Gradient - Revision history

Rsalter at 17:35, 4 April 2018

2018-04-04T17:35:48Z

← Older revision		Revision as of 17:35, 4 April 2018
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	Your model should now be ready to run, and should look something like this:		Your model should now be ready to run, and should look something like this:
	[[File:gradient_model.png\|~~left~~\|Thumb]]		[[File:gradient_model.png\|center\|Thumb]]

	Finally, set your DT to be 0.01 and the Method to be RT4. We are ready to run the model. Click launch, then run, and graphical output should be visible on your graph. Notice how the two stocks meet in the middle at 300? Your stocks have reached equilibrium, and your graph should look something like this:		Finally, set your DT to be 0.01 and the Method to be RT4. We are ready to run the model. Click launch, then run, and graphical output should be visible on your graph. Notice how the two stocks meet in the middle at 300? Your stocks have reached equilibrium, and your graph should look something like this:

	[[File:gradient.png\|~~left~~\|Thumb]]		[[File:gradient.png\|center\|Thumb]]

Rsalter at 17:35, 4 April 2018

2018-04-04T17:35:08Z

← Older revision		Revision as of 17:35, 4 April 2018
Line 13:		Line 13:

	Your model should now be ready to run, and should look something like this:		Your model should now be ready to run, and should look something like this:
	[[File:gradient_model.png\|Thumb]]		[[File:gradient_model.png\|left\|Thumb]]

	Finally, set your DT to be 0.01 and the Method to be RT4. We are ready to run the model. Click launch, then run, and graphical output should be visible on your graph. Notice how the two stocks meet in the middle at 300? Your stocks have reached equilibrium, and your graph should look something like this:		Finally, set your DT to be 0.01 and the Method to be RT4. We are ready to run the model. Click launch, then run, and graphical output should be visible on your graph. Notice how the two stocks meet in the middle at 300? Your stocks have reached equilibrium, and your graph should look something like this:

	[[File:gradient.png\|Thumb]]		[[File:gradient.png\|left\|Thumb]]

Rsalter at 17:18, 4 April 2018

2018-04-04T17:18:04Z

← Older revision		Revision as of 17:18, 4 April 2018
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	Now lets make a graph to visually represent changes in stocks 1 and 2. Drag a '''LineGraph''' onto the canvas and name it '''Contents'''. Select stocks 1 and 2 to be graphed in the time series.		Now lets make a graph to visually represent changes in stocks 1 and 2. Drag a '''LineGraph''' onto the canvas and name it '''Contents'''. Select stocks 1 and 2 to be graphed in the time series.

	~~Finally, set your DT to be 0.01 and the Method to be RT4.~~ Your model should now be ready to run, and should look something like this:		Your model should now be ready to run, and should look something like this:
	[[File:gradient_model.png\|Thumb]]		[[File:gradient_model.png\|Thumb]]

	We are ready to run the model. Click launch, then run, and graphical output should be visible on your graph. Notice how the two stocks meet in the middle at 300? Your stocks have reached equilibrium, and your graph should look something like this:		Finally, set your DT to be 0.01 and the Method to be RT4. We are ready to run the model. Click launch, then run, and graphical output should be visible on your graph. Notice how the two stocks meet in the middle at 300? Your stocks have reached equilibrium, and your graph should look something like this:

	[[File:gradient.png\|Thumb]]		[[File:gradient.png\|Thumb]]

Rsalter at 17:17, 4 April 2018

2018-04-04T17:17:25Z

← Older revision		Revision as of 17:17, 4 April 2018
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	Now lets make a graph to visually represent changes in stocks 1 and 2. Drag a '''LineGraph''' onto the canvas and name it '''Contents'''. Select stocks 1 and 2 to be graphed in the time series.		Now lets make a graph to visually represent changes in stocks 1 and 2. Drag a '''LineGraph''' onto the canvas and name it '''Contents'''. Select stocks 1 and 2 to be graphed in the time series.

