Search Results (868)

In this paper, we study direct and inverse problems for a spatial-fractional Black–Scholes equation with space-dependent volatility. For the direct problem, we provide CN-WSGD (Crank–Nicholson and the weighted and shifted Grünwald difference) scheme to solve the initial boundary value problem. The latter aims to recover the implied volatility via observable option prices. Using a linearization technique, we rigorously derive a mathematical formulation of the inverse problem in terms of a Fredholm integral equation of the first kind. Based on an integral equation, an efficient numerical reconstruction algorithm is proposed to recover the coefficient. Numerical results for both problems are provided to illustrate the validity and effectiveness of proposed methods. Full article

Cold-formed steel (CFS) channel beams are increasingly used as primary structural elements in modern construction due to their lightweight and high-strength characteristics. To accommodate building services, these members often feature perforations—typically circular and unstiffened—produced by punching. Recent studies indicate that adding edge stiffeners, particularly around circular web openings, can improve flexural strength. Extending this idea, attention has shifted to hexagonal web perforations; however, limited research exists on the bending performance of hexagonal cold-formed steel channel beams (HCFSBs). This study presents a detailed nonlinear finite element (FE) analysis to evaluate and compare the flexural behaviour of HCFSBs with unstiffened (HUH) and edge-stiffened (HEH) hexagonal openings. The FE models were validated against experimental results and expanded to include a comprehensive parametric study with 810 simulations. Results show that HEH beams achieve, on average, a 10% increase in moment capacity compared to HUH beams. However, when evaluated using current Direct Strength Method (DSM) provisions, moment capacities were underestimated by up to 47%, particularly in cases governed by lateral–torsional or distortional buckling. A reliability analysis confirmed that the proposed design equations yield accurate and dependable strength predictions. Full article

In order to explore the essence of the anticoccidiosis of anticoccidial drugs under bioelectric currents, the intermolecular double-proton transfer and conformational transformation of 4-pyridone-3-carboxylic acid were investigated by quantum chemistry calculations (at the M06-2X/6-311++G**, M06-2X/aug-cc-pVTZ and CCSD(T)/aug-cc-pVTZ levels) and finite temperature string (FTS) under external electric fields. The solvent effect of H₂O on the double-proton transfer was evaluated by the integral equation formalism polarized continuum model. The results indicate that the influences of the external electric fields along the direction of the dipole moment on double-proton transfer are significant. The corresponding products are controlled by the direction of the external electric field. Due to the first-order Stark effect, some good linear relationships form between the changes of the structures, atoms in molecules (AIMs) results, surface electrostatic potentials, barriers of the transition state, and the external electric field strengths. From the gas to solvent phase, the barrier heights increased. The spatial order parameters (ϕ, ψ) of the conformational transformation could be quickly converged through the umbrella sampling and parameter averaging, and thus the free-energy landscape for the conformational transformation was obtained. Under the external electric field, there is competition between the double-proton transfer and conformational transformation. The external electric field greatly affects the cooperativity transfer, while it has little effect on the conformational transformation. This study is helpful in the selection and updating of anticoccidial drugs. Full article

The model explicitly incorporates boundary conditions that account for the complex interplay between sections experiencing varying degrees of reduction. This interaction significantly influences the overall deformation behavior and force loading. The control effect is associated with boundary conditions determined by the unevenness of the compression, which have certain quantitative and qualitative characteristics. These include additional loading, which is less than the main load, which implements the process of plastic deformation, and the ratio of control loads from the entrance and exit of the deformation site. According to this criterion, it follows from experimental data that the controlling effect on the plastic deformation site occurs with a ratio of additional and main loading in the range of 0.2–0.8. The next criterion is the coefficient of support, which determines the area of asymmetry of the force load and is in the range of 2.00–4.155. Furthermore, the criterion of the regulating force ratio at the boundaries of the deformation center forming a longitudinal plastic shear is within the limits of 2.2–2.5 forces and 1.3–1.4 moments of these forces. In this state, stresses and deformations of the plastic medium are able to realize the effects of plastic shaping. The force effect reduces with an increase in the unevenness of the deformation. This is due to a change in height of the longitudinal interaction of the disparate sections of the strip. There is an appearance of a new quality of loading—longitudinal plastic shear along the deformation site. The unbalanced additional force action at the entrance of the deformation source is balanced by the force source of deformation, determined by the appearance of a functional shift in the model of the stress state of the metal. The developed theory, using the generalized method of an argument of functions of a complex variable, allows us to characterize the functional shift in the deformation site using invariant Cauchy–Riemann relations and Laplace differential equations. Furthermore, the model allows for the investigation of material properties such as the yield strength and strain hardening, influencing the size and characteristics of the identified limit state zone. Future research will focus on extending the model to incorporate more complex material behaviors, including viscoelastic effects, and to account for dynamic loading conditions, more accurately reflecting real-world milling processes. The detailed understanding gained from this model offers significant potential for optimizing mill roll designs and processes for enhanced efficiency and reduced energy consumption. Full article

