Fundamental Model Research Articles

Time-fractional of cubic-quartic Schrödinger and cubic-quartic resonant Schrödinger equations with parabolic law: various optical solutions

Abstract Schrödinger's nonlinear equation is a fundamental model in fiber optics and many other areas of science. Using the Jacobi elliptic expansion function method, the time-fractional cubic-quartic nonlinear Schrödinger equation and cubic-quartic resonant nonlinear Schrödinger equation are investigated. By applying the effective Jacobi elliptic expansion function method, optical soliton solutions such as bright, dark, singular, periodic singular, exponential, and Jacobi elliptic function solutions have been obtained. The effect of the time-fractional derivative on the solutions is also revealed. Graphical representations are illustrated to showcase the physical properties of raised solutions, providing a comprehensive understanding of the solutions’ functionality.

Investigating the fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation: An iterative framework for nonlinear wave dynamics

Abstract This paper addresses the solution of the fractional Caudrey Dodd Gibbon Sawada Kotera (CDGSK) equation using the Conformable Laplace Decomposition Method (CLDM). The CDGSK equation, a fundamental model in wave dynamics and fluid mechanics, is explored for its applications in quantum mechanics and nonlinear optics. By employing fractional calculus, we demonstrate how fractional derivatives influence the physical characteristics of wave propagation in both optical and quantum systems. The exact solutions obtained provide insight into soliton behavior, essential for understanding wave-particle interactions in quantum fields and light-matter interactions in optics. The fractional nature of the equation allows for more accurate modeling of non-integer order dynamics commonly found in optical fibers and quantum waveguides. The CLDM method proves to be highly effective, providing approximate solutions with minimal computational effort. These findings offer significant contributions to the fields of quantum mechanics and nonlinear optics, where the fractional CDGSK equation can be applied to solve complex wave equations with great accuracy.

Research on temperature rise prediction model for circuit breaker based on numerical laplace transform

Abstract The temperature rise in circuit breakers' thermal paths is a critical indicator influencing their tripping characteristics, directly affecting response speed, reliability, and safety. Existing models for predicting circuit breaker temperature rise are often structurally limited, lack generality, and exhibit low predictive accuracy. Addressing this issue, this paper investigates an efficient, precise, and widely applicable theoretical model for predicting circuit breaker temperature rise. This model focuses on the thermal conduction mechanisms within small-scale circuit breakers, establishing a fundamental numerical heat transfer model based on Newton's cooling formula and Fourier's heat conduction law. By applying numerical Laplace transformation, the model is simplified into the complex frequency domain, and employing residue theorem for solving, it is transformed back into the time domain using Laplace inverse transformation to derive the predictive model. Experimental validation using a 32A rated current circuit breaker demonstrates the model's high predictive accuracy, suitability across various circuit breaker structures, with an average deviation below the permissible deviation in industry standards. This research holds significant implications for enhancing the thermal tripping characteristics of circuit breakers.

Run-and-tumble motion of ellipsoidal microswimmers

A hallmark of bacteria is their so-called “run-and-tumble” motion and its variants, consisting of a sequence of linear directed “runs” and distinct rotation events that constantly alternate due to biochemical feedback. It plays a crucial role in the ability of bacteria to move through chemical gradients and has inspired a fundamental active particle model. Nevertheless, synthetic active particles generally do not exhibit run-and-tumble motion but rather active Brownian motion. We show in experiments that ellipsoidal thermophoretic Janus particles, propelling along their short axis, can yield run-and-reverse motion, i.e., where rotation events flip the direction of motion, even without feedback. Their hydrodynamic wall interactions under strong confinement give rise to an effective double-well potential for the declination of the short axis. The geometry-induced timescale separation of the in-plane rotational dynamics and noise-induced transitions in the potential then yield run-and-reverse motion. Published by the American Physical Society 2024

Global Hilbert expansion for some nonrelativistic kinetic equations

AbstractThe Vlasov–Maxwell–Landau (VML) system and the Vlasov–Maxwell–Boltzmann (VMB) system are fundamental models in dilute collisional plasmas. In this paper, we are concerned with the hydrodynamic limits of both the VML and the noncutoff VMB systems in the entire space. Our primary objective is to rigorously prove that, within the framework of Hilbert expansion, the unique classical solution of the VML or noncutoff VMB system converges globally over time to the smooth global solution of the Euler–Maxwell system as the Knudsen number approaches zero. The core of our analysis hinges on deriving novel interplay energy estimates for the solutions of these two systems, concerning both a local Maxwellian and a global Maxwellian, respectively. Our findings address a problem in the hydrodynamic limit for Landau‐type equations and noncutoff Boltzmann‐type equations with a magnetic field. Furthermore, the approach developed in this paper can be seamlessly extended to assess the validity of the Hilbert expansion for other types of kinetic equations.

BrainSim: AI-Driven Brain MRI Simulation for Alzheimer’s Disease Diagnosis

Alzheimer's Disease, a progressive neurodegenerative disorder with no cure, presents a formidable challenge to global healthcare. The simulation of brain states, encompassing both rejuvenation and aging, aids clinicians in understanding disease progression and early detection. Recent advances in deep adversarial neural networks, effective in generating age-varied facial images, are now applied to brain MRI simulations across different time states. However, existing methods for brain MRI synthesis predominantly focus on aging simulation, lacking rejuvenation capabilities, and relying heavily on longitudinal data. Access to rejuvenated brain scans is essential as it can help researchers track the structural changes and biomarkers in the early stage of AD, facilitating AD research and personalized treatments. Additionally, previous methods are often 2D-based, failing to capture complex 3D spatial information obtained by 3D scans. To overcome these limitations, I propose BrainSim, a novel longitudinal brain MRI synthesis framework. Specifically, BrainSim leverages a bidirectional cycle-consistent generative neural network to generate rejuvenated and aged MRI scans simultaneously using cross-sectional scans only. BrainSim incorporates a 3D conditional U-Net as its fundamental model, facilitating the direct generation of 3D MRI scans conditioned on the subject's health state and sex. BrainSim was evaluated against benchmark models using longitudinal data and a pre-trained age predictor to assess the quality of generated images. Experiments using the ADNI dataset show BrainSim's state-of-the-art performance in brain aging and rejuvenation tasks, marking significant advancements in MRI synthesis for Alzheimer's research and drug development.

Optomechanical Photonics: feature issue introduction

We introduce the Optical Materials Express feature issue on Optomechanical Photonics. This issue comprises a collection of eight research articles on optomechanical photonics, including studies of new fundamental phenomena, device applications, experimental characterizations, and theoretical models.

A fundamental analytical model for micro topography of skived gear surface

Surface topography is important for gear components, as it exerts influence on noise, wear, lubrication, and life expectancy. Different gear finishing processes result in varying micro tooth topographies, which lead to different driving and lubricating performances. The advanced technology of gear skiving, a recent industry application known for its high efficiency and flexibility in both roughing and finishing of cylindrical gears, has become the focus of extensive research. However, investigations into the micro topography of skived tooth flanks have been limited, primarily due to the absence of a highly efficient algorithm, which hinders the prediction and optimization of driving performance. By demonstrating that the skived surface can be obtained through the collection of micro-sections of the cutter trace in a specific order, this paper proposes a comprehensive analytical model for the micro topography of the skived surface. Both numerical and experimental studies reveal the topology texture, surface roughness, and the effects of the cutter and cutting settings. Results indicate that a higher installation angle, feed rate, and cutter tooth number are more effective in reducing roughness.

Random Walks and Lorentz Processes

Random walks and Lorentz processes serve as fundamental models for Brownian motion. The study of random walks is a favorite object of probability theory, whereas that of Lorentz processes belongs to the theory of hyperbolic dynamical systems. Here we first present an example where the method based on the probabilistic approach led to new results for the Lorentz process: concretely, the recurrence of the planar periodic Lorentz process with a finite horizon. Afterwards, an unsolved problem—related to a 1981 question of Sinai on locally perturbed periodic Lorentz processes—is formulated as an analogous problem in the language of random walks.

CellSAM: Advancing Pathologic Image Cell Segmentation via Asymmetric Large-Scale Vision Model Feature Distillation Aggregation Network.

