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Precambrian/Life origins

Welcome to the Wikiversity learning project for Life Origins. Participants in this project explore key originating steps in the evolution of life including the abiotic origin of life, the endosymbiotic origin of eukaryotes, the origin of action potentials and brains, the origin of the human species and the origin of human language.

Organization of this learning project
At least initially, there are page sections with short introductions and a list of suggested reading. Participants should feel free to learn by editing, in particular, feel free to start subsections for questions and discussion.

Origin of life
Early speculations about the origin of life were very limited due to the difficulty in revealing details of the chemical basis of life. Naturalists like Darwin could express vague suspicions about the boundary between non-living chemical systems and life, but it was not clear what constituted the most simple forms of life. Experimentalists such as Pasteur began to test how easy it is to make the transition from non-living chemical systems to microbial life, but they had no understanding of the likely differences between environmental conditions in the current biosphere of Earth and conditions when life first arose.
 * Darwin - Darwin (1809-1882) was reluctant to speculate about the origin of life, but in private he speculated that chemical reactions alone, "in some warm little pond, with all sorts of ammonia and phosphoric salts, light, heat, electricity," might have been the origin of life.
 * Louis Pasteur (1822–1895) and the debate of spontaneous generation. When natural selection first became known as a mechanism for change in living systems, very little was known about life at the microscopic level. It was not clear if transition from non-living chemistry to living cells was something that might easily take place at any time. Pouchet (1800-1872) claimed that boiled water and hay provided suitable conditions for the generation of new microbes. Pasteur showed that Pouchet's methods allowed living microbes back into the boiled hay after cooling. After heat sterilization, if care is taken to prevent contamination by living microbes, sterilized materials remain sterile. See: Louis Pasteur. Achievements and disappointments, 1861 by J. R. Porter (1961), starting on page 394.

Modern era
In the early 1900s biochemistry continued to mature, genetics began as a science and viruses began to be appreciated as very small biologically active agents near the boundary between non-living chemical systems and living cells. It became widely recognized that free oxygen on Earth is of biological origin, with profound implications for the abiotic production of organic molecules.
 * viruses and the boundary between replication chemicals and living organisms: The origin of life (1927) Viruses as non-living chemical systems that can replicate their genetic material by "taking over" living cells: viruses begin to provide a good model of the boundary between life and non-life.
 * Alexander Oparin (1894–1980) - idea that Earth's atmosphere did not have free oxygen when life began. In thinking about the transition from non-living chemical systems to life, it is important to take into account the actual chemical environment of the early Earth.
 * An example of early concerns about the evolvability of complex metabolic pathways: On the Evolution of Biochemical Syntheses (1945) by N. H. Horowitz
 * On the Early Chemical History of the Earth and the Origin of Life (1952) by Harold Urey (1893–1981)
 * Miller-Urey experiment. "Organic compound synthesis on the primitive earth" in Science (1959) Volume 130, pages 245-251.
 * The origin of self-replicating systems of macro-molecules. On the Origin of Macromolecular Sequences by Howard H. Pattee in Biophys J. (1961) Volume 1, pages 683–710. Leading up to the existence of a genetic code, can there be processes of "molecular selection" acting on the formation, survival, and eventually, self-replication of polymers?
 * Hydrogen cyanide dimer and chemical evolution by Robert M. Kliss and Clifford N. Matthews (1962). Speculation about abiotic formation of polymers with C-C-N backbones. What polymers might have been the first to form under abiotic conditions? See also:
 * Prebiological protein synthesis by C. N. Matthews and R. E. Moser (1966).
 * Synthesis of biologically pertinent peptides under possible primordial conditions by G. Steinman and M. N. Cole (1967).
 * The condensation of the adenylates of the amino acids common to protein by Gottfried Krampitz and Sidney W. Fox (1969).
 * An approach to the evolution of metabolism by Robert E. Eakin (1963). Early speculation about possible abiotic metabolism with high-energy phosphate-containing molecules. What types of catalysis would have predominated before enzymes existed?
 * The origins of life (1964) by George Wald (1906–1997). Discussion of issues such as why carbon is used in living organisms, not silicon.

Although biologists and biochemists have constructed their ideas about the origin of life upon the tenet of the "reducing atmosphere" (i.e. containing no free-oxygen), geologists have never been unanimous. /The Ecopoesis model/ is a recent proposal for a new approach to the issue.

Enzymes vs genes
The "classical" period of molecular biology revealed the capacity of nucleic acid molecules to function as genetic molecules. Proteins were thought of as the critically important biological catalysts in control of the chemistry of life. All life on Earth depends on a complex process by which genetic information stored in nucleic acid sequences is converted into the structure of proteins.

Francis Crick speculated about possible stages by which an initially simple translation system with a few amino acid types might have evolved into the more complex code used by existing organisms. At that time, everyone thought of proteins as the only kind of enzymes and ribozymes had not yet been found. However, even this speculation about an initially simplified genetic code did not generate much enthusiasm for the idea that a translation system depending on many proteins could evolve from a pre-biological "organic soup". The origin of translation appeared to be an impossible chicken-or-egg problem. Faced with this conceptually baffling problem, Crick and Orgel speculated about the possibility that the original production of living systems might be a very rare event, but once it had happened once it might be spread by intelligent life forms using space travel, a process they called "Directed Panspermia".

Related resource: Origin of translation

Ribozyme era
The conceptual log-jam in origin of life research was broken by a new fundamental biological discovery made in the 1980s: enzymatically-active RNA.

In a retrospective article, Crick and Orgel noted that they had been overly pessimistic about the chances of abiogenesis on Earth when they had assumed that some kind of self-replicating protein-based system was the molecular origin of life. With the discovery of ribozymes it became possible to imagine an RNA world and the origin of life in the form of possibly a single self-replicating polymer that could function as both a genetic molecule and as a source of enzymatic activities. See also: the RNA World learning resource at Wikiversity.

The fact that RNA is not a particularly stable molecule immediately raises thoughts about the possibility of some other polymer that was more stable than RNA serving as the first genetic molecule. Also, some interest began to shift from the problem of abiotic synthesis of polymers to the related problem of stabilizing useful polymers once they were created.

Another conceptual change from about the same time as the discovery of ribozymes was recognition that many microbes are not dependent on sunlight for energy. New knowledge of microbes that harvest chemical energy in deep sea and deep ground environments, including a diverse collection of extremophiles, has broadened thinking about the possibilities for early chemical systems that might have made the transition to a living state. Reviewed by Ronald F. Fox (1993). Stuart Kauffman - Wikipedia article.
 * A model for the RNA-catalyzed replication of RNA by T. R. Cech (1986).
 * Selection by differential molecular survival: a possible mechanism of early chemical evolution by Christian de Duve (1987).
 * An all-purine precursor of nucleic acids by G. Wächtershäuser (1988).
 * Before enzymes and templates: theory of surface metabolism by G. Wächtershäuser (1988).
 * Two-dimensional life? Christian de Duve and Stanley L. Miller (1991).
 * Evolution of the first metabolic cycles by G. Wächtershäuser (1990).
 * The deep, hot biosphere by T. Gold (1992).
 * Impact melting of frozen oceans on the early Earth: Implications for the origin of life by J. L. Bada, C. Bigham and Stanley L. Miller (1994). Snowball Earth - at Wikipedia.
 * Geomicrobiology of the Ocean Crust: A Role for Chemoautotrophic Fe-Bacteria by Katrina J. Edwards, Wolfgang Bach and Daniel R. Rogers (2003).
 * Review of Stuart Kauffman, The Origins of Order: Self-Organization and Selection in Evolution

Life: Classification and Origins
What are the evolutionary origins of Earth's major forms of life?

Thomas Cavalier-Smith reviewed the issue of life form origins in Deep phylogeny, ancestral groups and the four ages of life. In his Figure 1 (image shown to the right), the origin of Eukaryotes is emphasized.

It has been proposed that early eukaryotic cells had an endomembrane system and membrane-delineated nucleus. Around 850,000,000 years ago, mitochondria originated as endocytosed bacteria.

Figure 1 shows three kinds of photosynthetic life forms (green), categorized as chromista, plants and photosynthetic bacteria. The two types of photosynthetic eukaryotes originated by endocytosis of cyanobacteria. Microfossil evidence indicates that bacteria were the earliest form of life on Earth. Cavalier-Smith's Figure 3 (image shown to the right) divides the bacteria into two major forms, negibacteria, with two distinct lipid bilayer membranes, and the unimembrana. Cavalier-Smith further divides the unimembrana into Posibacteria and Archaebacteria.

