Article
Engineering, Civil
L. Yang, H. Liang, J. Du, S. C. Wong
Summary: This study summarizes the first-order and high-order macroscopic models for solving the pedestrian flow problem and proposes a solution algorithm. The models are rewritten in the form of unified scalar or system hyperbolic conservation laws, and high-order discontinuous Galerkin methods and a second-order fast-sweeping scheme are applied for solving them. Numerical results demonstrate the accuracy and effectiveness of the proposed method and highlight the advantages of triangular meshes.
JOURNAL OF ADVANCED TRANSPORTATION
(2023)
Article
Mathematics, Applied
Philippe G. LeFloch, Hendrik Ranocha
Summary: This study investigates numerical methods for nonlinear hyperbolic conservation laws with non-convex flux, computing kinetic functions to characterize macro-scale dynamics. It demonstrates that entropy stability does not guarantee uniqueness of numerical solutions, and designs entropy-dissipative schemes for systems with delta shocks.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
Subhankar Sil, T. Raja Sekhar
Summary: This article investigates a system of first order quasilinear hyperbolic partial differential equations governing the macroscopic production model for high-volume product flows. The system is shown to have a nonlinear self-adjointness property, and various conservation laws are constructed using the direct multipliers method. Nonclassical symmetry analysis is performed to compute hidden symmetries, leading to new exact solutions and discussions on their physical behavior. The evolution of characteristic shock and weak discontinuity is also studied using one of the obtained solutions.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Yannick Holle
Summary: This article studies the maximum entropy dissipation problem at a traffic junction and its corresponding coupling condition. The author proves that this problem is equivalent to a coupling condition introduced by Holden and Risebro. The role of the entropies involved in the macroscopic coupling condition at the traffic junction is also discussed.
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
(2022)
Article
Economics
Elhabib Moustaid, Gunnar Flotterod
Summary: This article presents a macroscopic model of pedestrian flows through networks of bidirectional corridors connected by multidirectional intersections. The model defines bidirectional sending and receiving flows based on an existing pedestrian bidirectional fundamental diagram, and utilizes the incremental transfer principle to simulate bidirectional flows across nodes with any number of adjacent links. The solution to the model is consistent with the kinematic wave model in its unidirectional properties.
TRANSPORTATION RESEARCH PART B-METHODOLOGICAL
(2021)
Article
Materials Science, Multidisciplinary
P. Prelovsek, M. Mierzejewski, J. Herbrych
Summary: This study investigates the high-temperature dynamical conductivity in two one-dimensional integrable quantum lattice models, the XXZ spin chain and the Hubbard chain. The results reveal a fine structure of conductivity spectra in the XXZ chain, but do not find clear evidence for a diffusive component, at least not for certain values of parameters. The conclusion is similar for the Hubbard model away from half-filling, showing more universal behavior in the spectra.
Article
Mathematics
Ning Jiang, Jiangyan Liang, Yi-Long Luo, Min Tang, Yaming Zhang
Summary: This study investigates the well-posedness of biological models with AHL-dependent cell mobility in engineered Escherichia coli populations. The local existence for large initial data is proven for a recently proposed kinetic model. The positivity and local conservation laws for density and nutrient concentration are justified with specific initial assumptions. Based on these properties, a global extension in time near the equilibrium is achieved. By considering the asymptotic behaviors of the CheZ turnover rate, an anisotropic diffusion model for engineered Escherichia coli populations (AD-EECP) is derived, and a key extra a priori estimate is found to overcome the difficulties from the nonlinearity of the diffusion structure. The local well-posedness, positivity, and local conservation laws for density and nutrient of the AD-EECP are justified, and the global existence around the stable steady-state is obtained.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Materials Science, Multidisciplinary
M. Mierzejewski, J. Herbrych, P. Prelovsek
Summary: In studying ballistic transport in integrable quantum lattice models, it is found that a discontinuous reduction occurs when interaction is introduced, which is related to the large degeneracy of the parent noninteracting models. These degeneracies can be accurately captured by degenerate perturbation calculations and trace back to the nonlocal character of the effective interaction.
Article
Engineering, Industrial
Francesco Zanlungo, Claudio Feliciani, Zeynep Yucel, Katsuhiro Nishinari, Takayuki Kanda
Summary: In this study, we reproduced the behavior of a human crowd in a cross-flow using a hierarchy of models. The most detailed model, incorporating body shape information and an elliptical body, outperformed the simplest model. When elliptical bodies were introduced without considering collision avoidance information, the model's performance was relatively poor. The differences between the models were mainly related to the tails of the observable distributions, suggesting that the more complex models may be useful in high density settings.
Article
Mathematics, Applied
Simone Goettlich, Michael Herty, Salissou Moutari, Jennifer Weissen
Summary: This paper presents a new approach for traffic flow modeling, which approximates the homogenized pressure well and shows effectiveness through numerical simulations and comparative analysis with other methods.
