Search Results (81)

In this article, we investigate the fractional soliton solutions as well as the chaotic analysis of the fourth-order nonlinear Ablowitz–Kaup–Newell–Segur wave equation. This model is considered an intriguing high-order nonlinear partial differential equation that integrates additional spatial and dispersive effects to extend the concepts to more intricate wave dynamics, relevant in engineering and science for understanding complex phenomena. To examine the solitary wave solutions of the proposed model, we employ sophisticated analytical techniques, including the generalized projective Riccati equation method, the new improved generalized exponential rational function method, and the modified F-expansion method, along with mathematical simulations, to obtain a deeper insight into wave propagation. To explore desirable soliton solutions, the nonlinear partial differential equation is converted into its respective ordinary differential equations by wave transforms utilizing $\beta$-fractional derivatives. Further, the solutions in the forms of bright, dark, singular, combined, and complex solitons are secured. Various physical parameter values and arrangements are employed to investigate the soliton solutions of the system. Variations in parameter values result in specific behaviors of the solutions, which we illustrate via various types of visualizations. Additionally, a key aspect of this research involves analyzing the chaotic behavior of the governing model. A perturbed version of the system is derived and then analyzed using chaos detection techniques such as power spectrum analysis, Poincaré return maps, and basin attractor visualization. The study of nonlinear dynamics reveals the system’s sensitivity to initial conditions and its dependence on time-decay effects. This indicates that the system exhibits chaotic behavior under perturbations, where even minor variations in the starting conditions can lead to drastically different outcomes as time progresses. Such behavior underscores the complexity and unpredictability inherent in the system, highlighting the importance of understanding its chaotic dynamics. This study evaluates the effectiveness of currently employed methodologies and elucidates the specific behaviors of the system’s nonlinear dynamics, thus providing new insights into the field of high-dimensional nonlinear scientific wave phenomena. The results demonstrate the effectiveness and versatility of the approach used to address complex nonlinear partial differential equations. Full article

This manuscript aims to explore localized waves for the nonlinear partial differential equation referred to as the $(1+1)$-dimensional generalized Kundu–Eckhaus equation with an additional dispersion term that describes the propagation of the ultra-short femtosecond pulses in an optical fiber. This research delves deep into the characteristics, behaviors, and localized waves of the $(1+1)$-dimensional generalized Kundu–Eckhaus equation. We utilize the multivariate generalized exponential rational integral function method (MGERIFM) to derive localized waves, examining their properties, including propagation behaviors and interactions. Motivated by the generalized exponential rational integral function method, it proves to be a powerful tool for finding solutions involving the exponential, trigonometric, and hyperbolic functions. The solutions we found using the MGERIF method have important applications in different scientific domains, including nonlinear optics, plasma physics, fluid dynamics, mathematical physics, and condensed matter physics. We apply the three-dimensional (3D) and contour plots to illuminate the physical significance of the derived solution, exploring the various parameter choices. The proposed approaches are significant and applicable to various nonlinear evolutionary equations used to model nonlinear physical systems in the field of nonlinear sciences. Full article

This study examines the influence mechanism of mining depth evolution on dust distribution, using the An Tai Bao open-pit coal mine as the research subject. A spatial coordinate system of the mining area was established utilizing a GIS positioning system, and high-resolution topographic data were extracted using Global Mapper. The research team developed a three-dimensional geological model updating algorithm with depth gradient as the characteristic parameter, enabling dynamic monitoring of mining depth with a model iteration accuracy of 0.5 m per update. A Fluent-based numerical simulation method was employed to construct a depth-dependent dust migration field solving system, aiming to elucidate the three-dimensional coupling mechanism between mining depth and dust dispersion. The findings reveal that mining depth demonstrates a three-stage critical response to dust migration. When the depth surpasses the threshold of 150 m, the wind speed attenuation rate at the pit bottom exhibits a marked change, and the dust dispersion distance decreases by 62% compared to shallow mining conditions. The slope pressure field evolution shows a significant depth-enhancement effect, with the maximum wind pressure at the leeward step boundary increasing by 22–35% for every additional 50 m of depth, resulting in dust accumulation zones with distinct depth-related characteristics. The west wind scenario demonstrates a particularly notable depth amplification effect, with the dust dispersion range in a 200-meter-deep pit expanding by 53.7% compared to the standard west wind condition. Furthermore, the interaction between particle size and depth causes the dust migration distance to exhibit exponential decay as depth increases. This research elucidates the progressive constraining influence of mining depth, a critical control parameter, on dust migration patterns. It establishes a depth-oriented theoretical framework for dust prevention and control strategies in deep open-pit mines. Full article

