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A simple Minkowskian time-travel spacetime
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| Pengarang | : | John D. Norton |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 3) |
| Halaman | : | 241-249 |
| Abstrak | : | This relativistic, time-travel spacetime is everywhere metrically flat, excepting a conical singularity. Observers following timelike geodesics can eventually encounter their past selves, aging in the opposite time sense. The spacetime is not time orientable. |
The surprising subtlety of electrostatic field lines
| Pengarang | : | Kevin Zhou; Tomas Brauner |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 3) |
| Halaman | : | 234-240 |
| Abstrak | : | Electric fields are commonly visualized with field line diagrams, which only unambiguously specify the field's direction. We consider two simple questions. First, can one deduce if an electric field is conservative, as required, e.g., in electrostatics, from its field lines alone? Second, are there conservative electric fields with straight field lines, besides the familiar textbook examples with spherical, cylindrical, or planar symmetry? We give a self-contained introduction to the differential geometry required to answer these questions, assuming only vector calculus background. |
Eddy currents of a magnet falling through a copper pipe with slits
| Pengarang | : | Keith Zengel; Lauren Boehnert; Jared Medina; Jieping Fang; Juliet Coe; Abby Curtis; William Fredenberg |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 3) |
| Halaman | : | 223-233 |
| Abstrak | : | We present a theoretical model for the eddy currents induced by a cylindrical magnet falling through a copper pipe with vertical slits and the resulting inductive drag force. This system maintains the mathematically convenient cylindrical geometry of the classic intact pipe problem while introducing boundary conditions that result in fascinating eddy current patterns. Previous experiments have demonstrated that the inductive drag force is smaller in a slit pipe than in an intact pipe of the same radius, suggesting that the presence of slits reduces but does not eliminate the horizontal induced eddy currents required to produce a vertical drag force. Our theoretical model suggests that the horizontal eddy currents are reduced in slit pipes partly because the formation of a slit requires the removal of conducting material where eddy currents would otherwise have formed, and partly because the induced currents must flow purely vertically along the slit walls. We show that our theoretical model is consistent with our experimental data for the terminal velocities of magnets falling through copper pipes with different size slits and different numbers of slits. This experiment might serve as an advanced undergraduate laboratory activity. |
Keplers Moon puzzle A historical context for pinhole imaging
| Pengarang | : | Thomas Quick; Johannes Grebe-Ellis |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 3) |
| Halaman | : | 215-222 |
| Abstrak | : | In 16th-century European astronomy, determining the sizes of the Sun and Moon using a pinhole camera was common. However, calculating the Moon's diameter from the concave segment of the partially obscured Sun yielded puzzling results due to a lack of a comprehensive theory of the influence of the aperture on the image. This inconsistency led Tycho Brahe to question prevailing assumptions in celestial mechanics. Recognizing this, Johannes Kepler conducted measurements during a solar eclipse in Graz on July 10, 1600 and soon developed a theory of the pinhole camera that remains valid today. In this article, we recount the historical episode leading to Kepler's theory through original works, complemented by a series of illustrative experiments for classroom use. This historical case study offers a rich context for reflecting on Nature of Science aspects within physics education. |
Fractal and Hurst Effects in Solenoidal and Irrotational Vector Random Fields
| Pengarang | : | Yaswanth Sai Jetti, Anatoliy Malyarenko, Martin Ostoja-Starzewski |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 2) |
| Halaman | : | 1006-1021 |
| Abstrak | : | Many phenomena in physics are described by a vector-valued homogeneous and isotropic random function in two or three space variables, or a random field. On the one hand, such a field can be uniquely represented as a sum of two components: a solenoidal one without divergence, and an irrotational one without curl. On the other hand, it may be represented as a sum of a longitudinal part, parallel to a fixed space direction, and a lateral part, orthogonal to that direction. If the longitudinal part of the solenoidal component has certain fractal and memory properties, what are the corresponding properties of its lateral part? Similarly, if the lateral part of the irrotational component has certain fractal and memory properties, what are the corresponding properties of its longitudinal part? We give an answer to those questions using well-known tools of classical real analysis. |
Modeling the Interaction of Cytotoxic T-Lymphocytes and Oncolytic Viruses in a Tumor Microenvironment
| Pengarang | : | Yan Zhao, Qi Deng, Zhipeng Qiu, Ting Guo, Shigui Ruan |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 2) |
| Halaman | : | 983-1005 |
| Abstrak | : | Oncolytic virotherapy has become a promising approach in treating cancer. Understanding the mechanism of interaction between oncolytic viruses (OVs) and the immune system is crucial for the interventional diagnosis and therapy of tumors. In this paper, a mathematical model is formulated to understand the interaction among cytotoxic T-lymphocytes (CTLs), OVs, and tumor cells in which the Gompertz curve is used to describe the tumor proliferation. The basic reproductive number (?0) is first derived, and then the local and global dynamics of the system are analyzed mainly in terms of ?0 and another threshold ?0?, the basic reproductive number of CTLs which determines the number of positive equilibria. The theoretical results suggest that the system may have periodic solutions and backward bifurcation. Furthermore, numerical simulations are explored to evaluate the influence of CTLs on virotherapy. CTL immune response plays an obstructive role on virotherapy, and once the CTL proliferation rate exceeds a threshold, the tumor will escape. In addition, the whole tumor population is inversely proportional to the viral infection rate as well as the tumor proliferation rate. |
Mathematical Models for Nonlinear Ultrasound Contrast Imaging with Microbubbles
| Pengarang | : | Vanja Nikolic, Teresa Rauscher |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 2) |
| Halaman | : | 961-982 |
| Abstrak | : | Ultrasound contrast imaging is a specialized imaging technique that applies microbubble contrast agents to traditional medical sonography, providing real-time visualization of blood flow and vessels. Gas-filled microbubbles are injected into the body, where they undergo compression and rarefaction and interact nonlinearly with the ultrasound waves. Therefore, the propagation of sound through a bubbly liquid is a strongly nonlinear problem that can be modeled by a nonlinear acoustic wave equation for the propagation of the pressure waves coupled via the source terms to a nonlinear ordinary differential equation of Rayleigh–Plesset type for the bubble dynamics. In this work, we first derive a hierarchy of such coupled models based on constitutive laws. We then focus on the coupling of Westervelt’s acoustic equation to Rayleigh–Plesset type equations, where we rigorously show the existence of solutions locally in time under suitable conditions on the initial pressure-microbubble data and final time. Third, we devise and discuss numerical experiments on both single-bubble dynamics and the interaction of microbubbles with ultrasound waves. |
General Reconstruction of Elastic Strain Fields from their Longitudinal Ray Transform
| Pengarang | : | C. M. Wensrich, S. Holman, W. R. B. Lionheart, M. Courdurier, A. Polyakova, I. Svetov, T. Doubikin |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 2) |
| Halaman | : | 945-960 |
| Abstrak | : | We develop an algorithm for reconstruction of elastic strain fields from their longitudinal ray transform (LRT) in either two or three dimensions. In general, the LRT only determines the solenoidal part of a symmetric tensor field, but elastic strain fields additionally satisfy mechanical equilibrium; an extra condition that allows for full reconstruction in many cases. Our method provides full reconstruction for general elastic strain fields in connected objects whose boundary only contains one component, while previous results included other requirements such as no residual stress, or zero boundary traction. This allows for full reconstruction in energy resolved neutron transmission imaging for simple objects. Along the way, we prove that the LRT of a potential rank-2 tensor restricted to a bounded set determines the potential on the boundary of the set up to infinitesimal rigid motions on each component of the boundary. The method is demonstrated with numerical examples in two dimensions. |
Modeling Floral and Arthropod Electrostatics Using a Two-Domain AAA-Least Squares Algorithm
| Pengarang | : | Samuel J. Harris, Ryan A. Palmer, N. R. McDonald |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 2) |
| Halaman | : | 916-944 |
| Abstrak | : | Relationships between plants and insects vitally underpin the health of global ecosystems and food production. Through coevolution, insects have acquired a variety of senses in response to the emergence of floral cues such as scent, color, and shape. Therefore, the recent discovery of electroreception among terrestrial arthropods motivates the investigation of floral electrics as part of their wider sensory ecology. We examine how a flower’s morphology and material properties produce and propagate detectable, ecologically relevant electrical signals in several biologically inspired scenarios. Since the electrical field both interior and exterior to the flower must be solved for, we develop an extension of the two-dimensional AAA-least squares algorithm for solving such two-domain electrostatics problems. It is found that the electrical signals produced by the plant can reveal information to the insect about the flower shape, available pollen, and the presence of other nearby arthropods. These results show good qualitative agreement with an equivalent three-dimensional scenario, computed using finite element methods. The extension of the AAA-least squares algorithm to two-domain problems provides a fast and accurate method for modeling electrostatic problems, with possible further application in fluid dynamics and magnetostatics. Biologically, our results highlight the significant role floral electrics may play in plant-pollinator and predator-prey relationships, unveiling previously unstudied facets of these key relationships. |
Addressing Complex Boundary Conditions of Miscible Flow and Transport in Two and Three Dimensions with Application to Optimal Control
| Pengarang | : | Yiqun Li, Hong Wang, Xiangcheng Zheng |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 85 (No. 2) |
| Halaman | : | 896-915 |
| Abstrak | : | We investigate complex boundary conditions of the miscible displacement system in two and three space dimensions with the commonly used Bear–Scheidegger diffusion-dispersion tensor, which describes, e.g., the porous medium flow processes in petroleum reservoir simulation or groundwater contaminant transport. Specifically, we incorporate the no-flux boundary condition for the Darcy velocity to prove that the general no-flux boundary condition for the transport equation is equivalent to the normal derivative boundary condition of the concentration, based on which we further prove several complex boundary conditions by the Bear–Scheidegger tensor and its derivative. The derived boundary conditions provide new insights and properties of the Bear–Scheidegger diffusion-dispersion tensor, facilitate the application of classical methods and results without technical treatments for complex boundary conditions, and accommodate the coupling and the nonlinearity of the miscible displacement system and the Bear–Scheidegger tensor in deriving the first-order optimality condition of the corresponding optimal control problem for practical application. |