Shooting Method Research Articles

Numerical Estimation of Bending in Holographic Volume Gratings by Means of RCWA and Deep Learning

In this paper, we introduce a novel approach to model bending phenomena on holographic volume gratings based on Rigorous Coupled Wave Analysis (RCWA), in which the bending as a phase in the dielectric permittivity expansion is introduced, and the Shooting Method (SM) is employed to solve the resulting system of equations. Further validation of our model is conducted by comparing its predictions to those obtained from reference Finite-Difference Time-Domain (FDTD) simulations and Coupled Wave Theory (CWT, referring to Kubota’s model that includes the bending phenomenon). Furthermore, we propose a methodology for estimating the bending from the diffraction efficiency curves in transmission volume gratings based on deep learning models, with a subsequent study of their accuracy and applicability.

Modified Shooting with Discretization Validation for Non-Standard Optimal Control Problem: Case Study for Four-Stage Royalty Payment Problem

A modified shooting method augmented by discretization validation is presented in this paper to address the challenges inherent in non-standard optimal control problems. Specifically, a specific case study involving four-stage royalty payment functions is focused on, with the aim of effectively optimizing these complex, non-differentiable functions. The shooting method is adapted and enhanced to compute optimal solutions, and its accuracy is rigorously confirmed through discretization techniques. The primary objectives involve maximizing the performance index and determining optimal control strategies for scenarios where the final state variable remains unknown. In this study, the royalty payment is defined as a four-stage piecewise function. The incorporation of piecewise royalty functions introduces non-differentiability at specific time intervals, necessitating innovative approaches for finding optimal solutions. This, in turn, leads to the utilization of the continuous hyperbolic tangent (tanh) function to address the non-differentiability issue. A hybrid shooting method, combining the Newton and Golden Section Search methods, is employed in the C++ programming language to compute the unknown final state value. A new natural boundary condition, based on established theory, is introduced to further facilitate the investigation. Discretization methods such as Euler, Runge-Kutta, Trapezoidal, and Hermite-Simpson approximations are employed for validation. The validation process entails the use of the AMPL programming language with the MINOS solver. Comparative analyses reveal that the modified shooting method yields more accurate optimal results than discretization methods, thus demonstrating the method’s effectiveness in addressing non-standard optimal control problems. The significance of fundamental theories in addressing real-world challenges is underscored by this research, providing valuable insights for future researchers exploring mathematical approaches in similar contexts. The study contributes to the continued relevance of the academic field, particularly in science and mathematics education.

Stability analysis of nonlinear synchronous vibration in an inclined rotor system supported by journal bearing with variational gravity

In vertical rotating shaft-bearing systems, synchronous vibration undergoes destabilization and stabilization owing to the self-excited vibration. Recently, these phenomena have been clarified numerically, experimentally, and analytically based on a newly proposed analytical method. In this method, a two-step linearization of the nonlinear journal bearing (JB) force and generalized eigenvalue analysis are proposed to directly determine the stability of the synchronous orbit. However, this method cannot be used directly for inclined-rotor systems with a large gravitational effect. Moreover, stability changes caused by gravity variations in inclined-rotor systems have not been fully investigated. This study extended the analytical method to one with weighted average dynamic coefficients to efficiently predict the stability changes of synchronous whirling vibrations in inclined rotor systems. The extended analytical method clearly clarifies gravity-induced stability changes in comparison with the numerical (shooting) method. Our analytical method enhances the ability of rotor dynamics software to calculate the stability thresholds of inclined rotor systems with gravity variations.

NMPC‐Based Control of Underactuated Spacecraft: A Neighboring Extremal Approach Extended to SE(3)

ABSTRACTThe present work revolves around employing the benefits of neighboring extremal approach in the nonlinear model predictive control of mechanical systems evolving on SE(3). In the NMPC process, necessary conditions of optimality are extracted based on some discrete‐time version of the equations of motion referred as LGVI and the obtained TPBVP equations are solved using simplified sensitivity derivatives by means of an indirect shooting method. Taking into consideration that the repetitive optimization process of the NMPC is time consuming, making its implementation challenging, a method of neighboring extremal is proposed here for recalculating the responses of the systems in scenarios that face some unexpected changes in their parameters or are encountering some last‐minute re‐planning schemes. Based on the existing responses of the system to the first set of initial conditions, the reaction of the system to the altered set of initial conditions can be reconstructed without the need to solve the whole optimization process from scratch by utilizing the features of the NE method. A spacecraft model evolving on SE(3) with actuation constraints confirms the efficiency of the whole process in term of accuracy versus computation burden. Forasmuch as actuator failure is a probable yet important event in aerial/spatial missions, the performance of the control system in dealing with such situations is examined. The algorithm robustness and its capability to compensate the effects of the actuator loss is checked.

