Article
Mathematics, Applied
Yuhang Zhu, Yinghao Zhao, Chaolin Song, Zeyu Wang
Summary: In this study, a novel approach called Time-Variant Reliability Updating (TVRU) is proposed, which integrates Kriging-based time-dependent reliability with parallel learning. This method enhances risk assessment in complex systems, showcasing exceptional efficiency and accuracy.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Dinh-Nho Hao, Thuy T. Le, Loc H. Nguyen
Summary: This article introduces a new technique for computing numerical solutions to the nonlinear inverse heat conduction problem. By truncating the Fourier series and employing the Runge-Kutta method, the high-dimensional problem is converted into a 1D problem, addressing the nonlinearity and lack of partial derivative data.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Samuel W. Akingbade, Marian Gidea, Matteo Manzi, Vahid Nateghi
Summary: This paper presents a heuristic argument for the capacity of Topological Data Analysis (TDA) to detect critical transitions in financial time series. The argument is based on the Log-Periodic Power Law Singularity (LPPLS) model, which characterizes financial bubbles as super-exponential growth (or decay) with increasing oscillations approaching a tipping point. The study shows that whenever the LPPLS model fits the data, TDA generates early warning signals. As an application, the approach is illustrated using positive and negative bubbles in the Bitcoin historical price.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Lianwen Wang, Xingyu Wang, Zhijun Liu, Yating Wang
Summary: This contribution presents a delayed diffusive SEIVS epidemic model that can predict and quantify the transmission dynamics of slowly progressive diseases. The model is applied to fit pulmonary tuberculosis case data in China and provides predictions of its spread trend and effectiveness of interventions.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Shuangxi Huang, Feng-Fei Jin
Summary: This paper investigates the error feedback regulator problem for a 1-D wave equation with velocity recirculation. By introducing an invertible transformation and an adaptive error-based observer, an observer-based error feedback controller is constructed to regulate the tracking error to zero asymptotically and ensure bounded internal signals.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Weimin Liu, Shiqi Gao, Feng Xu, Yandong Zhao, Yuanqing Xia, Jinkun Liu
Summary: This paper studies the modeling and consensus control of flexible wings with bending and torsion deformation, considering the vibration suppression as well. Unlike most existing multi-agent control theories, the agent system in this study is a distributed parameter system. By considering the mutual coupling between the wing's deformation and rotation angle, the dynamics model of each agent is expressed using sets of partial differential equations (PDEs) and ordinary differential equations (ODEs). Boundary control algorithms are designed to achieve control objectives, and it is proven that the closed-loop system is asymptotically stable. Numerical simulation is conducted to demonstrate the effectiveness of the proposed control scheme.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Marzia Bisi, Nadia Loy
Summary: This paper proposes and investigates general kinetic models with transition probabilities that can describe the simultaneous change of multiple microscopic states of the interacting agents. The mathematical properties of the kinetic model are proved, and the quasi-invariant asymptotic regime is studied and compared with other models. Numerical tests are performed to demonstrate the time evolution of distribution functions and macroscopic fields.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mechanics
Sampson Davis, Eli Shellabarger, James Miller, Thomas Ward
Summary: The present work focuses on studying the effects of shock wave - boundary layer interaction in 2D hypersonic flow at the sharp leading edge of a flat plate and a flat plate followed by a compression ramp. A key parameter, the hypersonic interaction parameter x, is defined and analyzed using a semi-analytic reduced-order model. The study aims to improve on existing methods by characterizing the viscous boundary layer and investigating the upstream influence resulting from the compression ramp.
EUROPEAN JOURNAL OF MECHANICS B-FLUIDS
(2024)
Article
Mathematics, Applied
Vy Khoi Le
Summary: This article mainly introduces the existence results for a quasilinear inclusion describing a prescribed mean curvature problem and establishes a functional analytic framework. It also introduces a general existence theory for inclusions defined on nonreflexive Banach spaces.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Haleem Afsar, Gao Peiwei, Touqeer Nawaz, Mohammad Mahtab Alam
Summary: Researchers in applied mathematics, physics, and engineering are studying methods to reduce noise to an acceptable level. This article focuses on a trifurcated waveguide structure with different porosity effects and examines the impact of various materials on scattered fields. A semi-analytical approach is introduced to predict acoustic properties at low frequencies and provide reasonable estimates at higher frequencies.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Abdelkrim Chakib, Ibrahim Khalil, Hamid Ouaissa, Azeddine Sadik
Summary: This paper investigates the numerical study of geometrical shape optimization problems in fluid mechanics. A shape optimization numerical process is proposed using the gradient descent algorithm and finite element discretization. Numerical tests demonstrate the validity and effectiveness of the proposed approach.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mechanics
Kun Sung Park, Ali Zamiri, Minsuk Choi, Byung Ju Lee, Jin Taek Chung
Summary: In this study, the stator geometry of a single-stage transonic fan was optimized to improve its aerodynamic performance and stall margin. Steady and unsteady simulations were conducted to analyze the impact of shock waves generated by the rotor blade on the stator inlet flow. Using a design of experiment and response surface method, an optimal geometry of the stator blade was obtained to increase the fan's efficiency and stall margin.