Related resource: Bacterial fossil structure and preservation.

Cavalier-Smith has suggested that enough oxygenic photosynthesis took place approximately 2,500,000,000 years ago to cause removal of methane from the atmosphere, resulting in a Palaeoproterozoic global freeze.

Anaerobic photosynthetic bacteria similar to extant Chloroflexi probably existed prior to the evolution of Photosystem II. Stromatolites have been reported that date to over 3,000,000,000 years old.

Related resources

 * RNA World - was RNA the primordial macromolecule of life?
 * Human Genetic Uniqueness Project - what is unique about humans?
 * The concept of irreducible complexity - is translation an irreducibly complex biological process?
 * Theoretical model protocell that should be realizable in the lab
 * Evolution of life

title: Precambrian/Life origins


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User:Mytanget

Philosophy  Introduction to Philosophy

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

title: User:Mytanget


text:
User:Mike's bot account

Tasks
These tasks are available by request:
 * 1) substituting templates on user talk: pages
 * 2) fixing double redirects
 * 3) checking for dead links
 * 4) moving pages
 * 5) mass categorization

title: User:Mike's bot account


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Wikiversity:Candidates for Custodianship/Erkan Yilmaz (full custodian)

See also: Candidates for Custodianship/Erkan Yilmaz.

 * Nomination
 * I nominate Erkan Yilmaz for full custodianship. Erkan Yilmaz has been a probationary custodian since August 26, 2007. Erkan Yilmaz has done page imports and blocked vandals (see). In addition, Erkan Yilmaz has performed other community services such as watching for copyright violations. Erkan Yilmaz's efforts for Wikiversity have been facilitated by participation at IRC freenode #wikiversity-en and Colloquium. After having served the community during the probationary period, Erkan Yilmaz should be confirmed by the Wikiversity community as a full custodian. --JWS 16:25, 26 September 2007 (UTC)

Questions and Requests

 * A real problem for custodians is stamina - maintaining long-term, regular commitment. I reckon that the more intense one's commitment, the greater the danger of burn-out. I'm sure this is an impossible question, but given my strong support for you, I'll ask the impossible question: what is your strategy for maintaining long-term commitment at the same level as you have recently done? -- McCormack 06:22, 27 September 2007 (UTC)

 * Thanks for the good question. Short answer would be: to continue being in IRC
 * Truth is: it makes very much fun. For me the ideas within this WV (IRC and recent changes, ...) give me some input. It is like reading the newspaper, everyday something different happens. Since the other Wikiversities are "less developed" (when looking only now at user numbers, page numbers, ...) I found this WV as an interesting place, where the goals of Wikiversity (mentioned e.g. on beta) are more to become reality, than just talking about it. I can use the examples with my work in the de.WV at least. As you will notice I also am more active in the wiki blog than in my normal blog.

 * But I would want to make this statement: if I do less custodian activities, my sysop flag should be removed. Especially in wiki world we should be more democratic than in the real world. Erkan Yilmaz ( my talk page, wiki blog ) 06:57, 27 September 2007 (UTC)
 * (quote) "if I do less custodian activities, my sysop flag should be removed." So you would support the view that the less active custodians (i.e. most of us!)... etc... ? --Devil's Advocate 07:03, 27 September 2007 (UTC)
 * Well, I can not speak what others should do or not, I only speak of myself. If I do less activities as custodian, why should I be custodian then ? People can also serve WV with not having sysop flag. For a change of policy for custodians in general I think the community should decide what to do. Erkan Yilmaz ( my talk page, wiki blog ) 07:08, 27 September 2007 (UTC)
 * Being serious, now: if your activites become fewer, I still think we should keep your sysop status! However I do think the burn-out thing needs to be thought about. My view is that a less active custodian who stays around for a long time is a good thing. It's easy to catch wiki-itis, and one needs to avoid this. --McCormack 07:55, 27 September 2007 (UTC)
 * Well, I will try to avoid burnout - let's just see the future. Only this will tell the truth :-) Erkan Yilmaz ( my talk page, wiki blog ) 16:42, 27 September 2007 (UTC)

Comments

 * There aren't enough superlatives available to me to express how completely I support Erkan. Er ist uns ganz gut! --SB_Johnny | talk 19:31, 26 September 2007 (UTC)
 * Ditto SB_Johnny. --Remi 23:45, 26 September 2007 (UTC)
 * Strong support. Nevertheless, I feel unemployed ;-) --McCormack 06:19, 27 September 2007 (UTC)
 * --Sundance Raphael 19:34, 30 September 2007 (UTC)
 * Strong support. Always there to help will be a great Custodian whatever that is. Eadthem 19:36, 30 September 2007 (UTC)
 * . He will do his job very well! --Michael Reschke 19:07, 2 October 2007 (UTC)

Discussion results are clear here as well, User:Erkan Yilmaz now has full custodianship status. Congratulations, enjoy the mop. sebmol ? 19:35, 3 October 2007 (UTC)

User:Erkan Yilmaz
I nominate User:Erkan Yilmaz for full custodianship. Erkan has given long and valued custodial service to Wikiversity and we need him back. --JWSchmidt 04:09, 19 September 2008 (UTC)

 * I agree Wikiversity is better off with Erkan than without, but I am also unsurprised that Erkan turned in their tools. I believe if Erkan could be happy and find value in contributing to Wikiversity again even in a non-custodian capacity that would be good. --dark[[Image:Yin yang.svg|12px]]lama 12:25, 19 September 2008 (UTC)

 * Indeed, it's a shame that Erkan has left us not sure for how long but it seems we've lost a great Custodian - If he comes back and request custodial tools then I'll give him my support, and hopefully the community will as well even with other former Custodians. DarkMage  20:45, 19 September 2008 (UTC)


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Knowledge transfer/UK

What is knowledge transfer?
Knowledge transfer is a system of support, operated by the UK knowledge transfer policy bodies, that aims to stimulate socially and economically productive interactions between higher education institutions and other communities. Ideas about knowledge transfer as a process are also undergoing great change; a shift that recognises the multiple facets of knowledge transfer, and knowledge transfer as a conversation, in many different stages of the research process.

RCUK, Department for Innovation, Universities and Skills (DIUS, previously OSI) and the Research Councils view knowledge transfer thus: (STFC 2007):

“The UK Research Councils seek to accelerate the two-way flow of people and ideas between the research environment and wider economy, and thereby contribute to national prosperity, the quality of life of UK citizens, and cultural enrichment of our society. Knowledge Transfer encompasses the systems and processes by which knowledge, expertise and skilled people transfer between the research environment (universities, centres and institutes) and its user communities in industry, commerce, public and service sectors.”

The most recent policy documents acknowledge that policy communities, as well as industry, can be involved in knowledge transfer. "Effective knowledge transfer requires specific institutional arrangements to pass knowledge from research establishments into wealth-creation and public policy-making, and an infrastructure of intellectual property rights, standards and metrology" (HM Treasury 2007).

UK policy organisations with an interest in Knowledge Transfer
This page highlights the UK policy organisations with an interest in knowledge transfer.

Funding for Knowledge Transfer
For institutions:

Public Sector Research Exploitation (PSRE) Fund This has invested £50 million in a diverse range of organisations to commercialise their research (HM Treasury 2007), establishing at least 12 new companies, which themselves have attracted over £14 million of third party funds and now employ more than 90 new staff (HM Treasury 2007). PSRE funds have also supported the NHS Innovation Hubs in England, which are designed to help translate ideas emerging from the NHS’s R&D budget and the practical experience of its 1.3 million staff into commercial products and improved patient care (HM Treasury 2007).

Higher Education Innovation Fund (HEIF)

Knowledge Exploitation Fund

Knowledge Transfer Grant

For departments:

For individual research fellows:

For students:

For members of the public, small businesses or other non-academic groups:

Resources for Knowledge Transfer
The British Library Business & IP Centre offers free onsite access to an enormous range of subscription databases, including Global Market Information Database, Euromonitor International, Thomson Business Intelligence and print publications covering market research, financial & company data, patents and trademarks. Anyone with a British Library Visitor's Pass can use these resources from the British Library in London.

title: Knowledge transfer/UK


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User:Josephdena

JOSEPH DENA is a personal name. 'BIO-DATA' Country - India, State - Mizoram www.josephdena.info

title: User:Josephdena


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Category:Erkan Yilmaz Blog

list of the blog pages for Erkan Yilmaz

title: Category:Erkan Yilmaz Blog


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Lunar Boom Town/Volume miner

Background: Due to a lack of atmosphere lunar facilities must be protected from micrometeorites and radiation. This can be accomplished by burying facilities.

