OpenLLM-France/wikimedia huggingface dataset:
# Strength of Materials/Torsion

Strength of Materials
Strength of Materials in Engineering Mechanics
Introduction | Introductory Concepts | Loading of Beams | Torsion | General State of Stress | Weakest link determination by use of three parameter Weibull statistics
next →
Torsion acting on a long bar tends to twist it in the direction of the torque. The analysis is performed on a section perpendicular to the axis, and the sum of the internal resisting torque is set equal to the external torque acting on the system. The following assumptions will be made for the bars studied in this chapter:
* Plane sections remain plane after the torque is applied.
* The shear strain γ varies linearly in the radial direction.
* The material is linearly elastic, so that Hooke's law applies.

### Torsion Formula

We want to find the maximum shear stress τ$_{max}$ which occurs in a circular shaft of radius c due to the application of a torque T. Using the assumptions above, we have, at any point r inside the shaft, the shear stress is τ$_r$ = r/c τ$_{max}$.
∫τ$_r$dA r = T
∫ r$^2$/c τ$_{max}$ dA = T
τ$_{max}$/c∫r$^2$ dA = T
Now, we know,
J = ∫ r$^2$ dA
is the polar moment of inertia of the cross sectional area..
Thus, the maximum shear stress
τ$_{max}$ = Tc/J
The above equation is called the torsion formula.
Now, for a solid circular shaft, we have,
J = π/32(d)$^4$
Further, for any point at distance r from the center of the shaft, we have, the shear stress τ is given by
τ = Tr/J
We only consider the torsional loading of simple circular shafts in this analysis, ie cylinders or non-eccentric tubes without splits. Circular shafts are most commonly used as torque carrying members in machinery with rotating parts (like drive shafts of motors). This is fortuitous, as the analysis of non circular members under torsion is not simple to perform analytically.

### Angle of Twist

The above image shows the twist of a shaft acted upon by a torque T at one end. We know that the shear angle γ is given by
γ = τ/G
For a shaft of radius c, we have
φ c = γ L
where L is the length of the shaft. Now, τ is given by
τ = Tc/J
so that
φ = TL/GJ
The angle of twist φ for a circular shaft acted upon by a torque T$_x$ at a point x along its axis is given by:
$\phi =\phi _{B}-\phi _{A}=\int _{A}^{B}{\frac {T_{x}}{J_{x}G}}dx$
where J$_x$ is the moment at section x. Note that you can use the torsion formula for shafts with slowly varying area as long as they are circular.
# Strengths-Based Social Work Practice/Copyleft

Copyright 2005 Todd Richard Lyons. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation. A copy of the license is included in the section entitled GNU Free Documentation License.
If you've helped with this document, please sign below!

## Contributors

* Todd Richard Lyons, LSW - Canadian - Indianapolis IN, USA - b.1970

## Editors and Proofreaders

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# Strength of Materials/Introduction