	Your model should now be ready to run, and should look something like this:		Finally, set your DT to be 0.01 and the Method to be RT4. Your model should now be ready to run, and should look something like this:
	[[File:gradient_model.png\|Thumb]]		[[File:gradient_model.png\|Thumb]]

Rsalter at 17:16, 4 April 2018

2018-04-04T17:16:16Z

← Older revision		Revision as of 17:16, 4 April 2018
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	Your model should now be ready to run, and should look something like this:		Your model should now be ready to run, and should look something like this:
	[[File:gradient_model\|Thumb]]		[[File:gradient_model.png\|Thumb]]

			We are ready to run the model. Click launch, then run, and graphical output should be visible on your graph. Notice how the two stocks meet in the middle at 300? Your stocks have reached equilibrium, and your graph should look something like this:

	[[File:gradient.png\|Thumb]]		[[File:gradient.png\|Thumb]]

	For this model, let”s set both stocks on the same scale. To do this, select a stock, select “self” from the dropdown menu by scale, and set the scale of the y-axis from 0 to 60, then click set. Do this for both stocks, and then click “ok.” Plotting these on the same scale makes it much easier to observe diffusion in action.
	We are ready to run the model. Click on the lambda icon, then capture, load, and run, and graphical output should be visible on your graph. Notice how the two stocks meet in the middle at 30? Your stocks have reached equilibrium, and your graph should look something like this:

Rsalter at 17:14, 4 April 2018

2018-04-04T17:14:41Z

← Older revision		Revision as of 17:14, 4 April 2018
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	In this tutorial we will consider a system in which some currency is transferred from one stock to another in a manner that is dependent on some diffusion constant K multiplied by the difference in concentration between the two stocks. Thus, this is ultimately a model of diffusion, and this formulation can be applied to many kinds of natural phenomena.		In this tutorial we will consider a system in which some currency is transferred from one stock to another in a manner that is dependent on some diffusion constant K multiplied by the difference in concentration between the two stocks. Thus, this is ultimately a model of diffusion, and this formulation can be applied to many kinds of natural phenomena.

	First, we will need two stocks, let”s call them '''stock_1''' and '''stock_2'''. You can imagine any kind of currency within these stocks: ions, water, nutrients, etc. Let”s set the initial conditions as stock_1 = 10 and stock_2 = 50.		First, we will need two stocks, let”s call them '''stock_1''' and '''stock_2'''. You can imagine any kind of currency within these stocks: ions, water, nutrients, etc. Let”s set the initial conditions as stock_1 = 100 and stock_2 = 500.
	Place stock_2 to the right of stock_1, but be sure to leave space for a flow in between them.		Place stock_2 to the right of stock_1, but be sure to leave space for a flow in between them.

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	Next, we”ll need a diffusion constant. Drag out a term and name this constant '''K''', and we”ll say it has a value of 0.3.		Next, we”ll need a diffusion constant. Drag out a term and name this constant '''K''', and we”ll say it has a value of 0.3.

	Now we need to configure the equation within our flow. Use connectors to connect both stocks and K to the flow. Now, view the flow's properties and set the equation to be K*(stock_1-stock2). Since this is a biflow, if the difference is positive (if stock_1 > stock_2) it will diffuse in the forward direction, and if the difference is negative (stock_2 > stock_1), it will diffuse in the backward direction. ~~Click Ok. Your model should now be ready to run, and should look something like this:~~		Now we need to configure the equation within our flow. Use connectors to connect both stocks and K to the flow. Now, view the flow's properties and set the equation to be <code>K*(stock_1-stock2)</code>. Since this is a biflow, if the difference is positive (if stock_1 > stock_2) it will diffuse in the forward direction, and if the difference is negative (stock_2 > stock_1), it will diffuse in the backward direction.

			Now lets make a graph to visually represent changes in stocks 1 and 2. Drag a '''LineGraph''' onto the canvas and name it '''Contents'''. Select stocks 1 and 2 to be graphed in the time series.

	~~Now lets make a graph to visually represent changes in stocks 1 and 2. Click on graph and click on the blank space next~~ to ~~your model. Let”s name the graph “diffusion.” Right click on the graph~~, and ~~select stocks 1 and 2 to be graphed in time series~~. For this model, let”s set both stocks on the same scale. To do this, select a stock, select “self” from the dropdown menu by scale, and set the scale of the y-axis from 0 to 60, then click set. Do this for both stocks, and then click “ok.” Plotting these on the same scale makes it much easier to observe diffusion in action.		Your model should now be ready to run, and should look something like this:
			[[File:gradient_model\|Thumb]]

			[[File:gradient.png\|Thumb]]

