sky and cloudy radiance simulations. This may be attributed to its bidirectional recurrent structure resembling physical radiative transfer processes and the attention mechanism's ability to link MWHS‐2 channels with corresponding vertical layers. Although DL models achieve high accuracy in forward prediction, they often struggle with instability in Jacobian calculations. To address this issue, the trained BiLSTM‐Attention model was fine‐tuned using the reference model Jacobians as physical constraints. The fine‐tuned BiLSTM‐Attention model accurately characterized radiance sensitivities to temperature, water vapor, and hydrometeors under different cloud conditions, indicating its potential to serve as a radiance observation operator in data assimilation and physical retrieval applications.

Set-Theoretical Solutions for the Yang–Baxter Equation in GE-Algebras: Applications to Quantum Spin Systems

This manuscript presents set-theoretical solutions to the Yang–Baxter equation within the framework of GE-algebras by constructing mappings that satisfy the braid condition and exploring the algebraic properties of GE-algebras. Detailed proofs and the use of left and right translation operators are provided to analyze these algebraic interactions, while an algorithm is introduced to automate the verification process, facilitating broader applications in quantum mechanics and mathematical physics. Additionally, the Yang–Baxter equation is applied to spin transformations in quantum mechanical spin-12 systems, with transformations like rotations and reflections modeled using GE-algebras. A Cayley table is used to represent the algebraic structure of these transformations, and the proposed algorithm ensures that these solutions are consistent with the Yang–Baxter equation, offering new insights into the role of GE-algebras in quantum spin systems.

Switching, amplifying, and chirping diode lasers with current pulses for high bandwidth quantum technologies.

A series of simple and low-cost devices for switching, amplifying, and chirping diode lasers based on current modulation are presented. Direct modulation of diode laser currents is rarely sufficient to establish precise amplitude and phase control over light, as its effects on these parameters are not independent. These devices overcome this limitation by exploiting amplifier saturation and dramatically outperform commonly used external modulators in key figures of merit for quantum technological applications. Semiconductor optical amplifiers operated on either rubidium D line are recast as intensity switches and shown to achieve ON:OFF ratios >106 in as little as 50ns. Current is switched to a 795nm wavelength (Rb D1) tapered amplifier to produce optical pulses of few nanosecond duration and peak powers of 3 W at a similar extinction ratio. Fast rf pulses are applied directly to a laser diode to shift its emission frequency by up to 300MHz in either direction and at a maximum chirp rate of 150MHzns-1. Finally, the latter components are combined, yielding a system that produces watt-level optical pulses with arbitrary frequency chirps in the given range and <2% residual intensity variation, all within 65ns upon asynchronous demand. Such systems have broad application in atomic, molecular, and optical physics and are of particular interest to fast experiments simultaneously requiring high power and low noise, for example, quantum memory experiments with atomic vapors.

Boundary element method for hypersingular integral equations: Implementation and applications in potential theory

The main objective of this paper is to develop effective numerical methods to solve hypersingular integral equations arising in various physical and mechanical applications. Both surface and contour integrals are considered. The novelty of the proposed approach lies in the exact formulas obtained for an arbitrary planar polygon in hypersingular integral estimations. A one-dimensional hypersingular integral equation is derived for axially symmetrical configurations, and analytical formulas are established for calculating the hypersingular parts. It is proved that the hypersingular component of the surface integral is equal to its hypersingular component along the tangent plane. These exact formulas enable the development of an effective numerical method based on boundary element implementation. Benchmark tests are considered, and the convergence of the proposed methods is demonstrated. Problems in crack analysis are formulated and solved using both surface and contour hypersingular integral equations. A comparison of the results is made between boundary element methods and finite element methods for penny-shaped cracks. Boundary value problems in fluid-structure interaction are considered, and numerical simulations are performed. An estimation of modes and frequencies of panel and blade vibrations when interacting with liquids is carried out.

Study on a (3+1)-dimensional B-type Kadomtsev–Petviashvili equation in nonlinear physics: Multiple soliton solutions, lump solutions, and breather wave solutions

In this work, we study an extended (3+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equations that appear in many nonlinear physics applications. We show that this extended equation retains its complete integrability via Painlevé analysis. We explore multiple soliton solutions by using the Hirota bilinear method. Moreover, we derive lump solutions where two numerical examples are tested. Breather wave solutions were also explored by using a variety of distinct schemes. We also determine other traveling wave solutions, rational solutions, periodic solutions, exponential solutions, ratio of trigonometric or hyperbolic functions, and others.

