text:
Wikiversity:Colloquium/archives/December 2006/Bureaucrats

Bureaucrats
In discussion on IRC, we were wondering about the process for setting up bureaucrats, and how many we should have. Currently, myself and Sebmol are the two bureaucrats on the English Wikiversity, and there is a nomination pending on Candidates for Custodianship for JWSchmidt.

The main questions, as I see them, include:
 * How many bureaucrats does this project need?
 * What is the due process for this taking place?
 * What kinds of actions should be delegated to bureaucrats, and how is this kept in check?
 * (Possibly minor point): Should this take place on its own page, rather than Candidates for Custodianship?

As always, our processes are in the open, and subject to scrutiny and consensus approval. If there is anything regarding this process (including my own bureaucratship*) that you would like to comment on, please do so here or on the above page or its talk page. Thanks. Cormaggio talk 16:41, 6 December 2006 (UTC)

* I was made bureaucrat by Brion Vibber on the opening day of Wikiversity, but I have never been approved by the community as a bureaucrat. Cormaggio talk 16:41, 6 December 2006 (UTC)
 * Well, what other powers do Bureaucrats have besides making new sysops? If that is it, having two would be plenty, as that is a job that is only needed around once a month.  If they also have the powers of check user and delete revision, then we might need more, depending on how wikiversity develops.(Looking at meta, Bureaucrat, looks like change name and grant bot status are the other powers they have, stewards have the checkuser and delete revision)--Rayc 17:07, 6 December 2006 (UTC)

 * I think we need Bureaucratship, a page that would be similar to Custodianship. --JWSchmidt 17:10, 6 December 2006 (UTC)

 * Cormac, i think you are a great bureaucrat. You are diplomatic and open to feedback, which is good for the community. The job of a bureaucrat is not only appointing sysops. You and Sebmol are also the official representatives (or authorities) of Wikiversity. I have no wish to be either a bureaucrat or a sysop. I would be happy to devote my time at the school of history or to debate here on what Wikiversity could be in the future. At the moment, our community is peaceful, there are no conflicts whatsoever. In the future, your task as bureaucrat could become one of great responsibility, since you will be the highest authority, who can make and break those who want to have influence in Wikiversity.--Daanschr 18:45, 6 December 2006 (UTC)

 * One of the main successes of Wikipedia is that Jimmy Wales is the leader of this organization. A history of Wikipedia has been written (i don't know how accurate it is, since i was not there at the moment), which could give you an indication on how to run a succesful organization.--Daanschr 19:03, 6 December 2006 (UTC)

 * Two things: let's just officially confirm Cormaggio as of this edit - a bureaucrat of Wikiversity, complete with its full rights and responsibilities.

 * As for the other questions, I need to think a bit more about it. I'd advocate promoting JWSchmidt though - the nomination has been up for months, and probably would be a healthy idea to resolve the issue. --HappyCamper 00:14, 7 December 2006 (UTC)
 * (+)Pro: and Pro: --Hillgentleman|User talk 07:48, 7 December 2006 (UTC)
 * ,, and why aren't we doing this on the right page?--Rayc 22:07, 7 December 2006 (UTC)

Discussion
Well, let me tiptoe a little here and answer Cormaggio's questions right at the top:

 * 1) 2 is already plenty. We could pospone the bureaucrat++, but I dislike this ambiguity. What I expect would happen, is that these bits would simply be in dormant but trusting hands. This sounds reasonable I think.
 * 2) Due process is anything which does not cause excessive drama. If we have contributors crying foul despite a carefully adjudicated, moderated process, where the "right" decisions have been made by the book, that is not due process. Due process is graceful and self evident.
 * 3) Bureaucrats need to know when to recuse themselves from making decisions...
 * 4) We can keep everything on the Candidates for Custodianship. Nice and centralised.

Now, I know I am not being particularly elegant with this response - it's supposed to be a block of marble to be shaped into a statue, hm? So, please, continue this thread. We can resolve this issue now, and move on to other fun things to work on. It's one of the housekeeping items which should be addressed.

A sketch: when I support a candidate for special sysop bits, I am giving them my vote of confidence that they can be more autonomous on this site - this is what it really says. I rarely babysit their actions - it's not why I am here, and it would defeat the purpose of trusting them in the first place. Granted, these bits should not have a high activation energy to get rid of - it is not, and should not, be something that defines a contributor's primary identity here. My expectation is that those users with sysop bits should act in a way with other editors such that their role as a custodian or regular user is clearly distinguished, and that this is carried out in an ethical way. There should not be any ambiguity in this. This place does not need accusations of a "cabal" or situations of a "corrupt custodian". Smart little steps serve a long way to keep the integrity of institutions that have served Wiki projects well since Day 1. A custodian, and especially a bureaucrat, should not compromise this. Poor morale accumulates, is extremely difficult to dissipate, and is unhealthy.

Note the rhetoric around "trust" and "integrity" though. The essence of this is that the community simply expects surprises to be kept to a minimum. To make an analogy, those in positions of power act as if they are taking care of the the macroeconomic engine. Measured is the key word. I would prefer to see bureaucrats not promote those that they have supported, or close forums for those whom they have opposed. The mind is abstract and one can read everything into anything. Sometimes, an ambiguous detached restraint is very apt.

Alirght! Back to our Colloquium... --HappyCamper 03:33, 8 December 2006 (UTC)

 * I agree with you. I prefer a kind of leadership that is reasonable and above the factions. Especially in an organization that is just starting and is in need of new volunteers it is good to have leaders that try to include others and want to serve the interest of the community as a whole. It is important to be positive and to try to come to all kinds of ideas on how we can make this project into a succes.--Daanschr 11:07, 8 December 2006 (UTC)

 * Well, this issue of leadership is quite complicated because the stratification on the Wiki is very loose. In a sense, it is not fair on the part of the community to burden bureaucrats with unequivocal leadership. At the end of the day, the accounts that they have are operated by people like you and me. On an open Wiki, leadership emerges sort of spontaneously - we associate authority and competence with mature accounts, not necessarily those with special bits. The correlation is high though, I'm confident to say. What we should have bureaucrats do, is in the future if we have "votes" of some sort, that they can close them and "officially" declare them as such. Some participants like to have this formality for a sense of professionalism and security, and there's no harm in having them do this I think. --HappyCamper 16:43, 8 December 2006 (UTC)

That sounds better then my idea on leadership.--Daanschr 19:07, 8 December 2006 (UTC)

 * Thank you. I'll come back with some other thoughts later. It looks like something is developing on Wikiversity talk:Bureaucratship. --HappyCamper 03:39, 9 December 2006 (UTC)


text:
Wikiversity:Colloquium/archives/December 2006/Dynamic Page List

Dynamic Page List
A very useful feature on Wikinews is the ability to create dynamic page lists. This allows the re-organisation and multiple display of content with out effecting the original pages. This would be very useful in creating a dynamic Colloquium, talk pages, course structures, blogs and other tools where content needs to be displayed in different ways. This extension can be added to any mediawiki could it be added to Wikiversity. Mystictim 16:40, 20 December 2006 (UTC)
 * That looks like an interesting module. I imagine that the more flexible the system is, the better. --Remi0o 21:57, 20 December 2006 (UTC)
 * This discussion is being continued over at Request custodian action Mystictim 18:08, 13 January 2007 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
Wikiversity:Colloquium/archives/December 2006/Learning Blogs

Learning Blogs
Yes, no? I'm seeing them start to pop up, and I remember blogs have been used as educational purposes. However, there is a huge potential for abuse. If we keep them, we might want to set up some guideline about what can and cannot be posted about.--Rayc 20:29, 9 December 2006 (UTC)
 * I think we need to be supportive of all types of communication that are intended to support the learning goals of Wikiversity participants. Wikipedia has been able to limp along with simple discussion pages, but discussions and commentaries can be an integral part of Wikiversity main namespace content. If we are serious about the importance of using the power of wiki-based collaboration to support learning, we need participants to be communicative about their personal learning goals, frustrations, plans and wiki-based activities. --JWSchmidt 22:32, 9 December 2006 (UTC)
 * I think that there is a place, and perhaps even a need, for so-called learning blogs. For instance, it is an integral part of the Learning to learn a wiki way project.  I would guess that many blogs like this would evolve away from the standard blog format or wiki discussion format into something that is more unique to wikiversity.  What kind of abuse are you concerned about?
 * Knew there was a reason that people seemed to be doing them similar --Rayc 23:22, 9 December 2006 (UTC)
 * I think learning blogs are a fantastic idea - in my view, the more reflective we become, the better we can understand our learning, as well as our impact on others' learning. People can start their blogs within this limited Mediawiki format (and it is no harm if people are critical, just possibly not excessively disruptive*), or they can start a blog elsewhere, and link to it from Wikiversity - both of which options are being pursued at the moment... Cormaggio talk 19:19, 10 December 2006 (UTC)
 * * Hmm, this possibly needs to be defined somehow - do we need a policy on blogs? Or is this against their very raison d'etre? Cormaggio talk 19:19, 10 December 2006 (UTC)

 * No doubt Wikiversity should be represented upon the "Blogosphere" as they call it, but I think this Colloquium is the key. As a learning community, we have a centralized discussion here that a lot of blog sites would die (or kill) for. What frustrates me about blogs is that they consume time and effort many times for no useful purpose (except maybe to vent) and it's difficult to find things I'm looking for.

 * The flexibility of the University context allows things like opinion, especially here in the colloquium and on talk pages, plus there is room for original research, collective reflection, essays, question and answer sessions and a myriad of other communicative activities. The neat thing (neat as in tidy) is that a university context facilitates organization and topical relevance like no other structure can. Topical disscusions are right there "beside" the topics covered. As Wikiversity grows (in quality and quantity) topics and subjects should become easier to find. Furthermore, people can actually assosiate and relate to one another as they learn to learn.

 * So, How does this Colloquium and the cumulative "Talk:o:sphere" at Wikiversity differ from a "Blog" (weblog)? I think we have it all! CQ 13:23, 23 December 2006 (UTC)

 * I very much agree with what Charley says above, but I also think that personal blogs are a vital way for each one of us to keep a record of our personal thoughts and feelings about what's going on from our perspective on Wikiversity. The Colloquium serves a crucial purpose, but people are not going to detail the minutiae of their personal thoughts on the Colloquium - that's more of what personal blogs are for. So, I think all of these things can work in tandem with eachother - to continue to develop Wikiversity into a collaborative, reflective, learning community. Cormaggio talk 15:26, 29 December 2006 (UTC)


text:
User talk:Mysha~enwikiversity

Hello Mysha, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. When leaving comments for others to read, remember to sign and date; it helps everyone keep track of who is writing messages. The signature icon in the edit window makes it simple. To help you get started:
 * Take a guided tour and learn how to edit;
 * Explore our learning projects;
 * Browse our portals, schools, and research pages; and
 * Read and help develop our community policies.

Also, don't forget to experiment with the links to your left. Be bold, and see you around Wikiversity! --JWSchmidt 12:52, 2 August 2007 (UTC)

Image copyright problems

 * Your currently affected images are below. Please provide a license template and source for each one. Thanks. – Mike.lifeguard | @en.wb 23:25, 13 February 2008 (UTC)

 * 2007-07-26 09:43, Mysha: TechWriting1.jpg: untagged! ; 2 (2)
 * 2007-07-26 09:45, Mysha: TechWriting2.jpg: untagged! ; 3 (3)
 * 2007-07-26 09:47, Mysha: TechWriting3.jpg: untagged! ; 0 (0)
 * 2007-07-26 09:49, Mysha: TechWriting4.jpg: untagged! ; 5 (5)
 * 2007-07-26 09:51, Mysha: TechWriting5.jpg: untagged! ; 8 (5)
 * 2007-07-26 09:56, Mysha: TechWriting6.jpg: untagged! ; 6 (6)
 * 2007-07-26 12:15, Mysha: TechWriting7.jpg: untagged! ; 2 (2)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Mysha. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Mysha~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:44, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:16, 19 April 2015 (UTC)

title: User talk:Mysha~enwikiversity


text:
User talk:Wlodek~enwikiversity

Hello Wlodek, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. When leaving comments for others to read, remember to sign and date; it helps everyone keep track of who is writing messages. The signature icon in the edit window makes it simple. To help you get started:
 * Take a guided tour and learn how to edit;
 * Explore our learning projects;
 * Browse our portals, schools, and research pages; and
 * Read and help develop our community policies.

Also, don't forget to experiment with the links to your left. Be bold, and see you around Wikiversity! --JWSchmidt 13:01, 2 August 2007 (UTC)

Image copyright problems

 * Your currently affected uploads are listed below. For each, please provide a license template and source. thanks. – Mike.lifeguard | @en.wb 23:41, 13 February 2008 (UTC)

 * 2007-08-07 11:15, Wlodek: Mypic.jpg: untagged! ; 1 (0)
 * 2007-08-07 11:50, Wlodek: WSnieguMale.JPG: untagged! ; 1 (0)
 * 2007-08-09 15:26, Wlodek: Wikiuni1.jpg: untagged! ; 1 (1)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Wlodek. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Wlodek~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:48, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:25, 19 April 2015 (UTC)

title: User talk:Wlodek~enwikiversity


text:
User talk:BartJuniorTW

Hello BartJuniorTW, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. When leaving comments for others to read, remember to sign and date; it helps everyone keep track of who is writing messages. The signature icon in the edit window makes it simple. To help you get started:
 * Take a guided tour and learn how to edit;
 * Explore our learning projects;
 * Browse our portals, schools, and research pages; and
 * Read and help develop our community policies.

Also, don't forget to experiment with the links to your left. Be bold, and see you around Wikiversity! --JWSchmidt 13:02, 2 August 2007 (UTC)

Image copyright problems

 * This is the image in question. Please provide license information and a source for this image. Thanks. – Mike.lifeguard | @en.wb 22:11, 13 February 2008 (UTC)

title: User talk:BartJuniorTW


text: File:Torsion of circular cylinder.png

title: File:Torsion of circular cylinder.png


text: File:Torsion of noncircular cylinder.png


text: File:Bob DeYager trill.ogg

title: File:Bob DeYager trill.ogg


text: File:Torsion elliptic cs stress.png

title: File:Torsion elliptic cs stress.png


text: File:Torsion elliptic cs disp.png

title: File:Torsion elliptic cs disp.png


text: File:Torsion of triangle cylinder.png

title: File:Torsion of triangle cylinder.png


text: File:Torsion triangle cs stress.png

title: File:Torsion triangle cs stress.png


text: File:Torsion triangle cs disp.png

title: File:Torsion triangle cs disp.png


text:
File:Storyboarding man boy offcenter.png

Used with the WikiU Film School Lesson on how to create 3D storyboards with FrameForge 3D Studio Demo Version.


text:
File:Storyboarding man boy close.png

Used with the WikiU Film School Lesson on how to create 3D storyboards with FrameForge 3D Studio Demo Version.

title: File:Storyboarding man boy close.png


text:
File:Storyboarding man boy far.png

Used with the WikiU Film School Lesson on how to create 3D storyboards with FrameForge 3D Studio Demo Version.

title: File:Storyboarding man boy far.png


text:
File:Shot number 04.jpg

Used with the WikiU Film School Lesson on how to create 3D storyboards with FrameForge 3D Studio Demo Version.

title: File:Shot number 04.jpg


text:
File:Shot 04 14mm.jpg

Used with the WikiU Film School Lesson on how to create 3D storyboards with FrameForge 3D Studio Demo Version.

title: File:Shot 04 14mm.jpg


text:
File:Shot 04 85mm on ground.jpg

Used with the WikiU Film School Lesson on how to create 3D storyboards with FrameForge 3D Studio Demo Version.

title: File:Shot 04 85mm on ground.jpg


text:
Talk:Java Tutorial

This seems very redundant as there is already a Learning JAVA lesson and an Advanced Java lesson... --Devourer09 19:08, 2 August 2007 (UTC)

I think we should remove Learning JAVA as this seems to be a much more reasonable path of learning. Also, it shouldn't cover advanced java topics? Cremisis13 14:52, 8 December 2007 (UTC)

Java Applets
I would like to add Java applets to the Java Tutorial. As far as I know this is currently already possible but quite difficult. An example is the Java player for media on Wikimedia Commons. mw:Extension:Java_Applet would be more convenient. --Bernhard Fastenrath 14:44, 16 May 2011 (UTC)
 * Interactive labs (Java applet)

ImageMagick from Java

 * http://www.jmagick.org/lenya/jmagick/live/index.html
 * http://im4java.sourceforge.net/docs/dev-guide.html

title: Talk:Java Tutorial


text:
EE 111 Digital Electronics/Final Exam

Essay Questions
for the course EE 111 - Digital Electronics in Electrical Engineering

1. What is an electron? How does it interact with other elementary particles and other electrons?

title: EE 111 Digital Electronics/Final Exam


text:
C Programming/Input and Output

Objective

 * Learn how to input and output data throught the console.
 * Learn how to input and output data using files.

Introduction
By now you should have noticed the frequent use of the function printf. This is the basic C function for printing text onto a command line terminal.

printf has an unusual (but very powerful) way of displaying text. All information to be displayed is placed between quotation marks. The unusual part is that in order to print the value of a variable, a placeholder must be used within the quotes. To use a placeholder, you write %datatype replacing datatype with a value corresponding to the type of the variable to be displayed. Finally, the name of the variable to be displayed is added after the last quotation mark, but before the semi-colon.

The values for variable placeholders are as follows:

For example, to print the value of an integer variable named "integer_var":

More than one variable can be included in a single printf function. However, for each variable placeholder within the quotation marks, a variable name of matching type must added to the end of the line. For example, to use an integer variable, a float variable, and a single character variable within a printf function, you could type:

Further, printf can also make use of escape characters to represent things that are kept in memory as text but cannot be written directly into your code. One commonly used escape code is \n, which is used to add a line feed to the output. Escape characters always start with a backslash "\".

For example:

will output: the number is 6 (followed by a blank line).

Escape Sequences
Here is a table of most of the escape sequences.

Add in use of stderr, scanf and fgets.

Simple input
For simple input we can use the function scanf. scanf reads formatted input which means it will need the format string to function. A very simple example:

- %d is the format string here, it means a simple integer, a digit.

- x is the variable we will store the integer we've just read, therefore we must pass the memory address of x to scanf. We can do that with the "address" operator &.

- cnt will store number of values we've actually read, if this is less than we intended then obviously something went wrong. So this provides us with some error checking capabilities!

scanf essentially uses the very same format strings as printf, see them on the top of this page.

File I/O
we can open a file in - binary - text modes.

Dealing with text files: Text files can be handled very similar to what we learned about the standard input/output, but now we will use fprintf/fscanf instead of printf/scanf! Their arguments are similar. The only difference is that fprintf/fscanf have 1 more argument. A file pointer! Also we need to open/close the files. It simply means to ask the OS to give us control over that particular file, then after we are done we give it back.

However first of all we need to open the file(s) we want to use.

Opening/using/closing a text file:

1.) First we need to declare a file pointer variable. 2.) Then we need to open it, telling the operating system how we want to open it (text/binary/read/write/append/etc). If the operation is successful we get a file pointer that will tells us where to read from/write. Otherwise we will get a NULL. So it is easy to find out if it was successful or not. 3.) After that we can actually read/write. In this example we write. The return value of fprintf/fscanf is the successfully read/wrote items. So it is easy to find out about errors here too. 4.) finally we need to close the file, it gives the control back to the OS.

'Dealing with binary files: Well binary files are really different than text files. In binary mode, you deal with bytes not characters, and it provides us with a method of storing data more efficiently. What is a matter of utmost importance when dealing with large amount of data (like databases), because it makes your program run faster. It's faster to read/write it from the disk, and takes less disk space! Let's see an example: The number 1985 in a text file, appears as 4 characters: '1','9','8','5'. This takes 4 bytes. However in a binary file it gets stored in the machine's internal format 0x07C1 (2 bytes if we are using short as the variable type). With this little trick we have already saved half the disk space. Opening and closing a file in binary mode is very similar to the method we learned about text mode files. We only have to add 1 more letter to the opening mode string in fopen. However to read and write such files we have brand new and totally different functions.

Opening/using/closing a binary file:

1.) first we need to declare a file pointer variable again, and a buffer variable (this is what we will write to the file). 2.) Now we need to open the file in binary mode. This can be done with adding a 'b' to the opening mode string. 3.) Now we can work with the file. We need to tell fwrite, what we want to write (need to pass a pointer to it, so we point on the data literally), how many times we want to write it, how big the data is we want to write, and where we want to write it. The fread function works almost exactly the same, just the other way around. 4.) Finally we need to close the file

Additional Resources

 * scanf on wikipedia
 * printf on wikipedia

Assignments

 * Previous Lesson: Strings
 * Next Lesson:
 * Course Home Page

title: C Programming/Input and Output


text:
User:Bgorges

I am a recent graduate of the University of Wyoming. I am now in Hawaii and working for the Telescopes on Mauna Kea. I am a computer engineer by training and so I have a general idea about the circuit stuff, technical I know. I also have software experience but I probably won't be writing about that for Wiki just quite yet. If you have any questions or comments, please, please tell/ask me.

