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Continuum mechanics/Thermoelasticity

Thermoelastic materials
A set of constitutive equations is required to close to system of balance laws. These are relations between appropriate kinematic quantities and stress measures that can be assigned a physical meaning.

Deformation gradient as the strain measure
In thermoelasticity we assume that the fundamental kinematic quantity is the deformation gradient ($$\boldsymbol{F}$$) which is given by

\boldsymbol{F} = \frac{\partial \mathbf{x}}{\partial \mathbf{X}} = \boldsymbol{\nabla}_{\circ} \mathbf{x} ~; \det\boldsymbol{F} > 0 ~. $$ A thermoelastic material is one in which the internal energy ($$e$$) is a function only of $$\boldsymbol{F}$$ and the specific entropy ($$\eta$$), that is

e = \bar{e}(\boldsymbol{F}, \eta) ~. $$ For a thermoelastic material, we can show that the entropy inequality can be written as At this stage, we make the following constitutive assumptions: 1) Like the internal energy, we assume that $$\boldsymbol{\sigma}$$ and $$T$$ are also functions only of $$\boldsymbol{F}$$ and $$\eta$$, i.e.,

\boldsymbol{\sigma} = \boldsymbol{\sigma}(\boldsymbol{F}, \eta) ~; T = T(\boldsymbol{F}, \eta) ~. $$

2) The heat flux $$\mathbf{q}$$ satisfies the thermal conductivity inequality and    if $$\mathbf{q}$$ is independent of $$\dot{\eta}$$ and $$\dot{\boldsymbol{F}}$$, we have

\mathbf{q}\cdot\boldsymbol{\nabla} T \le 0 \qquad\implies\qquad -(\boldsymbol{\kappa}\cdot\boldsymbol{\nabla} T)\cdot\boldsymbol{\nabla} T \le 0 \qquad\implies\qquad \boldsymbol{\kappa}\ge\mathbf{0} $$ i.e., the thermal conductivity $$\boldsymbol{\kappa}$$ is positive semidefinite. Therefore, the entropy inequality may be written as

\rho~\left(\frac{\partial \bar{e}}{\partial \eta} - T\right)~\dot{\eta} + \left(\rho~\frac{\partial \bar{e}}{\partial \boldsymbol{F}} - \boldsymbol{\sigma}\cdot\boldsymbol{F}^{-T}\right):\dot{\boldsymbol{F}} \le 0 ~. $$ Since $$\dot{\eta}$$ and $$\dot{\boldsymbol{F}}$$ are arbitrary, the entropy inequality will be satisfied if and only if

\frac{\partial \bar{e}}{\partial \eta} - T = 0 \implies T = \frac{\partial \bar{e}}{\partial \eta} \qquad\text{and}\qquad \rho~\frac{\partial \bar{e}}{\partial \boldsymbol{F}} - \boldsymbol{\sigma}\cdot\boldsymbol{F}^{-T} = \mathbf{0} \implies \boldsymbol{\sigma} = \rho~\frac{\partial \bar{e}}{\partial \boldsymbol{F}}\cdot\boldsymbol{F}^T ~. $$ Therefore,

Given the above relations, the energy equation may expressed in terms of the specific entropy as

Effect of a rigid body rotation of the internal energy
If a thermoelastic body is subjected to a rigid body rotation $$\boldsymbol{Q}$$, then its internal energy should not change. After a rotation, the new deformation gradient ($$\hat{\boldsymbol{F}}$$) is given by

\hat{\boldsymbol{F}} = \boldsymbol{Q}\cdot\boldsymbol{F} ~. $$   Since the internal energy does not change, we must have

e = \bar{e}(\hat{\boldsymbol{F}}, \eta) = \bar{e}(\boldsymbol{F}, \eta) ~. $$   Now, from the polar decomposition theorem,  $$\boldsymbol{F} = \boldsymbol{R}\cdot\boldsymbol{U}$$ where $$\boldsymbol{R}$$ is the orthogonal rotation tensor (i.e., $$\boldsymbol{R}\cdot\boldsymbol{R}^T = \boldsymbol{R}^T\cdot\boldsymbol{R} = \boldsymbol{\mathit{1}}$$) and $$\boldsymbol{U}$$ is the symmetric right stretch tensor. Therefore,

\bar{e}(\boldsymbol{Q}\cdot\boldsymbol{R}\cdot\boldsymbol{U}, \eta) = \bar{e}(\boldsymbol{F}, \eta) ~. $$   We can choose any rotation $$\boldsymbol{Q}$$. In particular, if we choose    $$\boldsymbol{Q} = \boldsymbol{R}^T$$, we have

\bar{e}(\boldsymbol{R}^T\cdot\boldsymbol{R}\cdot\boldsymbol{U}, \eta) =         \bar{e}(\boldsymbol{\mathit{1}}\cdot\boldsymbol{U}, \eta) = \tilde{e}(\boldsymbol{U}, \eta)~. $$   Therefore,

\bar{e}(\boldsymbol{U}, \eta) = \bar{e}(\boldsymbol{F}, \eta) ~. $$   This means that the internal energy depends only on the stretch  $$\boldsymbol{U}$$ and not on the orientation of the body.

Other strain and stress measures
The internal energy depends on $$\boldsymbol{F}$$ only through the stretch $$\boldsymbol{U}$$. A strain measure that reflects this fact and also vanishes in the reference configuration is the Green strain Recall that the Cauchy stress is given by

\boldsymbol{\sigma} = \rho~\frac{\partial \bar{e}}{\partial \boldsymbol{F}}\cdot\boldsymbol{F}^T ~. $$ We can show that the Cauchy stress can be expressed in terms of the Green strain as Also, recall that the first Piola-Kirchhoff stress tensor is defined as

\boldsymbol{P} = J~(\boldsymbol{\sigma}\cdot\boldsymbol{F}^{-T})~\text{where}~ J = \det\boldsymbol{F} $$ Alternatively, we may use the nominal stress tensor

\boldsymbol{N} = J~(\boldsymbol{F}^{-1}\cdot\boldsymbol{\sigma}) $$ From the conservation of mass, we have $$\rho_0 = \rho~\det\boldsymbol{F}$$. Hence, The first P-K stress and the nominal stress are unsymmetric. Also recall that we can define a symmetric stress measure with respect to the reference configuration called the second Piola-Kirchhoff stress tensor ($$\boldsymbol{S}$$): In terms of the derivatives of the internal energy, we have

\boldsymbol{S} = \cfrac{\rho_0}{\rho}~\boldsymbol{F}^{-1}\cdot \left(\rho~\boldsymbol{F}\cdot\frac{\partial \bar{e}}{\partial \boldsymbol{E}}\cdot\boldsymbol{F}^T\right)\cdot\boldsymbol{F}^{-T} = \rho_0~\frac{\partial \bar{e}}{\partial \boldsymbol{E}} $$ Therefore,

\boldsymbol{P} = \rho_0~\boldsymbol{F}\cdot\frac{\partial \bar{e}}{\partial \boldsymbol{E}} ~. $$ and

\boldsymbol{N} = \rho_0~\frac{\partial \bar{e}}{\partial \boldsymbol{E}}\cdot\boldsymbol{F}^T ~. $$ That is,

Stress Power
The stress power per unit volume is given by $$\boldsymbol{\sigma}:\boldsymbol{\nabla}\mathbf{v}$$. In terms of the stress measures in the reference configuration, we have

\boldsymbol{\sigma}:\boldsymbol{\nabla}\mathbf{v} = \left(\rho~\boldsymbol{F}\cdot\frac{\partial \bar{e}}{\partial \boldsymbol{E}}\cdot\boldsymbol{F}^T\right): (\dot{\boldsymbol{F}}\cdot\boldsymbol{F}^{-1}) ~. $$ Using the identity $$\boldsymbol{A}:(\boldsymbol{B}\cdot\boldsymbol{C}) = (\boldsymbol{A}\cdot\boldsymbol{C}^T):\boldsymbol{B}$$, we have