Approximate Solutions of the Coupled M-Truncated Fractional mKdV System Using the Adomian Decomposition Technique

This manuscript employs the Adomian decomposition technique (ADT) to develop solutions for the fractional space-time nonlinear mKdV system, incorporating an M-truncated fractional order and supposed initial conditions. The technique yields a power series expansion solution without the need for linearization, weak nonlinear assumptions, or perturbation theory. Software such as Maple or Mathematica was utilized to compute the Adomian formulas for the solution expansion. This technique can also be utilized for a range of nonlinear fractional-order models in mathematical physics. A graphical analysis is provided to demonstrate the behavior of Adomian solutions and how variations in non-integer order values influence the results. The technique is straightforward, clear, and widely applicable to other nonlinear fractional problems in both physics and mathematics. It is believed that these studies significantly advance our understanding of the nonlinear coupled fractional mKdV system and its potential applications in physics and engineering.

Advanced fabrication process for particle absorbers of highly pure electroplated gold for microcalorimeter applications

Magnetic microcalorimeters (MMCs) have become a key technology for applications requiring outstanding energy resolution, fast signal rise time and excellent linearity. MMCs measure the temperature rise upon absorption of a single particle within a particle absorber by using a paramagnetic temperature sensor that is thermally coupled to the absorber. The design and fabrication of the particle absorber is key for excellent detector performance. Here, we present a microfabrication process for free-standing particle absorbers made of two stacked and independently electroplated high-purity Au layers. This enables, for example, the embedding of radioactive sources within the absorber for realizing a 4π detection geometry in radionuclide metrology or preparing detector arrays with variable quantum efficiency and energy resolution as requested for future applications in high-energy physics. Due to careful optimization of photoresist processing and electroplating parameters, the Au films are of very high purity and very high residual resistivity ratio values above 40, allowing for fast internal absorber thermalization.

Dynamic description of soliton solutions of nonlinear schrödinger equation with higher order dispersion and nonlinear terms

Abstract The article presents an analytical solution for the higher-order nonlinear Schrödinger equation (NLSE), which describes the propagation of short light pulses in monomode optical fibers. Various traveling wave solutions are obtained using the generalized exponential rational function method, a technique with substantial applications in physics and mathematics. Additionally, the parameters leading to the occurrence of optical bright and multipeak solitons in this medium are provided along with their formation conditions. The derived solutions are graphically displayed to enhance the understanding of the model’s physical phenomena. This approach is credible, potent, and successful in solving a wide variety of different models of this kind that arise in the applied sciences. Its robustness, strength, and efficiency make it suitable for addressing various higher-order nonlinear problems in current research fields, extending beyond the models encountered in the applied sciences.&amp;#xD;

Encoding the lattice in the holography

One of the most wanted features of holography in its condensed matter physics application is to encode the structure of lattice, which is the most direct data of the material. In this paper, we propose a method to encode the lattice structure by embedding the tight binding data into the Dirac equation in the anti–de Sitter bulk. We explicitly worked out the idea for the graphene and Haldane models, and the result shows that some degrees of freedom escape the free-electron on-shell curve, and Green’s function loses the pole structure completely. It implies that the electronic structure is not described by the band structure only, which is consistent with what many angle-resolved photoemission spectroscopy data tell us, and it also implies that the system is in non-Fermi liquid even for the graphene, which is consistent with recent experiments for the clean graphene. Published by the American Physical Society 2024

A reliable technique for nonlinear evolution equations with applications in mathematical physics

This study presents a reliable and precise solver for solving several kinds of nonlinear evolution equations. The subequation approach is the basic ingredient of this solver. In this regard, a solver is created to precisely resolve and depict the nonlinear evolution equations’ whole wave structures. This analysis offers the whole information obtained in the representation of solutions to these equations. The robust solver offers hyperbolic, trigonometric, and rational forms of solutions. A set of test problems drawn from the literature are provided in order to validate the accuracy of the proposed solver. The solutions that were discovered could be useful for a vital recent applied science observations. The method that was demonstrated is a tool that mathematics, engineers, and physicists can use as a box solver. Theoretical analysis and reported solutions show that the suggested solver is suitable and efficacious.