SIAM JOURNAL ON APPLIED MATHEMATICS
(2021)
Article
Engineering, Industrial
Francesco Zanlungo, Claudio Feliciani, Zeynep Yucel, Katsuhiro Nishinari, Takayuki Kanda
Summary: In this research, the behavior of a human crowd crossing an intersection is investigated through controlled experiments. The study defines and investigates macroscopic and microscopic observables, including traditional indicators such as density and velocity, as well as walking and body orientation. Additionally, a preliminary quantitative analysis is conducted on the emergence of self-organizing patterns in the crossing area.
Article
Mathematics, Applied
Maria Colombo, Gianluca Crippa, Elio Marconi, Laura V. Spinolo
Summary: In this work, we discuss the singular local limit of nonlocal conservation laws in the modeling of vehicular traffic. We obtain general convergence results under assumptions that are entirely natural in view of applications to traffic models, plus a convexity requirement on the convolution kernels. We also provide a general criterion for entropy admissibility of the limit and a convergence rate.
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2023)
Article
Mathematics, Applied
Nicolas Laurent-Brouty, Guillaume Costeseque, Paola Goatin
Summary: This paper introduces a new macroscopic traffic flow model that takes into account the boundedness of traffic acceleration. By using a wave-front tracking algorithm, the paper constructs approximate solutions and proves the existence of entropy weak solutions to the associated Cauchy problem. Numerical simulations are provided to illustrate the solution behavior.
SIAM JOURNAL ON APPLIED MATHEMATICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Chao Yan, James G. McDonald
Summary: The ten-moment equations are a first-order alternative to the Navier-Stokes equations in the absence of heat transfer. They are advantageous due to their first-order hyperbolic conservation laws. However, the lack of suitable turbulence models limits their applicability.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Engineering, Multidisciplinary
Jeffrey Belding, Monika Neda, Rihui Lan
Summary: In this paper, a finite element study is conducted for the family of Time Relaxation models using the EMAC discretization method. The conservation properties, stability, and error estimates are analyzed in the fully discrete case, and comparisons with the classical skew symmetric non-linear formulation are made. It is shown that the error estimate for EMAC is improved compared to the skew symmetric scheme, and numerical experiments in 2D and 3D demonstrate the advantage of EMAC over skew symmetric.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics, Applied
Marco Di Francesco, Simone Fagioli, Massimiliano Daniele Rosini, Giovanni Russo
KINETIC AND RELATED MODELS
(2017)
Article
Mathematics, Interdisciplinary Applications
Andrea Corli, Lorenzo di Ruvo, Luisa Malaguti, Massimiliano D. Rosini
NETWORKS AND HETEROGENEOUS MEDIA
(2017)
Article
Mathematics, Applied
Boris Andreianov, Carlotta Donadello, Ulrich Razafison, Massimiliano D. Rosini
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
(2018)
Article
Mathematics, Applied
Nikodem S. Dymski, Paola Goatin, Massimiliano D. Rosini
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2018)
Article
Mathematics, Applied
Andrea Corli, Magdalena Figiel, Anna Futa, Massimiliano D. Rosini
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2018)
Article
Mathematics, Applied
Mohamed Benyahia, Carlotta Donadello, Nikodem Dymski, Massimiliano D. Rosini
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS
(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, Applied
Mohamed Benyahia, Massimiliano D. Rosini
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(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
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
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
M. Di Francesco, S. Fagioli, M. D. Rosini
BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA
(2017)
Article
Mathematical & Computational Biology
Marco Di Francesco, Simone Fagioli, Massimillano D. Rosini
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2017)
Article
Mathematics
Daniele Cassani, Zhisu Liu, Giulio Romani
Summary: This article investigates the strongly coupled nonlinear Schrodinger equation and Poisson equation in two dimensions. The existence of solutions is proved using a variational approximating procedure, and qualitative properties of the solutions are established through the moving planes technique.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2024)
Article
Mathematics
Giovanni Alessandrini, Romina Gaburro, Eva Sincich
Summary: This paper considers the inverse problem of determining the conductivity of a possibly anisotropic body Ω, subset of R-n, by means of the local Neumann-to-Dirichlet map on a curved portion Σ of its boundary. Motivated by the uniqueness result for piecewise constant anisotropic conductivities, the paper provides a Hölder stability estimate on Σ when the conductivity is a priori known to be a constant matrix near Σ.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2024)
Article
Mathematics
Nuno Costa Dias, Cristina Jorge, Joao Nuno Prata
Summary: This article studies the time dependent Euler-Bernoulli beam equation with discontinuous and singular coefficients, and obtains an explicit formulation of the differential problem using an extension of the Hormander product of distributions. The dynamics of the Euler-Bernoulli beam model with discontinuous flexural stiffness and structural cracks are further explored, and the relationship between the characteristic frequencies of the beam and the singularities in the flexural stiffness is investigated.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2024)
Article
Mathematics
Baoquan Zhou, Hao Wang, Tianxu Wang, Daqing Jiang
