Nonlinear Conditions Research Articles

Probing nonlinear excitation conditions: photoluminescence and nonlinear absorption studies in laser-irradiated dielectrics

Understanding the fundamentals of laser-matter interactions is crucial for developing and optimizing ultrafast laser processing strategies. In optically transparent solids, the key event by which energy is deposited in the material is through the generation of an electron–hole plasma via nonlinear excitation mechanisms. As the energy stored in the plasma relaxes, local distortions of the lattice may occur, such as point defects. These defects give rise to new discrete energy states located in the bandgap. In this study, we investigate how the presence of these energy states influences the transmission of ultrashort near-infrared laser pulses in fused silica. Experimental results of laser pulse transmission and photoluminescence from defects are correlated with optical microscopy of the irradiated spots, allowing us to identify different nonlinear interaction regimes. Numerical simulations indicate that photo-induced defects influence the nonlinear losses of ultrashort laser pulses and explain why a non-destructive damage regime with detectable excitation is only observed for a narrow intensity range in multipulse experiments.

Adaptive stabilization of stochastic systems with polynomial nonlinear conditions, unknown parameters, and dead‐zone actuator

AbstractMany practical dynamic models always suffer from complex nonlinearities, parameter uncertainties and random noises. Such kind of models are always characterized by uncertain stochastic nonlinear systems. Besides, many factors will lead to dead‐zone actuator, which further adds more challenges to control engineering. This paper studies stabilization issue of stochastic systems with polynomial nonlinear conditions, unknown parameters and dead‐zone actuator. An adaptive control approach is proposed by exploring homogeneous domination control and using dynamic‐gain‐based adaptive design strategy. It shows that all the signals are bounded almost surely and the system states converge to the origin almost surely. The presented method is successfully applied to the mass spring mechanical system.

INTELLIGENT CONTROL SYSTEM OF MULTI-MOTION MOBILE ROBOT

Technical devices with irregular motion are described by complex non-linear differential equations, as they have an uncertain environment. Due to interactions and simplifications in these types of control objects, their mathematical models may have certain errors. For this reason, by known methods, for example, the linear matrix inequality method, Lyapunov's quadratic function, etc. The synthesized automatic control systems (ACS) for dynamic objects written by nonlinear mathematical models based on the quadratic matrix determined by The synthesis of regulators for the management of dynamic objects described in nonlinear and uncertain conditions is based on fuzzy logic theory. Since the controllers synthesized by fuzzy logic are based on knowledge, their application to other objects (robots) is limited. In such systems, it is difficult or not at all to determine the dependencies between ACS quality indicators, stability and object parameters. Taking into account the above, a method of analytically parametric synthesis of regulators that ensures the degree of stability and accuracy in ACS’s designed for fuzzy TS-type dynamic objects is proposed. In the article, the solution to the problem of the synthesis of the control system of the mobile robot was considered, and it was successfully applied in the multi-motion mobile robot system. Modeling and experimental results confirm that the operation and stability of the obtained system fully meet the technical requirements. The proposed method has led to an increase in both tracking and control accuracy during high-speed movements. Keywords: multi-motion mobile robot, mathematical model, mechatronic modules, fuzzy TS model, robust controller, fuzzy logic.

Some multidimensional fixed point theorems for nonlinear contractions in C-distance spaces with applications

In this manuscript, we use the concept of multidimensional fixed point in a generalized space, namely, C-distance space with some nonlinear contraction conditions, such as Jaggi- and Dass-Gupta-type contractions. We provide results with a Jaggi-type hybrid contraction for the mentioned space. Moreover, we use control functions to get the desired results. After each theorem, we compare our results with previous ones to show that they are generalized. We provide examples to support our results. An application is also performed to solve the system of integral equations.

