Binary adders are digital circuits often used in computers for basic arithmetic operations. Using the digital library in the standard Modelica library, we have constructed an 8-bit adder that takes two 8-bit integers and calculates their sum.

Allosteric regulation is a prime drug target because it reduces the risk of overdose and side effects and can be used to fine-tune pharmacological processes. This model studies a naturally occurring allosteric reaction: the first step in the pyrimidine synthesis, catalyzed by the allosteric enzyme aspartate carbamoyltransferase (ATCase).

Model the spread of an influenza virus in a population with components from the SystemDynamics library.

Model a pendulum dangling from a slider-crank.

The Wolfram Model Plug library allows you to connect your simulation models to the real world using Arduino boards, thereby further increasing the capability for fast prototyping in System Modeler. Here, we will show how Model Plug can be used to interactively control a robot arm from a control panel.

Construct a model of an asynchronous induction machine with a slip‐ring rotor.

Create a model of a ball rolling on top of a beam and control the movement of the ball.

Implement the V-model for control system design, deployment and testing. Model your system in System Modeler, then design a controller in the Wolfram Language. Use the Microcontroller Kit to generate automated code and deploy it into a microcontroller. Subsequently, validate your standalone model with the control targets. This example shows how to design, deploy and test a PID controller to balance a ball on a beam.

This model allows you to analyze how a battery responds to thermal conditions as well as to charge and discharge cycles.

Analyze impact of defects in roller bearings.

Model a free kick in soccer and examine what happens when taking drag and Magnus effect into account.

Counters are used in a variety of digital applications as a way of counting events. In this example, we have constructed a simple 4-bit asynchronous up-counter using the Digital library, which is a part of the Modelica Standard Library.

Digital circuits are everywhere, from personal computers to smart TVs. In this example, you will learn how digital circuits work and create some basic circuits. Finally, you will test your digital circuits by connecting to hardware using Arduinos.

Calculate peak-to-peak current ripple in a boost converter, used to step up voltage from a lower level to a higher level.

Model and simulate balls bouncing on the ground or in a box, taking advantage of powerful event handling in System Modeler.

Buck-boost converters are used both to step up voltage from a lower level to a higher level and to step down voltage from a higher level to a lower level. Buck-boost converters can be found in applications where the supply voltage changes over time, such as battery-powered applications.

Compare efficiency for a switched-mode DC-to-DC converter with a linear Zener regulator.

Construct a model of a bungee jumper consisting of a mass attached to a platform by a spring and damper.

Design and prototype mechanisms such as cams with the symbolic component creation capabilities in System Modeler.

Compares the deflection of cantilever beams for different materials and for different cross-sectional areas.

Most chemical reactions are not irreversible and in fact go in both directions. However, all reversible reactions reach a steady state in which the concentrations of the substrates within the reaction become constant. In this example, you will learn to model a reversible chemical reaction and analyze the dynamics of the reaction. You will learn about equilibrium constants and reaction rates.

When doing a chemical experiment, it is useful to know how much product you will obtain when you mix certain amounts of reactants. This is particularly useful in real-world settings, such as in chemical production or chemical analysis. In this example, you will learn how to predict the outcome of a reaction, given the initial amounts of reactants and the ratio between the products and substrates.

Chua’s circuit is the simplest electronic circuit that displays chaotic behavior. Due to its simplicity, it is especially suitable as a demonstrative real-world example of a chaotic system.

Combinational circuits are used to perform Boolean algebra on input signals and on stored data. They are made up of basic logic gates that are combined to produce powerful switching circuits. In this example, you will create a 3-bit adder and connect to hardware using Arduinos.

Study how a fast (quasi-stationary) model of a direct current permanent magnet (DCPM) motor behaves differently compared to a fully transient one.

Connect a process plant model and a real-world Programmable Logic Controller (PLC) in System Modeler.

Find an optimal control signal for a continuously stirred tank reactor (CSTR).

It is often noted that CO2 causes global warming, but keeping track of CO2 concentrations is also an important aspect of preserving indoor air quality. This example shows how you can control the concentration of CO2 in a room and subsequently check if climate change puts more pressure on the ventilation system.

