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Modelling of Initially Stressed Solids: Structure of the Energy Density in the Incompressible Limit
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| Pengarang | : | Marco Magri, Davide Riccobelli |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 84 (No. 6) |
| Halaman | : | 2342-2364 |
| Abstrak | : | This study addresses the modelling of elastic bodies, particularly when the relaxed configuration is unknown or nonexistent. We adopt the theory of initially stressed materials, incorporating the deformation gradient and stress state of the reference configuration (initial stress tensor) into the response function. We show that for the theory to be applicable, the response function of the relaxed material is invertible up to an element of the material symmetry group. Additionally, we establish that commonly imposed constitutive restrictions, namely the initial stress compatibility condition and initial stress reference independence, naturally arise when assuming the initial stress is generated solely from elastic distortion. This paper delves into modelling aspects concerning incompressible materials, showcasing the expressibility of strain energy density as a function of the deviatoric part of the initial stress tensor and the isochoric part of the deformation gradient. This not only reduces the number of independent invariants in the energy functional, but also enhances numerical robustness in finite element simulations. The findings of this research hold significant implications for modelling materials with initial stress, extending potential applications to areas such as mechanobiology, soft robotics, and 4D printing. |
Infinite-Thin Shock Layer Solutions for Stationary Compressible Conical Flows and Numerical Results via Fourier Spectral Method
| Pengarang | : | Aifang Qu, Xueying Su, Hairong Yuan |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 84 (No. 6) |
| Halaman | : | 2321-2341 |
| Abstrak | : | We consider the problem of steady uniform supersonic inviscid flows passing straight solid cones with attack angles, by studying Radon measure solutions with infinite-thin shock layers for the nonisentropic compressible Euler equations, particularly for the Chaplygin gas and limiting hypersonic flows. This approach also provides a generalized Newton–Busemann law on the distribution of pressures on the cone’s boundary. The construction of Radon measure solutions is reduced to solving a system of nonlinear ordinary differential equations (ODE) for weights of Dirac measures supported on the edge of the cone on the unit 2-sphere. It is further reduced to solving nonnegative periodic solutions of a singular and nonlinear nonautonomous ODE. A numerical algorithm based on the combination of the Fourier spectral method and Newton’s method is developed to solve the ODE. The numerical simulations for different attack angles exhibit proper theoretical properties and excellent accuracy. This research demonstrates the benefits of Radon measure solutions and could be useful for engineering applications in hypersonic aerodynamics. |
Dynamics of an LPAA Model for Tribolium Growth: Insights into Population Chaos
| Pengarang | : | Samantha J. Brozak, Sophia Peralta, Tin Phan, John D. Nagy, Yang Kuang |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 84 (No. 6) |
| Halaman | : | 2300-2320 |
| Abstrak | : | Flour beetles (genus Tribolium) have long been used as a model organism to understand population dynamics in ecological research. A rich and rigorous body of work has cemented flour beetles’ place in the field of mathematical biology. One of the most interesting results using flour beetles is the induction of chaos in a laboratory beetle population, in which the well-established LPA (larvae-pupae-adult) model was used to inform the experimental factors that would lead to chaos. However, whether chaos is an intrinsic property of flour beetles remains an open question. Inspired by new experimental data, we extend the LPA model by stratifying the adult population into newly emerged and mature adults and considering cannibalism as a function of mature adults. We fit the model to longitudinal data of larvae, pupae, and adult beetle populations to demonstrate the model’s ability to recapitulate the transient dynamics of flour beetles. We present local and global stability results for the trivial and positive steady states and explore bifurcations and limit cycles numerically. Our results suggest that, while chaos is a possibility, it is a rare phenomenon within realistic ranges of the parameters obtained from our experiment and is likely induced by environmental changes connected to media changes and population censusing. |
Spectral Diffusion of MMT Model with Condensate in Two or Higher Dimensions
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 84 (No. 6) |
| Halaman | : | 2283-2299 |
| Abstrak | : | We study the spectral evolution of four-wave-resonant systems in the presence of a large-scale strong condensate, using the two-dimensional Majda–McLaughlin–Tabak model as a generalizable example. We show that, under dominance of nonlocal interactions with the condensate, the high-wavenumber spectral evolution is governed by a diffusion equation. Two approaches are developed in deriving the diffusion equation, one starting from the wave kinetic equation of MMT model, and the other starting from the MMT model itself with a WKB analysis, with both yielding the same end result. We further analyze the diffusion dynamics, which is shown to be remarkably different for cases with ?<1 and ?>1, where ? controls the dispersion relation ?=??. For ?<1, the diffusion has similar time scale in radial and circumferential directions, with a stationary constant-flux solution of wave action ??∼?−4? (where ? controls the order of derivatives in the nonlinear term of the MMT model). For ?>1, the diffusion is much faster in circumferential direction, with a stationary solution of ??∼?−4?−3+3?. We finally discuss the extension of results to higher dimensions and the validity of the diffusion equation depending on ? and ?. |
Effects of Dispersal Asymmetry on Disease Spread
| Pengarang | : | Daozhou Gao, Ailing Wang |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 84 (No. 6) |
| Halaman | : | 2258-2282 |