Strength of Materials
Strength of Materials in Engineering Mechanics
Introduction | Introductory Concepts | Loading of Beams | Torsion | General State of Stress | Weakest link determination by use of three parameter Weibull statistics
next →
Solid Mechanics is the study of load carrying members in terms of forces, deformations, and stability. There are three length scales: Atomic scale, Micro scale, Continuum scale. In this book, we take the continuum mechanics approach. We will consider the material to be homogeneous and isotropic (unless specified). Thus the material properties are even when we consider infinitesimal areas and volumes. The alternative approach is to build up material properties from basic equations relating atomic forces and interactions, and extending it to larger sets of such entities (e.g., ab-initio, molecular dynamics). Other approaches include micro-scale theories like dislocations to explain behavior of materials, especially for plasticity. However, the approach in this book is applicable to a large variety of practical problems, where we deal with structural members, usually under elastic deformation.
The images on the right show a body which is acted upon by external forces $\mathbf {F} _{1}\,$, $\mathbf {F} _{2}\,$, etc. The supports provide reaction forces ($\mathbf {R} _{1}\,$, $\mathbf {R} _{2}\,$) so that the body is stationary.
In addition to external forces, which act at points on the surface, we can also have forces which are body forces ($\mathbf {b} \,$), i.e., they act on each point in the body. Forces acting at a distance (Eg: Gravity, Magnetic) can be examples of body forces.
Consider a body which has several external forces acting on it. If a body is in static equilibrium, then every section of the body should also be in static equilibrium. Now, consider an elemental area dA in that section. Let the force acting on the elemental area so that the whole body is in equilibrium be dF. We can resolve this force in three mutually perpendicular directions. Let the component of the force normal to the surface be dF$_z$. Let the components in the plane of dA be dF$_x$ and dF$_y$ respectively. Then for the body to be in static equilibrium, we should have:
$\sum {\mathbf {dF} _{i}}=0,i=1,2,3$
There are three other conditions concerned with moments for completely defining static equilibrium. We will look in to it in the later chapters.
# Structural Biochemistry/Directed Changes in DNA

Proteins with new functions can be created through directed changes in DNA. In the classic genetic approach, mutations are generated randomly throughout the genome. Analysis of mutatants reveal which genes are altered and DNA sequencing identifies the exact changes. Now, utilizing recombinant DNA technology, specific mutations can be made in vitro. New genes can be constructed by three changes to the sequence: deletions, insertions, and substitutions.

## Deletions

Deletions occur when one or multiple base pairs are cleaved from a DNA sequence. A specific deletion can be produced by cleaving a plasmid at two sites with a restriction enzyme which removes a large segment of DNA. A smaller deletion can be made by cutting a plasmid at a one site and the linear DNA can be digested by an exonuclease that removes nucleotides from both strands. T
Deletion is when a base pair is removed from the DNA sequence. This causes the DNA strand to be shorter.

## Substitutions

Single amino acid substitutions can be produced by oligonuleotide-directed mutagenesis. This mutation can be made if (1) a plasmid containing the gene or cDNA for the protein is obtained and (2) the base sequence around to site to be altered is known. If serine is to be changed to cystine, the code TCT needs to be changed to TGT, a point mutation. The key to this mutation is to prepare an oligonucleotide primer that is complementary to this region except that it contains TGT instead of TCT. The mismatch of one base pair out of 15 does not make a large difference. Replication of these DNA strands with the mutated primers leads to two kinds of plasmids, one with the original sequence and one with the mutated sequence.
A substitution occurs when one base pair is replaced with another. There are three main effects of substitutions in DNA:
1. The substituted base could encode a stop codon. This will stop the DNA from producing the rest of the amino acids and could lead to a nonfunctioning protein that might be harmful to the biological system or damaging to the DNA.
2. The new substituted base could encode a different amino-acid, which will make the DNA produce a different amino-acid than it was supposed to.
3. Silent Mutation- This is when the changed base still codes for the same amino acid. These mutations are rarely harmful to the DNA or biological system.

## Insertions

Insertions of a DNA sequence can be made using cassette mutagenesis. In this technique, plasmid DNA is cut with a pair of restriction enzymes to remove a short segment which can be replaced by a synthetic double stranded oligonucleotide.
Insertions are the result of extra bases added into the DNA sequence.

## Frame Shifts

This is caused by insertions and deletions. Deletions will make the DNA sequence shorter, while insertions will extend the DNA sequence’s length. Codons are encoded in groups of 3 bases. A deletion or insertion of bases will shift the whole sequence, and the DNA could potentially encode a whole new set of amino-acids.
# Structural Biochemistry/Dianabol

Dianabol (also called methandrostenolone, averbol, danabol, methandienone or methanienone) is an anabolic steroid that some athletes use to increase the size and strength of their muscles. This is similar to male hormone testosterone. Some studies suggest that the effects of the drug are minimal, but some side effects keep people from using it.