Efficiency assessment of thermal radiation utilizing flow of advanced nanocomposites on riga plate

Utilizing nanostructured materials to optimize thermal processes for renewable energy is an important strategy that has been applied in numerous engineering disciplines for diverse interventions such as photovoltaic thermal systems. Ternary nanofluids have demonstrated potential for improving the cooling capabilities of this kind of system. The current research focuses on enhancing the thermal performance of convective flow of a water-based trihybrid nanofluid across a Riga plate incorporating carbon nanotubes in spherical, graphene in cylindrical and Al2O3 in platelet shapes. Several mechanisms like non-linear heat production, thermal radiation, velocity and thermal slip conditions have all been investigated regarding the flow describing equations. Due to the high complexity of the problem modeling and numerical methods, conventional techniques to the parametric work that incorporate various model factors can fail to derive accurate solutions. This study assesses the ability of soft computing techniques to determine the behavior of a problem with various connected parameters to resolve this issue. With help from numerical scheme Lobatto IIIa technique reference data, the artificial neural network is trained. Furthermore, a constructive technique using artificial neural networks (Levenberg–Marquardt) is used to quantitatively determine the rate of heat transmission on the surface of Riga plates. With the use of correlation, fitting analysis, regression, mean squared error, absolute error, and error histogram, the prediction performance of the proposed algorithms is examined. The Cfx and Nux reach convergence with mean squared errors close to 10−8 and 10−10 after 626 and 100 epochs. The investigation illustrates the benefits of using soft computing methods to accurately investigate the behavior of complex flow models. The most important discovery is that, in comparison to mono- and binary-hybrid nanofluids, ternary hybrid nanofluids have a greater thermal responsiveness.

Existence analysis of a cross-diffusion system with nonlinear Robin boundary conditions for vesicle transport in neurites

A one-dimensional cross-diffusion system modeling the transport of vesicles in neurites is analyzed. The equations are coupled via nonlinear Robin boundary conditions to ordinary differential equations for the number of vesicles in the reservoirs in the cell body and the growth cone at the end of the neurite. The existence of bounded weak solutions is proved by using the boundedness-by-entropy method. Numerical simulations show the dynamical behavior of the concentrations of anterograde and retrograde vesicles in the neurite.

Modeling of Machine Learning-Based Extreme Value Theory in Stock Investment Risk Prediction: A Systematic Literature Review.

The stock market is heavily influenced by global sentiment, which is full of uncertainty and is characterized by extreme values and linear and nonlinear variables. High-frequency data generally refer to data that are collected at a very fast rate based on days, hours, minutes, and even seconds. Stock prices fluctuate rapidly and even at extremes along with changes in the variables that affect stock fluctuations. Research on investment risk estimation in the stock market that can identify extreme values is nonlinear, reliable in multivariate cases, and uses high-frequency data that are very important. The extreme value theory (EVT) approach can detect extreme values. This method is reliable in univariate cases and very complicated in multivariate cases. The purpose of this research was to collect, characterize, and analyze the investment risk estimation literature to identify research gaps. The literature used was selected by applying the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) and sourced from Sciencedirect.com and Scopus databases. A total of 1107 articles were produced from the search at the identification stage, reduced to 236 in the eligibility stage, and 90 articles in the included studies set. The bibliometric networks were visualized using the VOSviewer software, and the main keyword used as the search criteria is "VaR." The visualization showed that EVT, the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models, and historical simulation are models often used to estimate the investment risk; the application of the machine learning (ML)-based investment risk estimation model is low. There has been no research using a combination of EVT and ML to estimate the investment risk. The results showed that the hybrid model produced better Value-at-Risk (VaR) accuracy under uncertainty and nonlinear conditions. Generally, models only use daily return data as model input. Based on research gaps, a hybrid model framework for estimating risk measures is proposed using a combination of EVT and ML, using multivariable and high-frequency data to identify extreme values in the distribution of data. The goal is to produce an accurate and flexible estimated risk value against extreme changes and shocks in the stock market. Mathematics Subject Classification: 60G25; 62M20; 6245; 62P05; 91G70.

Manifestly covariant polynomial M5-brane lagrangians

We present polynomial and manifestly covariant M5-brane Lagrangians along with their analyses involving their dynamics, gauge symmetries and their nonlinear self-duality condition. Such Lagrangians can be particularly useful for developments that are otherwise hindered by a non-polynomial structure and singularity of the Lagrangian such as its quantisation. Although on integrating out some of the auxiliary fields these polynomial Lagrangians reduce to the M5-brane Lagrangian given by the Pasti-Sorokin-Tonin (PST) formalism, in the analysis of the polynomial Lagrangians the only remnant of the non-polynomial structure of the PST type Lagrangian appears in the gauge transformation corresponding to an infinitesimal shift of a Stückelberg field. This transformation does not affect the dynamics or the on-shell self-duality condition of the polynomial M5-brane Lagrangians.