The chiral nonlinear Schrödinger equation (CNLSE) serves as a simplified model for characterizing edge states in the fractional quantum Hall effect. In this paper, we leverage the generalization and parameter inversion capabilities of physics-informed neural networks (PINNs) to investigate both forward and inverse problems of 1D and 2D CNLSEs. Specifically, a hybrid optimization strategy incorporating exponential learning rate decay is proposed to reconstruct data-driven solutions, including bright soliton for the 1D case and bright, dark soliton as well as periodic solutions for the 2D case. Moreover, we conduct a comprehensive discussion on varying parameter configurations derived from the equations and their corresponding solutions to evaluate the adaptability of the PINNs framework. The effects of residual points, network architectures, and weight settings are additionally examined. For the inverse problems, the coefficients of 1D and 2D CNLSEs are successfully identified using soliton solution data, and several factors that can impact the robustness of the proposed model, such as noise interference, time range, and observation moment are explored as well. Numerical experiments highlight the remarkable efficacy of PINNs in solution reconstruction and coefficient identification while revealing that observational noise exerts a more pronounced influence on accuracy compared to boundary perturbations. Our research offers new insights into simulating dynamics and discovering parameters of nonlinear chiral systems with deep learning. Full article

This article discusses the transformation of a continuous-time model of the fractional system into a discrete-time model of the fractional system. For the continuous-time model, the exact solution of the nonlinear equation with fractional derivatives (FDs) that has the form of the damped rotator type with power non-locality in time is obtained.This equation with two FDs and periodic kicks is solved in the general case for the arbitrary orders of FDs without any approximations. A three-stage method for solving a nonlinear equation with two FDs and deriving discrete maps with memory (DMMs) is proposed. The exact solutions of the nonlinear equation with two FDs are obtained for arbitrary values of the orders of these derivatives. In this article, the orders of two FDs are not related to each other, unlike in previous works. The exact solution of nonlinear equation with two FDs of different orders and periodic kicks are proposed. Using this exact solution, we derive DMMs that describe a kicked damped rotator with power-law non-localities in time. For the discrete-time model, these damped DMMs are described by the exact solution of nonlinear equations with FDs at discrete time points as the functions of all past discrete moments of time. An example of the application, the exact solution and DMMs are proposed for the economic growth model with two-parameter power-law memory and price kicks. It should be emphasized that the manuscript proposes exact analytical solutions to nonlinear equations with FDs, which are derived without any approximations. Therefore, it does not require any numerical proofs, justifications, or numerical validation. The proposed method gives exact analytical solutions, where approximations are not used at all. Full article

This paper addresses the problem of optimal stabilization for stochastic dynamical systems characterized by Markov switches and concentration points of jumps, which is a scenario not adequately covered by classical stability conditions. Unlike traditional approaches requiring a strictly positive minimal interval between jumps, we allow jump moments to accumulate at a finite point. Utilizing Lyapunov function methods, we derive sufficient conditions for exponential stability in the mean square and asymptotic stability in probability. We provide explicit constructions of Lyapunov functions adapted to scenarios with jump concentration points and develop conditions under which these functions ensure system stability. For linear stochastic differential equations, the stabilization problem is further simplified to solving a system of Riccati-type matrix equations. This work provides essential theoretical foundations and practical methodologies for stabilizing complex stochastic systems that feature concentration points, expanding the applicability of optimal control theory. Full article

The ultimate goal of research on seismic mitigation technologies is engineering application. However, current studies primarily focus on the application of dampers in planar structures, while actual engineering structures are three-dimensional (3D) in nature. A type of damper, making up tuned mass dampers (TMDs) and inerters, has excellent vibration mitigation performance and needs brackets to connect to structures. In this work, a coupled dynamic model of an energy dissipation system (EDS) comprising a TMD, an inerter, a bracket, and a 3D building structure is presented, along with analytical solutions for stochastic seismic responses. The main work is as follows. Firstly, based on D’Alembert’s dynamics principle, the seismic dynamic equations of an EDS considering a realistic damper and a 3D structure are formulated. The general dynamic equations governing the bidirectional horizontal motion of the EDS are further derived using the dynamic finite element technique. Secondly, analytical expressions for spectral moments and variances of seismic responses are obtained. Finally, four numerical examples are presented to investigate the following: (1) verification of the proposed response solutions, showing that the calculation time of the proposed method is approximately 1/500 of that of the traditional method; (2) examination of spatial effects in 3D structures under unidirectional excitation, revealing that structural seismic responses in the direction along the earthquake ground motion is approximately 10⁴ times that in the direction perpendicular to the ground motion; (3) investigation of the spatial dynamic characteristics of a 3D structure subjected to unidirectional seismic excitation, showing that the bracket parameters significantly affect the damping effects on an EDS; and (4) application of the optimization method for the damper’s parameters that considers system dynamic reliability and different weights of the damper’s parameters as constraints, indicating that the most economical damping parameters can achieve a reduction in displacement spectral moments by 30–50%. The proposed response solutions and parameter optimization technique provide an effective approach for evaluating stochastic seismic responses and optimizing damper parameters in large-scale and complex structures. Full article