Volume miners dig into surface to create useable volume for sell to volume developers. The material extracted is sold various raw material processers such as an oxygen extractor[[Lunar_Boom_Town/LOX_Domestic_and_Exports] or sold delivered to a customer/developer for berming/burying material.

Startup can be as easy as a shovel and explosives and a regolith hauler. Next phase might add a horizontal drilling machine and a front end loader or backhoe. Largest operators construct and operate large tunnel boring machines.Tunnel_boring_machine

As a by product valuable volatiles set free by the mining process would by collected by binding them to  liquid salts.

title: Lunar Boom Town/Volume miner


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User:Rectaangle

$$$$

title: User:Rectaangle


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User talk:Bart Simpson~enwikiversity

Spike Wrestling League II

PPV Events:-

(Jan.)-Guilty as Charged (Feb.)-PrisonYard (Mar.)-SpikeMare (Apr.)-Barely Legal (May.)-SpikeMania (June.)-Beach Blast (July.)-Heat Wave (Aug.)-BlackedOut (Sep.)-LightsOut (Oct.)-HallowScare (Nov.)-NightMare (Dec.)-WinterSlam (Dec.)-Unbreakable Match Types:-

Circle Steel Cage Match(A steel cage Match,but in a circle cage.)- Spiderweb Match (To roll your opponent in the netting and tie it.)- Inferno Match  (Light Your Oppnent's body on fire.)- Battle Inferno Match (Where there are two fighters in the ring surrounded by fire and wrestlers hanging from the top of the cage.)- LightsOut Match (Were someone terns off the lights and the first superstar to pin their opponent wins.)- "I Forfeit" Match (Related to a "I Quiet" Match, but you have to put your opponent through a stack of tables or chairs and make them say "I forfeit")-

Championships:-

Spike Championship Canadian Championship U.S. Championship

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 Bart Simpson. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Bart Simpson~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 23:30, 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) 06:03, 19 April 2015 (UTC)

title: User talk:Bart Simpson~enwikiversity


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User:Hhristov

Hristo Hristov Bulgaria 7000

Business and scientific interests: Logistics, SUpply Chain Management,Supply networks, Clusters Education: 2006-2007 - Master of Industrial Management and Marketing 2002-2006 - Bachelor of Industrial Management

title: User:Hhristov


text: User:Darklama/Sandbox

title: User:Darklama/Sandbox


text: Template:Displayname

title: Template:Displayname


text:
MediaWiki:Displayname.js

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title: MediaWiki:Displayname.js


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User talk:Eadthem

Welcome
Hello Eadthem, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; for it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
 * Take a guided tour and learn to edit;
 * Explore our learning projects;
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 * Chat with other wikiversiters on.

And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! --JWSchmidt 02:28, 27 September 2007 (UTC)

Electronics Images
Hey Eadthem, I tried to find you today on #Wikiversity-en, but you were nowhere to be seen. I took a bunch of pictures of test equipment like you wanted today. Some of the pictures didnt come out because they were all blurry, or the flash obscured the front panels or something like that. I've got about 15 images that did turn out though, and i will try to take some more tomorrow. The images are all uploaded onto commons, and are copyleft licensed, so you can do with them what you please: commons:User:Whiteknight/My Images. Let me know what else you need. --Whiteknight (Versity) (Books) 02:54, 15 November 2007 (UTC)

Dropped by to Hi!
Hi Eadthem, nothing interesting ever happens it seems on my talk page so I thought I would enliven yours with a brief Hello! If I were a barnstar kind of guy you would have already earned one for your continuous and valuable efforts at EE. Maybe we will whip up a Lunar Boom Town Barnstar for critical infrastructure contributors or something soon. Easier to spam people that way. 8) Catch you next time on #wikiversity-en IRC.  Mirwin 04:59, 18 December 2007 (UTC)

 * Decided your reward should not wait for Lunar Boom Town grapics designers to show up so I hearby award you the following for improving EE learning resources we will need, and thanks for your support!

Thanks
Hi. Thanks for sorting out my DIV's and things on the main page. I was about to go back again today and try to sort them out - and lo-and-behold someone else got there first! Looks like very pretty and well-ordered source now. -- McCormack 11:52, 20 December 2007 (UTC)

Vertical alignment problem on main page
Hi, Eadthem. As you sorted my previous alignment problems so well, I asking for some help! Some extra news was added to the main page a couple of days ago, which lengthened the right column and revealed a vertical alignment problem with the 4 topic boxes in the centre. It looks like a simple "valign=top" is missing somewhere in your tables, and I went over this very thoroughly and tried things out in preview mode - with no luck. Perhaps your more expert eye can see where the alignment problem is? McCormack 06:03, 28 December 2007 (UTC)

 * Nice to talk to you on IRC yesterday. Did you check out the new alignment and table configuration on different browsers? I'm guessing that if you did, I'd know about it by now! :-) --McCormack 06:31, 30 December 2007 (UTC)

Electronic engineering merge
Thanks for the heads up. The following, "sometimes referred to as electrical and electronic engineering" from Electrical engineering threw me off. I suppose it may just be best to remove the commented merge... which I will do. --Remi 21:01, 17 March 2008 (UTC)

Portal talk:Engineering and Technology/ - Electrical/Electronic Engineering Orientation/Aptitude Course
ping- Thuvack 11:12, 10 April 2008 (UTC)

Electronic engineering/School Face Lift
ping- Thuvack 13:04, 10 April 2008 (UTC)
 * Please have a look at this proposed School Face lift. It incorporates catergorisation and course wish list on sub pages see School of Electrical Engineering new look. Also Department news are moved to a sub page. Please see this discussion for clarity on motivations towards this standardisation. I will be moving the Proporsal to the school page on Wed 23rd July. Your input on this will be apreciated. ;-)Thuvack 06:39, 21 July 2008 (UTC)

voting
Hi ead, the voting here was already closed. Sorry, but it wa snot archived yet :-( So your voice will not count. You can still vote here. Erkan Yilmaz uses the Chat (try) 20:48, 16 August 2008 (UTC)

Wikiversty:Fair use
I noticed that this page was misspelled. I moved it to Fair use and I deleted the previous page. I hope this doesn't interfere with anything. If there are any problems, please feel free to contact me. Ottava Rima (talk) 03:10, 16 September 2008 (UTC)

Image license
I saw, you were uploading a new images under GFDL. I would like to note, that images uplaoded under this licence are useless, because:
 * each copy of the image distributed to the third parties should go with the complete licence (so its difficult to disribute it via print)
 * each copy of the image distributed to the third parties should go with full history list, all contributers must be listed

So I would recomend you, to license these files under CC-BY-SA 3.0 license.--Juandev 08:14, 4 January 2009 (UTC)

page moved into your userspace
Guy vandegrift (discuss • contribs) 02:38, 18 March 2024 (UTC)

title: User talk:Eadthem


text:
File:Sunayana Anand SBDS2.pdf

Used with the WikiU Film School Lesson on how to format a movie script

title: File:Sunayana Anand SBDS2.pdf


text:
Talk:Lecture 6, Flip-flops

Starting basic layout and content
just started to get content and page set up  there is at this point 1 uncited source to a sr latch datasheet    the source is prob not needed but it would be verification   I will do it later if someone hasn't beet me to it.Eadthem 05:48, 27 September 2007 (UTC)

redirected for uniformity
this also will make it place a back link at the top of the page

title: Talk:Lecture 6, Flip-flops


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User:Gangsterdogz~enwikiversity

Hi guys. i don't know whats going on.

title: User:Gangsterdogz~enwikiversity


text:
User talk:Gangsterdogz~enwikiversity

I saw your user page, can I help you ? Here is some info:

Welcome
Hello Gangsterdogz, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; for it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
 * Take a guided tour and learn to edit;
 * Explore our learning projects;
 * Browse our portals, schools, and research activities;
 * Read and help develop our community policies；or
 * Chat with other wikiversiters on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! Erkan Yilmaz ( my talk page, wiki blog ) 05:52, 27 September 2007 (UTC)

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 Gangsterdogz. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Gangsterdogz~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 23:36, 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) 06:09, 19 April 2015 (UTC)

title: User talk:Gangsterdogz~enwikiversity


text:
User:EVula/header

 user page  //  talk page • matrix •

de:Benutzer:EVula/header es:Usuario:EVula/header fr:Utilisateur:EVula/header it:Utente:EVula/header

title: User:EVula/header


text:
User talk:Arabicpod~enwikiversity

Welcome
Hello Arabicpod, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; for it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
 * Take a guided tour and learn to edit;
 * Explore our learning projects;
 * Browse our portals, schools, and research activities;
 * Read and help develop our community policies；or
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And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! --McCormack 07:48, 27 September 2007 (UTC)

Deleted page
Hi, Arabicpod. I'm afraid I deleted your very first mini-page. Putting a URL into a page title isn't really good practice. However you can write about yourself and your web activities on your new user page (which you now have). Feel welcome to contact me if you need help. --McCormack 07:50, 27 September 2007 (UTC)

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 Arabicpod. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Arabicpod~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 23:28, 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) 06:03, 19 April 2015 (UTC)

title: User talk:Arabicpod~enwikiversity


text: Category:BCP/Family/Campanulaceae

title: Category:BCP/Family/Campanulaceae


text: Category:BCP/Family/Convolvulaceae

title: Category:BCP/Family/Convolvulaceae


text: Category:BCP/Family/Oxalidaceae

title: Category:BCP/Family/Oxalidaceae


text: Category:BCP/Family/Urticaceae

title: Category:BCP/Family/Urticaceae


text:
User:CorsaiR

Welcome to the virtual office of Alex Petrenko (a.k.a. CorsaiR). My e-mail as Alezander82@mail.ru

I am a teacher of Information technology and programming in Ukrainian university. Not along ago I uphold a master's degree in applied mathematics.

title: User:CorsaiR


text:
User:Akaustav

Hi, I'm Ameet Kaustav. I study in the Department of Electrical and Electronics Engineering at Manipal Institute of Technology, Manipal, Karnataka, India. My hobbies include application software programming, electronics and robotics.

title: User:Akaustav


text:
Talk:BCP/Chenopodium album

I don't think that Chenopodium is commonly called "sheepsorrel" - though I could be wrong. I have called it "lambs quarters" since I was a child, and I have also heard it called "goosefoot". Wikipedia lists both these as common names as well as a few others - but sheepsorrel is not among them.

On the other hand, I have heard the name "sheep sorrel" applied to Rumex acetosella. The Peterson's Field Guides do for one. Wikipedia does for another.

I suppose that if there is a region somewhere where Chenopodium is called "sheepsorrel", it really serves to underscore the importance of binomial names. --Jomegat 12:49, 27 September 2007 (UTC)

 * No, I think it's a braino on my part :). Oddly enough I always have to lok up the English names... scientific ones I know. --SB_Johnny | talk 09:09, 28 September 2007 (UTC)

title: Talk:BCP/Chenopodium album


text:
User talk:Abdulricks

Hello, I saw your edit here. What kind of material do you search ? Also some info for you:

Welcome
Hello Abdulricks, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; for it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
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And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! Erkan Yilmaz ( my talk page, wiki blog ) 16:24, 27 September 2007 (UTC)

title: User talk:Abdulricks


text:
User talk:CorsaiR

Welcome
Hello CorsaiR, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; for it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
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And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! Erkan Yilmaz ( my talk page, wiki blog ) 16:31, 27 September 2007 (UTC)

title: User talk:CorsaiR


text:
User:Rklawton

Robert Lawton

 * Technology consultant
 * Textbook contributor (McGraw-Hill)
 * Former professor (Western Illinois University, Northern Michigan University)
 * Wikipedia administrator Rklawton
 * Master Skydiver, FB#4000.

title: User:Rklawton


text:
User talk:Rklawton

Welcome
Hello Rklawton, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; for it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may
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And don't forget to explore Wikiversity with the links to your left. Be bold, and see you around Wikiversity! --Rklawton 19:03, 27 September 2007 (UTC)

title: User talk:Rklawton


text: File:QuantumSystem.svg

title: File:QuantumSystem.svg


text:
Talk:Economics/Introduction

following text got deleted without explanation, I put it therefore here
This is moved to here, so it does not get lost. Erkan Yilmaz ( my talk page, wiki blog ) 21:57, 27 September 2007 (UTC)

Another Perspective

Think about all the people in power right now in the US

When you have a society based on Economy, Morality comes second or third or fourth.

Economics is subjective, when at our true essence, life is objective, but the line has been so misconstrued over the years, people have lost sight of this.

Economics is great, but it should not be put over our livilihood. Economics is designed to create want, if this creation was never created then we would live off of needs and why not emphasize our needs instead of creating want. Instead of creating wants to make money, why don't people create real bonds with their family, friends and anyone else in the world. When's the last time you had a meaningful conversation where money, or anything material had nothing to do with it?

But the truth is too much money would be lost if it was like this, so it will not happen, money creates too much greed in the world and it's a shame.

But please prove me wrong.

Not out to prove you wrong, merely advocating for the other side: Clayson's book, 'The Richest Man In Babylon' suggests, an immaterial resource such as money, can alleviate-burdens-of-labor, rather than amplify them. Its my contention, that if money is accurately-representive of the labor, resource, and value of that resource, than money can leverage-labor and do more work in essence that didn't exist before.

Here state-side, income-tax is basically: 30-percent. Ideally if laborers work 30-percent harder for there paychecks, and if that said-30-percent pools the right-resources than the laborers-dependents get taken care of. That is, if the proper-authorities, allocate them to do so.

Than its merely a question of scale, to increase quality-of-life for the country in question.

Learner6822 (discuss • contribs) 21:49, 10 September 2019 (UTC)

title: Talk:Economics/Introduction


text:
Nonlinear finite elements/Updated Lagrangian formulation

Updated Lagrangian formulation
We will now derive the finite element equations for the updated Lagrangian formulation for three-dimensional problems in solid mechanics.

Updated Lagrangian governing equations
The updated Lagrangian equations are

\begin{align} \rho_0(\mathbf{X}) & = J(\mathbf{X},t)~\rho(\mathbf{X},t) \\ \rho~\dot{\mathbf{v}} &= \boldsymbol{\nabla} \cdot \boldsymbol{\sigma}^T + \rho~\mathbf{b} \\ \boldsymbol{\sigma} & = \boldsymbol{\sigma}^T \\ \rho~\dot{e} & = \boldsymbol{\sigma}:\boldsymbol{d} - \boldsymbol{\nabla} \cdot \mathbf{q} + \rho~s \\ \mathcal{L}_\varphi~\boldsymbol{\sigma} &= \boldsymbol{G}(\boldsymbol{\sigma}, \boldsymbol{d}, T, \dots) \\ \boldsymbol{d} & = \frac{1}{2}(\boldsymbol{l} + \boldsymbol{l}^T) \end{align} $$ The boundary conditions are

\begin{align} \boldsymbol{\sigma}^T\cdot\mathbf{n} & = \mathbf{t} \qquad \text{on}\partial \Omega _t \\ \mathbf{v} & = \overline{\mathbf{v}} \qquad \text{on}\partial \Omega _v \end{align} $$ The initial conditions are

\begin{align} \mathbf{v}(\mathbf{X},0) & = \mathbf{v}_0(\mathbf{X}) \\ \boldsymbol{\sigma}(\mathbf{X},0) & = \boldsymbol{\sigma}_0(\mathbf{X}) \qquad \text{or} \qquad \mathbf{u}(\mathbf{X},0) & = \mathbf{u}_0(\mathbf{X}) \end{align} $$

Dependent variables
Note that the dependent variables in this case are all expressed as functions of the Lagrangian (material) coordinates, i.e.,

 * 1) Velocity ($$\mathbf{v}(\mathbf{X},t)$$)
 * 2) Cauchy stress ($$\boldsymbol{\sigma}(\mathbf{X},t)$$)
 * 3) Rate of deformation ($$\boldsymbol{d}(\mathbf{v},t)$$)

Also note that instead of $$\boldsymbol{\sigma}$$ and $$\boldsymbol{d}$$, we may use $$\boldsymbol{S}$$ and $$\boldsymbol{E}$$ in our calculations and then transform to $$\boldsymbol{\sigma}$$.

Weak form of the balance of linear momentum
Another name for the weak form is the  Principle of Virtual Power (or  Principle of Virtual Work if rates are not involved).

The strong form consists of the balance of linear momentum and the traction boundary conditions. That is,

{ \begin{align} \boldsymbol{\nabla} \cdot \boldsymbol{\sigma}^T + \rho~\mathbf{b} & = \rho~\mathbf{a} \qquad \text{in}\Omega \\ \boldsymbol{\sigma}^T\cdot\mathbf{n} & = \mathbf{t} \qquad \text{on}\partial \Omega _t \end{align} } $$ where $$\mathbf{a} = \dot{\mathbf{v}} = \ddot{\mathbf{u}}$$ is the acceleration.

The weak form of this equation can be written as

{ \int_{\Omega} \rho~\mathbf{a}\cdot\mathbf{w}~\text{dV} + \int_{\Omega} \boldsymbol{\sigma}:(\boldsymbol{\nabla} \mathbf{w})~\text{dV} = \int_{\Omega} \rho~\mathbf{b}\cdot\mathbf{w}~\text{dV} + {\int_{\partial \Omega}}_t \mathbf{t}\cdot\mathbf{w}~\text{dA} } $$ where $$\mathbf{w}$$ is a vector valued weighting function (also called a  test function) that is zero at the points on the boundary where the essential boundary conditions on $$\mathbf{v}$$ are applied. Therefore we can think of $$\mathbf{w}$$ as a variation of $$\mathbf{v}$$.

Derivation of the weak form
We proceed in the usual manner to derive the weak form. We multiply the differential equation with the weighting function and integrate over the volume to get

\int_{\Omega} \mathbf{w}\cdot\left(\boldsymbol{\nabla} \cdot \boldsymbol{\sigma}^T + \rho~\mathbf{b} - \rho~\mathbf{a}\right)~\text{dV} = 0 $$ Using the identity

\boldsymbol{\nabla} \cdot (\boldsymbol{A}^T\cdot\mathbf{b}) = \mathbf{b}\cdot(\boldsymbol{\nabla} \cdot \boldsymbol{A}) + \boldsymbol{A}:(\boldsymbol{\nabla} \mathbf{b}) $$ and noting that $$\boldsymbol{\sigma} = \boldsymbol{\sigma}^T$$ (conservation of angular momentum), we have

\int_{\Omega} \mathbf{w}\cdot(\boldsymbol{\nabla} \cdot \boldsymbol{\sigma}^T)~\text{dV} = \int_{\Omega} \boldsymbol{\nabla} \cdot (\boldsymbol{\sigma}\cdot\mathbf{w})~\text{dV} - \int_{\Omega} \boldsymbol{\sigma}:(\boldsymbol{\nabla} \mathbf{w})~\text{dV} $$ From the divergence theorem we have

\int_{\Omega} \boldsymbol{\nabla} \cdot (\boldsymbol{\sigma}\cdot\mathbf{w})~\text{dV} = \int_{\partial \Omega} \mathbf{n}\cdot(\boldsymbol{\sigma}\cdot\mathbf{w})~\text{dA} $$ where $$\mathbf{n}$$ is the outward unit normal to the boundary. So,

\int_{\Omega} \mathbf{w}\cdot(\boldsymbol{\nabla} \cdot \boldsymbol{\sigma})~\text{dV} = \int_{\partial \Omega} \mathbf{n}\cdot(\boldsymbol{\sigma}\cdot\mathbf{w})~\text{dA} - \int_{\Omega} \boldsymbol{\sigma}:(\boldsymbol{\nabla} \mathbf{w})~\text{dV} $$ Now, on the boundary

\mathbf{n}\cdot(\boldsymbol{\sigma}\cdot\mathbf{w}) \equiv n_i~\sigma_{ij}~w_j = \sigma_{ji}~n_i~w_j \equiv (\boldsymbol{\sigma}^T\cdot\mathbf{n})\cdot\mathbf{w} = \mathbf{t}\cdot\mathbf{w} $$ On the part of the boundary where no tractions are applied, we have $$\mathbf{t} = \mathbf{0}$$ and hence $$\mathbf{n}\cdot(\boldsymbol{\sigma}\cdot\mathbf{w}) = \mathbf{0}$$. Therefore we can write

\int_{\Omega} \mathbf{w}\cdot(\boldsymbol{\nabla} \cdot \boldsymbol{\sigma})~\text{dV} = {\int_{\partial \Omega}}_t \mathbf{t}\cdot\mathbf{w}~\text{dA} - \int_{\Omega} \boldsymbol{\sigma}:(\boldsymbol{\nabla} \mathbf{w})~\text{dV} $$ where $$\partial\Omega_t$$ is the part of the boundary where the tractions are applied.

Plugging this expression into the weighted average form of the balance of linear momentum we get

{\int_{\partial \Omega}}_t \mathbf{t}\cdot\mathbf{w}~\text{dA} - \int_{\Omega} \boldsymbol{\sigma}:(\boldsymbol{\nabla} \mathbf{w})~\text{dV} + \int_{\Omega} \mathbf{w}\cdot\left(\rho~\mathbf{b} - \rho~\mathbf{a}\right)~\text{dV} = 0 $$ Rearranging terms we get the required weak form

\int_{\Omega} \rho~\mathbf{a}\cdot\mathbf{w}~\text{dV} + \int_{\Omega} \boldsymbol{\sigma}:(\boldsymbol{\nabla} \mathbf{w})~\text{dV} = \int_{\Omega} \rho~\mathbf{b}\cdot\mathbf{w}~\text{dV} + {\int_{\partial \Omega}}_t \mathbf{t}\cdot\mathbf{w}~\text{dA} $$

Physical interpretation of terms
To provide a physical interpretation of the four terms in the weak form, we write the weighting function as a variation of the velocity, i.e., $$\mathbf{w} = \delta \mathbf{v}$$. Then we have the familiar principle of virtual power:

\int_{\Omega} \rho~\mathbf{a}\cdot\delta \mathbf{v}~\text{dV} + \int_{\Omega} \boldsymbol{\sigma}:(\boldsymbol{\nabla} \delta \mathbf{v})~\text{dV} = \int_{\Omega} \rho~\mathbf{b}\cdot\delta \mathbf{v}~\text{dV} + {\int_{\partial \Omega}}_t \mathbf{t}\cdot\delta \mathbf{v}~\text{dA} $$ The first term on the left can then be identified as the virtual kinetic power, the second term on the left as the virtual internal power, and the sum of the two terms on the right as the virtual external power. In other words, we have

\begin{align} \delta P_{\text{kin}} & := \int_{\Omega} \rho~\mathbf{a}\cdot\delta \mathbf{v}~\text{dV} \\ \delta P_{\text{int}} & := \int_{\Omega} \boldsymbol{\sigma}:(\boldsymbol{\nabla} \delta \mathbf{v})~\text{dV} \\ \delta P_{\text{ext}} & := \int_{\Omega} \rho~\mathbf{b}\cdot\delta \mathbf{v}~\text{dV} + {\int_{\partial \Omega}}_t \mathbf{t}\cdot\delta \mathbf{v}~\text{dA} \end{align} $$ and

\delta P_{\text{kin}} + \delta P_{\text{int}} = \delta P_{\text{ext}}~. $$

We can see why the second terms is identified as the virtual internal power as follows. Note that

\boldsymbol{\nabla} \delta \mathbf{v} = \delta \boldsymbol{l} = \delta (\boldsymbol{d} + \boldsymbol{w}) $$ where $$\boldsymbol{l}$$ is the velocity gradient, $$\boldsymbol{d}$$ is symmetric rate of deformation tensor, and $$\boldsymbol{w}$$ is the skew symmetric spin tensor. Therefore, since the product of a symmetric and a skew symmetric tensor is zero, we have

\boldsymbol{\sigma}:\boldsymbol{\nabla} \delta \mathbf{v} = \boldsymbol{\sigma}:\delta \boldsymbol{d} + \boldsymbol{\sigma}:\delta \boldsymbol{w} = \boldsymbol{\sigma}:\delta \boldsymbol{d} $$ Hence,

\delta P_{\text{int}} = \int_{\Omega} \boldsymbol{\sigma}:\delta \boldsymbol{d}~\text{dV} $$ This has the same form as the expression for internal power that we discussed earlier.

