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在天体物理剪切流中,当存在足够强的顺流磁场时,Kelvin-Helmholtz(KH)不稳定性通常会被磁张力抑制。 这通常用于推断在剪切驱动的波动被观测到(或未被观测到)的系统中磁场强度的上限(或下限),其依据是扰动在没有线性不稳定性的情况下无法增长。 相反,通过计算这种系统中小振幅扰动在有限时间内可以达到的最大增长率,我们表明即使流动是亚阿尔芬的,扰动的能量也可以增加几个数量级,这提出了即使在强磁场存在的情况下也可能发现剪切驱动湍流的可能性,并对从观测到的剪切驱动波动的存在或不存在得出的推论提出了挑战。 我们进一步表明,与流体动力学情况相比,磁场引入了额外的非模态增长机制,并且二维模拟遗漏了这些增长机制的关键方面。
In astrophysical shear flows, the Kelvin-Helmholtz (KH) instability is generally suppressed by magnetic tension provided a sufficiently strong streamwise magnetic field. This is often used to infer upper (or lower) bounds on field strengths in systems where shear-driven fluctuations are (or are not) observed, on the basis that perturbations cannot grow in the absence of linear instability. On the contrary, by calculating the maximum growth that small-amplitude perturbations can achieve in finite time for such a system, we show that perturbations can grow in energy by orders of magnitude even when the flow is sub-Alfvénic, raising the possibility that shear-driven turbulence may be found even in the presence of strong magnetic fields, and challenging inferences from the observed presence or absence of shear-driven fluctuations. We further show that magnetic fields introduce additional nonmodal growth mechanisms relative to the hydrodynamic case, and that 2D simulations miss key aspects of these growth mechanisms.
我展示了在环形格子上进行的囚徒困境的空间模型的结果。 每个个体都有一个默认策略,要么合作($C$),要么背叛($D$)。 测试了两种策略,包括“以牙还牙”(TFT),其中个体会按照对手的上次行为进行回应,或者只是按照自己的默认行为进行回应。 每个个体还有可能如实说明($0 \leq P_{truth} \leq 1$)自己上次的行为。 这个参数可以随时间进化,使得个体可能是背叛者,但在关于自己上次行为的描述中却表现出合作。 这导致了有趣的动态,其中具有$P_{truth} \geq 0.75$的背叛者和合作者的混合种群会向说真话的合作者种群发展。 同样,具有$P_{truth} < 0.7$的混合种群会变成说谎的背叛者种群。 这两种种群都是稳定的,因为它们的平均得分都高于具有$P_{truth}$中间值的种群。 讨论了该模型在人类和动物中的应用。
I present the results from a spatial model of the prisoner's dilemma, played on a toroidal lattice. Each individual has a default strategy of either cooperating ($C$) or defecting ($D$). Two strategies were tested, including ``tit-for-tat'' (TFT), in which individuals play their opponent's last play, or simply playing their default play. Each individual also has a probability of telling the truth ($0 \leq P_{truth} \leq 1$) about their last play. This parameter, which can evolve over time, allows individuals to be, for instance, a defector but present as a cooperator regarding their last play. This leads to interesting dynamics where mixed populations of defectors and cooperators with $P_{truth} \geq 0.75$ move toward populations of truth-telling cooperators. Likewise, mixed populations with $P_{truth} < 0.7$ become populations of lying defectors. Both such populations are stable because they each have higher average scores than populations with intermediate values of $P_{truth}$. Applications of this model are discussed with regards to both humans and animals.
