September 30, 2013 — Johan Rhodin, Kernel Developer

What is the cost of extending a warranty for a car? I’d be interested to know, since my car broke down just past the 100,000 mile marker on a road trip through America. With *Mathematica* 9 comes complete functionality for reliability analysis that can help us analyze systems like cars. I thought it might be worthwhile to take *Mathematica* for a spin and look at how some technical systems can be modeled and analyzed.

June 11, 2013 — Mikael Forsgren, Wolfram MathCore

Wolfram *SystemModeler* ships with model libraries for a large selection of domains such as electronics, mechanics, and biochemistry. Now I am pleased to present a new library in the family, the SystemDynamics library by François E. Cellier and Stefan Fabricius. System dynamics, a methodology developed by Jay Forrester in the ’60s and ’70s, is well suited for understanding the dynamics of large-scale systems with diverse components. It has been famously applied by the Club of Rome to investigate the limits of human growth; other applications include production management, life sciences, and economics (some showcases of the methodology can be found here).

December 11, 2012 — Mikael Forsgren, Wolfram MathCore

Yesterday, the Nobel Prize in Chemistry was awarded to Robert J. Lefkowitz and Brian K. Kobilka for having mapped how a family of cellular receptors called G-protein-coupled receptors (GPCRs) work. The Nobel Prize winners’ research has proven to be very important in the development of novel therapeutic drugs—about 40–50% of all therapeutic drugs in use today are centered on GPCRs. The real beauty of GPCR-based response systems is that they include components that are used over and over again for the response to external signals in many kinds of cellular functions throughout our bodies. Sight, smell, and the adrenaline response are examples of these GPCR-mediated responses with physiologically important functions.

Identifying new targets for therapeutic drug intervention includes analysis of the complex webs of signaling pathways and feedback systems in our cells, extending beyond the first event of a signal connecting with the GPCR on the cell surface, which is non-trivial. Lately the cost-effective practice of using mathematical models as an initial step for finding those elusive new targets, and also as a tool for understanding how other reactions of a cell might be affected by a new drug, has been growing. In this blog post we are going to use modeling and simulation in order to illustrate how the GPCR-based cellular response to an external signal can be modified. And by performing this analysis, I thought we should also see how we can find promising targets for therapeutic drug design, which are then aimed at either increasing or decreasing the response. Since the first two steps in the pathways are identical in most of the GPCR-based signal responses in a cell, we can freely choose a representative model. One such well understood signal response pathway that uses GPCR is the mating pheromone response in yeast, which we are here going to explore using *Mathematica* and Wolfram *SystemModeler*.

October 25, 2012 — Robert Palmer, Applications Engineer

During the last decades, the development and use of therapeutic monoclonal antibodies (mAbs) have grown rapidly. Today, more than 30 different mAbs are successfully used in the clinic—playing important roles in treating complex diseases such as cancers and auto-immune disorders—and more than 200 are in clinical trials.

The history of mAbs has, however, not been without problems. In 2006, a first-in-human clinical trial of an mAb, aimed at treating leukemia and rheumatoid arthritis, went terribly wrong. Although the trial was run according to an approved protocol, all volunteers receiving the drug had severe inflammatory reactions and multiple organ failure. The tragic event shocked the medical community and highlighted a very important issue: how do you select a safe starting dose in first-in-human trials?

Now, as you may guess, the complete answer to this question is not an easy one. It’s also beyond the scope of this blog post. However, as a consequence of the dramatic happenings in 2006, the European Medicines Agency (EMEA) recently published new guidelines to address the issue of starting dose selection in first-in-human trials. Interestingly, the guidelines recommend that the use of modeling and simulation should play an integral part in the selection process, and in this post I thought we would study what such an approach might look like using Wolfram *SystemModeler* and *Mathematica*.

August 23, 2012 — Peter Aronsson, Wolfram MathCore

Since my childhood, I have always been impressed by big mechanical structures, especially things that are used for demolition of some kind, like demolition machines (cranes with big metallic balls thrown hard at concrete buildings) or machines for warfare. All kids are by nature intrigued by demolishing, and I guess that some of us never lose that interest.

When we grow up, our interest may shift toward understanding the physics behind the machines used for demolition more than the actual demolished result. Wouldn’t it be nice to be able to study medieval warfare, and in particular, the mechanical system of a catapult? How should you design your catapult for maximal effect? How far can you hurl a projectile with a given design? What is required to throw a piano?

The mechanics behind a catapult are rather simple to describe using ready-made components in Wolfram *SystemModeler*. The model could be used to fine-tune the design and calculate properties such as the maximum length of a hurl for a specific counterweight.

August 16, 2012 — Malte Lenz, Wolfram MathCore

Today we rely heavily on satellites orbiting Earth for a variety of purposes. Mapping satellites are used to collect satellite images used in maps. Communication satellites are used for both telecommunication and internet access or for navigation services like GPS and GLONASS. Other usage areas are weather study, scientific observation, and reconnaissance.

The following model, created in Wolfram *SystemModeler*, is of a geocentric, inclined circular Low Earth Orbit (LEO) satellite. Geocentric means that it orbits around the Earth. An inclined circular orbit means that the orbit follows a circle, but is not aligned with the equator of the Earth. LEO is the name given to the altitude range below 2,000 kilometers (1,200 miles).

Suppose you are considering using this geocentric LEO satellite to collect image data. To achieve this, you would want to know where it is at the moment, how high it is, and how fast it’s going. If you want images of cities, you want to know over which cities it currently is. A *SystemModeler* model combined with data and computational resources in *Mathematica* can answer all of these questions.

Creating such a model is straightforward in *SystemModeler*. Using drag-and-drop, create three subsystems. Model the Earth using a mass with constant rotation, the satellite using a mass with propulsion forces, and the control logic using two proportional derivative (PD) controllers.

This blog post focuses on illustrating the orbit and flight of the satellite in the above model.

August 9, 2012 — Johan Rhodin, Kernel Developer

How do different activities such as making phone calls, watching video, listening to music, or browsing the web affect cell phone battery life? What about the temperature—does it matter if the cell phone is in a warm pocket or out in the cold? In this blog post, we’ll investigate how a model constructed with Wolfram *SystemModeler* can help in finding answers to such questions.

An area where battery usage is taking off right now is cell phones. There are different kinds of battery types used in cell phones: nickel metal hydride, lithium-polymer, and Li-ion. The superior energy density, power density, low self-discharge, and long cycle life of the Li-ion batteries makes them interesting for cell phone applications. In this blog post, we’ll look at Li-ion cells of the type LiFePO_{4}, where lithium ions move from the negative electrode to the positive electrode during discharge and the other way around when charging.

The are many types of battery models: analytical, electrical circuits, electrochemical, and combinations of these types. Our model of choice is the electrical circuit model, which provides sufficient accuracy for top-level performance analysis and is easy to connect to other systems.

A typical schematic for an electrical circuit model of a battery cell might look something like this:

August 1, 2012 — Malte Lenz, Wolfram MathCore

Refrigerators and freezers are common household appliances, present in almost every home. That means most people use one every day, but how do they actually work? And what happens to the temperature when you open the door? Or when the power goes out during a storm?

Those are some of the questions this blog post seeks to answer by building a refrigerator model in Wolfram *SystemModeler*.

A common way to construct a combined refrigerator and freezer is to keep the freezer compartment cool with a heat pump and to then transfer some of the air to the fridge compartment. That way only one heat pump is needed, and both compartments can be kept at different temperatures.

The following diagram shows our goal: modeling a connected freezer and fridge complete with doors, casing, food contents, and a heat pump. At the top we see the freezer compartment together with the heat pump that cools the air, some frozen food in the freezer, and a door for the freezer. At the bottom we see a similar structure for the fridge. The two are connected with a component for air circulation at the middle right of the diagram, which will transfer cold air from the freezer to the fridge. Finally, to the left, we have components modeling the casing and insulation to the room temperature outside.

June 11, 2012 — Wolfram Blog Team

We are excited to announce the first Wolfram *SystemModeler* Virtual Conference, to be held Tuesday, June 19.

*SystemModeler* is a complete modeling and simulation tool that handles modeling of systems with mechanical, electrical, thermal, chemical, biological, and other components, as well as combinations of different types of components.

May 23, 2012 — Stephen Wolfram

Today I’m excited to be able to announce that our company is moving into yet another new area: large-scale system modeling. Last year, I wrote about our plans to initiate a new generation of large-scale system modeling. Now we are taking a major step in that direction with the release of Wolfram *SystemModeler*.

*SystemModeler* is a very general environment that handles modeling of systems with mechanical, electrical, thermal, chemical, biological, and other components, as well as combinations of different types of components. It’s based—like *Mathematica*—on the very general idea of representing everything in symbolic form.

In *SystemModeler*, a system is built from a hierarchy of connected components—often assembled interactively using *SystemModeler*‘s drag-and-drop interface. Internally, what *SystemModeler* does is to derive from its symbolic system description a large collection of differential-algebraic and other equations and event specifications—which it then solves using powerful built-in hybrid symbolic-numeric methods. The result of this is a fully computable representation of the system—that mirrors what an actual physical version of the system would do, but allows instant visualization, simulation, analysis, or whatever.

Here’s an example of *SystemModeler* in action—with a 2,685-equation dynamic model of an airplane being used to analyze the control loop for continuous descent landings: