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applied mathematics and Mechanics(English Edition) 2024年第3期45卷 563-580页

作者： N.HUMNEKAR D.SRINIVASACHARYA department of mathematics National Institute of TechnologyWarangal 506004TelanganaIndia

The influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel is *** DarcyBrinkman model is used to characterize the fluid flow dynamics in porous *** analytical solutions are obtained for the unidirectional and completely developed *** on a normal mode analysis,the generalized eigenvalue problem under a perturbed state is *** eigenvalue problem is then solved by the spectral ***,the critical Rayleigh number with the corresponding wavenumber is evaluated at the assigned values of the other flow-governing *** results show that increasing the Darcy number,the Lewis number,the Dufour parameter,or the Soret parameter increases the stability of the system,whereas increasing the inclination angle of the channel destabilizes the ***,the flow is the most unstable when the channel is vertically oriented.

关键词： nanofluid inclined channel variable viscosity linear stability double dif-fusion porous medium

Discovery of Partial Differential Equations from Highly Noisy and Sparse Data with Physics-Informed Information Criterion

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Research 2024年第1期2023卷 247-259页

作者： Hao Xu Junsheng Zeng Dongxiao Zhang BIC-ESAT EREand SKLTCSCollege of EngineeringPeking UniversityBeijing 100871P.R.China Institute of applied Physics and Computational mathematics Beijing 100088P.R.China Eastern Institute for Advanced Study Eastern Institute of TechnologyNingbo 315200ZhejiangP.R.China National Center for applied mathematics Shenzhen(NCAMS) Southern University of Science and TechnologyShenzhen 518055GuangdongP.R.China department of mathematics and Theories Peng Cheng LaboratoryShenzhen 518000GuangdongP.R.China

Data-driven discovery of partial differential equations(PDEs)has recently made tremendous progress,and many canonical PDEs have been discovered successfully for proof of ***,determining the most proper PDE without prior references remains challenging in terms of practical *** this work,a physics-informed information criterion(PIC)is proposed to measure the parsimony and precision of the discovered PDE *** proposed PIC achieves satisfactory robustness to highly noisy and sparse data on 7 canonical PDEs from different physical scenes,which confirms its ability to handle difficult *** PIC is also employed to discover unrevealed macroscale governing equations from microscopic simulation data in an actual physical *** results show that the discovered macroscale PDE is precise and parsimonious and satisfies underlying symmetries,which facilitates understanding and simulation of the physical *** proposition of the PIC enables practical applications of PDE discovery in discovering unrevealed governing equations in broader physical scenes.

关键词： process canonical proof

Femtosecond laser direct written fiber Bragg gratings with narrow bandwidth and high sideband suppression

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Chinese Optics Letters 2024年第1期22卷 1-7页

作者：邱文平刘爽程光华湛欢张国栋任冠品孙中瑞张敏 department of applied Physics College of Mathematics and PhysicsChengdu University of TechnologyChengdu 610059China School of Electronics and Information Northwestern Polytechnical UniversityXi’an 710072China Chengdu Development Center of Science and Technology of CAEP Chengdu 610299China

Aiming for suppressing side-mode and spectrum broadening,a slit beam-shaping method and super-Gaussian apodization processing for femtosecond laser point-by-point(PbP)inscription technology of fiber Bragg gratings(FBGs)are reported ***-quality FBGs,featuring narrow bandwidth of less than 0.3 nm,high reflectivity above 85%,low insertion loss(0.21 dB),and low cladding loss(0.82 dB),were obtained *** a semi-automatic PbP inscription process,an array consisting of six FBGs,exhibiting almost no side-mode peaks with high suppression ability and narrow bandwidth,was fabricated along three independently developed single-mode fibers with an interval of 20 mm.

关键词： femtosecond laser processing fiber Bragg grating slit beam shaping

Galerkin-Bernstein Approximations for the System of Third-Order Nonlinear Boundary Value Problems

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Journal of applied mathematics and Physics 2024年第6期12卷 2083-2101页

作者： Snigdha Dhar Md. Shafiqul Islam department of applied mathematics University of Dhaka Dhaka Bangladesh

This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We derive mathematical formulations in matrix form, in detail, by exploiting Bernstein polynomials as basis functions. A reasonable accuracy is found when the proposed method is used on few examples. At the end of the study, a comparison is made between the approximate and exact solutions, and also with the solutions of the existing methods. Our results converge monotonically to the exact solutions. In addition, we show that the derived formulations may be applicable by reducing higher order complicated BVP into a lower order system of BVPs, and the performance of the numerical solutions is satisfactory. .

