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Theoretical Analysis of Rolling Fluid Turbines
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| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 1) |
| Halaman | : | 313-329 |
| Abstrak | : | The rolling fluid turbine is a bladeless hydraulic device that exhibits peculiar behavior, making it interesting from the aspect of fluid dynamics. The rotor of this turbine has an unusually symmetrical shape and can rotate in two directions---the one it “chooses" seems to be random. Explanation of the underlying hydraulic mechanism is an open problem, which we tackle here. This paper suggests that the hydraulic force on the rotor acts as positive feedback on the motion of the rotor itself. Such an effect can exist since the system is thermodynamically open. Power generation is described in an analytical computation based mostly on the arguments of symmetry. The result is then tested in a numerical simulation. |
Piecewise Linear Model of Phytoplankton Wave Propagation in Periodical Vortex Flow
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 1) |
| Halaman | : | 294-312 |
| Abstrak | : | A piecewise linear model of phytoplankton growth in the presence of a convective flow has been proposed in the paper. The model, in one-dimensional formulation, admits a stable autowave solution, propagating with a certain critical minimum velocity. The main purpose of the work is to study the features of the phytoplankton front propagation in the presence of vortex flow. The vortex flow represents chain of two-dimensional vortices described by the Taylor--Green solution of incompressible Navier--Stokes equations. Different regimes of wave propagation are revealed depending on the intensity of the vortex flow and the model parameters. In particular, the wobbling, zigzag, and jumping regimes are found if the velocity of convective flow is less or comparable, exceeds, and is much greater than the front propagation speed in still media, respectively. The front propagation velocity is characterized by definite types of dependence on the flow intensity in different regimes. |
Development of Fibrin Branch Structure Before and After Gelation
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 1) |
| Halaman | : | 267-293 |
| Abstrak | : | In [Fogelson and Keener, Phys. Rev. E, 81 (2010), 051922], we introduced a kinetic model of fibrin polymerization during blood clotting that captured salient experimental observations about how the gel branching structure depends on the conditions under which the polymerization occurs. Our analysis there used a moment-based approach that is valid only before the finite time blow-up that indicates formation of a gel. Here, we extend our analyses of the model to include both pregel and postgel dynamics using the PDE-based framework we introduced in [Fogelson and Keener, SIAM J. Appl. Math., 75 (2015), pp. 1346--1368]. We also extend the model to include spatial heterogeneity and spatial transport processes. Studies of the behavior of the model reveal different spatial-temporal dynamics as the time scales of the key processes of branch formation, monomer introduction, and diffusion are varied. |
Modified Sampling Method with Near Field Measurements
| Pengarang | : | Xiaodong Liu |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 1) |
| Halaman | : | 244-266 |
| Abstrak | : | This paper investigates the inverse scattering problems using sampling methods with near field measurements. The near field measurements appear in two classical inverse scattering problems: inverse scattering for obstacles and interior inverse scattering for cavities. We propose modified sampling methods to treat these two classical problems using near field measurements without making any asymptotic assumptions on the distance between the measurement surface and the scatterers. We provide theoretical justifications based on the factorization of the near field operator in both the symmetric factorization case and the nonsymmetric factorization case. Furthermore, we introduce a data completion algorithm which allows us to apply the modified sampling methods to treat the limited-aperture inverse scattering problems. Finally, numerical examples are provided to illustrate the modified sampling methods with both full- and limited-aperture near field measurements. |
Stability of a Nonlocal Traffic Flow Model for Connected Vehicles
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 1) |
| Halaman | : | 221-243 |
| Abstrak | : | The emerging connected and automated vehicle technologies allow vehicles to perceive and process traffic information in a wide spatial range. Modeling nonlocal interactions between connected vehicles and analyzing their impact on traffic flows become important research questions to traffic planners. This paper considers a particular nonlocal LWR model that has been studied in the literature. The model assumes that vehicle velocities are controlled by the traffic density distribution in a nonlocal spatial neighborhood. By conducting stability analysis of the model, we obtain that, under suitable assumptions on how the nonlocal information is utilized, the nonlocal traffic flow is stable around the uniform equilibrium flow and all traffic waves dissipate exponentially. Meanwhile, improper use of the nonlocal information in the vehicle velocity selection could result in persistent traffic waves. Such results can shed light on the future design of driving algorithms for connected and automated vehicles. |
Reconstructing the Thermal Phonon Transmission Coefficient at Solid Interfaces in the Phonon Transport Equation
| Pengarang | : | Irene M. Gamba |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 1) |
| Halaman | : | 194-220 |
| Abstrak | : | The ab initio model for heat propagation is the phonon transport equation, a Boltzmann-like kinetic equation. When two materials are put side by side, the heat that propagates from one material to the other experiences thermal boundary resistance. Mathematically, it is represented by the reflection coefficient of the phonon transport equation on the interface of the two materials. This coefficient takes different values at different phonon frequencies, between different materials. In experiments scientists measure the surface temperature of one material to infer the reflection coefficient as a function of phonon frequency. In this article, we formulate this inverse problem in an optimization framework and apply the stochastic gradient descent (SGD) method for finding the optimal solution. We furthermore prove the maximum principle and show the Lipschitz continuity of the Fre?chet derivative. These properties allow us to justify the application of SGD in this setup. |
Economy and Foreign Exchange Reserves in Cross-Strait Relations: An Analysis from the Dynamics of Taiwan's Economy and Trade Policy
| Pengarang | : | Harryanto Aryodiguno |
| Nama Majalah/Jurnal | : | The Indonesian Quarterly |
| Volume / Edisi | : | 52 (No. 3) |
| Halaman | : | 199-219 |
| Abstrak | : | Abstrak tidak tersedia. |
Homogenization of Spirally Wound High-Contrast Layered Materials
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 1) |
| Halaman | : | 168-193 |
| Abstrak | : | Asymptotic homogenization is used to systematically derive reduced-order macroscopic models of conductive behavior in spirally wound layered materials in which the layers have very different conductivities. The problem is motivated by the need for simplified models of the electrical and thermal behavior of lithium-ion cells, accounting for the highly conductive metallic current collectors and relatively poorly conductive electrodes. We identify and study three distinguished limits and then describe two composite models which each provide a uniform approximation spanning two distinguished limits. We compare the results of the various reduced-order models with calculations of the full model on a detailed geometry to give a guide to the accuracy of the approximations. |
Assessing Chinas Economic Influence in Indonesia: The Case of Jakarta-Bandung High-Speed Rail
| Pengarang | : | Rocky Intan |
| Nama Majalah/Jurnal | : | The Indonesian Quarterly |
| Volume / Edisi | : | 52 (No. 3) |
| Halaman | : | 186-198 |
| Abstrak | : | Abstrak tidak tersedia. |
A Novel Derivation of Rigorous Macroscopic Limits from a Micro-Meso Description of Signal-Triggered Cell Migration in Fibrous Environments
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 1) |
| Halaman | : | 142-167 |
| Abstrak | : | In this work we upscale a prototypical kinetic equation model for a cell population moving in a fibrous environment with a chemo- or haptotactic signal influencing both the direction and the magnitude of the cell velocity. The presented approach to scaling does not rely on orthogonality and treats parabolic and hyperbolic scalings in a unified manner. It is shown that the steps of the formal limit procedures are mirrored by rigorous operations with finite measures provided that the measure-valued position-direction fiber distribution enjoys some spatial continuity. |