			For this model, let”s set both stocks on the same scale. To do this, select a stock, select “self” from the dropdown menu by scale, and set the scale of the y-axis from 0 to 60, then click set. Do this for both stocks, and then click “ok.” Plotting these on the same scale makes it much easier to observe diffusion in action.
	We are ready to run the model. Click on the lambda icon, then capture, load, and run, and graphical output should be visible on your graph. Notice how the two stocks meet in the middle at 30? Your stocks have reached equilibrium, and your graph should look something like this:		We are ready to run the model. Click on the lambda icon, then capture, load, and run, and graphical output should be visible on your graph. Notice how the two stocks meet in the middle at 30? Your stocks have reached equilibrium, and your graph should look something like this:

Rsalter at 16:54, 4 April 2018

2018-04-04T16:54:56Z

← Older revision		Revision as of 16:54, 4 April 2018
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	In this tutorial we will consider a system in which some currency is transferred from one stock to another in a manner that is dependent on some diffusion constant K multiplied by the difference in concentration between the two stocks. Thus, this is ultimately a model of diffusion, and this formulation can be applied to many kinds of natural phenomena.		In this tutorial we will consider a system in which some currency is transferred from one stock to another in a manner that is dependent on some diffusion constant K multiplied by the difference in concentration between the two stocks. Thus, this is ultimately a model of diffusion, and this formulation can be applied to many kinds of natural phenomena.

	First, we will need two stocks, let”s call them '''~~stock 1~~''' and '''~~stock 2~~'''. You can imagine any kind of currency within these stocks: ions, water, nutrients, etc. Let”s set the initial conditions as ~~stock 1~~ = 10 and ~~stock 2~~ = 50.		First, we will need two stocks, let”s call them '''stock_1''' and '''stock_2'''. You can imagine any kind of currency within these stocks: ions, water, nutrients, etc. Let”s set the initial conditions as stock_1 = 10 and stock_2 = 50.
	Place ~~stock 2~~ to the right of ~~stock 1~~, but be sure to leave space for a flow in between them.		Place stock_2 to the right of stock_1, but be sure to leave space for a flow in between them.

	Now we will need a flow connecting the two stocks. For the sake of this model, we will just name it '''flow''' and you can imagine this flow as any number of paths or processes: the vasculature of a plant, an ion channel on a cell, and so on. Since this is the thing carrying our currency from one stock to another, it is quite analogous to vasculature or other mechanisms of nutrient transfer in living things. In this case, this flow should be a '''biflow''', because the currency can diffuse in either direction depending on the gradient. Connect the clouds of this biflow to each stock.		Now we will need a flow connecting the two stocks. For the sake of this model, we will just name it '''flow''' and you can imagine this flow as any number of paths or processes: the vasculature of a plant, an ion channel on a cell, and so on. Since this is the thing carrying our currency from one stock to another, it is quite analogous to vasculature or other mechanisms of nutrient transfer in living things. In this case, this flow should be a '''biflow''', because the currency can diffuse in either direction depending on the gradient. Connect the clouds of this biflow to each stock.
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	Next, we”ll need a diffusion constant. Drag out a term and name this constant '''K''', and we”ll say it has a value of 0.3.		Next, we”ll need a diffusion constant. Drag out a term and name this constant '''K''', and we”ll say it has a value of 0.3.

	Now we need to configure the equation within our flow. Use connectors to connect both stocks and K to the flow. Now, view the flow's properties and set the equation to be K*(~~stock 1~~-stock2). Since this is a biflow, if the difference is positive (if ~~stock 1~~ > ~~stock 2~~) it will diffuse in the forward direction, and if the difference is negative (~~stock 2~~ > ~~stock 1~~), it will diffuse in the backward direction. Click Ok. Your model should now be ready to run, and should look something like this:		Now we need to configure the equation within our flow. Use connectors to connect both stocks and K to the flow. Now, view the flow's properties and set the equation to be K*(stock_1-stock2). Since this is a biflow, if the difference is positive (if stock_1 > stock_2) it will diffuse in the forward direction, and if the difference is negative (stock_2 > stock_1), it will diffuse in the backward direction. Click Ok. Your model should now be ready to run, and should look something like this:


