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2021/2022 Training Classes

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Luca Richardson
Luca Richardson

Too Much Light [v0.5e Max]

It may not seem like we did much there, but this is the foundation for solving equations in the future. Before we get to solving equations, we have a few more details to consider. Next, we consider evaluating functions on arrays of values.

Too Much Light [v0.5e Max]

Suppose we have a parameter that has two different values depending on the value of a dimensionless number. For example when the dimensionless number is much less than 1, x = 2/3, and when x is much greater than 1, x = 1. We desire a smooth transition from 2/3 to 1 as a function of x to avoid discontinuities in functions of x. We will adapt the smooth transitions between functions to be a smooth transition between constants.

The loop method is straightforward to code, and looks alot like the formula that defines the trapezoid method. the vectorized methods are not as easy to read, and take fewer lines of code to write. However, the vectorized methods are much faster than the loop, so the loss of readability could be worth it for very large problems.

A common need in engineering calculations is to integrate an equation over some range to determine the total change. For example, say we know the volumetric flow changes with time according to \(d\nu/dt = \alpha t\), where \(\alpha = 1\) L/min and we want to know how much liquid flows into a tank over 10 minutes if the volumetric flowrate is \(\nu_0 = 5\) L/min at \(t=0\). The answer to that question is the value of this integral: \(V = \int_0^10 \nu_0 + \alpha t dt\).

You can see a slight trend of decreasing value of the residuals as the Temperature increases. This may indicate a deficiency in the model with no intercept. For the ideal gas law in degC: \(PV = nR(T+273)\) or \(P = nR/V*T + 273*nR/V\), so the intercept is expected to be non-zero in this case. Specifically, we expect the intercept to be 273*R*n/V. Since the molar density of a gas is pretty small, the intercept may be close to, but not equal to zero. That is why the fit still looks ok, but is not as good as letting the intercept be a fitting parameter. That is an example of the deficiency in our model.

The odds of you winning the last bet are slightly stacked in your favor. There is only a 49% chance your friend wins, but a 51% chance that you win. Lets play the game a lot of times times and see how many times you win, and your friend wins. First, lets generate a bunch of numbers and look at the distribution with a histogram.

You can see that the 1/interpolated f(x) underestimates the value, while interpolated (1/f(x)) overestimates the value. This is an example of where you clearly need more data in that range to make good estimates. Neither interpolation method is doing a great job. The trouble in reality is that you often do not know the real function to do this analysis. Here you can say the time is probably between 3.6 and 5.5 where 1/f(t) = 100, but you can not read much more than that into it. If you need a more precise answer, you need better data, or you need to use an approach other than interpolation. For example, you could fit an exponential function to the data and use that to estimate values at other times.

When we have data at two points but we need data in between them we use interpolation. Suppose we have the points (4,3) and (6,2) and we want to know the value of y at x=4.65, assuming y varies linearly between these points. we use the interp1d command to achieve this. The syntax in python is slightly different than in matlab.

There is some minor disagreement between the final transient solution and the steady state solution. That is due to the approximation in discretizing the reactor volume. In this example we used 100 nodes. You get better agreement with a larger number of nodes, say 200 or more. Of course, it takes slightly longer to compute then, since the number of coupled odes is equal to the number of nodes.

Let us define some commands that will take datasring as an argument, and return the modified text. The idea is to find all the cmds, and then run them. We use python's eval command to get the function handle from a string, and the cmd functions all take a datastring argument (we define them that way). We will create commands to replace :cmd:`datastring` with html code for a light gray background, and :red:`some text` with html code making the text red.

A slightly harder example is to find all the words that are actually numbers. We could use a regular expression for that, but we will instead use a function we create. We use a function that tries to cast a word as a float. If this fails, we know the word is not a float, so we return False.

In the end, we have illustrated how to construct a spline smoothing interpolation function and to find maxima in the function, including generating some initial guesses. There is more art to this than you might like, since you have to judge how much smoothing is enough or too much. With too much, you may smooth peaks out. With too little, noise may be mistaken for peaks.

The fits are not perfect. The small peak is pretty good, but there is an unphysical tail on the larger peak, and a small mismatch at the peak. There is not much to do about that, it means the model peak we are using is not a good model for the peak. We will still integrate the areas though.

Since there is no change in moles for this reaction, we can directly calculation the pressures from the equilibrium conversion and the initial pressure of gases. you can see there is a slightly higher pressure of H_2 and CO_2 than the reactants, consistent with the equilibrium constant of about 1.44 at 1000K. At a lower temperature there would be a much higher yield of the products. For example, at 550K the equilibrium constant is about 58, and the pressure of H_2 is 4.4 atm due to a much higher equilibrium conversion of 0.88.

One way we can verify our solution is to plot the gibbs function and see where the minimum is, and whether there is more than one minimum. We start by making grids over the range of 0 to 0.5. Note we actually start slightly above zero because at zero there are some numerical imaginary elements of the gibbs function or it is numerically not defined since there are logs of zero there. We also set all elements where the sum of the two extents is greater than 0.5 to near zero, since those regions violate the constraints.

YAML configuration of MQTT entities under the platform key (e.g., light),which was deprecated in Home Assistant Core 2022.6, is no longer supported.The configuration must instead be done under the mqtt key.

The PV Array block is a five-parameter model using a light-generated currentsource (IL), diode, series resistance (Rs), and shunt resistance(Rsh) to represent the irradiance- and temperature-dependent I-V characteristics of themodules.

Current for one module under STC, flowing out of the controllable current source thatmodels the light-generated current. An optimization function determinesthis parameter to fit the module data. This parameter isread-only.

The wand has an additional effect, though. After zapping it, it will empower other wands to be the same level as it for 4 turns, though the empowerment only applies to one zap. This mechanic makes investing in the wand much more interesting, though only certain wands really benefit from Magic Charge and the wand of magic missile still needs to be zapped to activate it.

This wand sends powerful lightning arcing through whatever it is shot at, dealing 5-10 damage. This electricity can bounce between many nearby foes, spreading damage between them. The lightning and damage spread much more effectively in water. If you're too close, you may get shocked as well!

The wand's mechanic of dealing less damage to chilled targets somewhat hinders its offensive potential, which would otherwise be comparable with the wand of lightning; without this mechanic, the wand of frost's base 1-8 damage and +1/+5 scaling would quickly make it better offensively than basically every wand in the game barring the wand of lightning. Regardless, a spammed wand of Frost will have similar damage output to a non-boosted wand of Prismatic Light, which is still usable. The limitation can be alleviated with the use of fire from a Wand of Fireblast, though the gimmicks of both wands are wasted this way.

This wand shoots rays of light which cut through the darkness of the dungeon, revealing hidden areas and traps. The beam can blind enemies, and deals 1-5 damage. Demonic and undead foes will burn in the bright light of the wand, taking bonus damage.

This wand will release a blast of corrupting energy which will debuff enemies and eventually bend them to your will. Enemies are able to resist the corruption, but weakened enemies are much easier to corrupt than healthy ones.

By studying the Hadza lifestyle, Pontzer thought he would find evidence to back the conventional wisdom about why obesity has become such a big problem worldwide. Many have argued that one of the reasons we've collectively put on so much weight over the past 50 years is that we're much less active than our ancestors.

"We know with confidence that some metabolic adaptions occur under some circumstances," said David Allison, "and we know with confidence some behavioral compensations occur under some circumstances. We don't know how much compensation occurs, under which circumstances, and for whom."

I was going crazy trying to determine why all of my 2.4 Ghz devices were continually losing connection to my Netgear R8000 running on (the latest version 2022.2) Fresh Tomato firmware.As you mentioned, the culprit in my instance was USB 3.0. After I unselected USB 3.0 my 2.4 Ghz devices connected immediately.So glad I found this article.Thank you so much!

On 26 January 2022, wish_z accepted the first batch of Beta Testers, opening the Closed Beta testing of Doodle World. Likewise, on the same date, it was the first time wish_z posted in the Discord servers' game updates channel. Updates below are based on wish's twitter, Discord's announcement channel and directly from alpha testers, and have much less information. 041b061a72


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