B-115 Software Data Processing and Review LC-MS/MS Workflow Improvements for Clinical Research

Abstract Background In the field of quantitative LC-MS/MS, the need for efficient, accurate and user-friendly data review software is paramount, with the data generated in the clinical laboratory meeting local guidelines, as well as rigorous method performance characteristics defined by the FDA Bioanalytical Method Validation and CLSI C62-Ed2 guidelines. The quantitative LC-MS/MS workflow is dependent on interfacing to LMS/LIMS for sample traceability, batch analysis using matrix-matched external calibrators and quality controls for quantification and acceptance, and stable-isotope labeled internal standards to compensate for sample extraction, recovery, matrix effects and analytical variability. The demands on the laboratory to run multiplexed analyte panels and analyze a greater number of samples produces large amounts of analytical data which must still go through batch and quality review before release from the laboratory to the clinicians. The Waters Quan Review Software significantly reduces the burdensome aspects of batch quality control by introducing a series of innovative features. These include improvements in workflow, a modernized interface, and the ability to flag exceptions based on acceptance criteria. Methods Samples for three multiplexed LC-MS/MS panels with previously defined analytical method performance characteristics were acquired using Waters IVD Systems controlled by MassLynx software. The data was processed, quantified, and reviewed using both the existing TargetLynx XS IVD Application Manager and the new Quan Review Software. The three quantitative LC-MS/MS methods were the analysis of four immunosuppressants drugs in whole blood, a twelve steroid panel in plasma and a urine dilute and shoot method for a drugs of abuse panel containing greater than 80 analytes. Each method used matrix matched calibrators and QCs for quantification and batch control with performance characteristics including calibration linearity, carryover, precision and accuracy. Results The analytical performance data generated using the new MS Quan data review software met the same performance criteria as the TargetLynx XS data. For immunosuppressants, the % difference of the mean repeatability and total precision (%CV) for the individual analyte QCs processed using both software was within ±1.3% and ±4.4% respectively. The mean % bias of External Quality Assurance Samples (n=40) for each immunosuppressant processed using both software was within ±7.9%. The modernized, task-oriented accelerated workflows and focused review by exception reduced review time by up to 50%. Conclusions The new Quan Review Software generated results equivalent to the existing TargetLynx XS Application Manager. The software’s enhanced workflow capabilities streamlined the review process in a new user-friendly interface which reduced the training burden enabling scientists to generate high-quality data quickly and easily. The exception focused review functionality allowed tailored rule sets which reduced the time spent reviewing data by up to 50%. Whilst the batch-level review and task-oriented workflow improved batch acceptance and simplified the review of complicated datasets into easy tasks. By integrating these features, Data Review software offers a comprehensive solution that not only improves the efficiency and accuracy of batch quality control but also contributes to the overall reliability and integrity of quantitative LC-MS/MS analysis. For Research Use Only. Not for Use in Diagnostic Procedures.

What's New in Diode Laser Hair Removal?