| Abstrak | : | Human movement is a leading cause of the rapid global spread of infectious diseases. Factors such as emerging pathogens and outbreaks, large-scale events, bilateral or multilateral agreements, resource allocation, and urban planning can lead to unsynchronized changes in population movement among regions. In this paper, based on a two-patch susceptible-infected-susceptible model, we investigate the dependence of disease persistence (measured by the basic reproduction number) and disease prevalence (proportion of people being infected) of both patches and each patch on dispersal asymmetry, respectively. It is shown that their dependencies are completely consistent, i.e., strictly increasing, strictly decreasing, or constant. Biologically speaking, an increase in migration from the high-risk patch (where the patch reproduction number is larger) to the low-risk patch (where the patch reproduction number is smaller) will reduce both infection risk and size. In addition, the basic reproduction number and the global and local disease prevalences at zero and infinite dispersal asymmetry are given. Numerical simulations suggest that there are some substantial differences between the two-patch case and the three or more patches case, such as the appearance of Simpson’s paradox on disease prevalence in the three-patch case. |
Existence and Stability of a Boundary Layer with an Interior Spike in the Singularly Perturbed Shadow Gierer–Meinhardt System
| Pengarang | : | Daniel Gomez, Juncheng Wei |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 84 (No. 6) |
| Halaman | : | 2238-2257 |
| Abstrak | : | The singularly perturbed Gierer–Meinhardt (GM) system in a bounded ?-dimensional domain (?≥2) is known to exhibit boundary layer (BL) solutions for a nonzero activator flux. It was previously shown that such BL solutions can be destabilized by decreasing the activator flux below a stability threshold. Moreover, numerical simulations previously indicated that solutions consisting of a boundary layer and an interior spike emerge after the destabilization of a BL solution. In this paper we use the method of matched asymptotic expansions to investigate the structure and stability of such “boundary layer spike” (BLS) solutions in the presence of an asymptotically small activator diffusivity ?2?1. We find that two types of BLS solutions, one of which is unconditionally linearly stable and the other unstable, can be constructed provided that the activator flux is sufficiently small. In this way we determine that there is an asymptotically large range of activator flux values for which both the BL solution and one of the BLS solutions are linearly stable. Formal asymptotic calculations are further validated by numerically simulating the singularly perturbed GM system. |
Population Dynamics on Periodically Evolving Domain with Periodic Growth Mechanisms
| Pengarang | : | |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 84 (No. 6) |
| Halaman | : | 2219-2237 |
| Abstrak | : | Understanding the role of a time-varying domain on population survival or extinction is an interesting question in ecology. In this study we construct a reaction-diffusion model on a periodically evolving domain subject to the no-flux boundary condition, with a novel feature that the growth mechanism of populations also periodically varies. For this model we identify key factors to determine the long-term behavior of populations when the growth is of KPP type, strong Allee type, and weak Allee type, respectively. In particular, when a bistability structure appears, by appealing to the dynamical system theory developed in [Y. Wang and J. Yao, J. Funct. Anal., 283 (2022), 109538] we obtain a sharp convergence to periodic solutions. For bistable populations, we prove that there exists a unique critical distribution distinguishing population survival and extinction when we continuously vary a family of ordered initial distributions. Further, numerical simulations indicate that such critical distributions may depend on the connectivity of the varying domain; the loss of connectivity may suppress population survival, although there is no loss in the emerging boundaries. |
Flaherty–Keller Formula on the Effective Property of Densely Packed Elastic Composite Media in Three Dimensions
| Pengarang | : | Haigang Li, Peihao Zhang |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 84 (No. 6) |
| Halaman | : | 2199-2218 |
| Abstrak | : | In this paper, we determine the effective extension modulus and shear modulus of an array of convex rigid inclusions centered at the points of a periodic lattice in a high-contrast elastic composite in three dimensions, where the equations of linear elasticity are assumed. We first derive and prove the Flaherty–Keller formulas in three dimensions for ellipsoid inclusions and then extend to establishing corresponding results for the general case of ?-convex inclusions, where ?>2, when the inclusions are curvilinear cubes with round-off angles. We demonstrate that these global effective properties are closely related to the local gradient estimates of the solution to the linear elastic equations. |
Simultaneously Cloaking Electric and Hydrodynamic Fields via Electro-Osmosis
| Pengarang | : | Hongyu Liu, Zhi-Qiang Miao, Guang-Hui Zheng |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 84 (No. 6) |
| Halaman | : | 2175-2198 |
| Abstrak | : | We develop a general mathematical framework for the design and analysis of a novel coupled-physics invisibility cloaking scheme that can simultaneously cloak microscale electric and hydrodynamic fields via scattering cancellation for the electric potential and electro-osmosis for the pressure in a Hele–Shaw configuration. As a proof of this concept, the perfect electric and hydrodynamic cloaking conditions are derived for the cloaks with the cross section being annulus or confocal ellipses using the layer potential techniques. Furthermore, we develop an optimization scheme for the design of approximate cloaks within general geometries and prove the well-posedness of the optimization problem. In particular, the conditions that can ensure the simultaneous occurrence of approximate cloaks for general geometries are established. Our theoretical findings are corroborated by several numerical results. Our results are new to the literature. |
PERANAN LIURAN DAN RITUAL LISAN DALAM ADOPSI INOVASI USAHATANI SAYURAN MELALUI FARMER FIELD SCHOOL DI TIMOR-LESTE
| Pengarang | : | GIL DA CONCEICAO |
| Nama Majalah/Jurnal | : | Agro Ekonomika |
| Volume / Edisi | : | 17 (No. 1) |
| Halaman | : | 91-102 |
| Abstrak | : | - |