\boldsymbol{\sigma}:\boldsymbol{\nabla}\mathbf{v} = \left[ \left(\rho~\boldsymbol{F}\cdot\frac{\partial \bar{e}}{\partial \boldsymbol{E}}\cdot\boldsymbol{F}^T\right)\cdot\boldsymbol{F}^{-T} \right] :\dot{\boldsymbol{F}} = \rho~\left(\boldsymbol{F}\cdot\frac{\partial \bar{e}}{\partial \boldsymbol{E}}\right):\dot{\boldsymbol{F}} = \cfrac{\rho}{\rho_0}~\boldsymbol{P}:\dot{\boldsymbol{F}} = \cfrac{\rho}{\rho_0}~\boldsymbol{N}^T:\dot{\boldsymbol{F}}~. $$ We can alternatively express the stress power in terms of $$\boldsymbol{S}$$ and $$\dot{\boldsymbol{E}}$$. Taking the material time derivative of $$\boldsymbol{E}$$ we have

\dot{\boldsymbol{E}} = \frac{1}{2}(\dot{\boldsymbol{F}^T}\cdot\boldsymbol{F} + \boldsymbol{F}^T\cdot\dot{\boldsymbol{F}}) ~. $$ Therefore,

\boldsymbol{S}:\dot{\boldsymbol{E}} = \frac{1}{2}[\boldsymbol{S}:(\dot{\boldsymbol{F}^T}\cdot\boldsymbol{F}) + \boldsymbol{S}:(\boldsymbol{F}^T\cdot\dot{\boldsymbol{F}})]~. $$ Using the identities $$\boldsymbol{A}:(\boldsymbol{B}\cdot\boldsymbol{C}) = (\boldsymbol{A}\cdot\boldsymbol{C}^T):\boldsymbol{B} = (\boldsymbol{B}^T\cdot\boldsymbol{A}):\boldsymbol{C}$$ and $$\boldsymbol{A}:\boldsymbol{B} = \boldsymbol{A}^T:\boldsymbol{B}^T$$ and using the symmetry of $$\boldsymbol{S}$$, we have

\boldsymbol{S}:\dot{\boldsymbol{E}} = \frac{1}{2}[(\boldsymbol{S}\cdot\boldsymbol{F}^T):\dot{\boldsymbol{F}}^T + (\boldsymbol{F}\cdot\boldsymbol{S}):\dot{\boldsymbol{F}}] = \frac{1}{2}[(\boldsymbol{F}\cdot\boldsymbol{S}^T):\dot{\boldsymbol{F}} + (\boldsymbol{F}\cdot\boldsymbol{S}):\dot{\boldsymbol{F}}] = (\boldsymbol{F}\cdot\boldsymbol{S}):\dot{\boldsymbol{F}} ~. $$ Now, $$\boldsymbol{S} = \boldsymbol{F}^{-1}\cdot\boldsymbol{P}$$. Therefore, $$\boldsymbol{S}:\dot{\boldsymbol{E}} = \boldsymbol{N}^T:\dot{\boldsymbol{F}}$$. Hence, the stress power can be expressed as

If we split the velocity gradient into symmetric and skew parts using

\boldsymbol{\nabla}\mathbf{v} = \boldsymbol{l} = \mathbf{d} + \boldsymbol{w} $$ where $$\mathbf{d}$$ is the rate of deformation tensor and $$\boldsymbol{w}$$ is the spin tensor, we have

\boldsymbol{\sigma}:\boldsymbol{\nabla}\mathbf{v} = \boldsymbol{\sigma}:\mathbf{d} + \boldsymbol{\sigma}:\boldsymbol{w} = \text{tr}~(\boldsymbol{\sigma}^T\cdot\mathbf{d}) + \text{tr}~(\boldsymbol{\sigma}^T\cdot\boldsymbol{w}) = \text{tr}~(\boldsymbol{\sigma}\cdot\mathbf{d}) + \text{tr}~(\boldsymbol{\sigma}\cdot\boldsymbol{w}) ~. $$ Since $$\boldsymbol{\sigma}$$ is symmetric and $$\boldsymbol{w}$$ is skew, we have $$\text{tr}~(\boldsymbol{\sigma}\cdot\boldsymbol{w}) = 0$$. Therefore, $$\boldsymbol{\sigma}:\boldsymbol{\nabla}\mathbf{v} = \text{tr}~(\boldsymbol{\sigma}\cdot\mathbf{d})$$. Hence, we may also express the stress power as

Helmholtz and Gibbs free energy
Recall that

\boldsymbol{S} = \rho_0~\frac{\partial \bar{e}}{\partial \boldsymbol{E}} ~. $$ Therefore,

\frac{\partial \bar{e}}{\partial \boldsymbol{E}} = \cfrac{1}{\rho_0}~\boldsymbol{S} ~. $$ Also recall that

\frac{\partial \bar{e}}{\partial \eta} = T ~. $$ Now, the internal energy $$e = \bar{e}(\boldsymbol{E}, \eta)$$ is a function only of the Green strain and the specific entropy. Let us assume, that the above relations can be uniquely inverted locally at a material point so that we have

\boldsymbol{E} = \tilde{\boldsymbol{E}}(\boldsymbol{S}, T) \qquad\text{and}\qquad \eta = \tilde{\eta}(\boldsymbol{S}, T) ~. $$ Then the specific internal energy, the specific entropy, and the stress can also be expressed as functions of $$\boldsymbol{S}$$ and $$T$$, or $$\boldsymbol{E}$$ and $$T$$, i.e.,

e = \bar{e}(\boldsymbol{E}, \eta) = \tilde{e}(\boldsymbol{S}, T) = \hat{e}(\boldsymbol{E}, T)~; \qquad \eta = \tilde{\eta}(\boldsymbol{S},T) = \hat{\eta}(\boldsymbol{E},T) ~; \qquad\text{and}\qquad \boldsymbol{S} = \hat{\boldsymbol{S}}(\boldsymbol{E},T) $$ We can show that

\cfrac{d}{dt}(e - T~\eta) = - \dot{T}~\eta + \cfrac{1}{\rho_0}~\boldsymbol{S}:\dot{\boldsymbol{E}} \qquad\text{or}\qquad \cfrac{d\psi}{dt} = - \dot{T}~\eta + \cfrac{1}{\rho_0}~\boldsymbol{S}:\dot{\boldsymbol{E}} ~. $$ and

\cfrac{d}{dt}(e - T~\eta - \cfrac{1}{\rho_0}~\boldsymbol{S}:\boldsymbol{E}) = - \dot{T}~\eta - \cfrac{1}{\rho_0}~\dot{\boldsymbol{S}}:\boldsymbol{E} \qquad\text{or}\qquad \cfrac{dg}{dt} = \dot{T}~\eta + \cfrac{1}{\rho_0}~\dot{\boldsymbol{S}}:\boldsymbol{E} ~. $$ We define the  Helmholtz free energy as

We define the  Gibbs free energy as

The functions $$\hat{\psi}(\boldsymbol{E},T)$$ and $$\tilde{g}(\boldsymbol{S},T)$$ are unique. Using these definitions it can be shown that

\frac{\partial \hat{\psi}}{\partial \boldsymbol{E}} = \cfrac{1}{\rho_0}~\hat{\boldsymbol{S}}(\boldsymbol{E},T) ~; \frac{\partial \hat{\psi}}{\partial T} = -\hat{\eta}(\boldsymbol{E},T) ~; \frac{\partial \tilde{g}}{\partial \boldsymbol{S}} = \cfrac{1}{\rho_0}~\tilde{\boldsymbol{E}}(\boldsymbol{S}, T) ~; \frac{\partial \tilde{g}}{\partial T} = \tilde{\eta}(\boldsymbol{S}, T)   $$ and

\frac{\partial \hat{\boldsymbol{S}}}{\partial T} = - \rho_0~\frac{\partial \hat{\eta}}{\partial \boldsymbol{E}} \qquad\text{and}\qquad \frac{\partial \tilde{\boldsymbol{E}}}{\partial T} = \rho_0~\frac{\partial \tilde{\eta}}{\partial \boldsymbol{S}} ~. $$

Specific Heats
The  specific heat at constant strain (or constant volume) is defined as

The  specific heat at constant stress (or constant pressure) is defined as

We can show that

C_v = T~\frac{\partial \hat{\eta}}{\partial T} = -T~\frac{\partial^2 \hat{\psi}}{\partial T^2} $$ and

C_p = T~\frac{\partial \tilde{\eta}}{\partial T} + \cfrac{1}{\rho_0}~\boldsymbol{S}:\frac{\partial \tilde{\boldsymbol{E}}}{\partial T} = T~\frac{\partial^2 \tilde{g}}{\partial T^2} + \boldsymbol{S}:\frac{\partial^2 \tilde{g}}{\partial \boldsymbol{S}\partial T}~. $$ Also the equation for the balance of energy can be expressed in terms of the specific heats as

where

\boldsymbol{\beta}_S := \frac{\partial \hat{\boldsymbol{S}}}{\partial T}    \qquad \text{and} \qquad \boldsymbol{\alpha}_E := \frac{\partial \tilde{\boldsymbol{E}}}{\partial T} ~. $$ The quantity $$\boldsymbol{\beta}_S$$ is called the  coefficient of thermal stress and the quantity $$\boldsymbol{\alpha}_E$$ is called the coefficient of thermal expansion.

The difference between $$C_p$$ and $$C_v$$ can be expressed as

C_p - C_v = \cfrac{1}{\rho_0}\left(\boldsymbol{S}-T~\frac{\partial \hat{\boldsymbol{S}}}{\partial T}\right): \frac{\partial \tilde{\boldsymbol{E}}}{\partial T} ~. $$ However, it is more common to express the above relation in terms of the elastic modulus tensor as

where the  fourth-order tensor of elastic moduli is defined as

\boldsymbol{\mathsf{C}} := \frac{\partial \hat{\boldsymbol{S}}}{\partial \tilde{\boldsymbol{E}}} = \rho_0~\frac{\partial^2 \hat{\psi}}{\partial \tilde{\boldsymbol{E}}\partial\tilde{\boldsymbol{E}}} ~. $$ For isotropic materials with a constant coefficient of thermal expansion that follow the St. Venant-Kirchhoff material model, we can show that

C_p - C_v = \cfrac{1}{\rho_0}\left[\alpha~\text{tr}{\boldsymbol{S}} + 9~\alpha^2~K~T\right]~. $$

title: Continuum mechanics/Thermoelasticity


text:
User:Bobola Akinola

I love PC Gaming. Half-life, CoD, max payne. I Wanna learn how to make games so that i can make games that satisfy people..............

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

title: User:Bobola Akinola


text:
User talk:Gadaba

Hello Gadaba, 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.

If you're already excited about editing, our sandbox is the perfect place for all test edits. Also, don't forget to experiment with the links to your left. Be bold, and see you around Wikiversity!

P.S. Do you want live feedback ? You can find us in #wikiversity-en (see Chat) Erkan Yilmaz ( evaluate me!, discussion ) 01:56, 11 September 2007 (UTC)

title: User talk:Gadaba


text:
Getting stats out of Wikiversity XML dumps

Someone was wondering how many users edit talk pages and not main namespace articles. So I wrote a couple scripts. Nothing serious but here they are in case someone finds this sort of thing fun. Linux, no windows, sorry... It's not efficient or nice either.

You go get the dump first, at http://download.wikimedia.org/backup-index.html and look for the first (most recent entry with enwikiversity in it.

When you get to the subpage, you want the full archive, bz2 or 7z depending on what utilities you have lying around. These are the ones that say "All pages with complete edit history". Uncompress it and you're ready to get crunching.

First I wanted to get the entire list of users out.

grep ' users.txt cat users.txt | uniq > users-1.txt cat users-1.txt | sort | uniq > users-uniq.txt cat users-uniq.txt | sed -e 's/^\(\s\)* //g; s/<\/username>//g;' > userlist.txt
 * 1) did this cause the file is otherwise slow and big in the sort)

Next I wanted information on each revision in the xml dump: username, title, namespace.

cat enwikiversity-20070903-pages-meta-history.xml | ./versity-xml.pl    > out

Here's the script:

 * 1) !/usr/bin/perl

binmode(STDOUT, ":utf8"); binmode(STDIN, ":utf8");

use encoding(UTF8);
 * 1) write out user, namespace, namespace, for each revision

 * 1) Wikiversity:Help desk
 * 2) Wikiversity talk:Help desk
 * 3) User_talk:

while () { $line=$_; if ($line =~ / /) { $user=""; $ns=""; $title=""; }   elsif ($line =~ / /) { if ($line =~ / ([^:]+):(.+)<\/title>/) { $ns=$1; $title=$2; }          elsif ($line =~ / (.*)<\/title>/) { print "ok here\n"; $ns="main"; $title=$1; }   }    elsif ($line =~ / /) { if ($line =~ / (.*)<\/username>/) { $user=$1; }   }    elsif ($line =~ / /) { $user=""; }   elsif ($line =~ /<\/revision>/) { $out = "$user\t$ns\t$title\n"; if ($out !~ /^\t\t$/) { print "$user\t$ns\t$title\n"; }   }    elsif ($line =~ /<\/page>/) { } }
 * 1)       $out = "$user\t$ns\t$title\n";
 * 2)       if ($out !~ /^\t\t$/) {
 * 3)           print "$user\t$ns\t$title\n";
 * 4)       }

Hey, didn't I say it wouldn't be pretty?

What you need to know to make the script make sense is the structure of the XML dump. If you look at one it has this sort of stuff in it: User:Cormaggio 2 4 2006-08-15T08:19:38Z Cormaggio 8 greetings :-)      Hello all, it's great to finally have Wikiversity up and running! I'm so looking forward to working on this project - but am pretty busy over the next month with my dissertation (about Wikiversity ;-)). I'll be happy to answer any questions about the project - I've been pretty active in getting this project started. Looking forward to worki ng with you! Cormaggio 08:19, 15 August 2006 (UTC) ...

IP address contributors are tagged with instead of.

You can see that the namespace is separated from the title of the page by a colon ':' and if there is no colon then the article is in the main namespace.

I only want one entry per user per page for this next bit...

cat out | uniq > out-1.txt cat out-1.txt | sort | uniq > out-uniq.txt
 * 1) did this cause the file is otherwise slow and big in the sort)

Now collect all the users that edited either the Help desk or User talk pages grep Wikiversity out-uniq.txt | grep Help| grep desk > these.txt grep 'Wikiversity talk' out-uniq.txt | grep Help | grep desk >> these.txt grep User_talk out-uniq.txt >> these.txt more these.txt | awk -F'\t' '{ print $1} ' | sort | uniq > possible

Get some numbers... ./check-these.sh

Here's the script for that: i='some user name here'; echo "$i" >> check2; echo "non-user_talk, helpdesk edits" >> check2;grep "$i" out | grep -v 'Help desk' | grep -v 'User talk' | grep -v User | wc -l >> check2; echo "helpdesk edits" >> check2; grep "$i" out | grep 'Help desk' | wc -l >> check2;echo "user talk edits" >> check2; grep "$i" out | grep 'User talk' | wc -l >> check2 i='some other user name here'; echo "$i" >> check2; echo "non-user_talk, helpdesk edits" >> check2;grep "$i" out | grep -v 'Help desk' | grep -v 'User talk' | grep -v User | wc -l >> check2; echo "helpdesk edits" >> check2; grep "$i" out | grep 'Help desk' | wc -l >> check2;echo "user talk edits" >> check2; grep "$i" out | grep 'User talk' | wc -l >> check2
 * 1) !/bin/bash

and so on, where the names came out of the "possible" list.

The output such as it is looks like

first_user_name non-user_talk, helpdesk edits 0 helpdesk edits 1 user talk edits 0 second_user_name non-user_talk, helpdesk edits 0 helpdesk edits 2 user talk edits 0

and that's it. There weren't so many folks who had edited the help desk or user talk pages in the past year, and we didn't really care about looking at earlier data, so once we had this file we could inspect it by hand to see any useful trends.


text:
User:CQ/2007/W39

Test page for journaling system

last week | this week | next week

title: User:CQ/2007/W39


text:
User:CQ/2007/W40

Test page for journaling system

last week | this week | next week

title: User:CQ/2007/W40


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User:CQ/2007/W37/2

11 September 2007 - So that was six years ago, hmmm

title: User:CQ/2007/W37/2


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BCP/Eupatorium purpureum/Logs

2007 Logs

 * --SB_Johnny | PA! 11:04, 14 July 2007 (UTC)
 * --Jomegat 23:55, 17 August 2007 (UTC)
 * --SB_Johnny | talk 16:27, 19 August 2006 (UTC)
 * --SB_Johnny | talk 12:23, 28 August 2006 (UTC)
 * --Jomegat 13:44, 6 September 2007 (UTC)
 * --Jomegat 16:51, 10 September 2007 (UTC)
 * --SB_Johnny | talk 06:44, 11 September 2007 (UTC)

2008 Logs

 * Jomegat 11:26, 17 July 2008 (UTC) - from photo
 * Jomegat 12:49, 21 July 2008 (UTC)
 * Jomegat 17:01, 26 July 2008 (UTC)
 * Jomegat 01:40, 31 July 2008 (UTC)
 * Jomegat 17:39, 2 August 2008 (UTC)
 * Jomegat 20:37, 9 August 2008 (UTC)
 * Jomegat 00:06, 30 August 2008 (UTC)

2009 Logs

 * Jomegat 03:47, 2 August 2009 (UTC)

Recent Logs

 * Jomegat 00:08, 26 July 2010 (UTC)

title: BCP/Eupatorium purpureum/Logs


text: Category:BCP/Family/Balsaminaceae

title: Category:BCP/Family/Balsaminaceae


text: Category:BCP/Family/Onagraceae

title: Category:BCP/Family/Onagraceae


text: Category:BCP/Family/Fabaceae

title: Category:BCP/Family/Fabaceae


text:
BCP/Trifolium arvense/Logs

2007 Logs

 * --SB_Johnny | talk 09:10, 16 June 2007 (UTC) (photographic log)
 * --SB_Johnny | talk 10:32, 5 July 2007 (UTC)
 * --Jomegat 03:24, 1 September 2007 (UTC)
 * --SB_Johnny | talk 12:52, 10 October 2007 (UTC)
 * --SB_Johnny | talk 13:10, 24 October 2007 (UTC)

2008 Logs

 * --SB_Johnny | talk 13:23, 21 June 2008 (UTC)
 * --Jomegat 17:18, 24 June 2008 (UTC)
 * --Jomegat 22:49, 1 July 2008 (UTC)
 * --Jomegat 02:57, 8 July 2008 (UTC)
 * --Jomegat 18:38, 12 July 2008 (UTC)
 * --SB_Johnny | talk 10:08, 20 July 2008 (UTC)
 * Jomegat 18:02, 9 August 2008 (UTC)
 * Jomegat 01:13, 17 August 2008 (UTC)
 * Jomegat 03:11, 21 August 2008 (UTC)
 * Jomegat 20:06, 20 September 2008 (UTC)
 * Jomegat 21:03, 29 September 2008 (UTC)
 * Jomegat 02:24, 13 October 2008 (UTC)
 * Jomegat 04:32, 19 October 2008 (UTC)

2009 Logs

 * Jomegat 04:04, 5 June 2009 (UTC)
 * Jomegat 00:13, 15 July 2009 (UTC)
 * Jomegat 23:39, 18 July 2009 (UTC)
 * Jomegat 04:01, 2 August 2009 (UTC)

Recent Logs

 * Jomegat 22:58, 1 June 2010 (UTC)

title: BCP/Trifolium arvense/Logs


text:
User talk:MartinPoulter

Hello MartinPoulter, 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.

If you're already excited about editing, our sandbox is the perfect place for all test edits. Also, don't forget to experiment with the links to your left. Be bold, and see you around Wikiversity!

P.S. Do you want live feedback ? You can find us in #wikiversity-en (see Chat) Erkan Yilmaz ( evaluate me!, discussion ) 10:56, 11 September 2007 (UTC)

ASGELE info box
Hi Martin, I see your point about the info box and have amended it: Template:Infobox_ASGELE, do you thinks this deals with the point you raised? I did get in contact with Todd Kaplan some time ago, but he was not keen to re-engage. I shall e-mail him again about adding the relevant logos.Leutha (discuss • contribs) 13:01, 3 August 2013 (UTC)

title: User talk:MartinPoulter


text: File:Unknown plant like bedstraw.jpg

title: File:Unknown plant like bedstraw.jpg


text:
User talk:Sandrasatheesh

Hello! I am sandra. Now studying 5th std. Today my team for a dance programme bagged ist prize! Sahodaya school kalotsav conducted at Thamarasseri. ,How r u ?
 * Namasté, I am fine :-)
 * I am happy for you about the prize.
 * Below you will get some general info - if you have more questions, please ask, don't be shy.

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.

If you're already excited about editing, our sandbox is the perfect place for all test edits. Also, don't forget to experiment with the links to your left. Be bold, and see you around Wikiversity!

P.S. Do you want live feedback ? You can find us in #wikiversity-en (see Chat) Erkan Yilmaz ( evaluate me!, discussion ) 13:31, 11 September 2007 (UTC)

title: User talk:Sandrasatheesh


text:
User:MartinPoulter

My WikiPedia Profile

My Home Page

Bias and Belief blog

Bias and Belief main site

title: User:MartinPoulter


text:
User:Tantum Erg0

Tantum Erg0 is the user Name of Tim Mason. While further information on this user can be found at his [home page], several of his online profiles describe him in the following manner:

I'm a 28 year old EMT deferring my admission to PA school for a year -- to explore creative outlets -- who spends as much time in an ambulance as I do in a class room. I am a fairly clean cut kinda guy, though not always clean shaven. I'm the kind of guy who can either tell you about the blood drive I'm working on or tell you about my tattoos. I feel as comfortable in a cathedral as I do in a bar, and by that I mean very. I've been told that I dangle modifiers. Family is important to me and though mine is far from perfect, it's one I care about deeply. I also care about politics, not that I care for politics, but I care about it. I love spending time at the Georgia Aquarium. If you need to find me, and I am not scheduled to be anywhere, chances are that I am watching the whales free dive, or telling tourists about giant groupers and whale sharks. I also really like to cook. I've been known to churn out dozens of cupcakes in a night and abandon them at the nurses station in the ER the next morning. More than one nurse blames me for her thighs.

When I'm not engaged in any of the above activities, I'm learning to play guitar, growing my own peppers for chilli, reading any number of books, debating Thomism or hitting Adoration. I have a couple of other hobbies as well, writing being chief among them. I've been published in a few small magazines, and have a novel that I have been working on and very nearly sold twice. I have a few ideas for interesting books. Interesting to me, mostly because they give me an excuse to travel far and wide, which brings me to my other hobby; travelling.

The last few years have been great for my domestic travelling, hitting all of the eastern states in some capacity (I drove through Delaware, but I am told that that is all anybody ever does)and making it as far west as Texas several times. I'm hoping for more international travel over the next few years.

If you wanted to pin me down in a sentence, I would tell you that I am a Tall Catholic Libertarian EMT who really wants to do the right thing. Then I would delete all of that because it sounds like I just fell out of an episode of "Timmy and Lassie" (Yeah, I said it). I'm the kind of guy who has dreams, goals and ideals, and who chases after all of them. Sometimes it's hard to discern my path from the outside looking in, but I see it clearly. You just have to know what my motivation is to know how it fits together.

title: User:Tantum Erg0


text:
User talk:Tantum Erg0

Hello Tantum Erg0, 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;
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If you're already excited about editing, our sandbox is the perfect place for all test edits. Also, don't forget to experiment with the links to your left. Be bold, and see you around Wikiversity!

P.S. Do you want live feedback ? You can find us in #wikiversity-en (see Chat) Erkan Yilmaz ( evaluate me!, discussion ) 15:39, 11 September 2007 (UTC)

title: User talk:Tantum Erg0


text:
BCP/Mollugo verticillata

Mollugo verticillata

title: BCP/Mollugo verticillata


text:
BCP/Mollugo verticillata/Logs

2007 Logs

 * --Jomegat 16:40, 11 September 2007 (UTC)
 * --Jomegat 17:21, 25 September 2007 (UTC)
 * --Jomegat 17:05, 3 October 2007 (UTC)

2008 Logs

 * (no archived logs yet)

Recent Logs

 * Jomegat 30 June, 2008
 * Jomegat 22:38, 1 July 2008 (UTC)
 * Jomegat 02:53, 15 July 2008 (UTC)
 * Jomegat 17:02, 28 July 2008 (UTC)
 * Jomegat 00:54, 2 August 2008 (UTC)
 * --SB_Johnny talk 11:23, 10 August 2008 (UTC)
 * Jomegat 23:29, 4 September 2008 (UTC)
 * --SB_Johnny talk 09:12, 5 September 2008 (UTC)

title: BCP/Mollugo verticillata/Logs


text:
Talk:Photoproject

Scope
How can we further define the purpose/scope of this learning project?Elatanatari 20:53, 12 July 2007 (UTC)
 * I think it might be useful to outline exactly why someone would add a photo here. I've added a "gallery" section which has a little more detail on this - feel free to refine/replace, etc. I'll try to find a photo of mine somewhere that might generate a discussion. Cormaggio talk 21:03, 12 July 2007 (UTC)
 * Constructive criticism on technique and composition?Elatanatari 00:42, 13 July 2007 (UTC)
 * Yes, that would be useful - and I think it would also be good to encourage people to ask how/why a photograph didn't turn out the way they wanted - an all-too-common occurrence! How else might we invite participation in this project? Cormaggio talk 16:26, 13 July 2007 (UTC)
 * I have that problem too. I'm not sure. We could have a brainstorming meeting on the IRC.69.216.108.34 01:22, 25 July 2007 (UTC)
 * If you have a photograph that disappointed you, please upload it here (or on Commons), and we can discuss it. Or, if you have an issue to raise - please add it in the "issues" section below.. Cormaggio talk 22:49, 25 July 2007 (UTC)

