Article
Automation & Control Systems
Chunting Ji, Zhengqiang Zhang
Summary: In this paper, we develop adaptive asymptotic stability for heterodirectional 2 x 2 hyperbolic PDEs with parametric-strict-feedback nonlinear actuator dynamics. We transform the PDEs into a stable target subsystem and construct an adaptive state feedback controller to ensure the boundedness of all signals in the closed-loop system. We also prove the convergence of PDE states, nonlinear ODE states, and control input to zero. A simulation example is provided to illustrate the effectiveness of the proposed method.
SYSTEMS & CONTROL LETTERS
(2023)
Article
Multidisciplinary Sciences
Robin M. Zech, Nora Molkenthin, Marc Timme, Malte Schroeder
Summary: The collective dynamics of capacity-constrained ride-pooling fleets are explored in this study. The effective fleet size is identified as an important scaling parameter characterizing the dynamics, and the scaling laws of ride-pooling efficiency are generalized to capacity-constrained fleets. These findings enable predictions of required fleet sizes in more complex settings.
SCIENTIFIC REPORTS
(2022)
Article
Mathematics
Qian Lei, Chi Seng Pun
Summary: We prove the existence, uniqueness, and stability of solutions to a class of nonlocal fully nonlinear parabolic PDEs. These equations arise from time-inconsistent problems in game theory or behavioral economics, where observations and preferences depend on reference time. We first study the linearized version of the nonlocal PDEs and establish solvability and a Schauder-type prior estimate. Then, by the linearization method, we establish the well-posedness under the fully nonlinear case and reveal the connection to forward-backward stochastic differential equations.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Biology
Frederick Laud Amoah-Darko Jr, Diana White
Summary: Microtubules are protein polymers that play crucial roles in cell development and transportation. This study presents a new mathematical model to describe the dynamics of microtubules, taking into account growth, shortening, and pausing. Additionally, the study explores the effects of stabilizing and destabilizing chemotherapeutic drugs on microtubule dynamics.
JOURNAL OF THEORETICAL BIOLOGY
(2022)
Article
Automation & Control Systems
Nils Christian A. Wilhelmsen, Henrik Anfinsen, Ole Morten Aamo
Summary: This paper derives minimum time convergent observers for n + m systems with different sensing methods, including unilateral, bilateral, and pointwise in-domain sensing. By using various coordinate transformations, unilateral and bilateral observers are obtained and demonstrated to have good performance in simulations.
EUROPEAN JOURNAL OF CONTROL
(2021)
Article
Computer Science, Interdisciplinary Applications
Emilio Jose Rocha Coutinho, Marcelo Dall'Aqua, Levi McClenny, Ming Zhong, Ulisses Braga-Neto, Eduardo Gildin
Summary: Physics-informed Neural Network (PINN) is a promising tool for physical phenomena described by partial differential equations (PDE), but it struggles with stiff problems that involve shocks in their solutions. Previous studies manually adjusted an artificial viscosity (AV) value to address this, but this paper proposes three methods that do not rely on predefined AV values. These methods successfully learn AV values and shock locations, and improve the approximation error.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Kevin J. Painter, Thomas Hillen, Jonathan R. Potts
Summary: The use of nonlocal PDE models in describing biological aggregation and movement behavior has gained significant attention. These models capture the self-organizing and spatial sorting characteristics of cell populations and provide insights into how animals perceive and respond to their surroundings. By deriving and analyzing these models, we can better understand biological movement behavior and provide a basis for explaining sociological phenomena.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2024)
Article
Automation & Control Systems
Iasson Karafyllis, Dionysios Theodosis, Markos Papageorgiou
Summary: This paper investigates a non-local conservation law with possible nudging terms on a ring road and provides conditions for its existence and uniqueness. The results indicate that nudging can increase traffic flow and have a stabilizing effect, even in cases where the ring road without nudging is unstable.
INTERNATIONAL JOURNAL OF CONTROL
(2022)
Article
Physics, Multidisciplinary
M. Henstridge, M. Foerst, E. Rowe, M. Fechner, A. Cavalleri
Summary: Nonlinear phononics is a method for creating transient structural changes in solids. This study extends nonlinear phononics to propagating polaritons, separating the functional response from the optical drive.
