Article
Mathematics
Kaijian Sha, Yun Wang, Chunjing Xie
Summary: In this paper, the authors prove the uniform nonlinear structural stability of Poiseuille flows with arbitrarily large flux in a two-dimensional periodic strip. They establish the a priori estimate for the corresponding linearized problem by analyzing the associated boundary layers. The well-posedness theory for the Navier-Stokes system is also proved, even when the L2-norm of the external force is large. These results demonstrate the uniqueness of solutions for the steady Navier-Stokes system, even when the flux is large and the flow is not symmetric.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics
Yun Wang, Chunjing Xie
Summary: In this paper, the uniqueness and uniform structural stability of Poiseuille flows in an infinitely long pipe with Navier boundary conditions are established for steady axisymmetric solutions of Navier-Stokes system. This is crucial for studying the general Leray problem for flows in a general infinitely long nozzle. The key point is the uniform estimate with respect to both the flux of flows and friction coefficient in Navier boundary conditions. The partition of the two-dimensional plane for parameters, friction coefficient, and Fourier variable associated with the axial coordinate plays a key role in achieving these estimates.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Yun Wang, Chunjing Xie
Summary: In this paper, the uniqueness and structural stability of Poiseuille flows for axisymmetric solutions of steady Navier-Stokes system with Navier boundary conditions in a periodic pipe are proven. The stability is also shown to be uniform with respect to both the flux and the slip coefficient of Navier boundary conditions. Furthermore, it is demonstrated that the nonzero frequency part of the velocity is bounded by a negative power function of the flux as long as the flux is suitably large. The analysis highlights the importance of uniform linear structural stability and detailed analysis of boundary layers and swirl velocity corresponding to the flux and slip coefficients in different regimes.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2023)
Article
Mechanics
P. T. Nagy, G. Paal, M. Kiss
Summary: This paper attempts to reduce the gap between the predicted critical Reynolds numbers and the experimental observations for incompressible shear flows by adding a non-linear constraint to the Reynolds-Orr equation. The results show that adding the constraint significantly increases the critical Reynolds number. However, numerical simulations demonstrate that the assumption of a single waveform is unreasonably strict and using the compatibility condition without assuming the single waveform has a negligible effect on the critical Reynolds number.
Article
Mechanics
Vignesh Ramakrishnan, Remil Mushthaq, Anubhab Roy, S. Vengadesan
Summary: In this study, the effect of wall slip on the stability of a two-layered plane Poiseuille flow was investigated using mathematical modeling and numerical methods. It was found that wall slip has both stabilizing and destabilizing effects on the flow system.
Article
Mechanics
Chunhui Ma, Weiwen Zhao, Decheng Wan
Summary: Minor changes to the surface of a cylinder, such as attaching symmetric strips, can have a significant impact on flow characteristics, affecting lift and drag forces. Experimental results demonstrate that the position, thickness, and coverage of the strips, as well as their influence on flow patterns, play a crucial role in determining the aerodynamic performance of the cylinder.
Article
Mathematics
Ali Feizmohammadi
Summary: This article studies an inverse boundary value problem, which focuses on determining the time-dependent thermal conductivity and volumetric heat capacity of a medium based on the given temperature and heat flux measurements on its boundary. We prove the uniqueness in all dimensions under an assumption on the thermal diffusivity of the medium, which is related to the construction of certain families of exponential solutions to the heat equation.
MATHEMATISCHE ANNALEN
(2023)
Article
Mathematics
Daomin Cao, Jie Wan, Weicheng Zhan
Summary: This paper addresses the nonlinear desingularization of steady vortex rings in three-dimensional incompressible Euler fluids. By utilizing the vorticity method, a family of steady vortex rings is constructed in various domains, with the precise localization of the singular vortex filament depending on circulation, far-field velocity, and domain geometry. Qualitative and asymptotic properties are also established in the study.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Automation & Control Systems
Ihab Haidar, Yacine Chitour, Paolo Mason, Mario Sigalotti
Summary: This article deals with infinite-dimensional nonlinear forward complete dynamical systems subject to uncertainties. The well-known Datko lemma is extended to provide characterizations of uniform local, semi-global, and global exponential stability through the existence of coercive and non-coercive Lyapunov functionals. The importance of the obtained results is emphasized through various applications.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2022)
Article
Mathematics
Guodong Wang
Summary: In this paper, the nonlinear stability of planar steady Euler flows related to the least energy solutions of the Lane-Emden equation in a smooth bounded domain is investigated. The orbital stability of these flows is proven with respect to both the Ls norm of the vorticity for any s belonging to (1, +oo) and the energy norm. Consequently, nonlinear stability is achieved when the least energy solution is unique, which applies to a large class of domains and exponents. The proofs are based on a new variational characterization of the least energy solutions in terms of the vorticity, a compactness argument, and the proper use of conserved quantities of the Euler equation.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Physics, Mathematical
Yun Wang, Chunjing Xie
Summary: This paper proves the uniform nonlinear structural stability of Hagen-Poiseuille flows in an infinitely long pipe with arbitrary fluxes in the axisymmetric case. It is a key step to study the Liouville type property for steady solutions of the Navier-Stokes system in a pipe, and may play an important role in proving the existence of solutions with arbitrary flux to steady Navier-Stokes system in a nozzle with Poiseuille flows. The a priori estimate for the associated linearized problem, as well as the elaborate analysis on the governing equation for the partial Fourier transform of the stream function, lead to the establishment of linear structural stability.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2022)
Article
Materials Science, Multidisciplinary
Ying Zhang, Xinbing Yun, Ruojing Zhao, Fengtong Zhu, Hongwang Fu
Summary: A novel continuous expanding extrusion process was proposed for manufacturing Cu-Cr-Zr strips. The microstructure and precipitates of the strips were characterized by EBSD and TEM, showing fine and uniform microstructure and dispersed Cr precipitates. The extruded strips exhibited smaller grain size, higher hardness, strength, and electrical conductivity, and maintained a high fracture elongation compared to the as-cast state. Grain boundary strengthening, precipitation strengthening, and dislocation strengthening were found to contribute to the improved properties.
JOURNAL OF MATERIALS RESEARCH AND TECHNOLOGY-JMR&T
(2023)
Article
Multidisciplinary Sciences
Chao Duan, Takashi Nishikawa, Deniz Eroglu, Adilson E. Motter
Summary: This study investigates the response of large complex network systems to dynamical perturbations. By analyzing a extensive dataset of real directed networks, the study identifies network structural properties that contribute to nonnormality and reactivity and develops a theory that quantitatively predicts and explains these phenomena. The results have important implications for network design and management.
Article
Mathematics, Applied
Mani Mallika Arjunan, Pratap Anbalagan, Qasem Al-Mdallal
Summary: This paper aims to establish the uniform stability criteria for fractional-order time-delayed gene regulatory networks with leakage delays (FOTDGRNL). The existence and uniqueness of the considered systems are established using the Banach fixed point theorem. The delay-dependent uniform stability and robust uniform stability of FOFGRNLT are investigated with the help of certain analysis techniques depending on equivalent norm techniques. Two numerical examples are provided to justify the applicability of the theoretical results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mechanics
Himanshu Mishra, Anubhab Roy, S. Vengadesan
Summary: This study investigated the linear stability characteristics of a two-layered liquid-liquid flow in an inclined channel with slippery walls. The role of wall slip on the multiple base states associated with each holdup solution was analyzed. It was found that the wall slip could have both stabilizing and destabilizing effects depending on the flow rates and the value of holdup-the location of an interface.