Peter Blaise says: May I suggest that we ask each photographer what they want in terms of feedback? If someone just wants to know where to market their photo, and instead we tell them how to change their composition to suite our own preferences, then we're not being much help, are we? And remember, all we see are little tiny JPGs, and each of us has different display screen size, resolution, gamma, contrast, brightness, colors, gamut, ambient lighting (and more?) upon which to base our judgments! peterblaise 18:47, 25 October 2007 (UTC)

title: Talk:Photoproject


text: Template:Boxed equation

title: Template:Boxed equation


text: Category:Mechanics

title: Category:Mechanics


text:
Continuum mechanics/Leibniz formula

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The Leibniz rule
The integral

F(t) = \int_{a(t)}^{b(t)} f(x, t)~\text{dx} $$ is a function of the parameter $$t$$. Show that the derivative of $$F$$   is given by

\cfrac{dF}{dt} = \cfrac{d}{dt}\left( \int_{a(t)}^{b(t)} f(x, t)~\text{dx}          \right) =  \int_{a(t)}^{b(t)} \frac{\partial f(x, t)}{\partial t}~\text{dx} + f[b(t),t]~\frac{\partial b(t)}{\partial t} - f[a(t),t]~\frac{\partial a(t)}{\partial t}~. $$ This relation is also known as the  Leibniz rule.
 * }

Proof:

We have,

\cfrac{dF}{dt} = \lim_{\Delta t\rightarrow 0} \cfrac{F(t + \Delta t) - F(t)}{\Delta t} ~. $$ Now,

\begin{align} \cfrac{F(t + \Delta t) - F(t)}{\Delta t} & = \cfrac{1}{\Delta t} \left[ \int_{a(t+\Delta t)}^{b(t+\Delta t)} f(x, t+\Delta t)~\text{dx} - \int_{a(t)}^{b(t)} f(x, t)~\text{dx}\right] \\ & \equiv \cfrac{1}{\Delta t} \left[ \int_{a+\Delta a}^{b+\Delta b} f(x, t+\Delta t)~\text{dx} - \int_{a}^{b} f(x, t)~\text{dx}\right] \\ & =     \cfrac{1}{\Delta t} \left[ -\int_{a}^{a+\Delta a} f(x, t+\Delta t)~\text{dx} + \int_{a}^{b+\Delta b} f(x, t+\Delta t)~\text{dx} - \int_{a}^{b} f(x, t)~\text{dx}\right] \\ & =     \cfrac{1}{\Delta t} \left[ -\int_{a}^{a+\Delta a} f(x, t+\Delta t)~\text{dx} + \int_{a}^{b} f(x, t+\Delta t)~\text{dx} + \int_{b}^{b+\Delta b} f(x, t+\Delta t)~\text{dx} - \int_{a}^{b} f(x, t)~\text{dx}\right] \\ & =       \int_{a}^{b} \cfrac{f(x, t+\Delta t) - f(x,t)}{\Delta t}~\text{dx} + \cfrac{1}{\Delta t}\int_{b}^{b+\Delta b} f(x, t+\Delta t)~\text{dx} - \cfrac{1}{\Delta t}\int_{a}^{a+\Delta a} f(x, t+\Delta t)~\text{dx} ~. \end{align} $$ Since $$f(x,t)$$ is essentially constant over the infinitesimal intervals $$a < x < a+\Delta a$$ and $$b < x < b+\Delta b$$, we may write

\cfrac{F(t + \Delta t) - F(t)}{\Delta t} \approx \int_{a}^{b} \cfrac{f(x, t+\Delta t) - f(x,t)}{\Delta t}~\text{dx} + f(b, t+\Delta t)~\cfrac{\Delta b}{\Delta t} - f(a, t+\Delta t)~\cfrac{\Delta a}{\Delta t}~. $$ Taking the limit as $$\Delta t\rightarrow 0$$, we get

\lim_{\Delta t \rightarrow 0} \left[\cfrac{F(t + \Delta t) - F(t)}{\Delta t}\right] = \lim_{\Delta t \rightarrow 0}\left[ \int_{a}^{b} \cfrac{f(x, t+\Delta t) - f(x,t)}{\Delta t}~\text{dx}\right] + \lim_{\Delta t \rightarrow 0}\left[f(b, t+\Delta t)~\cfrac{\Delta b}{\Delta t}\right] - \lim_{\Delta t \rightarrow 0}\left[f(a, t+\Delta t)~\cfrac{\Delta a}{\Delta t}\right] $$ or,

{  \cfrac{dF(t)}{dt} = \int_{a(t)}^{b(t)} \frac{\partial f(x, t)}{\partial t}~\text{dx} + f[b(t),t]~\frac{\partial b(t)}{\partial t} - f[a(t),t]~\frac{\partial a(t)}{\partial t}~. } \qquad\qquad\qquad\square $$

title: Continuum mechanics/Leibniz formula


text:
Why is Media Literacy Important

Recognizing Non-Transparency of Media Representations
Media literacy is a significant way to challenge students to understand the constructed nature of media representations and how that might influence their own beliefs about themselves and others. '''Renee: But it is not the only way. General semantics offers another approach to helping students reflect on the constructed nature of symbol systems. Poststructuralism is another. Gaining awareness of the ways that symbol systems shape our perception and interpretation is one of the powerful "aha" moments in media literacy. I wonder if that "aha" is particularly strong or resonant when the medium is perceived as "natural." Could the "aha" offered by post-structuralism or general semantics be more powerful because its focus is on language as a symbol system, which does not appear to us as constructed, biased or limiting?'''

A representation is a constructed message about reality that can influence viewers’ attitudes and beliefs about the real world. Examining issues of representation in the media teaches students to be critical when encountering representations that often include stereotypes about gender, race, class, sexuality, and disability. Students become more aware about the complexity of representations they encounter in the media and gain a multifaceted understanding of their fabrication.

Media literacy enables students to look upon the world and its representation by the media with a critical eye by providing them with specific skills, tools and techniques. Media literacy empowers students to understand and actively participate in discussions about government and politics, including using the media to make their voices heard. At the same time, from their point of view of citizens, media literate students learn to be skeptical about the role of politicians and to critically examine politicians’ work as representatives of the public’s needs and interests. (Hobbs, 2006)

Media literacy allows for people to question motivations of any form of media communication, such as websites, social media messages and even memes. Today, the "author" is not just the byline, but also the entity, the advertisers and supporters and affiliates. Media literate individuals connect the dots about what or whom is behind the curtain and check for credibility.

Motivation and Engagement
Media literacy allows students to draw on their experience of media forms and connect it to classroom activities. Research shows that when students are engaged in their topic, and can actively connect it to the real world, they are more excited and engaged in learning (Hobbs, 2006). Little research has been conducted on whether or not media literacy may have an impact on school attendance and quality of class participation.

Media literacy can be especially powerful for youth who do not perform well in the school system. Kist (2005) found that "at risk" and marginalized youth became excited and engaged with reading and writing after their experience with media literacy in the classroom (p. 103).

Media literate teenagers are more likely to recognize what Goodman (2003) calls “the cultural triangle of fashion, sports and music” (p. 27) created and promoted by the entertainment industry. By learning to analyze and critique commercial media representations of their own experiences of marginalization and rebellion, poor and minority youth become capable of adopting roles other than those of consumers or criminals (Goodman, 2003). Instead, as media producers, they are empowered to join mainstream society’s discourse by speaking with a voice of their own.

In addition to joining the public discourse, the voices of inner city youth challenge it. According to Goodman, (2003), "Their observations and insights can serve to challenge adult perceptions of teens as hostile and threatening, and also bring diversity to the voices informing public policy" (Cahill, 1997, as sited in Goodman, 2003, p. 30).

