text:
Nonlinear finite elements/Homework 6/Hints

Hints for Homework 6: Problem 1: Section 8
Use Maple to reduce your manual labor.

The problem becomes easier to solve if we consider numerical values of the parameters. Let the local nodes numbers of element $$5$$ be $$1$$ for node $$5$$, and $$2$$ for node $$6$$.

Let us assume that the beam is divided into six equal sectors. Then,

\theta = \cfrac{\pi}{4}~; \theta_1 = \cfrac{\pi}{3}~; \theta_2 = \cfrac{\pi}{6} ~. $$ Let $$r_1 = 1$$ and $$r_2 = 1.2$$. Since the blue point is midway between the two, $$r = 1.1$$.

Also, let the components of the stiffness matrix of the composite be

C_{11} = 10; C_{33} = 100; C_{12} = 6; C_{13} = 60; C_{44} = 30~. $$ Let the velocities for nodes $$1$$ and $$2$$ of the element be

\mathbf{v}_1 = \begin{bmatrix} v_1^x \\ v_1^y \\ \omega_1 \end{bmatrix} = \begin{bmatrix} 1 \\ 2 \\ 1 \end{bmatrix} ~; \mathbf{v}_2 = \begin{bmatrix} v_2^x \\ v_2^y \\ \omega_2 \end{bmatrix} = \begin{bmatrix} 2 \\ 1 \\ 1 \end{bmatrix} $$ The $$x$$ and $$y$$ coordinates of the master and slave nodes are

\begin{bmatrix} x_1 \\ y_1 \\ x_2 \\ y_2 \end{bmatrix} = \begin{bmatrix} r\cos\theta_1 \\ r\sin\theta_1 \\ r\cos\theta_2 \\ r\sin\theta_2 \end{bmatrix} $$

\begin{bmatrix} x_{1-} \\ y_{1-} \\ x_{2-} \\ y_{2-} \end{bmatrix} = \begin{bmatrix} r_1\cos\theta_1 \\ r_1\sin\theta_1 \\ r_1\cos\theta_2 \\ r_1\sin\theta_2 \end{bmatrix} $$

\begin{bmatrix} x_{1+} \\ y_{1+} \\ x_{2+} \\ y_{2+} \end{bmatrix} = \begin{bmatrix} r_2\cos\theta_1 \\ r_2\sin\theta_1 \\ r_2\cos\theta_2 \\ r_2\sin\theta_2 \end{bmatrix} $$ Since there are two master nodes in an element, the parent element is a four-noded quad with shape functions
 * $$\begin{align}

N_{1-}(\xi,\eta) & = \cfrac{1}{4}(1-\xi)(1-\eta) & N_{2-}(\xi,\eta) & = \cfrac{1}{4}(1+\xi)(1-\eta) \\ N_{1+}(\xi,\eta) & = \cfrac{1}{4}(1-\xi)(1+\eta) & N_{2+}(\xi,\eta) & = \cfrac{1}{4}(1+\xi)(1+\eta) ~. \end{align}$$ The isoparametric map is
 * $$\begin{align}

x(\xi, \eta) & = x_{1-}~N_{1^-}(\xi,\eta) + x_{2-}~N_{2^-}(\xi,\eta) + x_{1+}~N_{1^+}(\xi,\eta) + x_{2+}~N_{2^+}(\xi,\eta)\\ y(\xi, \eta) & = y_{1-}~N_{1^-}(\xi,\eta) + y_{2-}~N_{2^-}(\xi,\eta) + y_{1+}~N_{1^+}(\xi,\eta) + y_{2+}~N_{2^+}(\xi,\eta)~. \end{align}$$ Therefore, the derivatives with respect to $$\xi$$ are
 * $$\begin{align}

x_{,\xi} = \frac{\partial x}{\partial \xi} \\ y_{,\xi} = \frac{\partial y}{\partial \xi} \end{align}$$ Since the blue point is at the center of the element, the values of $$\xi$$ and $$\eta$$ at that point are zero. Therefore,

\mathbf{x}_{,\xi} = x_{,\xi} \mathbf{e}_x - y_{,\xi} \mathbf{e}_y, \lVert\mathbf{x}_{,\xi}\rVert_{}= \sqrt{x_{,\xi}^2 + y_{,\xi}^2} ~. $$ The local laminar basis vector $$\widehat{\mathbf{e}}_x$$ is given by

\widehat{\mathbf{e}}_x = \cfrac{\mathbf{x}_{,\xi}}{\lVert\mathbf{x}_{,\xi}\rVert_{}} $$ The laminar basis vector $$\widehat{\mathbf{e}}_y$$ is given by

\widehat{\mathbf{e}}_y = \mathbf{e}_z\times\widehat{\mathbf{e}_x} $$

To compute the velocity gradient, we have to find the velocities at the slave nodes using the relation

\begin{bmatrix} v^x_{i-} \\ v^y_{i-} \\ v^x_{i+} \\ v^y_{i+} \end{bmatrix} = \begin{bmatrix} 1 & 0 & - (y_{i-}-y_i) \\ 0 & 1 &(x_{i-}-x_i)\\ 1 & 0 & - (y_{i+}-y_i) \\ 0 & 1 &(x_{i+}-x_i) \end{bmatrix} \begin{bmatrix} v_i^x \\ v_i^y \\ \omega_i \end{bmatrix} $$ For master node 1 of the element (global node 5), the velocities of the slave nodes are

\begin{bmatrix} v^x_{1-} \\ v^y_{1-} \\ v^x_{1+} \\ v^y_{1+} \end{bmatrix} $$ For master node 2 of the element (global node 6), the velocities of the slave nodes are

\begin{bmatrix} v^x_{2-} \\ v^y_{2-} \\ v^x_{2+} \\ v^y_{2+} \end{bmatrix} $$ The interpolated velocity within the element is given by

\begin{align} \mathbf{v}(\boldsymbol{\xi}, t) & = \cfrac{D}{Dt}[\mathbf{x}(\boldsymbol{\xi},t)] \\ & = \sum_{i- = 1}^2 \frac{\partial }{\partial t}[\mathbf{x}_{i-}(t)]~N_{i^-}(\xi,\eta) + \sum_{i+ = 1}^2 \frac{\partial }{\partial t}[\mathbf{x}_{i+}(t)]~N_{i^+}(\xi,\eta)\\ & = \sum_{i- = 1}^2 \mathbf{v}_{i-}(t)~N_{i-}(\xi,\eta) + \sum_{i+ = 1}^2 \mathbf{v}_{i+}(t)~N_{i+}(\xi,\eta) ~. \end{align} $$ The velocity gradient is given by

\boldsymbol{\nabla} \mathbf{v} = v_{i,j} = \frac{\partial v_i}{\partial x_j} ~. $$ The velocities are given in terms of the parent element coordinates ($$\xi,\eta$$). We have to convert them to the ($$x,y$$) system in order to compute the velocity gradient. To do that we recall that
 * $$\begin{align}

\frac{\partial v_x}{\partial \xi} & = \frac{\partial v_x}{\partial x}\frac{\partial x}{\partial \xi} + \frac{\partial v_x}{\partial y}\frac{\partial y}{\partial \xi} \\ \frac{\partial v_x}{\partial \eta} & = \frac{\partial v_x}{\partial x}\frac{\partial x}{\partial \eta} + \frac{\partial v_x}{\partial y}\frac{\partial y}{\partial \eta} \\ \frac{\partial v_y}{\partial \xi} & = \frac{\partial v_y}{\partial x}\frac{\partial x}{\partial \xi} + \frac{\partial v_y}{\partial y}\frac{\partial y}{\partial \xi} \\ \frac{\partial v_y}{\partial \eta} & = \frac{\partial v_y}{\partial x}\frac{\partial x}{\partial \eta} + \frac{\partial v_y}{\partial y}\frac{\partial y}{\partial \eta} ~. \end{align}$$ In matrix form

\begin{bmatrix} \frac{\partial v_x}{\partial \xi} \\ \frac{\partial v_x}{\partial \eta} \end{bmatrix} = \begin{bmatrix} \frac{\partial x}{\partial \xi} & \frac{\partial y}{\partial \xi} \\ \frac{\partial x}{\partial \eta} & \frac{\partial y}{\partial \eta} \\ \end{bmatrix} \begin{bmatrix} \frac{\partial v_x}{\partial x} \\ \frac{\partial v_x}{\partial y} \end{bmatrix} = \mathbf{J} \begin{bmatrix} \frac{\partial v_x}{\partial x} \\ \frac{\partial v_x}{\partial y} \end{bmatrix} $$ and

\begin{bmatrix} \frac{\partial v_y}{\partial \xi} \\ \frac{\partial v_y}{\partial \eta} \end{bmatrix} = \begin{bmatrix} \frac{\partial x}{\partial \xi} & \frac{\partial y}{\partial \xi} \\ \frac{\partial x}{\partial \eta} & \frac{\partial y}{\partial \eta} \\ \end{bmatrix} \begin{bmatrix} \frac{\partial v_y}{\partial x} \\ \frac{\partial v_y}{\partial y} \end{bmatrix} = \mathbf{J} \begin{bmatrix} \frac{\partial v_y}{\partial x} \\ \frac{\partial v_y}{\partial y} \end{bmatrix}~. $$ Therefore,

\begin{bmatrix} \frac{\partial v_x}{\partial x} \\ \frac{\partial v_x}{\partial y} \end{bmatrix} = \mathbf{J}^{-1} \begin{bmatrix} \frac{\partial v_x}{\partial \xi} \\ \frac{\partial v_x}{\partial \eta} \end{bmatrix} \qquad \text{and} \qquad \begin{bmatrix} \frac{\partial v_y}{\partial x} \\ \frac{\partial v_y}{\partial y} \end{bmatrix} = \mathbf{J}^{-1} \begin{bmatrix} \frac{\partial v_y}{\partial \xi} \\ \frac{\partial v_y}{\partial \eta} \end{bmatrix}~. $$ The rate of deformation is given by

\boldsymbol{D} = \frac{1}{2}[\boldsymbol{\nabla} \mathbf{v} + (\boldsymbol{\nabla} \mathbf{v})^T] ~. $$ The global base vectors are

\mathbf{e}_x = \begin{bmatrix} 1 \\ 0 \end{bmatrix}; ~\qquad \mathbf{e}_y = \begin{bmatrix} 0 \\ 1 \end{bmatrix}~. $$ Therefore, the rotation matrix is

\mathbf{R}_{\text{lam}} = \begin{bmatrix} \mathbf{e}_x\bullet\widehat{\mathbf{e}_x} & \mathbf{e}_x\bullet\widehat{\mathbf{e}_y} \\ \mathbf{e}_y\bullet\widehat{\mathbf{e}_x} & \mathbf{e}_y\bullet\widehat{\mathbf{e}_y} \end{bmatrix} $$ Therefore, the components of the rate of deformation tensor with respect to the laminar coordinate system are

\mathbf{D}_{\text{lam}} = \mathbf{R}^T_{\text{lam}}\mathbf{D}\mathbf{R}_{\text{lam}} $$ The rate constitutive relation of the material is given by

