In gravitation, several key equations describe the behavior of gravitational forces, fields, and potentials.
Fluid mechanics is a complex field of study that encompasses a wide range of phenomena related to the behavior of fluids (liquids and gases) in motion and at rest. Below is a list of some fundamental equations and principles commonly used in fluid mechanics: ### 1.
The Lamb shift is a small difference in energy levels of hydrogen-like atoms, specifically in the electron energy levels of these atoms, that is a result of quantum electrodynamics (QED) effects. More specifically, it refers to the splitting between the 2s and 2p energy levels in hydrogen, which was first observed experimentally by Willis Lamb and Robert Retherford in 1947.
Irradiance is a measure of the power of solar radiation or other forms of electromagnetic radiation received by a surface per unit area. It is typically expressed in watts per square meter (W/m²). Irradiance quantifies how much solar energy is available at a given location and time, making it an important parameter in fields such as solar energy, meteorology, and climatology.
Ionic strength is a measure of the concentration of ions in a solution. It quantifies the total concentration of ions in a solution by taking into account not just the number of ions, but also their charges. This is important in various fields such as chemistry, biology, and environmental science, as it affects various properties of the solution, including solubility, activity coefficients, and reaction kinetics.
Ionic conductivity in the solid state refers to the ability of a solid material to conduct electric current through the movement of ions. Unlike metals, which conduct electricity primarily through the movement of electrons, ionic conductors transport charge via the migration of ions. This phenomenon is particularly important in various applications, including batteries, fuel cells, and solid electrolytes.
The ion transport number, also known as the transference number, is a measure of the contribution of a particular ion to the total electrical conductivity of an electrolyte solution. It quantifies the fraction of the total current conducted by a specific ion as it migrates in an electric field. In an electrochemical system, when an electric field is applied, ions in solution will move towards the electrodes.
Invariant mass is a concept from physics, particularly in the context of special relativity and particle physics. It refers to the mass of a system of particles as measured in a specific reference frame, and it remains constant regardless of the motion of the observer. Invariant mass is particularly useful for understanding systems involving multiple particles or decaying particles. In technical terms, the invariant mass \( M \) of a system of particles can be calculated using the energy and momentum of those particles.
In physics, the term "invariant" refers to a property or quantity that remains unchanged under a specific transformation or set of transformations. This concept applies in various branches of physics, including classical mechanics, electromagnetism, and the theory of relativity.
The International System of Quantities (ISQ) is a comprehensive framework used to define physical quantities and their relationships, aiming to provide a consistent and standardized way to express measurements and scientific data. Its primary purpose is to ensure clarity and uniformity in the representation of measurements across various disciplines in science and engineering. The ISQ is built upon the principles established by the International System of Units (SI), which focuses specifically on the units of measurement.
In the context of physics, intensity is generally defined as the amount of energy transferred per unit area per unit time. It is a measure of the power (energy per unit time) received or transmitted through a surface, often associated with waves, such as light waves, sound waves, or other forms of electromagnetic radiation.
The integral length scale is a concept from turbulence and fluid mechanics that characterizes the size of the large-scale eddies in a turbulent flow. It is a measure of the extent over which turbulent fluctuations are correlated. In other words, it provides an estimation of the spatial scale of the largest coherent structures present in a turbulent flow field. Mathematically, the integral length scale \(L\) can be defined using the correlation function of the velocity field in turbulence.
Infinitesimal strain theory, also known as small strain theory, is a fundamental concept in solid mechanics that deals with the deformation of materials under small loads or displacements. It assumes that the deformations are small enough that the linearization of the strain and displacement fields is valid. This theory is widely used in engineering applications, particularly in structural analysis, geotechnics, and materials science.
Immittance is a term used in electrical engineering and electronics to refer to the combined effects of resistance and reactance in an electrical circuit. It is a complex quantity that encompasses both the resistance (real part) and the reactance (imaginary part) of a circuit element or network.
Illuminance is a measure of the amount of light incident on a surface per unit area. It quantifies how much luminous flux (measured in lumens) is spread over a given area (measured in square meters). The unit of measurement for illuminance is the lux (lx), where 1 lux equals 1 lumen per square meter.
ISO 31 was an international standard that provided a set of rules and recommendations for the use of quantities, units, and their symbols within various fields of science and engineering. Issued by the International Organization for Standardization (ISO), it aimed to create a consistent framework for expressing measurements, promoting clarity and reducing misunderstandings in scientific communication.
ISO/IEC 80000 is a standard that addresses the quantities and units of measurement in various fields of science and technology. It is part of the International Organization for Standardization (ISO) and the International Electrotechnical Commission (IEC) standards series focused on providing a clear, consistent, and international way of dealing with measurements and their units.
Hypervelocity refers to extremely high speeds, typically defined as speeds exceeding 1,000 meters per second (about 3,280 feet per second), or approximately Mach 3, depending on the context. In various fields, hypervelocity has specific implications: 1. **Aerospace and Engineering**: In aerospace engineering, hypervelocity is often associated with the motion of objects re-entering the atmosphere from space, such as spacecraft and meteoroids.
Humidity refers to the amount of water vapor present in the air. It is an important factor in weather and climate and can significantly impact comfort levels, human health, and the environment. There are two main ways to express humidity: 1. **Absolute Humidity**: This measures the actual amount of water vapor in a given volume of air, typically expressed in grams of water vapor per cubic meter of air (g/m³).

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 5. . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact