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Local Bifurcation Analysis of Circular von Karman Plate with Kirchhoff Rod Boundary
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| Pengarang | : | Deepankar Das, Basant Lal Sharma |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 4) |
| Halaman | : | 1749-1784 |
| Abstrak | : | Symmetry based reduction is applied to the buckling of a circular von-Kármán plate with Kirchhoff rod boundary, where a mismatch between the edge length and the perimeter of the plate is treated as the bifurcation parameter. A nonlinear operator formulation describes the equilibrium of the elastic rod-plate system. The critical points, as potential bifurcation points, are stated using the linearized operator. The symmetry of null space for each critical point is identified as a subgroup of the complete symmetry group of the nonlinear problem; the equivariance associated with the nonlinear operator is used in this process. Sufficient evidence is provided for each critical point to be a bifurcation point for the symmetry-reduced problem, and postbuckling analysis is carried out using Lyapunov–Schmidt reduction. Bifurcation curves are obtained up to quadratic order in the bifurcation parameter away from each critical value. Theoretical results for bifurcation curves are validated against the numerical simulation based on a symmetry-reduced finite element method for some illustrative examples of critical points. A numerical study is carried out for the dependence of the coefficient of quadratic term in the bifurcation parameter when structural parameters are varied in a neighborhood of four fixed sets of structural parameters. Numerical results based on a symmetry-reduced finite element analysis confirm that the nonlinear solution agrees with the local theoretical behavior close to a critical point but deviates further away from it. Using these tools, two main conclusions are reached. First, it is observed that the critical points of the linearized problem are indeed bifurcation points. Second, an alteration in the nature of bifurcation is observed during the parameter sweep study when the plate is under tension. That is, near certain values of the structural parameters, a supercritical pitchfork bifurcation locally evolves into a subcritical pitchfork. |
ExoMars Rover PanCam: Autonomy and Computational Intelligence
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | IEEE Computational intelligence |
| Volume / Edisi | : | 8 (No. 4) |
| Halaman | : | 52-61 |
| Abstrak | : | - |
Optimal Satellite Formation Reconfiguration Based on Closed-Loop Brain Storm Optimization
| Pengarang | : | Changhao Sun,Yuhui Shi,Haibin Duan |
| Nama Majalah/Jurnal | : | IEEE Computational intelligence |
| Volume / Edisi | : | 8 (No. 4) |
| Halaman | : | 39-51 |
| Abstrak | : | In recent years, satellite formation flying has become an increasingly hot topic for both the astronomy and earth science communities due to its potential merits compared with a single monolithic spacecraft system. This paper proposes a novel approach based on closed-loop brain storm optimization (CLBSO) algorithms to address the optimal formation reconfiguration of multiple satellites using twoimpulse control. The optimal satellite formation reconfiguration is formulated as an optimization problem with the constraints of overall fuel cost minimization, final configuration, and collision avoidance. Three versions of CLBSOs are developed by replacing the creating operator in basic brain storm optimization (BSO) with closed-loop strategies, which facilitate search characteristic capture and enhance the optimization performance by taking advantage of feedback information in the search process. Numerical simulations are carried out using particle swarm optimization (PSO), basic BSO, and the three versions of CLBSOs. Comparison results show that all versions of CLBSOS outperform PSO and the original BSO in terms of final results and convergence speed. In addition, CLBSO reduces the computation burden and shortens CPU time to a certain extent in contrast with basic BSO. Furthermore, among the three CLBSO algorithms, the one using the strategy of difference with the best gains the best overall performance, which is inspired by the updating rule in PSO that each particle tends to move towards the individual with the best fitness. |
Scaling Limit of the Kuramoto Model on Random Geometric Graphs
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 4) |
| Halaman | : | 1719-1748 |
| Abstrak | : | We consider the Kuramoto model on a graph with nodes given by ???? i.i.d. points uniformly distributed on the ???? dimensional torus. Two nodes are declared neighbors if they are at distance less than ????. We prove a scaling limit for this model in compact time intervals as ???? →∞ and ???? →0 such that ????????+2?????/log????? →∞. The limiting object is given by the heat equation. On the one hand, this shows that the nonlinearity given by the sine function disappears under this scaling and, on the other hand, provides evidence that stable equilibria of the Kuramoto model on these graphs are, as ???? →∞, in correspondence with those of the heat equation, which are explicit and given by twisted states. In view of this, we conjecture the existence of twisted stable equilibria with high probability as ???? →∞. |
Information Open Electromagnetic Cloaks: Mathematical Analysis and Numerical Simulations
| Pengarang | : | Fuhao Liu, Jiangqiong Mao, Wei Yang, Jichun Li |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 4) |
| Halaman | : | 1690-1718 |
| Abstrak | : | In this paper, we develop the governing equations for two-dimensional (2D) arbitrary star-shaped information-open (IO) electromagnetic cloaks. These equations consist of time-dependent Maxwell’s equations coupled with ordinary differential equations arising from the Drude dispersion model. We establish the well-posedness of our IO cloak model using the Hille–Yosida theorem. To demonstrate the invisibility cloaking capabilities of our model, we introduce a novel edge finite element time-domain (FETD) scheme for solving this system of governing equations. We provide proof of discrete stability and optimal error estimates for our scheme. Our multifrequency FETD simulations further validate the effective cloaking performance of our IO cloak model. This work represents the first mathematical analysis and time-domain simulation of 2D star-shaped IO electromagnetic cloaks, with promising applications in advanced electromagnetic shielding and stealth technology. |