An important control problem is to design controllers for nonlinear systems using model inversion control. The following example uses an InverseBlockConstraints component to easily construct inverse models. It also uses the Modelica_Synchronous Library to automatically discretize the continuous-time nonlinear feedforward controller.

By coupling clutches together, a variable structure drivetrain can be achieved. With different clutches engaged at different times, torque is supplied to different parts of the system.

Control an experiment in real time with input from Mathematica.

Control an experiment in real time with input from Mathematica.

Digital adders are used in the arithmetic logic units (ALU) that are a fundamental building block of CPUs and GPUs. In this example, you will design a half adder and a full adder and combine them to form adder units of any bit size.

Understand a dose selection process by building pharmacokinetic and pharmacodynamic models.

Have you ever been annoyed by watching shaky footage taken by your cell phone? In that case, you might have thought about using a gimbal or a camera stabilizer. Ever wondered how they work? In this example, you will understand the dynamics behind them and design your own camera stabilizer.

A model can be used for many things, and one of them is the possibility to calculate the reliability for the system modeled. With information about the lifetime of each component, the lifetime of the complete system can be studied. In this example, we look at how heat affects the mean time to failure (MTTF) for an amplifier.

Recruitment and training of new employees need to be carefully planned to prevent shortages or surpluses. Using this example, a human resource manager or decision maker can vary the control parameters that relate to aspects of the human resource planning (HRP) process to test different HRP strategies.

Incorporate real data from the international fuel market and regional demand into this model of a 5.6 GW electricity producing plant.

Enzymes play a part in almost every biochemical reaction known, from human metabolism to beer brewing. This model showcases a generic substrate to product reaction and catalyzes it to illustrate the power of enzymes.

Create a pharmacokinetic model to describe the distribution and transfer rates of contrast agent between different parts of the body.

This model analyzes the stresses that a pressure vessel experiences from expanding and contracting gases. Characteristics for different gases are built in, taken from the Modelica.Media library.

This model analyzes the robustness of a state estimator, taking measurements from an electrical radiator. The state estimator blends together different measurements and a model of the system in order to estimate the current radiator temperature. To evaluate the robustness, noise is added using blocks from the Modelica.Noise library.

Create a library for aircraft modeling, which can be used to study flight dynamics during different flight conditions.

Compute the reliability of a Cessna 441 flap system using lifetime data for the individual hydraulic parts.

Flip‐flops are digital logic circuits commonly used in processes where there is a need for digital data storage and transfer. In this example we will use the Digital library, a part of the Modelica Standard Library, to demonstrate the use of basic logic gates in a pulse‐triggered master‐slave flip‐flop.

How does the food you consume affect your body, and what type of food should you consume to build muscle? Most people have thought about this question at least once. In this example, you will explore how your chosen food options contribute toward fat and muscle gain.

Many applications require direct current, DC. However, transporting direct current through the power lines has several disadvantages compared to alternating current, AC. AC can be used in transformers and allows for higher-efficiency power conversion and transmission. For the electricity found in power outlets to be used in DC circuits, it first needs to be converted into direct current. One way to do this is to use a full-wave bridge rectifier.

Genetic testing is an important tool, not only in clinical settings but also in research. In this example, you will explore how DNA is manipulated in genetic testing. You will use polymerase chain reaction (PCR) to amplify a DNA sample and then use electrophoresis to diagnose patients with genetic diseases.

Import an SBML model and use it to study oscillations near a Hopf bifurcation.

Simulate a soccer kick and a golf strike. Test different scenarios using configurable models.

Of all currently used therapeutic drugs, about 40-50% are centered on the mechanisms of so-called G-protein‐coupled receptors (GPCRs). Here, we use the SBML import function in Wolfram System Modeler to import a model that describes the behavior of GPCRs and G proteins in a yeast cell.

Gyroscopic effects have been a source of both amazing engineering and amusement for many people. This phenomenon affects a variety of applications. The most obvious might be the helicopter, which behaves in a quite surprising way. In this example, the concept of gyroscopic precession is explored.

The Hardy–Weinberg principle is a fundamental principle in population genetics. It describes populations that are no longer undergoing evolution and thus reach a steady state. In this example, you will learn to construct a genetic inheritance model and analyze scenarios when the assumptions of Hardy–Weinberg equilibrium are violated.

This model explores a typical predator/prey system based on Lotka–Volterra dynamics. This relatively simple system is a good way to get started with understanding population dynamics.

When a large percentage of the population becomes immune to a disease such as COVID-19, you can consider the population to be protected from the disease by herd immunity. This means that although 100% of the population may not be vaccinated, a sufficient proportion of the population is, and the rate of infection starts to decrease. In this example, you will investigate the concept of herd immunity using the SIR (susceptible, infected and recovered) model.

Heterogenous equilibrium refers to reversible reactions where the substrates of the reactions are in different phases. One of the most useful types of such reactions is where a solid is dissolved in an aqueous solution. In this example, you will learn about heterogenous equilibrium and understand the concept of solubility.

Understand the significance of incorporating mast flexibility into the analysis of design loads.

Most people have had headaches that prevent them from focusing on their tasks. In this example, you will study how ibuprofen can relieve headaches. Your goal is to find out what dosage works best to relieve the headache without getting any side effects.

Model a biochemical process and study how insulin signaling in fat cells works.

Stabilize the unstable pendulum with a linear-quadratic regulator.

Linearization makes it possible to use tools for linear systems to study nonlinear systems around an operating point. In this example, an inverted pendulum is linearized around its upright position. The goal is to analyze the behavior of the controlled inverted pendulum system for varying lengths of the pendulum.

Compare three designs for a spring-based recentering mechanism in an analog joystick.

Use the concept of kinematics to understand a stunt car jump and simulate daring scenarios. Visualize the jump from different reference frames, like the audience, the car or a moving helicopter.

Build a control system for a Segway constructed out of LEGO Mindstorms NXT components.

Build a control system for a Segway constructed out of LEGO Mindstorms NXT components.

The classic Lotka–Volterra model was originally proposed to explain variations in fish populations in the Mediterranean, but it has since been used to explain the dynamics of any predator-prey system in which certain assumptions are valid. Here, using System Modeler, the oscillations of the snowshoe hare and the lynx are explored.

Explore the oscillations of the snowshoe hare and the lynx using components created in the Wolfram Language.

Simulates the process that maintains healthy blood glucose levels in the human body after eating a meal.

A simple enzyme reaction that is not affected by negative feedback, allosteric effects or cooperativity can be simplified using Michaelis–Menten kinetics.

The world model is one of the most famous applications of the system dynamics methodology.

Systematically design a controller for a nonlinear system using model inversion control.

Natural selection is fundamental in understanding how populations evolve over time. It helps with understanding why some traits die out while others flourish. In this example, you will explore the effect that environmental selection pressures have on the genetic makeup of a population.

Create a classical demonstration of important physics principles with Newton’s cradle.

Control the water level in a series of tanks using PI controllers.

Understand the workings of PI controllers used in a three-tank system and visualize the tanks.

Build 2D mechanical models with the Planar Mechanics library. The two‐dimensional piston engine model can be animated in both 2D and 3D.

The plasma membrane not only acts as a cell barrier, but also controls what comes into and out of a cell. In this example, you will explore the concept of osmosis and how molar concentrations of solutes affect the movement of water across a semipermeable membrane.

This example will demonstrate how you can use Model Plug to create your own Pong game, played with external controllers. This is a very playful example, but it highlights how easy the connection to external hardware becomes when using the Model Plug library.

Potentiometers, also known as pots, are useful electrical components that allow a person or a machine to directly tune the voltage or resistance in one part of a circuit.

Business process modeling (BPM) has become a ubiquitous activity in support of management decision making and business analytics. This example looks at a production chain for a company producing a durable good (e.g. intruder alarm systems).