Highly detailed structural integrity assessment of the reactor pressure vessel nozzle of Atucha-I during a pressurized thermal shock event

In pressurized water reactor (PWR) nuclear plants, reactor pressure vessel (RPV) nozzles are critical due to geometric stress concentrations that worsen with large temperature gradients. In the context of Atucha-I Long Term Operation (LTO) assessment, this work presents a high-fidelity thermo-mechanical simulation approach to verify the stress levels on the main nozzles of the vessel under a pressurized thermal shock event. Nucleoeléctrica Argentina S.A. (NA-SA) has provided the boundary conditions, including the thermal plume that results from computational fluid dynamics (CFD) simulations of the transient event. Then, using a one-way and non-conformal projection procedure, CFD data is coupled to a highly-detailed 3D finite element model (FEM), including the RPV, closure head, nuts and bolts, and moderator tank, all interconnected through non-linear contact condition that accounts for friction. Finally, a 3D FEM submodel assuming an elastoplastic material behavior with non-linear isotropic hardening is used to verify the structural integrity of the nozzle. Results indicate that the plastic strain and stresses on the nozzles are low enough to ensure the correct function of the reactor during the LTO period.

Honey Badger Algorithm Based PI Controller for DC Link Voltage Control of Solar Photovoltaic System Connected to Grid for Enhanced Power Quality

The parameters of the proportional integral (PI) controller used for DC link voltage control play a vital role in regulating the DC link voltage of grid-connected solar photovoltaic system that experiences heavy DC voltage fluctuation and various power quality issues due to integration of non-linear loads, varying irradiance and loading conditions. The existing strategies might fail to respond to the above complications due to fixed PI gains which restrict their scope of controlling domain. Therefore, adaptive PI gain values should be selected to quickly adjust to the varying conditions and dynamically obtain the optimal control settings. This article employs the honey badger algorithm (HBA), developed in Matlab to adaptively tune the PI controller gains value by minimizing the DC link voltage deviation. The advantages of using this technique over conventional PI controllers are its quick response, adaptability, stability, and optimal self-tuning process. The proposed algorithm has been tested under steady-state and dynamic conditions for different irradiation and loading conditions. Further, results of the proposed algorithm have been compared with PI controller and particle swarm optimization-PI controller to validate the efficacy of the proposed algorithm for grid-connected solar photovoltaic systems. It has been observed that the proposed algorithm maintains THD <3% in all the tested conditions.

Mathematical Modelling and Statistical Analysis of Improved Grey Wolf Optimized Maximum Tracking for Solar Photovoltaic Energy System Under Non Linear Operational Conditions

IAs the utilization of solar photovoltaic (PV) energy systems continues to expand, the efficient extraction of energy under non-linear operational conditions becomes paramount. This research focuses on the development and enhancement of a Maximum Power Point Tracking (MPPT) algorithm, specifically tailored for solar PV systems, through the integration of Improved Grey Wolf Optimization (IGWO) techniques. The study utilizes mathematical modeling and statistical analysis to evaluate the performance of the proposed IGWO-based MPPT algorithm. This research, we first establish a comprehensive mathematical model of a solar PV energy system that accurately represents its non-linear operational characteristics, taking into account factors such as temperature variations, shading effects, and changing environmental conditions. Subsequently, we introduce the Improved Grey Wolf Optimization algorithm to optimize the MPPT process, aiming to enhance energy extraction efficiency by dynamically adapting to varying conditions. The statistical analysis includes the comparison of the IGWO-based MPPT algorithm with conventional MPPT methods, such as Perturb and Observe (P&amp;O) and Incremental Conductance (IncCond), under various non-linear operational scenarios. Key performance metrics, including energy conversion efficiency, response time, and tracking accuracy, are thoroughly evaluated to assess the algorithm's effectiveness in real-world conditions. The results of this study demonstrate the superior performance of the IGWO-based MPPT algorithm in enhancing the energy harvesting capabilities of solar PV systems under non-linear operational conditions. The proposed approach not only improves the overall energy conversion efficiency but also reduces the adverse effects of environmental variables on the system's performance. In conclusion, the integration of Improved Grey Wolf Optimization into the MPPT process represents a promising advancement in the field of solar photovoltaic energy systems. The mathematical modeling and statistical analysis conducted in this research provide valuable insights into the practical benefits of this approach, paving the way for more efficient and reliable solar energy utilization in the future.