\cfrac{D}{Dt} \begin{bmatrix} \sigma_{11} \\ \sigma_{22} \\ \sigma_{33} \\ \sigma_{23} \\ \sigma_{31} \\ \sigma_{12} \end{bmatrix} = \begin{bmatrix} C_{11} & C_{12} & C_{13} & 0 & 0 & 0 \\ C_{12} & C_{11} & C_{13} & 0 & 0 & 0 \\ C_{13} & C_{13} & C_{33} & 0 & 0 & 0 \\ 0 & 0 & 0 & C_{44} & 0 & 0 \\ 0 & 0 & 0 & 0 & C_{44} & 0 \\ 0 & 0 & 0 & 0 & 0 & (C_{11}-C_{12})/2 \end{bmatrix} \begin{bmatrix} D_{11} \\ D_{22} \\ D_{33} \\ D_{23} \\ D_{31} \\ D_{12} \end{bmatrix}~. $$ Since the problem is a 2-D one, the reduced constitutive equation is

\cfrac{D}{Dt} \begin{bmatrix} \sigma_{11} \\ \sigma_{33} \\ \sigma_{31} \end{bmatrix} = \begin{bmatrix} C_{11} & C_{13} & 0 \\ C_{13} & C_{33} & 0\\ 0& 0& C_{44} \end{bmatrix} \begin{bmatrix} D_{11} \\ D_{33} \\ D_{31} \end{bmatrix}~. $$ The laminar $$x$$-direction maps to the composite $$3$$-direction and the laminar $$y$$-directions maps to the composite $$1$$-direction. Hence the constitutive equation can be written as

\cfrac{D}{Dt} \begin{bmatrix} \sigma_{yy} \\ \sigma_{xx} \\ \sigma_{xy} \end{bmatrix} = \begin{bmatrix} C_{11} & C_{13} & 0 \\ C_{13} & C_{33} & 0\\ 0& 0& C_{44} \end{bmatrix} \begin{bmatrix} D_{yy} \\ D_{xx} \\ D_{xy} \end{bmatrix}~. $$ Rearranging,

\cfrac{D}{Dt} \begin{bmatrix} \sigma_{xx} \\ \sigma_{yy} \\ \sigma_{xy} \end{bmatrix} = \begin{bmatrix} C_{33} & C_{13} & 0\\ C_{13} & C_{11} & 0 \\ 0& 0& C_{44} \end{bmatrix} \begin{bmatrix} D_{xx} \\ D_{yy} \\ D_{xy} \end{bmatrix}~. $$ The plane stress condition requires that $$\sigma_{yy} = 0$$ in the laminar coordinate system. We assume that the rate of $$\sigma_{yy}$$ is also zero. In that case, we get

0 = \cfrac{D}{Dt}(\sigma_{yy}) = C_{13}~D_{xx} + C_{11}~D{yy} $$ or,

D_{yy} = - \cfrac{C_{13}}{C_{11}}~D_{xx} ~. $$ To get the global stress rate and rate of deformation, we have to rotate the components to the global basis using

\cfrac{D}{Dt}(\boldsymbol{\sigma}) = \mathbf{R}_{\text{lam}} \cfrac{D}{Dt}(\boldsymbol{\sigma}_{\text{lam}}) \mathbf{R}^T_{\text{lam}} ~; \qquad \mathbf{D} = \mathbf{R}_{\text{lam}} \mathbf{D}_{\text{lam}} \mathbf{R}^T_{\text{lam}} ~. $$


text:
User:Scottbadger~enwikiversity

Hello my name is Scott Badger

I've been [researching] free E-Learning Technology

Information about Educational Wikis

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

title: User:Scottbadger~enwikiversity


text:
User talk:Scottbadger~enwikiversity

Hello Scottbadger, 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:
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Also, don't forget to experiment with the links to your left. Be bold, and see you around Wikiversity! --JWSchmidt 01:25, 19 August 2007 (UTC)

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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 Scottbadger. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Scottbadger~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 23:56, 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) 06:21, 19 April 2015 (UTC)

title: User talk:Scottbadger~enwikiversity


text:
Enhanced oil recovery

Mainly the following process are done for Enhanced oil recovery

→Water injection

→Gas injection

→Reducing residual oil saturation, SOR (alcohol, polymers, surfactants injection)

→Thermal: steam injection (to heating of the reservoir to lower the viscosity)

However, all the above techniques are dependent on reservoir conditions and crude properties.

Water injection/water flooding

Conventionally, based on the type of production and nature of reservoir the following patters are followed an injection well. Once the primary energy of the reservoir tends to deplete it becomes necessary to maintain the pressure inside the reservoir to achieve optimum production and maximise ultimate recovery. In such condition the pressure maintenance can be done by injecting water into the reservoir which is compatible to the formation water present in the reservoir through several water injection wells. Such kind of operation is known as water flooding/Water injection.

In this process, the primary objective is to fill the voidage created by the produced oil fractions thus avoiding the reservoir pressure to decrease with the increased production. When the water is injected in the reservoir, it tends to push the oil upwards, thereby increasing the life and the ultimate recovery of the reservoir. Water injection and water flooding are quite similar terms the only difference being the level at which injection water is being discharged and the displacement phenomena

Water injection:

For water injection operations, the injected water is discharged in the aquifer through several injection wells surrounding the production well. The injected water creates a bottom water drive on the oil zone which pushes the oil upwards. In earlier practices, water injection was done in the later phase of the reservoir life, but now it is often carried out in an earlier phase as to not create voidage in the secondary gas cap. Using water injection in earlier phases helps in improving production because once the secondary gas cap is formed the injected water initially tends to compress the free gas cap and later on pushes the oil, therefore the amount of injection water required is much greater. The water injection is generally carried out when the solution gas drive is present or the water drive is weak. Thus, to reduce costs the water injection is carried out when the reservoir pressure is greater than the saturation pressure.

The selection of injection water {displacing fluid} depends upon the mobility rate between the displacing fluid {injection water} and the displaced fluid {oil}

DISADVANTAGE OF WATER INJECTION

• Reaction of injected water with the formation water can cause formation damage.

• Corrosion of surface and sub-surface equipment.

Water flooding:

In this operation, displacing fluid is injected in the oil zone through the surrounding water injection wells creating an edge water drive flooding oil towards the production well. For better efficiency, the pressure of the reservoir should be such that no secondary gas cap is formed. Water flooding is generally more effective than water injection when no voidage is being created. Water flooding in other regards is similar to water injection including selection parameters of the displacing fluid, the only difference being the displacing phenomenon. However, in practice the above patterns are not necessarily followed It is to be noted that water injection and water flooding are essentially the same process, however, while in the case of former we inject the water in the water zone of the reservoir, in the latter we inject it directly into the hydrocarbon zone

title: Enhanced oil recovery


text:
Talk:Enhanced oil recovery

Added
A small description of EOR.Will add more in some time. Photographs coming up soon Yourdeadin 04:31, 19 August 2007 (UTC)Yourdeadin

title: Talk:Enhanced oil recovery


text: Talk:Reservoir engineering

title: Talk:Reservoir engineering


text:
BCP/Acalypha rhomboidea

Acalypha rhomboidea

title: BCP/Acalypha rhomboidea


text:
BCP/Acalypha rhomboidea/Logs

2007 Logs

 * --SB_Johnny | PA! 09:31, 23 July 2007 (UTC)
 * --SB_Johnny | PA! 10:48, 10 August 2007 (UTC)
 * --SB_Johnny | PA! 22:39, 19 August 2007 (UTC)
 * --SB_Johnny | talk 09:11, 1 September 2007 (UTC)
 * SB Johnny-LM 08:59, 8 September 2007 (UTC)
 * SBJ 18:24, 4 September 2007 (UTC)
 * --SB_Johnny | talk 10:04, 19 September 2007 (UTC)

2008 Logs

 * --SB_Johnny | talk 08:42, 14 July 2008 (UTC)
 * --SB_Johnny talk 10:27, 17 August 2008 (UTC)
 * Jomegat 19:08, 24 August 2008 (UTC)
 * Jomegat 00:10, 30 August 2008 (UTC)
 * Jomegat 23:19, 4 September 2008 (UTC)

title: BCP/Acalypha rhomboidea/Logs


text:
BCP/Kirengeshoma koreana

Kirengeshoma koreana

title: BCP/Kirengeshoma koreana


text:
BCP/Kirengeshoma koreana/Logs

This page contains recent bloom logs for the plant Kirengeshoma koreana (Kirengeshoma).

Recent Logs

 * --SB_Johnny | PA! 09:58, 11 August 2007 (UTC)

=====Archived Logs===== (If there are more than 5 signatures under the recent logs heading, move the oldest logs to under this heading (generally leave the 3 most recent).
 * (no archived logs yet)

title: BCP/Kirengeshoma koreana/Logs


text:
BCP/Hackelia virginiana

Hackelia virginiana

title: BCP/Hackelia virginiana


text:
BCP/Hackelia virginiana/Logs

This page contains recent bloom logs for the plant Hackelia virginiana (Beggar's Lice).

Recent Logs

 * --SB_Johnny | PA! 09:32, 15 July 2007 (UTC)
 * --SB_Johnny | PA! 13:47, 11 August 2007 (UTC) (mostly gone to seed, still blooming on terminals)
 * --SB_Johnny | talk 09:56, 14 July 2008 (UTC)

=====Archived Logs===== (If there are more than 5 signatures under the recent logs heading, move the oldest logs to under this heading (generally leave the 3 most recent).
 * (no archived logs yet)

title: BCP/Hackelia virginiana/Logs


text:
Help:Table2

Actual Example 1
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Actual Example 2
Image:Crystal Clear action 2uparrow.png

Or can be used like this:

Image:Crystal Clear action 2uparrow.png

Actual Example 4
A useful location finder for all Wikiversity pages.

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Practical Example 2
Table of contents

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#eeeeff" style="border: 1px #cccccc solid;" |Page 2: What is narrative music?
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#eeeeff" style="border: 1px #cccccc solid;" |Page 3: What computer software do I need?
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#eeeeff" style="border: 1px #cccccc solid;" |Page 4: Getting started with GarageBand
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#eeeeff" style="border: 1px #cccccc solid;" |Page 5: List of moods and actions for you to work on
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 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#eeeeff" style="border: 1px #cccccc solid;" |Page 6: Narrative music created by Mad Max's students
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#f0ffff" style="border: 1px #cccccc solid;" |Supplemental A: Examples of Narrative Music
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#f0ffff" style="border: 1px #cccccc solid;" |Supplemental B: A simple movie for scoring
 * }
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#eeeeff" style="border: 1px #cccccc solid;" |Page 2: What is narrative music?
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#eeeeff" style="border: 1px #cccccc solid;" |Page 3: What computer software do I need?
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#eeeeff" style="border: 1px #cccccc solid;" |Page 4: Getting started with GarageBand
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#eeeeff" style="border: 1px #cccccc solid;" |Page 5: List of moods and actions for you to work on
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#eeeeff" style="border: 1px #cccccc solid;" |Page 6: Narrative music created by Mad Max's students
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#f0ffff" style="border: 1px #cccccc solid;" |Supplemental A: Examples of Narrative Music
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#f0ffff" style="border: 1px #cccccc solid;" |Supplemental B: A simple movie for scoring
 * }
 * }

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Practical Example 3
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Practical Example 5
This is a film strip.

{| cellpadding="0" cellspacing="5" style="width: 500px; background-color: #e0e0ff; margin-left: auto; margin-right: auto"
 * style="width: 100%; background-color: white; border: 1px solid #777777; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" |

 * }

{| cellpadding="0" cellspacing="5" style="width: 500px; background-color: #e0e0ff; margin-left: auto; margin-right: auto"
 * style="width: 100%; background-color: white; border: 1px solid #777777; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" |

 * }

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Practical Example 7
A good way to close a lesson

{| cellpadding="20" cellspacing="5" style="width: 99%; background-color: inherit; margin-left: auto; margin-right: auto"
 * style="width: 100%; background-color: #ffffff; border: 1px solid #777777; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" rowspan="2" |

The Next Page

 * The next page tells you what to look for on the "Follow Dave?" Editing Workshop CD.
 * Page 1 - Disk contents of the "Follow Dave?" Editing Workshop CD [[Image:Crystal Clear action forward.png|24px]]

Contact Your Instructor

 * Your instructor for this class is Robert Elliott. To email me, you simply  Click Here. [[Image:Crystal Clear app xfmail.png|32px]]

 * }

{| cellpadding="20" cellspacing="5" style="width: 99%; background-color: inherit; margin-left: auto; margin-right: auto"
 * style="width: 100%; background-color: #ffffff; border: 1px solid #777777; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" rowspan="2" |

The Next Page

 * The next page tells you what to look for on the "Follow Dave?" Editing Workshop CD.
 * Page 1 - Disk contents of the "Follow Dave?" Editing Workshop CD [[Image:Crystal Clear action forward.png|24px]]

Contact Your Instructor

 * Your instructor for this class is Robert Elliott. To email me, you simply  Click Here. [[Image:Crystal Clear app xfmail.png|24px]]

 * }

---

.

Practical Example 10
A simple framework working example

{| cellspacing="0" cellpadding="0" style="margin:0em 0em 1em 0em; width:100%" A quick summary of this course
 * style="width:100%; vertical-align:top; border:1px solid #777; background-color:Cornsilk;" |

 * }

Practical Example 12
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{| cellpadding="20" cellspacing="5" style="width: 100%; background-color: inherit; margin-left: auto; margin-right: auto"
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 * }

title: Help:Table2


text:
User:Ldysnow

I love learning. Can't believe I just found this part of the site.

I currently want to learn Bulgarian, as I have friends I can practice with. In the future I will be learning other languages. Right now I speak English (my native), and Brazillian Portugues (not fluently, but I can hold a slow conversation).

title: User:Ldysnow


text:
User talk:Ldysnow

Salutations, Ldysnow! I'm Angelica Klosky, a fellow new student who discovered Wikiversity yesterday. Hopefully, we can band together and reform the L&L section of Humanities! (It's a mess, and I'm not entirely sure they have Bulgarian.)

Angelica Klosky 17:00, 19 August 2007 (UTC)

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

Also, don't forget to experiment with the links to your left. Be bold, and see you around Wikiversity! --JWSchmidt 17:13, 19 August 2007 (UTC)

title: User talk:Ldysnow


text:
Talk:Histology/Slide Preparation

I know this page is messy. The quiz is one I made up for classmates in our OSMT class.

Page name change
Hello, Is there any way the name of this page can be changed to "Introduction to Dynamic Histology"? Histology is a broad domain, and the study of tissues at the microscopic level is actually termed "dynamic histology". --Spyder212 (discuss • contribs) 22:45, 9 May 2015 (UTC)

 * Yes, but don't. Instead, consider either renaming it Histology, or create a parent page for Histology and then move this page under Histology as Histology/Dynamic Histology.  The reason being that there are hundreds of pages of Introduction to ..., and they prevent all of it from being located by quick search.  It's much easier if we name our major learning projects by the corresponding Wikipedia name, or that name as plural when we study multiples of them.

 * To rename, use the More link at the top of the page and "Move" the content. Moving will leave a redirect.  In this case, that's exactly what you want.  If you rename something and don't want the redirect, just add  at the top.

 * Dave Braunschweig (discuss • contribs) 02:40, 10 May 2015 (UTC)
 * Thank you! --Spyder212 (discuss • contribs) 04:07, 10 May 2015 (UTC)

title: Talk:Histology/Slide Preparation


text:
Fiction writing support group

Welcome to the Wikiversity Fiction writing support group. This is a "learn by doing" project in which participants share ideas and information about writing fiction.

Kellyv2. I am interested in fiction writing of the interraction of biological tissue and electronic devices in creating a super human, who hitherto has had mutation of his genes. Resulting in a special human species with a hiden powers whose full potential is revealed by the electronic devices. And the functioning of the device is possible only when individuals with same bloodline wore such device. Findout the mysteries behind the most gifted scientist and their beliefs and the outcome.

Reading and discussion
Reading about writing.

Advice to authors
There is no shortage of published authors willing to share advice about writing, but do they agree on anything?

If you are working towards the publication of a commercial novel, whether genre or literary upmarket, you have to understand your market and how to write for that market. Mysteries, thrillers, SF/F, etc., all have their foundational tropes while demanding of the new author the creation of high-concept premise within the parameters formed by those tropes.

Reading
Read: Writing advice by Chris Moriarty.
 * red comments by JWSchmidt
 * pink comments by Angelica Klosky
 * black comments by Michael Neff

Discussion

 * "Step 1: Read".
 * This "rule" makes me think that we should start a series of "book reports".....I'm thinking of short accounts of why we like particular works of fiction.
 * True, but it may be a warning of, "You are what you read." For instance, if you devour romantic comedies like a starving child would devour a ton of green-iced donuts (as I do- the books, not the donuts), sooner or later, that child will start to turn green, and you find all of your work being tainted by romance and comedy.
 * Read but also do hook, scene, and character arc analysis of your favorite authors, perhaps authors you might wish to emulate in some manner. Devour the mechanics and artistry of scene development as much as possible.

 * "Step 2: the key to successful writing is setting a regular writing schedule and sticking to it".
 * It makes me sad to think about "successful writers" who have to force themselves to write. Too bad there are not more writers who struggle to set a regular living schedule in order to keep from writing when they know they should be doing all the other things that make a complete life.
 * I struggle to set a regular living schedule so that I don't go blind!
 * The key to successful writing is also looking five years into the future and asking yourself where you want to be. Set a firm goal. Learn all you can and press forward.

 * "Step 3: Write what you love".
 * Another sad aspect of the writing world: that writers have to be reminded to have fun. Maybe for many professional writers it is important to be able to force yourself to write what sells even when you do not really enjoy doing it. Ick.
 * Yes, that is sad. Reminds me of the bad old days, during my time in the HM fandom, where I'd force myself to update every friday.
 * If you don't have passion for your genre, or the subject matter of the novel you are writing (or even short story or screenplay), you will never be a success because you won't have the stamina for rejection and multiple rewrites.

 * "Step 4: Imitation".
 * I like the idea of "studying" the work of other writers and learning from what others have written. I also like to imagine that after a certain amount of such "studying", every writer can reach the point where they create their own solutions to problems without having to copy what someone else did before.
 * See comment on Step 1.
 * Consider it rather like learning from the masters so that you can stand on their shoulders.

Rewriting
Advice on rewriting and the value of multiple versions of a story.

Reading

 * Falling In Love With a Serial Killer! by Evelyn David. "....it's fine to fall in love with one of your characters, enough to save her or him from the gallows, there are some pitfalls to these transformations. Here are some tips to consider before you start any revisions...."

 * Never a Dearer Friend: a Conversation with Dot Jackson
 * Jeremy Jones: "Would you agree that encountering multiple versions of the same story lends a particular vitality to the story?"
 * Dot Jackson: "Your perceptions are right on."

 * red comments by JWSchmidt

Discussion

 * "if you decide to fundamentally change a character, you've got to make sure that you go whole hog".
 * I think there is truth to this. You can try to be sly and make a major transformation of a character without doing a major re-write of the existing version of the story the character is in.....this is tempting....rewriting can be painful. However, rewriting can also be rewarding. Ludwig Wittgenstein, in describing what must be done to accomplish a complex task, wrote about the need to, "travel over a wide field of thought criss-cross in every direction". During such a process he found that, "the same points were always being approached afresh from new directions, and new sketches made." Eventually, after taking the time to explore the subject from several different perspectives you truly understand the landscape and can efficiently provide others with a well-crafted account.

 * "One of the many advantages of using a computer to write fiction is that you can work with multiple versions of a book at the same time. You can try a character 'on-for-size' and if the change doesn't work, you can hit the delete key".
 * I love the ways that computer technology empowers writers to go in directions that were not really possible before computers. Why does a story have to have one beginning, one middle and one end? Why not a couple of each? Even if in the end just one version that is the "best", the process of making multiple versions can be useful for developing a character.

You can be as unconventional with your style as you like..as long as it is not done out of ignorance.

Related resources

 * Introduction to Creative Writing
 * Composition
 * Exploring science through fiction
 * Science Fiction Challenge
 * Digital Storytelling
 * Computer Based Literature
 * Portal:Writing Center
 * Fiction writing

External resources

 * Creative Writing/Novels at Wikibooks.
 * Novelas - The fiction wikia. Collaborative fiction.
 * Advanced Novel and Fiction Craft from Author Salon by Michael Neff.
 * Young Writers Program - National Novel Writing Month
 * Rocky Mountain Fiction Writers - A "support group for writers of novel length fiction" with "more than 400 members, including more than 50 published novelists".
 * Writing fiction blog by Crawford Kilian.
 * The First Novelists' Handbook by Allen Meece.
 * Writing a novel - "Mini-course", includes, "finding the right ideas for a novel; fleshing the story out; creating reasons for readers to stick with your book; writing your first chapter". Links to h2g2; you need to create a free account before you can view the course.

title: Fiction writing support group


text:
User:Dkcreatto

About DkCreAtto
DkCreAtto is my alias, derived from DK-dhaval's knowledge base and Creation, which I often use when ever I want to join a community to prevent my privacy from malicious ones. My original name is Dhaval Shah. I am, for now, a student to bachelors in commerce in Gujarat University. Right now I am in my final year of graduation. You can find me at my PC, College, or any where around Ahmedabad, my hometown.

Latests
Working on several Wiki Projects. Apart from various projects I often love to check some articles and I am used to edit when ever I feel for some possibility of improvement.

In life, I am preparing for my MBA entrance. I am also planning to start my own web portal, but it'll take time.

Personal Info

title: User:Dkcreatto


text:
BCP/Verbena urticifolia

Verbena urticifolia

title: BCP/Verbena urticifolia


text:
BCP/Verbena urticifolia/Logs

2008 Logs

 * (no archived logs yet)

Recent Logs

 * --SB_Johnny | talk 16:41, 22 July 2007 (photolog)
 * --SB_Johnny | PA! 12:40, 19 August 2007 (UTC)
 * --SB_Johnny | talk 10:09, 20 July 2008 (UTC)
 * Jomegat 02:27, 13 August 2008 (UTC)
 * Jomegat 20 August, 2008

title: BCP/Verbena urticifolia/Logs


text:
Fiction writing support group/Participants

Introduce yourself and your fiction writing goals.