关键词： System of Third-Order BVP Galerkin Method Bernstein Polynomials Nonlinear BVP Higher-Order BVP

Estimating the frequency of traffic overloading on road bridges

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Journal of Traffic and Transportation Engineering(English Edition) 2024年第4期11卷 776-796页

作者： Roberto Ventura Benedetto Barabino Giulio Maternini department of Civil Environmental Architectural Engineering and Mathematics University of Brescia

Load limits, which appear to be routinely exceeded by trucks, occasionally result in road bridge failures. Therefore, predicting failures is crucial for safeguarding road safety. Past studies have largely focused on forecasting bridge failure event probability using the reliability analysis method, whilst occasionally accounting for vehicular overloading effects. Only recently, a study has investigated design traffic overloading event frequency using generalised linear regression models(GLRMs), including a power component and negative binomial regressions(NBRs). However, as far as the authors know, artificial neural network models(ANNMs) have never been applied to this field. This paper is an attempt to fill in these gaps. First a frequencybased metric of traffic overloading was adopted as a driver of failure probability. Second, two alternative ‘frequency' models were specified, calibrated, and validated. The former was based on a GLRM, the latter on ANNMs. Then, these models were compared using regression plots(RPs), measures of errors(Mo Es) and the ratio between the number of observed vs predicted design load overcoming events to evaluate their performance. The models analysed more than 2 million weigh-in-motion(WIM) data records from a pilot station on a bridge on a heavily used ring road in Brescia(Italy). Results showed that ANNMs outperformed *** have a higher correlation coefficient(between predicted and target frequencies),lower Mo Es, and a closer-to-unity ratio(between predicted and target frequencies). These findings may increase prediction accuracy of design traffic overloading events and give road authorities more effective traffic management to protect bridges from load hazards.

关键词： Road bridges Traffic load hazard Econometry Machine learning Weigh-in-motion Big-data analysis

Nonlinear interaction of head-on solitary waves in integrable and nonintegrable systems

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Chinese Physics B 2024年第5期33卷 480-487页

作者：张树甜刘世鲲矫滕菲孙敏胡凤兰黄德财 department of applied Physics Nanjing University of Science and TechnologyNanjing 210094China

This study numerically investigates the nonlinear interaction of head-on solitary waves in a granular chain(a nonintegrable system)and compares the simulation results with the theoretical results in fluid(an integrable system).Three stages(the pre-in-phase traveling stage,the central-collision stage,and the post-in-phase traveling stage)are identified to describe the nonlinear interaction processes in the granular *** nonlinear scattering effect occurs in the central-collision stage,which decreases the amplitude of the incident solitary *** with the leading-time phase in the incident and separation collision processes,the lagging-time phase in the separation collision process is *** asymmetrical nonlinear collision results in an occurrence of leading phase shifts of time and space in the post-in-phase traveling *** next find that the solitary wave amplitude does not influence the immediate space-phase shift in the granular *** space-phase shift of the post-in-phase traveling stage is only determined by the measurement position rather than the wave *** results are reversed in the *** increase in solitary wave amplitude leads to decreased attachment,detachment,and residence times for granular chains and *** the immediate time-phase shift,leading and lagging phenomena appear in the granular chain and the fluid,*** results offer new knowledge for designing mechanical metamaterials and energy-mitigating systems.

关键词： integrable system nonintegrable system granular chain solitary wave

Heat and Mass Transfer on Non-Newtonian Peristaltic Flow in a Channel in Presence of Magnetic Field: Analytical and Numerical Analysis

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applied mathematics 2024年第8期15卷 568-583页

作者： Md. Maruf Hasan Md. Enamul Karim Md. Abdus Samad department of mathematics Comilla University Comilla Bangladesh department of applied mathematics University of Dhaka Dhaka Bangladesh

A study has been arranged to investigate the flow of non-Newtonian fluid in a vertical asymmetrical channel using peristalsis. The porous medium allows the electrically conductive fluid to flow in the channel, while a uniform magnetic field is applied perpendicular to the flow direction. The analysis takes into account the combined influence of heat and mass transfer, including the effects of Soret and Dufour. The flow’s non-Newtonian behavior is characterized using a Casson rheological model. The fluid flow equations are examined within a wave frame of reference that has a wave velocity. The analytic solution is examined using long wavelengths and a small Reynolds number assumption. The stream function, temperature, concentration and heat transfer coefficient expressions are derived. The bvp4c function from MATLAB has been used to numerically solve the transformed equations. The flow characteristics have been analyzed using graphs to demonstrate the impacts of different parameters.

