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Mod. Math. Phys., Volume 1, Issue 1 (June 2025) – 5 articles

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15 pages, 848 KiB  
Article
Chebyshev Collocation Solutions to Some Nonlinear and Singular Third-Order Problems Relevant to Thin-Film Flows
by Călin-Ioan Gheorghiu
Mod. Math. Phys. 2025, 1(1), 5; https://doi.org/10.3390/mmphys1010005 - 5 Jun 2025
Viewed by 259
Abstract
This paper concerns accurate spectral collocation solutions, more precisely Chebyshev collocation (ChC), to some third-order nonlinear and singular boundary value problems on unbounded domains. The problems model some draining or coating fluid flows. We use exclusively ChC, in the form of Chebfun, avoid [...] Read more.
This paper concerns accurate spectral collocation solutions, more precisely Chebyshev collocation (ChC), to some third-order nonlinear and singular boundary value problems on unbounded domains. The problems model some draining or coating fluid flows. We use exclusively ChC, in the form of Chebfun, avoid any obsolete shooting-type method, and provide reliable information about the convergence and accuracy of the method, including the order of Newton’s method involved in solving the nonlinear algebraic systems. As a complete novelty, we combine a graphical representation of the convergence of the Newton method with a numerical estimate of its order of convergence for a more realistic value. We treat five challenging examples, some of which have only been solved by approximate methods. The found numerical results are judged in the context of existing ones; at least from a qualitative point of view, they look reasonable. Full article
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18 pages, 339 KiB  
Article
Antiparticles in Non-Relativistic Quantum Mechanics
by Alexander D. Popov
Mod. Math. Phys. 2025, 1(1), 4; https://doi.org/10.3390/mmphys1010004 - 18 Apr 2025
Viewed by 341
Abstract
Non-relativistic quantum mechanics was originally formulated to describe particles. Using ideas from the geometric quantization approach, we show how the concept of antiparticles can and should be introduced in the non-relativistic case without appealing to quantum field theory. We discuss this in detail [...] Read more.
Non-relativistic quantum mechanics was originally formulated to describe particles. Using ideas from the geometric quantization approach, we show how the concept of antiparticles can and should be introduced in the non-relativistic case without appealing to quantum field theory. We discuss this in detail using the example of the one-dimensional harmonic oscillator. Full article
18 pages, 290 KiB  
Article
The Compactified D-Brane Cylinder Amplitude and T Duality
by Jian-Xin Lu
Mod. Math. Phys. 2025, 1(1), 3; https://doi.org/10.3390/mmphys1010003 - 28 Feb 2025
Viewed by 608
Abstract
In this paper, we address how to implement T-duality to the closed string tree cylinder amplitude between a Dp brane and a Dp′ brane with pp=2n. To achieve this, we compute the closed string tree cylinder [...] Read more.
In this paper, we address how to implement T-duality to the closed string tree cylinder amplitude between a Dp brane and a Dp′ brane with pp=2n. To achieve this, we compute the closed string tree cylinder amplitude, for the first time, between these two D-branes with common longitudinal and transverse circle compactifications. We then show explicitly how to perform a T-duality for this amplitude along either a longitudinal or a transverse compactified direction to both branes. At the decompactification limit, we show that either the compactified cylinder amplitude or the T dual compactified cylinder gives the known non-compactified one as expected. Full article
2 pages, 127 KiB  
Editorial
Modern Mathematical Physics: A New Open Access Journal
by Chang-Pu Sun, Murray Batchelor and Yupeng Wang
Mod. Math. Phys. 2025, 1(1), 2; https://doi.org/10.3390/mmphys1010002 - 27 Dec 2024
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Abstract
It is our great pleasure to be involved in the launch of Modern Mathematical Physics (MMP) [...] Full article
2 pages, 139 KiB  
Editorial
Welcome to Modern Mathematical Physics: A Note from the Editorial Office
by Lin Li
Mod. Math. Phys. 2025, 1(1), 1; https://doi.org/10.3390/mmphys1010001 - 18 Oct 2024
Viewed by 1270
Abstract
On 6 June 2024, we had the privilege of visiting Professor Chang-Pu Sun at the China Academy of Engineering Physics [...] Full article
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