Article
Mathematics
Qinbo Chen, Danijela Damjanovic
Summary: In this paper, we study local rigidity for isometric toral extensions of partially hyperbolic Zk (k ≥ 2) actions on the torus. We prove a C infinity local rigidity result for such actions, under the assumption that smooth perturbations of the actions satisfy the intersection property. We also provide a local rigidity result within a class of volume preserving actions. Our method mainly relies on a generalization of the Kolmogorov-Arnold-Moser iterative scheme.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2023)
Article
Mathematics, Applied
Qiao Liu
Summary: This paper studies a local rigidity property, where any smooth perturbations close enough to an affine action can be smoothly conjugate to the affine action with constant time change.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2021)
Article
Mathematics, Applied
Boris Petkovic
Summary: We generalize Moser's results on the circle to T-d by showing that a smooth sufficiently small perturbation of a Z(m) action can be smoothly conjugate to the unperturbed action under certain conditions, and we answer Moser's question by proving the existence of a continuum of m-tuples of Diophantine vectors such that every element of the induced Z(m) action is Liouville.
REGULAR & CHAOTIC DYNAMICS
(2021)
Article
Robotics
Jing Liang, Kasun Weerakoon, Tianrui Guan, Nare Karapetyan, Dinesh Manocha
Summary: We propose a novel outdoor navigation algorithm that generates stable and efficient robot actions to reach a goal. Our approach, based on the Proximal Policy Optimization (PPO) algorithm, achieves multiple capabilities for outdoor local navigation tasks, such as reducing drifting, maintaining stability on bumpy terrains, avoiding steep hills, and preventing collisions. By training with rich features from a Lidar sensor in a high-fidelity Unity simulator, our method mitigates the gap between simulation and the real world. Evaluation results demonstrate significant improvements in stability, drifting reduction, and elevation changes compared to state-of-the-art approaches.
IEEE ROBOTICS AND AUTOMATION LETTERS
(2023)
Article
Mathematics
Jingyin Huang, Bruce Kleiner, Stephan Stadler
Summary: This is the first paper in a series that focuses on Morse quasiflats, a generalization of Morse quasigeodesics to arbitrary dimension. The paper introduces alternative definitions and demonstrates their equivalence and quasi-isometry invariance under appropriate assumptions on the ambient space. Various examples are also provided.
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
(2022)
Article
Automation & Control Systems
Liyun Tong, Jinling Liang
Summary: This paper proposes two methods for investigating the initial state estimation problem in discrete event systems (DESs): a matrix-based dimension reduction tracking observation system and a matrix-based reversal observation system. The initial state estimation is treated as the initial-state detectability (I-S detectability). By using the Boolean semi-tensor product method of matrices, the algebraic forms of the partially-observed DES are constructed, reducing the computational complexity to some extent. Necessary and sufficient criteria are established for determining the I-S detectability of the system based on the newly defined state transition output-event observation matrix. Illustrative examples are provided to demonstrate the feasibility of the derived results.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2023)
Article
Mathematics
Yannick Guedes Bonthonneau, Thibault Lefeuvre
Summary: This article aims to extend a recent result on the local rigidity of the marked length spectrum from compact negatively-curved Riemannian manifolds to manifolds with hyperbolic cusps. We deal with the nonlinear version of the problem and prove that such manifolds are locally rigid for nonlinear perturbations of the metric that slightly decrease at infinity. Our proof relies on the linear theory and careful analytic study of the generalized X-ray transform operator.
JOURNAL DE L ECOLE POLYTECHNIQUE-MATHEMATIQUES
(2023)
Article
Mathematics
Xinsheng WANG
Summary: This paper introduces and investigates the local unstable metric entropy, local unstable topological entropy, and local unstable pressure for partially hyperbolic endomorphisms. Specifically, two variational principles concerning the relationships among the mentioned numbers are formulated.
