OPAC - Pencarian Artikel Jurnal & Majalah Library USD
Menampilkan semua artikel (Halaman 228 dari 34169, Total: 341690 data)
Minnaert Resonances for Bubbles in Soft Elastic Materials
klik untuk membaca file PDF
| Pengarang | : | Hongjie Li |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 1) |
| Halaman | : | 119-141 |
| Abstrak | : | Minnaert resonance is a widely known acoustic phenomenon, and it has many important applications, in particular in the effective realization of acoustic metamaterials using bubbly media in recent years. In this paper, motivated by the Minnaert resonance in acoustics, we consider the low-frequency resonance for acoustic bubbles embedded in soft elastic materials. This is a hybrid physical process that couples the acoustic and elastic wave propagations. By delicately and subtly balancing the acoustic and elastic parameters as well as the geometry of the bubble, we show that Minnaert resonance can occur (at least approximately) for rather general constructions. Our study highlights the great potential for the effective realization of negative elastic materials by using bubbly elastic media. |
A Spatiotemporal Model for the Effects of Toxicants on Populations in a Polluted River
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 1) |
| Halaman | : | 95-118 |
| Abstrak | : | One reason why polluted water is the growing global concern is because it persists to pose threats to the health of aquatic life. To study the effects of environmental toxicants on population dynamics in polluted rivers, we develop a process-oriented model that describes the interaction between a population and a toxicant in an advective environment. The model consists of two reaction-diffusion-advection equations, one of which governs the dispersal and growth of the population under the influence of toxicants, while the other describes the dispersal, input, as well as decay of the toxicant. We explore the existence and stability of steady states based on the analysis of eigenvalue problems, which yields sufficient conditions that lead to population persistence or extinction. We numerically analyze how the interplay between several factors (toxicant input, flow velocity, the diffusion and advection characteristics of the population and the toxicant) affects the persistence and spatial distribution of the population. |
Elementary Mechanics of the Mitral Valve
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 1) |
| Halaman | : | 75-94 |
| Abstrak | : | We illustrate a bare-bones mathematical model that is able to account for the elementary mechanics of the mitral valve when the leaflets of the valve close under the systolic pressure. The mechanical model exploits the aspect ratio of the valve leaflets that are represented as inextensible rods, subject to the blood pressure, with one fixed endpoint (on the endocardium) and an attached wire anchored to the papillary muscle. Force and torque balance equations are obtained exploiting the principle of virtual work, where the first contact point between rods is identified by the Weierstrass--Erdmann condition of variational nature. The chordae tendineae are modeled as a force applied to the free endpoint of the flaps. Different possible boundary conditions are investigated at the mitral annulus, and, by an asymptotic analysis, we demonstrate that in the pressure regime of interest generic boundary conditions generate a tensional boundary layer. Conversely, a specific choice of the boundary condition inhibits the generation of high tensional gradients in a small layer. |
Defect Resonances of Truncated Crystal Structures
| Pengarang | : | Jianfeng Lu |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 1) |
| Halaman | : | 49-74 |
| Abstrak | : | Defects in the atomic structure of crystalline materials may spawn electronic bound states, known as defect states, which decay rapidly away from the defect. Simplified models of defect states typically assume the defect is surrounded on all sides by an infinite perfectly crystalline material. In reality the surrounding structure must be finite, and in certain contexts the structure can be small enough that edge effects are significant. In this work we investigate these edge effects and prove the following result. Suppose that a one-dimensional infinite crystalline material hosting a positive energy defect state is truncated a distance ???? from the defect. Then, for sufficiently large ????, there exists a resonance exponentially close (in ????) to the bound state eigenvalue. It follows that the truncated structure hosts a metastable state with an exponentially long lifetime. Our methods allow both the resonance frequency and associated resonant state to be computed to all orders in ????−????. We expect this result to be of particular interest in the context of photonic crystals, where defect states are used for wave-guiding and structures are relatively small. Finally, under a mild additional assumption we prove that if the defect state has negative energy, then the truncated structure hosts a bound state with exponentially close energy. |
Optimizing Noisy Complex Systems Liable to Failure
| Pengarang | : | Davin Lunz |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 1) |
| Halaman | : | 25-48 |
| Abstrak | : | Inspired by complex systems in social and industrial contexts, we consider a family of coupled diffusion processes modeling system components and an associated system objective. Each process is inherently noisy, driven by a controllable drift, and fails upon reaching a critical state. Interdependence is captured via the global objective and the governing dynamics (correlated noise, cascading failures). Analytical and numerical calculations reveal that the optimal strategies to steer such systems to maximize the objective are highly coupled, depending strongly on the state of the entire system. Strikingly, they exhibit a rich set of bifurcations, describing qualitatively different strategies throughout the parameter space. |
On Geometrical Properties of Electromagnetic Transmission Eigenfunctions and Artificial Mirage
| Pengarang | : | Youjun Deng |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 1) |
| Halaman | : | 1-24 |