User:JWSchmidt. I've been an amateur writer of fiction for about thirty years. I enjoy using fiction to explore and play with new ideas. I'm particularly interested in hard science fiction, social science fiction and alternate history. I write fiction in order to explore ideas about how thinking creatures can arise and evolve, become aware of their place in the universe and then develop technology that allows them to shape themselves and their surroundings. I'm interested in using computer technology to explore new ways of producing and sharing fiction. I'd like to experiment with Wikiversity as a place where strangers can meet and collaborate on fiction writing projects and the development of new software tools that facilitate such collaborations. I think fiction writing has a bright future as part of Web 2.0....a future in which many more people will become creators and sharers of fiction rather than consumers of the few stale plots and stories that dominate a commercial market.--JWSchmidt 21:49, 19 August 2007 (UTC)

 * Angelica Klosky. I've been a fiction writer for most of the time that I've known how to use a pencil, but only in the last six months have I embarked on seriously writing a story that I intend for strangers to read. (My first attempt at this was a novella which died, incomplete, around the 20 thousandth word. The second, which is currently in progress, is going much better.) My goals are mainly to get all of the ideas driving me insane onto the screen. (The ideas for my latest story keep me up at night, and absolutely beg me to type them at 74 WPM.) Both of these stories were/are being released serially through The Internet, because I just couldn't pull these characters out of the video-game-universe that inspired them, darnit! (How this relates to Wikiversity: If anybody would like to help me reform the story so it's entirely original material in return, I would be infinitely grateful, and will totally try to help you with your fiction projects to the best of my ability.) --Angelica Klosky 22:34, 19 August 2007 (UTC)

 * Luai lashire. I've been making up stories in my head for as long as I can remember, and sometime in my early school years I began to write them down.  Most of what I write is novel-length fantasy, generally aimed at a young adult audience, though I dable in other genres and also write a lot of poetry.  My work is driven by intricate worldbuilding, which often interests me much more than the plot, although I try to have engaging plotlines too.   I like exploring ways societies would have developed differently with the powerful resource of magic to draw on.  I've had work published in literary magazines three times and am currently finishing my first novel, titled Sapphire Eyes (I'm currently at roughly 40,000 words and about two chapters from the end).  I would really enjoy sharing what I know about writing, getting useful critique, and collaborating with other writers to make a finished work.  --Luai lashire 19:00, 27 October 2007 (UTC)

 * Bryan See. I've been started making stories in my head for years, and sometime in 2005, particularly after the release of Star Wars Episode III, I started on the story of Fan Wars with the same plot from the 1999 fanfilm of the same name but with a different setting: Fans invading an apartment building, and the good men in the military and the government agents are trapped with no way of calling backup, as well as worldbuilding in my universe of which Fan Wars set in. My Fan Wars is right now in development hell, and yet most of my family are not in a position to help me in creative fiction writing right now. I like exploring the uses of realism and "naturalistic science fiction", a term coined by Ronald D. Moore, creator of the re-imagined Battlestar Galactica, because I believe it is perhaps the only way to take science fiction out of space opera, in which Star Wars and Star Trek are parts (I am a Star Wars and Star Trek fan). I didn't read books as of now, and I don't know about interesting, believable, compelling, and popular character building and creation, as well as most of the fiction writing itself. I like to share what I know about writing, getting useful critique, collaborating with other writers to make a finished work that will someday turn into a film, and need some writing advice and guide. Bryan See 16:09, 15 January 2008 (UTC)

 * User:KirbyPuckettFan. I have wanted to be a novelist since I was ten years old, and I like to think I have sufficient enough talent for it (I think dialogue is my strongest suit).  But I have a few weak points that I'd like to work on as a member of this group, the most discouraging being "discipline."  I just don't have enough of it to sustain writing like I should.  I have literally hundreds of opening sequences for stories that I've written and abandoned.  I'll get a flash of inspiration one day and just knock out one, two, three, four paragraphs (sometimes even one to two pages!) on the spot.  When I'm in the zone, writing, developing an idea, it's the best natural high ever.  But then I either run into a wall with the plot or lose interest in it all together.  When I come up with story ideas, I get lots of broad, sweeping ones that I think will be great, but once I try to fill in the specific details, I really struggle.  I need to find the structure and discipline that will prevent my stories from dying before they've even had a chance to live.  My other huge problem is a lack of "thick skin" and distance with regard to receiving constructive criticism of my work.  I need to work on separating myself from what I write, so that I no longer feel that someone pointing out a flaw in my story is somehow saying that I'm flawed as a person.  This is probably due in part to the fact that a lot of my main characters are fictional derivatives of my real self; I use fiction as a way to place myself in a more desirable state than the one in which reality has put me (I'm handicapped in a wheelchair with Cerebral Palsy).  My fiction allows me to escape my physical confines and live through my characters; I've lived a rather sheltered life and writing helps me use my imagination to escape it and reflect on it.  I've been told my writing is crisp and clear when I avoid abstractions and don't gloss over the details of a scene.  I'd like to work on improving as a writer.--KirbyPuckettFan 22:42, 21 October 2008 (UTC)

 * Davichito: I have been an amateur science fiction writer for six months but in this time I have written one novel, started another and wrote 3 full short stories. I like hard science fiction but I can include esoteric plots into it. See The search for Kalid, for instance. I like to write novels in collaboration; I have written one novel along with JWSchmidt. --Davichito 15:54, 27 October 2008 (UTC)

 * Trinity507: I've been writing pretty much as long as I can remember, primarily fiction. Originally my interests were in historical fiction, then they shifted to fantasy, and now rest primarily in science fiction. I've had a few of my reviews and poems published and have short stories in the works, as well as two full-length novels. Unfortunately my story attention span is very short so I'd like to improve my focus as well as my writing! :-) Trinity507 05:14, 17 October 2009 (UTC)


text:
BCP/Lobularia maritima/Logs

2007 Logs

 * SBJ 16:16, 7 June 2007 (UTC)
 * SortaQuiet 23:02, 17 June 2007 (UTC)
 * SBJ 16:16, 30 June 2007 (UTC)
 * SBJ 10:58, 15 August 2007 (UTC)
 * SBJ 08:49, 3 October 2007 (UTC)
 * --SB_Johnny | talk 22:44, 3 November 2007 (UTC)
 * SBJ 13:12, 29 November 2007 (UTC)

2008 Logs

 * --SB_Johnny talk 09:18, 23 September 2008 (UTC)

2009 Logs

 * (no archived logs yet)

Recent Logs

 * Jomegat 00:26, 9 June 2009 (UTC)

title: BCP/Lobularia maritima/Logs


text:
User:JWSchmidt/2006

Leave a message for JWSchmidt | my Wikiversity blog "Openness and inclusiveness are ..... our radical means to our radical ends." (source)

Jimmy Wales recently said, "I think we should run small experiments, tests, see what works, what doesn't, and be prepared to be flexible and change, and not be too locked into stone about how things should work."

I am interested in Wikiversity as a playground for explorers and active learners. I hope that the Wikiversity community can learn how to facilitate learning projects that will allow Wikiversity participants to reach and discover their learning goals. I became interested in Wikiversity back in 2004. After the 2005 community vote on the original Wikiversity project proposal the Board of Trustees asked for some changes to the proposal, I started conspiring with folks like Cormaggio to fix the Wikiversity proposal. I think the Board was correct to direct the Wikiversity community away from conventional courses. We need to find new ways to use wiki technology to facilitate online learning. Towards that end, a new Wikiversity model for e-learning was developed at the Wikimedia meta-wiki and included in the modified Wikiversity project proposal, as requested by the Board.

So the modified Wikiversity project proposal was finally approved. As an "emergency" measure, Cormaggio, acting as the first Wikiversity bureaucrat, made me a custodian on the English language Wikiversity. If you need the help of a custodian, use my talk page, send me an email, or go to the page that is used to Request custodian action.

Other Wiki Projects
On 27 February 2003 I registered as JWSchmidt on the English language Wikipedia. In December of 2005 I became an administrator at Wikipedia. There is more information about me on my Wikipedia user page. I am also a custodian at Wikiversity beta.

I remain intrigued and challenged by the way wiki projects first fragment then the fragments struggle to cooperate. I hope the Wikiversity community can support good editing for Wikibooks textbooks and Wikipedia encyclopedia articles.

Learning projects of interest

 * Jargon project - promotes use of hyperlinks, gloassaries, invitations for people to ask questions.
 * A. S. Neill School of Free Learning - students are assisted as they explore the topics that are of greatest personal interest.
 * Wiki learning project - explore how to use wikis in education
 * Learn to learn a wiki way
 * Human Genetic Uniqueness Project - What makes humans human?
 * Molecular Paleontology Reading Group
 * MediaWiki Project - develop new MediaWiki features for the Wikiversity community
 * Wikiversity NPC - $$$$$$$ for Wikiversity
 * Cell Biology - Hub for Cell Biology-related learning activities
 * Cell biology improvement drive - service project for Wikipedia
 * Citing Sources - Fostering the Wikiversity culture of scholarly citation of sources
 * Why 10 dimensions - learning about String theory
 * Wikiversity the Movie - need to link to from relevant pages
 * Wiki - learning how to use wiki technology to facilitate online learning.
 * Science as Religion - explore the relationships between science and religion
 * Science teaching materials for creationism - What should Wikiversity do if a an editor wants to add learning materials to Wikiversity that aim to teach creationism as science?
 * Unsolved problems in neuroscience
 * Free Will as control philosophytalk
 * Topic:New Age Religions
 * Consilience
 * Exploring science through fiction
 * Wikihigh
 * Stem Cells
 * Virtual cell project example
 * Introduction to Medical Microbiology
 * Sexually transmitted diseases/Sexually Transmitted Diseases
 * Infectious Disease and Public Health
 * Wikiversity scholarship learning project for all Wikiversity participants
 * Introduction to GarageBand
 * Nobel Prize in Physiology or Medicine

Divisions and Departments

 * Topic:Science research and the Law
 * Topic:Cell Biology
 * Topic:Basic sciences

Other

 * Comments on courses at Wikiversity.
 * History and visions
 * Wikipedia, the Free Online Encyclopedia, Ponders a New Entity: Wikiversity - old news (pre-launch)
 * It's New Media: But is it Art Education? by Trebor Scholz (links to wikiversity.org)

title: User:JWSchmidt/2006


text:
Continuum mechanics/Nonlinear elasticity

There are two types models of nonlinear elastic behavior that are in common use. These are :
 * Hyperelasticity
 * Hypoelasticity

Hyperelasticity
Hyperelastic materials are truly elastic in the sense that if a load is applied to such a material and then removed, the material returns to its original shape without any dissipation of energy in the process. In other word, a hyperelastic material stores energy during loading and releases exactly the same amount of energy during unloading. There is no path dependence.

If $$\psi\,$$ is the Helmholtz free energy, then the stress-strain behavior for such a material is given by

\boldsymbol{\sigma} = \rho~\boldsymbol{F}\bullet\cfrac{\partial \psi}{\partial \boldsymbol{E}}\bullet \boldsymbol{F}^T = 2~\rho~\boldsymbol{F}\bullet\cfrac{\partial \psi}{\partial \boldsymbol{C}}\bullet \boldsymbol{F}^T $$ where $$\boldsymbol{\sigma}$$ is the Cauchy stress, $$\rho$$ is the current mass density, $$\boldsymbol{F}$$ is the deformation gradient, $$\boldsymbol{E}$$ is the Lagrangian Green strain tensor, and $$\boldsymbol{C}$$ is the left Cauchy-Green deformation tensor.

We can use the relationship between the Cauchy stress and the 2nd Piola-Kirchhoff stress to obtain an alternative relation between stress and strain.

\boldsymbol{S} = 2~\rho_0~\cfrac{\partial \psi}{\partial \boldsymbol{C}} $$ where $$\boldsymbol{S}$$ is the 2nd Piola-Kirchhoff stress and $$\rho_0$$ is the mass density in the reference configuration.

