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Two Novel proofs of Spectral Monotonicity of Perturbed Essentially Nonnegative Matrices with Applications in Population Dynamics
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| Pengarang | : | Shanshan Chen |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 2) |
| Halaman | : | 654-676 |
| Abstrak | : | Threshold values in population dynamics can be formulated as spectral bounds of matrices, determining the dichotomy of population persistence and extinction. For a square matrix ????????? +????, where ???? is an essentially nonnegative matrix describing population dispersal among patches in a heterogeneous environment and ???? is a real diagonal matrix encoding within-patch population dynamics, the monotonicity of its spectral bound with respect to dispersal rate/coupling strength/travel frequency ???? has been established by Karlin and generalized by Altenberg while investigating the reduction principle in evolution biology and evolution dispersal in patchy landscapes. In this paper, we provide two new proofs rooted in our investigation of persistence in spatial population dynamics. The first one is an analytic derivation utilizing a graph-theoretic approach based on Kirchhoff's matrix-tree theorem; the second one employs the Collatz--Wielandt formula from matrix theory and complex analysis arguments. This monotonicity result has numerous applications in persistence and stability analysis of complex biological systems in heterogeneous environments. We illustrate this by applying it to well-known ecological models of single species, predator-prey, and competition. |
Modeling Electrode Heterogeneity in Lithium-Ion Batteries: Unimodal and Bimodal Particle-Size Distributions
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 2) |
| Halaman | : | 625-653 |
| Abstrak | : | In mathematical models of lithium-ion batteries, the highly heterogeneous porous electrodes are frequently approximated as comprising spherical particles of uniform size, leading to the commonly used single-particle model (SPM) when transport in the electrolyte is assumed to be fast. Here electrode heterogeneity is modeled by extending this to a distribution of particle sizes. Unimodal and bimodal particle-size distributions (PSD) are considered. For a unimodal PSD, the effect of the spread of the distribution on the cell dynamics is investigated, and choice of effective particle radius when approximating by an SPM assessed. Asymptotic techniques are used to derive a correction to the SPM valid for narrow, but realistic, PSDs. In addition, it is shown that the heterogeneous internal states of all particles (relevant when modeling degradation, for example) can be efficiently computed after the fact. For a bimodal PSD, the results are well approximated by a double-particle model (DPM), with one size representing each mode. Results for lithium iron phosphate with a bimodal PSD show that the DPM captures an experimentally observed double plateau in the discharge curve, suggesting it is entirely due to bimodality. |
Inverse Transport and Diffusion Problems in Photoacoustic Imaging with Nonlinear Absorption
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 2) |
| Halaman | : | 602-624 |
| Abstrak | : | Motivated by applications in imaging nonlinear optical absorption by photoacoustic tomography, we study in this work inverse coefficient problems for a semilinear radiative transport equation and its diffusion approximation with internal data that are functionals of the coefficients and the solutions to the equations. Based on the techniques of first- and second-order linearization, we derive uniqueness and stability results for the inverse problems. For uncertainty quantification purposes, we also establish the stability of the reconstruction of the absorption coefficients with respect to the change in the scattering coefficient. |
A New Monotonicity for Principal Eigenvalues with Applications to Time-Periodic Patch Models
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 2) |
| Halaman | : | 576-601 |
| Abstrak | : | A new monotonocity of principal eigenvalues in time-periodic patch environments is established. As an application, a patch model for two competing species in spatio-temporally varying environments is investigated. When two species are identical except for their relaxation time, the species with the shorter relaxation time will always drive the other one to extinction. When two species are identical except for their diffusion rates, our results suggest that the faster diffusing species could be favored for some intermediate range of relaxation time, while the slower diffusing species will be favored for both short and long relaxation time. In general, short relaxation time and slow diffusion rate tend to help species gain advantage in competition. |
Qualitative and Numerical Aspects of a Motion of a Family of Interacting Curves in Space
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 2) |
| Halaman | : | 549-575 |
| Abstrak | : | In this article we investigate a system of geometric evolution equations describing a curvature driven motion of a family of three-dimensional curves in the normal and binormal directions. Evolving curves may be the subject of mutual interactions having both local or nonlocal character where the entire curve may influence evolution of other curves. Such an evolution and interaction can be found in applications. We explore the direct Lagrangian approach for treating the geometric flow of such interacting curves. Using the abstract theory of nonlinear analytic semiflows, we are able to prove local existence, uniqueness, and continuation of classical Ho?lder smooth solutions to the governing system of nonlinear parabolic equations. Using the finite volume method, we construct an efficient numerical scheme solving the governing system of nonlinear parabolic equations. Additionally, a nontrivial tangential velocity is considered allowing for redistribution of discretization nodes. We also present several computational studies of the flow combining the normal and binormal velocity and considering nonlocal interactions. |
From the President: A Clear Vision Forward
| Pengarang | : | Edil Torres Rivera |
| Nama Majalah/Jurnal | : | Counseling Today |
| Volume / Edisi | : | 67 (No. 2) |
| Halaman | : | 6 |
| Abstrak | : | Abstrak tidak tersedia. |
A Stochastic Framework for Atomistic Fracture
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 2) |
| Halaman | : | 5256-548 |
| Abstrak | : | We present a stochastic modeling framework for atomistic propagation of a Mode I surface crack, with atoms interacting according to the Lennard--Jones interatomic potential at zero temperature. Specifically, we invoke the Cauchy--Born rule and the maximum entropy principle to infer probability distributions for the parameters of the interatomic potential. We then study how uncertainties in the parameters propagate to the quantities of interest relevant to crack propagation, namely, the critical stress intensity factor and the lattice trapping range. For our numerical investigation, we rely on an automated version of the so-called numerical-continuation enhanced flexible boundary NCFlex algorithm. |
The Breaking Point
| Pengarang | : | Lisa R. Rhodes |
| Nama Majalah/Jurnal | : | Counseling Today |
| Volume / Edisi | : | 67 (No. 2) |
| Halaman | : | 38-41 |
| Abstrak | : | Six years ago, Angela Kaloudis, LMHC, had been working with a client for about a year in her private practice in Massachusetts. In one session, the two were revisiting the client’s treatment goals to discuss whether weekly therapy was still necessary. While reflecting on her experience in therapy, the client’s eyes began to tear up as she shared how helpful and transformative the work had been for her. In response, Kaloudis said, “One day, I’ll be a blip on your radar.” The energy in the room quickly shifted. The client averted her eyes, withdrew and changed where she was sitting on the couch to move away from Kaloudis. When Kaloudis mentioned the shift in energy in the room, the client confronted her: “That comment makes me feel that this relationship is not very mutual,” the client said. What began as an opportunity to review the success of their work together suddenly became a therapeutic alliance rupture between Kaloudis and her client. |
Localization of Defects Via Residence Time Measures
| Pengarang | : | Alessandro Ciallella |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 2) |
| Halaman | : | 502-525 |
| Abstrak | : | We show that residence time measures can be used to identify the geometrical and transmission properties of a defect along a path. The model we study is based on a one-dimensional simple random walk. The sites of the lattice are regular, i.e., the jumping probabilities are the same in each site, except for a site, called defect, where the jumping probabilities are different. At each side of the lattice an absorbing site is present. We show that by measuring the fraction of particles crossing the channel and/or the typical time they need to cross it, it is possible to identify the main features of the lattice and of the defect site, namely, the jumping probabilities at the regular and at the defect site and the position of the defect in the lattice. |
Construction and Numerical Assessment of Local Absorbing Boundary Conditions for Heterogeneous Time-Harmonic Acoustic Problems
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 2) |
| Halaman | : | 476-501 |
| Abstrak | : | This article is devoted to the derivation and assessment of local absorbing boundary conditions (ABCs) for numerically solving heterogeneous time-harmonic acoustic problems. To this end, we develop a strategy inspired by the work of Engquist and Majda to build local approximations of the Dirichlet-to-Neumann operator for heterogeneous media, which is still an open problem. We focus on three simplified but characteristic examples of increasing complexity to highlight the strengths and weaknesses of the proposed ABCs: the propagation in a duct with a longitudinal variation of the speed of sound, the propagation in a nonuniform mean flow using a convected wave operator, and the propagation in a duct with a transverse variation of the speed of sound and density. For each case, we follow the same systematic approach to construct a family of local ABCs and explain their implementation in a high-order finite element context. Numerical simulations allow us to validate the accuracy of the ABCs and to give recommendations for the tuning of their parameters. |