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- Aiki, Toyohiko, et al.
(författare)
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Differentiability of a solution of a free boundary problem describing water adsorption
- 2020
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Ingår i: Advances in Mathematical Sciences and Applications. - : GAKKO TOSHO CO. - 1343-4373. ; 29, s. 247-282
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Tidskriftsartikel (refereegranskat)abstract
- Sato-Aiki-Murase-Shirakawa [7, 16] proposed a free boundary problem in order to describe water adsorption appearing in moisture transport of concrete carbonation process. The problem is to find a pair of a curve and a function for given boundary and initial functions. In this paper we consider that the boundary and initial functions depend on some parameter. Kumazaki [9, 10] already proved the continuous and measurable properties of solutions with respect to the parameter. The aim of this paper is to establish differentiability of solutions with respect to the parameter as a new property. This result will be applied to research of the multi-scale model to water adsorption in concrete carbonation.
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| 5. |
- Cirillo, Emilio N. M., et al.
(författare)
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Anticipation decides on lane formation in pedestrian counterflow - a simulation study
- 2020
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Ingår i: Advances in Mathematical Sciences and Applications. - Tokyo, Japan : Gakko Tosho. - 1343-4373. ; 29:1, s. 171-185
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Tidskriftsartikel (refereegranskat)abstract
- Human crowds base most of their behavioral decisions upon anticipated states oftheir walking environment. We explore a minimal version of a lattice model to study lanesformation in pedestrian counterow. Using the concept of horizon depth, our simulationresults suggest that the anticipation eect together with the presence of a small backgroundnoise play an important role in promoting collective behaviors in a counterow setup. Theseingredients facilitate the formation of seemingly stable lanes and ensure the ergodicity of the system.
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| 6. |
- Eden, Michael, 1987-
(författare)
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Homogenization of a moving boundary problem with prescribed normal velocity
- 2019
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Ingår i: Advances in Mathematical Sciences and Applications. - Tokyo, Japan : Gakkō Tosho. - 1343-4373. ; 28:2, s. 313-341
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Tidskriftsartikel (refereegranskat)abstract
- The analysis and homogenization of a heat conduction problem with moving boundary for a two-phase medium is considered. The medium in question is assumed to be highly heterogeneous with a high contrast in the heat conductivities. In this context, the normal velocity governing the motion of the interface separating the two competing phases is assumed to be prescribed. Parametrizing the boundary motion via a height function, the so-called Direct Mapping Method is employed to construct a coordinate transform characterizing the changes with respect to the initial setup of the geometry. Using this transform, well-posedness of the problem is established. After characterizing the limit behavior (with respect to the heterogeneity parameter) of the functions related to the transformation, the corresponding homogenized problem is deduced.
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| 8. |
- Grützner, Simon, et al.
(författare)
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Identifying processes governing damage evolution in quasi-static elasticity : Part 1- Analysis
- 2021
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Ingår i: Advances in Mathematical Sciences and Applications. - : GAKKO TOSHO. - 1343-4373. ; 30:2, s. 305-334
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Tidskriftsartikel (refereegranskat)abstract
- We present a quasi-static elasticity model that accounts for damage evolution. We show well-posedness of the resulting strongly nonlinear system of differential equations. The specific feature is the connection of dis-placements to damage evolution via a Nemytskii- or superposition- operator. From a material modelling perspective, the shape of this operator defines the afforementioned connection. The novelty in this work is the presentation of an inverse problem to identify the shape of this Nemytskii-operator. We establish the Fréchet-derivative of the forward operator as well as the adjoint of the derivative and characterize both via systems of linear differential equations. We prove ill-posedness of the inverse problem and provide asufficient condition for the classical nonlinear Landweber method to converge.
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| 9. |
- Grützner, Simon, et al.
(författare)
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Identifying processes governing damage evolution in quasi-static elasticity. : Part 2 - Numerical simulations
- 2022
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Ingår i: Advances in Mathematical Sciences and Applications. - : GAKKO TOSHO. - 1343-4373. ; 31:1, s. 147-173
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Tidskriftsartikel (refereegranskat)abstract
- We investigate numerically a quasi-static elasticity system of Kachanov-type. To do so we propose an Euler time discretization combined with a suitable finite elements scheme (FEM) to handle the discretization is space. We use ODE-type arguments to prove the consistency of the scheme as well as its convergence rate. We rely on the computational platform FEniCS© to perform the FEM discretizations in space needed to compute the model output. The simulation results show a good agreement with both the physics of the problem and with our previous qualitative mathematical analysis results obtained for precisely the same problem setting. Furthermore, our implementation recovers nicely the theoretically expected convergence rate. This is a preliminary study preparing the framework for the rigorous numerical identification of the damage process in Kachanovtype models.
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