Changes in the Quality of Parent-child Interactions
Scholars have proposed the possibility of improving the quality of parent-child interactions through media education in school. Students at Concord High School are required to take the Media/ Communication course in 11th grade. Their parents have shared that the quality of family communication has been improved since their kids took the course. Students were more engaged with what they had learned about the media, and enjoyed talking about the course at home. They discussed topics or ideas about media, technology, and society with their parents. Such a change of family communication happened not only to top students but also to ordinary students who have not often shared their school works with their parents.

Student Teacher Relationships
Along the same line, media education can help teachers to build better relationship with students. Students connect themselves more with the topics covered in Media/Communication class than what they learn in other traditional academic courses. Teachers also get to learn more about their students, as students give unpredictable and original responses regarding various topics.

Social and Interpersonal Relationship Skills
It has been hypothesized that media literacy builds social skills through extensive opportunities for sharing ideas, listening, teamwork, and collaboration. For example, in the Snow Lake School in Manitoba, eighth grade students were assigned an advertising project. Students were to complete a print ad, a radio ad and an Internet ad. Once they performed research on current advertising, they were able to construct their own campaign, which in turn were constructing meaning. Interestingly enough, when the students were asked about their assignment, they were unable to articulate the core meaning behind the assignment. More comments were given about the social interaction and the ability to work together, which students saw as a primary learning experience. They felt that this assignment better prepared them for the professional world (Kist, 2005).

Through media production, a core element of media literacy, students have the rare opportunity to challenge established rules of social interaction and power relations by asking instead of answering questions (Goodman, 2003). This is valid for the interaction dynamics between adults and teenagers, as well as between marginalized and privileged communities.

Reading Positions
Through media literacy educators can demonstrate how different people interpret a text depending on the reader’s historical and social background. It is important in today’s curriculum because the proliferation of media in today’s youth creates the need for students to be able to “read” the abundance of messages they are exposed to (Hobbs, 2006).

Civic Involvement
Media literacy is crucial for the development of citizenship skills needed to promote a thriving democracy. Political campaigns and issues are primarily conveyed through 30-second television ads or, at best, half-hour news interviews on Sunday mornings. With so little attention paid to issues from our primary forms of media consumption, it is imperative for people to learn how to read the messages they are bombarded with and recognize the reasons and decisions behind what is being presented to them (Thoman & Jolls, 2005).

Competitive Power
In this media-saturated society, information comes not only through the written words but also through the images and sounds. Media literacy can allow students to fluently read and write audio/visual language would have more competitive power to better thrive in our multimedia culture (Thoman & Jolls, 2005).

Critical Thinking Skills
Media analysis, which is a crucial part of media literacy education, can develop critical thinking skills, by strengthening observation and interpretation. For example, students can examine and challenge the stereotypes, biases, and hidden motivation of the producers. (Thoman & Jolls, 2005).

New Ways of Learning
Formal education is facing a formidable challenge in adapting to a media-saturated environment, in which traditional schooling methods are obsolete or irrelevant. Instead of assisting students in memorizing facts about the world or information storage, modern education should impart higher-order thinking skills such as analyzing and evaluating an overwhelming amount of information that is usually just a few clicks away. (Thoman and Jolls, 2005)

“And now yet children--particularly younger children—are increasingly participating in cultural and social worlds that are inaccessible, even incomprehensible to their parents.” (Buckingham, 2003, p. 32). The new world that children inhabit is largely the world of the media. Buckingham documents that the media plays a significant part in the lives of children, and how they construct meaning. The significance of the media in the lives of children is largely ignored by the school system, which results in a gap between children’s ‘in school’ and ‘out of school’ experience. Children should feel that their education has personal relevance. It is more important to build skills that children will use in their daily lives, than to do things because of traditions set 200 years ago. The school system needs to change as students change, it needs to evolve and progress. This will make the process of education more enriching and meaningful for the children involved. A strong connection to school and the outside world may powerfully affect the lives of teenagers, who may feel profound disconnect between their life experience and their school experience. Using media text (text students already know) may decrease drop out rates and increase student interest. Perhaps media education can educate teachers about students as well. When teachers know their student’s media preferences, they can use media to open up dialogue about a multitude of topics.

“Yet, if media education is to help bridge the widening gap between the school and the world of children’s out-of-school experience, it must surely begin with the knowledge children already possess” (Buckingham, 2003, p. 34). Buckingham places value on the experience that children gain as participants in their surrounding culture. This ideology positions the student as knowledgeable not just as a vessel that needs to be filled with information. This idea alone could revolutionize the field of education. Giving value to children’s knowledge may help them to own their experiences and opinions. Teaching should extend beyond “right” and “wrong” answers. Critical thinking will prepare children for the real world, where issues are much more complex than black and white. Children should learn how to sort through life’s complexities, and this involves having their opinions, experiences, and voices validated. Treating each child as a knowledgeable human being with important beliefs and experiences may help to draw children out of their protective shell. In addition, it may help incorporate children of different learning abilities and/or background beliefs into the classroom. Valuing the child's unique input may help those who are “at risk” of failing out of the school system. Many of these children may not believe they are intelligent, and may associate school with personal failure. What remains untouched here is the actual state of schools in the United States. Conditions may vary significantly school by school, or teacher by teacher. Buckingham’s area of expertise lies predominantly within the British school system. More research is needed to understand the perspectives of students, teachers, and school administrators.

Buckingham (2003) provides very explicit goals for media education, which seem at odds with traditionally established notions of education and learning: “Media education is seen here not as a form of protection, but as a form of preparation… In broad terms, it aims to develop young people’s understanding of, and participation in, the media culture that surrounds them (Balazgette, 1989)… Broadly speaking, therefore, this new approach seeks to begin with what students already know, and with their existing tastes and pleasures in the media, rather than assuming that these are merely invalid or ‘ideological’. This approach does not seek to replace ‘subjective’ responses with ‘objective’ ones, or to neutralize the pleasures of the media through rational analysis. On the contrary, it aims to develop a more reflexive style of teaching and learning, in which students can reflect on their own activity both as ‘readers’ and as ‘writers’ of media texts, and understand the broader social and economic factors that are in play. Critical analysis is seen here as a process of dialogue, rather than a matter of arriving at an agreed or predetermined position” (Buckingham, 2003, p. 13-14).

In other words, according to Buckingham, media education does not provide the right answers, but prefers to state the right questions instead. Also, it creates a new kind of learning environment, where students are not armed with insights, skills or tools for withstanding the temptations or threats of the media. On the contrary, the departing point of media education are existing media-related practices and pleasures. Such premise is fair and justified if teachers are to approach learners not as traditional authority figures who judge and sermonize about the perils of media use and its implications. We should not consider this a simplistic trick aimed at engaging students’ interest and taking advantage of their out-of-school experiences. Instead, media education aims at broadening established media-based learning practices by stimulating reflection on media use and, from there, on understanding the cultural, social, economic and political aspects of media producers, products and audiences. Positioning teachers as partners in a dialogue rather than guardians of longstanding truth and wisdom is a challenging precept for teachers and students alike, not to mention parents and the public. Century-long pedagogic norms may seem undermined by media education’s innovative approach to the positioning of teachers, learners and media in the learning process. However, Buckingham rightfully points to the decreasing authority of schools as a socializing actor in modern society; thus media education is not making groundbreaking discoveries, but merely reflects ongoing processes that ought to find their place in the formal education system.

The Place of Traditional Teaching in Media Education
One product of progressivist pedagogical ideology may be the demonization of certain traditional teaching methods. While he admits that learner centered reforms have made education more humane, Alvarado (1981) makes powerful claims for more traditional methods, including direct teaching (lecturing, teachers delivering facts from a position of authority), competitive learning structures, and teaching to the test. For Alvarado,“it is necessary to construct a pedagogy that precisely does not depend upon personal experience and, in certain ways, critiques it.” Direct teaching allows educators to present information efficiently and to confront and inform challenges from students who may make comments from perspectives that endanger other students (e.g. racist, sexist, heteronormative, etc). Teaching in competitive structures and teaching to the test both prepare students for economic realities beyond the classroom. Alvarado argues that an exclusively critical and learner centered focus in media education may lead teachers to fail in their responsibility to offer students training to compete in the current dominant culture. By including political economy of media as content and explicitly discussing the ideological and economic rationale for teaching choices, Alvarado suggests that these dualities may be balanced.