Phosphogypsum leachate significantly accelerates carbonate rock dissolution in karst regions. The dissolution mechanism of phosphogypsum leachate associated with carbonate rock interaction and the corresponding numerical simulation need further study. In this study, 3D digital core imaging was used to scan undisturbed carbonate rock specimens from phosphogypsum landfill sites, and corresponding 3D structural models were constructed. We carried out indoor dissolution experiments in which we used Scanning Electron Microscopy as well as Energy Dispersive Spectrometer to observe changes in the surface micromorphology and elemental content of the rock specimens under different dissolution conditions. A reactive numerical model was developed based on the 3D structural model obtained from 3D digital core imaging, and numerical simulation studies were conducted. The dissolution reaction between phosphogypsum leachate and carbonate rocks exhibited an initial rapid phase followed by gradual stabilization. The pH of the leachate showed an exponential negative correlation with the dissolution amount per unit area of the rock specimens, while a power-law negative correlation was observed between pH and chemical dissolution rates. The numerical model effectively reproduced the reactant concentration states observed in experiments, confirming its capability to simulate reaction processes within rock specimens. Simulation results demonstrated that preferential flow through fracture channels led to higher reactant concentrations near fractures due to incomplete reactions, whereas lower concentrations occurred in sub-fracture regions. As the fracture aperture increased, the concentration disparity between these regions became more pronounced, with higher concentration of reactants at the outlet. Full article

Particle dispersion models (PDMs) are essential to capture the influence of unresolved turbulent eddies on particle transport in computational fluid dynamics (CFD) simulations. However, the validation of these models remains challenging, especially when relying on experimental data or CFD simulations that are based on turbulence models. In this work, we use time-averaged data obtained in a direct numerical simulation (DNS) instead of relying on turbulence models to model particle dispersion. In addition, a new particle dispersion model is presented, referred to as the limited particle–eddy interaction time (LPI) model. For a detailed and systematic evaluation of the new LPI model, we compare its performance with that of other commonly used models, such as the mean particle–eddy interaction time (MPI) model implemented in OpenFOAM^® and the randomized particle–eddy interaction time (RPI) model from the literature. The MPI model shows good agreement with the DNS for the largest particles tested (Stokes number, St = 0.2) but exhibits erratic and unphysical trajectories for smaller particles (St ≤ 0.05). To mitigate this erratic behavior, we have adjusted the eddy interaction time in the new LPI model. Full article

Viscosimetric experiments and microscopy measurements on microdispersions of polycaprolactone (PCL) plastics showed an unexpected exponential decrease in viscosity over the first 3 months and a plateau for a further 4 months of observations. This behavior is due to the release of nanoplastics from semicrystalline particles that reduce the viscosity of the dispersion, and leave stable and fine crystalline microplastics ranging in size from 30 to 180 μm. The development of nonlinear kinetic models for the fragmentation process from macro- to meso-, micro-, and nanoplastics reveals complex behavior that we call a cracking–leaching mechanism. The autocatalytic mechanical cracking of macroplastics larger than 5 mm is followed by a logistic-type mechanical cracking of mesoplastics between 5 and 1 mm. Therefore, microplastics smaller than 1 mm experience the leaching diffusion modeled via nonlinear coupled kinetic differential equations: semicrystalline microplastics quickly release nanoplastics from the amorphous fraction, followed by fine and stable crystalline microplastics. This proposed mechanism explains the size distribution of floating plastic debris in the oceans, with an unexpected gap of microplastics. Considering the outcome, a general reflection is made on the critical issues that currently appear unsolvable regarding plastic pollution. Full article