逆向设计已实现了超紧凑和高性能纳米光子组件的系统设计。 然而,在逆向设计过程中强制执行制造厂设计规则仍然是一个主要挑战,因为优化后的器件经常违反最小特征尺寸和间距的约束。 现有的制造约束方法通常依赖于惩罚项、投影滤波器或启发式二值化计划,这些方法限制了可访问的设计空间,需要大量的超参数调整,并且常常无法在整个优化轨迹中保证合规性。 在此,我们引入了一种纳米光子逆向设计框架,通过设计空间的生成重新参数化,内在地执行设计规则,将优化限制在学习到的DRC合规几何体流形上。 我们通过设计代表性的硅光子组件来验证这一范式,包括在电子束光刻和光刻平台上的1,500-1,600 nm波段工作的宽带功率分路器、光谱双工器和模式转换器。 在所有器件中,基于流形的公式在计算成本比基于像素的表示方式减少5倍以上的同时,达到了最先进的性能指标,并在整个设计过程中确保了可制造的几何结构。 通过将制造约束视为设计表示的基本属性而非外部惩罚,这项工作为广泛适用、平台无关且内在符合DRC的纳米光子学建立了一条直接路径。
Inverse design has enabled the systematic design of ultra-compact and high-performance nanophotonic components. Yet enforcing foundry design rules during inverse design remains a major challenge, as optimized devices frequently violate constraints on minimum feature size and spacing. Existing fabrication-constrained approaches typically rely on penalty terms, projection filters, or heuristic binarization schedules, which restrict the accessible design space, require extensive hyperparameter tuning, and often fail to guarantee compliance throughout the optimization trajectory. Here, we introduce a framework for nanophotonic inverse design with intrinsic enforcement of design rules through a generative reparameterization of the design space, restricting optimization to a learned manifold of DRC-compliant geometries. We validate this paradigm by designing representative silicon photonic components including broadband power splitters, spectral duplexers, and mode converters operating across the 1,500-1,600 nm band for both electron-beam lithography and photolithography platforms. Across all devices, the manifold-based formulation reaches state-of-the-art performance metrics with over a 5-fold reduction in computational cost compared to pixel-based representations, while ensuring fabrication-compatible geometries throughout the entire design process. By treating fabrication constraints as a fundamental property of the design representation rather than an external penalty, this work establishes a direct pathway toward broadly applicable, platform-agnostic, and intrinsically DRC-compliant nanophotonics.
标题问题的答案是肯定的。 在三维欧几里得空间中连续和可微曲线的几何分析表明,点表示电子电荷中心的位置,满足四阶常微分方程组,并以光速运动。 电子的质心是一个不同的点,将由电荷中心的演化来确定。 电荷中心相对于质心的相对运动导致了自旋和磁性特性。 对于质心观察者来说,质量的不变性和自旋绝对值的不变性意味着在电子与外部电磁场相互作用时,粒子必须辐射。
The answer to the title-question is affirmative. The analysis of the geometry of continuous and differentiable curves in three-dimensional Euclidean space suggests that the point represents the location of the center of charge of the electron, satisfies a system of ordinary differential equations of fourth order, and moves at the speed of light. The center of mass of the electron is a different point and will be determined by the evolution of the center of charge. It is the relative motion of the center of charge around the center of mass that gives rise to the spin and magnetic properties. The invariance of the mass and the absolute value of the spin for the center of mass observer imply that in the interaction of the electron with an external electromagnetic field the particle has to radiate.
波速是成像复杂介质的关键参数,但体内测量通常局限于反射几何结构,在这种结构中只能获取来自小尺度不均匀性的后向散射波。 因此,传统的反射成像无法恢复波速分布的大尺度变化。 在这里,我们展示了矩阵成像通过利用波聚焦的质量作为内在引导星来克服这一限制。 我们将波传播建模为一个可训练的多层网络,该网络利用优化和深度学习工具来推断波速分布。 我们通过在组织模拟幻象和人体乳腺组织上的超声实验验证了这种方法,证明了其在肿瘤检测和表征方面的潜力。 我们的方法适用于任何可以测量反射矩阵的波和介质。
Wave velocity is a key parameter for imaging complex media, but in vivo measurements are typically limited to reflection geometries, where only backscattered waves from short-scale heterogeneities are accessible. As a result, conventional reflection imaging fails to recover large-scale variations of the wave velocity landscape. Here we show that matrix imaging overcomes this limitation by exploiting the quality of wave focusing as an intrinsic guide star. We model wave propagation as a trainable multi-layer network that leverages optimization and deep learning tools to infer the wave velocity distribution. We validate this approach through ultrasound experiments on tissue-mimicking phantoms and human breast tissues, demonstrating its potential for tumour detection and characterization. Our method is broadly applicable to any kind of waves and media for which a reflection matrix can be measured.