Summary: This paper is Part I of a two-part series that presents a mathematical framework for approximating the invariant probability measures and density functions of stochastic generalized Kolmogorov systems with small diffusion. It introduces two new approximation methods and demonstrates their utility in various applications.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2024)
Article
Mathematics
Yun Li, Danhua Jiang, Zhi-Cheng Wang
Summary: In this study, a nonlocal reaction-diffusion equation is used to model the growth of phytoplankton species in a vertical water column with changing-sign advection. The species relies solely on light for metabolism. The paper primarily focuses on the concentration phenomenon of phytoplankton under conditions of large advection amplitude and small diffusion rate. The findings show that the phytoplankton tends to concentrate at certain critical points or the surface of the water column under these conditions.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2024)
Article
Mathematics
Monica Conti, Stefania Gatti, Alain Miranville
Summary: The aim of this paper is to study a perturbation of the Cahn-Hilliard equation with nonlinear terms of logarithmic type. By proving the existence, regularity and uniqueness of solutions, as well as the (strong) separation properties of the solutions from the pure states, we finally demonstrate the convergence to the Cahn-Hilliard equation on finite time intervals.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2024)
Article
Mathematics
Qi Qiao
Summary: This paper investigates a volume-filling chemotaxis model with a small cell diffusion coefficient and chemotactic sensitivity. By using the geometric singular perturbation theory, the existence of a positive traveling wave connecting two constant steady states is confirmed. The monotonicity of the wave is analyzed for different parameter ranges, and spectral instability is observed in some exponentially weighted spaces.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2024)
Article
Mathematics
Xiaolong He
Summary: This article employs the CWB method to construct quasi-periodic solutions for nonlinear delayed perturbation equations, and combines the techniques of Green's function estimate and the reducibility method in KAM theory to solve the linear equation, thus extending the applicability of the CWB method. As an application, it studies the positive quasi-periodic solutions for a class of Lotka-Volterra equations with quasi-periodic coefficients and time delay.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2024)
Article
Mathematics
Nicolas Camps, Louise Gassot, Slim Ibrahim
Summary: In this paper, we consider the probabilistic local well-posedness problem for the Schrodinger half-wave equation with a cubic nonlinearity in quasilinear regimes. Due to the lack of probabilistic smoothing in the Picard's iterations caused by high-low-low nonlinear interactions, we need to use a refined ansatz. The proof is an adaptation of Bringmann's method on the derivative nonlinear wave equation [6] to Schrodinger-type equations. In addition, ill-posedness results for this equation are discussed.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2024)
Article
Mathematics
Elie Abdo, Mihaela Ignatova
Summary: In this study, we investigate the Nernst-Planck-Navier-Stokes system with periodic boundary conditions and prove the exponential nonlinear stability of constant steady states without constraints on the spatial dimension. We also demonstrate the exponential stability from arbitrary large data in the case of two spatial dimensions.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2024)
Article
Mathematics
Peter De Maesschalck, Joan Torregrosa
Summary: This paper provides the best lower bound for the number of critical periods of planar polynomial centers known up to now. The new lower bound is obtained in the Hamiltonian class and considering a single period annulus. The key idea is the perturbation of a vector field with many cusp equilibria, which is constructed using elements of catastrophe theory.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2024)
Article
Mathematics
Leyi Jiang, Taishan Yi, Xiao-Qiang Zhao
Summary: This paper studies the propagation dynamics of a class of integro-difference equations with a shifting habitat. By transforming the equation using moving coordinates and establishing the spreading properties of solutions and the existence of nontrivial forced waves, the paper contributes to the understanding of the propagation properties of the original equation.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2024)
Article
Mathematics
Mckenzie Black, Changhui Tan
Summary: This article investigates a family of nonlinear velocity alignments in the compressible Euler system and shows the asymptotic emergent phenomena of alignment and flocking. Different types of nonlinearity and nonlocal communication protocols are studied, resulting in a variety of different asymptotic behaviors.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2024)
Article
Mathematics
Lorenzo Cavallina
Summary: In this paper, the concept of variational free boundary problem is introduced, and a unified functional-analytical framework is provided for constructing families of solutions. The notion of nondegeneracy of a critical point is extended to this setting.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2024)
Article
Mathematics
Ying-Chieh Lin, Kuan-Hsiang Wang, Tsung-Fang Wu
Summary: In this study, we investigate a linearly coupled Schrodinger system and establish the existence of positive ground states under suitable assumptions and by using variational methods. We also relax some of the conditions and provide some results on the existence of positive ground states to a linearly coupled Schrodinger system in a bounded domain.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2024)