	Now lets make a graph to visually represent changes in stocks 1 and 2. Click on graph and click on the blank space next to your model. Let”s name the graph “diffusion.” Right click on the graph, and select stocks 1 and 2 to be graphed in time series. For this model, let”s set both stocks on the same scale. To do this, select a stock, select “self” from the dropdown menu by scale, and set the scale of the y-axis from 0 to 60, then click set. Do this for both stocks, and then click “ok.” Plotting these on the same scale makes it much easier to observe diffusion in action.		Now lets make a graph to visually represent changes in stocks 1 and 2. Click on graph and click on the blank space next to your model. Let”s name the graph “diffusion.” Right click on the graph, and select stocks 1 and 2 to be graphed in time series. For this model, let”s set both stocks on the same scale. To do this, select a stock, select “self” from the dropdown menu by scale, and set the scale of the y-axis from 0 to 60, then click set. Do this for both stocks, and then click “ok.” Plotting these on the same scale makes it much easier to observe diffusion in action.
	We are ready to run the model. Click on the lambda icon, then capture, load, and run, and graphical output should be visible on your graph. Notice how the two stocks meet in the middle at 30? Your stocks have reached equilibrium, and your graph should look something like this:		We are ready to run the model. Click on the lambda icon, then capture, load, and run, and graphical output should be visible on your graph. Notice how the two stocks meet in the middle at 30? Your stocks have reached equilibrium, and your graph should look something like this:

Rsalter: /* Gradient Tutorial */

2018-04-04T16:53:21Z

Gradient Tutorial

← Older revision		Revision as of 16:53, 4 April 2018
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	~~==Gradient Tutorial==~~
	In this tutorial we will consider a system in which some currency is transferred from one stock to another in a manner that is dependent on some diffusion constant K multiplied by the difference in concentration between the two stocks. Thus, this is ultimately a model of diffusion, and this formulation can be applied to many kinds of natural phenomena.		In this tutorial we will consider a system in which some currency is transferred from one stock to another in a manner that is dependent on some diffusion constant K multiplied by the difference in concentration between the two stocks. Thus, this is ultimately a model of diffusion, and this formulation can be applied to many kinds of natural phenomena.

	First, we will need two stocks, let”s call them ~~“stock 1”~~ and ~~“stock~~ 2.” You can imagine any kind of currency within these stocks: ions, water, nutrients, etc. Let”s set the initial conditions as stock 1 = 10 and stock 2 = 50. Place stock 2 to the right of stock 1, but be sure to leave space for a flow ~~inbetween~~ them.		First, we will need two stocks, let”s call them '''stock 1''' and '''stock 2'''. You can imagine any kind of currency within these stocks: ions, water, nutrients, etc. Let”s set the initial conditions as stock 1 = 10 and stock 2 = 50.
	Now we will need a flow connecting the two stocks. For the sake of this model, we will just name it ~~“flow”~~ and you can imagine this flow as any number of paths or processes: the vasculature of a plant, an ion channel on a cell, and so on. Since this is the thing carrying our currency from one stock to another, it is quite analogous to vasculature or other mechanisms of nutrient transfer in living things. In this case, this flow should be a biflow, because the currency can diffuse in either direction depending on the gradient. Connect the clouds of this biflow to each stock.		Place stock 2 to the right of stock 1, but be sure to leave space for a flow in between them.
	Next, we”ll need a diffusion constant. ~~Click on the~~ term ~~button~~ and ~~click above our flow. Let”s~~ name ~~the~~ constant “K,” and we”ll say it has a value of 0.3.
	Now we need to configure the equation within our flow. Use ~~red arrows~~ to connect both stocks and K to the flow. Now, ~~right click on~~ the flow, and ~~using the list displayed on the left of the window,~~ set the equation = K*(stock 1-stock2). Since this is a biflow, if the difference is positive (if stock 1 > stock 2) it will diffuse in the forward direction, and if the difference is negative (stock 2 > stock 1), it will diffuse in the backward direction. Click Ok. Your model should now be ready to run, and should look something like this:		Now we will need a flow connecting the two stocks. For the sake of this model, we will just name it '''flow''' and you can imagine this flow as any number of paths or processes: the vasculature of a plant, an ion channel on a cell, and so on. Since this is the thing carrying our currency from one stock to another, it is quite analogous to vasculature or other mechanisms of nutrient transfer in living things. In this case, this flow should be a '''biflow''', because the currency can diffuse in either direction depending on the gradient. Connect the clouds of this biflow to each stock.

			Next, we”ll need a diffusion constant. Drag out a term and name this constant '''K''', and we”ll say it has a value of 0.3.