Balancing Responsibility: Teaching for Success in the Cultural of Power and Teaching for Change
Alvarado (1981) makes a sweeping, universal claim for “two strands [that should be] running through every classroom situation: 1) recognition of the power and importance of the structures of the present social formation and a recognition of the need for all people to work within those structures successfully, and 2) a recognition of the importance and potential power of all forms of oppositional knowledge and groupings.” (p. 205)

The first claim recognizes the responsibility of teachers to offer students training in skills valued by the culture of power so that they may compete within that culture for economic advantage. However, this axiom is problematic in that it privileges the teacher’s reading or understanding of “the present social formation.” In the second claim, Alvarado stops well short of seeing the possible agency of students as cultural producers realized by critical or creative practice, student choice and teacher facilitation. This strand denies altogether the possibility of agency outside established, known norms in favor of “recognition of...potential”--a chimera of agency. Some teachers may find this approach a bit timid. Still, the balance of critical training and training within the culture of power is an important issue with which all teachers should consciously struggle.

Cultural Theory and Popular Culture
John Storey’s Cultural Theory and Popular Culture is his approach to ‘map out the general conceptual landscape of popular culture’. This is an important exploration for teachers of Media Education for it lends assistance to the struggle of cultivating critical thinking skills in students rather than imposing one’s own view about good/bad culture. This is accomplished through summations of various schools of thought found in the works of key theorists.

Continuing his mapping in Chapter 3, Culturalism, Storey compares the works of Richard Hoggart, Raymond Williams, E. P. Thompson, Stuart Hall, and Paddy Whannel in the late 1950s and early 1960s.

Each Theorist introduces a perspective on how culture is made and should be studied in order to understand the progression of popular culture. While Hoggart believes popular culture was once pure, created by and for the people of the working-class, and then corrrupted by an industry spawned mass culture, Williams points out that full access to understanding a culture comes from those who lived it. However, once the lived historical moment has passed the ‘structure of feeling’ fragments leaving the cultural analysis a documentary record that is selective in nature; thus analysis itself can never be made with absolute certainties. As teachers of Media Education facilitate media analysis with students it is worth self-searching for patterns of cultural traditions of selectivity in one’s own teaching methods.

Storey then briefly shares E.P. Thompson’s intent to share that the working-class was made through a process that manifested over a period of time. Furthermore, to study it is to be actively listening all the time. This is significant to remember in this fast changing modern media culture. Hall and Whannel set out to refute the notion that ‘all high culture is good and that all popular culture is bad.’ They contend that there is a hierarchy that lies within popular culture and the goal is to point out the good from the bad. Regardless of what truth may lie in this argument from a teacher’s point of view, it is again, an opportunity for self-reflection about one’s own interest when teaching students how to study media.

Media Literacy, Cultural Theory, Feminisms, and Gender Studies
Media literacy can also be associated with feminisms and gender studies, which have long looked at the media to provide texts for cultural analysis. John Storey discusses gender and sexuality in Chapter 7 of Cultural Theory and Popular Culture (2006). Within this chapter, Storey discusses three feminisms, and several critical feminist studies, as well as men’s studies and queer theory.

Regarding feminisms, Storey points out that three feminists exist. First, marxist feminism posits that capitalism is the source of women’s oppression. Second, liberal feminism points to male prejudice against women as the source of the oppression of women. Finally, the dual-system theory of feminism combines marxist and liberal feminism to claim that both patriarchy and capitalism result in the oppression of women. These theories have played out in a significant body of research, including several notable studies.

Jackie Stacey’s (1994) Star Gazing: Hollywood and Female Spectatorship rejected older, patriarchal cine-psychoanalysis and used a new feminist perspective to look at women at the cinema. Stacey found that there were three primary reasons that women go to the cinema. First, escapism is a factor as women use the cinema both to escape into the movie theater and away from the hardships of everyday life. Second, identification is a factor because women identify with movie stars and gain a sense of empowerment, self-confidence, and control. Thirdly, consumption is a factor as women learn from the alternative femininity presented by movie stars and learn how to push accepted social boundaries themselves.

Tania Modleski’s (1982) Loving with a Vengeance looked at women who read romance novels and found that, while feminine narratives in these books seem to contradict with the goals of feminism, in fact these novels demonstrate an important point, namely, that women are dissatisfied with their lives. As such, reading the novels are a form of protest. Janice Radway’s (1984) Remale Desire reached similar conclusions, namely, that women read romance novels, not in approval of patriarchy, but rather in the act of a “utopian protest” and longing for a better world.

Ien Ang’s (1985) Watching Dallas considered the views of women regarding the television show Dallas. Ang divided the participants in her study into three categories. First, there are individuals who view Dallas negatively because they view it as an example of mass culture. The second group enjoyed watching Dallas, but viewed it as an example of mass culture, and as such laughed at it. Finally, a group enjoyed watching Dallas and rationalized their opinion in one of several ways. Some in the third group felt that they could acknowledge the ‘dangers’ of Dallas and deal with them, others felt the show had substance, and still others resorted to watching the show with a sense of irony. As such, Ang explained the way in which viewers attempted to reconcile their own enjoyment of the television show Dallas.

In Inside Women’s Magazines, Janice Winship (1987) considered women who read women’s magazines. Winship argued that women who read women’s magazines are not “cultural dupes of the media institutions” but rather producers of meaning themselves. Conducting 80 interviews of men and women, Winship found that individuals categorize magazines differently, and notably concluded that the way an audience categorizes the magazine and reads the text will have a key role in determining the meaning they will take away from it.

Regarding men’s studies, Storey refers to Anthony Easthope’s (1986) article What a Man’s Gotta Do, which notes that masculinity is a cultural construct, and that the dominant masculinity is only a norm which measures itself against other lived masculinities.

Finally, queer theory is discussed by Storey. Not a discipline “about” lesbian women or gay men, queer theory seeks to breakdown the assumption that gender is natural. Queer theory argues against the assumption that there are only two biological sexes which generate two genders. Further, the theory focuses on the construction of gender in culture.

Each of these theoretical perspectives can be incorporated into a broader understanding of the messages contained in the media, and are a part of media literacy.

Teaching Students to Filter Information
In his essay Technology as a Dazzling Distraction (1994), Neil Postman argued that the modern emphasis towards including technology as an integral part of the education system in America is actually overlooking the real issues which education ought to address. Postman argues that technologies tend to limit peoples’ options more than they increase them: society creates needs to match available and new technologies, instead of creating technology to match existing needs. In this argument, Postman appears to be agreeing with McLuhan’s famed claim that “the medium is the message,” and that the form of media employed by a society is, in itself, a far more powerful force of cultural change than any particular statement conveyed by means of that media.

However, Postman’s argument goes beyond a claim that technology can shape society, and the educational system, in unintended or unnecessary ways. Postman argues that schools no longer serve the purpose of information-giving. Since the advent of mass media, people have had access to far more information outside of a school setting than can be accessed within the school itself. This point becomes even more clear when considering the growth of the internet and the easy, near-instantaneous access to a plethora of information. Thus, since information, in itself, is no longer particularly difficult to gain, schools need to focus on two other goals: teaching students how to behave as part of a community and, how to ignore and disregard useless information. Thus, the problem of education today is no longer obtaining information; it is now filtering information. This point is, in many ways, addresses a central goal of media literacy education.

Online Resources for Learning More

 * PODCASTS: Learn about Reel Vision, the Boston filmmaking group that works with young people (Episode 15)
 * ORGANIZATIONS: European Centre for Media Literacy Alliance for a Media Literate America

title: Why is Media Literacy Important


text:
Continuum mechanics/Reynolds transport theorem

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Reynolds transport theorem
Let $$\Omega(t)$$ be a region in Euclidean space with boundary $$\partial \Omega (t)$$. Let $$\mathbf{x}(t)$$ be the positions of points in the region and let $$\mathbf{v}(\mathbf{x},t)$$ be the velocity field in the region. Let $$\mathbf{n}(\mathbf{x},t)$$ be the outward unit normal to the boundary. Let $$\mathbf{f}(\mathbf{x},t)$$ be a vector field in the region (it may also be a scalar field). Show that

\cfrac{d}{dt}\left(\int_{\Omega(t)} \mathbf{f}~\text{dV}\right) = \int_{\Omega(t)} \frac{\partial \mathbf{f}}{\partial t}~\text{dV} + \int_{\partial \Omega(t)} (\mathbf{v}\cdot\mathbf{n})\mathbf{f}~\text{dA} ~. $$ This relation is also known as the  Reynold's Transport Theorem and is a generalization of the Leibniz rule. Content of example.
 * }