EUROPEAN JOURNAL OF MECHANICS B-FLUIDS
(2024)
Article
Mechanics
Ying Chen, Longxiang Liu, Jie Li, Zhaoxin Gong, Xin Chen
Summary: In this study, large eddy simulation is used to investigate the tip-leakage flows around hydrofoils with different tip clearance and skew angle. The results show that tip separation vortex (TSV) grows from the entire lower edge of the tip and twines with the tip-leakage vortex (TLV) into a primary vortex tube. Cavitation effect significantly accelerates the roll-up process of the vortices and the tip-leakage flow turns from wake-like to jet-like when the clearance is reduced. The skewness of the hydrofoil has a significant effect on the laminar-turbulent transition of the flow.
EUROPEAN JOURNAL OF MECHANICS B-FLUIDS
(2024)
Article
Mathematics, Applied
Nana Ding, Gui Guan, Shuling Shen, Linhe Zhu
Summary: This study explores the trends and control of online rumor dissemination. By analyzing the boundedness of solutions and the existence of rumor-spreading equilibrium points, as well as calculating the basic reproduction number, this study draws some fundamental conclusions. Furthermore, through the analysis of local stability and global stability, the equilibrium points of rumor spreading are thoroughly examined. In addition, this study discusses the forward and backward bifurcation phenomena and optimal control problem, which are seldom addressed in the bilingual environment. Numerical simulations are conducted to verify the accuracy of the main results.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
G. Soundararajan, G. Nagamani, Ardak Kashkynbayev
Summary: The purpose of this paper is to design a compatible filter for a class of classical discrete-time neural networks, addressing the uncertain complex-valued weighting parameters and time-varying delayed responses subject to the H. performance measure. The proposed complex-valued filter scheme and the derived inequalities provide a more precise linearized lower bound for the quadratic summing terms. The sufficient conditions based on linear matrix inequalities are proposed for designing a robust H. filter, and the applicability and efficiency of the proposed scheme are demonstrated through numerical examples and simulation outcomes.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Massimiliano Zanin
Summary: We propose a novel methodology based on continuous ordinal patterns to preprocess time series and uncover the non-linear temporal structures within them. Through synthetic and real-world examples, we demonstrate how this transformation overcomes a major limitation of the Granger Causality test and efficiently detects non-linear causality relations without any prior assumptions. We also show that this transformation can be optimized based on the specific time series under study, or random ordinal patterns can be used to achieve good results, similar to Reservoir Computing.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Shi Liu, Song Chen, Tehuan Chen, Zhigang Ren
Summary: This paper proposes a residual neural network-based observer for CSTR systems, which can quickly and accurately observe the state changes during the CSTR reaction.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
M. Johnson, V. Vijayakumar
Summary: In this paper, we study the existence and optimal control results for second-order Sobolev type delay systems with Clarke's subdifferential type. The existence of a mild solution is established for the proposed second-order delay differential system using the novel ideas of Clarke's subdifferential. The fixed point theorem of condensing multi-valued maps, the strongly continuous cosine family, and the properties of Clarke's subdifferential are used to establish the existence of a mild solution. Moreover, the existence of an optimal control pair governed by the presented system is verified through Balder's theorem. Finally, an example is provided to illustrate the main results.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mechanics
Nang X. Ho, Truong V. Vu
Summary: The present paper reports numerical results on the solidification process of a hollow drop on an inclined surface. The drop undergoes deformation and forms an asymmetric tip as the surface angle increases. The solidification time, however, is not affected by the surface angle. The fluid accumulates at the bottom of the drop and the bubble moves upwards before being trapped by solidification. A larger bubble reduces the tip shift. The effect of Bond number and Stefan number on solidification is also considered.
EUROPEAN JOURNAL OF MECHANICS B-FLUIDS
(2024)
Article
Mathematics, Applied
Vasily E. Tarasov
Summary: This paper introduces non-Lagrangian field theory and its non-holonomic variational equations, and discusses how to derive field equations and apply Noether's theorem using these equations. It also discusses the energy-momentum tensor and angular-momentum tensor in non-Lagrangian field theory, and proposes the possibility and properties of dissipative structures.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