			Now we need to configure the equation within our flow. Use connectors to connect both stocks and K to the flow. Now, view the flow's properties and set the equation to be K*(stock 1-stock2). Since this is a biflow, if the difference is positive (if stock 1 > stock 2) it will diffuse in the forward direction, and if the difference is negative (stock 2 > stock 1), it will diffuse in the backward direction. Click Ok. Your model should now be ready to run, and should look something like this:


	Now lets make a graph to visually represent changes in stocks 1 and 2. Click on graph and click on the blank space next to your model. Let”s name the graph “diffusion.” Right click on the graph, and select stocks 1 and 2 to be graphed in time series. For this model, let”s set both stocks on the same scale. To do this, select a stock, select “self” from the dropdown menu by scale, and set the scale of the y-axis from 0 to 60, then click set. Do this for both stocks, and then click “ok.” Plotting these on the same scale makes it much easier to observe diffusion in action.		Now lets make a graph to visually represent changes in stocks 1 and 2. Click on graph and click on the blank space next to your model. Let”s name the graph “diffusion.” Right click on the graph, and select stocks 1 and 2 to be graphed in time series. For this model, let”s set both stocks on the same scale. To do this, select a stock, select “self” from the dropdown menu by scale, and set the scale of the y-axis from 0 to 60, then click set. Do this for both stocks, and then click “ok.” Plotting these on the same scale makes it much easier to observe diffusion in action.
	We are ready to run the model. Click on the lambda icon, then capture, load, and run, and graphical output should be visible on your graph. Notice how the two stocks meet in the middle at 30? Your stocks have reached equilibrium, and your graph should look something like this:		We are ready to run the model. Click on the lambda icon, then capture, load, and run, and graphical output should be visible on your graph. Notice how the two stocks meet in the middle at 30? Your stocks have reached equilibrium, and your graph should look something like this:

Rsalter: Created page with "==Gradient Tutorial== In this tutorial we will consider a system in which some currency is transferred from one stock to another in a manner that is dependent on some diffusio..."

2018-04-04T16:48:35Z

Created page with "==Gradient Tutorial== In this tutorial we will consider a system in which some currency is transferred from one stock to another in a manner that is dependent on some diffusio..."

New page

==Gradient Tutorial==
In this tutorial we will consider a system in which some currency is transferred from one stock to another in a manner that is dependent on some diffusion constant K multiplied by the difference in concentration between the two stocks. Thus, this is ultimately a model of diffusion, and this formulation can be applied to many kinds of natural phenomena.

First, we will need two stocks, let”s call them “stock 1” and “stock 2.” You can imagine any kind of currency within these stocks: ions, water, nutrients, etc. Let”s set the initial conditions as stock 1 = 10 and stock 2 = 50. Place stock 2 to the right of stock 1, but be sure to leave space for a flow inbetween them.
Now we will need a flow connecting the two stocks. For the sake of this model, we will just name it “flow” and you can imagine this flow as any number of paths or processes: the vasculature of a plant, an ion channel on a cell, and so on. Since this is the thing carrying our currency from one stock to another, it is quite analogous to vasculature or other mechanisms of nutrient transfer in living things. In this case, this flow should be a biflow, because the currency can diffuse in either direction depending on the gradient. Connect the clouds of this biflow to each stock.
Next, we”ll need a diffusion constant. Click on the term button and click above our flow. Let”s name the constant “K,” and we”ll say it has a value of 0.3.
Now we need to configure the equation within our flow. Use red arrows to connect both stocks and K to the flow. Now, right click on the flow, and using the list displayed on the left of the window, set the equation = K*(stock 1-stock2). Since this is a biflow, if the difference is positive (if stock 1 > stock 2) it will diffuse in the forward direction, and if the difference is negative (stock 2 > stock 1), it will diffuse in the backward direction. Click Ok. Your model should now be ready to run, and should look something like this:

Now lets make a graph to visually represent changes in stocks 1 and 2. Click on graph and click on the blank space next to your model. Let”s name the graph “diffusion.” Right click on the graph, and select stocks 1 and 2 to be graphed in time series. For this model, let”s set both stocks on the same scale. To do this, select a stock, select “self” from the dropdown menu by scale, and set the scale of the y-axis from 0 to 60, then click set. Do this for both stocks, and then click “ok.” Plotting these on the same scale makes it much easier to observe diffusion in action.
We are ready to run the model. Click on the lambda icon, then capture, load, and run, and graphical output should be visible on your graph. Notice how the two stocks meet in the middle at 30? Your stocks have reached equilibrium, and your graph should look something like this: