Wolfram Computation Meets Knowledge

Date Archive: 2016 September

Best of Blog

Mersenne Primes and the Lucas–Lehmer Test


A Mersenne prime is a prime number of the form Mp = 2p – 1, where the exponent p must also be prime. These primes take their name from the French mathematician and religious scholar Marin Mersenne, who produced a list of primes of this form in the first half of the seventeenth century. It has been known since antiquity that the first four of these, M2 = 3, M3 = 7, M5 = 31 and M7 = 127, are prime.
Leading Edge

New in the Wolfram Language: Audio

I have always liked listening to music. In high school, I started wondering how it is that music seems to be so universally pleasing, and how it differs from other kinds of sounds and noises. I started learning to play guitar, and later at the University of Trieste, I learned about acoustics and signal processing. I picked up the guitar in high school, but once I began learning to program, the idea of being able to create and process any sound using a computer was liberating. I didn't need to buy expensive and esoteric gear; I just needed to write some (or a lot!) of code. There are many programming languages that focus on music and sound, but complex operations (such as sampling a number from a special distribution, or the simulation of random processes) often require a lot of effort. That's why the audio capabilities in the Wolfram Language are special: the ability to deal with audio objects is combined with all the knowledge and computational power of the Wolfram Language! First, we needed a brand-new atomic object in the language: the Audio object.
Announcements & Events

Announcing Wolfram Enterprise Private Cloud

Today I'm pleased to announce Wolfram Enterprise Private Cloud (EPC), which takes the unique benefits of the Wolfram technology stack---ultimate computation, integrated language and deployment---and makes them available in a centralized, private, secure enterprise solution. In essence, EPC enables you to put computation at the heart of your infrastructure and in turn deliver a complete enterprise computation solution for your organization.
Education & Academic

How to Teach Computational Thinking

The Computational Future Computational thinking is going to be a defining feature of the future—and it’s an incredibly important thing to be teaching to kids today. There’s always lots of discussion (and concern) about how to teach traditional mathematical thinking to kids. But looking to the future, this pales in comparison to the importance of […]

Computation & Analysis

Rolling Bearings: Modeling and Analysis in Wolfram SystemModeler


Explore the contents of this article with a free Wolfram SystemModeler trial. Rolling bearings are one of the most common machine elements today. Almost all mechanisms with a rotational part, whether electrical toothbrushes, a computer hard drive or a washing machine, have one or more rolling bearings. In bicycles and especially in cars, there are a lot of rolling bearings, typically 100--150. Bearings are crucial---and their failure can be catastrophic---in development-pushing applications such as railroad wheelsets and, lately, large wind turbine generators. The Swedish bearing manufacturer SKF estimates that the global rolling bearing market volume in 2014 reached between 330 and 340 billion bearings. Rolling bearings are named after their shapes---for instance, cylindrical roller bearings, tapered roller bearings and spherical roller bearings. Radial deep-groove ball bearings are the most common rolling bearing type, accounting for almost 30% of the world bearing demand. The most common roller bearing type (a subtype of a rolling bearing) is the tapered roller bearing, accounting for about 20% of the world bearing market. With so many bearings installed every year, the calculations in the design process, manufacturing quality, operation environment, etc. have improved over time. Today, bearings often last as long as the product in which they are mounted. Not that long ago, you would have needed to change the bearings in a car's gearbox or wheel bearing several times during that car's lifetime. You might also have needed to change the bearings in a bicycle, kitchen fan or lawn mower. For most applications, the basic traditional bearing design concept works fine. However, for more complex multidomain systems or more advanced loads, it may be necessary to use a more advanced design software. Wolfram SystemModeler has been used in advanced multidomain bearing investigations for more than 14 years. The accuracy of the rolling bearing element forces and Hertzian contact stresses are the same as the software from the largest bearing manufacturers. However, SystemModeler provides the possibilities to also model the dynamics of the nonlinear and multidomain surroundings, which give the understanding necessary for solving the problems of much more complex systems. The simulation time for models developed in SystemModeler is also shorter than comparable approaches.