Proof:

Let $$\Omega_0$$ be reference configuration of the region $$\Omega(t)$$. Let the motion and the deformation gradient be given by

\mathbf{x} = \boldsymbol{\varphi}(\mathbf{X}, t)~; \qquad\implies\qquad \boldsymbol{F}(\mathbf{X},t) = \boldsymbol{\nabla}_{\circ} \boldsymbol{\varphi} ~. $$ Let $$J(\mathbf{X},t) = \det[\boldsymbol{F}(\mathbf{X},t)]$$. Then, integrals in the current and the reference configurations are related by

\int_{\Omega(t)} \mathbf{f}(\mathbf{x},t)~\text{dV} = \int_{\Omega_0} \mathbf{f}[\boldsymbol{\varphi}(\mathbf{X},t),t]~J(\mathbf{X},t)~\text{dV}_0 = \int_{\Omega_0} \hat{\mathbf{f}}(\mathbf{X},t)~J(\mathbf{X},t)~\text{dV}_0 ~. $$ The time derivative of an integral over a volume is defined as

\cfrac{d}{dt}\left( \int_{\Omega(t)} \mathbf{f}(\mathbf{x},t)~\text{dV}\right) = \lim_{\Delta t \rightarrow 0} \cfrac{1}{\Delta t}    \left(\int_{\Omega(t + \Delta t)} \mathbf{f}(\mathbf{x},t+\Delta t)~\text{dV} -            \int_{\Omega(t)} \mathbf{f}(\mathbf{x},t)~\text{dV}\right) ~. $$ Converting into integrals over the reference configuration, we get

\cfrac{d}{dt}\left( \int_{\Omega(t)} \mathbf{f}(\mathbf{x},t)~\text{dV}\right) = \lim_{\Delta t \rightarrow 0} \cfrac{1}{\Delta t}    \left(\int_{\Omega_0} \hat{\mathbf{f}}(\mathbf{X},t+\Delta t)~J(\mathbf{X},t+\Delta t)~\text{dV}_0 -            \int_{\Omega_0} \hat{\mathbf{f}}(\mathbf{X},t)~J(\mathbf{X},t)~\text{dV}_0\right) ~. $$ Since $$\Omega_0$$ is independent of time, we have

\begin{align} \cfrac{d}{dt}\left( \int_{\Omega(t)} \mathbf{f}(\mathbf{x},t)~\text{dV}\right) & = \int_{\Omega_0} \left[\lim_{\Delta t \rightarrow 0} \cfrac{ \hat{\mathbf{f}}(\mathbf{X},t+\Delta t)~J(\mathbf{X},t+\Delta t) - \hat{\mathbf{f}}(\mathbf{X},t)~J(\mathbf{X},t)}{\Delta t} \right]~\text{dV}_0 \\ & = \int_{\Omega_0} \frac{\partial }{\partial t}[\hat{\mathbf{f}}(\mathbf{X},t)~J(\mathbf{X},t)]~\text{dV}_0 \\ & = \int_{\Omega_0} \left(         \frac{\partial }{\partial t}[\hat{\mathbf{f}}(\mathbf{X},t)]~J(\mathbf{X},t)+          \hat{\mathbf{f}}(\mathbf{X},t)~\frac{\partial }{\partial t}[J(\mathbf{X},t)]\right) ~\text{dV}_0 \end{align} $$ Now, the time derivative of $$\det\boldsymbol{F}$$ is given by (see Gurtin: 1981, p. 77)

\frac{\partial J(\mathbf{X},t)}{\partial t} = \frac{\partial }{\partial t}(\det\boldsymbol{F}) = (\det\boldsymbol{F})(\boldsymbol{\nabla} \cdot \mathbf{v}) = J(\mathbf{X},t)~\boldsymbol{\nabla} \cdot \mathbf{v}(\boldsymbol{\varphi}(\mathbf{X},t),t) = J(\mathbf{X},t)~\boldsymbol{\nabla} \cdot \mathbf{v}(\mathbf{x},t) ~. $$ Therefore,

\begin{align} \cfrac{d}{dt}\left( \int_{\Omega(t)} \mathbf{f}(\mathbf{x},t)~\text{dV}\right) & = \int_{\Omega_0} \left(         \frac{\partial }{\partial t}[\hat{\mathbf{f}}(\mathbf{X},t)]~J(\mathbf{X},t)+          \hat{\mathbf{f}}(\mathbf{X},t)~J(\mathbf{X},t)~\boldsymbol{\nabla} \cdot \mathbf{v}(\mathbf{x},t)\right) ~\text{dV}_0 \\ & =     \int_{\Omega_0} \left(\frac{\partial }{\partial t}[\hat{\mathbf{f}}(\mathbf{X},t)]+         \hat{\mathbf{f}}(\mathbf{X},t)~\boldsymbol{\nabla} \cdot \mathbf{v}(\mathbf{x},t)\right)~J(\mathbf{X},t) ~\text{dV}_0  \\ & =     \int_{\Omega(t)} \left(\dot{\mathbf{f}}(\mathbf{x},t)+         \mathbf{f}(\mathbf{x},t)~\boldsymbol{\nabla} \cdot \mathbf{v}(\mathbf{x},t)\right)~\text{dV} \end{align} $$ where $$\dot{\mathbf{f}}$$ is the material time derivative of $$\mathbf{f}$$. Now, the material derivative is given by

\dot{\mathbf{f}}(\mathbf{x},t) = \frac{\partial \mathbf{f}(\mathbf{x},t)}{\partial t} + [\boldsymbol{\nabla} \mathbf{f}(\mathbf{x},t)]\cdot\mathbf{v}(\mathbf{x},t) ~. $$ Therefore,

\cfrac{d}{dt}\left( \int_{\Omega(t)} \mathbf{f}(\mathbf{x},t)~\text{dV}\right) = \int_{\Omega(t)} \left(        \frac{\partial \mathbf{f}(\mathbf{x},t)}{\partial t} + [\boldsymbol{\nabla} \mathbf{f}(\mathbf{x},t)]\cdot\mathbf{v}(\mathbf{x},t) +         \mathbf{f}(\mathbf{x},t)~\boldsymbol{\nabla} \cdot \mathbf{v}(\mathbf{x},t)\right)~\text{dV} $$ or,

\cfrac{d}{dt}\left( \int_{\Omega(t)} \mathbf{f}~\text{dV}\right) = \int_{\Omega(t)} \left(        \frac{\partial \mathbf{f}}{\partial t} + \boldsymbol{\nabla} \mathbf{f}\cdot\mathbf{v} +         \mathbf{f}~\boldsymbol{\nabla} \cdot \mathbf{v}\right)~\text{dV} ~. $$ Using the identity

\boldsymbol{\nabla} \cdot (\mathbf{v}\otimes\mathbf{w}) = \mathbf{v}(\boldsymbol{\nabla} \cdot \mathbf{w}) + \boldsymbol{\nabla}\mathbf{v}\cdot\mathbf{w} $$ we then have

\cfrac{d}{dt}\left( \int_{\Omega(t)} \mathbf{f}~\text{dV}\right) = \int_{\Omega(t)} \left(\frac{\partial \mathbf{f}}{\partial t} + \boldsymbol{\nabla} \cdot (\mathbf{f}\otimes\mathbf{v})\right)~\text{dV} ~. $$ Using the divergence theorem and the identity $$(\mathbf{a}\otimes\mathbf{b})\cdot\mathbf{n} = (\mathbf{b}\cdot\mathbf{n})\mathbf{a}$$ we have

{ \cfrac{d}{dt}\left( \int_{\Omega(t)} \mathbf{f}~\text{dV}\right) = \int_{\Omega(t)}\frac{\partial \mathbf{f}}{\partial t}~\text{dV} + \int_{\partial \Omega(t)}(\mathbf{f}\otimes\mathbf{v})\cdot\mathbf{n}~\text{dA} = \int_{\Omega(t)}\frac{\partial \mathbf{f}}{\partial t}~\text{dV} + \int_{\partial \Omega(t)}(\mathbf{v}\cdot\mathbf{n})\mathbf{f}~\text{dA} ~. } $$

References

 * 1) M.E. Gurtin. An Introduction to Continuum Mechanics. Academic Press, New York, 1981.
 * 2) T. Belytschko, W. K. Liu, and B. Moran. Nonlinear Finite Elements for Continua and Structures. John Wiley and Sons, Ltd., New York, 2000.