Segment anything model (SAM) has attracted extensive interest as a potent large-scale image segmentation model, with prior efforts adapting it for use in medical imaging. However, the precise segmentation of cell nucleus instances remains a formidable challenge in computational pathology, given substantial morphological variations and the dense clustering of nuclei with unclear boundaries. This study presents an innovative cell segmentation algorithm named CellSAM. CellSAM has the potential to improve the effectiveness and precision of disease identification and therapy planning. As a variant of SAM, CellSAM integrates dual-image encoders and employs techniques such as knowledge distillation and mask fusion. This innovative model exhibits promising capabilities in capturing intricate cell structures and ensuring adaptability in resource-constrained scenarios. The experimental results indicate that this structure effectively enhances the quality and precision of cell segmentation. Remarkably, CellSAM demonstrates outstanding results even with minimal training data. In the evaluation of particular cell segmentation tasks, extensive comparative analyzes show that CellSAM outperforms both general fundamental models and state-of-the-art (SOTA) task-specific models. Comprehensive evaluation metrics yield scores of 0.884, 0.876, and 0.768 for mean accuracy, recall, and precision respectively. Extensive experiments show that CellSAM excels in capturing subtle details and complex structures and is capable of segmenting cells in images accurately. Additionally, CellSAM demonstrates excellent performance on clinical data, indicating its potential for robust applications in treatment planning and disease diagnosis, thereby further improving the efficiency of computer-aided medicine.

A step function based recursion method for 0/1 deep neural networks

The deep neural network with step function activation (0/1 DNNs) is a fundamental composite model in deep learning which has high efficiency and robustness to outliers. However, due to the discontinuity and lacking subgradient information of the 0/1 DNNs model, prior researches are largely focused on designing continuous functions to approximate the step activation and developing continuous optimization methods. In this paper, by introducing two sets of network node variables into the 0/1 DNNs and by exploring the composite structure of the resulted model, the 0/1 DNNs is decomposed into a unary optimization model associated with the step function and three derivational optimization subproblems associated with the other variables. For the unary optimization model and two derivational optimization subproblems, we present a closed form solution, and for the third derivational optimization subproblem, we propose an efficient proximal method. Based on this, a globally convergent step function based recursion method for the 0/1 DNNs is developed. The efficiency and performance of the proposed algorithm are validated via theoretical analysis as well as some illustrative numerical examples on classifying MNIST, FashionMNIST and Cifar10 datasets.

Integrated System Modal and Mistuning Identification for Integrally Bladed Rotors

Abstract The safety of Integrally Bladed Rotors (IBRs) is often assessed through bench-level vibration tests to measure amplification factors and back-out sector frequency deviations via mistuning identification (ID) algorithms. This process is usually composed of two separate steps. First, a system ID step is completed to identify system modal data. Then, this data is input into mistuning ID algorithms. Errors in identified modal data will then propagate to produce errors in the system's predicted mistuning. Obtaining robust mistuning estimates then requires larger quantities of accurate modal data. This effort seeks to attain accurate mistuning data by coupling the system and mistuning ID steps into a more parallel, versus serial, process that is capable of identifying many system modes. An iterative Polyreference-Least Squares Complex Frequency- domain (P-LSCF) algorithm finds modal data, and a mistuning ID algorithm obtains mistuning data at each iteration. An outlier detection method is proposed to remove spurious modes that cause erroneous mistuning results. Then, a weighted, least-squares regression approach is employed to remove the impact of sector-specific outlier data. This method reduces errors in identified mistuning parameters from the Fundamental Mistuning Model (FMM) ID algorithm. Furthermore, the approaches eliminate the need for users to determine true versus spurious system modes in each iteration of the P-LSCF algorithm, thus removing ambiguity. The developed approaches are tested on simulated and bench-top test data. Results show the efficacy of the developed approaches and their ability to account for uncertainty in mistuning parameters.

Analysing the feasibility of agro-based value chain configurations in the rural context with B2B marketing

Purpose This paper aims to advocate for small-scale entrepreneurship with commercial cultivation to earn better profits at the farmer level. This paper explores potential value chain configurations of vertical coordination. Design/methodology/approach The aloe vera supply chain was examined for the study where aloe vera juice is the product. The various configurations are complete vertical coordination, semi-vertical coordination and non-vertical coordination. These were analysed to find feasibility and market prospects based on parameters. The cyclic view of supply chains, comparative analysis and fuzzy-analytical hierarchy process algorithm are presented. Findings The semi-vertically coordinated supply chain is indicated as the optimum setup to initiate value chains. The entrepreneurs in this configuration will be able to sell semi-finished produce to a brand that will process and distribute the final product. This B2B setup will help the farmer to earn better revenues in the post-COVID-19 scenario. Effective marketing with improved execution and innovation will boost the food processing industry. Research limitations/implications This study uses an established methodology to distinguish among alternatives based on underlying factors. The study is based on data collected from stakeholders. The study reflects the most accurate picture of real-world scenarios at the farm and market level in the Indian context. Practical implications This study’s learnings will help understand the organisational approach to serve demand by designing unique business configurations. Adapting the fundamental model with technological intervention will improve supply chain performance and sustainability. The most modern approaches in agri-business, such as subscription models, vertical farming, corporate entrepreneurship and technological intervention, will be covered in future work. Social implications This study will help stakeholders, including the government, decide whether to introduce training skills, subsidy policies, business expansion ideas and feasibility studies. Originality/value The study highlights the strategic role of developing the B2B platform to support customer values and customer ecosystem with better product availability.

Vibrio cholerae: a fundamental model system for bacterial genetics and pathogenesis research.

Species of the Vibrio genus occupy diverse aquatic environments ranging from brackish water to warm equatorial seas to salty coastal regions. More than 80 species of Vibrio have been identified, many of them as pathogens of marine organisms, including fish, shellfish, and corals, causing disease and wreaking havoc on aquacultures and coral reefs. Moreover, many Vibrio species associate with and thrive on chitinous organisms abundant in the ocean. Among the many diverse Vibrio species, the most well-known and studied is Vibrio cholerae, discovered in the 19th century to cause cholera in humans when ingested. The V. cholerae field blossomed in the late 20th century, with studies broadly examining V. cholerae evolution as a human pathogen, natural competence, biofilm formation, and virulence mechanisms, including toxin biology and virulence gene regulation. This review discusses some of the historic discoveries of V. cholerae biology and ecology as one of the fundamental model systems of bacterial genetics and pathogenesis.

Mathematical Analysis of Four Fundamental Epidemiological Models for Monkeypox Disease Outbreaks: On the Pivotal Role of Human–Animal Order Parameters—In Memory of Hermann Haken

Four fundamental models that describe the spread of Monkeypox disease are analyzed: the SIR-SIR, SEIR-SIR, SIR-SEIR, and SEIR-SEIR models. They form the basis of most Monkeypox diseases models that are currently discussed in the literature. It is shown that the way the model subpopulations are organized in disease outbreaks and evolve relative to each other is determined by the relevant unstable system eigenvectors, also called order parameters. For all models, analytical expressions of the order parameters are derived. Under appropriate conditions these order parameters describe the initial outbreak phases of exponential increase in good approximation. It is shown that all four models exhibit maximally two order parameters and maximally one human–animal order parameter. The human–animal order parameter firmly connects the outbreak dynamics in the animal system with the dynamics in the human system. For the special case of the SIR-SIR model, it is found that the two possible order parameters completely describe the dynamics of infected humans and animals during entire infection waves. Finally, a simulation of a Monkeypox infection wave illustrates that in line with the aforementioned analytical results the leading order parameter explains most of the variance in the infection dynamics.

Three limit cycles in the Kim–Forger model of the mammalian circadian clock

The Kim–Forger model is a fundamental mathematical model for understanding circadian rhythms. The limit cycles presented in the model is the dynamic mechanism of the periodic phenomena in the mammalian circadian clock. However, the full dynamics of the Kim–Forger model remain not completely understood. In this paper, we theoretically demonstrate that this model can undergo supercritical Hopf bifurcation, subcritical Hopf bifurcation, and generalized Hopf bifurcation of codimension two. Numerically, the system can exhibit 0, 1, 2, or 3 limit cycles. Our work complements and enriches the dynamical insights in the field of circadian rhythms.

An Analytical Study on the Effects of Non-Uniform Vane Spacing on Forced Response Reduction in a Mistuned Blisk Rotor in a Multistage Axial Compressor

