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Optical Soliton Dynamics in Nonlinear Evolution Equations: Modified Kawahara and Modified Benjamin Bona Mahony Models
Get PDFThis paper explores the dynamic behavior of optical soliton solutions for the modified Kawahara (mK) equation and the modified BenjaminBona-Mahony (mBBM) equation, two significant nonlinear evolution equations. Using an advanced analytical approach, a diverse set of soliton solutions is derived, including bell-shaped, anti-bell-shaped, W-shaped, M-shaped, and periodic waveforms. These solutions unveil the intricate nonlinear dynamics underlying the equations. The robustness of the method is demonstrated through comprehensive 2D, 3D, and contour visualizations, offering clear insights into the physical significance of the solitons. The study enhances the existing catalog of soliton solutions, contributing to a deeper understanding of nonlinear wave propagation and its potential applications in fields such as optical communication and fluid dynamics.OPEN ACCESS Received: 06/05/2025 Accepted: 09/06/2025 Published: 15/08/202
Reducing the number of input variables through symbolic regression
Get PDFSymbolic regression, a type of machine learning technique, can efficiently disregard variables that are not significant to the final output, even if they were initially preselected as inputs. Various input parameters are tested in the three examples presented here, where the outputs are modeled using symbolic regression: estimating the middle plasma torch temperature used for waste gasification, the active energy of a solar power plant, and the diameter of a pipe with a known flow and pressure drop through it. Final highly accurate formulas are produced after numerous attempts with lower performances. The process for rejecting the parameters without or with limited influence is automatic and can be performed without human intervention and supervision. The results obtained using symbolic regression are easily interpretable by human experts. This approach shows how to use machine learning-based modeling as an additional tool for sensitivity analysis
Statistical Analysis of Progressive Interval Type-I Partially Accelerated Test and Its Inspection of Optimum Periods
Get PDFThis study explores a general framework for reliability analysis named progressive interval Type-I censoring within a multi-stage step-stress partially accelerated life testing setting. A more flexible alternative to the traditional exponential model, known as the length-biased exponential (LBE) distribution, is employed to model failure times. Due to its symmetrical feature, it has extensive applications in real-world domains such as survival analysis, actuarial science, reliability, and mathematical finance. The maximum likelihood approach of estimation is utilized to estimate the model parameters, along with bootstrapping techniques to assess estimation efficiency. Confidence intervals for the LBE parameters are also derived based on asymptotic variances. To optimize the inspection period, two competing optimality criteria—variance minimization (Varoptimality) and determinant maximization (D-optimality)—are investigated. A comprehensive Monte Carlo simulation study is conducted to evaluate the performance of different estimation strategies, demonstrating the superiority of the proposed methodology. Steel is particularly valued for its toughness, wear resistance, and hardness, all of which can be significantly modified through heat treatment and annealing processes. So, a real-world application using hardened steel failure data validates the practical relevance of the developed inferential framework. The findings offer valuable insights for statisticians and reliability engineers in designing efficient life-testing experiments under constrained resources.OPEN ACCESS Received: 21/03/2025 Accepted: 07/05/2025 Published: 22/09/202
Numerical Simulation Analysis on the Stress and Strain Behavior of Composite Geomembrane in Rigid Landfill
Get PDFIn order to investigate the stress characteristics of a composite geomembrane during the operation of a rigid landfill, a three-dimensional finite element model was developed for a specific rigid landfill project in Tongling China. This model takes into account the contact behavior between the composite geomembrane and concrete unit pool. It aims to calculate and analyze the distribution of stress and strain in both the composite geomembrane and rigid landfill under various working conditions, including empty and full storage. At the same time, the influence of the change of friction coefficient between the composite geomembrane and the concrete cell pool on the stress and strain of the geomembrane is analyzed under the condition of full reservoir. The results indicate that the stress and displacement distribution of the composite geomembrane and concrete structures in the landfill site remain reasonable and safe before and