Definition
Simulation
A model that behaves in the same way as a real-world entity or process.
Simulations are often used to study or predict the behavior of complex systems.
Models vs. Simulations
- Although they are closely related, they serve distinct purposes and operate in different ways.
- This section explores the differences between models and simulations, highlighting their roles in scientific and engineering contexts.
What is a Model?
Definition
Model
A simplified representation of a system or phenomenon.
- It captures the essential features of the system while omitting unnecessary details.
- Models can be physical , mathematical , or conceptual, and they are used to describe, explain, or predict the behaviour of the system.
Types of Models
- Physical Models: Tangible representations, such as scale models of buildings or bridges.
- Mathematical Models: Equations or algorithms that describe relationships between variables. For example, the equation F = ma models the relationship between force, mass, and acceleration.
- Conceptual Models: Diagrams or flowcharts that illustrate the structure or function of a system.
- Mathematical Model of Population Growth:
- The logistic growth model describes how a population grows over time:
- $$ \frac{dP}{dt} = rP\left(1 - \frac{P}{K}\right) $$
- Where:
- $P$ is the population size
- $r$ is the growth rate
- $K$ is the carrying capacity
- The logistic growth model describes how a population grows over time:
What is a Simulation?
- It involves running experiments on the model to observe how the system responds to different conditions or inputs.
- Simulations are often used when real-world experimentation is impractical, expensive, or dangerous.
Types of Simulations
- Deterministic Simulations:
- Produce the same results every time, given the same initial conditions.
- For example, simulating the trajectory of a projectile using Newton's laws.
- Stochastic Simulations: Incorporate randomness, leading to different outcomes in each run.
- For example, simulating the spread of a disease where transmission is probabilistic.
- Weather Simulation:
- Weather forecasts are generated by simulating the atmosphere using complex mathematical models.
- These simulations consider factors like temperature, humidity, wind speed, and pressure to predict future weather conditions.