Chemical reactions occur at different rates and vary widely in the speeds at which they occur. Some reactions occur very fast; for example, an explosion or combustion of fuel in a race car. In this example, you are going to work with chemical kinetics and the study of rates of chemical processes. You will learn how to calculate rate, reaction order and half-life of a reaction.

Understand how to troubleshoot excessive vibrations by adding external damping to a turbine model.

Ever wondered how your refrigerator or air conditioner works? In this example, you will explore how vapor compression refrigeration cycle works and figure out what the capacity of your air conditioner should be.

Find the optimal way between two points for an industrial robot arm.

Ever wondered what the power rating of the radiator in your house should be, or how the ambient conditions affect your room temperature? This example will model all the components of a house and combine them to see how your room temperature changes with ambient temperature fluctuations.

Model a satellite with a combination of 3D mechanics and block-based control logic and visualize the path for the satellite.

Sequential circuits are widely used in modern devices such as computers and smartphones to store information. In this example, you will learn to design memory elements like latches and flip-flops that can store binary information.

Use a directional control valve to route fluid to and from a cylinder with the purpose of moving a load to different specified positions.

Not all traits are inherited on autosomes—there are a large number of traits inherited on the sex chromosomes. In this example, you will explore how traits are inherited on the sex chromosomes and how this affects the proportion of individuals with each genotype in the population.

The SIR or Kermack–McKendrick model is a classical approach in mathematical epidemiology to study the spread of infectious diseases. Here, you can explore how parameters like the effective contact rate affect social diffusion.

Examining different car wheel setups is crucial to evaluating if a certain wheel is suitable to drive on a certain terrain. The model presented here will examine different wheel types interacting with different ground types.

Model a spool with a preload to avoid chattering.

Understand the dynamics of a spring-mass system. This example uses a cellphone, attached vertically to a spring, to record accelerations. The experimental data is then used to calibrate the model parameters.

Use the Functional Mock-up Interface (FMI) to export a model from System Modeler and import it in NI VeriStand to test a system in real time.

The tennis racket theorem or the Dzhanibekov effect states that for a rigid body with three unique moments of inertia, rotation about the intermediate axis is unstable, while rotation about the other two axes is stable. You can see this theorem in action in this wing nut example.

The tennis racket theorem or the Dzhanibekov effect states that for a rigid body with three unique moments of inertia, rotation about the intermediate axis is unstable, while rotation about the other two axes is stable. You can see this theorem in action in this wing nut example.

Addition of heat can lead to flow of fluid from a high entropy to a low entropy region. In this example, we see how solar radiation can lead to fluid flow between a storage tank and a tanker.

When a train is moving, the forces acting between the railcars while braking are very strong. This wears out or even breaks the couplings between the railcars. In this example, you will examine different designs for the couplings and through this learn about the spring and damper systems.

A trampoline is a recreational device consisting of fabric stretched between a steel frame, using many springs. However, using it can be dangerous if the jumper loses control and falls. In this example, you will analyze the dynamics of the jumper by changing different parameters such as the weight of the jumper, the tilt of the ground and the jumper’s initial velocity.

Have you ever tried to understand the structure of a problem using qualitative models? Using causal loop diagrams, you can quickly create such models that are easy to understand. This example shows a causal loop model for the world dynamics in order to understand how a campaign can reduce the environmental load.

An Uninterruptible power supply (UPS) is used to protect electrical devices such as computers from power failures, when the main power fails. Using a model where both the physical behavior and the reliability is modeled, conclusions can be drawn about both the switching behavior and the system reliability.

Automatically measure performance of a controlled system, such as rise time, settling time, overshoot and more. In this example, you can observe the climb, descent and hover motion of a drone.

Do you find it surprising that your washing machine starts to vibrate vigorously at a certain rotational speed? Why does this happen, and what can you do to avoid it? In this example, we will analyze the cause of these vibrations and tweak certain parameters to see if they can be minimized.

Construct a virtual test rig to investigate the effects of dry friction on a rolling wheel.

Check the backlash effects in a planetary gear that induce vibrations during the initial stages of motion.