Search Results (26)

This paper investigates strain-, twist-, and electric-field-tuned optical absorption in bilayer MoS₂, emphasizing spin-orbit coupling (SOC). A continuum model reveals competing mechanisms: geometric perturbations (strain/twist) and Stark effects govern one-/two-photon absorption, with critical thresholds (~9% strain, ~2.13° twist) switching spin-independent to spin-polarized regimes. Strain gradients and twist enhance nonlinear responses through symmetry-breaking effects while electric fields dynamically modulate absorption via band alignment tuning. By linking parameter configurations to absorption characteristics, this work provides a framework for designing tunable spin-resolved optoelectronic devices and advancing light–matter control in 2D materials. Full article

Geometric properties of fractures, such as aperture and width, among others, significantly affect the fluid flow behaviors in fractured media. Previous studies have shown that fractures exhibit fractal properties. In this study, we examine the impact of nonlinear flow regimes and aperture and width fractal distributions on the flow behavior through fractal fractures. Both the aperture and width are treated independently following fractal distribution, but with distinct fractal dimensions. We explicitly examine the flow features without using Darcy’s law concept, which relies on the linear flow assumption with an effective permeability of fractal fractures. We directly consider the flow rate in a fracture with average aperture, average flow rate, and flow rate of linear flow in all the fractures, and nonlinear flow rate in all the fractures, and more realistically, the average flow rate when linear and nonlinear flows may coexist in different fractures and their differences. The results demonstrate that the nonlinear flow regime significantly reduces the flow rate through the fractal fractures, which could be quantified by the ratio of critical aperture to the minimum aperture in the fractal fractures. A large ratio of the maximum over the minimum apertures results in a large average flow rate in the fractal fractures. The increase in the minimum aperture also enhances the average flow rate. When the minimum aperture is close to the critical aperture, however, the flow rate in the fractal fractures starts to turn into nonlinear flow in all the fractures, and the average flow rate decreases. The nonlinear effect is amplified in fractal fractures compared to that in a single fracture. A larger fractal dimension of aperture leads to a lower average flow rate in the fractal fractures, as the average aperture decreases with the fractal dimension. However, the fraction of flow rate from the linear flow portion in the fractal fractures over the pure linear flow in all the fractures increases with the fractal dimension. Full article

The detection of limit cycles of differential equations poses a challenge due to the type of the nonlinear system, the regime of interest, and the broader context of applicable models. Consequently, attempts to solve Hilbert’s sixteenth problem on the maximum number of limit cycles of polynomial differential equations have been uniformly unsuccessful due to failing results and their lack of consistency. Here, the answer to this problem is finally obtained through information geometry, in which the Riemannian metrical structure of the parameter space of differential equations is investigated with the aid of the Fisher information metric and its scalar curvature R. We find that the total number of divergences of $\left|\mathrm{R}\right|$ to infinity provides the maximum number of limit cycles of differential equations. Additionally, we demonstrate that real polynomial systems of degree $n\ge 2$ have the maximum number of $2(n-1)\left(4\right(n-1)-2)$ limit cycles. The research findings highlight the effectiveness of geometric methods in analyzing complex systems and offer valuable insights across information theory, applied mathematics, and nonlinear dynamics. These insights may pave the way for advancements in differential equations, presenting exciting opportunities for future developments. Full article

The linkage between the salt wedge, tidal patterns, and the Magdalena River discharge is established by assessing the ensuing parameters: stratification (ϵ), buoyancy frequency (β), potential energy anomaly (φ), Richardson number by layers (RL), and bottom turbulent energy production (P). The salinity, temperature, density, and water velocity data utilized were derived from MOHID 3D, a previously tailored and validated model for the Magdalena River estuary. To grasp the dynamics of the river, a flow regime analysis was conducted during both the wet and dry climatic seasons of the Colombian Caribbean. The utilization of this model aimed to delineate the estuary’s spatial reach, considering flow rates spanning from 2000 to 6500 m³/s across two tidal cycles. This approach facilitates the prediction of the position, stability, and stratification degree of the salt front. Among the conclusions drawn, it is highlighted that: 1. The river flow serves as the principal conditioning agent for the system, inducing a strong estuary response to weather stations; 2. The extent of wedge intrusion and the river discharge exhibit a non-linear, inversely correlation; 3. Tidal waves cause differences of up to 1000 m in the horizontal extent of the wedge; 4. Widespread channel erosion occurs during the rainy season when the salt intrusion does not exceed 2 km; 5. Flocculation processes intensify during the transition between the dry and wet seasons; 6. The stability of the salt layering and the consolidation of the FSI–TMZ are contingent upon the geometric attributes of the channel. Full article