## History

Dianabol was developed in Germany and released in US in 1960s by Ciba Specialty Chemicals. It is a controlled substance in United States, though popular with body builders.

## Dr. Zeigler

Dr. Zeigler, the team physician for U.S. gold Olympic weightlifting team, played a large role in the research of altering testosterone to make it safer for the body. However, due to misuse of the drug by athletes, Dr. Zeigler became the voice of opposition of sport doping.

## Side Effects

* Increased risk of liver cancer
* Increased risk of heart disease
* Oily skin, acne and bodily and facial hair growth
* Liver dysfunction
* Androgenic side effects
* For women, deepening of voice and irregular menstrual cycles.

## References

* http://en.wikipedia.org/wiki/Methandrostenolone
* http://www.dianabol.org/
# Structural Biochemistry/Differentiation
## Differentiation

    During the differentiation stage the cells acquire an identity (phenotype). Each cell's axon thus begins to grow toward the target and acquires/expresses specific enzymes to produce neurotransmitters and receptors. And the most importantly, myelination of the neurons begin during this stage. There are numerous ways that axons find its target: 1. pathway selection 2. target selection, address selection 3.direct cell to cell communication 4. detection of extracellular signals from other cells 5.communication via diffusable chemical signals from cells at a distance.
# Structural Biochemistry/Diverse Interactions of retroviral Gag proteins with RNAs
## Introduction

Retroviruses are created by Gag, a single virus-encoded protein. Assembling an infectious particle means there are very diverse interactions (specific and nonspecific) between Gag proteins and RNA. These interactions are vital for the particle construction, packing of viral RNA in the particle, and how the primer is placed for viral DNA synthesis.

## Gag proteins: the building blocks of retroviruses

Retroviruses are composed of 6 genera (alpha-, beta-, gamma-, delta-, epsilon-, and lenti-retrovirsuses) and also a subfamily called Spumaviridae. Th Gag protein is the building block for retrovirus particles; expression of this protein allows for efficient assembly of virus-like particles in most, if not all, mammalian cells. When viruses are being assembled, Gag proteins interact with lipids in the plasma membrane with RNAs and other Gag molecules. These interactions involve the formation of the particle, selecion of what RNA species will be included in the particle, and the refolding of the packages RNAs.

## A nonspecific interaction with RNAs drives virus particle assembly

Purified, recombinant Gag proteins are soluble in aqueous solutions so they aren't interested for protein-protein interactions that needs to occur for virus particle formation. However, if a single-stranded nucleic acid is added, it triggers in vitro assembly on the Gag proteins into VLPs. In vivo, particle assembly is dependent on Gag-nucleic acids (NA) interactions because NAs are about 20-40 nucleotides, so they can support assembly in vitro. The NAs are so short, though, that they can only bind to a few Gag molecules. The NC domain of Gag is where the site of interaction is at with NAs.When the NC domain binds with NA, the conformation is altered of the capsid domain. This ultimately exposes new interfaces for protein-protein interaction. In many retroviruses, the NC domain of Gag is most attracted to RNA.However, the matrix domain at the N-terminus is positively charged and is also able to interact with RNAs.

## Reference

Rein, Alan, et al. "Diverse interactions of retroviral Gag proteins with RNAs" Trends in Biochemical Sciences 36.7 (2011) 373-379. Academic Search Complete. Web. 21 Nov. 2012.
# Using GNOME/History of GNOME

GNOME was started in late 1997 due to unhappiness over licensing problems with KDE. In 1999 the first version was released.
In late 2001 the main focus switched to usability and GNOME 2.0 was released in June 2002. Gnome 2.6, was released in March 2004. Releases occur every six months. The current release is 3.22.
See also: http://www.linuxvalley.com/encyclopedia/ldp/lg/issue35/icaza.html
# Using GNOME/Main desktop

