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由保罗·狄拉克于1931年提出的磁单极子模型长期以来一直是物理学理论研究的兴趣所在,因为它有可能解释电荷的量子化。 尽管对非狄拉克单极子给予了大量关注,但涉及一个称为狄拉克弦的无限细螺线管的狄拉克模型,在单极子之间的相互作用中表现出细微之处。 在本文中,我们表明两个狄拉克单极子之间的力遵循类似库仑的相互作用定律。 这一推导为基本电磁学概念提供了有启发性的练习,并适合本科和早期研究生水平的学生。
The model of magnetic monopoles that was proposed by Paul Dirac in 1931 has long been a subject of theoretical interest in physics because of its potential to explain the quantization of electric charge. While much attention has been given to non-Dirac monopoles, Dirac's model, which involves an infinitely thin solenoid known as a Dirac string, presents subtleties in the interaction between monopoles. In this paper, we show that the force between two Dirac monopoles obeys a Coulomb-like interaction law. This derivation offers an instructive exercise in fundamental electromagnetism concepts and is appropriate for undergraduate and early graduate-level students.
开发以更环保芯材为基础的生物基复合夹层结构的目标是促进航空和海洋等工业的去碳化。 这一研究领域在过去几十年中受到了越来越多的关注。 例如,巴尔萨木已作为一种高度有前景的泡沫或蜂窝芯材替代品出现,提供了一种轻质、快速可再生且成本效益高的解决方案。 然而,如巴尔萨木和亚麻等植物纤维通常表现出较高的亲水性,这可能会影响它们的机械性能和长期耐久性。 因此,迫切需要进一步研究巴尔萨木芯夹层结构的循环湿热老化行为的表征,特别是识别皮肤和芯材中的湿度引起的应变和内部应力,以及研究木材纤维、树脂和玻璃纤维中的湿度脱附过程及相关的热收缩现象。 因此,本工作采用两个完整的吸湿-脱湿循环来表征由三种不同材料组成的试样的湿扩散行为,包括纯巴尔萨木、树脂浸渍巴尔萨木和具有两种玻璃纤维增强聚合物(GFRP)皮肤的巴尔萨木芯夹层结构。 研究了所有试样在厚度、长度和宽度方向上的含水量和吸湿应变的变化,旨在识别长期老化循环中表现出的吸湿膨胀和热收缩行为。
The objective of developing bio-based composite sandwich structures with greener core materials is to facilitate the decarbonization of industries such as aviation and maritime. This field of research has received increasing attention over the past decades. For example, balsa wood has emerged as a highly promising alternative to foam or honeycomb cores, offering a lightweight, rapidly renewable and cost-effective solution. However, plant fibers such as balsa wood and flax often display high hydrophilic behavior, which could affect their mechanical performance and long-term durability. It is therefore imperative to promote further research into the characterization of the cyclic hygrothermal aging behavior of balsa wood core sandwich structures, in particular the identification of moistureinduced strains and internal stresses in the skins and cores, as well as the investigation of moisture desorption processes and the associated thermal shrinkage phenomena in wood fibers, resins and glass fibers. Accordingly, this work employs two complete moisture absorption-desorption cycles to characterize the moisture diffusion behavior of specimens comprising three different materials, including the pure balsa wood, resin-infused balsa and balsa core sandwich structures with two Glass-Fiber-Reinforced-Polymer (GFRP) skins. The changes in moisture content and hygroscopic strains in the thickness, length and width directions of all specimens were investigated with a view to identifying the hygroscopic swelling and thermal shrinkage behaviors exhibited during long-term aging cycles.
非线性谐振器对多频驱动的响应揭示了超越传统单音理论的丰富动力学行为。 我们研究在双频激励下的杜芬谐振器,并确定两种驱动之间的竞争,这种竞争由它们的失谐和相对幅度决定。 在慢拍 regime 中,当两个频率非常接近时,次级驱动作为一种调制,会在共存的稳态之间引起动态相变。 我们引入周期平均振幅作为序参数,并绘制出随驱动失谐和振幅比变化的相图,捕捉到了实验中观察到的蓝移与红移之间的显著不对称性。 我们设计了一个模型,将这些相变的起始与系统非线性稳态模式附近的共振特性联系起来。 我们的结果为控制受驱动的非线性系统提供了一个框架,实现了状态操控以及在纳米机械、光学和超导电路平台中的传感。
The response of nonlinear resonators to multifrequency driving reveals rich dynamics beyond conventional single-tone theory. We study a Duffing resonator under bichromatic excitation and identify a competition between the two drives, governed by their detuning and relative amplitudes. In the slow-beating regime, where the tones are closely spaced, the secondary drive acts as a modulation that induces dynamical phase transitions between coexisting stationary states. We introduce the cycle-averaged amplitude as an order parameter and map the resulting phase diagram as a function of the drive detuning and amplitude ratio, capturing the pronounced asymmetry observed for blue versus red detuning in experiment. We devise a model to link the onset of these transitions to the resonance properties around the nonlinear stationary mode of the system. Our results provide a framework for controlling driven nonlinear systems, enabling state manipulation, and sensing in nanomechanical, optical, and superconducting circuit platforms.
约翰·伯努利对最速降线问题的光学解法是建立在底层(非光学)原理上的。 随后给出了一个“光学解释”。
Johann Bernoulli's optical solution of the brachistochrone problem is rebuilt on underlying (non-optical) principles. An "optical interpretation" is given afterwards.