Bgorges 19:38, 2 August 2007 (UTC)

title: User:Bgorges


text:
User:RationalPuff

About Me

 * I'm a Civil Engineer from India currently employed in UK
 * I have an extensive experience in Road Design Projects

My Interests

 * Transportation Engineering
 * Computer Science
 * Wild Life
 * Painting
 * Photography
 * Travel

title: User:RationalPuff


text:
Electrical Engineering Fundamentals

A Bridge to Circuit Analysis

 * Lecture 1: /Basics of Electricity/
 * Lecture 2: /Voltage Sources/
 * Lecture 3: /Current Sources/
 * Lecture 4: /Resistance/
 * Lecture 5: /Capacitance/
 * Lecture 6: /Induction/
 * Lecture 7: /Impedance/

Return:School:Electrical engineering

title: Electrical Engineering Fundamentals


text:
Elasticity/Compatibility

Compatibility
For an arbitrary strain field $$\textstyle \boldsymbol{\varepsilon}$$, the strain-displacement relation $$\textstyle \boldsymbol{\varepsilon} = \cfrac{1}{2}(\boldsymbol{\nabla}\mathbf{u}+\boldsymbol{\nabla}\mathbf{u}^T)$$ is the partial differential equation that can be solved to obtain the displacement $$\textstyle \mathbf{u}$$. The solution to this equation must exist and must be unique.

Uniqueness (Kirchhoff's Theorem)
If two displacement fields $$\textstyle \mathbf{u}$$ and $$\textstyle \mathbf{u}^{'}$$ correspond to the same strain field, then $$\textstyle \mathbf{u} = \mathbf{u}^{'} + \mathbf{w}$$, where $$\textstyle \mathbf{w}$$ is a rigid displacement field.

Existence (Compatibility Theorem)
The strain field $$\textstyle \boldsymbol{\varepsilon}$$ corresponding to a $$\textstyle C^2$$ continuous displacement field satisfies the compatibility equation
 * $$ \boldsymbol{\nabla}\times{\boldsymbol{\nabla}\times{\boldsymbol{\varepsilon}}} = 0 $$

In index notation

e_{ijk} e_{lmn} \cfrac{\partial^2 \varepsilon_{jm}}{\partial X_k \partial X_n} = 0 $$

The converse also holds if the body is simply connected. The compatibility equations can also be written as

\begin{align} 2 \cfrac{\partial^2 \varepsilon_{12}}{\partial X_1 \partial X_2} &= \cfrac{\partial^2 \varepsilon_{11}}{\partial X_2^2} + \cfrac{\partial^2 \varepsilon_{22}}{\partial X_1^2} \\ 2 \cfrac{\partial^2 \varepsilon_{23}}{\partial X_2 \partial X_3} &= \cfrac{\partial^2 \varepsilon_{22}}{\partial X_3^2} + \cfrac{\partial^2 \varepsilon_{33}}{\partial X_2^2} \\ 2 \cfrac{\partial^2 \varepsilon_{31}}{\partial X_3 \partial X_1} &= \cfrac{\partial^2 \varepsilon_{33}}{\partial X_1^2} +            \cfrac{\partial^2 \varepsilon_{11}}{\partial X_3^2} \\ \cfrac{\partial^2 \varepsilon_{11}}{\partial X_2 \partial X_3} &= \cfrac{\partial^2 \varepsilon_{12}}{\partial X_3 \partial X_1} - \cfrac{\partial^2 \varepsilon_{23}}{\partial X_1^2} + \cfrac{\partial^2 \varepsilon_{31}}{\partial X_1 \partial X_2} \\ \cfrac{\partial^2 \varepsilon_{22}}{\partial X_3 \partial X_1} &= \cfrac{\partial^2 \varepsilon_{23}}{\partial X_1 \partial X_2} - \cfrac{\partial^2 \varepsilon_{31}}{\partial X_2^2} + \cfrac{\partial^2 \varepsilon_{12}}{\partial X_2 \partial X_3} \\ \cfrac{\partial^2 \varepsilon_{33}}{\partial X_1 \partial X_2} &= \cfrac{\partial^2 \varepsilon_{31}}{\partial X_2 \partial X_3} - \cfrac{\partial^2 \varepsilon_{12}}{\partial X_3^2} + \cfrac{\partial^2 \varepsilon_{23}}{\partial X_3 \partial X_1} \end{align} $$

The compatibility condition also implies the following relationship between the infinitesimal strain tensor and the axial vector corresponding to the infinitesimal rotation tensor:
 * $$ \boldsymbol{\nabla}\times{\boldsymbol{\varepsilon}} = \boldsymbol{\nabla}{\boldsymbol{\omega}} $$

Problem 1
Show that the compatibility relation for plane stress is satisfied by unrestrained thermal expansion ($$\varepsilon_{11} = \varepsilon_{22} = \alpha T$$, $$\varepsilon_{12} = 0$$), where $$\alpha$$ is the coefficient of thermal expansion and $$T$$ is the temperature, provided that the temperature is a two-dimensional harmonic function, i.e.,

\frac{\partial^2 T}{\partial x_1^2} + \frac{\partial^2 T}{\partial x_2^2} = 0$$

Hence deduce that, subject to certain restrictions which you should explicitly specify, no thermal stresses will be induced in a thin body with a steady-state, two-dimensional temperature distribution and no surface tractions.

Solution
The plane stress compatibility equation is

\varepsilon_{11,22} + \varepsilon_{22,11} - 2\varepsilon_{12,12} = 0 $$ Plugging in the expressions for strain,

\alpha T_{,22} + \alpha T_{,11} = 0 \, $$ or,

\frac{\partial^2 T}{\partial x_1^2} + \frac{\partial^2 T}{\partial x_2^2} = 0 $$ The above equation is the steady-state heat conduction equation without any internal sources.

If there are no surface tractions, the state $$\sigma_{11} = \sigma_{22} = \sigma_{12}$$ satisfies the BCs. Since the steady-state heat conduction equation is also the compatibility equation, compatibility is automatically satisfied by the above stress state. Therefore, no thermal stresses are induced in this situation. However, extra conditions need to be applied if the body is multiply-connected.

title: Elasticity/Compatibility


text:
Electric Circuit Analysis

This course deals with the fundamentals of electric circuits, their components and the mathematical tools used to represent and analyze electrical circuits. By the end of the course, the student must be able to confidently analyze and build simple electric circuits.

It cannot be emphasized enough that as a foundation course it is important to understand the basics laid out in this course. Read carefully through given material and attempt all quizzes/questionnaires in this course.

Learn by doing, try out all home laboratories and don't forget to follow necessary precautionary measures.

WARNING
SEE Wikipedia: Electric shock AND UNDERSTAND THE RISKS.

As little as 10 mA AC current can cause temporary paralysis and an inability to let go or withdraw from the current source. If the current bypasses the skin, as little as 10 uA may cause heart failure. Direct current is much less dangerous, unless voltages are high or there is direct connection bypassing the skin. Wet skin has lower resistance, never approach AC-mains-connected electrical equipment or wiring with wet skin or bare feet. Pay special attention to proper grounding of AC power plugs and of anything which may be, deliberately or accidentally, connected to a hot (energized) wire. With good grounding, an accidental short circuit is likely to blow a fuse or circuit breaker, instead of maintaining a shock hazard. Low-voltage circuits, up to 12 VAC or DC may be handled quite safely, as long as the skin is not bypassed (such as with wide contact -- such as grasping non-insulated pliers -- or wet skin, or a metal ring). Working with higher voltages requires serious caution.

Syllabus
By the end of the course a student must be comfortable with the following:
 * Circuit Variables
 * Circuit Elements
 * Simple Resistive Circuits
 * Techniques of Circuit Analysis
 * Kirchhoff's Voltage Law Problems
 * Kirchhoff's Current Law Problems
 * Nodal Analysis Problems
 * Mesh Analysis Problems

Prerequisites
This is a level 1 course. It is assumed that the student has undertaken all currently available Level 0 courses. The following courses ( topics ) are recommended pre-requisite materials before registering/attempting this course.
 * Electrical Engineering Orientation
 * Ohm's Law
 * Voltage

Lessons

 * 1) /Passive Sign Convention/
 * 2) /Simple Resistive Circuits/
 * 3) /Resistors in Series/
 * 4) /Resistors in Parallel/
 * 5) /Circuit Analysis Quiz 1/
 * 6) /Kirchhoff's Voltage Law/
 * 7) /Kirchhoff's Current Law/
 * 8) /Nodal Analysis/
 * 9) /Mesh Analysis/
 * 10) /Circuit Analysis Quiz 2/
 * 11) /Circuit Analysis - Lab1/

Hints in Solving Circuit Analysis Problems
The following is based on the typical problem solving techniques and tricks that professors and tutors have reported as helpful in solving circuit analysis problems:
 * 1) Don't convert fractions until the last step in the problem
 * 2) Be able to re-derive any needed equation from the basic V=I*R and P=I*V equations
 * 3) Learn Cramer's rule
 * 4) Often KW are divided by mA so don't bother moving the decimal around to the end
 * 5) Draw every problem out
 * 6) Never forget the ground
 * 7) Try using symbols in working out your expressions and only substitute numbers at the final stage

If you keep your calculation parallel to your line of thought, then you will avoid many pitfalls.

title: Electric Circuit Analysis


text:
Elasticity/Polynomial solutions

Using the Airy Stress Function : Polynomial Solutions
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Example 1
Given: $$    \varphi = a~x_1^2 + b~x_1~x_2 + c~x_2^2 $$ Find the problem which fits this solution. $$    \sigma_{11} = \varphi_{,22} = 2c ~; \sigma_{22} = \varphi_{,11} = 2a ~; \sigma_{12} = -\varphi_{,12} = -b $$ This is a homogeneous stress field. An infinite number of problems can satisfy these conditions.
 * }

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Example 2
Given: $$    \varphi = a~x_1^3 + b~x_1^2~x_2 + c~x_1~x_2^2 + d~x_2^3 $$ Find the problem which fits this solution. $$    \sigma_{11} = 2cx_1 + 6dx_2 ~; \sigma_{22} = 6ax_1 + 2bx_2 ~; \sigma_{12} = -2bx_1 - 2cx_2 $$ An infinite set of problems can have this stress field as a solution.

If $$a = b = c= 0$$, then $$    \sigma_{11} =  6dx_2 ~; \sigma_{22} = 0 ~; \sigma_{12} = 0 $$ which corresponds to a plane stress beam under pure bending. {| cellspacing="0" cellpadding="0" style="margin:0em 0em 1em 0em; width:100%"
 * }
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Example 3
Consider a cantilevered beam that is fixed at one end and has a vertical force F applied at the free end. The boundary conditions on the beam are
 * $$\begin{matrix}

\sigma_{12} & = 0 ~; x_2 = \pm b \\ \sigma_{22} & = 0 ~; x_2 = \pm b \\ \sigma_{11} & = 0 ~; x_1 = 0 \\ \int_{-b}^{b}\sigma_{12} dx_2 & = F ~; x_1 = 0 \\ \mathbf{u} & = \mathbf{0} ~; x_1 = a \end{matrix}$$

We will use Maple to solve the problem.

First, assume a polynomial Airy stress function that has a high enough order. In this case a fourth order polynomial will suffice

\begin{align} \phi &:= \mathit{C1}\,x^{2} + \mathit{C2}\,x\,y + \mathit{C3}\,y ^{2} + \mathit{C4}\,x^{3} + \mathit{C5}\,x^{2}\,y + \mathit{C6}\, x\,y^{2} + \mathit{C7}\,y^{3} \\ & + \mathit{C8}\,x^{4} +\mathit{C9}\,x^{3}\,y + \mathit{C10}\,x^{2}\,y^{2} + \mathit{C11}\,x\,y^{3} + \mathit{C12}\,y^{4} \end{align} $$ Take the derivatives of the stress function to obtain the expressions for the stresses.

\begin{align} \mathit{sxx1} & := 2\,\mathit{C3} + 2\,\mathit{C6}\,x + 6\,\mathit{ C7}\,y + 2\,\mathit{C10}\,x^{2} + 6\,\mathit{C11}\,x\,y + 12\, \mathit{C12}\,y^{2} \\ \mathit{syy1} & := 2\,\mathit{C1} + 6\,\mathit{C4}\,x + 2\,\mathit{ C5}\,y + 12\,\mathit{C8}\,x^{2} + 6\,\mathit{C9}\,x\,y + 2\, \mathit{C10}\,y^{2} \\ \mathit{sxy1} & := - \mathit{C2} - 2\,\mathit{C5}\,x - 2\,\mathit{ C6}\,y - 3\,\mathit{C9}\,x^{2} - 4\,\mathit{C10}\,x\,y - 3\, \mathit{C11}\,y^{2} \end{align} $$ Next, use the command  to configure the stresses as functions of x,y so that we can find the value at various points, e.g.,  $$y=b$$.

We now find the tractions on $$y=b$$ as

\begin{align} \mathit{t1} &:= 2\,\mathit{C1} + 6\,\mathit{C4}\,x + 2\,\mathit{C5 }\,b + 12\,\mathit{C8}\,x^{2} + 6\,\mathit{C9}\,x\,b + 2\, \mathit{C10}\,b^{2}\\ \mathit{t2} &:= - \mathit{C2} - 2\,\mathit{C5}\,x - 2\,\mathit{C6 }\,b - 3\,\mathit{C9}\,x^{2} - 4\,\mathit{C10}\,x\,b - 3\, \mathit{C11}\,b^{2} \end{align} $$ and on $$y=-b$$

\begin{align} \mathit{t3} &:= 2\,\mathit{C1} + 6\,\mathit{C4}\,x - 2\,\mathit{C5 }\,b + 12\,\mathit{C8}\,x^{2} - 6\,\mathit{C9}\,x\,b + 2\, \mathit{C10}\,b^{2}\\ \mathit{t4} &:= - \mathit{C2} - 2\,\mathit{C5}\,x + 2\,\mathit{C6 }\,b - 3\,\mathit{C9}\,x^{2} + 4\,\mathit{C10}\,x\,b - 3\, \mathit{C11}\,b^{2} \end{align} $$

On $$x=0$$, we have

\begin{align} \mathit{t5} &:= 2\,\mathit{C3} + 6\,\mathit{C7}\,y + 12\,\mathit{C12}\,y^{2} \\ \mathit{t6} &:= - \mathit{C2} - 2\,\mathit{C6}\,y - 3\,\mathit{C11}\,y^{2} \end{align} $$

The stress function is order 4, so the stresses are order 2 in x and y. The tractions on $$y=+b$$ or $$-b$$ might therefore be polynomials in $$x$$ of order 2.

We calculate the coefficients of each power of x in these expressions as

\begin{align} \mathit{s1} &:= 12\,\mathit{C8} \\ \mathit{s2} &:= 6\,\mathit{C4} + 6\,\mathit{C9}\,b \\ \mathit{s3} &:= 2\,\mathit{C1} + 2\,\mathit{C5}\,b + 2\,\mathit{ C10}\,b^{2} \\ \mathit{s4} &:= - 3\,\mathit{C9} \\ \mathit{s5} &:= - 2\,\mathit{C5} - 4\,\mathit{C10}\,b \\ \mathit{s6} &:= - \mathit{C2} - 2\,\mathit{C6}\,b - 3\,\mathit{ C11}\,b^{2} \\ \mathit{s7} &:= 12\,\mathit{C8} \\ \mathit{s8} &:= 6\,\mathit{C4} - 6\,\mathit{C9}\,b \\ \mathit{s9} &:= 2\,\mathit{C1} - 2\,\mathit{C5}\,b + 2\,\mathit{ C10}\,b^{2} \\ \mathit{s10} &:= - 3\,\mathit{C9} \\ \mathit{s11} &:= - 2\,\mathit{C5} + 4\,\mathit{C10}\,b \\ \mathit{s12} &:= - \mathit{C2} + 2\,\mathit{C6}\,b - 3\,\mathit{ C11}\,b^{2} \end{align} $$ The biharmonic equation is 4th order, so applying it to a 4th order polynomial generates a constant. And this constant must be equal to zero.

\mathit{biharm} := 24\,\mathit{C8} + 24\,\mathit{C12} + 8\,\mathit{C10} $$

We also calculate the three force resultants on x=0 by integrating over y:

We now solve for the constants so as to satisfy (i) the strong boundary conditions, (ii) the biharmonic equation and (iii) the weak boundary conditions.

\begin{align} \text{solution} & := \{ \mathit{C7}=0, \,\mathit{C8}=0, \,\mathit{C9}=0, \,\mathit{C4}=0, \,\mathit{C10}=0, \,\mathit{C5}=0, \\ & \mathit{C12}=0, \,\mathit{C1}=0, \,\mathit{C3}=0, \, \mathit{C6}=0, \,\mathit{C11}= \cfrac {F}{4\,b^{3}}, \,\mathit{C2}= - \cfrac {3\,F}{4\,b} \} \end{align} $$

Notice that there are more equations than there are constants. Some of the equations are not linearly independent. However, Maple can handle this if there is a solution.

Substitute the solution into the original stress function and calculate the final stresses.

\phi :=  - { \cfrac {3\,F\,x\,y}{4\,b}}  + { \cfrac {F\,x\,y^{3}}{4\,b^{3}}} $$ and

\begin{align} \mathit{sxx3} & := { \cfrac {3\,F\,x\,y}{2\,b^{3}}} \\ \mathit{syy3} & := 0 \\ \mathit{sxy3} & := { \cfrac {3\,F}{4\,b}} - { \cfrac {3\,F\,y^{2}}{4\,b^{3}}} \end{align} $$

Displacement Boundary Condition

The displacement potential function must satisfy the relations $$\psi_{,12} = \nabla^2{\varphi}$$ and $$\nabla^2{\psi} = 0$$.

In this problem, $$  \varphi =  - \cfrac{3Fx_1x_2}{4b} + \cfrac{Fx_1x_2^{3}}{4b^{3}} $$ Therefore, $$   \psi_{,12} = \cfrac{6Fx_1x_2}{4b^3} $$ Integrating, $$   \psi = \cfrac{3F}{8}x_1^2x_2^2 + f(x_1) + g(x_2) $$ $$\nabla^2{\psi} = 0$$ only if $$ \cfrac{3F}{4}(x_1^2 + x_2^2) + f^{}(x_1) + g^{}(x_2) = 0 $$ which means that $$   f^{''}(x_1) = -\cfrac{3F}{4}x_1^2 + G ~; g^{''}(x_2) = -\cfrac{3F}{4}x_2^2 - G ~; $$ These can be integrated to find $$f(x_1)$$ and $$g(x_2)$$ in terms of $$x_1$$, $$x_2$$ and constants. The constants can be determined from the displacement BCs applied so as to fix rigid body motion.

The displacements are given by $$\begin{matrix} u_1 &= -\cfrac{P}{2EI}(a^2-x_1^2)x_2 -\cfrac{P(2+\nu)}{6EI}x_2^3 +\cfrac{P(1+\nu)b^2}{8EI}x_2\\ u_2 &= -\cfrac{Pa^3}{6EI}\left[2 -\cfrac{3x_1}{a}\left(1-\cfrac{\nu x_2^2}{a^2}\right) + \cfrac{x_1^3}{a^3} + \cfrac{3b^2(1+\nu)}{4a^2}\left(1-\cfrac{x_1}{a}\right)\right] \end{matrix}$$ where $$I = (1/12)w(2b)^3 \,$$, and $$w$$ = thickness of the beam. $$             u_2(x_1,0) = -\cfrac{Pa^3}{6EI}\left[2 -\cfrac{3x_1}{a} + \cfrac{x_1^3}{a^3} +             \cfrac{3b^2(1+\nu)}{4a^2}\left(1-\cfrac{x_1}{a}\right)\right] $$
 * Since $$u_1$$ is no a linear function of $$x_2$$, plane sections do not remain plane.
 * $$u_1(a,x_2) \ne 0$$ and $$u_2(a,x_2) \ne 0$$, but St. Venant's principle can be applied.
 * The deflection of the neutral axis ($$x_2 = 0$$) is
 * If $$b/a \rightarrow 0$$, this prediction approaches beam theory.

$$ u_2(0,0) = -\cfrac{Pa^3}{3EI} -\cfrac{Pa^3}{6EI}\cfrac{3b^2(1+\nu)}{4a^2} $$
 * The maximum deflection is
 * }

General Approach For Beam Problems

 * Find the highest order polynomial terms $$n$$ and $$m$$ for the     normal and shear tractions on $$x_2 \equiv y = \pm b$$.
 * Use a polynomial of order max($$m+4, n+5$$) excluding constant and     linear terms.  For example, for a polynomial of order $$5$$
 * $$\begin{align}       \varphi = & C_1 x^5 + C_2 x^4 y + C_3 x^3 y^2 + C_4 x^2 y^3 + C_5 x y^4 +                 C_6 y^5 + \\        & C_7 x^4 + C_8 x^3 y + C_9 x^2 y^2 + C_{10} x y^3 + C_{11} y^4 +\\        & C_{12} x^3 + C_{13} x^2 y + C_{14} x y^2 + C_{15} y^3 + \\        & C_{16} x^2 + C_{17} x y + C_{18} y^2       \end{align}

$$
 * Substitute ($$\varphi$$) into the biharmonic equation to get a set of constraint equations. Also compute the stresses.
 * Apply boundary conditions to obtain the tractions at the boundary.
 * For the strong BCs, find the coefficients of powers of x and y and      equate with expressions for the tractions.
 * For the weak BCs, find algebraic expressions.
 * Solve the set of equations and back-substitute.

title: Elasticity/Polynomial solutions


text:
User talk:Rorschnarch

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title: User talk:Rorschnarch


text: File:Triangle cantilever.png

title: File:Triangle cantilever.png


text:
User talk:RationalPuff

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title: User talk:RationalPuff


text:
Elasticity/Fourier series solutions

Using the Airy Stress Function : Fourier Series Solutions
Useful for more general boundary conditions.

Suppose $$  \varphi = f(x_2) \cos(\lambda x_1) =or= \varphi = f(x_2) \sin(\lambda x_1) $$ Substitute into the biharmonic equation. Then, $$  f(x_2) = (A + Bx_2)e^{\lambda x_2} +  (C + Dx_2)e^{-\lambda x_2} $$ or, equivalently, $$  f(x_2) = (A + Bx_2)\cosh{\lambda x_2} +  (C + Dx_2)\sinh{\lambda x_2} \, $$ The hyperbolic form allows us to take advantage of symmetry about the $$x_2 = 0$$ plane.

If $$\varphi = f(x_2) \cos(\lambda x_1)$$, $$  \sigma_{11} = -\lambda^2 f(x_2) \cos(\lambda x_1) ~; \sigma_{22} = f^{''}(x_2) \cos(\lambda x_1) ~; \sigma_{12} = \lambda f^{'}(x_2) \sin(\lambda x_1) $$

Example of Fourier Series Technique
The traction boundary conditions are $$\begin{align} \sigma_{12} & = 0 ~; x_2 = \pm b \\ \sigma_{22} & = -p_1(x_1) ~; x_2 = b \\ \sigma_{22} & = -p_2(x_1) ~; x_2 = -b \\ \sigma_{11} & = 0 ~; x_1 = \pm a  \end{align}$$ The problem is broken up into four subproblems which are superposed. The subproblems are chosen so that the even/odd properties of hyperbolic functions can be exploited.

The loads for the four subproblems are chosen to be $$\begin{align} f_1(x_1) = f_1(-x_1) & = \cfrac{1}{4}\left[p_1(x_1)+p_1(-x_1)+p_2(x_1)+p_2(-x_1)\right]\\ f_2(x_1) = -f_2(-x_1) & = \cfrac{1}{4}\left[p_1(x_1)-p_1(-x_1)+p_2(x_1)-p_2(-x_1)\right]\\ f_3(x_1) = f_3(-x_1) & = \cfrac{1}{4}\left[p_1(x_1)+p_1(-x_1)-p_2(x_1)-p_2(-x_1)\right]\\ f_4(x_1) = -f_4(-x_1) & = \cfrac{1}{4}\left[p_1(x_1)-p_1(-x_1)-p_2(x_1)+p_2(-x_1)\right] \end{align}$$ The new boundary conditions are $$\begin{align} \sigma_{12} & = 0 ~; x_2 = \pm b \\ \sigma_{22} & = -f_1(x_1)-f_2(x_1)-f_3(x_1)-f_4(x_1) ~; x_2 = b \\ \sigma_{22} & = -f_1(x_1)-f_2(x_1)+f_3(x_1)+f_4(x_1) ~; x_2 = -b \\ \sigma_{11} & = 0 ~; x_1 = \pm a  \end{align}$$ Let us look at the subproblem with loads $$\pm f_3(x_1)$$ applied on the top and bottom of the beam. The problem is even in $$x_1$$ and odd in $$x_2$$. So we use, $$\begin{align} \varphi & = \sum^{\infty}_{n=1} f_n(x_2) \cos(\lambda_n x_1) \\ & = \sum^{\infty}_{n=1} \left[A_n x_2\cosh(\lambda_n x_2)+ B_n\sinh(\lambda_n x_2)\right]\cos(\lambda_n x_1) \end{align}$$ At $$x_1 = a$$, $$  \sigma_{11} = -\sum^{\infty}_{n=1} \lambda_n^2 f_n(x_2) \cos(\lambda_n a)  $$ Hence $$\sigma_{11} = 0$$ if $$\lambda_n = (2n-1)\pi/2a$$. We can substitute $$\varphi$$ and express the stresses in terms of Fourier series. Applying the boundary conditions of $$x_2 = \pm b$$ we get $$\begin{align} \sum^{\infty}_{n=1} \left[A_n \lambda_n \cosh(\lambda_n b)+ A_n \lambda_n^2 b \sinh(\lambda_n b)+ B_n \lambda_n^2 \cosh(\lambda_n b)\right]\sin(\lambda_n x_1) & = 0\\ \sum^{\infty}_{n=1} \left[A_n \lambda_n^2 b \cosh(\lambda_n b)+ B_n \lambda_n^2 \sinh(\lambda_n b)\right]\cos(\lambda_n x_1) & = f_3(x_1) \end{align}$$ The first equation is satisfied if  $$ A_m \lambda_m \cosh(\lambda_m b)+ A_m \lambda_m^2 b \sinh(\lambda_m b)+ B_m \lambda_m^2 \cosh(\lambda_m b) = 0 \qquad (1) $$ Integrate the second equation from $$-a$$ to $$a$$ after multiplying by $$\cos(\lambda_m x_1)$$.

All the odd functions are zero, except the case where $$n=m$$.

Therefore, all that remains is $$ \left[A_m \lambda_m^2 b \cosh(\lambda_m b)+ B_m \lambda_m^2 \sinh(\lambda_m b)\right] a = \int_{-a}^{a} f_3(x_1) \cos(\lambda_m x_1) dx_1 \qquad (2) $$ We can calculate $$A_m$$ and $$B_m$$ from equations (1) and (2), substitute them into the expressions for stress to get the solution.

We do the same thing for the other subproblems.

The Fourier series approach is particularly useful if we have discontinuous or point loads.

title: Elasticity/Fourier series solutions


text:
Elasticity/Polar coordinates

The Edge Dislocation Problem
Assume that stresses vanish at $$r = r_i$$ and that $$r_i$$ is the radius of an undeformed cylindrical hole. Also stresses vanish at $$r_o\rightarrow\infty$$. Relative displacement $$b$$ is prescribed on each face of the cut.

The edge dislocation problem is a  plane strain problem. However, it is not axisymmetric.

It is probable that $$\sigma_{rr}$$ and $$\sigma_{\theta\theta}$$ are symmetric about the $$x_2 - x_3$$ plane. Similarly, it is probable that $$\sigma_{r\theta}$$ is symmetric about the $$x_1 - x_3$$ plane.

These probable symmetries suggest that we can use a stress function of the form $$    \varphi = f(r) \sin\theta $$ In cylindrical co-ordinates, the gudir beta Airy stress function leads to $$\begin{align} \sigma_{rr} & = \cfrac{1}{r}\cfrac{\partial\varphi}{\partial r} + \cfrac{1}{r^2}\cfrac{\partial^2\varphi}{\partial \theta^2} \\ \sigma_{\theta\theta} & = \cfrac{\partial^2\varphi}{\partial r^2} \\ \sigma_{r\theta} & = -\cfrac{\partial}{\partial r}                      \left(\cfrac{1}{r}\cfrac{\partial\varphi}{\partial \theta}\right) \end{align}$$ $$   \nabla^4\varphi = \nabla^2{(\nabla^2{\varphi})} = \left(\cfrac{\partial^2}{\partial r^2}+\cfrac{1}{r}\cfrac{\partial}{\partial r}+            \cfrac{1}{r^2}\cfrac{\partial^2}{\partial \theta^2}\right) \left(\cfrac{\partial^2\varphi}{\partial r^2}+\cfrac{1}{r}\cfrac{\partial\varphi}{\partial r}+            \cfrac{1}{r^2}\cfrac{\partial^2\varphi}{\partial \theta^2}\right) $$ and $$\begin{matrix} 2\mu u_r & = -\cfrac{\partial\varphi}{\partial r} + \alpha r \cfrac{\partial\psi}{\partial \theta} \\ 2\mu u_{\theta} & = -\cfrac{1}{r}\cfrac{\partial\varphi}{\partial \theta} + \alpha r^2 \cfrac{\partial\psi}{\partial r}  \end{matrix}$$ Proceeding as usual, after plugging the value of $$\varphi$$ in to the biharmonic equation, we get $$    f(r) = Ar^3 + \cfrac{B}{r} + Cr + Dr \ln r  $$ Applying the stress boundary conditions and neglecting terms containing $$1/r^3$$, we get $$   \sigma_{rr} = \sigma_{\theta\theta} = \cfrac{D}{r} \sin\theta ~; \sigma_{r\theta} = -\cfrac{D}{r} \cos\theta $$ Next we compute the displacements, in a manner similar to that shown for the cantilever beam problem. The displacement BCs are $$u_r = 0$$ at $$\theta = 0+$$ and $$u_r = b$$ at $$\theta = 2\pi-$$. We can use these to determine $$D$$ and hence the stresses.

Rigid body motions are eliminated next by enforcing zero displacements and rotations at $$r = r_i$$ and $$\theta = 0+$$. The final expressions for the displacements can then be obtained.

Problem 1
Consider the Airy stress function

\varphi = C~r^2~(\alpha + \theta - \sin\theta\cos\theta - \cos^2\theta\tan\alpha) $$

 * Show that this stress function provides an approximate solution for a cantilevered triangular beam with a uniform traction $$p$$ applied to the upper surface. The angle $$\alpha$$ is the angle subtended by the free edges of the triangle.
 * Find the value of the constant $$C$$ in terms of $$p$$ and $$\alpha$$.

Solution:
Given:

\varphi = Cr^2(\alpha + \theta - \sin\theta\cos\theta - \cos^2\theta\tan\alpha) $$ Using a cylindrical co-ordinate system, the stresses are
 * $$\begin{align}

\sigma_{rr} & = 2C\left(\alpha + \theta + \sin\theta\cos\theta - \tan\alpha +   \cos^2\theta\tan\alpha\right) \\ \sigma_{r\theta} & = -2C + \cos^2\theta - \sin\theta\cos\theta\tan\alpha \\ \sigma_{\theta\theta} & = 2C\left(\alpha + \theta - \sin\theta\cos\theta      - \cos^2\theta\tan\alpha\right) \end{align}$$ At $$\theta = 0$$, $$t_r = 0$$, $$t_{\theta} = -p$$, $$\widehat{\mathbf{n}}{} = \widehat{\mathbf{e}}{\theta}$$. Therefore, $$\sigma_{\theta\theta} = -p$$ and $$\sigma_{r\theta} = 0$$.
 * $$\begin{align}

0 & = 0 \\ -p & = 2C(\alpha - \tan\alpha) \end{align}$$ Hence, the shear traction BC is satisfied and the normal traction BC is satisfied if

{C = -\frac{p}{2(\alpha - \tan\alpha)}} $$ At $$\theta = -alpha$$, $$t_r = 0$$, $$t_{\theta} = 0$$, $$\widehat{\mathbf{n}}{} = -\widehat{\mathbf{e}}{\theta}$$. Therefore, $$\sigma_{\theta\theta} = 0$$ and $$\sigma_{r\theta} = 0$$. Both these BCs are identically satisfied by the stresses (after substituting for $$C$$). Hence, equilibrium is satisfied.

\varphi = -\frac{pr^2}{2(\alpha - \tan\alpha)} (\alpha + \theta - \sin\theta\cos\theta - \cos^2\theta\tan\alpha) $$ To satisfy compatibility, $$\nabla^4{\phi} = 0$$. Use Maple to verify that this is indeed true.

The remaining BC is the fixed displacement BC at the wall. We replace this BC with weak BCs at $$r = L$$. The traction distribution on the surface $$r = L$$ are $$t_r = \sigma_{rr}$$ and $$t_{\theta} = \sigma_{r\theta}$$. The statically equivalent forces and moments are
 * $$\begin{align}

F_1 = \int_{-\alpha}^0 (\sigma_{rr}\cos\theta - \sigma_{r\theta}\sin\theta) L d\theta = 0 \\ F_2 = \int_{-\alpha}^0 (\sigma_{rr}\sin\theta + \sigma_{r\theta}\cos\theta) L d\theta = -pL\\ M_3 = \int_{-\alpha}^0 L \sigma_{r\theta} L d\theta = \frac{pL^2}{2} \end{align}$$ You can verify these using Maple.

Hence, the given stress function provides an approximate solution for the cantilevered beam (in the St. Venant sense).

title: Elasticity/Polar coordinates


text:
Ocean remote sensing satellites

This course gives an overview of the ocean remote sensing satellites systems and what they do and see and how they work.

Overview
Ocean satellites have traditionally had interest coming from two quite separate areas. These are from the geophysics community who have been largely interested in ocean physical phenomena and bathometry and the other is the biologists and marine scienists who are interested in the biological activity of the oceans. This usually means trying to measure the concentration of chlorophyll in the seawater as this is directly related to the quantity of algae present and will be a good correlator of the food supply available for marine animals.

Current and Past Ocean Related Satellites
MODIS http://oceancolor.gsfc.nasa.gov/

TOPEX/Poseidon -launched Aug 1992

Jason-1 -launched Dec 2001

OSTM Ocean Surface Topography Mission -2008? -to replace Jason-1

SeaStar (SeaWiFS instrument) -launched Aug 1997 to 2008

Glossary

 * CZCS -Coastal Zone Colour Scanner
 * Bathometry -study of

title: Ocean remote sensing satellites


text:
Talk:Ocean remote sensing satellites

It is intended to give some details on the early satellites and discoveries in this field. This will also require a section outlining the main types of instruments used. These need to go together really in order to grasp what it is all about.Terence wiki 21:55, 2 August 2007 (UTC)

title: Talk:Ocean remote sensing satellites


text:
Template:Archive2

Note: This template contains ParserFunctions which prevent it from working properly when substed. So... don't subst it!

title: Template:Archive2


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Middle School Science

Earth and Space Science
The Middle_School_Science/Earth_and_Space_Science is now a Wikiversity page. The page is still under construction, but only needs headings--and of course peer review to check all the facts.

Important to wv are the ideas behind the Scientific Method, which is below. The material there should evolve into a higher-level article, allowing this reference to become more appropriate for middle school learners. Important in the Scientific Method is the newer technique of implementing a model as opposed to the more accepted method of fielding a hypothesis to prove an idea.

The difficulty for me is in merging the related documents into a meaningful single documents; that least 10% of work seems to demand another 100% of effort. Further adding to the task is that I have found another test outline from New York State, which I may also try to integrate.

I am adding to each test reference (for now kept on google docs), a GACE equivalent to each Praxis II reference. Documents put here on Wikiveristy will be free of non-original text, with the possible exception of text from Wikipedia or other public domain web sites. Even when I do incorporate text I feel a need to rewrite that I cannot ignore; the language necessary for teaching young children has to be very well composed and free of complication or contradiction, so as not to discourage children from science learning by frustrating them with confusion.

Here is the first GACE study guide: Physical Science, including Chemistry.

In the end, what is needed is an outline that addresses each topic as students might best be introduced to them from the perspective of the knowledge that they bring to school. Then when rearranging the topics so as to best fit the students' introduction to Science, the topics tend to merge together to explain surrounding phenomena in ways that are meaningful for the students that contradict the way Science is presented cognitively and didactically.

Schools by district boards of directors, and in my experience boards of directors are anything but democratic as they try to mimic the control systems that has been passed down to us from generation to generation to benefit the universal "human capital" system. Because of this, truly developmental approaches to middle school Science teaching, probably the most important phase of education, is left to individual teachers around the world who do not have the resources, or the power, to document a framework for an interdisciplinary approach incorporating project-type discovery. It seems the task is left to me by writing this Wikiversity article.

Within the science topics themselves I found contradictory information while trying to satisfying the requirements. The study of waves is a good example. For instance, diffusion, dispersion, and refraction, appear to be the same thing, yet they are defined and applied differently. Also, the concepts of wavelength and frequencies are made interchangeable without explanation when describing light and sound waves; this is possible, of course, because light and sound travel at a constant speed, easily provable with a single equation; I have yet to see this revealed except in my own writing. A single approach to the study of waves is necessary, and uniform rules need to be followed with respect to each kind of wave so that students can conceptualized about waves rather than have to memorize seemingly contradictory facts to succeed at test taking. The same criticism applies to the ideas of kinetic and potential radiation especially in relation to thermal energy. In fact this last issue goes back to waves, as thermal radiation is that of infrared waves; go check for yourself if you don't believe how confused things are at the moment.

Ultimately I think that this reference needs to simplify science knowledge to the very basic conceptualizations so that the teachers can easily integrate pure science into the projects that students will do that reflect their own experiences in the world around them. Because the most successful students, or the ones to best self-actualize, come to their chosen careers earliest, it is important to allow them to bring Science to their chosen interests so that the can develop as individuals, and contribute meaningfully to their class groups. Since this includes all students, not just the successful ones (as district boards are biased to support), then all different aspects of science need to promoted: those of pure experimentation, and those of the necessary community support.

The community support feature, which includes documentation, presentation and communication, is of course not addressed in the tests, as the testing culture is about weeding out the weak for the promotion of "human capital," so we will not find it in my present references.

Another focus that is missing is technology, and especially computer communications technolgy -- the most important feature of the world we live in today. Exactly why this is missing presents itself as a mystery; but investigating regressive tendencies, especially with respect to those of district boards, we can trace their motivations to a single desire: the top down control of young humans for the resource centralization of capital, which is now global. At the heart of global capital is computer communication, and at the heart of computer communication is the Microsoft Corporation; all boards, not only district boards, are beholden to this central control operation; it seems the whole world is.

Because of the information technology laws, all of which include criminal punishment, no student can legally take apart a proprietary computer operating system. Of course any student who has the skills and perseverance can work with the Linux operating system (and its GNU shell), but after my working with Linux for so many years, I feel Linux has passed its time as a viable contribution, and it has also failed to support its user base with the exceptions of mega-organizations, such as Google and the NOAA US national weather service.

What is coming over the horizon, however, is rescue in the form of the L4 operating system, which is an evolution of the systems similar to the system underlying Apple's OSX operating system. Technically, it is not an operating system in the sense that XP or Linux is, but a microkernel upon which functional systems can be built. My final reference work will introduce technology for kids, and in this will use non-proprietary software systems. Non-proprietary (sometimes called open source, free and open, or public domain), are necessary for education so that the kids successful with technology can integrate these various levels of systems holistically into the rest of their science exploration as they see fit, not as a dominating corporation, such as Microsoft, dictates.

The final feature that I think is unfortunately missing from middle school Science is that of social science. Social science is studied as social studies, but from what I have seen the topics of social studies are better viewed as current events. Social Science has become a significant branch of Science, and the Social Sciences are increasingly affecting the Scientific Method.

Science, society, and children
Society needs scientists, and every student needs to have a positive exposure to science in middle school; exposure to science in high school is often too late. There are also social benefits from science learning in real life. Students can learn to leverage inquiry to understand the circumstances in their lives, and make proper life's  choices based on solid knowledge independent of influences around them that may not necessarily be helping them, or may even be hurting their chances for success.With science they will have a better chance in having a good job.

Preamble
My goal for this middle school science wiki is to create a framework that supplies future and practicing teachers with a reference of the factual knowledge necessary for taking teacher exams.

The major testing for for middle school science teachers in the US is the Praxis II exam, which has provided the frame work for these study pages. Another test is the GACE exam from National Evaluation Systems in Amherst, MA. I have synopsized their framework, which seems to be less detailed than the Praxis II exam, and somewhat better organized. The GACE framework seems to be better organized as well. The GACE testing information is released with a "free for non-commercial use by educators" license. My goal however is to create for these articles completely original writing as a reference for group learning projects.

A difference between the GACE and Pr axis II exams is the approach to physics and chem. In the GACE exam, the reliance on pure chemistry lessened and chemistry is combined with physics as physical sciences. To me this makes sense, as there are aspects of both that are shared. Even in the Praxis II framework there is a section called "basic" science that contains physics concepts that are more relevant to chemistry.

Furthermore, the very definitions of chemistry and physics are becoming so interrelated that an interdisciplinary approach can easily spread to include Earth and Space Science. Physics goes to Space studies, as physics covers such concepts as gravity and nuclear reactions, and chemistry can go to Earth Science, and even biology, where an excellent example is the study of the water cycle with its chemical effects on physical planet, and its support fr the life cycles of life in general. An example of this interdisciplinary nature is "Physics and Chemistry of the Earth."

This brings me to the conclusion that there needs to be a major restructuring of the factual information content away from the Praxis II format towards the GACE format. Ultimately, the structure will be dictated by the students themselves, and the factual information content will be wrapped in the projects they generate structured by their own relationship with the world around them.

Here are the content pages; they are temporarily in Google docs as, so far, only one is completely original writing. Please contact me to collaborate on any of these pages, Google docs allows multiple editors, and the editors do not have to be Gmail users. As the development of the reference material evolves, my goal will be to wrap this learning in conceptual framework that help students relate the world they see around them to their learning, and hopefully develop for all of them enthusiasm for science. The effect of the frame work should resemble a Russian matryoshka nesting doll, by allowing students to cyclically increase their understanding of each topic as they return to it throughout their learning careers.

By starting the discussions at a very high level, I will reorganize the concepts to gradually create the learning paths that add more and more detail to each of the topics. These topics can possibly be introduced by the students themselves based on their personal experiences.

This structure should follow a natural evolution of the children's learning, perhaps parallel to the development of science through history, and also template for lesson planning that allows students to develop their own learning framework.

''The matryoshka doll is becoming a common analogous symbol for the evolution of empathy and morality from their animal roots. Childhood growth through inquiry is of course an example of evolution, as it follows the path of science as experimental science corrected long held misconceptions.''

Learning Science, The Scientific Method, and the Construction of Knowledge
Scientific Method development page - required learning

 * The intrusion of social sciences into the scientific method, or perhaps model, is making a fuss. The ivory tower is giving way to the action research model; action research initially recruited prostitutes as researchers in the research of their sub-culture giving them the ability to construct the "steps" for their escape from their self-imposed dangers.

 * The difficulty in writing about education for youngsters is in making the writing applicable to both the teachers as well as the youngsters. Perhaps the scientific method information can move to its own page, leaving behind something kids can discuss in class.

The required learning for this reads:
 * Scientific methods of problem solving
 * Scientific facts, models, theories and laws
 * Science process skills in experiments and investigations, and to solve problems
 * Experimental design

Working here is the classical approach where observations lead to a hypothesis, and a model is created that can be used to predict future behaviors, which leads in turn to the development of a theory that can be subjected to peer review. Peer review is many times what it sounds like; mutual support amongst scientists with similar views, or perhaps mutual fund raising goals.

This will not, in my opinion, create enthusiasm in kids, except in exceptionally strange ones. Far more useful would be a taxonomic approach -- one which anchors inquiry and explanations with the basics that kids have already identified as they are coming into science learning. Explaining questions in such a way that the new questions created by the explanations are themselves an achievement will give them direction for their future studies.

Here is a more socially constructed model for the scientific method that stresses elimination of bias and enlists community in scientific development:

The goals of science
 * To develop unified explanations of phenomena using the scientific method that are applicable everywhere
 * Use objectivity and honesty to control or assess all variables to prevent biases and mistakes from skewing the experimental process.
 * Rely on verifiable evidence and repeat experiments to prove models
 * Look for problems in existing science for opportunities solidify existing knowledge and create more inquiry.
 * Create community and communication to exchange ideas and collaborate.

Techniques for problem solving
 * Observing and describing - obtain information about the environment
 * Classifying - systematically impose on collected information of objects or events / by size, shape, or color
 * Measuring - to gather, analyze, and interpret scientific data
 * Communicating - reports, discussions / cooperative teamwork / raise points for investigation or discussion, problems
 * Hypothesizing - generalizations to explain large number of events, immediate or eventual testing, explaining an observation in terms of previous experience
 * Designing experiments - planning data-gathering to create hypothesis for testing
 * Controlling variables - controlled conditions for observation and experimentation
 * Consensus - reaching agreement

Pitfalls
 * Hypothesis is a assumed to be already proved
 * Data is assumed to be false if it doesn't support expected results
 * Bias, or assumptions, introduces flaws into experiments
 * Systematic errors go unnoticed and are repeated skewing meta-data
 * Equipment or conditions are not adequate

Best practices
 * Design experiments collaboratively to eliminate errors of assumption.
 * Handle all data in the same ways so as not to exclude data that does not support the hypothesis or specific ideas.
 * Systematic errors can be located by estimating quantitatively results in parallel.
 * Share experimentation responsibilities across communities to cancel out potential biases.
 * Use different experimental setups to isolate sources of systematic errors caused by equipment characteristics.
 * Allow for time and communication to mature and reinforce data quality and eliminate biases.

Scientific Method development page

Earth and Space Science
Earth and Space Science Development Page

The study of Earth and Space Science may be the best launching point for integrating required learnings into students' conceptions of the world around them. Developing a feel for the effects of the universe, such as gravity, in mathematical terms, will steer students in the direction of learning about one of the greatest scientist in history, Albert Einstein. Einstein often reflected to Humanists that his theories were the product of subjective conceptualization, not the product of mathematical derivations.

Students can bring to class knowledge of the Earth and Space as they have observed it through various media: television, movies and the internet or through personal observations made during exploration of the world around them.

Biology
Biology development page

"Where to start?" in biology should be a concern for teachers. Biology exists on multiple interrelating levels more so than any other science, except possibly psycho- and sociology.

Key to understanding is the life of a cell, and the different kinds of cells. Why this is all relevant is because these low-level life forms make up the bigger pictures of what is plainly visible everywhere: life. Like Earth and Space Science, Biology has the advantage that all student's have conceptions about life that they can bring to class and express, giving teachers anchors form which to launch learning.

Possibly of great help here is evolution. In the evolutionary chart, the greatest species, the ones at the ends of their evolutionary paths, the species we see everyday, can find their basic components in their evolutionary histories. By explaining where typically sophisticated species come from, it is easy to create a path to microbial basics. From there a discussion of the details on the microscopic level is relevant to the students' basic observations in life.

Biology for me presents multiple difficulties, not the least of which is that biology is the discipline I never studied beyond the barest requirements.

Physics
Physics development page

Physics is quantitative science that can be integrated into the learning if it is supported by math learning. Students are certainly aware of the work of gravity from their everyday experience, feeling drain of energy after a long workout or playing games. Some maybe award of the planets and the universe is held together by gravity. Physics tells the story of infinitesimally small, such as elementary particles, to the colossally large, such as the universe. If taught right, it can captivate the imagination of learners. Students should also be made awareness of the physics behind engineering, from suspension bridge to rocket back to the smartphone, as common applications of physics.

Both topics can implement math, and a practical approach to technology; a hands on exploration of the machines in everyday life can help students embed the laws of mechanics and electricity and magnetism into their basic neurology to make them available throughout life. Knowledge of these laws may help them be critical when dealing with technology, and self-reliant when repairing broken technology.

The challenge to become competent in physic is that the student must simultaneously master abstract thinking, best developed from hands on exploration, and master the basic skills of mathematics, and the imagination to apply what is learned. Hence there are three components to master the learning of physics: - Understanding of the basics of physical concepts (there are only few of them) - Ability to transfer the concepts into mathematics (so that related equations that tell a story) - Ability to generalize quantitative concepts (the story) and apply it to situation that is not taught before This post a tough challenge for students who are not well prepared in mathematics and those who got so used to rote learning. Once these three are mastered, physics is enjoyable; but it is rather hill that all learners has to climb.

Chemistry
Chemistry development page

Chemistry seems to be loved or hated, and also chemistry is more distant from everyday life than other areas of learning. The students that like chemistry seem to like the analytic nature of, for instance, balancing equations.

Finding observable everyday examples that can be used to wrap more esoteric learning may be a challenge; it may be better to try to wrap practical chemistry exercises within other learnings.

Math for middle school science
Math development page

Math is naturally important to science; students not proficient in math are going to have difficulty enhancing their learning to the point where their assumptions can be proved and can become solidified knowledge. Depending on the resources a community has and the educational backgrounds of students' parents', math skills will vary among students and communities. When students arrive at this level of learning, they may not have the necessary math skills, and it is very likely that districts will try to force the learning on these students through didactic drill practices. They may even, for this reason, attempt to deny students who have not had the necessary math experience the benefits of engaging in scientific inquiry.

A far better approach is to help students by developing their enthusiasm for science. As they begin to learn the scientific process of explaining their observations, they can then learn how quantify their new learning with examples of analytic math. If, or when, they become troubled with the math, the class can digress and, perhaps mutually, fill in the missing learning.

Math requirements have to be an early consideration in planning science learning, partly to discover the students' levels of expertise, but mostly to be able to know when and where to apply a required math learning to help a student develop a scientific concept. If a student feels the benefit of a math learning; if it supports the student's understanding of the world, then that student will very likely carry that learning not just through to graduation, but through life.

Benefits and impacts of science, and the history of Science
Social aspects of science development page

Students come to study science with an already well-developed relationship with the world around them. Generally speaking, the scientific conceptions of the world (sometimes called misconceptions) parallel the conceptions of nature scientists have developed in previous centuries. Student growth parallels the evolution of the understanding of science itself.

I have found that the study of technology is in many ways the study of humanity, as science seems wrap all the material and social benefits of human society, as well as its failures.

The information structure that our society is built on seems to have been handed down directly from the ancient Egyptian empire (Mumford, Technics and Civilization). The economic structure of the world, now called globalism, seems to resemble the ancient Roman structure's equally faitfully.

Project Science, group learning, or project-based learning
The word "project" from project Science is loaded.

I think I can put the issues that inspire project Science in bullet form:
 * kids develop a relationship with the world as they become more aware of it
 * as they begin to socialize and interrelate, this relationship develops into a shared conception
 * when they get to school, and teachers try to straighten them on certain misconceptions,
 * they think the teachers are crazy

Children will tell you what you want to hear, but they think they are really being taught patience with elders. As soon as they are back with their friends, the misconceptions are restored, and all is well from their perspective.

The project, or group, science, strategy is to allow them to discover the realities of science on their own by providing them with much the same equipment that our early scientists had, such as prisms, telescopes, microscopes. Their misconceptions are not actually wrong so much as "intelligently wrong," and often the entire community holds the same misconceptions. Here is were the true value is; as the students develop scientific technique and learn how things really are, they go back home and tell their parents what they did. In this way the entire community gets educated -- now that's value.

Science today is seeing a rise in the social science; as we apply scientific technique to social situations, we are far better able to get from these situations the kinds of results we are looking for. When kids do this, they can better experiment with life and conclude earlier what it is that they are good at, and what they like to do. This gives them factors better chances of getting the highest potential out of life, of self-actualizing.

title: Middle School Science


text:
Talk:Evolutionary psychology

I am surprised there is no talk here yet. What I learned from evolutionary psychology is that the very basis of our psychology has evolved from our distant ancestors, and it has evolved along different paths. Darwin referred to it as "natural affection," and modern researchers link it to our sense of morality.John van v 23:09, 2 August 2007 (UTC)
 * Maybe we could create a reading list. --JWSchmidt 23:36, 2 August 2007 (UTC)

title: Talk:Evolutionary psychology


text:
Electric Circuit Analysis/Simple Resistive Circuits

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Lesson Review: Lesson 1
The first lesson was about passive sign convention. The lesson introduced circuit components which will be encountered in electric circuit analysis.

 * Active components
 * Passive components
 * Passive sign convention
 * Guidelines for passive sign convention

Lesson Preview
This lesson is about simple resistive circuits. The student is expected to have understood the following at the end of the lesson:

 * Voltage: (V or v - Volts)The electrical potential between two points in a circuit.
 * Current: (I or i - Amperes)The amount of charge flowing through a part of a circuit.
 * Power: (W - Watts)Simply P = IV. It is the current times the voltage.
 * Source: A voltage or current source is the supplier for the circuit.
 * Resistor: (R measured in Ω - Ohms)A circuit element that "constricts" current flow.
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 * }

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Voltage Source
This is possibly the simplest circuit. The voltage source supplies a voltage to the circuit. When this voltage is applied over a resistor, R, there is a current.

Equation 2.1

$$V = I * R\!$$

This equation explains the relation between all three elements in the circuit. In this case the voltage source has the same magnitude as the voltage drop across the resistor. We know that it is V. The resistor has a certain amount of Ohms depending on its rating. We now know R. With algebra I = V/R. So as long as you know two of the variables then you can find the third.

Now comes the power part of the circuit analysis.

Equation 2.2

$$P = I * V\!$$

Once Equation 2.1 is solved then this equation should follow quickly. The I and V are the same variables so insert them into the equation and solve for P (Watts). With these two equations, 1.1 and 1.2, and a little bit of algebra you get:

Equation 2.3

$$P = I^2 * R\! $$

Equation 2.4

$$P = \frac {V^2}{R}$$

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Part 2
As an explanation, the power running through is the voltage times the current. This is instantaneous power rather than power used over time. Power has to be supplied and consumed. In a perfect world without heat-loss both are equal. The source supplies the required power that is consumed in this case by the resistor.

Example 2.1
Given': $$V_s ~=~ 12V,~R ~=~ 20 \Omega$$

Find: I, the current in Amps. The power produced by the source. The power consumed by the resistor.

Solution: Using the equations:

$$\begin{align} I &= V/R\\ &= 12V/20\Omega\\ I &= .6A\\ \end{align} $$

$$\begin{align} P &= I * V\\ &= .6A * 12V\\ P &= 7.2W\\ \end{align} $$

Remember: The power supplied equals the power consumed.

 * }

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Current Source
All that will happen here is that the givens will change. Rather than knowing what the voltage is across the resistor we now know what the current is flowing through the resistor.

Don't forget in the description of resistors that a similar model in fluid physics is a smaller pipe that constricts the amount of flow. Well, current is flow of charge. With the fluid the side of the smaller section being supplied with fluid will have a greater pressure than the out flowing side. The difference between these is potential. In circuits this potential is known as voltage, but then again this is all review, right?

So now we use equation 2.1 again. The current source gives us the current through the resistor. Given the resistor value it should be just a matter of multiplication.

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Example: 2.1
Given': $$I_s ~=~ 2A,~R ~=~ 10\Omega$$

Find: V, the voltage. The power produced by the source. The power consumed by the resistor.

Solution: Using the equations:

$$\begin{align} V &= I * R\\ &= 2A * 10\Omega\\ V &= 20V\\ \end{align} $$

$$\begin{align} P &= I * V\\ &= 2A * 20V\\ P &= 40W\\ \end{align} $$

Of course, power consumed equals power supplied in this perfect universe, which is only found in this course.

 * }

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Example 2.2
Given': $$V_s ~=~ 5V, ~ R ~=~ 50\Omega$$

Find: I, the current in Amps. The power produced by the source. The power consumed by the resistor.

Solution: Using the equations:

$$\begin{align} I &= V/R\\ &= 5V/50\Omega\\ I &= .1A\\ \end{align} $$

$$\begin{align} P &= I * V\\ &= .1A * 5V\\ P &= .5W\\ \end{align} $$
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Example 2.3
Given': $$I_s ~=~ .3A, ~ R ~=~ 30\Omega$$

Find: V, the voltage. The power produced by the source. The power consumed by the resistor.

Solution: Using the equations:

$$\begin{align} V &= I * R\\ &= .3A * 30\Omega\\ V &= 9V\\ \end{align} $$

$$\begin{align} P &= I * V\\ &= .3A * 9V\\ P &= 2.7W\\ \end{align} $$

 * }

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Example 2.4
Given': $$I_s ~=~ 5A, ~ P_{consumed}~=~30W$$

Find: V, the voltage. R, the resistance

Solution: Using the equations:

$$\begin{align} V &= P/I\\ &= 30W/5A\\ V &= 6V\\ \end{align} $$

$$\begin{align} R &= V/I\\ &= 6V/5A\\ R &= 1.2\Omega\\ \end{align} $$
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Example 2.5
Given': $$V_s ~=~ 12V,~P ~=~ 5W$$

Find: I, the current in Amps. R, the resistance.

Solution: Using the equations:

$$\begin{align} I &= P/V\\ &= 5W/12V\\ I &= 0.4167A\\ \end{align} $$

$$\begin{align} R &= V/I\\ &= 12V/0.4167A\\ R &= 28.798\Omega,~rounded~to~29\Omega.\\ \end{align} $$

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Example 2.6
Given': $$P = 32W,~R = 2\Omega$$

Find: V, the voltage. I, the current.

Solution: Using the equations:

$$\begin{align} P &= I^2 * R\\ I &= \sqrt{P/R}\\ &= \sqrt{32/2}\\ I &= 4A\\ \end{align} $$

OR

$$\begin{align} P &= V^2/R\\ V &= \sqrt{P*R}\\ &= \sqrt{32*2}\\ V &= 8V\\ \end{align} $$

OR

$$\begin{align} V &= I * R\\ \end{align} $$

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Part 10: Exercise 2

 * 1) If the given current is 300 Amps and the resistance is 2 Ohms, what is the Voltage across the resistor and how much power is being produced or consumed?
 * 2) An engineer measures the resistivity of a resistor before putting it into a simple circuit. It is 50 Ohms. After putting the resistor into place the engineer measures 2 Volts across the resistor. How many Amps are going through the resistor?
 * 3) A 60 Watt bulb is found to have 300 Ohms of resistance. What is the necessary voltage and current to have the bulb run optimally?
 * 4) A large voltage supply has 10,000V. The company wants to know how big a resistance can be put on the voltage supply along with how much power will be consumed. Is this a solvable problem?
 * 5) Practice drawing the elements of a simple resistive circuit. Draw a resistor and Ω 5 times. Draw 5 current sources and 5 voltage sources.

 * Answers to Exercise 2

Completion list
Once you finish your Exercises you can post your score here! To post your score just e-mail your course co-ordinator your name and score *@undefined.

 * Ozzimotosan -- 100%
 * Doldham -- 75% & Corrected

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text:
Elasticity/Body force potential

Body force potential
How do we find the body force potential? Before we proceed let us examine what conservative vector fields are.

Conservative vector fields
$$ f_{2,1} - f_{1,2} = 0 ~;           f_{3,2} - f_{2,3} = 0 ~;           f_{1,3} - f_{3,1} = 0  \qquad \text{(28)} $$       or        $$ \boldsymbol{\nabla}\times{\mathbf{f}} = 0 \qquad \text{(29)}      $$ The field has to be irrotational.
 * Work done in moving a particle from point A to point B in the field should be  path independent.
 * The local potential at point P in the field is defined as the work done to move a particle from infinity to P.
 * For a vector field to be conservative

Determining the body force potential
Suppose a body is rotating with an angular velocity $$\dot{\theta}$$ and an angular acceleration of $$\ddot{\theta}$$. Then,
 * $$ \text{(30)} \qquad

\mathbf{a}_r = -\dot{\theta}^2 r \widehat{\mathbf{e}}_{r} ~; \mathbf{a}_{\theta} = -\ddot{\theta} r \widehat{\mathbf{e}}_{\theta} $$ Let us assume that the $$(r,\theta)$$ coordinate system is oriented at an angle $$\theta$$ to the $$(x_1,x_2)$$ system. Then,
 * $$\text{(31)} \qquad

\begin{bmatrix}a_1\\a_2\end{bmatrix} = \begin{bmatrix}\cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix} \begin{bmatrix}a_r\\a_{\theta}\end{bmatrix} $$ or,
 * $$\text{(32)} \qquad

\begin{bmatrix}a_1\\a_2\end{bmatrix} = \begin{bmatrix}\cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix} \begin{bmatrix}-\dot{\theta}^2r\\-\ddot{\theta}r\end{bmatrix} $$ or,
 * $$\begin{align}

\text{(33)} \qquad a_1 & = -\dot{\theta}^2r\cos\theta + \ddot{\theta}r\sin\theta\\ \text{(34)} \qquad a_2 & = -\dot{\theta}^2r\sin\theta - \ddot{\theta}r\cos\theta \end{align}$$ or,
 * $$\begin{align}

\text{(35)} \qquad a_1 & = -\dot{\theta}^2 x_1 + \ddot{\theta} x_2 \\ \text{(36)} \qquad a_2 & = -\dot{\theta}^2 x_2 - \ddot{\theta} x_1 \end{align}$$ If the origin is accelerating with an acceleration $$\mathbf{a}_0$$ (for example, due to gravity), we have,
 * $$\begin{align}

\text{(37)} \qquad a_1 & = a_{01} -\dot{\theta}^2 x_1 + \ddot{\theta} x_2 \\ \text{(38)} \qquad a_2 & = a_{02} -\dot{\theta}^2 x_2 - \ddot{\theta} x_1 \end{align}$$: The body force field is given by
 * $$\begin{align}

\text{(39)} \qquad f_1 & = -\rho\left(a_{01}-\dot{\theta}^2x_1+\ddot{\theta}x_2\right) \\  \text{(40)} \qquad f_2 & = -\rho\left(a_{02}-\dot{\theta}^2x_2-\ddot{\theta}x_1\right) \end{align}$$ For this vector body force field to be conservative, we require that,

f_{1,2} - f_{2,1} = 0 \Rightarrow 2\ddot{\theta} = 0 $$ Hence, the field $$\mathbf{f}$$ is conservative only if the rotational acceleration is zero, i.e. = the rotational velocity is constant.=
 * $$\begin{align}

\text{(41)} \qquad f_1 & = -\rho\left(a_{01}-\dot{\theta}^2x_1\right)\\ \text{(42)} \qquad f_2 & = -\rho\left(a_{02}-\dot{\theta}^2x_2\right) \end{align}$$ Now,

f_1 = - V_{,1} ~; f_2 = - V_{,2} $$ Hence,
 * $$\begin{align}

\text{(43)} \qquad V_{,1} & = \rho\left(a_{01}-\dot{\theta}^2x_1\right)\\ \text{(44)} \qquad V_{,2} & = \rho\left(a_{02}-\dot{\theta}^2x_2\right) \end{align}$$ Integrating equation (43),
 * $$\text{(45)} \qquad

V = \rho\left(a_{01} x_1 -\dot{\theta}^2\cfrac{x_1^2}{2}\right) + h(x_2) $$ Hence,
 * $$(\text{46)} \qquad

V_{,2} = h^{'}(x_2) = \rho\left(a_{02}-\dot{\theta}^2x_2\right) $$ Integrating,
 * $$\text{(47)} \qquad

h(x_2) = \rho\left(a_{02} x_2 -\dot{\theta}^2\cfrac{x_2^2}{2}\right) + C $$ Without loss of generality, we can set $$C = 0$$. Then,
 * $$\text{(48)} \qquad

V = \rho\left(a_{01} x_1 -\dot{\theta}^2\cfrac{x_1^2}{2}\right) + \rho\left(a_{02} x_2 -\dot{\theta}^2\cfrac{x_2^2}{2}\right) $$ or,
 * $$\text{(49)} \qquad

V = \rho\left[a_{01} x_1 + a_{02} x_2 - \cfrac{\dot{\theta}^2}{2} \left(x_1^2 + x_2^2\right)\right] $$ For a body loaded by gravity only, we can set $$a_{01} = 0$$, $$a_{02} = -g$$ and $$\dot{\theta} = 0$$, to get
 * $$\text{(50)} \qquad

V = -\rho g x_2 \, $$ For a body loaded by rotational inertia only, we can set $$a_{01} = 0$$, and $$a_{02} = 0$$, and get
 * $$\text{(51)} \qquad

V = -\cfrac{\rho\dot{\theta}^2}{2} \left(x_1^2 + x_2^2\right) $$

We can see that an Airy stress function + a body force potential of the form shown in equation (49) can be used to solve two-dimensional elasticity problems of plane stress/plane strain.

title: Elasticity/Body force potential