| 1. |
- Abdul Salam, Parveena Shamim, et al.
(författare)
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Disease contagion models coupled to crowd motion and mesh-free simulation
- 2021
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Ingår i: Mathematical Models and Methods in Applied Sciences. - : World Scientific. - 0218-2025. ; 31:6, s. 1277-1295
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Tidskriftsartikel (refereegranskat)abstract
- Modeling and simulation of disease spreading in pedestrian crowds have recently become a topic of increasing relevance. In this paper, we consider the influence of the crowd motion in a complex dynamical environment on the course of infection of the pedestrians. To model the pedestrian dynamics, we consider a kinetic equation for multi-group pedestrian flow based on a social force model coupled with an Eikonal equation. This model is coupled with a non-local SEIS contagion model for disease spread, where besides the description of local contacts, the influence of contact times has also been modeled. Hydrodynamic approximations of the coupled system are derived. Finally, simulations of the hydrodynamic model are carried out using a mesh-free particle method. Different numerical test cases are investigated, including uni- and bi-directional flow in a passage with and without obstacles.
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| 2. |
- Abdulle, Assyr, et al.
(författare)
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A parabolic local problem with exponential decay of the resonance error for numerical homogenization
- 2021
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Ingår i: Mathematical Models and Methods in Applied Sciences. - 0218-2025. ; 31:13
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Tidskriftsartikel (refereegranskat)abstract
- This paper aims at an accurate and efficient computation of effective quantities, e.g., the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods are based on a micro-macro coupling, where the macromodel describes the coarse scale behaviour, and the micro model is solved only locally to upscale the effective quantities, which are missing in the macro model. The fact that the micro problems are solved over small domains within the entire macroscopic domain, implies imposing artificial boundary conditions on the boundary of the microscopic domains. A naive treatment of these artificial boundary conditions leads to a first order error in ε/δ, where ε < δ represents the characteristic length ofthe small scale oscillations and δ^d is the size of micro domain. This error dominates all other errors originating from the discretization of the macro and the micro problems, and its reduction is a main issue in today’s engineering multiscale computations. The objective of the present work is to analyse a parabolic approach, first announced in [A. Abdulle,D. Arjmand, E. Paganoni, C. R. Acad. Sci. Paris, Ser. I, 2019], for computing the homogenized coefficients with arbitrarily high convergence rates in ε/δ. The analysis covers the setting of periodic microstructure,and numerical simulations are provided to verify the theoretical findings for more general settings, e.g. non-periodic micro structures.
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| 3. |
- Abdulle, Assyr, et al.
(författare)
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A parabolic local problem with exponential decay of the resonance error for numerical homogenization
- 2021
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Ingår i: Mathematical Models and Methods in Applied Sciences. - : World Scientific Pub Co Pte Ltd. - 0218-2025 .- 1793-6314. ; 31:13, s. 2733-2772
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Tidskriftsartikel (refereegranskat)abstract
- This paper aims at an accurate and efficient computation of effective quantities, e.g. the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods are based on a micro–macro-coupling, where the macromodel describes the coarse scale behavior, and the micromodel is solved only locally to upscale the effective quantities, which are missing in the macromodel. The fact that the microproblems are solved over small domains within the entire macroscopic domain, implies imposing artificial boundary conditions on the boundary of the microscopic domains. A naive treatment of these artificial boundary conditions leads to a first-order error in ?/??/δ, where ?<??<δ represents the characteristic length of the small scale oscillations and ??δd is the size of microdomain. This error dominates all other errors originating from the discretization of the macro and the microproblems, and its reduction is a main issue in today’s engineering multiscale computations. The objective of this work is to analyze a parabolic approach, first announced in A. Abdulle, D. Arjmand, E. Paganoni, C. R. Acad. Sci. Paris, Ser. I, 2019, for computing the homogenized coefficients with arbitrarily high convergence rates in ?/??/δ. The analysis covers the setting of periodic microstructure, and numerical simulations are provided to verify the theoretical findings for more general settings, e.g. non-periodic microstructures.
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| 4. |
- Altmann, Robert, et al.