Unreinforced masonry (URM) walls are common load-bearing structural elements in most existing buildings, consisting of masonry units (bricks) and mortar joints. They indicate a highly nonlinear and complex behaviour when subjected to combined compression–shear loading influenced by different factors, such as pre-compression load and boundary conditions, among many others, which makes predicting their structural response challenging. To this end, the present study offers a discontinuum-based modelling strategy based on the discrete element method (DEM) to investigate the in-plane cyclic response of URM panels under different vertical pressures with and without a damp-proof course (DPC) membrane. The adopted modelling strategy represents URM walls as a group of discrete rigid block systems interacting along their boundaries through the contact points. A novel contact constitutive model addressing the elasto-softening stress–displacement behaviour of unit–mortar interfaces and the associated stiffness degradation in tension–compression regimes is adopted within the implemented discontinuum-based modelling framework. The proposed modelling strategy is validated by comparing a recent experimental campaign where the essential data regarding geometrical features, material properties and loading histories are obtained. The results show that while the proposed computational modelling strategy can accurately capture the hysteric response of URM walls without a DPC membrane, it may underestimate the load-carrying capacity of URM walls with a DPC membrane. Full article

Understanding the fluid pattern is of special significance for estimating the hydraulic conductivity of fractured rock masses. The nonlinearity of fluid flow in discrete fracture networks (DFNs) originates from inertial effects and is enhanced by complex geometric topologies, which produces additional viscous friction and is subject to inertia effects, consequently transitioning the fluid to the nonlinear flow regime. Therefore, it is important to obtain the critical conditions for the transition of a fluid from laminar to turbulent flow. To investigate the role of fracture aperture and fracture intersection on the onset of the transition of a fluid to nonlinear flow in fractured rocks, the fluid dynamic computation was performed by solving Navier–Stokes (N–S) equations in DFN models. The results show that the flow flux initially linearly correlates with the hydraulic gradient ($J$) and the permeability of DFNs initially remains constant. As the hydraulic gradient increases, the flow flux presents a strong nonlinear relationship with the hydraulic gradient, and the permeability decreases dramatically. In particular, significant inertial effects appear earlier with a large fracture aperture or a dense fracture intersection. A critical hydraulic gradient ($J_c$) is proposed to judge the onset of nonlinear flow. The mathematical expression of $J_c$ and Forchheimer coefficients A and B involving the fracture aperture and fracture intersection density is established through a multiple regression algorithm. Finally, the reliability of the predictive model was verified by comparing the results of the prediction and fluid dynamic computation of a series of DFN models with well-known geometric distributions. The consistency of the fitted equations and a correlation coefficient greater than 0.9 between them indicate that the predictive model proposed in this study is reliable. Full article

The purpose of this paper is to develop a constitutive description and to numerically simulate a propagating instability phenomenon called the Portevin–Le Chatelier (PLC) effect, which is observed for metallic materials. It manifests itself by moving plastic shear bands in the sample and serrations in the stress–strain diagram. In this paper, the PLC is modeled by geometrically non-linear thermo-visco-plasticity with the hardening function of the Estrin–McCormick type to reproduce a serrated response. To regularize softening, which in this model comes from thermal, geometrical and strain-rate effects, the viscosity and heat conductivity are incorporated. Plasticity description can additionally include degradation of the yield strength, and then the model is enhanced by higher-order gradients. Simulations are performed using AceGen/FEM. Two tensioned specimens are tested: a rod and a dog-bone sample. The first specimen is used for general verification. The results obtained for the second specimen are compared with the experimental results. Studies for different values of model parameters are performed. The results of the simulations are in good agreement with the experimental outcome and the sensitivity to model parameters is in line with the expectations for the pre-peak regime. In the presented tests, the gradient enhancement does not significantly influence the results. Full article

