July 20, 2012 — Michael Trott, Chief Scientist
(This is the first post in a three-part series about electrostatic and magnetostatic problems involving sharp edges.)
Mathematica can do a lot of different computations. Easy and complicated ones, numeric and symbolic ones, applied and theoretical ones, small and large ones. All by carrying out a Mathematica program.
Wolfram|Alpha too carries out a lot of computations (actually, tens of millions every day), all specified through free-form inputs, not Mathematica programs. Wolfram|Alpha is heavily based on Mathematica, and many of the mathematical calculations that Wolfram|Alpha carries out rely on the mathematical power of Mathematica. And while Wolfram|Alpha can carry out a vast amount of calculations, it cannot carry out all possible calculations, either because it does not (yet) know how to do a calculation or because the (underlying Mathematica) calculation would take a longer time than available through Wolfram|Alpha. So for a detailed investigation of a more complicated engineering, physics, or chemistry problem, having a copy of Mathematica handy is mandatory.
But there is also the reverse relation between Mathematica and Wolfram|Alpha: Wolfram|Alpha’s knowledge, especially its data knowledge, allows it to carry out investigations and calculations that can substantially increase the power of pure Mathematica. And all of this is because Wolfram|Alpha’s knowledge is accessible through the WolframAlpha function within Mathematica.
August 26, 2011 — Maryka Baraka, Marketing Content Manager
Now that the Computable Document Format (CDF) is officially released, the real fun has begun. At least for me. Whether or not you plan to start using CDF in your own work anytime soon, you’ve got to admit, it’s pretty cool. From publishing textbooks and making complex information easy to understand to recreational games and everyday blogging, CDF truly makes it possible to communicate ideas in a more participatory way—as adopters of the format have already proven.
It has been exciting to see the tremendous interest in CDF following last month’s launch. Although CDF is a new advancement, it’s clear that the possibilities it presents resonate with authors and readers alike, and hence with publishers as well.
May 17, 2011 — Wolfram Blog Team
Ever wondered how to grill the perfect steak? Or how well dunking food into an ice bath stops the cooking process? Nathan Myhrvold used Mathematica to answer these questions, and many others.
Myhrvold, the first chief technology officer at Microsoft, has had a longtime interest in cooking and has a background in science and technology. When he started using new techniques like sous vide, in which food is slowly cooked in vacuum-sealed bags in water at low temperature, he discovered that many chefs don’t know much about the science behind cooking. He decided to change that with a massive cookbook that was released in March. In 2,438 pages, Modernist Cuisine covers a wide range of cooking techniques and their scientific backgrounds, including heat transfer and the growth of pathogens. (It has recipes, too.)
March 17, 2011 — Jon McLoone, International Business & Strategic Development
There is an old word game where you try to get from one word to another through connections with other words. For example, you might get from “cold” to “stationary” via the word “frozen”, since “cold” and “frozen” are synonyms and “frozen” and “stationary” are synonyms, albeit for different meanings of the word “frozen”.
I thought of this game when I started to learn the new graph theory functions in Mathematica 8. We can think of the words in the English language as the vertices of one large graph and the synonym connections between them as the graph edges. If you do that, it looks like this:
So let’s see if we can generally solve this synonym chain problem.
March 1, 2011 — Andrew Moylan, Technical Communication & Strategy
In the previous post in this series, we looked at how to model a stabilized inverted pendulum using the control systems design features in Mathematica 8. We were quickly able to simulate a linearly controlled cart-and-pendulum system, and show that it is stable against some fairly large perturbations.
But what about a double (or triple or quadruple… ) pendulum? A general n-link pendulum is depicted below. In this post we’ll see how to derive the equations of motions for this system, find out whether we can stabilize it with a linear control scheme, and produce some animations of the results.
January 19, 2011 — Andrew Moylan, Technical Communication & Strategy
Can you balance a ruler upright on the palm of your hand? If I concentrate, I can just barely manage it by constantly reacting to the small wobbles of the ruler. This challenge is analogous to a classic problem in the field of control systems design: stabilizing an upside-down (“inverted”) pendulum.
One of the best things about Mathematica is that it makes specialist areas like control systems accessible to non-specialists. This lets you freely combine and develop new ideas without needing to be an expert in everything. It also makes Mathematica a great platform for learning and exploring new areas.
Using the new control systems features (one of several new application areas integrated into Mathematica 8), I’ve been experimenting with models of stabilized inverted pendulums. I’m no expert in control theory, but you’ll see that one doesn’t need to be.
October 7, 2010 — Jon McLoone, International Business & Strategic Development
Mathematica has always had the most complete collection of special functions available. You might think that by now there were no more to add, but the next release of Mathematica will add another five. You might also think that any that are left to add are too obscure for you to care about. They are getting fairly obscure, but you should still care.
Let’s look at one of them: Owen’s T function.
December 30, 2009 — Deepa Nair, Technical Communications & Strategy
During discussions at the International Mathematica User Conference 2009 with bioinformaticians using Mathematica, I learned a lot of very important things—like why protein folding isn’t something you can order at the dry cleaner. I also learned that a lot of people seriously dig Mathematica‘s modeling and automatic interface construction capabilities, which make it easy for them to create interactive applications and simulations.
Whether it is protein structure prediction using comparative modeling and fold recognition, or visualizing large-scale sequence alignments, Mathematica makes it fast and accurate. To make it easy for you to check out Mathematica‘s capabilities for this field, we have designed the Mathematica Solution for Bioinformatics portal. This website, which I researched and created, highlights Mathematica‘s capabilities and features several case studies, articles, and tutorials to help you get started.
One of the cool things I enjoyed researching were the interactive Demonstrations. If you are like me and learn best by looking at an example, there’s no better resource for learning how to create interactive applications in Mathematica, because the code used for creating the application is freely available right there.
December 10, 2009 — Wolfram Blog Team
The global H1N1 outbreak has researchers stepping up their efforts to build a mathematical model that health authorities can use to identify optimal medication strategies for emerging infectious diseases. Zhilan Feng, a mathematics professor at Purdue University, is one of those researchers.
Feng, who’s collaborating with the Centers for Disease Control and Prevention (CDC), is using Mathematica to develop and analyze a model of the dynamics and medication control of influenza. In this video, she demonstrates why Mathematica is the perfect tool for their work.
October 15, 2009 — Stephanie Harpst, Commercial Account Executive
I am always intrigued by the many ways people use Mathematica. But it was even more exciting to be a part of the American Chemical Society Fall 2009 National Meeting and hear the true excitement and awe of our users’ latest discoveries of what is possible in Mathematica. I also had a lot of fun introducing new users to our software!
In August, we traveled to ACS in beautiful Washington, DC, USA. The ACS meeting brought together the largest scientific society and its members’ families, colleagues, and students. It provided an ideal venue to demonstrate Mathematica‘s capabilities in chemistry and chemical engineering. We demonstrated a broad range of features, including Mathematica 7‘s fully curated chemical, genomic, and proteomic data, built-in parallelization capabilities, and unsurpassed modeling and visualization capabilities. The ability to visualize any data as well as update it on the fly has bridged a gap many researchers and scientists have had to work around when using other tools. You can even rapidly develop and test algorithms as well as generate accurate structural renderings in 2D and 3D using the integrated data, which is easy to retrieve programmatically.