ABSTRACTIntroductionLaser hair removal remains one of the most common procedures in cosmetic dermatology. It has always been challenging because of the higher competing epidermal melanocyte as the targeted hair chromophore is also melanin. As a result, to avoid unwanted side effects from laser therapy while maintaining high efficacy levels, the use of the right laser device, appropriate settings, and customized pre and posttreatment care are crucial. With more efficient versions of existing lasers in the market, the safety profile has been taken care of without compromising the efficacy. Diode lasers along with long pulsed Nd:YAG and alexandrite are considered as the safest hair removal lasers.ObjectiveTo summarize recent developments in diode laser hair reduction focusing on improvements in efficiency, safety, and patient compliance with recent innovations.Materials and MethodsA review of recent literature updates in diode laser hair reduction technology focusing on multiwavelength systems, safety profiles, and innovations in laser device was searched using keywords diode laser hair removal and mutliwavelength diode laser devices.ResultsCurrently, 810 nm diode laser is the most extensively used technology for the long term elimination of unwanted hair, thus establishing itself as an efficacious and safe modality. The rapid multiple pass in motion technique with lesser fluence and gradual heating of the skin epidermis was more well tolerated in patients than the higher fluence single shot method. Most popular combination of triple wavelength was 755, 810, and 1064 nm, which is considered most effective with least complications.ConclusionDiode lasers still remain the gold standard in laser hair removal especially on darker skin types. Recent innovations in diode laser have significantly improved the efficacy, safety, and patient compliance with hair reduction. Multiwavelength platforms seems to be the way forward, however the basic principles and certain problems like minimal pain, treating thin hair, paradoxical hair growth, white hair removal still remains a challenge.

Analyzing the effectiveness of Nields constraint and stratification on dynamics of non-Newtonian fluid by executing numerical and machine learning approaches

Stratified flows are commonly observed in numerous industrial processes. For example, a gas-condensate pipeline typically uses a stratified flow regime. However, this flow arrangement is stable only under a specific set of operating conditions that allows the formation of stratification. In this study, the authors analyzed the flow attributes of Prandtl Eyring liquid past an inclined sheet immersed in a stratified medium. The flow also characterizes the features of the magnetic field along with a first-order chemical reaction. Convective boundary constraints associated with the thermosolutal exchange at the extremity of the domain are also prescribed. The fundamental equations of the study are formulated in dimensional PDEs and converted into dimensionless ODEs via similar variables. The numerical solution of the modelled setup is acquired by executing computations using shooting and RK-4 methods. The intelligent computing paradigm working on the mechanism of the back-propagated Levenberg-Marquardt strategy is also capitalized to forecast the behavior of related physical quantities. Graphs and tables are drawn to elaborate the impression of pertinent factors on flow distributions. It is perceived that the momentum profile diminishes with the magnetic field effect, whereas the opposite behavior is observed for the skin friction coefficient. The thermal and concentration distributions were found to dominate in the absence of stratification. Consideration of convective heating and concentration tends to elevate thermal and mass distributions.

Limit cycles as stationary states of an extended harmonic balance ansatz

A limit cycle is a self-sustained, periodic, isolated motion appearing in autonomous differential equations. As the period of a limit cycle is unknown, finding it as a stationary state of a rotating ansatz is challenging. Correspondingly, its study commonly relies on numerical methodologies (e.g., brute-force time evolution, and variational shooting methods) or circumstantial evidence such as instabilities of fixed points. Alas, such approaches are (i) , as they rely on specific initial conditions, and (ii) do not provide analytical intuition about the physical origin of the limit cycles. Here, we (I) develop a multifrequency rotating ansatz with which we (II) find limit cycles as stationary-state solutions via a semianalytical homotopy continuation. We demonstrate our approach and its performance on the Van der Pol oscillator. Moving beyond this simple example, we show that our method captures all coexisting fixed-point attractors and limit cycles in a modified nonlinear Van der Pol oscillator. Our results facilitate the systematic mapping of out-of-equilibrium phase diagrams, with implications across multiple fields of the natural sciences. Published by the American Physical Society 2024

The influence of temperature-dependent variable viscosity and suction on a natural convective heat transfer in magneto generated plume

