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Quantitative Analysis of the Elastic Field for Rod Shape Inclusion and Its Application to Related Inverse Problem
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| Pengarang | : | Youjun Deng, Wanjing Tang |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 1) |
| Halaman | : | 164-187 |
| Abstrak | : | We are concerned with the quantitative study of the elastic field perturbation due to the presence of the rod shape inclusion. We quantify the relationship of the perturbed elastic field on the geometry of the inclusion by making use of the layer potential techniques and asymptotic estimates. Then we apply the quantitative results to uniquely recover the rod shape inclusion by using only one boundary measurement. |
Optimal Design of Equilibrium Solutions of the Vlasov–Poisson System by an External Electric Field
| Pengarang | : | A. Borzì, G. Infante, G. Mascali |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 1) |
| Halaman | : | 143-163 |
| Abstrak | : | A new optimization framework to design steady equilibrium solutions of the Vlasov–Poisson system by means of external electric fields is presented. This optimization framework requires the minimization of an ensemble functional with Tikhonov regularization of the control field under the differential constraint of a nonlinear elliptic equation that models equilibrium solutions of the Vlasov–Poisson system. Existence of optimal control fields and their characterization as solutions to first-order optimality conditions are discussed. Numerical approximations and optimization schemes are developed to validate the proposed framework. |
Extreme First Passage Times for Populations of Identical Rare Events
| Pengarang | : | James MacLaurin, Jay Newby |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 1) |
| Halaman | : | 109-142 |
| Abstrak | : | A collection of identical and independent rare event first passage times is considered. The problem of finding the fastest out of ? such events to occur is called an extreme first passage time. The rare event times are singular and limit to infinity as a positive parameter scaling the noise magnitude is reduced to zero. In contrast, previous work has shown that the mean of the fastest event time goes to zero in the limit of an infinite number of walkers. The combined limit is studied. In particular, the mean time and the most likely path taken by the fastest random walker are investigated. Using techniques from large deviation theory, it is shown that there is a distinguished limit where the mean time for the fastest walker can take any positive value, depending on a single proportionality constant. Furthermore, it is shown that the mean time and most likely path can be approximated using the solution to a variational problem related to the single-walker rare event. |
Mean First Passage Times for Transport Equations
| Pengarang | : | Thomas Hillen, Maria R. D’Orsogna, Jacob C. Mantooth, Alan E. Lindsay |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 1) |
| Halaman | : | 78-108 |
| Abstrak | : | Many transport processes in ecology, physics, and biochemistry can be described by the average time to first find a site or exit a region, starting from an initial position. Typical mathematical treatments are based on formulations that allow for various diffusive forms and geometries but where only initial and final positions are taken into account. Here we develop a general theory for the mean first passage time (MFPT) for velocity jump processes. For random walkers, both position and velocity are tracked and the resulting Fokker–Planck equation takes the form of a kinetic transport equation. Starting from the forward and backward formulations we derive a general elliptic integro-PDE for the MFPT of a random walker starting at a given location with a given velocity. We focus on two scenarios that are relevant to biological modeling; the diffusive case and the anisotropic case. For the anisotropic case we also perform a parabolic scaling, leading to a well-known anisotropic MFPT equation. To illustrate the results we consider a two-dimensional circular domain under radial symmetry, where the MFPT equations can be solved explicitly. Furthermore, we consider the MFPT of a random walker in an ecological habitat that is perturbed by linear features, such as wolf movement in a forest habitat that is crossed by seismic lines. |
Mathematical Modeling and Solution Landscape Reveal Cancer Progression Dynamics in Tumor Ecological Microenvironment
| Pengarang | : | Shun Wang, Tengfei Wang, Shuonan Wu, Lei Zhang, Xiufen Zou |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 1) |
| Halaman | : | 50-77 |
| Abstrak | : | The cancer microenvironment is increasingly being viewed as an ecosystem, in which tumor cells interact with surrounding cells through diverse ecological relationships. However, the ecological principles governing the dynamics of cancer development and progression remain a mystery, hindering efforts to develop better treatment strategies. Here, we propose a novel ecological network of “predation-mutualism-amensalism” among tumor cells, immune cells, and mutualist cells. We found that this ecological model can accurately recapitulate the dynamic states and their transitions during cancer immunoediting by integrating mathematical modeling, stability and bifurcation analysis, and validation using experiment data. In contrast, two current models that only described predation and amensalism interactions failed to achieve it, suggesting the essential contribution of mutualism to the evolution of cancer immunoediting. Further, the immune barrier as a quantitative index was exploited to investigate the interlinkages between ecological relationships and cancer progression. Surprisingly, we found that the mutualism-mediated and amensalism-mediated inhibition of antitumor immune response only affects the transition from dormancy to escape phase, while the predation-mediated antitumor immune response affects all the phase transition dynamics of cancer progression. Moreover, by constructing the solution landscape of cancer progression dynamics, we revealed that tumor cell migration enables cancer progression to enter the dormancy phase by evading immunosurveillance, while mutualist cell migration facilitates the tumor’s evasion from dormancy to escape phase. The discovery of these ecological principles and the understanding of cell motility within the cancer microenvironment provide a potential for improved intervention of ecological interactions that could impact cancer progression and treatment. |
Twisted TMDs in the Small-Angle Limit: Exponentially Flat and Trivial Bands
| Pengarang | : | Simon Becker, Mengxuan Yang |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 1) |
| Halaman | : | 27-49 |
| Abstrak | : | Recent experiments discovered fractional Chern insulator states at zero magnetic field in twisted bilayer MoTe\(_2\) [Cai et al., Nature, 622 (2023), pp. 63–68; Zeng et al., Nature, 622 (2023), pp. 69–73] and WSe\(_2\) [Morales-Durán et al., Phys. Rev. Res., 5 (2023), L032022]. In this article, we study the MacDonald Hamiltonian for twisted transition metal dichalcogenides (TMDs) and analyze the low-lying spectrum in TMDs in the limit of small twisting angles. Unlike in twisted bilayer graphene Hamiltonians, we show that TMDs do not exhibit flat bands. The flatness in TMDs for small twisting angles is due to spatial confinement by a matrix-valued potential. We show that by generalizing semiclassical techniques developed by Simon [Ann. Inst. H. Poincaré, 38 (1983), pp. 295–307] and Helffer and Sjöstrand [Comm. Partial Differential Equations, 9 (1984), pp. 337–408] to matrix-valued potentials, there exists a wide range of model parameters such that the low-lying bands are of exponentially small width in the twisting angle, are topologically trivial, and obey a harmonic oscillator type of spacing with explicit parameters. |
Appropriate State-Dependent Friction Coefficient Accelerates Kinetic Langevin Dynamics
| Pengarang | : | Keunwoo Lim, Molei Tao |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 1) |
| Halaman | : | 1-26 |
| Abstrak | : | We consider the convergence of kinetic Langevin dynamics to its ergodic invariant measure, which is Gibbs distribution. Instead of the standard setup where the friction coefficient is a constant scalar, we investigate the position-dependent friction coefficient and the possible accelerated convergence it enables. We show that by choosing this coefficient matrix to be 2Hess?, convergence is accelerated in the sense that no constant scalar friction coefficient can lead to faster convergence for a large subset of (nonlinear) strongly convex potential ?’s. The speed of convergence is quantified in terms of Chi-square divergence from the target distribution and proved using a Lyapunov approach, based on viewing sampling as optimization in the infinite dimensional space of probability distributions. |
Motion of Spinning Rings and Washers on a Vertical Rod
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The Physics Teacher |
| Volume / Edisi | : | 63 (No. 5) |
| Halaman | : | 312-316 |
| Abstrak | : | A ring that spins on a vertical rod descends much more slowly than one might expect. It can even hover at the same height for several seconds before it starts to fall. Experimental results are presented using flat metal washers and toroidal rings to describe different effects that can arise, together with plausible explanations. The effects are visually appealing and would be of interest to physics students of all ages. |
Using Banana-to-Banana Plug Test Leads to Extend the Usefulness of CASTLE Kits
| Pengarang | : | Bogdan M. Leu; Dean A. Stocker |
| Nama Majalah/Jurnal | : | The Physics Teacher |
| Volume / Edisi | : | 63 (No. 5) |
| Halaman | : | 310-311 |
| Abstrak | : | CASTLE Kits1,2 are versatile tools that have been used to teach introductory circuits labs for the past 30 years. In some of the algebra-based general physics labs at our institution, students are guided to use scientific reasoning to design experiments to qualitatively test current flow, for which brightness is a proxy, through components that are in series and parallel. We use CASTLE Kits for these experiments, but we have sometimes struggled with poor electrical connections that cause students to come to incorrect conclusions about current flow in parallel circuits. Students already come to class with enough misconceptions about circuits3; we would rather not add to the confusion with equipment that behaves in unexpected ways. Replacing the wires originally provided in the CASTLE Kits with banana-to-banana plug (BB) test leads effectively eliminated this problem, extending the usefulness of the CASTLE Kits for our scientific reasoning labs. |
Expanding the horizons of depression: beyond the monoamine hypothesis
| Pengarang | : | I. Hindmarch |
| Nama Majalah/Jurnal | : | Human Psychopharmacology |
| Volume / Edisi | : | 16-3, APRIL (No. 3) |
| Halaman | : | 203-218 |
| Abstrak | : | The monoamine hypothesis has dominated our understanding of depression and of pharmacological approaches to its management and it has produced several generations of antidepressant agents, ranging from the monoamine oxidase inhibitors (MAOIs), through tricyclics (TCAs) and selective serotonin reuptake inhibitors (SSRIs), to the recently introduced selective noradrenaline reuptake inhibitor (NARI), reboxetine. Greater receptor selectivity has improved tolerability, but not efficacy, when newer compounds are compared with the original tricyclic antidepressants (TCAs) and monoamine oxidase inhibitors. Essentially, the newer antidepressants have the same distinguishing feature as older ones, i.e. acute enhancement of monoaminergic neurotransmission. The monoamine hypothesis cannot conclusively link the acute biochemical action of antidepressants on monoamine levels with their delayed clinical effect of 10–14 days, nor can it explain the mode of action of antidepressants that are effective despite being very weak inhibitors of monoaminergic transmission (e.g. iprindole) or, incongruously, enhancing monoamine uptake (e.g. tianeptine). Compared with other fields of medicine, there has been a lack of progress in understanding the pathophysiology of depression and producing truly novel antidepressant agents. Other biological approaches to depression, such as overactivity of the hypothalamic–pituitary–adrenal axis, hippocampal neural plasticity in response to stress, and the link between the inflammatory response and depression, offer new approaches to finding pharmacological agents, aided by improved techniques for visualising the human brain, better animal models, and increased knowledge of human markers of depression. |