Enhanced approximate expressions for the incipient indicial lift of thin wings in subsonic potential flow are presented in this study, featuring explicit analytical corrections for the unsteady downwash. Lifting-line and acoustic-wave theories form the basis of the method, within an effective synthesis of the governing physics, which grants a consistent generalised framework and unifies previous works. The unsteady flow perturbation consists of a step-change in angle of attack or a vertical sharp-edged gust. The proposed model is successfully evaluated against numerical results in the literature for the initial airload development of elliptical and rectangular wings with a symmetric aerofoil, considering several aspect ratios and Mach numbers. While nonlinear downwash and compressibility terms demonstrate marginal (especially for the case of a travelling gust), both linear and nonlinear geometrical effects from a significant taper ratio, sweep angle or curved leading-edge are found to be more important than linear downwash corrections (which are crucial for the circulation growth at later times instead, along with linear compressibility corrections). The present formulae may then be used as a rigorous reduced-order model for validating higher-fidelity tools and complex simulations in industrial practice, as well as for estimating parametric sensitivities of unsteady aerodynamic loads within the preliminary design of aircraft wings in the subsonic regime. Full article

The construction of a transmission line (TL) for a wide tunable broad-spectrum THz radiation source is not a simple task. We present here a platform for the future use of designs of the TL through our homemade simulations. The TL is designed to be a component of the construction of an innovative accelerator at the Schlesinger Family Center for Compact Accelerators, Radiation Sources and Applications (FEL). We developed a three-dimensional space-frequency tool for the analysis of a radiation pulse. The total electromagnetic (EM) field on the edge of the source is represented in the frequency domain in terms of cavity eigenmodes. However, any pulse can be used regardless of its mathematical function, which is the key point of this work. The only requirement is the existence of the original pulse. This EM field is converted to geometric-optical ray representation through the Wigner transform at any desired resolution. Wigner’s representation allows us to describe the dynamics of field evolution in future propagation, which allows us to determine an initial design of the TL. Representation of the EM field by rays gives access to the ray tracing method and future processing, operating in the linear and non-linear regimes. This allows for fast work with graphics cards and parallel processing, providing great flexibility and serving as future preparation that enables us to apply advanced libraries such as machine learning. The platform is used to study the phase-amplitude and spectral characteristics of multimode radiation generation in a free-electron laser (FEL) operating in various operational parameters. Full article

In this study, the geometrically nonlinear behaviour caused by large displacements and rotations in the cross sections of thin-walled composite beams subjected to axial loading is investigated. Newton–Raphson scheme and an arc length method are used in the solution of nonlinear equations by finite element method to determine the mechanical effect. The Carrera-Unified formulation (CUF) is used to solve nonlinear, low or high order kinematic refined structure theories for finite beam elements. In the study, displacement area and stress distributions of composite structures with different angles and functionally graded (FG) structures are presented for Lagrange polynomial expansions. The results show the accuracy and computational efficiency of the method used and give confidence for new research. Full article

We report the results of the characterization of local Monte Carlo (MC) dynamics of an equilibrium bond fluctuation model polymer matrix (BFM), in time interval typical for MC simulations of non-linear optical phenomena in host-guest systems. The study contributes to the physical picture of the dynamical aspects of quasi-binary mosaic states characterized previously in the static regime. The polymer dynamics was studied at three temperatures (below, above and close to the glass transition), using time-dependent generalization of the static parameters which characterize local free volume and local mobility of the matrix. Those parameters play the central role in the kinetic MC model of host-guest systems. The analysis was done in terms of the probability distributions of instantaneous and time-averaged local parameters. The main result is the characterization of time scales characteristic of various local structural processes. Slowing down effects close to the glass transition are clearly marked. The approach yields an elegant geometric criterion for the glass transition temperature. A simplified quantitative physical picture of the dynamics of guest molecules dispersed in BFM matrix at low temperatures offers a starting point for stochastic modeling of host-guest systems. Full article