The study provides novel and valuable insights into the behavior of fluid flow and heat transfer in a generated plume under the influence of an aligned magnetic field, which is a complex and less-explored area in fluid dynamics. Incorporating variable viscosity and suction effects adds to the realism and applicability of the model, as it accounts for more realistic conditions where fluid properties change with temperature and external forces influence the flow. A mathematical model is formulated as a system of coupled partial differential equations to analyze the flow dynamics. Subsequently, a numerical solution is derived with stream function formulation for the system of coupled partial differential equations, which transmuted it into ordinary differential equations. To achieve this, the numerical properties of the problem are established through the utilization of a Shooting method in tandem with the MATLAB tool bvp4c. The graphical representations of both missing and specified boundary conditions, analyzes the influences of the viscosity parameter ε, suction parameter ξ, magnetic force parameter S, Prandtl number Pr and magnetic Prandtl number γ. The impact of these parameters on the heat transfer and fluid flow is given in detail. Inclusion of suction velocity counteracted the effects of temperature-dependent viscosity. The velocity f′, current density ϕ″, temperature θ, skin friction f″ and magnetic flux ϕ′ depicted an enhanced behavior while heat transfer rate θ′ dropped with an increment in viscosity parameter ε. However, for an increasing suction parameter ξ, the reverse trend of these properties is observed as compared to the viscosity parameter ε. The inclusion of suction counteracted to the effects of variable viscosity. Understanding how heat plumes behave under magnetic fields the study aims to provide insights that can be applied to real-world scenarios, such as improving cooling systems in industrial applications, enhancing environmental safety measures, and optimizing biomedical engineering processes.

Impulsive thrust strategy for orbital pursuit-evasion games based on impulse-like constraint

This paper proposes a novel impulsive thrust strategy guided by optimal continuous thrust strategy to address two-player orbital pursuit-evasion game under impulsive thrust control. The strategy seeks to enhance the interpretability of impulsive thrust strategy by integrating it within the framework of differential game in traditional continuous systems. First, this paper introduces an impulse-like constraint, with periodical changes in thrust amplitude, to characterize the impulsive thrust control. Then, the game with the impulse-like constraint is converted into the two-point boundary value problem, which is solved by the combined shooting and deep learning method proposed in this paper. Deep learning and numerical optimization are employed to obtain the guesses for unknown terminal adjoint variables and the game terminal time. Subsequently, the accurate values are solved by the shooting method to yield the optimal continuous thrust strategy with the impulse-like constraint. Finally, the shooting method is iteratively employed at each impulse decision moment to derive the impulsive thrust strategy guided by the optimal continuous thrust strategy. Numerical examples demonstrate the convergence of the combined shooting and deep learning method, even if the strongly nonlinear impulse-like constraint is introduced. The effect of the impulsive thrust strategy guided by the optimal continuous thrust strategy is also discussed.

A new method for solving fractional optimal control problems

In this article, we present a novel approach that utilizes the operational matrix method to solve fractional optimal control problems. We address the challenge of missing initial conditions for the co-state function by incorporating the linear shooting method. Our objective is to provide a method that not only enhances computational efficiency and reduces cost but also improves accuracy and usability. With our new approach, we can calculate the coefficients of the expansion solution without the need to solve an algebraic system. These coefficients can be generated explicitly or through an iterative process. We provide a proof of the uniform convergence of the approximate series of functions to the unique solution of the optimal control problem. To demonstrate the effectiveness of our proposed method, we solve several numerical examples and compare the results with those obtained by other researchers. Additionally, we extend the application of this new method to solve problems with multiple states, thereby expanding its scope to a wider range of problem domains. This allows us to address diverse scenarios using the same efficient and accurate approach. Through our research, we contribute to the development of a powerful and versatile method for solving fractional optimal control problems, offering significant advantages over existing techniques.

Fuel-Optimal Trajectory Planning for Lunar Vertical Landing

In this paper we consider a trajectory planning problem arising from a lunar vertical landing with minimum fuel consumption. The vertical landing requirement is written as a final steering angle constraint, and a nonnegative regularization term is proposed to modify the cost functional. In this way, the final steering angle constraint will be inherently satisfied according to Pontryagin’s Minimum Principle. As a result, the modified optimal steering angle has to be determined by solving a transcendental equation. To this end, a transforming procedure is employed, which allows for finding the desired optimal steering angle by a simple bisection method. Consequently, the vertical landing trajectory can be found offline by the indirect shooting method. Finally, some numerical examples are presented to demonstrate and verify the developments of the paper.

Thermoablative Treatment of Papillary Microcarcinomas of Thyroid.