Article
Operations Research & Management Science
Ning Guo, Wai Wong, Rui Jiang, S. C. Wong, Qing-Yi Hao, Chao-Yun Wu
Summary: Cycling has become an important mode of transportation, but the dynamics of bicycle flow at bottlenecks have not been extensively studied. This study conducted real-world experiments to investigate the dynamics of bicycle flow at bottlenecks, and found that the capacity drop was mainly due to the difference in speeds of the two processes after the bottleneck activation, which could potentially be explained by behavioral inertia.
TRANSPORTATION SCIENCE
(2023)
Article
Computer Science, Theory & Methods
Indranil Chowdhury, Olav Ersland, Espen R. Jakobsen
Summary: In this study, numerical approximations for Mean Field Games with fractional or nonlocal diffusions are constructed. The proposed schemes, based on semi-Lagrangian approximations and dual approximations, are proven to be monotone, stable, and consistent. Convergence results are established for degenerate and nondegenerate equations in different dimensions, and tests conducted on various nonlocal diffusions support the analytical findings.
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
(2023)
Article
Mathematics, Applied
Shoufeng Shen, Xiangrong Zhu
Summary: This note discusses a Fourier integral operator T-phi,T-a under certain conditions, and provides boundedness results in different function spaces. It is shown that the operator is bounded in L-infinity and BMO spaces under certain conditions, and also bounded in L-p spaces.
ANALYSIS AND MATHEMATICAL PHYSICS
(2023)
Article
Mathematics, Applied
J. Limaco, Miguel R. Nunez-Chavez, Dany Nina Huaman
Summary: This paper addresses the internal and boundary exact controllability of certain nonlinear hyperbolic systems in one dimension, considering both local and nonlocal nonlinearities. The linearized result is proven based on the Hilbert Uniqueness Method and observability inequality results, followed by the application of a Fixed-Point technique to prove the nonlinear result with internal and boundary control. Possible extensions and open problems regarding other nonlocal systems are also presented.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2022)
Article
Automation & Control Systems
Ji Wang, Miroslav Krstic
Summary: This study presents an event-triggered adaptive output-feedback boundary control design to address lateral vibration suppression of a mining cable elevator. By designing a continuous-in-time observer-based adaptive backstepping control law, a dynamic event-triggering mechanism is successfully established.
Article
Statistics & Probability
Michele Coghi, Torstein Nilssen
Summary: This study focuses on a nonlinear Fokker-Planck equation driven by a deterministic rough path for analyzing the conditional probability of a McKean-Vlasov diffusion with common noise. To investigate this equation, the researchers developed a self-contained framework of non-linear rough integration theory to study McKean-Vlasov equations perturbed by rough paths. They successfully established an appropriate notion of solution for the corresponding Fokker-Planck equation and demonstrated its well-posedness.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2021)
Article
Mathematics, Applied
Boris Andreianov, Carlotta Donadello, Ulrich Razafison, Massimiliano D. Rosini
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
(2018)
Article
Mathematics, Applied
Edda Dal Santo, Carlotta Donadello, Sabrina F. Pellegrino, Massimiliano D. Rosini
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
(2019)
Article
Mathematics, Applied
Andrea Corli, Massimiliano D. Rosini
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
(2019)
Article
Mathematics
Boris Andreianov, Matthieu Brassart
JOURNAL OF DIFFERENTIAL EQUATIONS
(2020)
Article
Mathematics, Applied
Mohamed Benyahia, Massimiliano D. Rosini
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2020)
Article
Mathematics, Applied
Nathael Alibaud, Boris Andreianov, Adama Ouedraogo
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
(2020)
Article
Mathematics, Applied
Boris Andreianov, Carlotta Doiladello, Massimiliano D. Rosini
Summary: The study investigates a macroscopic two-phase transition model for vehicular traffic flow subject to a point constraint on the density flux. A new definition of admissible solutions for the Cauchy problem is introduced, ensuring compatibility with the modeling assumption at the level of the Riemann solver.