A Novel Approach for Locating Point Sources in a Diffusive Medium
| Pengarang | : | Shiwei Sun, Haibing Wang |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 4) |
| Halaman | : | 1667-1689 |
| Abstrak | : | We consider the localization of the point sources in a diffusive medium from a single boundary measurement, which can be formulated as an inverse source problem for a diffusion equation. First, using the unique continuation property of solutions to the diffusion equation, we establish the uniqueness of this inverse problem. Then we develop a non-iterative method called the range test (RT) to recover the locations of the point sources. That is, for the point sources located inside a bounded domain Ω, we can detect their locations by examining the solvability of a specified boundary integral equation for a given test domain ???? ?Ω. More precisely, we prove that there are no point sources in Ω ?–––???? if and only if the boundary integral equation associated with ???? is solvable, which reveals the essence of the RT. Next, we design a numerical algorithm to locate a single point source from the boundary measurement. The algorithm consists of two steps: we first determine the annular domain where the point source is located and then orientate the source using an apple-shaped test domain. Moreover, to further show the effectiveness of the RT, we provide two algorithms for two specific cases of multiple point sources: one is that there are two point sources in Ω, and the other is that all point sources are distributed inside a certain annular domain. The algorithms enable us to locate the point sources and estimate the relative magnitude of their intensities in the second case. Then we carry out various numerical experiments to demonstrate the efficiency and effectiveness of our algorithms. The numerical results are reasonable and satisfactory even in the noisy measurement case. Furthermore, for the case that a single point source moves inside Ω, we also give a numerical scheme to track its trajectory. We highlight that the RT can locate the point sources using only a single boundary measurement and requires little a priori information on the point sources. |
Reconstruction Formulae for 3D Field Free Line Magnetic Particle Imaging
| Pengarang | : | Vladyslav Gapyak, Thomas März, Andreas Weinmann |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 4) |
| Halaman | : | 1643-1666 |
| Abstrak | : | Magnetic particle imaging is a promising noninvasive in vivo imaging modality that makes it possible to map the spatial distribution of superparamagnetic nanoparticles by exposing them to dynamic magnetic fields. In the field-free line (FFL) scanner topology, the spatial encoding of the particle distribution is performed by applying magnetic fields vanishing on straight lines. The voltage induced in the receiving coils by the particles when exposed to the magnetic fields constitutes the signal from which the particle distribution is to be reconstructed. To avoid lengthy calibration, model-based reconstruction formulae have been developed for the two-dimensional (2D) FFL scanning topology. In this work we develop reconstruction formulae for 3D FFL. Moreover, we provide a model-based reconstruction algorithm for 3D FFL and we validate it with a numerical experiment. |
PENDUDUK, ANGKATAN KERJA DAN PEMBAGIAN PENDAPATAN: INDONESIA DAN BRASILIA DALAM PERBANDINGAN
| Pengarang | : | Murwatie B. Rahardjo |
| Nama Majalah/Jurnal | : | Analisa |
| Volume / Edisi | : | IX-6, JUNI (No. 6) |
| Halaman | : | 553-572 |
| Abstrak | : | - |
Sharp Material Interface Limit of the Darcy Boussinesq System
| Pengarang | : | Hongjie Dong, Xiaoming Wang |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 4) |
| Halaman | : | 1621-1642 |
| Abstrak | : | We investigate the sharp material interface limit of the Darcy–Boussinesq model for convection in layered porous media with diffused material interfaces, which allow a gradual transition of material parameters between different layers. We demonstrate that as the thickness of these transition layers approaches zero, the conventional sharp interface model with interfacial boundary conditions, commonly adopted by the fluids community, is recovered under the assumption of constant porosity. Our results validate the widely used sharp interface model by bridging it with the more physically realistic case of diffused material interfaces. This limiting process is singular and involves a boundary layer in the velocity field. Our analysis requires delicate estimates for elliptic and parabolic equations with discontinuous coefficients and the subtle validation of the boundary layer. |
The Iterative Persuasion Polarization Opinion Dynamics and Its Mean Field Analysis
| Pengarang | : | Fei Cao, Stephanie Reed |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 4) |
| Halaman | : | 1596-1620 |
| Abstrak | : | In this paper, we introduce the iterative persuasion-polarization (IPP) model to study the dynamics of opinion formation and change within a population. The IPP model integrates mechanisms of persuasion and repulsion, where individuals influence one another through interactions that can either align opinions incrementally or lead to greater divergence. The probability of each interaction type is governed by a parameter ????, representing the population’s receptiveness to persuasion. We investigate how these interaction dynamics shape the long-term distribution of opinions, examining conditions that promote consensus or polarization. By deriving a system of nonlinear and autonomous ordinary differential equations (ODEs), we provide a rigorous mathematical framework for analyzing the distributional behavior of opinions in large populations. Our findings contribute to a deeper understanding of social influence dynamics and their implications in complex social systems. |