| Abstrak | : | Transmission eigenfunctions are certain interior resonant modes that are of central importance to the wave scattering theory. In this paper, we present the discovery of novel global rigidity properties of the transmission eigenfunctions associated with the Maxwell system. It is shown that the transmission eigenfunctions carry the geometrical information of the underlying domain. We present both analytical and numerical results of these intriguing rigidity properties. As an interesting application, we propose an illusion scheme of artificially generating a mirage image of any given optical object. |
Phase Separation in Systems of Interacting Active Brownian Particles
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 4) |
| Halaman | : | 1635-1660 |
| Abstrak | : | The aim of this paper is to discuss the mathematical modeling of Brownian active particle systems, a recently popular paradigmatic system for self-propelled particles. We present four microscopic models with different types of repulsive interactions between particles and their associated macroscopic models, which are formally obtained using different coarse-graining methods. The macroscopic limits are integro-differential equations for the density in phase space (positions and orientations) of the particles and may include nonlinearities in both the diffusive and advective components. In contrast to passive particles, systems of active particles can undergo phase separation without any attractive interactions, a mechanism known as motility-induced phase separation (MIPS). We explore the onset of such a transition for each model in the parameter space of occupied volume fraction and Pe?clet number via a linear stability analysis and numerical simulations at both the microscopic and macroscopic levels. We establish that one of the models, namely, the mean-field model which assumes long-range repulsive interactions, cannot explain the emergence of MIPS. In contrast, MIPS is observed for the remaining three models that assume short-range interactions that localize the interaction terms in space. |
On the Validity of the Tight-Binding Method for Describing Systems of Subwavelength Resonators
| Pengarang | : | Habib Ammari |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 4) |
| Halaman | : | 1611-1634 |
| Abstrak | : | The goal of this paper is to relate the capacitance matrix formalism to the tight-binding approximation. By doing so, we open the way to the use of mathematical techniques and tools from condensed matter theory in the mathematical and numerical analysis of metamaterials, in particular for the understanding of their topological properties. We first study how the capacitance matrix formalism, both when the material parameters are static and modulated, can be posed in a Hamiltonian form. Then, we use this result to compare this formalism to the tight-binding approximation. We prove that the correspondence between the capacitance formulation and the tight-binding approximation holds only in the case of dilute resonators. On the other hand, the tight-binding model is often coupled with a nearest-neighbor approximation, whereby long-range interactions are neglected. Even in the dilute case, we show that long-range interactions between subwavelength resonators are relatively strong and nearest-neighbor approximations are not generally appropriate. |
On the Dynamics of a Diffusive Foot-and-Mouth Disease Model with Nonlocal Infections
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 4) |
| Halaman | : | 1587-1610 |
| Abstrak | : | Foot-and-mouth disease (FMD) is an acute and highly contagious infectious disease of cloven-hoofed animals. In order to reveal the transmission dynamics and explore effective control measures of FMD, we formulate a diffusive FMD model with a fixed latent period and nonlocal infections. The threshold dynamics of the FMD model are determined by using the basic reproduction number R0: if R0 <1, then the disease-free equilibrium ????0 is globally asymptotically stable; otherwise ????0 is unstable, and there exists an endemic equilibrium ????∗. Numerical simulations confirm the theoretical results and suggest that reducing the direct contact rate ????1 and the indirect contact rate ????2 is important in relieving FMD outbreaks. More importantly, we obtain the effect of diffusion on the time from initial values to steady state when R0 >1: at a low infection level, the faster the infectious individuals and virus diffuse, the faster the disease reaches the steady state. However, at a high infection level (i.e., the value of R0 is relatively large), the influence of diffusion on time from initial values to steady state is more complicated, but at least it is certain that the time will be shortened overall. By carrying out some sensitivity analysis of R0?( >1) and the equilibrium value of the infectious individuals ????∗ in terms of ????1 and ????2, it is found that the (????1,????2)-plane is divided into two regions by the intersection of two parameter-related surfaces; the sensitivity of R0 and ????∗ varies when ????1 and ????2 belong to different regions. When the values of both ????1 and ????2 are very large or very small, ????1 plays a more significant role in the transmission of FMD. These results indicate that stamping out the infected individuals and blocking the epidemic spots and areas are effective in preventing and controlling the spread of FMD. |
Efficient and Reliable Overlay Networks for Decentralized Federated Learning
| Pengarang | : | Yifan Hua |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 4) |
| Halaman | : | 1558-1586 |
| Abstrak | : | We propose near-optimal overlay networks based on ????-regular expander graphs to accelerate decentralized federated learning (DFL) and improve its generalization. In DFL a massive number of clients are connected by an overlay network, and they solve machine learning problems collaboratively without sharing raw data. Our overlay network design integrates spectral graph theory and the theoretical convergence and generalization bounds for DFL. As such, our proposed overlay networks accelerate convergence, improve generalization, and enhance robustness to client failures in DFL with theoretical guarantees. Also, we present an efficient algorithm to convert a given graph to a practical overlay network and maintain the network topology after potential client failures. We numerically verify the advantages of DFL with our proposed networks on various benchmark tasks, ranging from image classification to language modeling using hundreds of clients. |