(författare)
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Quantitative Anderson localization of Schrodinger eigenstates under disorder potentials
- 2020
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Ingår i: Mathematical Models and Methods in Applied Sciences. - : World Scientific. - 0218-2025. ; 30:5, s. 917-955
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Tidskriftsartikel (refereegranskat)abstract
- This paper analyzes spectral properties of linear Schrodinger operators under oscillatory high-amplitude potentials on bounded domains. Depending on the degree of disorder, we prove the existence of spectral gaps among the lowermost eigenvalues and the emergence of exponentially localized states. We quantify the rate of decay in terms of geometric parameters that characterize the potential. The proofs are based on the convergence theory of iterative solvers for eigenvalue problems and their optimal local operator preconditioning by domain decomposition.
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| 5. |
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| 6. |
- Babuska, I., et al.
(författare)
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Solving stochastic partial differential equations based on the experimental data
- 2003
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Ingår i: Mathematical Models and Methods in Applied Sciences. - 0218-2025. ; 13:3, s. 415-444
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Tidskriftsartikel (refereegranskat)abstract
- We consider a stochastic linear elliptic boundary value problem whose stochastic coefficient a(x, omega) is expressed by a finite number N-KL of mutually independent random variables, and transform this problem into a deterministic one. We show how to choose a suitable N-KL which should be as low as possible for practical reasons, and we give the a priori estimates for modeling error when a(x, omega) is completely known. When a random function a(x, omega) is selected to fit the experimental data, we address the estimation of the error in this selection due to insufficient experimental data. We present a simple model problem, simulate the experiments, and give the numerical results and error estimates.
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| 7. |
- Beilina, L., et al.
(författare)
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A posteriori error estimation in computational inverse scattering
- 2005
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Ingår i: Mathematical Models and Methods in Applied Sciences. - 0218-2025. ; 15:1, s. 23-35
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Tidskriftsartikel (refereegranskat)abstract
- We prove an a posteriori error estimate for an inverse acoustic scattering problem, where the objective is to reconstruct an unknown wave speed coefficient inside a body from measured wave reflection data in time on parts of the surface of the body. The inverse problem is formulated as a problem of finding a zero of a Jacobian of a Lagrangian. The a posterori error estimate couples residuals of the computed solution to weights the reconstruction reflecting the sensitivity of the reconstruction obtained by solving an associated linaerized problem for the Hessian of the Lagrangian. We show concrete examples of reconstrution including a posteriori error estimation.
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| 8. |
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| 9. |
- Carlen, E., et al.
(författare)
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Kinetic Limits for Pair-Interaction Driven Master Equations and Biological Swarm Models
- 2013
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Ingår i: Mathematical Models and Methods in Applied Sciences. - 0218-2025. ; 23:7, s. 1339-1376
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Tidskriftsartikel (refereegranskat)abstract
- We consider a class of stochastic processes modeling binary interactions in an N-particle system. Examples of such systems can be found in the modeling of biological swarms. They lead to the definition of a class of master equations that we call pair-interaction driven master equations. In the spatially homogeneous case, we prove a propagation of chaos result for this class of master equations which generalizes Mark Kac's well-known result for the Kac model in kinetic theory. We use this result to study kinetic limits for two biological swarm models. We show that propagation of chaos may be lost at large times and we exhibit an example where the invariant density is not chaotic.
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| 10. |
- Ciallellla, Alessandro, et al.
(författare)
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Free to move or trapped in your group : Mathematical modeling of information overload and coordination in crowded populations
- 2018
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Ingår i: Mathematical Models and Methods in Applied Sciences. - Singapore : World Scientific. - 0218-2025. ; 28:9, s. 1831-1856
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Tidskriftsartikel (refereegranskat)abstract
- We present modeling strategies that describe the motion and interaction of groups of pedestrians in obscured spaces. We start off with an approach based on balance equations in terms of measures and then we exploit the descriptive power of a probabilistic cellular automaton model. Based on a variation of the simple symmetric random walk on the square lattice, we test the interplay between population size and an interpersonal attraction parameter for the evacuation of confined and darkened spaces. We argue that information overload and coordination costs associated with information processing in small groups are two key processes that influence the evacuation rate. Our results show that substantial computational resources are necessary to compensate for incomplete information - the more individuals in (information processing) groups the higher the exit rate for low population size. For simple social systems, it is likely that the individual representations are not redundant and large group sizes ensure that this non-redundant information is actually available to a substantial number of individuals. For complex social systems, information redundancy makes information evaluation and transfer inefficient and, as such, group size becomes a drawback rather than a benefit. The effect of group sizes on outgoing fluxes, evacuation times and wall effects is carefully studied with a Monte Carlo framework accounting also for the presence of an internal obstacle.
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