Finite element discretization
Let us go back to the original weak form that we derived, i.e.,

\int_{\Omega} \rho~\mathbf{a}\cdot\mathbf{w}~\text{dV} + \int_{\Omega} \boldsymbol{\sigma}:(\boldsymbol{\nabla} \mathbf{w})~\text{dV} = \int_{\Omega} \rho~\mathbf{b}\cdot\mathbf{w}~\text{dV} + {\int_{\partial \Omega}}_t \mathbf{t}\cdot\mathbf{w}~\text{dA} $$

Trial function
To start the discretization process we have to first choose an approximate solution $$\mathbf{v}_h$$ from the space $$\mathcal{S}_h$$ of admissible finite element  trial functions. These functions must satisfy at least $$C^0$$ continuity and the essential boundary condition $$\mathbf{v} = \overline{\mathbf{v}}$$ on $${\partial \Omega }_v$$.

More formally, we choose $$\mathbf{v}_h(\mathbf{X},t) \in \mathcal{S}_h$$ where

\mathcal{S}_h = \{ \mathbf{v}~|~ \mathbf{v} \in C^0(\mathbf{X}), \mathbf{v} = \overline{\mathbf{v}}~\text{on}~ \partial \Omega _v \} $$

If we discretize the body into a number of elements with $$n$$ nodes, then we can write the approximate solution as

\mathbf{v}_h(\mathbf{X},t) = \sum_{I=1}^n N_I(\mathbf{X})~\mathbf{v}_I(t) $$ The quantities $$N_I(\mathbf{X})$$ are the  shape functions which provide the required level of continuity and are chosen so that $$\mathbf{v}_h \in \mathcal{S}_h$$.

Test function
We also have to choose appropriate weighting functions ($$\mathbf{w}_h$$) which are also known as  test functions.

In Galerkin finite elements we choose these functions from the same space as the trial functions with the additional restriction that these functions go to zero at points on the boundary where essential boundary conditions are applied.

Formally, choose $$\mathbf{w}_h(\mathbf{X}) \in \mathcal{S}_t$$ where

\mathcal{S}_t = \{ \mathbf{w}~|~ \mathbf{w} \in C^0(\mathbf{X}), \mathbf{w} = \mathbf{0}~\text{on}~ \partial \Omega _v \} $$

For finite element analysis, these weighting functions have the same form as the trial function, i.e.,

\mathbf{w}_h(\mathbf{X}) = \sum_{I=1}^n N_I(\mathbf{X})~\mathbf{w}_I $$

Motion
Instead of a trial function for the velocity, we can start with one for the motion and then take time derivatives. In this case, we choose the motion to be approximated by

\mathbf{x}_h(\mathbf{X},t) = \sum_{I=1}^n N_I(\mathbf{X})~\mathbf{x}_I(t) $$ where $$N_I(\mathbf{X})$$ are the nodal shape functions (note that these are functions of $$\mathbf{X}$$) and $$\mathbf{x}_I(t)$$ are the positions of nodes $$i$$ in the current configuration. Therefore, nodes remain coincident with material point labels at all times.

Therefore, in the reference configuration, we have

\mathbf{x}_h(\mathbf{X},0) = \sum_{I=1}^n N_I(\mathbf{X})~\mathbf{x}_I(0) = \sum_{I=1}^n N_I(\mathbf{X})~\mathbf{X}_I $$

The shape functions are also chosen such that

N_I(\mathbf{X}_J) = \delta_{IJ} $$

Then the displacement $$\mathbf{u} = \mathbf{x} - \mathbf{X}$$ can be approximated by

\mathbf{u}_h(\mathbf{X},t) = \mathbf{x}_h(\mathbf{X},t) - \mathbf{X}_h = \sum_{I=1}^n N_I(\mathbf{X})~\left[\mathbf{x}_I(t) - \mathbf{X}_I\right] = \sum_{I=1}^n N_I(\mathbf{X})~\mathbf{u}_I(t) $$

The velocity $$\mathbf{v}$$ is given by the time derivative of $$\mathbf{u}$$ keeping $$\mathbf{X}$$ fixed. So we have

\mathbf{v}_h(\mathbf{X},t) = \sum_{I=1}^n N_I(\mathbf{X})~\dot{\mathbf{u}}_I(t) = \sum_{I=1}^n N_I(\mathbf{X})~\mathbf{v}_I(t) $$ Note that this approximation has the same form as the trial function for the velocity that we started with.

The acceleration $$\mathbf{a}$$ is given by the time derivative of $$\mathbf{v}$$. Hence

\mathbf{a}_h(\mathbf{X},t) = \sum_{I=1}^n N_I(\mathbf{X})~\ddot{\mathbf{u}}_I(t) = \sum_{I=1}^n N_I(\mathbf{X})~\dot{\mathbf{v}}_I(t) = \sum_{I=1}^n N_I(\mathbf{X})~\mathbf{a}_I(t) $$

Velocity gradient and rate of deformation
The spatial velocity gradient $$\boldsymbol{l}$$ is given by

\boldsymbol{l}(\mathbf{x},t) = \boldsymbol{\nabla} \mathbf{v}(\mathbf{x},t) $$ Note that the derivatives are with respect to $$\mathbf{x}$$ and not $$\mathbf{X}$$.

Therefore, the approximation that we seek has the form

\boldsymbol{l}_h(\mathbf{x},t) = \sum_{I=1}^n \boldsymbol{\nabla} [N_I(\mathbf{X})~\mathbf{v}_I(t)] $$ Using the identity

\boldsymbol{\nabla} (\varphi~\mathbf{a}) = \mathbf{a}\otimes(\boldsymbol{\nabla} \varphi) + \varphi~\boldsymbol{\nabla} \mathbf{a} $$ we get

\boldsymbol{l}_h(\mathbf{x},t) = \sum_{I=1}^n \mathbf{v}_I(t)\otimes\boldsymbol{\nabla} N_I(\mathbf{X}) $$ In index notation,

[l_{ij}]_h = \sum_{I=1}^n v_{Ii}~\frac{\partial N_I(\mathbf{X},t)}{\partial x_j} = v_{Ii}~N_{I,j} $$

The rate of deformation is then given by

\boldsymbol{d}_h(\mathbf{x},t) = \frac{1}{2}~\left(\boldsymbol{l}_h + \boldsymbol{l}_h^T\right) = \sum_{I=1}^n \frac{1}{2}\left[\mathbf{v}_I(t)\otimes\boldsymbol{\nabla} N_I(\mathbf{X}) + \boldsymbol{\nabla} N_I(\mathbf{X})\otimes\mathbf{v}_I(t)\right] $$ In index notation,

[d_{ij}]_h = \sum_{I=1}^n \frac{1}{2}[v_{Ii}~N_{I,j} + v_{Ij}~N_{I,i}] $$

Approximate weak form
We can now substitute the trial and test functions into the weak form of the momentum equation to get (using the same procedure as in one-dimension)

{ \int_{\Omega} \rho~N_I~\mathbf{a}_h~\text{dV} + \int_{\Omega} \boldsymbol{\sigma}\cdot(\boldsymbol{\nabla} N_I)~\text{dV} = \int_{\Omega} \rho~N_I~\mathbf{b}~\text{dV} + {\int_{\partial \Omega}}_t N_I~\mathbf{t}~\text{dA} } $$ We can write this approximate weak form as

\mathbf{f}_I^{\text{kin}} + \mathbf{f}_I^{\text{int}} = \mathbf{f}_I^{\text{ext}} $$ where the first term represents the inertial force, the second term the internal force, and the third term the external force. Thus,

{ \begin{align} \mathbf{f}_I^{\text{kin}} & := \int_{\Omega} \rho~N_I~\mathbf{a}_h~\text{dV} \\ \mathbf{f}_I^{\text{int}} & := \int_{\Omega} \boldsymbol{\sigma}\cdot(\boldsymbol{\nabla} N_I)~\text{dV} \\ \mathbf{f}_I^{\text{ext}} & := \int_{\Omega} \rho~N_I~\mathbf{b}~\text{dV} + {\int_{\partial \Omega}}_t N_I~\mathbf{t}~\text{dA} \end{align} } $$

The mass matrix
The term

\mathbf{f}_I^{\text{kin}} := \int_{\Omega} \rho~N_I~\mathbf{a}_h~\text{dV} $$ is the  inertial force term.