Starting from a contact Hamiltonian description of Liénard systems, we introduce a new family of explicit geometric integrators for these nonlinear dynamical systems. Focusing on the paradigmatic example of the van der Pol oscillator, we demonstrate that these integrators are particularly stable and preserve the qualitative features of the dynamics, even for relatively large values of the time step and in the stiff regime. Full article

The aim of this paper is to present experimental data and the constitutive model for the inelastic behavior of polyoxymethylene in wide strain rate and temperature ranges. To capture the non-linearity of the stress responses for both loading and unloading regimes, the composite model of inelastic deformation is utilized and further developed. The equivalent inelastic strain rate is described by the Prandtl–Eyring law, while the temperature dependence is characterized by the modified Arrhenius-type law. Generalized equivalent stress and the flow rule are formulated to capture pressure sensitivity, transverse strain and volumetric strain responses. The results obtained by the constitutive law are compared with experimental data for stress vs. axial strain from standard tension tests as well as with axial and transverse strains measured by digital image correlation. The developed composite model is able to capture the non-linearity of stress–strain curves for complex loading paths within the small strain regime. For higher strains, apart from geometrically non-linear theory, evolution laws for the volume fraction of the constituents should be modified and calibrated. For the small strain regime, the inelastic dilatation is negligible. For higher axial strain values, a decrease in Poisson’s ratio under tension and increase in it under compression are observed. The Drucker–Prager-type equivalent stress and the developed flow rule provide a better description of both the transverse and volumetric strains than that of the classical von Mises–Odqvist flow rules. Full article

The macroscopic mechanical behavior of open-porous cellular materials is dictated by the geometric and material properties of their microscopic cell walls. The overall compressive response of such materials is divided into three regimes, namely, the linear elastic, plateau and densification. In this paper, a constitutive model is presented, which captures not only the linear elastic regime and the subsequent pore-collapse, but is also shown to be capable of capturing the hardening upon the densification of the network. Here, the network is considered to be made up of idealized square-shaped cells, whose cell walls undergo bending and buckling under compression. Depending on the choice of damage criterion, viz. elastic buckling or irreversible bending, the cell walls collapse. These collapsed cells are then assumed to behave as nonlinear springs, acting as a foundation to the elastic network of active open cells. To this end, the network is decomposed into an active network and a collapsed one. The compressive strain at the onset of densification is then shown to be quantified by the point of intersection of the two network stress-strain curves. A parameter sensitivity analysis is presented to demonstrate the range of different material characteristics that the model is capable of capturing. The proposed constitutive model is further validated against two different types of nanoporous materials and shows good agreement. Full article

This work investigates the possibility of applying Fourier Transform (FT) analysis of the force signal to follow fatigue behavior of metals under oscillatory displacement-controlled tests in uniaxial tension/tension. As a first step, three different materials were selected (cold rolled steel, aluminium and brass). The FT analysis revealed a low level of nonlinearities in the force response, which was possible to measure and quantify as higher harmonics of the imposed sinusoidal deformation. Due to geometric reasons, the odd higher harmonics represent the symmetric nonlinearity while even ones are related to asymmetry, so both odd and even harmonics need to be analyzed separately. The time evolution of the higher harmonics showed that the odd higher harmonics continuously increase during the test. Criteria to better predict the mechanical fatigue and failure (life time) are then proposed based on the integral and derivative based on the time evolution the odd higher harmonics. In contrast, for tests in the high cycle fatigue regime, the even higher harmonics are mainly noise at the beginning of the test (undamaged state), but start to rise after the occurrence of a crack due to internal crack friction. Based on the analysis performed, FT analysis of the force during mechanical fatigue testing of metals is a sensitive tool used to predict failure and to improve our understanding of the dynamics involved in mechanical fatigue. Full article