帕邢-巴克效应

铁磁性是某些材料（例如铁）形成永磁体的机制。它源于量子力学交换相互作用，这种相互作用导致原子磁矩在称为磁畴的区域内自发排列。在居里温度以下，这些磁畴可以通过外部磁场进行排列，即使在外部磁场移除后也能形成强而持久的磁体。

A pH meter measures the voltage between two electrodes and converts it to a pH value. The core component is the glass electrode, which has a thin glass bulb sensitive to hydrogen ion activity. The potential difference, E, between the glass electrode and a stable reference electrode is linearly proportional to the pH according to a form of the Nernst equation: [latex]E = K + \frac{2.303RT}{F}pH[/latex].

在非均相催化中，催化剂与反应物处于不同的相态。通常，固体催化剂与气态或液态反应物一起使用。该过程涉及几个步骤：反应物扩散至催化剂表面、吸附到活性位点、表面发生化学反应、产物解吸以及产物扩散离开表面。

广义相对论的一个关键预测是，在不同的引力势下，时间流逝的速率不同。在强引力场（靠近大质量物体）中，时钟的走时会比在弱引力场中慢。这种效应被称为引力时间膨胀，已得到实验验证，并且是GPS等现代技术的关键因素。

The Einstein Field Equations (EFE) are a set of ten coupled, non-linear partial differential equations that form the core of general relativity. They describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy. The equation is concisely written as [latex]G_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}[/latex], relating spacetime geometry to its energy-momentum content.

等效原理是广义相对论的基石。它假定均匀引力场的效应与均匀加速度的效应无法区分。这意味着，在无窗自由落体电梯中的观察者会体验到失重感，就像在远离任何引力源的深空中观察者一样，这构成了引力作为一种几何现象的概念基础。

In 1911, Heike Kamerlingh Onnes discovered superconductivity while studying the resistance of solid mercury at cryogenic temperatures. He observed that the electrical resistance of mercury abruptly dropped to zero at a critical temperature ([latex]T_c[/latex]) of 4.2 K. This phenomenon, termed superconductivity, represents a state of matter with exactly zero electrical resistance and expulsion of magnetic fields.

The von Mises yield criterion predicts that yielding of a ductile material begins when the second deviatoric stress invariant, [latex]J_2[/latex], reaches a critical value. It is often expressed in terms of the von Mises stress, [latex]\sigma_v[/latex], a scalar value that must be less than the material's yield strength, [latex]\sigma_y[/latex]. Yielding occurs when [latex]\sigma_v = \sigma_y[/latex].

广义相对论首次精确解释了水星近日点的异常进动。牛顿引力无法完全解释水星椭圆轨道方向缓慢而渐进的变化。爱因斯坦的理论正确地预测了水星每世纪43角秒的误差，并将其归因于太阳周围时空的曲率，这是该理论早期的重大胜利。

黑洞是时空中一个引力极强的区域，任何物质——包括粒子甚至光——都无法逃脱。该区域的边界被称为事件视界。广义相对论预测黑洞是场方程的解，它是大质量恒星引力完全坍缩的结果。

The Henderson-Hasselbalch equation relates the pH of a solution of a weak acid to its acid dissociation constant ([latex]pK_a[/latex]) and the ratio of the concentrations of the deprotonated species (conjugate base, [latex][A^-][/latex]) to the protonated species (acid, [latex][HA][/latex]). The equation is [latex]pH = pK_a + \log_{10}\left(\frac{[A^-]}{[HA]}}\right)[/latex]. It is fundamental for understanding and preparing buffer solutions.