If we substitute

\mathbf{a}(\mathbf{X},t) = \sum_{J=1}^n N_J(\mathbf{X})~\mathbf{a}_J(t) $$ into the inertial force terms, we get

\mathbf{f}_I^{\text{kin}} = \sum_{J=1}^n \left[\int_{\Omega} \rho~N_I~N_J~\text{dV}\right]~\mathbf{a}_J $$ We define the  mass matrix as the quantity

{ M_{IJ} :=  \int_{\Omega} \rho~N_I~N_J~\text{dV} = \int_{\Omega_0} \rho_0~N_I~N_J~\text{dV}_0 } $$ Therefore, the inertial force can be expressed, in analogy with Newton's second law, as

\mathbf{f}_I^{\text{kin}} = \sum_{J=1}^n M_{IJ}~\mathbf{a}_J $$

Semi-discrete finite element equations
We can then write the semi-discrete version of the weak form in the shape of a matrix equation as

[\mathbf{M}][\mathbf{a}] = [\mathbf{f}^{\text{ext}}] - [\mathbf{f}^{\text{int}}] $$ These equations are ordinary differential equations because we still have time derivatives on the left hand side - hence the system of equations is semi-discrete.

There are a number of ways in which the discretization in time can be effected. Some common approaches are the generalized midpoint rule, the Newmark $$\beta$$ method, or Runge-Kutta explicit integration schemes. There is a large literature on the best way of doing the discretization in time with the goal of conserving both momentum and energy as accurately as possible.

Taking derivatives and calculating integrals
At this stage we are faced with the problem of calculating derivatives and integrals with respect to $$\mathbf{x}$$ of quantities that depend on $$\mathbf{X}$$. How can we proceed?

The standard way of resolving this issue is to do all our calculations with respect to a  parent element and then map the results to the reference or current configurations as necessary.

To make things more concrete let us consider a single element and label the three domains as

 * 1) Parent element ($$\square$$).
 * 2) Reference element ($$\Omega_0$$).
 * 3) Current element ($$\Omega$$).

Let the maps that we need be

 * 1) Parent $$\rightarrow$$ Reference : $$\mathbf{X} = \mathbf{X}(\boldsymbol{\xi}) = \mathbf{x}(\boldsymbol{\xi}, 0)$$.
 * 2) Parent $$\rightarrow$$ Current : $$\mathbf{x} = \mathbf{x}(\boldsymbol{\xi}, t)$$.
 * 3) Reference $$\rightarrow$$ Current : $$\mathbf{x} = \mathbf{x}(\mathbf{X},t)$$.

This situation is illustrated (for a two dimensional situation) in the following figure.

We define the map between the parent element and the element in the current configuration as

\mathbf{x}(\boldsymbol{\xi}, t) = \sum_{I} N_I(\boldsymbol{\xi})~\mathbf{x}_I(t) $$ Then,

\mathbf{v}(\boldsymbol{\xi}, t) = \sum_{I} N_I(\boldsymbol{\xi})~\mathbf{v}_I(t) $$

Let us now try to compute the spatial velocity gradient. We have

\frac{\partial \mathbf{v}(\mathbf{x},t)}{\partial \boldsymbol{\xi}} = \frac{\partial \mathbf{v}}{\partial \mathbf{x}}\cdot\frac{\partial \mathbf{x}}{\partial \boldsymbol{\xi}} = \frac{\partial \mathbf{v}}{\partial \mathbf{x}}\cdot\boldsymbol{F}_{\xi} $$ The quantity

\boldsymbol{F}_{\xi} := \frac{\partial \mathbf{x}}{\partial \boldsymbol{\xi}} = \sum_{I} \mathbf{x}_I\otimes\frac{\partial N_I}{\partial \boldsymbol{\xi}} $$ is called the  Jacobian of the motion and is a function of time.

Inverting, we get

{ \frac{\partial \mathbf{v}}{\partial \mathbf{x}} = \frac{\partial \mathbf{v}}{\partial \boldsymbol{\xi}}\cdot\boldsymbol{F}_{\xi}^{-1} } $$ But the spatial velocity gradient is

\boldsymbol{l} = \frac{\partial \mathbf{v}}{\partial \mathbf{x}} $$ Therefore,

\boldsymbol{l} = \frac{\partial \mathbf{v}}{\partial \boldsymbol{\xi}}\cdot\boldsymbol{F}_{\xi}^{-1} $$ If we substitute the approximation

\mathbf{v}(\boldsymbol{\xi},t) = \sum_{I} N_I(\boldsymbol{\xi})~\mathbf{v}_I(t) $$ we get a formula for the velocity gradient

{ \boldsymbol{l} = \left[\sum_{I} \mathbf{v}_I\otimes\frac{\partial N_I}{\partial \boldsymbol{\xi}}\right] \cdot\boldsymbol{F}_{\xi}^{-1} } $$ A similar procedure can be followed when other spatial gradients need to be calculated. The most frequently encountered situation is the calculation of the gradient of the shape functions. In that case, we have

{ \boldsymbol{\nabla} N_I(\mathbf{X}) = \frac{\partial N_I(\mathbf{X})}{\partial \mathbf{x}} = \frac{\partial N_I}{\partial \boldsymbol{\xi}}\cdot\boldsymbol{F}_{\xi}^{-1} } $$

For computing integrals, we observe that for a function $$f(\mathbf{x})$$ on $$\Omega$$ we can write

\int_{\Omega} f(\mathbf{x})~\text{dV} = \int_{\Omega_0} \hat{f}(\mathbf{X})~J~\text{dV}_0 = \int_{\square} \tilde{f}(\boldsymbol{\xi})~J_{\xi}~\text{d}\square $$ where

J_{\xi} = \det\left(\frac{\partial \mathbf{x}}{\partial \boldsymbol{\xi}}\right) = \det(\boldsymbol{F}_{\xi}) $$ Similarly for a function $$g(\mathbf{X})$$ over $$\Omega_0$$, we have

\int_{\Omega_0} g(\mathbf{X})~\text{dV}_0 = \int_{\square} \tilde{g}(\boldsymbol{\xi})~J^0_{\xi}~\text{d}\square $$ where

J^0_{\xi} = \det\left(\frac{\partial \mathbf{X}}{\partial \boldsymbol{\xi}}\right) = \det(\boldsymbol{F}^0_{\xi}) $$ Recall that the internal force terms have the form

\mathbf{f}_I^{\text{int}} = \int_{\Omega} \boldsymbol{\sigma}\cdot(\boldsymbol{\nabla} N_I)~\text{dV} $$ Expressed in terms of an integral over the parent element, we then have

{ \mathbf{f}_I^{\text{int}} = \int_{\square} \boldsymbol{\sigma}\cdot(\boldsymbol{\nabla} N_I)~J_{\xi}\text{d}\square } $$ where

\boldsymbol{\nabla} N_I = \frac{\partial N_I}{\partial \boldsymbol{\xi}}\cdot\boldsymbol{F}_{\xi}^{-1} ~. $$

Finite element implementation
Recall that the finite element system of equations can be written as

[\mathbf{M}][\mathbf{a}] = [\mathbf{f}^{\text{ext}}] - [\mathbf{f}^{\text{int}}] $$ where

M_{IJ} = \int_{\Omega_0} \rho_0~N_I~N_J~\text{dV}_0 ~; \mathbf{f}_I^{\text{int}} = \int_{\Omega} \boldsymbol{\sigma}\cdot(\boldsymbol{\nabla} N_I)~\text{dV} ~;\text{and} \mathbf{f}_I^{\text{ext}} = \int_{\Omega} \rho~N_I~\mathbf{b}~\text{dV} + {\int_{\partial \Omega}}_t N_I~\mathbf{t}~\text{dA} $$ To get a feel for the structure of the equation, let us consider a four-noded plane element. If the components of the velocity in the two coordinate directions are $$(u, v)$$, the acceleration vector has the form

\mathbf{a} = \begin{bmatrix}\mathbf{a}_1 \\ \mathbf{a}_2 \\ \mathbf{a}_3 \\ \mathbf{a}_4\end{bmatrix} = \begin{bmatrix}\dot{u}_1 & \dot{v}_1 \\ \dot{u}_2 & \dot{v}_2 \\ \dot{u}_3 & \dot{v}_3 \\ \dot{u}_4 & \dot{v}_4\end{bmatrix} $$ The mass matrix has the form

\mathbf{M} = \begin{bmatrix} \mathbf{M}_{11} & \mathbf{M}_{12} & \mathbf{M}_{13} & \mathbf{M}_{14} \\ \mathbf{M}_{21} & \mathbf{M}_{22} & \mathbf{M}_{23} & \mathbf{M}_{24} \\ \mathbf{M}_{31} & \mathbf{M}_{32} & \mathbf{M}_{33} & \mathbf{M}_{34} \\ \mathbf{M}_{41} & \mathbf{M}_{42} & \mathbf{M}_{43} & \mathbf{M}_{44} \end{bmatrix} $$ In expanded form