Abstract Stators with non-uniform vane spacing (NUVS) have been sought as an effective way to reduce the rotor-forced response at certain resonance crossing of concern. A comprehensive experimental study has been conducted in Purdue three-stage axial research compressor to evaluate the effectiveness of the NUVS stator on reducing the forced response of the downstream rotor using strain gauge measurement. The experimental results showed that the classical estimation method failed to predict the reduction factor correctly, mainly due to the lack of consideration for the damping and mistuning effects. To better understand the experimental results, and to provide an efficient and more accurate analysis tool for the rotor forced response under NUVS stator excitation, a detailed analytical study was conducted in this paper. The blade-forced response was solved using an efficient, steady-state linearized approach. A single-blade analysis was done first to study the effect of damping. The case studies show that higher damping causes more overlap of the blade forced response from adjacent engine order excitations and, thus, increases the total normalized blade response under NUVS stator excitation. A mistuned blisk aeroelastic model was introduced next, with the mistuning effect modeled using the fundamental mistuning model. Both structural coupling and aerodynamic coupling effects can be included in the aeroelastic model. Similar to the experimental results, the mistuned blisk case study shows a large blade-to-blade variation in the blade-forced response under both symmetric and asymmetric NUVS stator excitation, even at a low, non-intentional mistuning level. A statistical study with 100 randomly generated mistuned blisks shows that the forced response reduction effect of a specific NUVS design could vary significantly with a small change of the mistuning pattern, which suggests that mistuning has to be carefully considered in the design, evaluation, and optimization of the NUVS stator.

A data-driven ductile fracture criterion for high-speed impact

Data-driven methods based on machine learning (ML) models offer new approaches for characterizing the fracture behavior of advanced elastoplastic materials. In this paper, a ML-based data-driven ductile fracture criterion is proposed to characterize the fracture behavior of elastoplastic materials under high-speed impact loading conditions. To reduce the required training dataset and enhance the predictability capability, several assumptions are used. Firstly, utilizing the decoupled assumption, two separate artificial neural network (ANN) models are employed to establish the fundamental fracture model and characterize the strain rate effect of ductile fracture behavior, respectively. In addition, the enhanced method with a logarithmic function is introduced to improve predictability capability of the proposed data-driven criterion under unknown high strain rates. To establish a complete numerical implementation framework, an enhanced rate-dependent data-driven constitutive model and a compatible numerical implementation algorithm are additionally introduced. Eventually, to assess the applicability of the proposed data-driven fracture criterion, numerical simulations of notched specimens and ballistic impact conditions of Ti-6Al-4V material are conducted, respectively. These investigation results demonstrate the effectiveness of the proposed data-driven ductile fracture criterion.

Experimental Investigation of Chloride Ion Monitoring in Concrete Considering the Coupling Effect of Temperature and Humidity

Ag/AgCl electrodes have acquired significant research attention due to their crucial role in the electrochemical monitoring of chloride ion concentration. However, the electrode potential is susceptible to changes in temperature and humidity, and comprehensive investigations regarding the influence of moisture are lacking. Existing studies on Ag/AgCl electrodes have been qualitative, primarily focusing on analyzing the trend of electrode potential to detect variations in Cl- concentration. This study proposes an experimental method that enables precise control of temperature and humidity within concrete. The effects of temperature and humidity coupling on Ag/AgCl electrode potential in a concrete environment and a fundamental model were established correlating Ag/AgCl electrode potential with temperature, humidity, and chloride ion concentration, thereby enhancing the sensing accuracy. The developed model corrected errors from temperature and humidity coupling effects on the Ag/AgCl electrode potential. A quantitative investigation on using Ag/AgCl electrodes for monitoring Cl- concentration was conducted, facilitating their application in engineering and the development of non-destructive monitoring systems for chloride ions in concrete structures.

Solutions to the Schrödinger equation using deep neural networks for integrated photonics

Abstract This paper introduces a novel method for solving the Schrödinger equation through the use of deep neural networks (DNNs), presenting a significant departure from traditional techniques. Conventional approaches to solving the Schrödinger equation, such as analytical methods and numerical algorithms, often face challenges when dealing with complex quantum systems due to their inherent limitations. These traditional methods can become cumbersome or even infeasible as the complexity of the systems increases. In contrast, our approach harnesses the capabilities of deep neural networks to approximate both the wavefunction and the energy eigenvalues of quantum systems. By leveraging the flexible and powerful nature of DNNs, we provide a new pathway to solving the Schrödinger equation that can potentially overcome the constraints of classical methods. To validate the effectiveness of our approach, we apply it to the particle in a box problem – a fundamental quantum mechanics model with well-established analytical solutions. This benchmark problem serves as a useful test case, allowing us to demonstrate that DNNs can not only replicate the known results accurately but also offer insights into how these networks can handle more intricate quantum systems. Our results reveal that DNNs are capable of accurately reproducing the analytical solutions for the particle in a box, illustrating their potential as a versatile tool for quantum mechanics.