In this paper, we investigate closed-form meromorphic solutions of the fifth-order Sawada-Kotera (fSK) equation and (3+1)-dimensional generalized shallow water (gSW) equation. The study of high-order and high-dimensional differential equations is pivotal for modeling complex nonlinear phenomena in physics and engineering, where higher-order dispersion, dissipation, and multidimensional dynamics govern system behavior. Constructing explicit solutions is of great significance for the study of these equations. The elliptic, hyperbolic, rational, and exponential function solutions for these high-order and high-dimensional differential equations are achieved by proposing the extended complex method. The planar dynamics behavior of the (3+1)-dimensional gSW equation and its phase portraits are analyzed. Using computational simulation, the chaos behaviors of the high-dimensional differential equation under noise perturbations are examined. The dynamic structures of some obtained solutions are revealed via some 2D and 3D graphs. The results show that the extended complex method is an efficient and straightforward approach to solving diverse differential equations in mathematical physics. Full article

This paper is concerned with the choice of data granularity for application of the EDF (Exponential Dispersion Family) chain ladder model to forecast a loss reserve. As the duration of individual accident and development periods is decreased, the number of data points increases, but the volatility of each point increases. This leads to a question as to whether a decrease in time unit leads to an increase or decrease in the variance of the loss reserve estimate. Is there an optimal granularity with respect to the variance of the loss reserve? A preliminary question is that of whether an EDF chain ladder that is valid for one duration (here called mesh size) remains so for another. The conditions under which this is so are established. There are various ways in which the mesh size of a data triangle may be varied. The paper identifies two of particular interest. For each of these two types of variation, the effect on variance of loss reserve is studied. Subject to some technical qualifications, the conclusion is that an increase in mesh size always increases the variance. It follows that one should choose a very high degree of granularity in order to maximize efficiency of loss reserve forecasting. Full article

Accurately predicting the remaining useful life (RUL) of critical mechanical components is a central challenge in reliability engineering. Stochastic processes, which are capable of modeling uncertainties, are widely used in RUL prediction. However, conventional stochastic process models face two major limitations: (1) the reliance on strict assumptions during model formulation, restricting their applicability to a narrow range of degradation processes, and (2) the inability to account for potential variations in the degradation mechanism during modeling and prediction. To address these issues, we propose a novel mechanism-equivalence-based Tweedie exponential dispersion process (ME-based TEDP) for adaptive degradation modeling and RUL prediction of mechanical components. The proposed model enhances the original Tweedie exponential dispersion process (TEDP) by incorporating degradation mechanism equivalence, effectively capturing the correlation between model parameters. Furthermore, it improves prediction accuracy and interpretability by employing a dynamic testing–modeling–predicting strategy. Application of the ME-based TEDP model to high-speed rail bogie systems demonstrates its effectiveness and superiority over existing approaches. This study advances the theory of degradation modeling and significantly improves the precision of RUL predictions. Full article

The Hirota equation, an advanced variant of the nonlinear Schrödinger equation with cubic nonlinearity, incorporates time-delay adjustments and higher-order dispersion terms, offering an enhanced approximation for wave propagation in optical fibers and oceanic systems. By utilizing the traveling wave transformation generated from Lie point symmetry analysis with the combination of generalized exponential differential rational function and modified Bernoulli sub-ODE techniques, several traveling wave solutions, such as periodic, singular-periodic, and kink solitons, emerge. To examine the solutions visually, parametric values are adjusted to create 3D, contour, and 2D illustrations. Additionally, the dynamic properties of the model are explored through bifurcation analysis. The exact results demonstrate that both techniques are practical and robust. Full article

In this article, we introduce a new three-parameter distribution called the discrete Weibull exponential (DWE) distribution, based on the use of a discretization technique for the Weibull-G family of distributions. This distribution is noteworthy, as its probability mass function presents both symmetric and asymmetric shapes. In addition, its related hazard function is tractable, exhibiting a wide range of shapes, including increasing, increasing–constant, uniform, monotonically increasing, and reversed J-shaped. We also discuss some of the properties of the proposed distribution, such as the moments, moment-generating function, dispersion index, Rényi entropy, and order statistics. The maximum likelihood method is employed to estimate the model’s unknown parameters, and these estimates are evaluated through simulation studies. Additionally, the effectiveness of the model is examined by applying it to three real data sets. The results demonstrate that, in comparison to the other considered distributions, the proposed distribution provides a better fit to the data. Full article