A Fractional Reduced Differential Transform Method for Solving Multi-Fractional Telegraph Equations

This paper presents a novel modification of the Fractional Reduced Differential Transform Method (FRDTM) to solve space-time multi-fractional telegraph equations. The telegraph equation is crucial in modeling voltage and current distribution in electrical transmission lines, and its solutions have applications in physics, economics, and applied mathematics. The proposed method effectively simplifies the fractional differential equations by omitting one fractional derivative term, allowing for the transformation of the remaining terms using the FRDTM. The solutions demonstrate the method’s accuracy and efficiency in fractional partial differential equations. This study advances the analytical solutions of fractional telegraph equations by providing a straightforward yet powerful approach to fractional differential problems.

A New Exponential Gompertz Distribution: Theory and Applications

With the rise of numerous phenomena that require interpretation and investigation, developing novel distributions has become an important need. This research introduced a new probability distribution called New Exponential Gompertz distribution based on the new exponential-X family to enhance flexibility and improve performance. The most significant benefit of this novel distribution is that its hazard function could be increasing, decreasing and bathtub which reflects the flexibility of the distribution to fit various applications. Furthermore, its density can adopt a variety of symmetric and asymmetric possible shapes. Some of the theoretical characteristics such as quantile, order statistic and moment are provided. The parameter estimates are derived using five different estimation methods including maximum likelihood, ordinary least square, weighted least square, Cramér-von mises and maximum product of spacing methods. Simulation studies are conducted to assess the effectiveness of the five estimation methods. The maximum likelihood estimate shows the most reliable estimate for estimating parameters since it provides the smallest mean square error While the maximum product of spacing method is less efficient. The performance of the proposed distribution is assessed through real-world applications in medical, engineering and physics with competitive distributions. The results indicate that the new distribution efficiently represents various types of data compared to other distributions.

Light-Triggered Droplet Gating Strategy Based on Janus Membrane Fabricated by Femtosecond Laser.

The characteristics of the directed transport of liquids based on Janus membranes play a crucial role in practical applications in energy, materials, physics, chemistry, medicine, biology, and other fields. Although extensive progress has been made, it is still difficult to realize the accurate controllability of liquid directional transmembrane transport. The current gating strategies for the directed transport of liquids based on Janus membranes still have some limitations: (a) using magnetic fluid may cause contamination due to the addition of new substances and (b) utilizing hydrophobicity/hydrophilicity conversion of titanium dioxide requires a long switching time (over 30 min). Herein, a strategy is proposed to precisely control liquid directional transport by altering the wettability of droplets on Janus films prepared by a femtosecond laser through photothermal effects. Infrared laser irradiation on Janus film coated with CNTs can effectively convert light energy into thermal energy, rapidly increase the surface temperature of Janus film, and change the wettability of the liquid on the film. Liquid transmembrane directional transport can be achieved within a few seconds without contaminating the transported liquid. The proposed gating strategy can enable the application of Janus membranes in various scenarios such as microchemical reactions, biological cell culture, and interface self-propulsion.

The hydrogen atom perturbed by a 1-dimensional Simple Harmonic Oscillator (1d-SHO) potential

Abstract The hydrogen atom perturbed by a constant 1-dimensional weak quadratic potential λz2 is solved at first-order perturbation theory using the eigenstates of the total angular momentum operator - the coupled basis. Physical applications of this result could be found, for example, in the study of a quadratic Zeeman effect weaker than fine-structure effects, or in a perturbation caused by instantaneous generalised van der Waals interactions.

An inverse nodal problem of a conformable Sturm-Liouville problem with restrained constant delay

This paper presents a new technique: a conformable derivative for the inverse problem of a Sturm-Liouville problem with restrained constant delay. Solutions to the Sturm-Liouville problem often involve eigenfunctions and eigenvalues, which have important applications in physics, engineering, and other fields. The presence of a constant delay introduces unique challenges in formulating and solving this problem. In this case, we derived the asymptotic formulas for the eigenvalues with their corresponding eigenfunctions and demonstrated the existence of the solution. Additionally, we identified the nodal points used to generate the problem’s potential function. Finally, we applied the Lipschitz stability approach and demonstrated the stability of the solution to the problem.