This paper primarily investigates the response and failure behavior of 6063-T5 aluminum alloy square tubes with varying outer side lengths under symmetric curvature-controlled cyclic bending in different bending directions. The response is characterized by the moment–curvature relationship and the variation in the outer side length with respect to curvature, whereas failure is characterized by the relationship between the controlled curvature and the number of cycles required to initiate buckling. The outer side lengths studied are 20 mm, 30 mm, 40 mm, and 50 mm, and the bending directions considered are 0°, 22.5°, and 45°. The moment–curvature curves exhibited cyclic hardening, and stable loops were formed for all outer side lengths and bending directions. An increase in the outer side length resulted in a higher peak bending moment, while a greater bending direction led to a slight increase in the peak bending moment. For a fixed bending direction, the curves representing the variation of the outer side length (defined as the change in length divided by the original length) with respect to curvature displayed symmetry, serrated features, and an overall increasing trend as the number of cycles increased, irrespective of the specific outer side length. In addition, increasing either the outer side length or altering the bending direction led to a larger variation in the outer side length. As for the relationship between curvature and the number of cycles required to initiate buckling, the data for each bending direction and each of the four outer side lengths formed distinct straight lines on a double-logarithmic plot. Based on the experimental observations, empirical equations were developed to characterize these relationships. These equations were then used to predict the experimental data and showed excellent agreement with the measured results. Full article

This work systematically addresses the dual challenges of non-inertial dynamic coupling and kinematic constraint redundancy encountered in dynamic modeling of serial–parallel–serial hybrid robotic mechanisms, and proposes an improved Newton–Euler modeling method with constraint compensation. Taking the Skiing Simulation Platform with 6-DOF as the research mechanism, the inverse kinematic model of the closed-chain mechanism is established through $G_F$ set theory, with explicit analytical expressions derived for the motion parameters of limb mass centers. Introducing a principal inertial coordinate system into the dynamics equations, a recursive algorithm incorporating force/moment coupling terms is developed. Numerical simulations reveal a 9.25% periodic deviation in joint moments using conventional methods. Through analysis of the mechanism’s intrinsic properties, it is identified that the lack of angular momentum conservation constraints on the end-effector in non-inertial frames leads to system controllability degradation. Accordingly, a constraint compensation strategy is proposed: establishing linearly independent differential algebraic equations supplemented with momentum/angular momentum balance equations for the end platform. Co-Simulation results demonstrate that the optimized model reduces the maximum relative error of actuator joint moments to 0.98%, and maintains numerical stability across the entire configuration space. The constraint compensation framework provides a universal solution for dynamics modeling of complex closed-chain mechanisms, validated through applications in flight simulators and automotive driving simulators. Full article

This paper outlines a structural qualification process to assess the use of newly developed high-modulus (HM) glass fiber-reinforced polymer (GFRP) bars with headed ends in the joint between concrete bridge barriers and decks. The main goals of the study are to evaluate the structural performance of GFRP-reinforced TL-5 barrier–deck systems under transverse loading and to determine the pullout capacity of GFRP anchorage systems for both new construction and retrofit applications. The research is divided into two phases. In the first phase, six full-scale Test-Level 5 (TL-5) barrier wall–deck specimens, divided into three systems, were constructed and tested up to failure. The first system used headed-end GFRP bars to connect the barrier wall to a non-deformable thick deck slab. The second system was similar to the first but had a deck slab overhang for improved anchorage. The third system utilized postinstalled GFRP bars in a non-deformable thick deck slab, bonded with a commercial epoxy adhesive as a solution for deteriorated barrier replacement. The second phase involves an experimental program to evaluate the pullout strength of the GFRP bar anchorage in normal-strength concrete. The experimental results from the tested specimens were then compared to the factored applied moments in existing literature based on traffic loads in the Canadian Highway Bridge Design Code. Experimental results confirmed that GFRP-reinforced TL-5 barrier–deck systems exceeded factored design moments, with capacity-to-demand ratios above 1.38 (above 1.17 with the inclusion of an environmental reduction factor of 0.85). A 195 mm embedment length proved sufficient for both pre- and postinstalled bars. Headed-end GFRP bars improved pullout strength compared to straight-end bars, especially when bonded. Failure modes occurred at high loads, demonstrating structural integrity. Postinstalled bars bonded with epoxy performed comparably to preinstalled bars. A design equation for the barrier resistance due to a diagonal concrete crack at the barrier–deck corner was developed and validated using experimental findings. This equation offers a conservative and safe design approach for evaluating barrier–deck anchorage. Full article

Balancing mechanisms require the minimization of both the Shaking Moment ($ShM$) and Shaking Force ($\mathbf{ShF}$), a complex multi-criteria challenge often tackled using single-objective algorithms. However, these methods face difficulties in navigating competing objectives. In contrast, multi-objective algorithms provide a more efficient and adaptable framework, while Fully Cartesian Coordinates ($FCC$) simplify the balancing equations compared to conventional Cartesian formulations. This study focuses on optimizing the dynamic balance of a six-bar Watt linkage using $FCC$. A wide set of optimization methods is analyzed and compared, and among them, the S-Metric Selection Evolutionary Multi-objective Optimization Algorithm (SMS-EMOA) demonstrates superior performance. This algorithm achieves the most significant hypervolume value in only 10.44 min of execution. The results indicate that multi-objective algorithms outperform single-objective approaches, offering faster and more diverse optimization solutions. Additionally, this study introduces an analytical method that enables the straightforward identification of removable counterweights, achieving an equally effective balance while minimizing the number of counterweights required. Full article

This study reports the synthesis and characterization of Co_xNi_1−xFe₂O₄ (x = 0, 0.2, 0.4, 0.6, 0.8, 1) nanoparticles using a co-precipitation method. In this approach, metal ions are precipitated in the presence of a stabilizing agent, which is a common and effective method for nanoparticle preparation. The microstructure and magnetic properties were studied after calcination at 600 °C and heat treatment at 1000 °C. X-ray diffraction (XRD) and Fourier transform infrared (FTIR) spectroscopy confirmed the formation of a single-phase spinel structure. The average crystallite size, calculated using the (311) diffraction peak and the Scherrer equation, ranged from 13 to 19 nm. Scanning electron microscopy (SEM) showed that the nanoparticles had a spherical morphology. Thermogravimetric and differential thermal analysis (TG-DTA) revealed a three-step weight loss process. Magnetic measurements, including remanent magnetization, saturation magnetization, and coercivity, were performed using a vibrating sample magnetometer (VSM) at room temperature. The replacement of Ni²⁺ with Co²⁺ enhanced the magnetic properties, resulting in increased magnetic moment and anisotropy. These effects are attributed to changes in cation distribution, exchange interactions, surface effects, and magnetocrystalline anisotropy. Overall, Co²⁺ doping improved the magnetic behavior of nickel ferrite, indicating its potential for application in memory devices and magnetic recording media. Full article

The moment of inertia and tidal deformability of idealized stars with polytropic equations of state (EOSs) are numerically calculated under both Newtonian gravity and general relativity (GR). The results explicitly confirm that the relation between the moment of inertia and tidal deformability, parameterized by the star’s mass, exhibits variations up to $1\%$ and $10\%$ for different polytropic indices in Newtonian gravity and GR, respectively. This indicates a more robust I-Love universal relation in the Newtonian framework. The theoretically derived I-Love universal relation for polytropic stars is subsequently tested against observational data for the moment of inertia and tidal deformability of the eight planets and some moons in our solar system. The analysis reveals that the theoretical I-Love universal relation aligns well with the observational data, suggesting that it can serve as an empirical relation. Consequently, it enables the estimation of either the moment of inertia or the tidal deformability of an exoplanet if one of these quantities, along with the mass of the exoplanet, is known. Full article

A mesoscopic lattice Boltzmann method based on the BGK model is proposed to solve a class of two-dimensional second-order nonlinear partial differential equations by incorporating an amending function. The model provides an efficient and stable framework for simulating initial value problems of second-order nonlinear partial differential equations and is adaptable to various nonlinear systems, including strongly nonlinear cases. The numerical characteristics and evolution patterns of these nonlinear equations are systematically investigated. A D2Q4 lattice model is employed, and the kinetic moment constraints for both local equilibrium and correction distribution functions are derived in the four velocity directions. Explicit analytical expressions for these distribution functions are presented. The model is verified to recover the target macroscopic equations in the continuous limit via Chapman–Enskog analysis. Numerical experiments using exact solutions are performed to assess the model’s accuracy and stability. The results show excellent agreement with exact solutions and demonstrate the model’s robustness in capturing nonlinear dynamics. Full article