CHINESE ANNALS OF MATHEMATICS SERIES B
(2022)
Article
Mathematics, Applied
Mao Okada
Summary: The study focuses on the local rigidity of certain actions of a solvable subgroup Γ subset of the group G of orientation-preserving isometries of a rank-one symmetric space X on the boundary of X, which is diffeomorphic to a sphere. The constructed action is locally rigid when X is either a quaternionic hyperbolic space or the Cayley hyperplane.
JOURNAL OF MODERN DYNAMICS
(2021)
Article
Thermodynamics
Fernando A. Rodrigues, Marcelo J. S. de Lemos
Summary: The study found that porosity has a slight impact on the turbulence field, while temperatures increase significantly faster for higher porosity cases. Turbulence in higher porosity cases was lower, leading to an increase in thermal efficiencies. Variation in Da number showed increased recirculation in the clear region for lower Da numbers, and increased porous region turbulence for higher Da numbers. Additionally, higher Da numbers resulted in decreased heat exchange between fluid and solid phases.
INTERNATIONAL JOURNAL OF THERMAL SCIENCES
(2021)
Article
Materials Science, Multidisciplinary
Tayyiaba Rasool, Rashida Hussain, Hadi Rezazadeh, Dariush Gholami
Summary: Novel results on the wave propagation over an incompressible fluid using the hyperbolic local (4+1)-dim Boiti-Leon-Manna-Pempinelli (BLMP) equation are presented in this article. The explicit solitary wave solutions of the equation are obtained using the generalized exponential rational function (GERF) approach and validated using computational tools. The effectiveness of the GERF approach for determining the solutions of the (4+1)-dim BLMP equation is demonstrated through the dynamic characteristics of the obtained solutions.
RESULTS IN PHYSICS
(2023)
Article
Engineering, Geological
Nailiang Xiang, Yang Feng, Xu Chen
Summary: Considering the computation time and convergence problems of shell-solid models, a fiber-based nonlinear modelling method is proposed for seismic analysis of partially concrete-filled steel tubular bridge piers. Experimental results validate the efficiency and effectiveness of the proposed fiber models in capturing the hysteretic behavior of CFST piers. The study highlights the importance of proper design parameters to mitigate local buckling and improve the seismic performance of partially CFST piers, and proposes a novel design method using layered concrete filling.
SOIL DYNAMICS AND EARTHQUAKE ENGINEERING
(2023)
Article
Geochemistry & Geophysics
Aurelie Louis-Napoleon, Thomas Bonometti, Muriel Gerbault, Roland Martin, Olivier Vanderhaeghe
Summary: We numerically investigate the development of crustal scale diapirism and convection in a heterogeneous continental crust, independently from regional tectonics. The study focuses on a hot crust with unmolten and partially molten domains, using the volume of fluid method to capture the behavior of deformable inclusions. Different flow regimes are observed, ranging from suspension to layering and diapiric regimes, depending on the properties of the unmolten and partially molten rock. These findings provide insights into the physical parameters required for the segregation of deformable inclusions in a partially molten crust and contribute to the understanding of continental crust differentiation.
GEOPHYSICAL JOURNAL INTERNATIONAL
(2022)
Article
Mathematics, Applied
Patrick Joly, Maryna Kachanovska
Summary: This work focuses on the construction and analysis of high-order transparent boundary conditions for the weighted wave equation on a fractal tree, modeling sound propagation in human lungs. The method proposed in this work, based on truncating the meromorphic series representing the symbol of the Dirichlet-to-Neumann operator, shows stability and convergence, with numerical results confirming theoretical findings.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Engineering, Multidisciplinary
Imtiaz Ahmad, Aly R. Seadawy, Hijaz Ahmad, Phatiphat Thounthong, Fuzhang Wang
Summary: This study introduces an efficient local meshless method based on radial basis function (RBF) for studying the numerical solution of three-dimensional second-order hyperbolic telegraph equations. The proposed method shows quick convergence compared to various existing numerical methods in recent literature.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2022)