Finite-time stability and uniqueness theorem of solutions of nabla fractional $ (q, h) $-difference equations with non-Lipschitz and nonlinear conditions

&lt;abstract&gt;&lt;p&gt;In this paper, the discrete $ (q, h) $-fractional Bihari inequality is generalized. On the grounds of inequality, the finite-time stability and uniqueness theorem of solutions of $ (q, h) $-fractional difference equations with non-Lipschitz and nonlinear conditions is concluded. In addition, the validity of our conclusion is illustrated by a nonlinear example with a non-Lipschitz condition.&lt;/p&gt;&lt;/abstract&gt;

Problem on string system vibrations on star-shaped graph with nonlinear condition at node

We consider a system of $n$ strings being in the equilibrium position along a geometrical star-graph. We suppose that the edges of the graph have the same lengths and the graph is oriented to the node. We study the case when the initial velocity of each string is zero. The initial shape of each string is defined by means of given functions on the edges. We assume that at the boundary vertices the strings are fixed. We study the oscillatory process for the case, when the node point of the string system is located inside the motion limiter. At the same time we suppose that the limiter can move in the direction perpendicular to the graph plane. While the limiter does not touch the node point of the string system, the transmission condition holds (the Kirchoff condition). Once the limiter touches the node, their joint motion begins and an additional restriction for the sign of the sum of derivatives at the node appears. Thus, at the node, a hysteresis type condition is satisfied. In the work we obtain a representation for the solution and prove its existence. For a particular case we consider a case on periodic oscillations of the node point of the string system. We solve a problem on boundary control of the oscillatory process under the assumption that the oscillation time does not exceed the length of the strings.

Multi-microgrid optimization operation strategy considering nonlinear conditions and renewable energy uncertainty: A data-driven method

Multi-microgrid optimization operation strategy considering nonlinear conditions and renewable energy uncertainty: A data-driven method

Deformations of Calabi–Yau varieties with k-liminal singularities

Abstract The goal of this paper is to describe certain nonlinear topological obstructions for the existence of first-order smoothings of mildly singular Calabi–Yau varieties of dimension at least $4$ . For nodal Calabi–Yau threefolds, a necessary and sufficient linear topological condition for the existence of a first-order smoothing was first given in [Fri86]. Subsequently, Rollenske–Thomas [RT09] generalized this picture to nodal Calabi–Yau varieties of odd dimension by finding a necessary nonlinear topological condition for the existence of a first-order smoothing. In a complementary direction, in [FL22a], the linear necessary and sufficient conditions of [Fri86] were extended to Calabi–Yau varieties in every dimension with $1$ -liminal singularities (which are exactly the ordinary double points in dimension $3$ but not in higher dimensions). In this paper, we give a common formulation of all of these previous results by establishing analogues of the nonlinear topological conditions of [RT09] for Calabi–Yau varieties with weighted homogeneous k-liminal hypersurface singularities, a broad class of singularities that includes ordinary double points in odd dimensions.

Normalized Nonlinear Impedance Boundary Condition in Anhysteretic Magnetic Material for Eddy Current Problems

Normalized Nonlinear Impedance Boundary Condition in Anhysteretic Magnetic Material for Eddy Current Problems

Multi-objective pedestrian tracking method based on YOLOv8 and improved DeepSORT.

A multi-objective pedestrian tracking method based on you only look once-v8 (YOLOv8) and the improved simple online and real time tracking with a deep association metric (DeepSORT) was proposed with the purpose of coping with the issues of local occlusion and ID dynamic transformation that frequently arise when tracking target pedestrians in real complex traffic scenarios. To begin with, in order to enhance the feature extraction network's capacity to learn target feature information in busy traffic situations, the detector implemented the YOLOv8 method with a high level of small-scale feature expression. In addition, the omni-scale network (OSNet) feature extraction network was then put on top of DeepSORT in order to accomplish real-time synchronized target tracking. This increases the effectiveness of picture edge recognition by dynamically fusing the collected feature information at various scales. Furthermore, a new adaptive forgetting smoothing Kalman filtering algorithm (FSA) was created to adapt to the nonlinear condition of the pedestrian trajectory in the traffic scene in order to address the issue of poor prediction attributed to the linear state equation of Kalman filtering once more. Afterward, the original intersection over union (IOU) association matching algorithm of DeepSORT was replaced by the complete-intersection over union (CIOU) association matching algorithm to fundamentally reduce the target pedestrians' omission and misdetection situation and to improve the accuracy of data matching. Eventually, the generalized trajectory feature extractor model (GFModel) was developed to tightly merge the local and global information through the average pooling operation in order to get precise tracking results and further decrease the impact of numerous disturbances on target tracking. The fusion algorithm of YOLOv8 and improved DeepSORT method based on OSNet, FSA and GFModel was named YOFGD. According to the experimental findings, YOFGD's ultimate accuracy can reach 77.9% and its speed can reach 55.8 frames per second (FPS), which is more than enough to fulfill the demands of real-world scenarios.