after transitioning from empty to full storage. Under critical conditions, specifically when the cell pool is fully loaded, significant tensile stress and strain occur at the top anchorage of the pool, the edge of the pool bottom, and the corners of the cell pool. The tensile stress in the concrete structure is notably higher at the junction between the side walls and the bottom floor of the cell pool, while compressive stress is more pronounced at the connection between the frame columns of the lower maintenance layer and the bottom floor of the cell pool. Increasing the friction between the composite geomembrane and the concrete cell pool can effectively mitigate stress concentration in the composite geomembrane, thereby enhancing the structural stability and safety.OPEN ACCESS Received: 14/03/2025 Accepted: 21/05/2025 Published: 22/09/202
Recent advances in the particle finite element method for fluid-structure interactions and multi-physics problems
Get PDFParticle Finite Element Method (PFEM) is a still rather young discretization method that seeks to merge the advantages of the classical FEM with those of modern particle-based methods, such as SPH. To this end, PFEM is designed as a Lagrangian method that combines computations over one time step using FEM with a fast remeshing algorithm, thereby avoiding mesh distortions consequent to very large deformations, such as those encountered in fluid flow with free surfaces. The method is thus quite flexible and can be applied to both solid and fluid material behavior (see e.g. [1] as a sample of the state of the art). PFEM has proven to be a very versatile method that not only allows tracking free evolving boundaries but also take into account thermo-mechanical coupling and thus tackle more complex multi-physics problems. For instance, thanks to its Lagrangian character and its ability to automatically track evolving free surfaces and interfaces, PFEM allows handling phase change due to solidification, melting and vaporization, as well as capillary and Marangoni effects from surface tension [2]. These physical ingredients are highly valuable for simulating melt pool dynamics, for example, in the context of additive manufacturing. Multiphysics problems can lead to models that are inherently incompatible or highly difficult to combine within the same numerical implementation. In such a case, it is convenient to split the physical models and solve them separately using dedicated software. Although this approach has been used mostly to address fluid-structure interaction problems in PFEM, it has also been used to couple thermo-mechanical models, for example, in the simulation of welding processes. This work gathers recent advances in the PFEM with special attention to the incorporation of multi-physics models and their applications. In addition, numerical examples of the PFEM will illustrate fluid-structure interaction problems including contact between different solid parts and plastic deformation of some components of the system. These advances will be complemented by new remeshing proposals to further improve the PFEM strategy, which aim at reducing numerical artifacts and improving the continuity and smoothness of the free surface on which complex physical phenomena take place
Constitutive Laws as Generative Graphs and Trees
Get PDFThis talk explores the various ways high-fidelity constitutive laws for a wide range of solids, such as soil, rock, alloys, and polymer composites, can be represented and how the choice of representations influences the accuracy, robustness, and data/computational efficiency for computer simulations of solids. To represent material models as points, we adopt a model-free approach that enables physical simulations of material behaviors without a smooth constitutive law. In this case, pointwise stress-strain pairs are selected in Gauss points of finite elements to be compatible with the conservation laws. To represent material models as meshes, we introduce a latent diffusion model where previous material models and experimental data are used to guide the reverse generation of models. This mesh-based material model is particularly efficient for non-smooth plasticity, where projection on segments can lead to significantly faster simulations. To represent material models as expression trees, we use the neural additive model in the projected space of strain measures. This technique enables us to search for hyperelasticity in high-dimensional space without sacrificing the expressivity of neural networks. We show that the proposed model may reproduce any polynomial of arbitrary orders and dimensions and thus achieve the universal approximation through the StoneWeierstrass theorem. Through a series of 1D post-hoc symbolic regressions, we obtain symbolic material models that significantly reduce the inference time for hydrocodes [1]. The pros and cons of these techniques for various practical applications will be discussed. 