Isotropic hyperelasticity
For isotropic materials, the free energy must be an isotropic function of $$\boldsymbol{C}$$. This also mean that the free energy must depend only on the principal invariants of $$\boldsymbol{C}$$ which are

\begin{align} I_{\boldsymbol{C}} = I_1 & = \text{tr}(\mathbf{C}) = C_{ii} = \lambda_1^2 + \lambda_2^2 + \lambda_3^2 \\ II_{\boldsymbol{C}} = I_2 & = \tfrac{1}{2}\left[\text{tr}(\mathbf{C}^2) - (\text{tr}~\mathbf{C})^2 \right] = \tfrac{1}{2}\left[C_{ik}C_{ki} - C_{jj}^2\right] = \lambda_1^2\lambda_2^2 + \lambda_2^2\lambda_3^2 + \lambda_3^2\lambda_1^2 \\ III_{\boldsymbol{C}} = I_3 & = \det(\mathbf{C}) = \lambda_1^2\lambda_2^2\lambda_3^2 \end{align} $$ In other words,

\psi(\boldsymbol{C}) \equiv \psi(I_1, I_2, I_3) $$ Therefore, from the chain rule,

\cfrac{\partial \psi}{\partial \boldsymbol{C}} = \cfrac{\partial\psi}{\partial I_1}~\cfrac{\partial I_1}{\partial\boldsymbol{C}} + \cfrac{\partial\psi}{\partial I_2}~\cfrac{\partial I_2}{\partial\boldsymbol{C}} + \cfrac{\partial\psi}{\partial I_3}~\cfrac{\partial I_3}{\partial\boldsymbol{C}} = a_0~\boldsymbol{\mathit{1}} + a_1~\boldsymbol{C} + a_2~\boldsymbol{C}^{-1} $$ From the Cayley-Hamilton theorem we can show that

\boldsymbol{C}^{-1} \equiv f(\boldsymbol{C}^2, \boldsymbol{C}, \boldsymbol{\mathit{1}}) $$ Hence we can also write

\cfrac{\partial \psi}{\partial \boldsymbol{C}} = b_0~\boldsymbol{\mathit{1}} + b_1~\boldsymbol{C} + b_2~\boldsymbol{C}^2 $$ The stress-strain relation can then be written as

\boldsymbol{S} = 2~\rho_0~\left[b_0~\boldsymbol{\mathit{1}} + b_1~\boldsymbol{C} + b_2~\boldsymbol{C}^2\right] $$ A similar relation can be obtained for the Cauchy stress which has the form

\boldsymbol{\sigma} = 2~\rho~\left[a_2~\boldsymbol{\mathit{1}} + a_0~\boldsymbol{B} + a_1~\boldsymbol{B}^2\right] $$ where $$\boldsymbol{B}$$ is the right Cauchy-Green deformation tensor.

Cauchy stress in terms of invariants
For isotropic hyperelastic materials, the Cauchy stress can be expressed in terms of the invariants of the left Cauchy-Green deformation tensor (or right Cauchy-Green deformation tensor). If the strain energy density function is $$W(\boldsymbol{F})=\hat{W}(I_1,I_2,I_3) = \bar{W}(\bar{I}_1,\bar{I}_2,J) = \tilde{W}(\lambda_1,\lambda_2,\lambda_3)$$, then

\begin{align} \boldsymbol{\sigma} & = \cfrac{2}{\sqrt{I_3}}\left[\left(\cfrac{\partial\hat{W}}{\partial I_1} + I_1~\cfrac{\partial\hat{W}}{\partial I_2}\right)\boldsymbol{B} - \cfrac{\partial\hat{W}}{\partial I_2}~\boldsymbol{B} \cdot\boldsymbol{B} \right] + 2\sqrt{I_3}~\cfrac{\partial\hat{W}}{\partial I_3}~\boldsymbol{\mathit{1}} \\ & = \cfrac{2}{J}\left[\cfrac{1}{J^{2/3}}\left(\cfrac{\partial\bar{W}}{\partial \bar{I}_1} + \bar{I}_1~\cfrac{\partial\bar{W}}{\partial \bar{I}_2}\right)\boldsymbol{B} - \cfrac{1}{3}\left(\bar{I}_1~\cfrac{\partial\bar{W}}{\partial \bar{I}_1} + 2~\bar{I}_2~\cfrac{\partial\bar{W}}{\partial \bar{I}_2}\right)\boldsymbol{\mathit{1}} - \right.\\ & \qquad \qquad \qquad \left. \cfrac{1}{J^{4/3}}~\cfrac{\partial\bar{W}}{\partial \bar{I}_2}~\boldsymbol{B} \cdot\boldsymbol{B} \right] + \cfrac{\partial\bar{W}}{\partial J}~\boldsymbol{\mathit{1}} \\ & = \cfrac{\lambda_1}{\lambda_1\lambda_2\lambda_3}~\cfrac{\partial\tilde{W}}{\partial \lambda_1}~\mathbf{n}_1\otimes\mathbf{n}_1 + \cfrac{\lambda_2}{\lambda_1\lambda_2\lambda_3}~\cfrac{\partial\tilde{W}}{\partial \lambda_2}~\mathbf{n}_2\otimes\mathbf{n}_2 + \cfrac{\lambda_3}{\lambda_1\lambda_2\lambda_3}~\cfrac{\partial\tilde{W}}{\partial \lambda_3}~\mathbf{n}_3\otimes\mathbf{n}_3 \end{align} $$ (See the page on the left Cauchy-Green deformation tensor for the definitions of these symbols).

 * {| class="toccolours collapsible collapsed" width="80%" style="text-align:left"

!Proof 1:
 * The second Piola-Kirchhoff stress tensor for a hyperelastic material is given by
 * The second Piola-Kirchhoff stress tensor for a hyperelastic material is given by

\boldsymbol{S} = 2~\cfrac{\partial W}{\partial \boldsymbol{C}} $$ where $$\boldsymbol{C} = \boldsymbol{F}^T\cdot\boldsymbol{F}$$ is the right Cauchy-Green deformation tensor and $$\boldsymbol{F}$$ is the deformation gradient. The Cauchy stress is given by

\boldsymbol{\sigma} = \cfrac{1}{J}~\boldsymbol{F}\cdot\boldsymbol{S}\cdot\boldsymbol{F}^T = \cfrac{2}{J}~\boldsymbol{F}\cdot\cfrac{\partial W}{\partial \boldsymbol{C}}\cdot\boldsymbol{F}^T $$ where $$J = \det\boldsymbol{F}$$. Let $$I_1, I_2, I_3$$ be the three principal invariants of $$\boldsymbol{C}$$. Then

\cfrac{\partial W}{\partial \boldsymbol{C}} = \cfrac{\partial W}{\partial I_1}~\cfrac{\partial I_1}{\partial \boldsymbol{C}} + \cfrac{\partial W}{\partial I_2}~\cfrac{\partial I_2}{\partial \boldsymbol{C}} + \cfrac{\partial W}{\partial I_3}~\cfrac{\partial I_3}{\partial \boldsymbol{C}} ~. $$ The derivatives of the invariants of the symmetric tensor $$\boldsymbol{C}$$ are

\frac{\partial I_1}{\partial \boldsymbol{C}} = \boldsymbol{\mathit{1}} ~; \frac{\partial I_2}{\partial \boldsymbol{C}} = I_1~\boldsymbol{\mathit{1}} - \boldsymbol{C} ~; \frac{\partial I_3}{\partial \boldsymbol{C}} = \det(\boldsymbol{C})~\boldsymbol{C}^{-1} $$ Therefore we can write

\cfrac{\partial W}{\partial \boldsymbol{C}} = \cfrac{\partial W}{\partial I_1}~\boldsymbol{\mathit{1}} + \cfrac{\partial W}{\partial I_2}~(I_1~\boldsymbol{\mathit{1}} - \boldsymbol{F}^T\cdot\boldsymbol{F}) + \cfrac{\partial W}{\partial I_3}~I_3~\boldsymbol{F}^{-1}\cdot\boldsymbol{F}^{-T} ~. $$ Plugging into the expression for the Cauchy stress gives

\boldsymbol{\sigma} = \cfrac{2}{J}~\left[\cfrac{\partial W}{\partial I_1}~\boldsymbol{F}\cdot\boldsymbol{F}^T+ \cfrac{\partial W}{\partial I_2}~(I_1~\boldsymbol{F}\cdot\boldsymbol{F}^T - \boldsymbol{F}\cdot\boldsymbol{F}^T\cdot\boldsymbol{F}\cdot\boldsymbol{F}^T) + \cfrac{\partial W}{\partial I_3}~I_3~\boldsymbol{\mathit{1}}\right] $$ Using the left Cauchy-Green deformation tensor $$\boldsymbol{B}=\boldsymbol{F}\cdot\boldsymbol{F}^T$$ and noting that $$I_3 = J^2$$, we can write

\boldsymbol{\sigma} = \cfrac{2}{\sqrt{I_3}}~\left[\left(\cfrac{\partial W}{\partial I_1} +          I_1~\cfrac{\partial W}{\partial I_2}\right)~\boldsymbol{B} - \cfrac{\partial W}{\partial I_2}~\boldsymbol{B}\cdot\boldsymbol{B}\right] + 2~\sqrt{I_3}~\cfrac{\partial W}{\partial I_3}~\boldsymbol{\mathit{1}}~. $$
 * }

 * {| class="toccolours collapsible collapsed" width="80%" style="text-align:left"

!Proof 2:
 * To express the Cauchy stress in terms of the invariants $$\bar{I}_1, \bar{I}_2, J$$ recall that
 * To express the Cauchy stress in terms of the invariants $$\bar{I}_1, \bar{I}_2, J$$ recall that

\bar{I}_1 = J^{-2/3}~I_1 = I_3^{-1/3}~I_1 ~; \bar{I}_2 = J^{-4/3}~I_2 = I_3^{-2/3}~I_2 ~; J = I_3^{1/2} ~. $$ The chain rule of differentiation gives us

\begin{align} \cfrac{\partial W}{\partial I_1} & = \cfrac{\partial W}{\partial \bar{I}_1}~\cfrac{\partial \bar{I}_1}{\partial I_1} + \cfrac{\partial W}{\partial \bar{I}_2}~\cfrac{\partial \bar{I}_2}{\partial I_1} + \cfrac{\partial W}{\partial J}~\cfrac{\partial J}{\partial I_1} \\ & = I_3^{-1/3}~\cfrac{\partial W}{\partial \bar{I}_1} = J^{-2/3}~\cfrac{\partial W}{\partial \bar{I}_1} \\ \cfrac{\partial W}{\partial I_2} & = \cfrac{\partial W}{\partial \bar{I}_1}~\cfrac{\partial \bar{I}_1}{\partial I_2} + \cfrac{\partial W}{\partial \bar{I}_2}~\cfrac{\partial \bar{I}_2}{\partial I_2} + \cfrac{\partial W}{\partial J}~\cfrac{\partial J}{\partial I_2} \\ & = I_3^{-2/3}~\cfrac{\partial W}{\partial \bar{I}_2} = J^{-4/3}~\cfrac{\partial W}{\partial \bar{I}_2} \\ \cfrac{\partial W}{\partial I_3} & = \cfrac{\partial W}{\partial \bar{I}_1}~\cfrac{\partial \bar{I}_1}{\partial I_3} + \cfrac{\partial W}{\partial \bar{I}_2}~\cfrac{\partial \bar{I}_2}{\partial I_3} + \cfrac{\partial W}{\partial J}~\cfrac{\partial J}{\partial I_3} \\ & = - \cfrac{1}{3}~I_3^{-4/3}~I_1~\cfrac{\partial W}{\partial \bar{I}_1} - \cfrac{2}{3}~I_3^{-5/3}~I_2~\cfrac{\partial W}{\partial \bar{I}_2} + \cfrac{1}{2}~I_3^{-1/2}~\cfrac{\partial W}{\partial J} \\ & = - \cfrac{1}{3}~J^{-8/3}~J^{2/3}~\bar{I}_1~\cfrac{\partial W}{\partial \bar{I}_1} - \cfrac{2}{3}~J^{-10/3}~J^{4/3}~\bar{I}_2~\cfrac{\partial W}{\partial \bar{I}_2} + \cfrac{1}{2}~J^{-1}~\cfrac{\partial W}{\partial J} \\ & = -\cfrac{1}{3}~J^{-2}~\left(\bar{I}_1~\cfrac{\partial W}{\partial \bar{I}_1}+     2~\bar{I}_2~\cfrac{\partial W}{\partial \bar{I}_2}\right) + \cfrac{1}{2}~J^{-1}~\cfrac{\partial W}{\partial J} \end{align} $$ Recall that the Cauchy stress is given by