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Boris Andreianov, Abraham Sylla
Summary: This study introduces a toy model for self-organized road traffic, taking into account the orderliness in drivers' behavior. By combining Kruzhkov and Panov methods to define the existence of acceptable solutions, a BV-stable finite volume numerical scheme is developed.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Boris Andreianov, Shyam Sundar Ghoshal, Konstantinos Koumatos
Summary: In this paper, we provide an answer to a quantitative variant of the controllability problem for the viscous Burgers equation with initial and terminal data. We investigate the influence of additional a priori bounds on the (nonlinear) operator associated with the terminal state. Our approach combines scaling and compactness arguments with observations on the non-controllability of the inviscid Burgers equation to identify wide sets of terminal states that cannot be reached from zero initial data. We prove that under certain conditions, a constant terminal state is not attainable by weak solutions of the viscous Burgers equation with a bounded amplification restriction.
JOURNAL OF EVOLUTION EQUATIONS
(2022)
Article
Mathematics
Boris Andreianov, El Houssaine Quenjel
Summary: This paper highlights the interest and limitations of the L-1-based Young measure technique for studying the convergence of numerical approximations for diffusion problems. CVFE and DDFV schemes are analyzed and convergence is proven in the case of a log-Holder continuous variable exponent. The paper also investigates the structural stability of weak solutions and describes situations where different solution notions are selected by approximation methods.
VIETNAM JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics
Boris Andreianov, Massimiliano D. Rosini, Graziano Stivaletta
Summary: This paper focuses on the one-dimensional formulation of Hughes' model for pedestrian flows in the context of entropy solutions. It introduces the concept of non-classical shocks at the turning curve and considers different crowd behaviors based on linear cost functions. The paper presents an existence result for general data in the framework of entropy solutions, which allows for the presence of non-classical shocks. The proofs rely on a many-particle approximation scheme and numerical simulations illustrate the model's ability to reproduce typical evacuation behaviors, with a focus on the impact of the parameter α on evacuation time.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Boris Andreianov, Mohamed Maliki
Summary: This study explores well-posedness classes for degenerate elliptic problems in R-N, focusing on the L-infinity setting with locally uniformly continuous nonlinearities. Sufficient conditions for uniqueness and comparison properties of solutions are given in terms of the moduli of continuity of u bar arrow phi(x,u). The existence results for corresponding classes of solutions and data are deduced under additional restrictions on the dependency of phi on x.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
(2021)
Article
Mathematics, Applied
Andrea Corli, Massimiliano D. Rosini
SIAM JOURNAL ON APPLIED MATHEMATICS
(2019)
Proceedings Paper
Mathematics, Applied
Rinaldo M. Colombo, Maria Gokieli, Massimiliano D. Rosini
NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS, MATHEMATICAL PHYSICS, AND STOCHASTIC ANALYSIS: THE HELGE HOLDEN ANNIVERSARY VOLME
(2018)
Article
Mathematics, Applied
Kevin J. Painter, Thomas Hillen, Jonathan R. Potts
Summary: The use of nonlocal PDE models in describing biological aggregation and movement behavior has gained significant attention. These models capture the self-organizing and spatial sorting characteristics of cell populations and provide insights into how animals perceive and respond to their surroundings. By deriving and analyzing these models, we can better understand biological movement behavior and provide a basis for explaining sociological phenomena.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2024)
Article
Mathematics, Applied
Nicola Bellomo, Massimo Egidi
Summary: This paper focuses on Herbert A. Simon's visionary theory of the Artificial World and proposes a mathematical theory to study the dynamics of organizational learning, highlighting the impact of decomposition and recombination of organizational structures on evolutionary changes.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2024)
Article
Mathematics, Applied
Tayfun E. Tezduyar, Kenji Takizawa, Yuri Bazilevs
Summary: This paper provides an overview of flows with moving boundaries and interfaces (MBI), which include fluid-particle and fluid-structure interactions, multi-fluid flows, and free-surface flows. These problems are frequently encountered in engineering analysis and design, and pose computational challenges that require core computational methods and special methods. The paper focuses on isogeometric analysis, complex geometries, incompressible-flow Space-Time Variational Multiscale (ST-VMS) and Arbitrary Lagrangian-Eulerian VMS (ALE-VMS) methods, and special methods developed in connection with these core methods.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2024)