Wave Behavior caused by Ladle Pouring and Plunger Advancing in Aluminum Alloy Die Casting using Particle-Based SPH Method
Get PDFCasting CAE software determines the operating conditions of ladle pouring and plunger advancing and prevents defects in aluminum alloy die casting. Quick operations of the ladle pouring and plunger advancing lead to disturbance of the molten metal flow and increase the risk of air entrapment. Conversely, if these operations are performed slowly, the temperature of the molten metal drops, and the risk of cold flake formation increases. Furthermore, since an oxide film exists on the surface of molten aluminum alloy and flows differently from water, it is necessary to perform simulations considering the oxide film. In conventional casting CAE simulation, the flow behavior by the plunger advancing is often simulated from a state in which the molten metal is stationary in the sleeve. In this study, we numerically analyze wave behavior caused by ladle pouring and plunger advancing processes. One is the superimposed ones of wave behavior when ladle pouring and plunger advance processes are simulated separately. The other is the wave behavior when simulated as a series of processes. The casting analysis software “COLMINA CAE” by the particle-based SPH method, which is considered the oxide film of molten aluminum alloy, is used to analyze the wave behaviors. Further, they have verified the wave behavior through visualization experiments. Comparing the simulated wave height and velocity, which shows the wave motion generated when the plunger advances from the stationary state of the molten metal in the sleeve is different from the wave motion in a series of processes, suggesting the need for simulation of a series of processes. These trends of wave behavior obtained in the simulation are similar to that of the actual phenomenon. Therefore, the present simulatio
Investigations regarding the influence of particle shape on the numerical simulation of air pluviation using the dem method
Get PDFAir pluviation or sand raining is a method in geotechnics to create homogenous sand samples [1]. To investigate the behavior of the sand particles during pluviation, DEM (discrete element method) can be used due to its ability to realistically model particle interactions [2] with other sand particles or the pluviation equipment. These interactions are in turn influenced by the material as well as interaction properties and particle scaling. However, particle shape also influences the behavior such that realistically considering real-world particles’ shapes may improve modelling of the pluviation process.
To investigate the influence of particle shape on the simulation of air pluviation, three different numerical representations for sand particles will be used: (I) homogenous sand with spherical particles, (II) homogenous sand with uniform non-spherical particle shape, representing the average particle shape, and (III) heterogenous sand with varying particle shapes. The non-spherical particles are created using bonded spheres. For investigation of the pluviation process four partial processes were identified which are most likely to be influenced by particle shape: (I) the outflow out of the sieve, which regulates deposition intensity, (II) interactions with the diffusor sieves, which distribute the sand homogeneously over the sample surface, (III) free falling and the resulting particle interactions as well as (IV) the resulting sample density. For these processes, the impact of particle shape will be determined, including resulting particle velocities, angular velocities as well as the reached sample density. The results will, were applicable, be compared to results of physical experiments for further evaluation and validation
Causal vs Retrocausal Attention Boundaries
Get PDFThis study quantifies the minimal right context that changes model decisions about authority bearing constructions under strict causal masking versus non causal access. We formalize flip probability P_flip(b to b+Δ), the instance level threshold τ(x), and the construction level threshold τ_C, and we measure breakpoint sharpness over a right context ladder b in {0, 1, 2, 4, 8, 16, 32}. The dataset contains minimal pair ladders per construction family, deontic stacks, nominalizations, enumerations, defaults, agent deletion, scope setting adverbs, role addressatives, across six languages, en, es, pt BR, fr, de, hi, with balanced length, domain, and register, and human gold labels. We evaluate frozen causal decoder models, non causal encoders and encoder decoders, and causal streaming variants with sliding windows. Masking primitives include hard truncation, stochastic truncation, and delayed reveal streaming with cache isolation and sentinel based leakage tests. Primary endpoints are τ_C by construction and language, P_flip curves, AUC_flip, and a latency accuracy frontier. Results map τ_C to observed compliance deltas on instructed tasks while holding administrative workflow constant. The contributions are a public dataset with right context ladders, an evaluation harness with tested masks, per construction τ atlases and P_flip plots, and a preregistered analysis that links regla compilada constraints, Type 0 production equivalence, to measurable authority judgments. Acknowledgment / Editorial Note This article is published with editorial permission from LeFortune Academic Imprint, under whose license the text will also appear as part of the upcoming book AI Syntactic Power and Legitimacy. The present version is an autonomous preprint, structurally complete and formally self-contained. No substantive modifications are expected between this edition and the print edition. LeFortune holds non-exclusive editorial rights for collective publication within the Grammars of Power series. Open access deposit on SSRN is authorized under that framework, if citation integrity and canonical links to related works (SSRN: 10.2139/ssrn.4841065, 10.2139/ssrn.4862741, 10.2139/ssrn.4877266) are maintained