Charting the Unknown: First Passage Time Probabilities for Pearson Diffusion Process and Application to Options Risk Management

The first passage time probabilities have applications in many fields, including Finance, Marketing, Economics, Physics, and Statistics. In this paper, we study the first passage time probabilities for a Pearson diffusion process and obtain the lower and upper bounds of the first passage time density. We show that the density may be approximated by the upper bound with an error of approximately five percent. We present an application by modelling the profit and loss function of the S&amp;P 500, FTSE 100 and DAX 40 index options using a Pearson diffusion process. Further, we establish the relation between first passage time probabilities and MaxVaR, i.e., the intra-horizon risk and obtain the MaxVaR for various index options based on first passage time probabilities. This is important as MaxVaR can capture the risk and potential losses incurred at any time of the trading horizon. In addition, we conduct a sensitivity analysis on the parameters for the purpose of robustness.

Near-complete extraction of maximum stored energy from large-core fibers using coherent pulse stacking amplification of femtosecond pulses

High field science relies on ultrashort pulse lasers with multi-joule pulse energies for studying light–matter interactions under extreme conditions and for driving particle accelerators and secondary radiation sources of x rays, gamma rays, neutrons, positrons, muons, and protons. Next-generation laser drivers will require a 103−104 times increase in pulse repetition rates, producing multi-joule energies at multi-kilowatt average powers to enable practical applications in nuclear engineering, advanced materials, medicine, biology, homeland security, and high-energy physics. Spatially coherently combined femtosecond fiber lasers are recognized as a pathway to these next-generation drivers, with significant practical advantages including high efficiency and the possibility of compact integration. However, chirped pulse amplification in fibers is capable of extracting only a small fraction (usually ∼1%) of the maximum stored energy. Here we demonstrate near-complete maximum stored energy extraction with low accumulated nonlinearity from a large-core fiber amplifier using coherent pulse stacking amplification. We have amplified a 81-pulse stacking burst in a 85 µm core chirally coupled core Yb-doped fiber, extracting up to 9.5 mJ (∼90% of stored energy) with &lt;4.5 radians of accumulated nonlinear phase, temporally combined this burst into a single pulse, and achieved 4.2 mJ pulses of 313 fs bandwidth-limited duration after compression. This represents, to our knowledge, the highest energy extracted and compressed into a femtosecond pulse from a single fiber amplifier, enabling approximately two orders of magnitude size reduction of future high-energy coherently spatially combined fiber laser arrays.

Some educational uses of EDXRF for technologists in health science

Abstract Physicists teach physics to students of various academic disciplines such as physics, chemistry, health sciences, biology, geology, environmental sciences, etc. Energy dispersive X-ray fluorescence spectroscopy (EDXRF) is a case of application of atomic physics in the real world. Students, through applications of EDXRF, may find out how the basic concepts of atomic physics can be used for elemental analysis of samples of their scientific interest and everyday life. This paper presents some educational implementations of EDXRF and highlights the importance of incorporating this spectroscopic method in undergraduate or postgraduate labs or lectures in the field of health sciences. Five experimental activities, a general one for understanding X-ray spectra and the others for the analysis of substances/materials related to chemistry/toxicology, dentistry, optics, and cosmetics, are presented and discussed.

An implicit GNN solver for Poisson-like problems

This paper presents Ψ-GNN, a novel Graph Neural Network (GNN) approach for solving the ubiquitous Poisson PDE problems on general unstructured meshes with mixed boundary conditions. By leveraging the Implicit Layer Theory, Ψ-GNN models an “infinitely” deep network, thus avoiding the empirical tuning of the number of required Message Passing layers to attain the solution. Its original architecture explicitly takes into account the boundary conditions, a critical pre-requisite for physical applications, and is able to adapt to any initially provided solution. Ψ-GNN is trained using a physics-informed loss, and the training process is stable by design. Furthermore, the consistency of the approach is theoretically proven, and its flexibility and generalization efficiency are experimentally demonstrated: the same learned model can accurately handle unstructured meshes of various sizes, as well as different boundary conditions. To the best of our knowledge, Ψ-GNN is the first physics-informed GNN-based method that can handle various unstructured domains, boundary conditions and initial solutions while also providing convergence guarantees.