\boldsymbol{\sigma} = \cfrac{2}{\sqrt{I_3}}~\left[\left(\cfrac{\partial W}{\partial I_1} +          I_1~\cfrac{\partial W}{\partial I_2}\right)~\boldsymbol{B} - \cfrac{\partial W}{\partial I_2}~\boldsymbol{B}\cdot\boldsymbol{B}\right] + 2~\sqrt{I_3}~\cfrac{\partial W}{\partial I_3}~\boldsymbol{\mathit{1}}~. $$ In terms of the invariants $$\bar{I}_1, \bar{I}_2, J$$ we have

\boldsymbol{\sigma} = \cfrac{2}{J}~\left[\left(\cfrac{\partial W}{\partial I_1}+          J^{2/3}~\bar{I}_1~\cfrac{\partial W}{\partial I_2}\right)~\boldsymbol{B} - \cfrac{\partial W}{\partial I_2}~\boldsymbol{B}\cdot\boldsymbol{B}\right] + 2~J~\cfrac{\partial W}{\partial I_3}~\boldsymbol{\mathit{1}}~. $$ Plugging in the expressions for the derivatives of $$W$$ in terms of $$\bar{I}_1, \bar{I}_2, J$$, we have

\begin{align} \boldsymbol{\sigma} & = \cfrac{2}{J}~\left[\left(J^{-2/3}~\cfrac{\partial W}{\partial \bar{I}_1} +          J^{-2/3}~\bar{I}_1~\cfrac{\partial W}{\partial \bar{I}_2}\right)~\boldsymbol{B} - J^{-4/3}~\cfrac{\partial W}{\partial \bar{I}_2}~\boldsymbol{B}\cdot\boldsymbol{B}\right] + \\    & \qquad 2~J~\left[-\cfrac{1}{3}~J^{-2}~\left(\bar{I}_1~\cfrac{\partial W}{\partial \bar{I}_1}+     2~\bar{I}_2~\cfrac{\partial W}{\partial \bar{I}_2}\right) + \cfrac{1}{2}~J^{-1}~\cfrac{\partial W}{\partial J}\right]~\boldsymbol{\mathit{1}} \end{align} $$ or,

\begin{align} \boldsymbol{\sigma} & = \cfrac{2}{J}~\left[\cfrac{1}{J^{2/3}}~\left(\cfrac{\partial W}{\partial \bar{I}_1} +          \bar{I}_1~\cfrac{\partial W}{\partial \bar{I}_2}\right)~\boldsymbol{B} - \cfrac{1}{3}\left(\bar{I}_1~\cfrac{\partial W}{\partial \bar{I}_1}+                           2~\bar{I}_2~\cfrac{\partial W}{\partial \bar{I}_2}\right)\boldsymbol{\mathit{1}} - \right. \\    & \qquad \left. \cfrac{1}{J^{4/3}}~ \cfrac{\partial W}{\partial \bar{I}_2}~\boldsymbol{B}\cdot\boldsymbol{B}\right] + \cfrac{\partial W}{\partial J}~\boldsymbol{\mathit{1}} \end{align} $$
 * }

 * {| class="toccolours collapsible collapsed" width="80%" style="text-align:left"

!Proof 3:
 * To express the Cauchy stress in terms of the stretches $$\lambda_1, \lambda_2, \lambda_3$$ recall that
 * To express the Cauchy stress in terms of the stretches $$\lambda_1, \lambda_2, \lambda_3$$ recall that

\cfrac{\partial \lambda_i}{\partial\boldsymbol{C}} = \cfrac{1}{2\lambda_i}~\boldsymbol{R}^T\cdot(\mathbf{n}_i\otimes\mathbf{n}_i)\cdot\boldsymbol{R}~; i = 1,2,3 ~. $$ The chain rule gives

\begin{align} \cfrac{\partial W}{\partial\boldsymbol{C}} & = \cfrac{\partial W}{\partial \lambda_1}~\cfrac{\partial \lambda_1}{\partial\boldsymbol{C}} + \cfrac{\partial W}{\partial \lambda_2}~\cfrac{\partial \lambda_2}{\partial\boldsymbol{C}} + \cfrac{\partial W}{\partial \lambda_3}~\cfrac{\partial \lambda_3}{\partial\boldsymbol{C}} \\ & = \boldsymbol{R}^T\cdot\left[\cfrac{1}{2\lambda_1}~\cfrac{\partial W}{\partial \lambda_1}~\mathbf{n}_1\otimes\mathbf{n}_1 + \cfrac{1}{2\lambda_2}~\cfrac{\partial W}{\partial \lambda_2}~\mathbf{n}_2\otimes\mathbf{n}_2 + \cfrac{1}{2\lambda_3}~\cfrac{\partial W}{\partial \lambda_3}~\mathbf{n}_3\otimes\mathbf{n}_3\right]\cdot\boldsymbol{R} \end{align} $$ The Cauchy stress is given by

\boldsymbol{\sigma} = \cfrac{2}{J}~\boldsymbol{F}\cdot \cfrac{\partial W}{\partial \boldsymbol{C}}\cdot\boldsymbol{F}^T = \cfrac{2}{J}~(\boldsymbol{V}\cdot\boldsymbol{R})\cdot \cfrac{\partial W}{\partial \boldsymbol{C}}\cdot(\boldsymbol{R}^T\cdot\boldsymbol{V}) $$ Plugging in the expression for the derivative of $$W$$ leads to

\boldsymbol{\sigma} = \cfrac{2}{J}~\boldsymbol{V}\cdot \left[\cfrac{1}{2\lambda_1}~ \cfrac{\partial W}{\partial \lambda_1}~\mathbf{n}_1\otimes\mathbf{n}_1 + \cfrac{1}{2\lambda_2}~ \cfrac{\partial W}{\partial \lambda_2}~\mathbf{n}_2\otimes\mathbf{n}_2 + \cfrac{1}{2\lambda_3}~ \cfrac{\partial W}{\partial \lambda_3}~\mathbf{n}_3\otimes\mathbf{n}_3\right] \cdot\boldsymbol{V} $$ Using the spectral decomposition of $$\boldsymbol{V}$$ we have

\boldsymbol{V}\cdot(\mathbf{n}_i\otimes\mathbf{n}_i)\cdot\boldsymbol{V} = \lambda_i^2~\mathbf{n}_i\otimes\mathbf{n}_i ~; i=1,2,3. $$ Also note that

J = \det(\boldsymbol{F}) = \det(\boldsymbol{V})\det(\boldsymbol{R}) = \det(\boldsymbol{V}) = \lambda_1\lambda_2\lambda_3 ~. $$ Therefore the expression for the Cauchy stress can be written as

\boldsymbol{\sigma} = \cfrac{1}{\lambda_1\lambda_2\lambda_3}~ \left[\lambda_1~\cfrac{\partial W}{\partial \lambda_1}~\mathbf{n}_1\otimes\mathbf{n}_1 + \lambda_2~\cfrac{\partial W}{\partial \lambda_2}~\mathbf{n}_2\otimes\mathbf{n}_2 + \lambda_3~\cfrac{\partial W}{\partial \lambda_3}~\mathbf{n}_3\otimes\mathbf{n}_3 \right] $$
 * }

Saint-Venant–Kirchhoff material
The simplest constitutive relationship that satisfies the requirements of hyperelasticity is the Saint-Venant–Kirchhoff material, which has a response function of the form

\boldsymbol{S} = \lambda~\text{tr}(\boldsymbol{E})~\boldsymbol{\mathit{1}} + 2~\mu~\boldsymbol{E} , $$ where $$\lambda$$ and $$\mu$$ are material constants that have to be determined by experiments. Such a linear relation is physically possible only for small strains.


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User:Lisasmall

Lisa Small is an attorney admitted to practice in the State of Maryland and before the United States Supreme Court. She is a former member of the Bar of the State of Pennsylvania.

Not every attorney named "Lisa Small" is this Lisa Small.

She is also a contributor to Wikipedia and Wiktionary.

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User talk:Lisasmall

Hello Lisasmall, 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:
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User:Joachim Grzega/AHEL

An Introduction to Applied Historical English Linguistics

= Goals of the Course =

The goal of this course is to provide learners with skills that allow them to answer questions on “irregular” forms and “strange” phenomena of present-day English with historical linguistic knowledge. Learners shall acquire knowledge of the basic developments in English language history and shall get a primary insight into the literature of earlier periods of English. This wikicourse book tries to use already existing Wikimedia material as far as possible.

= Structure of the Course =

Each lesson, or chapter, first presents the core knowledge for the corresponding topic. Key-terms will occur in boldprint. In a second section, the learners are encouraged to think about a number of questions. The questions can be discussed on the talk page.

The single lessons are:
 * 1) General Introduction
 * 2) Phonology and Spelling
 * 3) Morphology and Syntax: Nouns and Adjectives
 * 4) Morphology and Syntax: Pronouns
 * 5) Morphology: Verbal System
 * 6) Syntax
 * 7) Lexicology: Creating New Words
 * 8) Lexicology: Re-Applying Old Words
 * 9) Pragmatics and Text Linguistics
 * 10) Dialects and Sociohistorical Linguistics
 * 11) Medieval and Early Modern Literature

= Credit for the Course (Portfolio) =

In contrast to prior courses I've held, crediting will this time be based on a portfolio. You can decide whether you want to get 6 cr. (Übungsschein), 10 cr. (Proseminarschein) or 15 cr. (Hauptseminarschein). Apart from the two compulsory elements, the choice of assignments is up to you. The completion of the portfolio will be due on 15 March 2008 (but single elements can, of course, be handed in earlier).

(Grading [6-grade system]: Ü 6-5/4/3/2/1/0, PS 10-9/8-7/6-5/4-3/2-1/0, HS 15-13/12-10/9-7/6-4/3-1/0)
 * compulsory: I’ve led one session of the course in a team: I’ve delved into one sub-branch of English historical linguistics, conveyed the core knowledge in class and answered questions of class participants. (2 cr.)
 * compulsory: learning biography: (1) I’ve written a list of target(-competence)s that I’ve set myself at the beginning of this class, given reasons for these target(-competence)s; (2) at the end of this class I have noted down which of these I have realized and self-evaluated the overall quality of my learning progress based on the corrections of the instructor. (1 cr.)
 * I’ve handed in the preparatory work for four sessions (a written copy has to be handed in before the class starts). (1 cr.)
 * I’ve drawn a 2-page table of the most important phonetic developments with examples of my choice (to be used for exam prep later). (1 cr.)
 * I’ve drawn a 2-page table of the most important developments of nominal inflections with examples of my choice (to be used for exam prep later). (1 cr.)
 * I’ve drawn a 2-page table of the most important developments of verbal inflections with examples of my choice (to be used for exam prep later). (1 cr.)
 * I’ve drawn a 2-page table of the most important loanword layers with examples of my choice (to be used for exam prep later). (1 cr.)
 * I’ve composed index cards showing the development of 7 frequent verbs (to be used for exam prep later; a list with possible items will be handed out in class). (1 cr.)
 * I’ve composed index cards showing the development of the designations of 5 concepts (to be used for exam prep later; a list with possible items will be handed out in class). (1 cr.)
 * I’ve composed index cards showing the development of the semantic development of 7 words (to be used for exam prep later; possible items will be given in class). (1 cr.)
 * I’ve composed a bibliography on a diachronic topic of my choice (I’ve also given a reason for my choice). (1 cr.)
 * I’ve selected an Old English text (from the Anglo-Saxon reader) of about 30 lines and translated it literally (I’ve also given a reason for my choice). (1 cr.)
 * I’ve selected Middle English text (from Chaucer’s works) of about 50 lines and translated it literally (I’ve also given a reason for my choice). (1 cr.)
 * I’ve summarized (as an abstract) an article from the field of historical English linguistics which appeared in an academic journal (no longer than 30 lines) (I’ve also given a reason for my choice). (1 cr.)
 * I’ve written a review of about 3 pages on a monograph of my choice from the field of historical English linguistics (I’ve also given a reason for my choice). (2 cr.)
 * I’ve written a 5-page academic essay on a diachronic question of my choice. (2 cr.)
 * I’ve contrasted the phonetic, morphological or lexical variants from three varieties of English (standard or non-standard) for one linguistic variable and explained them historically (1 p.).
 * I’ve written three popular linguistic contributions of about 15 lines on a layperson’s diachronic question. (1 cr.)
 * I’ve contributed at least 15 lines to an already existing or new Wikipedia article from the field of historical English linguistics. (1 p.)

= Recommended Literature =

Among the printed literature, learners may want to consult the following books:
 * Baugh, Albert C. / Cable, Thomas (1978), A History of the English Language, 3rd ed., London: Routledge & Kegan Paul.
 * Denison, David (1993), English Historical Syntax: Verbal Constructions, London et al.: Longman.
 * Görlach, Manfred (1997), The Linguistic History of English, Basingstoke: Macmillan. (important is the collection of synoptic Bible texts)
 * Hogg, Richard M. (ed.) (1992-2002), The Cambridge History of the English Language, 6 vols., Cambridge: Cambridge University Press.
 * Jucker, Andreas H. (2000), History of English and English Historical Linguistics, Stuttgart: Klett.
 * Mitchell, Bruce (1995), An Invitation to Old English and Anglo-Saxon England, Oxford: Blackwell.
 * Mitchell, Bruce / Robinson, Fred C. (1994), A Guide to Old English, revised ed. with texts and glossary, Oxford: Blackwell.
 * Nielsen, Hans Frede (1998), The Continental Backgrounds of English and Its Insular Development until 1154, [North-Western Language Evolution Supplement 19], Odense: Odense University Press.
 * Scragg, D. G. (1974), A History of English Spelling, Manchester: Manchester University Press.

Good introductions in other languages are:
 * Brunner, Karl (1960-1962), Die englische Sprache, 2 vols., 2., rev. ed., Tübingen: Niemeyer.
 * Fichte, Joerg O. / Kemmler, Fritz (1994), Alt- und Mittelenglische Literatur: Eine Einführung, 2., compl. rev. ed.., [Literaturwissenschaft im Grundstudium 6], Tübingen: Narr.
 * Obst, Wolfgang / Schleburg, Florian (1999), Die Sprache Chaucers: Ein Lehrbuch des Mittelenglischen auf der Grundlage von Troilus and Criseyde, Heidelberg: Winter.
 * Obst, Wolfgang / Schleburg, Florian (2004), Lehrbuch des Altenglischen, Heidelberg: Winter.

Important text collections:
 * Corpus of Middle English Prose and Verse, ed. by the Humanities Texts Initiative.
 * The Riverside Chaucer (1987), ed. by Larry D. Benson, Oxford: Oxford University Press.
 * Sweet’s Anglo-Saxon Reader in Prose and Verse (1967), revised throughout by Dorothy Whitelock, Oxford: Clarendon.

Important dictionaries and linguistic atlasses:
 * BoTo = Bosworth, Joseph & Toller, Thomas Northcote (1898), An Anglo-Saxon Dictionary, repr. and enlarged ed., London: Oxford University Press; (1921), An Anglo-Saxon Dictionary—Supplement, London: Oxford University Press.
 * EDD = Wright, Joseph (1898-1905), The English Dialect Dictionary: Complete Vocabulary of All Dialect Words Still in Use, or Known to Have Been in Use During the Last Two-Hundred Years, Oxford: Oxford University Press.
 * MED = Kurath, Hans et al. (1956-2001), Middle English Dictionary, Ann Arbor (Michigan): University of Michigan Press. [available as part of the Middle English Compendium online
 * OEC = DiPaolo Healey, Antonette (ed.) (2000), Dictionary of Old English – Old English Corpus. Ann Arbor: University of Michigan Press.
 * OED = Murray, James A. H. et al. (1928ff), The Oxford English Dictionary. Oxford: Oxford University Press.
 * SED = Orton, Harold & Dieth, Eugen (1964-1971), Survey of English Dialects, Leeds: Arnold.
 * TOE = Roberts, Jane et al. (1995), A Thesaurus of Old English [King’s College London medieval studies 11], London: King’s College London, Centre for Late Antique and Medieval Studies.

Etymological dictionaries:
 * Klein = Klein, Ernest (1966/1967), A Comprehensive Etymological Dictionary of the English Language Amsterdam: Elsevier.
 * ODEE = Onions, C. T. (1966), The Oxford Dictionary of English Etymology, with the assistance of G. W. S. Friedrichsen and R. W. Burchfield, Oxford: Clarendon.
 * OED = Murray, James A. H. et al. (1928ff), The Oxford English Dictionary. Oxford: Oxford University Press.
 * Terasawa, Yoshio (1998), The Kenkyusha Dictionary of English Etymology, Tokyo: Kenkyusha.

There are also some useful internet links

 * the Wikipedia article Old English
 * the Wikipedia article English
 * the Wikipedia article Early Modern English
 * the Online Etymology Dictionary

=Lessons=

Core Knowledge
English language history is normally divided into the following periods:
 * 450 (449) – 1100 (1066) Old English (Anglo-Saxon): the language of Beowulf
 * 1100 (1066) – 1500 (1476/1492) Middle English: the language of Chaucer
 * 1500 (1476/1492) – 1700 (1776) Early Modern English: the language of Shakespeare
 * 1700 (1776) – present Modern English

Read the following Wikipedia articles:
 * English language
 * History of the English Language
 * Language Change

Make yourself familiar with the books listed in the bibliography and think for what kind of questions (phonetic, morphological, syntactic, lexical, pragmatic) each single work might especially be helpful in later sessions.

You may want to start reading some short Bible passages in a synoptic way to get accustomed to older stages of the English language (cf. also the remarks in the last lesson).

Questions

 * What criteria is the periodization of English language history based on?
 * What is meant by the following terms: Norman Conquest, West Saxon, Anglo-Saxons?

Core Knowledge
Read the following Wikipedia articles:
 * History of the English Language
 * Great Vowel Shift
 * History of the English Spelling System

Make yourself particularly familiar with the following notions (you may need to consult books from the list of recommended literature beyond the Wikipedia articles): the ME sound system (roughly), the development of OE /y/, the elements of the Great Vowel Shift, the developments of ME /u/, vowels before /r/, OE and ME voice opposition in fricatives, the developments of ME /x/, /k-/, /g-/ and stress; the OE sound system (roughly), the developments of OE /a:/ and diphthongs, quantitative changes from OE to ME, the developments of OE geminates, i-umlaut, Grimm's law

Questions

 * How can the discrepancy between ModE spelling and pronunciation be explained?
 * How do you explain in the homophonies of write:right, wear:where? How do you explain the homographies in (vb.:adj.), (sb.:vb.), and (sb.:vb.)?
 * What are the differences between BrE and AmE pronunciation and how do you explain them: forehead, gooseberry, dance, clerk?
 * How do you explain the discrepancy between and [ˈbɪzi]?
 * How do you explain the phonetic history of o’clock, gospel, woman, lord, lady, daisy?
 * What is Grimm's law? Why is this phenomenon called a law? What does it have to do with Grimm Brothers?
 * How do you explain the use of the apostrophe with the possessive marker (e.g. Uncle Tom’s Cabin).

Core Knowledge
Read the respective sections of the Wikipedia articles:
 * Old English Morphology
 * Middle English

Make yourself particularly familiar with the following notions (you may need to consult books from the list of recommended literature beyond the Wikipedia articles): a-stems (in detail), ō-stems, root nouns, n-stems, further development of OE declension classes, further development of plural formations, further development of the OE possessive case, further development of grammatical gender, OE strong and weak adjective patterns and their further developments, OE gradation patterns of adjectives and their further development

Questions

 * How do you explain the following irregular plural forms: feet, women, oxen, dice, children, wives?
 * How do you explain the existence of the following double plural forms: brothers~brethren, mice~mouses, appendices~appendixes, referendums~referenda, fish~fishes, hoofs~hooves
 * We can sometimes read: “America and her 50 states”, “The Titanic—she is the most known ship world-wide.” Moreover, in British and American dialects we find many more instances of he and she with reference to inanimate objects.
 * Explain how we got the choice between I gave my dad this book and I gave this book to my dad.
 * Explain how we got the choice between my dad’s book and the book of my dad.
 * Explain how we got the choice between happier and more happy.
 * Adverbs are regularly formed with -ly. But how did we get the difference between he is a a hard-working man vs. he is a hardly working man?

Core Knowledge
Read the respective sections of the Wikipedia articles:
 * Old English Morphology
 * Middle English

Make yourself particularly familiar with the following notions (you may need to consult books from the list of recommended literature beyond the Wikipedia articles): personal pronouns of the 2nd sg. vs. 2nd pl., 3rd pl., 3rd sg. fem., 3rd sg. neut.; this/that/these/those, a(n)/the

Questions

 * Explain why there is only one form you for both one addressee and more than one addressee.
 * Comment on the bold-printed parts of the following Bible quotation (AV): “Ye are the salt of the earth: but if the salt have lost his savour, wherewith shall it be salted” (Mt 5.13)
 * Comment on the bold-printed parts of the following Bible quotations (AV): “Whether of the twain will ye that I release unto you?”
 * Comment on the bold-printed parts of the following Bible quotation (AV): “Thou preparest a table before me in the presence of mine enemies: thou anointest my [in some editions also: mine] head with oil; my cup runneth over” (Ps 23.5).
 * Where does the form ’em as often found in written reflections of colloquial speech come from?
 * Explain how we got the choice between a and an.
 * Explain how we got the choice between Everybody has his rights ~ Everybody has one’s rights ~ Everybody has their rights.

Core Knowledge
Read the respective sections of the Wikipedia articles:
 * Old English Morphology
 * Middle English

Make yourself particularly familiar with the following notions (you may need to consult books from the list of recommended literature beyond the Wikipedia articles): strong verb system (classes I, III, IV, V in detail), weak verb system (class II in detail), preterite-present verbs, ablaut, grammatical change, suppletion, development of future tenses, development of subjunctive, development of 3sg. ending

Questions

 * How do you explain that the paradigm of be is I am, you are, he/she/it is, not I be, you be, he/she/it bes?
 * The two basic ways of forming the preterite is attaching -ed or changing the stem vowel. The form kept seems to be a mixture of both. Is there an historical explanation?
 * Where does the past tense went come from?
 * How do you explain the number opposition was vs. were, absent with other verbs?
 * How do you explain the difference between EnglE dive—dived—dived vs. AmE dive—dove—dived?
 * Comment on the bold-printed parts of the following Bible quotation (AV): “Thou preparest a table before me in the presence of mine enemies: thou anointest my head with oil; my cup runneth over” (Ps 23.5).
 * How do you explain that there is no -s with he can/could/shall/should/may/might/ought to/must/will?

Core Knowledge
Make yourself particularly familiar with the following notions (you may need to consult books from the list of recommended literature beyond the Wikipedia articles): word-order patterns (sentence elements, noun phrases, verb phrases) in OE/ME/ModE, relative clauses

Questions

 * How do we explain that it is possible to use need and dare either as full verbs or as auxiliary verbs? Is there a difference in meaning?
 * How do we explain the many future forms (will do, be going to do, will be doing, be doing, do, will have done)?
 * Why is it God save the queen, not God saves the queen or May God save the queen?
 * Why is there are differentiation between simple and progressive?
 * Why is there a variation in the following sentences? Is there a difference in meaning? (a) A whole bunch of students is/are waiting out there. (b) The orchestra is/are rehearsing right now.
 * Why do we have to use an auxiliary do to form a question?
 * How come that in an English passive sentence the subject can also go back to the indirect and not necessarily to the direct object of the active clause?

Lexicology: Creating New Words
A speech community can find designations by way of word-formation, by way of borrowing or by way of semantic change. The first two shall be the topic of this lesson, the latter on the topic of next lesson.

Read the following Wikipedia articles (or section of articles):
 * onomasiology
 * classification of borrowings
 * semantic change

A student-friendly introduction to historical lexicology is the book English and General Historical Lexicology (by Joachim Grzega and Marion Schöner).

Core Knowledge
Make yourself particularly familiar with the following notions (you may need to consult books from the list of recommended literature beyond the Wikipedia articles): loanword sources in OE (Celtic, Latin, Scandinavian), calques, later loanword sources (northern French, Parisian French, Latin & Greek, other languages), (morphological) dissociation, consociated vocabulary, hard words, inkhorn terms, opaque compounds, transparency, popular etymology, etymological dublets, cognates, prominent word-formation patterns in OE/ME/ModE (esp. agent-noun formation, conversion), superstratum, substratum

Questions

 * Where does the from -wright as in playwright come from? Explain what elements the OE consisted of and say what happened to these elements in course of time.
 * How are the words dish, disc, disk, discus, desk, dais related?
 * Where do the following words come from? What is special about them? chestnut, mistletoe, peacock, Sunday, Saturday, mutton, OE leorning-cniht vs. ME/ModE disciple, ask vs. question vs. interrogate
 * English distinguishes between living animal and dead animal as food: swine/pig—pork, calf—veal, ox—beef, deer—venison. Where does this differentation go back to?
 * Many anatomic terms are inherited and shared by both English and German (and other Germanic relatives), e.g. heart—Herz, lung—Lunge, blood—Blut, tongue—Zunge. But how can we explain the discrepancy between kidney and Niere?
 * Not infrequently you find inherited terms aside from Latin terms in English everyday language: what’s the difference between fatherly—paternal, deep—profound, building—edifice?
 * How do you explain the syntax in secretary general and princess royal?

Core Knowledge
Make yourself particularly familiar with the Bloomfield's, Ullmann's, Blank's and Grzega's typologies of semantic change.

Questions

 * The words ill, sky, nay, die, take, cast, skin, raise, (to and) fro are Scandinavisms. What happened to the original English words?
 * Describe the further history of the OE words sǣlig ‘happy,’ cniht ‘boy,’ cnafa ‘boy’, cwene ‘girl’?
 * What do the terms sandwich, boycott and kleenex have in common?
 * The semantic ranges of the following terms differ in EnglE and AmE: sick, student, bug, pants, chips, to be through (on the phone). What are the differences and how do you explain them?
 * Explain the use and history of let in the formula without let or hindrance.
 * Explain why corn means ‛wheat’ in England, ‛oats’ in Scotland and ‛maize’ in the US.
 * In older songs of the 20th c. you can still hear a couple of a boy and a girl being described as “gay”: What’s the semantic history of this word?

Core Knowledge
Read the following Wikipedia article:
 * Historical Pragmatics

A more thorough introduction with examples is given in Jucker (2000). As an example for a study in the field of historical pragmatics you should read the article "Adieu, Bye-Bye, Cheerio: The ABC of Leave-Taking Terms in English Language History" (by Joachim Grzega).

Questions

 * How do you explain the existence of one pronoun only as both an informal and a formal address term (you), in comparison to other European languages.
 * Explain the history of the following salutation terms: Welcome!, Hi!, How do you do!, Hello!, Good-bye!, Cheerio!
 * What’s the history of the word please and its use?
 * Where does the interjection Gee! come from and how did we get this ModE result?
 * In polls and archaic speech you can occasionally read or hear yea and nay instead of yes and no. Where do these forms come from?
 * In e-mails we not infrequently come across the preposition re and the verb to cc. What’s the origin of these terms?
 * The more formal the style, the higher the probability that you will step over one of the following abbreviations in an English text: etc., e.g., i.e., cf., et al., viz., RSVP, Esq., &. What do these signs mean, where do they come from?

Dialects and Sociohistorical Linguistics
Read the following Wikipedia articles:
 * Dialectology
 * Sociohistorical Linguistics
 * Survey of English Dialects

A more thorough introduction with examples is given in Jucker (2000).

Questions

 * Where do General American (GA) and Received Pronunciation (RP) originate in?
 * Is it true that American English is more innovative and that British English is more conservative.
 * In IrE the present perfect of some verbs is formed with be instead of have, e.g. He is gone out, she is run to the store, he is come in, she is swum to other side of the river, he is stood up. Do you see any system? Where does it come from?
 * A Cockney cab driver tells a professor: In Hapril there’s halways a big festival at the Hapollo Theater and some other ’ouses. Explain these aberrations from standard speech.
 * Explain the following differences.
 * StandE:	I love, you love, he/she/it loves, we love, they love
 * Wessex:	I loves, you loves, he/she/it loves, we loves, they loves
 * East Anglia: I love, you love, he/she/it love, we love, they love
 * Here are some features of African American Vernacular English (AAVE). Try to explain them historically: (a) existential it: it is a lot of a people here, (b) lack of copula vs. habitual be: He busy right now vs. He be busy every Monday. (c) lack of 3rd sg. marker: She like ice-cream very much.
 * Is there any medieval work where English authors play with dialects, comparable, for instance, to Mark Twain, who played with dialect in Huckleberry Finn?

Core Knowledge
The earliest document of the English language are glosses. The most important literary work of the OE period is the epic Beowulf. Apart from that a linguistically as well as historically interesting work is the Anglo-Saxon Chronicle, or Peterborough Chronicle, shedding light on English history until 1154. The most important piece of ME literary work are the Canterbury Tales by Geoffrey Chaucer. The most important writer of EME is William Shakespeare. Read the respective Wikipedia articles.

The Wikisource project offers the following texts:
 * the Bible (see especially the West-Saxon version, Wycliffe's version and the Authorised Version)
 * Beowulf
 * the Canterbury Tales

You can actually hear Chaucer texts on The Chaucer MetaPage

You may want to proceed your voyage into older English literature the following way:
 * 1) synoptic reading of Bible passages
 * 2) Shakespearean texts
 * 3) introduction of the Canterbury Tales
 * 4) Anglo-Saxon chronicle
 * 5) other passage from the Canterbury Tales, other OE texts from the Anglo-Saxon reader
 * 6) Beowulf

Questions

 * Give an outline of the Beowulf story.
 * What is the structure of the Canterbury Tales?
 * Is Shakespeare's language conservative or innovative for his times?

title: User:Joachim Grzega/AHEL


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File:Jhenryconrad scr-seduced by the Dark Side.pdf

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


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Musical instruments/Ocarina

The ocarina is a woodwind instrument developed in 19th Century Italy. Earlier instruments existed which functioned in the same manner, namely a globular flute with fipple mouthpiece, including the bird whistles of the North and South American Indians and the gemshorns of Renaissance Europe. But the earlier antecedents of the ocarina did not have enough range to be widely used as musical instruments.

The 19th Century ocarina was made of clay, and had a range of over an octave. The shape was similar to a sweet potato. Sets of ocarinas in various sizes were made, and small orchestras toured playing light classics on them, popularizing the instrument throughout Europe. They were also exported to the United States by the early 20th Century and sold by the popular catalogue merchants, such as Sears.

The Ocarina in Video Games

Most likely because of its beautiful tone, the Ocarina was featured in one of the most famous Video Games of all time. The Legend of Zelda: Ocarina of Time used the ocarina as a teleportation device, among other things. While pressing the "C-Stick", players can produce different notes on the Ocarina, and by using the "D-Pad", players can produce Flat and Sharp notes on the Ocarina.

title: Musical instruments/Ocarina


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Applied linear operators and spectral methods

Welcome to this learning project about !

Learning Project Summary

 * Project code:
 * Suggested Prerequisites:
 * Introduction to real analysis
 * Introduction to ordinary differential equations
 * Time investment: 6 months
 * Portal:Mathematics
 * School:Applied Mathematics
 * Level: Graduate

Content summary
The course covers the theory of linear operators applied to matrix, differential, and integral equations. We also discuss Fredholdm integral equations and spectral theory.

Goals
This learning project aims to help applied mathematicians and engineers gain the understanding needed to read and critically assess papers that deal with functional analysis in its various forms.

We will talk about operator theory and linear operators as applied to functional analysis.

Readings and other resources

 * Principles of Applied Mathematics, Transformation and Approximation: 2nd Edition, by J. Keener, 2000.
 * Green's Functions and Boundary Value Problems, by Ivar Stakgold, Wiley.
 * Methods of Modern Mathematical Physics. I - Functional Analysis, by Michael Read and Barry Simon, Elsevier.
 * Applied Functional Analysis: Applications to Mathematical Physics, by Eberhard Zeidler, Springer Series on the Applied Mathematical Sciences, vol. 108. This is a more technical book than the others..
 * Applied Functional Analysis: Main Principles and their Applications, by Eberhard Zeidler, Springer Series on the Applied Mathematical Sciences, vol. 109. This is a more technical book than the others..

Lectures

 * Lecture 1: Linear vector spaces
 * Lecture 2: Normed inner product spaces, orthogonal vectors, linear operators
 * Lecture 3: Adjoint operators, spectral theory for matrices
 * Lecture 4: More on spectral decompositions
 * Differentiation of distributions
 * Convergence of distributions
 * Differential equations in the sense of distributions
 * Differentiation of distributions with severe discontinuities
 * Green's functions for linear differential operators

Assignments

 * Assignment 1: ...


text:
Category:Functional analysis

This category deals with all aspects of functional analysis.

ru:Категория:Функциональный анализ

title: Category:Functional analysis


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User:Eye.vulgar

Khob inam az khoone zendegie maa to wiki! alan hosele nadaram doros hesaaabi dorostesh konam, baashe vaaase badan!

title: User:Eye.vulgar