Recently, locoregional treatment with ultrasound-guided radiofrequency has been proposed as a new, effective, and safe procedure for low-risk papillary thyroid microcarcinoma (PTC < 1 cm), not eligible or recruitable for surgery. Until now, the gold standard has been the surgery and then the active surveillance. The aim of the study is to present our experience of ultrasound-guidedthermoablation, a procedure performed before demolitive surgery and post-active surveillance. It is a non-invasive treatment that does not require general anesthesia, with a low risk of complications, hypothyroidism, and hypoparathyroidism. All nodules described on ultrasound showed a volumetric increase (follow-up from 12 to 36 months). The cytological examination in all cases showed TIR 4b and TIR 5 papillary microcarcinoma. All the patients were offered the possibility of radiofrequency thermoablation; they were all informed and gave their consent. 18G active tip electrode needles 7 or 10 mm (Amica Gen HS) were used with the moving shot method under local anesthesia in a day hospital setting. No severe complications were reported. Contrast-Enhanced Ultrasonography (CEUS) with SonoVue (CEUS Sonovue) was performed post-procedure and then at 1, 3, 6, and 12 months, which documented complete revascularization and progressive volumetric reduction of the treated area. Our experience has confirmed that radiofrequency ablation can effectively eliminate small papillary thyroid carcinomas with fewer complications. In our opinion, it is a valid alternative for the treatment of low-risk and indolent papillary thyroid microcarcinomas, even in the absence of surgical contraindications.

Robust Trajectory Planning of Gliding-Guided Projectiles with Weak Maneuverability

Due to constraints in launch platforms and cost, the maneuverability of gliding-guided projectiles is limited, necessitating a rational design of their trajectory schemes. To reduce the sensitivity of trajectory schemes to uncertainties while ensuring compatibility between flight schemes and guidance control systems and fully exploiting the control capability of the projectile, a closed-loop robust trajectory planning method is proposed. Models of major uncertain factors and state deviation at the control start point are established. Based on the NIPCE method, the stochastic dynamic model is transformed into a high-dimensional deterministic model with PCE coefficients as state variables, and the uncertainty propagation law is obtained. A PID algorithm is employed to design a tracking guidance law based on position error feedback, and open-loop and closed-loop robust trajectory planning models are established accordingly. The optimal control problem is solved by transforming it into a nonlinear programming problem using the direct shooting method. Our simulation results indicate that the NIPCE method can significantly improve the computational efficiency of uncertainty propagation while ensuring accuracy; compared with parallel MCS, the computation time is reduced by 96.8%. Open-loop robust planning can effectively mitigate the sensitivity of gliding trajectories to uncertainties (the standard deviations of terminal altitude and lateral deviations are reduced by 23.6% and 35.3%, respectively, compared to deterministic planning) but cannot completely eliminate terminal dispersion. Closed-loop robust planning effectively improves control effort consumption on the basis of open-loop planning.

디지털 영상 합성촬영 방법의 차이와 활용에 따른 영상 콘텐츠 분류의 목적과 방향성에 대한 고찰

This study aims to classify and define video content according to composite shooting methods to minimize confusion becauseXR and virtual production are used interchangeably in video content production sites without a distinction of terms.XR Studio (or Stage)—a video compositing system that combines the physical reality world with the digital virtual world—and Virtual Production are video compositing technologies that use the same software, rendering technology, real-time engines, and media technology systems that are synchronized to the LED wall. Communication at the video content production site is therefore unclear. Although XR Studio and Virtual Production are connected and may use some of the same technologies, they are ultimately separate entities. XR Studio and Virtual Production should be used separately,depending on the type of video content being produced. This study examines the similarities and differences in the technical approaches of XR and virtual production systems and presents a classification of video content according to the use of XR and virtual production.

Lie scaling transformations for the analysis of MHD flow with radiation, Soret, and Dufour effects as well as viscous dissipation across a convective surface during triple diffusion

The dynamics of an incompressible, triple-diffusive medium flowing across a linearly stretched surface are examined in this study, taking into account the effects of radiation, viscous dissipation, magnetohydrodynamics (MHD), and the Boussinesq approximation. The work uses simulations to investigate how the combined effects of Soret (thermal-diffusion) and Dufour (diffusion-thermo) phenomena interact with MHD restrictions. Using the Lie-group transformation approach, the goal is to find symmetry reductions in the governing partial differential equations. The method of Runge-Kutta shooting is used to solve the modified system of equations. To show the effects of key factors, such as the buoyancy ratio and magnetic field parameters, a visual analysis is performed. The results show that for both fluid flow scenarios, a rise in the magnetic field parameter causes a drop in the velocity profile, with velocity gradients decreasing by a good percentage. Similar to this, changes in the buoyancy ratio factors cause notable adjustments to the distributions of salt concentrations. When the magnetic parameter varies, the Nusselt number decreases approximately 14.29 %. While interesting behavior is depicted in triple diffusion scenarios, the Nusselt number increase approximately 9.52%. when values of soret effect Sr varies, the percentage of Sherwood number Shr in double diffusion decreases by 40% whereas in triple diffusion the Sherwood number increase interestingly about 33.33%. The precision and dependability of the conclusions are verified by contrasting the simulation results with previously published research.

Application and Analysis of Montage Shooting Techniques in the Film The King's Speech

The method of montage shooting is to express the film story more directly by splicing the shots. When telling the story that a person's thinking and doing things are not understood, it can be recalled through the narration, and the reason for the development of the story can be narrated at the end so that the audience can have a feeling of enlightenment. This also makes the film more layered and expressive. Through an in-depth study of the film The King's Speech, this paper analyzes the application of montage shooting techniques in the film. This paper first introduces the importance of montage in film production and the basic background of The King's Speech, then analyzes in detail how different types of montage shots promote the plot and express the complex emotions between the protagonists, and finally evaluates and reflects on the effect of using montage shooting techniques. This study not only contributes to an in-depth understanding of this classic film but also provides valuable enlightenment for future film and television production.

Real-Time Co-optimization of Gear Shifting and Engine Torque for Predictive Cruise Control of Heavy-Duty Trucks

Fuel consumption is one of the main concerns for heavy-duty trucks. Predictive cruise control (PCC) provides an intriguing opportunity to reduce fuel consumption by using the upcoming road information. In this study, a real-time implementable PCC, which simultaneously optimizes engine torque and gear shifting, is proposed for heavy-duty trucks. To minimize fuel consumption, the problem of the PCC is formulated as a nonlinear model predictive control (MPC), in which the upcoming road elevation information is used. Finding the solution of the nonlinear MPC is time consuming; thus, a real-time implementable solver is developed based on Pontryagin’s maximum principle and indirect shooting method. Dynamic programming (DP) algorithm, as a global optimization algorithm, is used as a performance benchmark for the proposed solver. Simulation, hardware-in-the-loop and real-truck experiments are conducted to verify the performance of the proposed controller. The results demonstrate that the MPC-based solution performs nearly as well as the DP-based solution, with less than 1% deviation for testing roads. Moreover, the proposed co-optimization controller is implementable in a real-truck, and the proposed MPC-based PCC algorithm achieves a fuel-saving rate of 7.9% without compromising the truck’s travel time.

The most probable transition pathway of a predator–prey system under noise

Stochastic population dynamics plays a crucial role in biological systems. The number and distribution of biological populations often affect the stability of ecosystems, and even lead to the transition of ecosystems from one steady-state to another. The transition between different states of a population has a significant impact on both population dynamics and biological evolution. In this paper, we examined a stochastic population model and used Onsager–Machlup action functional and neural shooting method to obtain the most probable transition pathway between different states. Moreover, we analyzed the influence of noise intensity, maximum harvest rate [Formula: see text] and time [Formula: see text] on most probable transition pathway in two different parameter scenarios. Our research may provide a better understanding of evolutionary process such as genetic variation in populations and the evolution of species adaptation, meanwhile, may provide a theoretical guidance for species conservation and management in real world.

Bioanalytical Method Development and Validation of UV Spectrophotometric Method for Estimation of Metformin Hydrochloride in Urine Sample

Purpose: To develop a simple, sensitive, accurate, precise and rapid UV spectrophotometric method for the determination of metformin in human urine. Methods: Extraction of metformin from urine samples was done by Dilute and shoot method in which urine was diluted up to 1:10 ratio to avoid interference of matrix. For estimation of Metformin hydrochloride, the solvent system employed was water. The metformin hydrochloride was scanned in range of 200nm to 400 nm and wavelength of detection (λdet) was found to be 234 nm. Result: The calibration curve was linear in the range of 1-17 μg/ml. the recovery and assay studies of metformin hydrochloride were within 93-94.85% indicating that the proposed method can be estimation of metformin hydrochloride