Dynamic vibration control of non-linear buildings using multiple tuned mass dampers

In the field of civil engineering, tuned mass dampers (TMDs) serve as passive devices designed for dynamic vibration control of structures. When dealing with buildings exhibiting nonlinear behavior under dynamic loads, the effectiveness of TMDs may be affected by detuning due to the degradation of the building’s strength. Therefore, addressing the non-linear behavior requires a unique strategy involving the tuning of TMDs to specific time periods following the onset of non-linearity. The proposed approach in this study entails a pushover analysis to establish the pushover capacity curve. The regions between the origin and a target drift of 1/150 are then represented using an idealized trilinear form, with the initial segment corresponding to linearity and subsequent segments capturing non-linear behavior. The second segment spans from the onset of non-linearity to a target drift of 1/400, and the third segment covers the drift range from 1/400 to 1/150. Examining this strategy involves calculating time periods for each segment. Subsequently, three single TMD (STMD) scenarios and one multiple TMD (MTMD) scenario with 3 TMDs, each tuned to time periods corresponding to specific segments of the idealized trilinear, are compared in this study. The evaluation includes non-linear dynamic analysis of 7-story and 25-story reinforced concrete buildings equipped with these TMD scenarios. The floor maximum displacement and peak acceleration results indicate that the STMDs tuned to the time periods corresponding to the non-linear segments exhibit robustness, surpassing the performance of the STMD tuned to the fundamental period. Remarkably, the MTMD scenario demonstrates superior robustness compared to all three STMD scenarios. Further analysis under wind load on the same 25-story building confirms the effectiveness of the MTMDs and STMD tuned to the nonlinearity segment compared to the STMD tuned to the fundamental period. This research provides valuable insights into TMD design for enhanced building performance under non-linear conditions.

Cooperative strategy based on a two-layer game model for inferior USVs to intercept a superior USV

Aiming at the problem of inferior USVs intercepting a superior USV, a cooperative interception strategy based on the two-layer game model is studied. Through the mathematical description of the USV's reachable set, the feasible interception point position is obtained. Two necessary conditions for completing regional defensive tasks under nonlinear motion conditions are proposed. By introducing the idea of a hierarchical task network, the complex regional defensive task is divided into different sub-tasks corresponding to the above necessary conditions. In order to better complete the switching between different sub-tasks, a two-layer game model is established. The selection of sub-tasks is modeled as an upper game, and the selection of basic maneuvers is modeled as a lower game. The Monte Carlo simulation results show that the cooperative interception strategy proposed in this paper has better performance under different conditions.

Simulation and real time implementation of shunt active power filter for power quality enhancement using adaptive neural network topology

With the rise in non-linear loads, the need for a veracious power filter to alleviate voltage and current harmonics for meeting power quality has been a challenging requirement of the existing power system. This paper presents a systematic approach to improve power quality with a shunt active power filter (SAPF). The controller consists of a neural network approach to enhance the switching control of SAPF under dynamic and non-linear loading conditions. DC link voltage has been regulated using proportional-Integral (PI) control. To extract reference current, instantaneous-reactive power (IRP) theory has been used. IRP theory employing indirect current control strategy provides reference source current signals as well as regulated PWM switching signals for hysteresis control. An ADALINE network has been devised to extract fundamental signals from the polluted supply voltage. The model has been simulated on the MATLAB®/Simulink platform and validated by SAPF prototype in the laboratory using the TMS320F28335 floating-point DSP controller.