From the outset, the goal of MaplePrimes was to provide the Maple & MapleSim user communities with a platform to ask questions, share knowledge and to collaborate with other users.  And for the most part, the site has exceeded these goals.  Since its inception in 2005, we have received tens of thousands of posts from over 10,000 members, and we are privileged to have accumulated a group of dedicated, knowledgeable users who have become the heart of this community.

Go Habs Go!

Since my blog (as well as other) posts are deleted here, I am not that anxious to continue posting here. Meanwhile, I started a blog at Windows Live and my mapleadvisor site.

I was also thinking about restoring my part of the wiki that was there, but don't have time for that at the moment.

Alec

I haven't been logged into this site regularly for a while, being busy with other things.

But I've just noticed that, some time in the past few weeks, Robert Israel's eponymous handle has attained a mapleprimes points number that exceeds the total of all the handles that I've ever used here. So... congratulations, Robert!

I've...

As of today, Maplesoft has an office in Germany, allowing us to provide local sales and support to customers in Germany and Austria.  With the opening of this office, Scientific Computers will no longer act as Maplesoft's reseller in these territories.

Additional details are contained in the press release.

On and off over the last few months I've been meaning to learn about computing a center manifold approximation and normal form of a dynamic system of three differential equations.

My main reading: Stephen Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Second Edition, Springer, 2003.

I want to apply the technique to a system I derived from an optimal control problem. As a first step, I decided to reproduce the steps for the following system, for which the solution has been published.

Below is the latest version of the code to draw iso-chrone lines and a salvo of arrows onto the phase diagram of a two-dimensional system of ordinary differential equations.

I have greatly benefited from inputs by Robert Israel (who wrote the first incarnation of the procedure), Joe Riel, and pagan. A big thankyou!

The procedure is sufficiently developed for my current purpose, so I don't plan to modify it much in the near future.

Tested on Maple 13/ Classic. The last plot combines the isochrones and the salvo.

what I learned today is that you cannot write 1e-i, where i is an unassigned variable (at least not like that):

I'm posting it here to keep a record for myself.

my second blog post, aka "the lost blog post", is here.

Still some way to go. The following still needs to be tweaked case by case. And it can be made more compact too. Are the arrows flying so much faster in the top triangular area or are the arrows not printing where I expected them to ...

funny that, how do I go from first blog post to third blog post!?!?!

that's because my second blog post appears as a comment to my first blog post.

you've just got to learn...

Since much of what I post couldn't possibly be of interest to anyone else, I thought I'd use the blog. If I remember its existence, I'll try to post here stuff to myself. After all it's less likely to be lost here than in the maze of my harddrive.

Every year my extended family does a "secret santa" gift exchange. Each person draws another person at random and then gets a gift for them. At first, none of my siblings were married, and so the draw was completely random. Then, as people got married, we added the restriction that spouses should not draw each others names. This restriction meant that we moved from using slips of paper on a hat to using a simple computer program to choose names. Then people began to complain when they would get the same person two years in a row, so the program was modified to keep some history and avoid giving anyone a name in their recent history. This year, not everyone was participating, and so after removing names, and limiting the number of exclusions to four per person, I had data something like this:

One of the most common foods prepared at this time of the year, and arguably the most common kitchen disaster, is turkey. 

There are several employees here at Maplesoft (myself included) who are full-fledged foodies:  not only do we enjoy eating good food, but we enjoy preparing it with all our cool kitchen gadgets.  Just as mathies may compare calculators, we compare chef’s knives.  So being a foodie and a mathie, I was quite intrigued when a co-worker sent me an article that found the optimal cooking temperature for a turkey.

For those of you who have had to take on the task of preparing a turkey, you’re probably familiar with this basic rule of thumb (thousands of burnt turkeys must have contributed to this rule): preheat the oven to 400°F, and then cook it for 20 min/lb at 350 °F.  Essentially what this rule means is that the time required to cook a turkey is directly proportional to the mass of the turkey.  We know that this cannot be true because some people who adhere to this rule will have a turkey that is moist and tender, and others will have a turkey that is dry and tough.  If we take more variables into account, like the size of the turkey (l), oven temperature (T), average density (ρ) and thermal conductivity (κ) we can create a function with respect to time . We can now do a bit of dimensional analysis on this to evaluate the accuracy of the traditional rule of thumb.  By using dimensional analysis, we can formulate a relation between a set of known variables, even though we are not sure of the relationship between these variables. The immediate advantage of this procedure is that less experimentation is required to establish a relationship between the variables, allowing us to take given data and see how it will fit with the equations that are created in the analysis.  I won’t go into full detail here, but I’ve created a Maple worksheet that shows the calculations used in the analysis.  The important part comes from the graphs that are generated:

The black dots represent various cooking times of various sizes of birds.  The red line is the old rule of thumb, which you can clearly see is not very reliable.  The green line represents the new rule of thumb which falls in line much better.  So, what is the magical formula that you should use?  Based on the analysis:  where x is in lbs and the resulting time is in minutes.  Now I will be honest, I haven’t put this to the test yet, but I’ll be sure to try it out this Christmas.