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Benoit Mandelbrot (1924-2010) was a French-American mathematician best known for his work in fractal geometry. He coined the term "fractal" to describe complex shapes that exhibit self-similarity at different scales, meaning they look similar whether viewed up close or from a distance. Mandelbrot's significant contributions include the visualization of the Mandelbrot set, a famous fractal that illustrates the concept of infinitely repeating patterns and intricate structures arising from simple mathematical equations.
As of my last update in October 2023, Aya Soffer does not appear to be a widely recognized public figure, concept, or entity. It's possible that Aya Soffer could refer to a private individual, or it may be a name that has gained prominence after my last training data. If you could provide more context or specify the field (e.g., entertainment, science, etc.
Arthur Samuel was a pioneering American computer scientist known for his contributions to the field of artificial intelligence, particularly in the area of machine learning. He is best known for his work on computer programs that could play games, most notably checkers (or draughts). Samuel's significant contributions include the development of one of the first programs that allowed a computer to learn from experience and improve its performance over time, which is a foundational concept in machine learning.
Wetting refers to the ability of a liquid to maintain contact with a solid surface, resulting from adhesive forces between the liquid and the solid. This phenomenon is particularly important in various fields such as chemistry, materials science, and biology. When a liquid is poured onto a solid surface, the extent to which the liquid spreads out or forms droplets depends on the balance between cohesive forces (the forces holding the liquid molecules together) and adhesive forces (the forces between the liquid molecules and the surface).
A water retention curve (WRC), also known as a soil water characteristic curve (SWCC) or moisture retention curve, is a graphical representation that illustrates the relationship between the water content of soil and the soil's matric potential or suction (often measured in units such as centimeters of water or kilopascals). The curve helps to understand how much water a soil can hold at different levels of moisture and suction.
Viscoelasticity is a property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. This means that these materials can both flow like a fluid (viscous behavior) and deform elastically (return to their original shape) when stress is applied. ### Key Characteristics: 1. **Viscous Behavior**: When a force is applied to a viscous material, it deforms and flows continuously over time.
A Schmitt trigger is an electronic circuit that acts as a bistable multivibrator and is designed to provide a clean switching action with hysteresis. It is commonly used to convert an analog input signal into a digital output signal. The key characteristics of a Schmitt trigger include: 1. **Hysteresis**: This means that the output state switches at different input voltage levels for rising and falling input signals.
The Preisach model of hysteresis is a mathematical representation used to describe and analyze the hysteretic behavior of materials and systems. It is particularly relevant in the study of ferromagnetic and ferroelectric materials, where the relationship between external inputs (like magnetic or electric fields) and outputs (like magnetization or polarization) exhibits a non-linear behavior that depends on the history of the applied field.
Multiferroics are materials that exhibit more than one primary ferroic order parameter simultaneously, typically ferroelectricity, ferromagnetism, and/or ferroelasticity. In simpler terms, these materials can display both magnetic and electric polarization simultaneously, which is a rare and fascinating property in the field of condensed matter physics.
The Mpemba effect is an observed phenomenon where hot water can freeze faster than cold water under certain conditions. Named after Tanzanian student Erasto Mpemba, who noticed this effect in the 1960s, the effect has intrigued scientists and led to various hypotheses explaining why it occurs.
Ferroics refer to a class of materials that exhibit specific types of ordering in their structure and properties, most notably ferromagnetism, ferroelectricity, and ferroelasticity. These materials have unique characteristics due to their dual nature—they can exhibit spontaneous ordered states (like magnetization or polarization) that can be reversed by external fields (magnetic or electric).
Ferroelasticity is a property of certain materials that exhibit a spontaneous strain, or deformation, in response to an applied stress. This behavior is analogous to ferromagnetism in magnetic materials, where a material can become magnetized in the presence of a magnetic field. In ferroelastic materials, the deformation is reversible and can be significant, depending on the applied stress.
The contact angle is a measure of the wettability of a solid surface by a liquid. It is defined as the angle formed between the tangent to the liquid interface and the solid surface at the three-phase contact line, where the solid, liquid, and gaseous phases meet. In practical terms, the contact angle can provide insights into how a liquid will interact with a solid surface: - **Low Contact Angle (0° to 90°)**: Indicates that the liquid wets the surface well.
The Bouc–Wen model is a mathematical model used to describe hysteretic behavior often observed in materials and systems, particularly in structural engineering, mechanical systems, and materials science. The model is widely employed to capture the nonlinear and hysteretic responses of systems subjected to cyclic loading, such as in seismic analysis or during material deformation.
Magnetic hysteresis refers to the dependence of the magnetic state of a material on its past magnetic history. This phenomenon is commonly observed in ferromagnetic materials, which can be magnetized and demagnetized, displaying a non-linear relationship between magnetic field strength and magnetization. When a ferromagnetic material is subjected to an external magnetic field, it becomes magnetized, aligning the magnetic moments of its atoms.
Ferroelectric materials are a class of dielectric materials that exhibit a spontaneous electric polarization that can be reversed by the application of an external electric field. This polarization occurs even in the absence of an external electric field, meaning that ferroelectric materials have a non-centrosymmetric crystal structure, allowing for the alignment of electric dipoles within the material.
A tachyonic field is a theoretical concept in physics associated with the idea of tachyons, which are hypothetical particles that always move faster than the speed of light. The name "tachyon" comes from the Greek word "tachys," meaning "swift." In the context of field theory, a tachyonic field is a scalar field that possesses a mass squared that is negative.
"Tachyon" can refer to a couple of different concepts depending on the context: 1. **Physics**: In theoretical physics, a tachyon is a hypothetical particle that travels faster than the speed of light. The concept of tachyons arises in certain interpretations of quantum field theory and relativity. If they exist, tachyons would have some counterintuitive properties, such as imaginary mass, leading to complex implications for causality and the structure of spacetime.
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!
Intro to OurBigBook
. Source. We have two killer features:
- 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-calculusArticles 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/derivativeVideo 2. OurBigBook Web topics demo. Source. - 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.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.Figure 3. Visual Studio Code extension installation.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. - Infinitely deep tables of contents:
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