\mathbf{M} = \int_{\Omega_0} \rho_0~\begin{bmatrix} N_1~N_1 & N_1~N_2 & N_1~N_3 & N_1~N_4 \\ N_2~N_1 & N_2~N_2 & N_2~N_3 & N_2~N_4 \\ N_3~N_1 & N_3~N_2 & N_3~N_3 & N_3~N_4 \\ N_4~N_1 & N_4~N_2 & N_4~N_3 & N_4~N_4 \end{bmatrix} ~\text{dV} $$ Next, we consider the internal force term. Let the components of the internal force in the two coordinate directions be ($$f, g$$). Then,

\mathbf{f}^{\text{int}} = \begin{bmatrix} \mathbf{f}^{\text{int}}_1 \\ \mathbf{f}^{\text{int}}_2 \\ \mathbf{f}^{\text{int}}_3\\ \mathbf{f}^{\text{int}}_4 \end{bmatrix} = \begin{bmatrix} f_1 & g_1 \\ f_2 & g_2 \\ f_3 & g_3 \\ f_4 & g_4 \end{bmatrix} $$ At this stage, recall that the velocity gradient is given by

\boldsymbol{l} = \boldsymbol{\nabla} \mathbf{v} = \sum_I \mathbf{v}_I\otimes\boldsymbol{\nabla} N_I = \sum_I \mathbf{v}_I\otimes\frac{\partial N_I}{\partial \mathbf{x}} $$ In index notation,

l_{ij} = \sum_I v_{Ii}~\frac{\partial N_I}{\partial x_j} ~. $$ We define

B_{Ij} := \frac{\partial N_I}{\partial x_j} $$ Then,

l_{ij} = \sum_I v_{Ii}~B_{Ij} $$ In matrix form

\mathbf{l} = \begin{bmatrix}\mathbf{v}_1 & \mathbf{v}_2 & \mathbf{v}_3 & \mathbf{v}_4\end{bmatrix} \begin{bmatrix}\mathbf{B}_1 \\ \mathbf{B}_2 \\ \mathbf{B}_3 \\ \mathbf{B}_4 \end{bmatrix} $$ Expanded out

\begin{bmatrix} l_{11} & l_{12} \\ l_{21} & l_{22} \end{bmatrix} = \begin{bmatrix} u_1 & u_2 & u_3 & u_4 \\ v_1 & v_2 & v_3 & v_4 \end{bmatrix} \begin{bmatrix} \frac{\partial N_1}{\partial x} & \frac{\partial N_1}{\partial y} \\ \frac{\partial N_2}{\partial x} & \frac{\partial N_2}{\partial y} \\ \frac{\partial N_3}{\partial x} & \frac{\partial N_3}{\partial y} \\ \frac{\partial N_4}{\partial x} & \frac{\partial N_4}{\partial y} \end{bmatrix} $$ In more compact form, we can just write

{ [\mathbf{l}] = [\mathbf{v}]^T~[\mathbf{B}] } $$ Similarly, for the internal force term,

\mathbf{f}^{\text{int}}_I = \int_{\Omega} \boldsymbol{\sigma}\cdot\boldsymbol{\nabla} N_I~\text{dV} $$ we have

f^{\text{int}}_{Ii} = \int_{\Omega} \sigma_{ij}~\frac{\partial N_I}{\partial x_j}~\text{dV} = \int_{\Omega} \sigma_{ij}~B_{Ij}~\text{dV} $$ In matrix form,

\begin{bmatrix} \mathbf{f}^{\text{int}}_1 \\ \mathbf{f}^{\text{int}}_2 \\ \mathbf{f}^{\text{int}}_3 \\ \mathbf{f}^{\text{int}}_4 \end{bmatrix} = \int_{\Omega} \begin{bmatrix} \mathbf{B}_1 \\ \mathbf{B}_2 \\ \mathbf{B}_3 \\ \mathbf{B}_4 \end{bmatrix}~\boldsymbol{\sigma}^T $$ Expanded out,

\begin{bmatrix} f_1 & g_1 \\ f_2 & g_2 \\ f_3 & g_3 \\ f_4 & g_4 \end{bmatrix} = \int_{\Omega} \begin{bmatrix} \frac{\partial N_1}{\partial x} & \frac{\partial N_1}{\partial y} \\ \frac{\partial N_2}{\partial x} & \frac{\partial N_2}{\partial y} \\ \frac{\partial N_3}{\partial x} & \frac{\partial N_3}{\partial y} \\ \frac{\partial N_4}{\partial x} & \frac{\partial N_4}{\partial y} \end{bmatrix} \begin{bmatrix} \sigma_{11} & \sigma_{21} \\ \sigma_{12} & \sigma_{22} \end{bmatrix}~\text{dV} $$ In compact form, we have

{ [\mathbf{f}^{\text{int}}] = \int_{\Omega} [\mathbf{B}][\boldsymbol{\sigma}]^T~\text{dV} } $$ We can express the external force term in a similar manner. Notice that we are not taking adavantage of the symmetry of the stress tensor in the above expressions.

A widely used alternative way of expressing the finite element system of equations is the Voigt notation. This notation can be found in discussions of introductory finite element analysis.

Algorithm for computing internal forces
The major complications and computational effort in the finite element implementation are encountered during the computation of internal forces.

The basic procedure for computing the internal force at the nodes of an element is given below.

 * 1) Set $$[\mathbf{f}^{\text{int}}] = [\mathbf{0}]$$.
 * 2) For all quadrature points in the parent element ($$\boldsymbol{\xi}_Q$$)
 * 3) Compute the gradient of the shape functions ($$[\mathbf{B}_I]$$) for all nodes $$I$$.
 * 4) Compute the velocity gradient $$[\mathbf{l}] = [\mathbf{v}_I][\mathbf{B}]$$.
 * 5) Compute the rate of deformation tensor.
 * 6) Compute the deformation gradient/ the Lagrangian Green tensor.
 * 7) Compute the Cauchy stress or the 2nd P-K stress using the constitutive equation.
 * 8) Update the nodal internal force ($$[\mathbf{f}_I^{\text{int}}]$$) using $$\mathbf{f}_I^{\text{int}} = \mathbf{f}_I^{\text{int}} + [\mathbf{B}_I][\boldsymbol{\sigma}]^T~J_\xi~W_Q$$ where $$W_Q$$ are the weights for Gaussian integration.

The mass matrix and integration in time will be discussed later.


text: File:ElementMaps.png

title: File:ElementMaps.png


text:
Talk:Business Law

Inquiry: I would be pleased to contribute posts to the educational video and materials at http://clientelevision.com/business_law.html. Please advise whether you believe this to be within the scope of the site.

title: Talk:Business Law


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Talk:Law of Contracts

Inquiry: I would be pleased to contribute posts to the educational video and materials at http://clientelevision.com/contracts.html. Please advise whether you believe this to be within the scope of the site.

Permission for usage
Hi, the content seems copied from this blog where there is a copyright disclaimer. Please clarify if the permission is given to use material here at Wikiversity under CC by-sa 3.0 + GFDL licence. Best: send this to the OTRS team, see OTRS, Erkan Yilmaz uses the Chat (try) 08:10, 21 March 2010 (UTC)

Permission is given
I run UK Law students, and therefore give myself permission, lol.

Ruwayda Mustafah 12:23, 21 March 2010 (UTC)

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User:Mheiden~enwikiversity

Hello Wiki-reader:

My Name is Mike Heiden and I first became a user of Wikiversity at 6:38 pm PST on 27-SEP-2007.

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After learning about the Web 2.0 and 3.0 movement of the technical community and how open source code, knowledge, and collaboration is shaping our world, I decided to join and benefit. I thought along the lines of you can either be clued in and benefit from the good people in the world who want to foster learning and collaboration to advance society and be an auditing source for the group who have historically controlled knowlege.... or you can remain blissfully ignorant on the sidelines.

My first goal is foster a greater confidence and appreciation of Mathematics. I believe we need to face all our fears and get over our regrets. The way I put the bare minimum into my Math courses in High School and College has really generated feelings of regret as I know how important a skill it is. As I'm also contemplating graduate school and other forms of advanced education, this journey into Wikiversity is something I see as carying the potential of assisting me in entrance exam preparation.

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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 Benau. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Benau~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.

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