Wolfram Computation Meets Knowledge

Date Archive: 2011 March

Best of Blog

Mathematica Q&A: Plotting Trig Functions in Degrees

Got a question about Mathematica? The Wolfram Blog has answers! We'll regularly answer selected questions from users around the web. You can submit your question directly to the Q&A Team using this form. This week's question comes from Brian, who is a part-time math teacher: How do you plot trigonometric functions in degrees instead of radians? Trigonometric functions in Mathematica such as Sin[x] and Cos[x] take x to be given in radians:
Announcements & Events

Launching a New Era in Large-Scale Systems Modeling

Over the past 25 years, we’ve been fortunate enough to make a mark in all sorts of areas of science and technology. Today I’m excited to announce that we’re in a position to tackle another major area: large-scale systems modeling. It’s a huge and important area, long central to engineering, and increasingly central to fields like […]

Education & Academic

Explore the Computational Universe at NKS Summer School 2011

There's still time to apply to NKS Summer School 2011, a complex systems research school based on Stephen Wolfram's seminal tract on the subject, A New Kind of Science (NKS), published in 2002. The first NKS Summer School was held soon after the book's publication, and, this summer, Wolfram Research will host its 9th annual program, centered on doing research on the topics and methods introduced by the book. The 2011 NKS Summer School is being held in Boston, Massachusetts, USA from June 27 through July 15, 2011. The concepts introduced in NKS have already made significant contributions to research and technological innovation.
Education & Academic

Built to Last: Understanding Earthquake Engineering

Last week, the world was shocked by the news of massive earthquakes and devastating tsunamis in Japan. The event is still unfolding and could become one of the most tragic natural disasters in recent history. Scientific understanding and modeling of complicated physical phenomena and engineering based on such analysis is imperative to prevent unnecessary loss of life from natural disasters. In this post, we'll explore the science behind earthquakes to better understand why they happen and how we prepare for them. Note: The dynamic examples in this post were built using Mathematica. Download the Computable Document Format (CDF) file provided to interact with the simulations and further explore the topics. First, let's start with locations. The following visualization is created from the U.S. Geological Survey (USGS) database of earthquakes that occurred between 1973 and early 2011 whose magnitudes were over 5. As you can clearly see, the epicenters are concentrated in narrow areas, usually on the boundaries of tectonic plates. In particular, there are severe seismic activities around the Pacific, namely the "Ring of Fire". Unfortunately, Japan is sitting right in the middle of this highly active area.
Leading Edge

The Distance between “Zero” and “Hero”: Exploring Synonym Chains with Mathematica

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.

Mathematica Q&A: Excluding Points from Plots

Got questions about Mathematica? The Wolfram Blog has answers! Each week, we'll answer a selected question from users around the web. You can submit your question directly to the Q&A Team. For our first post in this new series of Mathematica Q&A articles, we're going to address a very frequently asked question about plotting in Mathematica. How can I control the appearance of discontinuities in a plot? The short answer is, use the options Exclusions and ExclusionsStyle! Let's see how they work. By default, Plot shows the function 1 ⁄ sin(x) with lines joining its discontinuities:

Innovating Interactive Web Publishing with Wolfram Demonstrations

Today we are pleased to announce an exciting new phase in the development of the Wolfram Demonstrations Project. In addition to its slick new design and structure, allowing for more intuitive navigation, the website now features a groundbreaking technology that takes interactivity on the web to a whole new level. This technology tightly integrates live computations into the web browser, making interaction with Demonstrations a fluent part of the online experience. Powered by a new web browser plugin, each Demonstration’s dynamic interface is now an element of the web page, similar to text, images, or videos, and yet is so much more than the typical inert content. Sliders, buttons, 3D graphic manipulations, color palettes, and the rest of the Wolfram interactive arsenal are now at your fingertips. They provide dynamic access to Mathematica’s universal engine spanning vast areas of pure and applied math, image processing, finance, control systems, wavelet analysis, and much more.
Leading Edge

Stabilized n-Link Pendulum

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.