When you log in to gnome, you will appear on the main desktop.?! This chapter will explain the items you are likely to see on the desktop.
* Desktop area
* Application windows
* File manager
* Menus
* Panel
* Applets
* Preferences
# Using GNOME/Force Quit

< Using GNOME/Applets
Force Quit is an action applet that it used to deal with crashed and non-responding applications by forcing them off the screen. It allows you to deal with them in just two clicks. This is often useful when beta testing applications and it crashes on you.
To add to the panel, select Add (Some systems use "Add to Panel..."), Actions, Force Quit. It will appear as a Window icon with a large red cross on it.
To use.
* Click the "Force Quit" button.
* Click the Application to wish to quit.
# Using GNOME/Further reading

Further reading and documentation
# Using GNOME/Icons

Icons are small pictures. There are many types of icons.
* Menu icon
* Action Buttons
* Icons on Buttons
* Launcher icons
# Using GNOME/Login

When you turn on your computer, you see the operating system load. Once the system has started, the computer will open the GNOME user interface. GNOME runs atop the operating system and provides a Graphical User Interface (GUI) for the user to interact with. The login screen is the first screen a user will see when GNOME starts.

## Types of login screen

There are two types of login screen, standard and graphical. GNOME allows the users to select a login theme to customize their computer. Different operating systems provide different “preferred” graphical themes.
A graphical login screen includes a “face browser”, which lets the user visually select their user name, while a standard login screen simply provides text boxes to enter a user name and password. There is no OK button on the login screen; instead, you press Enter once you have entered your password. If you entered your password correctly, GNOME will display the main desktop.

## Shutting down the computer

But suppose you want to shut down your computer instead. There is a way to do this from the login screen.
In the top-right corner of the login screen you will see two icons. We will be focused on the one with the power-button icon. (The person icon, if clicked, reveals a list of accessibility-related features, such as High Contrast or Mouse Keys.) A dropdown will appear. Confusingly, all you will see there is a button labeled “Dark Style” and another power-button icon. To shut down this computer, you must click the second icon to display the restart and power-off (shut down) commands. Clicking Suspend will put the computer to sleep.

## Screenshots

* GNOME login screen
* Accessibility menu
* Shutdown menu
# Using GNOME/File manager wastebasket

The Waste basket is a place to store unwanted files. Emptying the wastebasket deletes all files in it permanently, so make sure there is no important files in there by mistake.
You can also have the option to delete files instantly without moving it to the wastebasket first. To enable this, choose "Edit, Preferences" from the file manager window, then on the behavior tab select "Include a Delete command that bypasses Wastebasket". use this with care. It is like using a shredder to destroy a document.
Back to contents page
# Using GNOME/Font

< Using GNOME/Preferences
GNOME makes changing fonts easy. Here's how.
First, Select Menu, Preferences, Font.

## Font types

There are Four types of font : Application Font, Desktop Font, Window Title Font and Terminal Font. To change them, just click them.

## Rendering

Rendering allows you to control the look of the fonts

## Details

Details allow you to control advanced properties of the fonts.
# Visual physics and mathematics/Heat

An initially cold bar is heated at one of its ends. It is assumed that its side walls are thermally insulated. The heat diffuses along the length of the bar:
The black line represents the temperature.
# Visual physics and mathematics/Vibrations

A body can have many modes of vibration.
Vibration modes of a circular drum:
A mode of vibration of a square plate:
# Visual physics and mathematics/Percolation

To model percolation (how a fluid passes through a porous material for example), we can randomly distribute bonds on a square network. p is the proportion of bonds among all possible links. As long as p < 1/2, the bonds do not percolate. A fluid passing through them cannot go very far. The material is not porous. But as soon as p is greater than 1/2, paths as long as desired appear:
When p = 1/2, we obtain a fractal structure. It is a structure which retains its structure when we change scale:
# Visual physics and mathematics/Quantum Physics

Quantum physics can be summarized by a single great principle, the principle of superposition of states:
Any physical system which can be in the states $|1\rangle$ and $|2\rangle$ can also be in a state $\alpha |1\rangle +\beta |2\rangle$ where $\alpha$ and $\beta$ are any complex numbers.
The same principle can be phrased in an equivalent way :
The space of states of any physical system is a complex vector space.
As far as we know the validity of the superposition principle is not restricted : any physical system. There is not any boundary between quantum systems, which obey the superposition principle, and classical systems, which would not. All known systems are fundamentally quantum systems, because they are all made of quantum particles.
The principle of superposition has three immediate consequences:
Spin and entanglement are difficult to represent visually. On the other hand, wave-particle duality can be shown easily, because it is enough to show waves:
This animation shows the quantum state (the wave function) of an initially very localized particle. Luminosity represents the probability of presence. The color represents the phase of the wave function.
A particle can propagate like a wave packet by spreading out slowly:
A particle can also be in a state of superposition of two wave packets:
A quantum particle can therefore interfere with itself.
The interference pattern of a particle with itself can be observed:
Or simulated by calculation:
There is something crazy in this universal validity of quantum superposition. Suppose that $|1\rangle$ and $|2\rangle$ are states of the moon in two different places. If the moon is in the state ${\frac {1}{\sqrt {2}}}(|1\rangle +|2\rangle$), it seems to be in two different places at the same time. This should be a general phenomenon. With quantum superposition, any system can be simultaneously in as many places as one wants. Could Don Juan multiply his affairs in a quantum way ?

## See also

* Some fundamental theorems of quantum physics
* Quantum theory of observation
# Visual physics and mathematics/How to contribute

On this page anyone can write how he or she invites others to participate.
Images and films may or may not be accompanied by comments which precede or follow them. If there is a conflict between publishers, the author of the image or of the film decides freely whether or not he or she accepts the comments.
The cover will be decided through election.
To make a film, just write the script. The machine takes care of the shooting.
If your machine is not powerful enough to do the shooting of your scripts, you can ask for help:

## 3D

For 3D, Blender is on top. Just know how to write the script in Python.

## 2D

With 2D, the screenwriter is the master of the color and brightness (usually three numbers between 0 and 255) of each pixel of each image.

### TD

I write my code in a simplified language, just what it takes to make the film, and the machine translates it into executable code. An example :
I will give tools which will automatically translate this code into an executable on the machines I know.
# Visual physics and mathematics/Pythagoras and the origin of harmony

The waves propagate but the sphere and the air around it oscillate around their equilibrium position and do not propagate.
A vibration, or oscillation, is a periodic movement, a movement that returns to its starting point and starts again. The period $T$ is the duration of the repeating movement, the duration of a round trip. The frequency $f$ is the number of periods per unit of time, therefore the inverse of the period:
$f=1/T$
If the unit of time is the second (s) then the unit of frequency is the Herz (Hz).
The movement above has a period equal to 3 s and a frequency equal to 1/3 Hz.
Even circular motion is an oscillation:
The human ear perceives as sounds vibrations whose frequency is higher than a few tens of Herz (the lowest sounds) and lower than approximately 20,000 Hz (the highest pitched sounds).
The fundamental mode of vibration of a string is the widest and the slowest: a single belly and no node. Its period is proportional to the length of the string:
Pythagoras discovered that musical chords appear when the lengths of the vibrating strings are in simple ratios (for strings that are equally taut and have the same mass per unit length).
| The octave | ratio of 2 to 1 |
| The perfect fifth | ratio of 3 to 2 |
| The perfect fourth | 4 : 3 |
| The major sixth | 5 : 3 |
| The major third | 5 : 4 |
Numbers are the cause of music which is the cause of everything that is, since all beings dance and sing. Numbers are therefore the cause of everything that is. “Everything is number” is the principle of the Pythagoreans.