关键词： Stream Function Mass Transfer Vertical Channel Casson Fluid

Stability and Time-Step Constraints of Implicit-Explicit Runge-Kutta Methods for the Linearized Korteweg-de Vries Equation

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Communications on applied mathematics and Computation 2024年第1期6卷 658-687页

作者： Joseph Hunter Zheng Sun Yulong Xing department of mathematics The Ohio State UniversityColumbusOH43210USA department of mathematics The University of AlabamaTuscaloosaAL35487USA

This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either finite difference(FD)or local discontinuous Galerkin(DG)spatial *** analyze the stability of the fully discrete scheme,on a uniform mesh with periodic boundary conditions,using the Fourier *** the linearized KdV equation,the IMEX schemes are stable under the standard Courant-Friedrichs-Lewy(CFL)conditionτ≤λ***,λis the CFL number,τis the time-step size,and h is the spatial mesh *** study several IMEX schemes and characterize their CFL number as a function ofθ=d/h^(2)with d being the dispersion coefficient,which leads to several interesting *** also investigate the asymptotic behaviors of the CFL number for sufficiently refined meshes and derive the necessary conditions for the asymptotic stability of the IMEX-RK *** numerical experiments are provided in the paper to illustrate the performance of IMEX methods under different time-step constraints.

关键词： Linearized Korteweg-de Vries(KdV)equation Implicit-explicit(IMEX)Runge-Kutta(RK)method Stability Courant-Friedrichs-Lewy(CFL)condition Finite difference(FD)method Local discontinuous Galerkin(DG)method

Study of damage behavior and repair effectiveness of patch repaired carbon fiber laminate under quasi-static indentation loading

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Defence Technology（防务技术） 2024年第4期34卷 29-41页

作者： Alok Kumar Chinmaya Kumar Sahoo A.Arockiarajan department of applied Mechanics Indian Institute of Technology MadrasChennai 600036India

Damage caused due to low-velocity impacts in composites leads to substantial deterioration in their residual strength and eventually provokes structural *** work presents an experimental investigation on the effects of different patch and parent laminate stacking sequences on the enhancement of impact strength of Carbon Fiber Reinforced Polymers(CFRP)composites by utilising the adhesively bonded external patch repair *** evolution study is also performed with the aid of Acoustic Emission(AE).Two different quasi-isotropic configurations were selected for the parent laminate,viz.,[45°/45°/0°/0°]s and[45°/0°/45°/0°]*** Static Indentation(QSI)test was performed on both the pristine laminates,and damage areas were detected by using the C-scan inspection *** laminates were repaired by using a single-sided patch of two different configurations,viz.,[45°/45°/45°/45°]and[45°/0°/0°/45°],and employing a circular plug to fill the damaged *** different combinations of repaired laminates with two configurations of each parent and patch laminate were produced,which were further subjected to the QSI *** results reveal the effectiveness of the repair method,as all the repaired laminates show higher impact resistance compared to the respective pristine *** of[45°/0°/0°/45°]configuration when repaired by taking[45°/45°/0°/0°]s and[45°/0°/45°/0°]s as parents exhibited 68%and 73%higher peak loads,respectively,than the respective pristine ***,parent and patch of configuration[45°/0°/45°/0°]s and[45°/0°/0°/45°],respectively,attain the highest peak load,whereas[45°/45°/0°/0°]s and[45°/45°/45°/45°]combinations possess the most gradual decrease in the load.

关键词： Carbon fiber reinforced polymers(CFRP) Quasi-isotropic laminate Quasi static indentation(QSI) Acoustic emission(AE) Composite repair

A REDUCED ORDER SCHWARZ METHOD FOR NONLINEAR MULTISCALE ELLIPTIC EQUATIONS BASED ON TWO-LAYER NEURAL NETWORKS

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Journal of Computational mathematics 2024年第2期42卷 570-596页

作者： Shi Chen Zhiyan Ding Qin Li Stephen J.Wright mathematics department University of Wisconsin-MadisonMadisonWI 53706USA department of mathematics University of California-BerkeleyBerkeley CA 94720USA mathematics department and Discovery Institute University of Wisconsin-Madison MadisonWI 53706USA Computer Sciences department University of WisconsinMadisonWI 53706USA

Neural networks are powerful tools for approximating high dimensional data that have been used in many contexts,including solution of partial differential equations(PDEs).We describe a solver for multiscale fully nonlinear elliptic equations that makes use of domain decomposition,an accelerated Schwarz framework,and two-layer neural networks to approximate the boundary-to-boundarymap for the subdomains,which is the key step in the Schwarz ***,the boundary-to-boundary map requires solution of boundary-value elliptic problems on each *** leveraging the compressibility of multiscale problems,our approach trains the neural network offline to serve as a surrogate for the usual implementation of the boundary-to-boundary *** method is applied to a multiscale semilinear elliptic equation and a multiscale p-Laplace *** both cases we demonstrate significant improvement in efficiency as well as good accuracy and generalization performance.

关键词： Nonlinear homogenization Multiscale elliptic problem Neural networks Do-main decomposition