Residuals are essential in regression analysis for evaluating model adequacy, validating assumptions, and detecting outliers or influential data. While traditional residuals perform well in linear regression, they face limitations in exponential family models, such as those based on the binomial and Poisson distributions, due to heteroscedasticity and dependence among observations. This article introduces a novel standardized combined residual for linear and nonlinear regression models within the exponential family. By integrating information from both the mean and dispersion sub-models, the new residual provides a unified diagnostic tool that enhances computational efficiency and eliminates the need for projection matrices. Simulation studies and real-world applications demonstrate its advantages in efficiency and interpretability over traditional residuals. Full article

The results of an experimental investigation of the temperature and wavelength dependence of the Kerr constant (K) of mixtures with an increasing amount of chiral dopant in an isotropic liquid crystal phase are reported. The material was composed of a nematic liquid crystal (5CB) and a chiral dopant (CE2), which formed non-polymer-stabilized liquid crystalline blue phases with an exceptionally large value of K∼2 × 10⁻⁹ mV⁻². The measurements were performed on liquid and blue phases at several concentrations covering a range of temperatures and using three wavelengths: 532 nm, 589 nm and 633 nm. The work focused on changes caused by concentration and their impact on the increase in the value of K, and it was found that in the case of the 5CB/CE2 mixture these changes were significant and quite systematic with temperature and wavelength. It is shown that the dispersion relation based on the single-band birefringence model described K well in isotropic liquid crystal phases at all of the measured concentrations. In an isotropic fluid, both temperature-dependent parameters in the dispersion relation had a simple linear form and, therefore, the K-surface could be described by only four constants. In the blue phase, the expression reproducing the temperature variation of K depended on concentration, which could vary from being almost linear to quasi-linear and could be represented well by an inverse exponential analytic expression. Full article

In real-life data, count data are considered more significant in different fields. In this article, a new form of the one-parameter discrete linear-exponential distribution is derived based on the survival function as a discretization technique. An extensive study of this distribution is conducted under its new form, including characteristic functions and statistical properties. It is shown that this distribution is appropriate for modeling over-dispersed count data. Moreover, its probability mass function is right-skewed with different shapes. The unknown model parameter is estimated using the maximum likelihood method, with more attention given to Bayesian estimation methods. The Bayesian estimator is computed based on three different loss functions: a square error loss function, a linear exponential loss function, and a generalized entropy loss function. The simulation study is implemented to examine the distribution’s behavior and compare the classical and Bayesian estimation methods, which indicated that the Bayesian method under the generalized entropy loss function with positive weight is the best for all sample sizes with the minimum mean squared errors. Finally, the discrete linear-exponential distribution proves its efficiency in fitting discrete physical and medical lifetime count data in real-life against other related distributions. Full article

The Maipo River estuary is a low-inflow bar-built estuary that includes a protected wetland, which harbors a rich ecosystem. The estuary and wetland have been threatened by a persistent drought for more than a decade, which has resulted in greater salinity intrusion and increased residence times. Previous studies have described salinity and pollutants in estuaries; however, almost all have focused on deeper and/or wider estuaries with dimensions much larger than those of the small-scale Maipo River estuary. In this study, we used the numerical model FVCOM to simulate the dynamics of the Maipo River estuary under drought scenarios and explored the interactions between river discharge and tides in terms of saline intrusion and particle dispersal. The model was validated against observations collected during a field campaign near the river mouth. The simulations successfully reproduced the water surface elevation but underestimated salinity values, such that the vertical salinity structure observed in the field was not captured by the model in this shallow and morphologically complex estuary. Consequently, our model results provide qualitative insight related to salinity and baroclinic dynamics. Results of maximum saline intrusion showed an exponential decay with increasing river discharge, and the analysis of salinity intrusion time series revealed that droughts may cause permanent non-zero salinity levels in the estuary, potentially affecting ecological cycles. The incorporation of passive tracers showed that decreasing river discharge increases the residence time of particles by allowing the tracers to re-enter the estuary. Model results showed the formation of accumulation zones (hotspots) in the shallower zones of the estuary. Full article