Importance Of Models

Models are an essential component of simulation. Before a new prototype design for an automobile braking system or a multimillion dollar aircraft is tested in the field, it is commonplace to‘‘test drive’’ the separate components and the overall system in a simulated environment based on some form of model. A meteorologist predicts the expected path of a tropical storm using weather models that incorporate the relevant climatic variables and their effect on the storm’s trajectory.


What is Model?

              The word‘‘model’’ is a generic term referring to a conceptual or physical entity that resembles,mimics, describes, predicts, or conveys information about the behavior of some process or system.

Why Models? 

• The benefit of having a model is to be able to explore the intrinsic behavior of a system in an
  economical and safe manner
• The physical system being modeled may be inaccessible or even nonexistent as in the case of a new design for an aircraft or automotive component.

Mathematical Models

Models describe our beliefs about how the world functions. In mathematical modelling, we translate those beliefs into the language of mathematics

         The behavior of dynamic systems can be explained by mathematical equations and formula, which embody either scientific principles or empirical observations, or both, related to the system. When the system parameters and variables change continuously over time or space, the models consist of coupled algebraic and differential equations. In some cases, look-up tables containing empirical data are employed to compute the parameters. Equations may be supplemented by mathematical inequalities, which constrain the variation of one or more dependent variables. The aggregation of equations and numerical data employed to describe the dynamic behavior of a system in quantitative terms is collectively referred to as a mathematical model of the system.

Distributed parameter models

        Partial differential equation models appear when a dependent variable is a function of two or more independent variables. For example, electrical parameters such as resistance and capacitance are distributed along the length of conductors carrying electrical signals (currents and voltages). These signals are attenuated over long distances of cabling. The voltage at some locations measured from an arbitrary reference is written v(x, t) instead of simply v(t), and the circuit is modeled accordingly.

    A mathematical model for the temperature in a room would necessitate equations to predict T(x, y, z, t) if a temperature probe placed at various points inside the room reveals significant variations in temperature with respect tox,y,zin addition to temporal variations. Partial differential equations describing the cable voltagev(x, t) and room temperature T(x, y, z, t) are referred to as ‘‘distributed parameter’’ models